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Study of concurrent recovery and precipitation on the mechanical behaviour of Al-Mg alloys with small… Medrano, Sebastian 2018

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Study of concurrent recovery and precipitation on the mechanical behaviourof Al-Mg alloys with small additions of CubySebastian MedranoM.Sc.-Eng., National Autonomous University of Mexico, 2012B.Eng., National Autonomous University of Mexico, 2010A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFDoctor of PhilosophyinTHE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES(Materials Engineering)The University Of British Columbia(Vancouver)December 2018c© Sebastian Medrano, 2018The following individuals certify that they have read, and recommend to the Faculty of Graduate and Post-doctoral Studies for acceptance, the thesis entitled:Study of concurrent recovery and precipitation on the mechanical behaviour of Al-Mg alloyswith small additions of Cusubmitted by Sebastian Medrano in partial fulfillment of the requirements for the degree of Doctor ofPhilosophy in Materials Engineering.Examining Committee:Chad W. Sinclair, Department of Materials EngineeringSupervisorWarren Poole, Department of Materials EngineeringSupervisory Committee MemberDaan Maijer, Department of Materials EngineeringSupervisory Committee MemberAnasavarapu Srikantha Phani, Department of Mechanical EngineeringUniversity ExaminerRizhi Wang, Department of Materials EngineeringUniversity ExaminerJoseph Robson, Materials Engineering, School of materials, The University of ManchesterExternal ExamineriiAbstractAluminum-magnesium alloys are commonly used as wrought products in the automotive industry. Coldforming of such alloys leads to strengthening by work hardening but some of this strength can be lost byexposure to elevated temperatures leading to recovery. Such softening by recovery occurs when car bodypanels are subjected to the industrial paint bake cycle (160-200◦C for ≈ 30 min).It has been previously shown that small (<< 1 wt%) additions of Cu to Al-Mg alloys can suppresssoftening under simulated paint bake conditions owing to the formation of small solute clusters. Two mech-anism(s) could control this phenomenon; precipitation hardening and precipitation induced suppression ofrecovery. Through this thesis, it was shown that precipitation hardening due to solute clusters / GBP zonesis the dominant effect, it being significant enough to counterbalance strength loss due to recovery. Using acombination of techniques, with a particular emphasis on atom probe tomography, the precipitation hard-ening in solution treated (undeformed) samples could be quantitatively related to clusters / GBP zones. Aquantitative evaluation of the effect of pre-deformation on the formation of clusters / GPB zones was alsoobtained showing that dislocations negatively affect the strengthening owing to the effect of rapid vacancyloss to dislocations. This conclusion was reached thanks to a technique developed as part of this thesis thatallows one to quantitatively assess, separately, the effects of precipitation hardening and forest hardeningfrom a detailed analysis of the work hardening response upon yielding.iiiLay SummaryThe transport industry contributes significantly to the production of CO2 which, by itself, accounts for thelargest proportion of green house gases accumulating in the atmosphere. Using aluminum alloys to reducethe total weight of vehicles on the road and consequently the total emission of CO2 can potentially reduce theimpact of this industry on the environment. To extend and optimize the use of aluminum alloys in automotiveapplications, namely inner body panels, a better understanding of the concurrent effect of hardening byprecipitation and softening by recovery during manufacture has to be attained. In this work, this has beenaccomplished by means of experimental characterization and modelling, using similar conditions as usedduring the manufacture of car body panels. Among other findings, a relationship between characterizedprecipitates and the mechanical strength of the studied alloys was established. Furthermore, it was seen thatdeformation negatively affects the strengthening by precipitation.ivPrefaceThe work done in this thesis has been developed by the author in continuous collaboration with his Ph.D.supervisor, Prof. C. W. Sinclair. All experiments done at UBC have been conducted by the author; theseinclude solution and aging heat treatments, uniaxial tensile testing and electrical resistivity (Chapter 5 and6).The alloys used in this work were provided by the Novelis Global Technology Centre. Colleaguesat Novelis also providing input for the experimental design in the early stages of this thesis and aided withproviding facilities for the characterization of samples. The observations made by STEM in SEM in Chapter6 were performed on material processed at UBC by the author, while the final preparation and microscopyobservations were made at Novelis Global Technology Centre, Kennesaw GA. The author performed thisanalysis himself at Novelis during a 5-day visit in July 2015, with assistance from the Novelis technicalpersonnel.In Chapter 5 and 6, the Atom Probe Tomography (APT) results were the product of a collaboration withDr. B. Gault and H. Zhao, from the Max-Planck-Institut fu¨r Eisenforschung, Du¨sseldorf. The experimentalconditions for the material analyzed by APT were selected by the author. These selected thermo-mechanicaltreatments and preliminary sample preparation for APT were performed at UBC before shipment to MPIE.The final preparation stage, APT observations, and volume reconstruction analysis was done by H. Zhaoand Dr. B. Gault. The author was involved in all stages of the interpretation of the final results. The PairCorrelation Analysis shown in Chapter 5, applied to the analysis of clusters from APT data, was developedin collaboration with Dr. F. De Geuser from University Grenoble Alpes, CNRS, Grenoble INP, SIMAP.The DSC studies, shown in Chapter 5 and 6, were carried out by the author during a three-week stay at theUniversity Grenoble Alpes, CNRS, Grenoble INP, SIMAP, in 2015.Finally, a journal paper based on sections of Chapter 5 has been accepted for publication in Acta Mate-rialia: S.Medrano, H.Zhao, F. De Geuser, B. Gault, L. T. Stephenson, A. Deschamps, D. Ponge, D. Raabe,C. W. Sinclair, ”Cluster hardening in Al-3Mg triggered by small Cu additions” Available online on August30th, 2018. https://doi.org/10.1016/j.actamat.2018.08.050vTable of contentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixList of figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.1 Age Hardening of Binary Al-Cu Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.2 Softening by Recovery in Wrought Binary Al-Mg Alloys . . . . . . . . . . . . . . . . . . . 82.3 Al-Cu-Mg alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.4 Al-Mg-Cu alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.5 The interaction between deformation and precipitation in aluminum alloys . . . . . . . . . . 202.5.1 The effect of deformation on precipitation . . . . . . . . . . . . . . . . . . . . . . . 202.5.2 Recovery in the presence of precipitation . . . . . . . . . . . . . . . . . . . . . . . 222.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 Scope and Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254 Experimental Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264.1 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264.2 Thermo-Mechanical Treatments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.2.1 Cold Rolling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27vi4.2.2 Solution Treatment and Recrystallization . . . . . . . . . . . . . . . . . . . . . . . 274.2.3 Aging treatments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284.2.4 Tensile Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284.3 Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294.3.1 Optical microscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294.3.2 Scanning Transmission Electron Microscopy in Scanning Electron Microscope . . . 294.3.3 Electrical Resistivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294.3.4 Differential Scanning Calorimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . 304.3.5 Atom Probe Tomography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304.3.6 Summary of Conditions Tested . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315 Characterization of Al-Mg-Cu System During Artificial Aging . . . . . . . . . . . . . . . . . 325.1 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325.1.1 Optical metallography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325.1.2 Differential Scanning Calorimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . 325.1.3 Mechanical Behaviour of Artificially Aged Al-Mg-Cu Alloys . . . . . . . . . . . . 335.1.4 Evolution of Electrical Resistivity on Aging . . . . . . . . . . . . . . . . . . . . . . 375.1.5 Microstructural Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 526 The Effect of Pre-Deformation on the Microstructural Evolution in Al-Mg-Cu Alloys . . . . 536.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 536.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 546.2.1 DSC, Electrical Resistivity and Microstructure Evolution on Aging . . . . . . . . . 546.2.2 Yield Stress Evolution on Aging . . . . . . . . . . . . . . . . . . . . . . . . . . . . 566.2.3 Microstructural Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 606.3 Rapid Hardening and the Role of Vacancies on Clustering/GPB Zone Formation . . . . . . 646.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 727 Separating the Effects of Cluster Hardening and Recovery on the Aging Response of Al-3.23at.% - 0.23 at.%Cu: Work Hardening Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 737.1 Experimental Results: Work Hardening Response Following Aging . . . . . . . . . . . . . 747.2 A Model for the Work Hardening Response of Pre-Deformed and Aged Samples . . . . . . 797.3 Predicting the Effect of Recovery on Work Hardening for the AA5252 Alloy . . . . . . . . . 877.3.1 Separating the Effects of Cluster/GPB Zone Hardening and Recovery Softening inthe Al-Mg-Cu alloy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 907.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93vii8 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 978.1 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100A No Deformed Al-Mg-Cu alloy: Complementary Mechanical Characterization Data . . . . . 114B Resistivity in Solid Solution State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117C Radial Distribution Function and Pair Correlation Function (PFC) . . . . . . . . . . . . . . . 120D Pair Correlation Function Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122E Results of Al-Mg-Cu Alloy Pre-Deformed Material During Aging at 160 ◦C . . . . . . . . . . 124F Mechanical Analysis of Al-Mg-Cu System: Complementary Results . . . . . . . . . . . . . . 126F.1 AA5252 alloy results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126F.2 Al-3.23 at.% - 0.23 at.%Cu alloy results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131viiiList of tablesTable 4.1 Composition obtained by OES of alloys studied. Balance is aluminum. . . . . . . . . . . 26Table 4.2 Composition obtained by OES of high purity AA5252 alloy. Balance is aluminum. . . . . 27Table 5.1 The mean particle size (〈R〉) and standard deviation (S) of assumed log-normal parti-cle size distribution, volume fraction ( fv), number density and composition of particlesobtained by fitting to the data in Figure 5.8 assuming two log-normal particle size dis-tributions in each aging condition. The Al content was fixed at 80 at% based on thecomposition profiles extracted in Figure 5.7. . . . . . . . . . . . . . . . . . . . . . . . . 44Table 5.2 Parameters used/calculated in predicting the yield strength of the alloy after aging for 20min and 160 min at 200◦C. The relative strengths of the particles (β = Fm/2Γ) are alsoreported . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47Table 5.3 Obtained A0 values used to collapse the data shown in Figure 5.11 . . . . . . . . . . . . 50Table 6.1 Selected levels of deformation in terms of increase in work hardening, for the study ofdeformation prior to precipitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54Table 6.2 Numerical values and their origin used in Equation 6.4 to predict vacancy formationduring plastic deformation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68Table 6.3 Numerical values used to predict vacancy annihilation during aging in Equation 6.8. . . . 69Table 7.1 Numerical values of parameters used in fitting the work hardening model to the workhardening response of the AA5252 alloy following pre-deformation and aging. In allcases k1 = 5.64 × 108 m−1 and k2 = 9.41. . . . . . . . . . . . . . . . . . . . . . . . . . . 89Table 7.2 Numerical values of parameters used in fitting the work hardening model to the workhardening response of the Al-3.23 at.% - 0.23 at.%Cu alloy following pre-deformationand aging. In all cases k1= 6.55× 108 m−1 and k2=9.97. Note that the fit obtained forboth conditions aged for 420 minutes at 200◦C gave less satisfactory fits to the modelcompared to the other conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91Table B.1 Resistivity contributions from solute elements in solid solution in Al-3.23 at.% Mg-0.23at.%Cu alloy. The contribution of minor alloying elements is not considered. . . . . . . . 117ixTable B.2 Resistivity contributions from solute elements in solid solution in Al-3.2 at.% Mg - 0.12at.%Cu alloy. The contribution of minor alloying elements is not considered. . . . . . . . 118Table B.3 Resistivity contributions from solute elements in solid solution in Al-2.9 at.% Mg alloy.The contribution of minor alloying elements is not considered. . . . . . . . . . . . . . . 118Table B.4 Average resistivity values experimentally obtained after solid solution treatment. . . . . . 119xList of figuresFigure 1.1 Aging behavior of Al-3.35at.%Mg-0.25 at.%Cu (Al-3wt.%Mg-0.6 wt.%Cu) alloy andAA5754 system (Al-3.35at.%Mg) at 180 ◦C, following a pre-strain of 10%. These areconditions similar to those experienced in a paint bake cycle . . . . . . . . . . . . . . . 2Figure 2.1 Al-rich corner of the Al-Cu phase diagram indicating regions of stability of the differenttransition phases observed during precipitation in this system. . . . . . . . . . . . . . . 4Figure 2.2 HRTEM observation of GP (A), θ” (C) and intermediate transition between the previoustwo phases (B). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5Figure 2.3 Calculated contributions to the yield stress during aging in Al- 4wt.%Cu alloy, aged at150 ◦C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6Figure 2.4 Interaction between precipitate and moving dislocation. . . . . . . . . . . . . . . . . . . 7Figure 2.5 a) Particle shearing, b) Orowan looping . . . . . . . . . . . . . . . . . . . . . . . . . . 7Figure 2.6 Hardness evolution of Al-2.5 wt.% Cu alloy aged at 200 ◦C. . . . . . . . . . . . . . . . 8Figure 2.7 Yield stress evolution during annealing of an Al-3 wt.%Mg alloy, cold rolled (equivalentstrain ε=3 ). The annealed temperatures are shown in the graph . . . . . . . . . . . . . 9Figure 2.8 Yield stress evolution during annealing of a AA5754 alloy, cold rolled (equivalent strainε=0.58). The annealed temperatures are shown in the graph . . . . . . . . . . . . . . . 9Figure 2.9 Recovery evolution in a deformed material . . . . . . . . . . . . . . . . . . . . . . . . 10Figure 2.10 a) Hardness evolution for Al-10wt.%Mg and Al-5wt.%Mg during aging at 30 ◦C, b)Resistivity evolution of Al-10wt.%Mg system aged at the indicated temperatures . . . . 12Figure 2.11 Al-rich corner of the Al-Cu-Mg phase diagram at 200 ◦C . . . . . . . . . . . . . . . . . 13Figure 2.12 Hardness evolution vs. time, aged at 200◦C. Concentration are given in at.%. after . . . 14Figure 2.13 Proposed GPB zone structure based on HRTEM observation and Ab Initio calculations.Adapted from . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16Figure 2.14 Solute concentration in precipitation distribution after artificial aging for 80 hrs. at 170◦ in a AA2024 alloy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17xiFigure 2.15 Aging behavior of Al-3.35at.%Mg-0.25at.%Cu (Al-3wt.%Mg-0.6 wt.%Cu), Al-3.35at.%Mg-0.08at.%Cu (Al-3wt.%Mg-0.2 wt.%Cu) alloy, and AA5754 system (Al-3.35at.%Mg) at180 oC, following a pre-strain of 10%. These are conditions similar to those experiencedin a paint bake cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18Figure 2.16 Al-4.2wt.%Mg-0.6wt%Cu yield stress evolution vs time, aged at 180 ◦C. after . . . . . . 19Figure 2.17 DSC thermogram of an Al-4.2wt.%Mg - 0.6wt.% Cu alloy system . . . . . . . . . . . . 22Figure 2.18 Yield stress evolution during aging at 190 ◦C, after artificial aging (425 ◦C for 80 minand 8 days) and cold roll (80% reduction) . . . . . . . . . . . . . . . . . . . . . . . . . 23Figure 4.1 Geometry of tensile samples used for the reported uniaxial tensile tests. Dimensions areindicated in millimeters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28Figure 4.2 Summary of samples/conditions tested without pre-deformation. The numbers corre-spond to the number of tensile samples tested per condition. . . . . . . . . . . . . . . . 31Figure 4.3 Summary of samples/conditions tested following pre-deformation. The numbers corre-spond to the number of tensile samples tested per condition. . . . . . . . . . . . . . . . 31Figure 5.1 Microstructure of Al-3.23 at.% - 0.23 at.%Cu alloy after solution/recrystallization treat-ment obtained by optical microscopy. . . . . . . . . . . . . . . . . . . . . . . . . . . . 33Figure 5.2 DSC thermogram corresponding to Al-3.23 at.% - 0.23 at.%Cu alloy. A scanning rateof 5 ◦C/minute was used. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34Figure 5.3 Stress vs. strain evolution of Al-3.23 at.%-0.23 at.%Cu alloy during artificial aging at a)200 ◦C, and b) 160 ◦C, and Al-3.2 at.%Mg-0.12 at.%Cu alloy, at c) 200 ◦C . All tensiletests were done at 77K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35Figure 5.4 Kocks-Mecking plot evolution of Al-3.23 at.%Mg-0.23 at.%Cu alloy during artificialaging at a) 160 ◦C, b) 200 ◦C, and Al-3.2 at.%Mg-0.12 at.%Cu alloy during aging atc) 200 ◦C. The flow stress has been reduced by the yield stress measured at ε = 0.2%offset. All tensile test were done at 77K. . . . . . . . . . . . . . . . . . . . . . . . . . . 36Figure 5.5 Yield stress evolution of tested Al-Mg-Cu alloys during artificial aging at 200 ◦C and160 ◦C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37Figure 5.6 Resistivity evolution for Al-3.23 at.% - 0.23 at.%Cu, Al-3.2 at.% - 0.12 at.%Cu alloyduring artificial aging at 200oC and 160oC. . . . . . . . . . . . . . . . . . . . . . . . . 38Figure 5.7 Atom probe volumes measured on samples aged for a) 20 min and b) 160 min at 200◦C.In each case, iso-surfaces corresponding to a) 3.13 atoms/nm3 Mg and 0.5 atoms/nm3Cu, and b) 3.5 atoms/nm3 Mg 1.0 atoms/nm3 Cu are plotted to reveal the presence ofsmall Mg and Cu rich particles. One dimensional composition plots are provided alongtwo perpendicular directions, the results being representative of the observations madein the other particles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39xiiFigure 5.8 Experimental (symbols) and fit (coloured lines) pair correlation functions for a) Cu-Cupairs, b) Mg-Mg pairs and c) Mg-Cu pairs from the APT datasets shown in Figure 5.7.If all particles belonged to the same population having a uniform composition, then thethree figures should simply scale with one another. . . . . . . . . . . . . . . . . . . . . 42Figure 5.9 Normalized pair correlation functions of Cu-Cu, Mg-Mg, and Cu-Mg pairs correspond-ing to the volume aged a) 20 minutes and b) 160 minutes. If all particles belonged tothe same population having a uniform composition, then the three figures should simplyscale with one another. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43Figure 5.10 The best fit log-normal size distributions corresponding to the pair correlations shownin Figure 5.8. Left: aging for 20 min at 200◦C. Right: aging for 160 min at 200◦C. Thegreen and red areas account for the respective amounts of Cu and Mg in the particles.The results are given as a volume weighted distribution, or d fvdR . . . . . . . . . . . . . . . 44Figure 5.11 Experimentally obtained log σppt vs log time representation, corresponding the agingtemperatures and alloy compositions indicated in the figure. The dashed red line has aslope of 1/6, compatible with coarsening kinetics. The experimental values have beennormalized by the obtained A0 value for each condition. . . . . . . . . . . . . . . . . . 51Figure 6.1 Differential scanning for Al-3.23 at.%Mg - 0.23 at.%Cu deformed to increase the flowstresses by ∆σ= 24 MPa (ε ≈ 0.5%), 34 MPa (ε ≈ 1%), 44 MPa (ε ≈ 2%), 114 MPa(ε ≈ 8%) and 174 MPa (ε ≈ 10%). The curves have been offset vertically for easiervisualization. A scanning rate of 5 ◦ C/min. was used. . . . . . . . . . . . . . . . . . . 55Figure 6.2 Resistivity evolution of Al-3.23 at.% Mg - 0.23 at.%Cu alloy with pre-deformed ∆σ =44 MPa and ∆σ = 174 MPa, aged at 200 ◦C. . . . . . . . . . . . . . . . . . . . . . . . . 56Figure 6.3 Resistivity evolution corresponding to a AA5252 alloy containing 2.93 at.% Mg, de-formed ∆σ =174 MPa, aged at 200◦C. . . . . . . . . . . . . . . . . . . . . . . . . . . . 57Figure 6.4 Yield stress evolution of samples with no pre-deformation, and pre-deformed ∆σ = 44MPa and ∆σ = 174 MPa, aged at 200 ◦C. . . . . . . . . . . . . . . . . . . . . . . . . . 58Figure 6.5 Yield stress evolution corresponding to the AA5252 alloy, pre-deformed ∆σ =44 MPa,and ∆σ =174 MPa, aged at 200◦C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60Figure 6.6 Contribution of precipitation to the total strength, considering recovery as measured inthe AA5252 alloy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61Figure 6.7 Analyzed APT reconstructed volume corresponding to Al-3.23 at.% - 0.23 at.%Cu alloy,deformed ∆σ =174 MPa, aged at 200 ◦C for 20 minutes. The isosuface has been definedusing a concentration of 3.2 atoms/nm3 of Mg. . . . . . . . . . . . . . . . . . . . . . . 62Figure 6.8 APT reconstructed volume corresponding to Al-3.23 at.% - 0.23 at.%Cu alloy, deformed∆σ =174 MPa, aged at 200 ◦C for 160 minutes. . . . . . . . . . . . . . . . . . . . . . . 63xiiiFigure 6.9 STEM in SEM observation of Al-3.23 at.% - 0.23 at.%Cu alloy, deformed by cold rollusing a reduction of ε =10 %, and aged at 200 ◦C for 1100 minutes. The retaineddislocations appear to be decorated by precipitates, most likely S phase. . . . . . . . . . 64Figure 6.10 Schematic illustration of the microstructural processes envisioned to occur during aging.Top row: Aging starting from an as-solutionized state with a very low dislocation den-sity Bottom row: Aging starting from a pre-deformed sample where significant vacancyannihilation can occur at forest dislocations. . . . . . . . . . . . . . . . . . . . . . . . . 66Figure 6.11 STEM image of Al-3.23 at.% - 0.23 at.%Cu alloy, aged after quench (No pre-deformation),aged for 2 min at 200 ◦C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67Figure 6.12 Resistivity contribution of vacancy and dislocation storage during deformation, com-pared to experimentally obtained resistivity measurements from Al-3.23 at.%Mg - 0.23at.%Cu and AA5252 alloy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68Figure 6.13 A prediction of vacancy loss during aging in materials containing different dislocationdensities (ρ). In all cases the samples were modelled assuming a heating rate of 100◦C/sfrom 25◦C to 200◦C. In the cases where ρ = 1010-1012 m−2 the initial dislocation densitywas taken to be the equilibrium vacancy concentration at 550◦C. In the case of thesamples with ρ = 1013 and 1014 m−2 an additional excess vacancy concentration wasadded corresponding to that arising from plastic deformation. . . . . . . . . . . . . . . 70Figure 7.1 Stress vs. strain evolution of Al-3.23 at.% - 0.23 at.%Cu alloy, deformed a) and b)∆σ=44 MPa (εp=2%), during artificial aging at 160 and 200 ◦C respectively, and de-formed c) and d) ∆σ=174 MPa (εp=10%), during artificial aging at 160 and 200 ◦Crespectively. All tensile tests were done at 77K. . . . . . . . . . . . . . . . . . . . . . . 75Figure 7.2 Kocks-Mecking plots resulting from the stress vs. strain data for Al-3.23 at.% - 0.23at.%Cu alloy pre-deformed to ∆σ= 44 MPa (a and b) and ∆σ= 174 MPa (c and d). Theplots on the left (a and c) show the response on aging at 160 ◦C while the plots on theright (b and d) show the response upon aging at 200◦C All tensile tests were done at 77K. 76Figure 7.3 Kocks-Mecking plots resulting from the stress vs. strain data for Al-3.23 at.% - 0.23at.%Cu alloy deformed a) and b) ∆σ= 44 MPa, during artificial aging at 160 and 200◦C respectively, and deformed c) and d) ∆σ=174 MPa, during artificial aging at 160 and200 ◦C respectively. All tensile tests were done at 77K. . . . . . . . . . . . . . . . . . . 77Figure 7.4 Stress vs. strain evolution for AA5252 alloy (Al-2.94 at.% Mg) pre-strained a) andb) ∆σ=44 MPa (εp=2%), during artificial aging at 160 and 200 ◦C respectively, anddeformed c) and d) ∆σ=174 MPa (εp=10%), during artificial aging at 160 and 200 ◦Crespectively. All tensile tests were done at 77K. . . . . . . . . . . . . . . . . . . . . . . 78xivFigure 7.5 Kocks-Mecking plots resulting from the stress vs. strain data for AA5252 alloy (Al-2.94at.% Mg) pre-strained a) and b) ∆σ= 44 MPa, during artificial aging at 160 and 200 ◦Crespectively, and pre-strained c) and d) ∆σ=174 MPa, during artificial aging at 160 and200 ◦C respectively. All tensile tests were done at 77K. . . . . . . . . . . . . . . . . . . 79Figure 7.6 Experimental and modeled Kocks-Mecking plots. . . . . . . . . . . . . . . . . . . . . . 81Figure 7.7 Schematic work hardening rate evolution. This a reproduction is based on the parame-ters used for the modeled Al-Mg alloy shown in Figure 7.6. . . . . . . . . . . . . . . . 82Figure 7.8 Representation of the modeled deformation accounting for an initial low mobile dislo-cation density, on the work hardening evolution represented by the Kocks-Mecking plot.The vertical line at the beginning of pre-strain curve represent the end of the elastic seg-ment. The representation was done using k1 = 5.64x108 [1/m], k2 = 9.41 (k1 and k2 asobtained from the continuously deformed AA5252 alloy), η =0.08, ε0,i = 1x10−4 andσ⊥,i=200 [MPa] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85Figure 7.9 Effect of additional term for the generation of dislocations during plastic deformation,on the work hardening evolution represented by the Kocks-Mecking plot. This curvewas constructed using the following parameters: kD = 1x1015[1/m2], k1 = 5.64x108[1/m], k2 = 9.41, and σ⊥,i = 200 [MPa]. The vertical lines at the beginning of each plotrepresent the end of the elastic segment. . . . . . . . . . . . . . . . . . . . . . . . . . . 86Figure 7.10 Effect of additional term for the generation of dislocations, and low initial mobile dislo-cation density during plastic deformation, on the work hardening evolution representedby the Kocks-Mecking plot. This curve was constructed using the following parame-ters: kD = 1x1015[1/m2], k1 = 5.64x108 [1/m], k2 = 9.41, η =0.08, ε0,i = 1x10−4, andσ⊥ = 200 [MPa] The vertical line at the beginning of the pre-strain plot represent theend of the elastic segment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87Figure 7.11 Experimental and modeled Kocks-Mecking representation of AA5252 (Al-2.94 at.%Mg) system, pre-deformed ∆σ=174 MPa, aged 2 min at 200 ◦C, and further re-strained. 88Figure 7.12 Experimental and modeled Kocks-Mecking representation of Al-3.23 at.% - 0.23 at.%Cualloy system, deformed ∆σ=174 MPa, aged 2 min at 200 ◦C. . . . . . . . . . . . . . . . 92Figure 7.13 Kocks-Mecking plot for Al-3.23 at.% - 0.23 at.%Cu aged at 200 ◦C, pre-deformed a)∆σ=44 MPa, and b) ∆σ=174 MPa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92Figure 7.14 Forest strength from conversion of extracted dislocation density for Al-3.23 at.% - 0.23at.%Cu aged at a) 160 ◦C and b) 200 ◦C, pre-strained ∆σ=44 MPa, and ∆σ=174 MPa. . 95Figure 7.15 Precipitation contribution to the total strength for Al-3.23 at.% - 0.23 at.%Cu agedat a) 160 ◦C and b) 200 ◦C, pre-strained ∆σ=44 MPa, and ∆σ=174 MPa. These re-sults have been plotted along the precipitation contribution for material without anypre-deformation as calculated in Section 6.2.2. . . . . . . . . . . . . . . . . . . . . . . 96xvFigure A.1 Stress vs. strain evolution of Al-3.23 at.%-0.23 at.%Cu alloy during artificial aging at200 oC, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114Figure A.2 Kocks-Mecking plot evolution of Al-3.23 at.%-0.23 at.%Cu alloy during artificial agingat a) 200 oC, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115Figure A.3 Stress vs. strain evolution of Al-3.23 at.%-0.23 at.%Cu alloy during artificial aging at160 oC, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115Figure A.4 Kocks-Mecking plot evolution of Al-3.23 at.%-0.23 at.%Cu alloy during artificial agingat a) 200 oC, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116Figure E.1 Resistivity evolution of Al-3.23 at.% - 0.23 at.%Cu alloy, artificially aged at 160 ◦C. . . 124Figure E.2 Yield stress evolution of Al-3.23 at.% - 0.23 at.%Cu alloy, artificially aged at 160 ◦C. . . 125Figure F.1 Experimental and modeled Kocks-Mecking representation of AA5252 (Al-2.94 at.%Mg) system, pre-deformed ∆σ= 44 MPa , during artificial aging at 160 ◦C. . . . . . . . 127Figure F.2 Experimental and modeled Kocks-Mecking representation of AA5252 (Al-2.94 at.%Mg) system, pre-deformed ∆σ= 44 MPa , during artificial aging at 160 ◦C. . . . . . . . 128Figure F.3 Experimental and modeled Kocks-Mecking representation of AA5252 (Al-2.94 at.%Mg) system, pre-deformed ∆σ= 44 MPa , during artificial aging at 160 ◦C. . . . . . . . 129Figure F.4 Experimental and modeled Kocks-Mecking representation of AA5252 (Al-2.94 at.%Mg) system, pre-deformed ∆σ= 44 MPa , during artificial aging at 160 ◦C. . . . . . . . 130Figure F.5 Experimental vs modeled Kocks-Mecking plots resulting from the stress vs. strain datafor Al-3.23 at.% - 0.23 at.%Cu alloy deformed ∆σ= 44 MPa (ε =2%), during artificialaging at 160 ◦C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131Figure F.6 Experimental vs modeled Kocks-Mecking plots resulting from the stress vs. strain datafor Al-3.23 at.% - 0.23 at.%Cu alloy deformed ∆σ= 44 MPa (ε =2%), during artificialaging at 200 ◦C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132Figure F.7 Experimental vs modeled Kocks-Mecking plots resulting from the stress vs. strain datafor Al-3.23 at.% - 0.23 at.%Cu alloy deformed ∆σ= 174 MPa (ε =10%), during artificialaging at 160 ◦C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133Figure F.8 Experimental vs modeled Kocks-Mecking plots resulting from the stress vs. strain datafor Al-3.23 at.% - 0.23 at.%Cu alloy deformed ∆σ= 174 MPa (ε =10%), during artificialaging at 200 ◦C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134xviAcknowledgementsThis work would not have been possible without the support of the brilliant, dedicated people that I havemet during this journey, sharing a lot of their wisdom, energy and time with me. Each one of them has madethis process possible, and I can only continue working to reciprocate and multiply their kindness.I would like to thank my supervisor Dr. Chad W. Sinclair for the opportunity to join the microstructureteam. I greatly appreciate his guidance during the past years, his continuous curiosity, as well as the sup-port for the different ideas that constitute this work. This project and my professional development havebeen greatly supported by our collaborators Dr. Frdrick DeGeuser and Professor Alexis Deschamps, fromSIMaP, University of Grenoble INP - UJF - CNRS, and Dr. Baptiste Gault, from the Max-Planck-Institutfr Eisenforschung. I feel proud not only to have met them, but also to have had the chance to work withthem. My work was always enriched by the comments and observations from Professor David Embury,Professor Emeritus at McMaster University, and Professor Warren Poole from the Department of MaterialsEngineering, at UBC.This journey would not have been possible without the love, support, and strength from Galina. I cannotstop feeling grateful and lucky to know that someone like you is on my side. Your passion and dedicationhave been always an example for me, a driving force to carry on under the most difficult moments. I’mlooking forward to continuing sharing a home with you, wherever that takes us.Despite the distance and time, I always found support from my parents, siblings, and the rest of family.Among all the positive results that this work produced, I can include a wonderful chosen family (in alpha-betical order): Alastair, Alejandra, Alicia, Ben, David G., David P., Deena, Emi, Jacob, Leon, Lora, Meggy,Michael, M.J., Paolo and Tegar. I admire each one of you, how unique and remarkable you are. Thank youfor seeing a friend in me.Finally, I want to acknowledge the Mexican National Council of Science and Technology (CONACyT),and the Natural Sciences and Engineering Research Council of Canada, for financial support for my project.I deeply value the kind of support that these institutions provide to generate talent and technology.xviiChapter 1IntroductionThe negative environmental consequences of greenhouse gases (GHG) has led multiple industries to developtechnologies to reduce their emissions. The global transportation industry (e.g. automotive, aerospace, ma-rine) is the second largest source of GHG emitters, accounting for approximately 24% of the total emissionof CO2 in the atmosphere [1]. In particular, road transportation accounts for 75% of the total share of emis-sions for this sector, leading the increase in emissions within it (a total increase of 68% from 1990 to thelatest IEA evaluation in 2015) [1]. One strategy to reduce the volume of GHG produced by the transporta-tion sector is by vehicle weight reduction. In the case of automobiles, reducing the weight by 10% resultsin a 7% reduction of the amount of fuel required to travel the same distance [2]. Weight reduction has beenachieved through a combination of design and material substitution, particularly replacing steel componentswith lower density metals such as aluminum and magnesium [3]. Aluminum has progressively increased itsshare among the materials being used in automobiles, with a projected increase of 13% from 2015 to 2020.An area of particular increase will be for its use in car body panels, where it is projected that it will have anincrease of 83% by 2020 [4].Automotive body panels are divided into inner and outer panels, both having different requirements.Outer panels have to retain a yield strength of at least 200 MPa after so-called paint bake (a heat treatmentbetween 160 to 200 ◦C, from 20 to 45 minutes), have flat hemming capability, good surface appearance, andbe corrosion resistant [5]. Inner panels require the ability to be formed, be weldable and capable of retaininga high yield strength after paint bake [5]. The most common aluminum alloy used for inner panels belongsto the 5XXX series, which have a comparatively low cost and high formability, making them attractive forthis application [5]. The confinement of 5XXX series to inner panels is due to the formation of visuallyunattractive surface marks, developed when these alloys are subjected to deformation during forming.The alloys used as inner panels attain their high strength due to deformation (work hardening). Someportion of this strength is however lost during subsequent heat treatments required in the ‘paint bake’ cycle.This is inefficient as the lost strength has to be accommodated by the use of thicker part sections or morecomplex design.Alloying that leads to precipitation can be used to partially counteract the softening experienced in the1Figure 1.1: Aging behavior of Al-3.35at.%Mg-0.25 at.%Cu (Al-3wt.%Mg-0.6 wt.%Cu) alloy andAA5754 system (Al-3.35at.%Mg) at 180 ◦C, following a pre-strain of 10%. These are condi-tions similar to those experienced in a paint bake cycle[6]‘paint bake’ heat treatment. The addition of Cu, for example, to 5XXX (Al-Mg) alloys is known to beeffective in producing precipitation hardenable alloys. The relatively ‘large’ additions of Cu in conventionalAl-Cu-Mg alloys (2xxx series alloys) is, however, undesirable as it raises alloy cost and reduces weldabilitydue to hot cracking sensitivity [7].It has been shown that even small additions of Cu to 5XXX series alloys can still be beneficial to strengthretention (or even improvement) during the paint bake process (Figure 1.1). Few studies of origins of theseimproved properties exist in the literature. While it is understood that it is precipitation that is at the root ofthese improvements, the relation between this precipitation and strength is not understood [8]. In a broadercontext, the effect of pre-deformation on precipitation, the relationship between precipitation and staticrecovery, and their combined contribution to the mechanical strength evolution are still subjects of study[9]. This thesis seeks to address these issues, with a specific aim of improving the post paint bake strengthof 5xxx alloys with small additions of Cu, by improving our understanding of the coupled microstructuralphenomena that occur during processing.2Chapter 2Literature ReviewThe following chapter provides an overview of the current understanding of the microstructural and me-chanical property changes that occur during the low temperature (T < 250◦C) heat treatment of aluminumalloys. This chapter starts by illustrating basic principles through two classic binary aluminum alloys, Al-Cuand Al-Mg alloys. The Al-Cu alloys section will be used to introduce the general concepts involved in pre-cipitation strengthening, whereas the section on Al-Mg alloys will discuss concepts related to the softeningof wrought alloys by ‘recovery’. These are the two fundamental processes controlling the evolution of themechanical strength of the Al-Mg-Cu alloys studied in this thesis. Following this, a review of clusteringand cluster/precipitation strengthening in Al-Cu-Mg and Al-Mg-Cu alloys will be presented. Finally, ourcurrent understanding of the coupled effects of precipitation and recovery will be discussed.2.1 Age Hardening of Binary Al-Cu AlloysThe first systematic studies of precipitation hardening in aluminum alloys were performed in the Al-Cusystem [10]. Like many other age hardenable aluminum alloys, the Al-Cu system does not proceed fromsupersaturated solid solution directly to an equilibrium precipitate phase. Instead, it undergoes a complextransition through a series of metastable phases before reaching the equilibrium precipitate phase. The low-temperature precipitation sequence in age-hardenable Al-Cu alloys progresses from the supersaturated solidsolution (αss) via [11–13]:αss⇒ GP zones⇒ θ ′′⇒ θ ′⇒ θThe exact sequence of phases observed depends on the aging temperature and alloy composition as each ofthe phases noted above has its own solvus curve (Figure 2.1). Thus, the progression shown above is onlyobserved when the aging temperature is low enough that the GP zone solvus is crossed. The preference forthe sequential formation of these metastable phases at low temperature has been attributed to an easier nu-cleation pathway associated with lower activation barriers between each of the metastable phases comparedto the barrier separating the solid solution from the equilibrium phase.The activation energy between the metastable phases is presumed to be lower because the crystal struc-3Figure 2.1: Al-rich corner of the Al-Cu phase diagram indicating regions of stability of the differenttransition phases observed during precipitation in this system.[9].tures of the intermediate phases are more similar to one another than that of the equilibrium phase and thesolid solution, meaning that better lattice matching between the metastable phases exists and, consequently,lower interfacial energy [9]. For very small nuclei, the interfacial energy is a dominant term (due to theGibbs-Thompson effect) in the classical description of the nucleation barrier [14]Generally speaking, the first metastable product arising from the decomposition of the supersaturatedsolid solution at low temperature is known as Guinier-Preston zones (GP or, in older literature, GP-I zones).GP zones in Al-Cu alloys were first detected by X-ray diffraction (XRD) [15], and changes in electricalresistivity [16], then later by Transmission Electron Microscopy (TEM) [9, 17]. In Al-Cu alloys, the GPzones are observed as fully coherent single, or multi-atomic-layer thick Cu discs or plates, lying in the 100-Al planes [11] (Figure 2.2(A)). The particular shape of the GP zones in Al-Cu alloys arises from the largeatomic volume difference of Al and Cu, the plate shaped morphology minimizing the elastic strain energy[9, 18].The θ ′′ phase (sometimes denoted as GP-II), comprises two parallel layers of Cu atoms laying on the Al{001} planes, separated by three parallel planes of Al atoms resulting in the Al3Cu stoichiometry (Figure2.2(C)). This phase is often found to form heterogeneously on pre-existing GP-zones [19].Unlike GP-zones and θ ′′, which are both fully coherent, the body-centered tetragonal θ ’ phase forms asbroad plates, the faces of the plates being coherent with the {100} planes of the aluminum but incoherent4Figure 2.2: HRTEM observation of GP (A), θ” (C) and intermediate transition between the previoustwo phases (B).[9].on the edges of the plates [11]. Nucleation of this phase is found to be difficult, resulting in it precipitatingheterogeneously on grain boundaries and on dislocations [11, 12]. The θ ′ phase is richer in Cu than θ ′′,having a stoichiometry of Al2Cu. Finally, the stable θ phase shares the same body centered tetragonal crystalstructure and Al2Cu composition, but is fully incoherent with the matrix. It is often found to precipitateheterogeneously on pre-existing θ ′ particles.Figure 2.6 shows the evolution of hardness with aging time for the case of an Al-4wt.%Cu alloy agedat 130 and 190◦C. The mechanistic origins of this evolution are typically described following the approachillustrated in Figure 2.3. In the earliest stages of aging, the formation of GP-zones occurs, removing Cufrom solid solution this leading to a drop in yield strength. This in turn is compensated by the formation ofthe GP-zones whose strength increases as aging proceeds. The critical shear stress for a dislocation to movethrough a population of small and, therefore, weak GP-zones/precipitates can be described via the Friedelmodel as [20]:τc =2Γβ 2/3cbLs(2.1)where Γ is the dislocation line tension (≈ 0.5Gb2), b the magnitude of the Burgers vector. The mean squarespacing of precipitates, Ls, is calculated directly from the number of particles per unit area on the glideplane, Ls = (Na)1/2. The magnitude of Ls is expected to decrease in the early stages of aging due to the5increasing number density of particles formed by nucleation, this giving an important contribution to theincreasing strength at early times. The strength of an individual GP-zone/precipitate is described by theparameter βc = cos ψc2 (Fig. 2.4). Here, ψc is the critical angle that a dislocation bends before overcomingthe GP-zone/precipitate (Figure 2.4). In the Friedel limit the critical angle is large (120 ◦ ≤ ψc ≤ 180◦)meaning that the dislocation bends only a small amount before overcoming the obstacle. In this limit, thedislocation typically overcomes the GP-zone by shearing or cutting through it [21] (Figure 2.5a). While thedetailed process of a dislocation cutting through a GP-zone/precipitate is complex, it has been found thata linear evolution of βc, this proportional to the mean precipitate size (i.e. βc ∝ r¯), generally reproducesexperimental results in an acceptable manner [22]. Thus the initial increase in strength in Figure 2.3 is dueto the strengthening of GP-zones, due to their increase in size, combined with a higher number density ofparticles (decreasing Ls) during aging.Figure 2.3: Calculated contributions to the yield stress during aging in Al- 4wt.%Cu alloy, aged at150 ◦C.[23]The above process occurs through the formation of θ ′′ particles, progressively evolving towards the for-mation of the θ ′ phase. At the point when the θ ′ phase is the dominant phase in the microstructure, theparticles have become sufficiently strong that cutting is no longer the interaction mechanism between dislo-cations and precipitates, and rather the dislocation bypasses the precipitate by bowing around it (dislocationor Orowan looping [20], Figure 2.5b). When looping becomes dominant, βc is considered to reach a con-stant value equal to 1. Also, as the microstructure changes from a fine, high number density of GP-zones/θ ′′precipitates to coarser θ ′/θ precipitates, the number density must decrease. In this case, Ls increases and, at6constant βc, the yield strength is predicted to drop.Figure 2.4: Interaction between precipitate and moving dislocation.[20]Implicit in equation 2.1 is that Ls and βc are related to one another. For precipitates that are strongerthan the Friedel limit (ψc < 120◦) the relationship between precipitate strength, size and number densityneeds to be evaluated numerically. Classically, this has been done using aerial glide simulations as previ-ously reported in [20, 25, 26]. Additionally, this expression assumes point obstacles as depicted in 2.4, notaccounting the effect of precipitate’s geometry on, for example, the effective distance between obstacles[20, 27], further constraining the effectiveness of this expression for early stages of precipitation.Finally, it is worth noting that minor additions of other alloying elements can have a major effect onthe precipitation sequence in Al-Cu alloys [18, 28]. It was realized early, for example, that small additionsof Sn, Cd, and In could help catalyze the nucleation of the θ ′ phase largely, if not entirely, avoiding theformation of GP-zones and θ ′′ precipitates [18, 28, 29], having a finer dispersion, resulting in a higherstrength (Fig. 2.6). The study of the source of the remarkably different aging process due to additionsof micro-alloying elements, have been supported by the development of Atom Probe Tomography (APT)[11, 18, 30]. This is a technique capable to study materials with atomic resolution, allowing study of veryearly stages of precipitation, as well as the distribution of the previously mentioned small addition of alloying(a) (b)Figure 2.5: a) Particle shearing, b) Orowan looping[18, 24]7elements. The use of APT on Al-Cu systems have revealed features that precede the formation of GP zones,denominated clusters [18], as well as clarification of the role of the mentioned micro-alloying elements [11]during aging. Due to the substantial effect on the study of early stages of precipitation in Al alloys, a detaileddescription of this experimental technique will be provided later in this literature review.Figure 2.6: Hardness evolution of Al-2.5 wt.% Cu alloy aged at 200 ◦C.[18].2.2 Softening by Recovery in Wrought Binary Al-Mg AlloysUnlike the Al-Cu alloys discussed in the previous section, commercial alloys based on the Al-Mg systemare not precipitation hardenable, within the industrially relevant times and temperatures. Instead, Al-Mgalloys are referred as wrought alloys, their strength coming from solid solution, and work hardening. Byadding Mg to pure Al, the material can be strengthened substantially due to plastic deformation (so-calledwork hardening), compared to pure Al, which work hardens much less. The source of this effect has beenassociated to dislocation drag and pinning by Mg in solid solution, inhibiting dynamic recovery (loss ofdislocations taking place during plastic deformation) [31–33]. The challenge outlined in the introduction tothe thesis is that annealing of a wrought alloy (e.g. paint bake process) will lead to a reduction of the storeddislocation density and, therefore, strength. This softening due to annealing, following work hardening, isknown as static recovery [32]. At a macroscopic level, the main manifestation of recovery is the gradualreduction in the hardness/yield strength during time after deformation, the rate of softening being faster athigher temperature (Figure 2.7).For sufficiently high temperatures and, in a lesser degree, higher prior imposed deformation, recoverywill give way to the process of recrystallization, e.g. Go et al. [34] observed onset of recrystallizationafter annealing > 104s at 275 ◦C, for material deformed an equivalent strain of ε =0.58 (see Figure 2.8). Byincreasing the annealing temperature by a ∆T =25 ◦C, the time required for the onset of recrystallization wasreduced by approximately an order of magnitude per increment of annealing temperature. While recovery ischaracterized by a steady drop in yield strength (linear in a logarithmic time-scale, Fig. 2.7), recrystallizationis characterized by a rapid drop in strength (sigmoidal in a logarithmic time-scale, Figure 2.8) [35]. Here,8the focus will remain on recovery owing to its importance during the processing conditions experienced inthe paint bake cycle of automotive parts. The reader interested in more details about recrystallization inAl-Mg alloys is pointed to the review in [33].Figure 2.7: Yield stress evolution during annealing of an Al-3 wt.%Mg alloy, cold rolled (equivalentstrain ε=3 ). The annealed temperatures are shown in the graph[32]Figure 2.8: Yield stress evolution during annealing of a AA5754 alloy, cold rolled (equivalent strainε=0.58). The annealed temperatures are shown in the graph[34]At the microstructure level, recovery is characterized by the rearrangement of dislocations leading to areduction of the dislocation density relative to the as-deformed state [32]. From a process point of view,first, at low levels of plastic deformation ( 10% strain), the material’s microstructure will be populated byindividual arrangements of dislocations (Figure 2.9 (a)). Larger levels of deformation will result in theformation of cells, these being volumes of the material delimited by densely populated arrangements ofdislocations (cell walls, Figure 2.9 (b)). Upon annealing, the dislocations forming the previously describedcell walls will consolidate (Figure 2.9 (c)), resulting in a sharper boundary and evolving into the so-called9subgrains, these separated by well-defined low angle sub-grain boundaries (Figure 2.9 (d)). These sub-grainswill continue growing with further annealing (Figure 2.9 (e)). The sub-grains developed on recovery willcontain a low density of dislocations compared to the delimiting walls [33].Figure 2.9: Recovery evolution in a deformed material[33]The rearrangement of dislocations during static recovery is governed by the processes of dislocationclimb and cross slip [32]. An important parameter in determining the rate of these processes is the material’sstacking fault energy (SFE). Material with a high SFE, like aluminum (SFE ≈170 mJ/m2), show higherrates of both dislocation climb and cross slip and, thus, high rates of recovery compared to low stackingfault energy materials [35]. The presence of Mg as a solid solution element in Al has two opposite effectson recovery. On the one hand, Mg in solution leads (for the same level of strain) to a reduction in dynamicrecovery, allowing for a higher density of stored dislocations and, consequently, a higher work hardeningrate. On the other hand, this higher dislocation density is translated to a higher driving force for staticrecovery compared to pure Al, at the same level of deformation, resulting in faster static recovery process inAl-Mg alloys (compared to pure Al) [32, 33].Several models have been developed to predict the reduction in yield stress due to recovery [35]. Nes[32] proposed a detailed model for static recovery, accounting for the cell/subgrain structure, and the dis-10location density within subgrains. While the Nes model was shown to well predict the softening due torecovery in Al alloys [32, 36], it requires calibration of a large number of fitting parameters that can bedifficult to experimentally assess [34].Following shortly after the Nes model was proposed, a second similar model was proposed by Verdier etal. [37]. While the basic physical principle of the Nes and Verdier models are the same, the Verdier modelhas an advantage in that it requires fewer parameters to be assessed. The Verdier model starts from the sameassumption as the earliest models for recovery have relied [37], namely, that the rate of reduction in theflow stress (σ ) is proportional the plastic strain rate (ε˙p), accomplished by dislocations as they move duringrecovery;dσdt= σ˙ =−E ε˙p (2.2)with E being the Young’s modulus. Using the Orowan equation [37] to relate the plastic strain rate to thedislocation density, and assuming thermally activated dislocation motion, then one obtains,σ˙Verdier =−64σ2νD9M3α2Eexp(−U0kT)sinh(σVkT) (2.3)Where σ is the dislocation contribution to the yield stress, νD the Debye frequency, M the Taylor factor,and T the temperature. Typically the activation energy U0, and the activation volume V for recovery aretaken as adjustable parameters. While the expected values for the activation energy would be ones (in asimple approximation) associated to the activation energy for the mechanisms envisioned for recovery (e.g.diffusion assisted dislocation climb and/or cross slip), reported values for an Al-2.5 wt.% Mg alloy [37] andAA5754 [34] are significantly higher[37]. Similarly, the activation volume should also be consistent withthe expected mechanism, but has been reported to be a decreasing function of the pre-strain [34, 37]. Thisobservation has been argued to be evidence of recovery within cell walls/ subgrain boundaries as being thedominant effect [32].Precipitation is possible in Al-Mg systems, but requires aging times that are outside of the industrialinterest. Furthermore, for parts constituted by this alloys and subjected to temperatures in the range from 50◦C to 200 ◦C during operation, the observed intergranular precipitation results in entitlement and corrosionproblems [38]. During aging at temperatures below 100 ◦C, the generally accepted precipitation sequenceis [13, 38–40]:αss⇒ GP⇒ β ′′⇒ β ′⇒ βWhere the use of the term GP zone is used, as discussed in the previous section, in the sense of beingthe first feature associated to precipitation. Its presence has been detected by means of increase of resistivityduring aging [41], DSC (as a the first exhothermic peak in naturally aged samples) [13, 39], and a modulatedperiodicity along the < 100 > direction in HRTEM studies [13]. Using SANS, Roth and Raynal [42]proposed the GP zones to have a sphere-like shape, with a radius between 2 to 6 nm, and a concentration11(a) (b)Figure 2.10: a) Hardness evolution for Al-10wt.%Mg and Al-5wt.%Mg during aging at 30 ◦C, b)Resistivity evolution of Al-10wt.%Mg system aged at the indicated temperaturesfrom 20 to 25 at.% of Mg. These finding have been further supported by Yi et al. [43] in their APTobservations of a AA 5083 alloy, aged at 50 ◦C for 24 months. The β ′′ phase (sometimes identified aswell as GP zones [13, 40], or ordered GP zones), posses a L12 crystal structure with a Al3Mg stoichiometry[13, 39, 43], the β ′ phase posses a HCP crystal structure with a Al3Mg2 stoichiometry, and the the stable βphase has a FCC structure with a Al3Mg2 composition [39, 43]. Sato et al. [40] investigated the hardnessand resistivity evolution in a Al-5 wt.%Mg and Al-10 wt.%Mg aged between -30 to 100 ◦C, revealing thatno hardening effect can be observed after more than 3000 hrs at room temperature in the Al-5 wt.%Mg,while the Al-10 wt.%Mg system barely increases in the same period span (Fig.2.10a. In contrast, andas mentioned in the description of the GP zones for this system, a clear change in the resistivity can beobserved, this shown in Figure 2.10b for the case of the Al-10 wt.%Mg system.2.3 Al-Cu-Mg alloysWhile precipitation hardenable, the long aging times required for precipitation hardening in binary Al-Cualloys, makes them impractical for commercial applications. Very early in aluminum alloy development[44], it was found that small additions (as small as 0.5wt.%) of Mg could enhance both the kinetics andmaximum strength achieved in Al-Cu alloys. Moreover, adding Mg also increases the strength of the alloyin the solid solution state. Such Al-Cu-Mg alloys serve as the basis of the majority of the of the commercialAA-2XXX series of aluminum alloys [18]. The majority of studies performed on Al-Cu-Mg alloys havebeen on alloys with a Cu concentration higher than the Mg concentration, this resembling the typical 2XXXcommercial compositions, which contain a concentration between 2 to 7 wt. % of Cu, and 0.2 to 2 wt. % ofMg [18] . This range in compositions can result in different stable phases, these shown in the phase diagram12in Figure 2.11. The S phase possess an orthorhombic structure, having a composition Al2CuMg [18]. Theθ phase is the same as the one described in the Al-Cu section, and the T phase has been reported to have acubic structure, with a composition Al6CuMg4 [30].Figure 2.11: Al-rich corner of the Al-Cu-Mg phase diagram at 200 ◦C[45]As noted above, additions of as little as ∼0.5 wt.% Mg are enough to cause a dramatic change in thekinetics of age hardening and maximum strength that these alloys can achieve during artificial aging (Figure2.12). The most drastic effect caused by the addition of Mg is the rapid increase in hardness during the firstseconds of artificial aging (Fig. 2.12). The magnitude of this ‘rapid hardening response’ depends on theproportion of alloying elements, but can contribute up to 70% of the peak aged hardness [46]. The initialrapid hardening is followed by a plateau of the observed hardness, subsequently evolving towards a secondhardening regime, leading to the peak strength of the alloy.Despite the large body of literature devoted to the study of precipitation in Al-Cu-Mg alloys [48], theorigin of the ‘rapid hardening response’, the sequence/composition/crystallography of phases formed (par-ticularly at short aging times), the role played by defects (vacancies and dislocations in particular), are stilltopics currently debated [47–52].Focusing on compositions where the stable phases fall in the α+S phase field, the first proposed sequenceof decomposition was made by Bagaryatsky [53, 54], using single crystal X-ray diffraction, as,αss⇒ zones(GP)⇒ S′′⇒ S′⇒ SWhere the defined zones were characterized as analogous as the GP zones described above, while theS′′ and S′ where defined as distorted version of the S phase, having different degrees of coherency with thematrix.13Figure 2.12: Hardness evolution vs. time, aged at 200◦C. Concentration are given in at.%. after[47].Silcock, using single crystal X-ray diffraction, questioned the existence of the S′′, proposing the follow-ing sequence [54],αss⇒ GPB⇒ S′⇒ SThis was the first description of the Guinier — Preston — Bagaryatsky or GPB zones, these being cylin-ders elongated in the < 100 >α directions (diameter between 1-2 nm, and aspect ratio ∼ 4), having a facecentered tetragonal crystal structure [54], and being responsible for initial rapid hardening behavior. Further-more, Silcock proposed the presence of a new phase GPB-2, following the precipitation of the previouslydefined GPB zones, this during artificial aging at higher temperatures (240 ◦C) [54].These previously proposed precipitation sequences have laid the basic nomenclature used in later re-search in Al-Cu-Mg alloys. Despite using the same nomenclature, very different descriptions of the chem-istry and crystallography of the transition phases, sequence during precipitation, and the final effect in thestrength of the material, have been proposed.Reports of rod and lath shaped S phase, having different lattice parameters, and orientation relationships,resulted in more complex interpretations of the characteristics of the S” and S’ phases preceding a stable Sphase [45, 55–57]. Styles et al. [45] have been able to provide a higher insight on the variations of S-Phasefound in literature. Using synchrotron light source X-ray diffraction, in addition to Rietveld refinement, theywere able to show that the source of the multiple interpretations of the S-phase, is the co-existence of twoS-phases variations, with slightly different lattice parameters. The S1 and S2 phases (in their terminology),the former is a lath-shapes, while the latter is a rod-shaped. The S2 phase has tendency of grow at theexpense of the S1 phase, making it the more stable phase.The definition of the S” and GPB-II phase has been more controversial. Wang et al. [58, 59] re-ported them as being the same phase, having an orthorhombic structure, and a composition defined by14Al10Cu3+xMg3−x. This interpretation and terminology was rejected by Kovarik et al. [57] who identifiedthe S” phase as what above has been termed S1 phase. Similarly, Rachev et al. [60] identified a quickformation of S” phase along dislocations, using electron diffraction. Kovarik et al. [61] pointed out thatRatchev’s diffraction pattern interpretations were incompatible with the previous descriptions of this phase(e.g. Charai et al. [62]), instead interpreting the diffraction patterns to be what they termed GPB-II zones,having a L10 crystal structure. Charai et al. [62], using electron diffraction, identified the S” phase as havinga monoclinic crystal structure, while no GPB-II zones where identified. Remarkably, a full overlap of GPBzones, S”, S’ and S phases was identified in their research. They proposed that the S” phase consists of anagglomeration of monolayer GPB zones, which showed no further transition to a S’ or S phase.With regards to the GPB zones, Silcock’s early findings have been generally confirmed by later studies,using HRTEM, HAADF-STEM and APT characterization techniques [8, 62, 63]. The GPB zones have beenconfirmed to be cylinders elongated in the < 100 >α directions (diameter between 1-2 nm, and aspect ratio∼ 4). Furthermore, Charai’s [62] idea of a continuous transformation and overlapping transition of phases,has been recently supported by the HAADF-STEM and DFT calculations done by Kovarik et al. [8, 49, 64].These authors proposed a progressive block addition theory, to explain the different structural arrangementsof GPB zones observed in their experimental work. They proposed that the GPB zones were constitutedby the agglomeration of basic crystal units (Figure 2.13 A)), termed 1D-GPB1. These units can stack alongthe long dimension (L dimension Figure 2.13 B)), to form the observed rod-like particles. These 1D-GPB1units can further bond with other 1D-GPB1 units, forming what they termed 1D-GPBx units ((Figure 2.13B) and C), w direction), where x is the number of zones clustered, reproducing the experimentally observedGPB zones. In their first calculations [49, 64], a stoichiometry defined as (Mg2x+2Cu2x+2Al3x−1) for theGPB zones was proposed, with the possibility of an evolving stoichiometry during their formation [49].For Kovarik et al. to observe GPB zones by HRTEM, very long aging was required (i.e. 24 hrs. at 180◦C [8]). More recent studies have focused more on identifying the microstructure corresponding to shortaging times, these being responsible for the rapid initial increase in strength shown in Figure 2.12. It hasbeen these recent studies, primarily using atom probe tomography, that have caused a reconsideration of theoriginally proposed precipitation processes [54], to include the effect of so-called ‘co-clusters’ on aging.As a brief introduction to the technique, given its importance later in the thesis, atom probe tomography(APT) is a combination of field evaporation, time-of-flight spectroscopy, and position sensitive detectionmeasurements [65, 66]. By applying a high electric field, or a combination of high electric field with a pulsedlaser, to a sample with a sharp needle (tip) geometry, field evaporation of atoms occurs [65]. A constant highvoltage applied between sample (positive) and detector (negative) leads to ionization of surface atoms, and areduced energy barrier for evaporation. To evaporate, a pulsed electric field or pulsed laser is used. The ionis accelerated toward the detector, where it is collected. The chemical identification of the evaporated ionis done by means of Time-of-flight spectroscopy, this based on identifying the mass to charge ratio M = mnfor the species, while a projection model for the ion trajectory allows for its location within the needle to beestimated. For more details, the interested reader is referred to the recent reviews in [65, 66].Using APT, Ringer et al. [67] observed a preferential clustering of Cu and Mg atoms (co-clusters) in the15Figure 2.13: Proposed GPB zone structure based on HRTEM observation and Ab Initio calculations.Adapted from[49]solid solution preceding the formation of other distinct phases (e.g. GPB zones). They identified that ratherthan a distinct phase, such ‘co-clusters’ are a form of non-random solid solution with each cluster beingcomprised of between 3 and 20 solute atoms. On this basis, Ringer et al. have referred to the strengtheningarising from such clusters as an ”exaggerated form of solid solution hardening” [68]. Since this earlywork, there have been several detailed APT studies of clustering/GPB zone formation in Al-Cu-Mg alloys[47, 63, 69–71]. Marceau et al. [47] provided detailed, quantitative information in terms of number density,size and composition evolution of solute clusters in model Al-1.1 at.%Cu- x at.%Mg alloys, with x=0.2,0.5and 1.7 at.% Mg.Marceau et al. [47] were able to further characterize these co-clusters, immediately after quench, andafter artificial aging for 60 seconds and 60 minutes at 150 ◦C using APT. These clusters were found tobe part of a continuous distribution of features ranging in size, from as few as 2 atoms up to tens of atoms,depending on the aging time. The number density of clusters were of the order of 1024m−3. In the alloys andaging conditions used, no GPB zones were reported. Based on their cluster analysis, they considered thatclusters, with high Mg:Cu ratio, produced a larger strengthening effect in the alloy. Sha et al. [63] analyzeda commercial AA2024 alloy, during artificial aging at 170 ◦C for 30 min., 80 hrs. and 114 hrs., providingsimilar results as Marceau et al. [47], in terms of size and number density of the identified co-clusters.After 30 minutes of aging, the average cluster contained 90 at.% Al, with Cu and Mg concentrations of4.5 at.% and 4 at.% respectively. These clusters were comprised of an average of 24 atoms. Additionally,they revealed a progressive transition from clusters to GPB zones, to S phase at peak aging, showing theco-existence of these different features during aging, this supports the observation of Charai et al. [62].Additional characterization techniques have been used to provide additional support for the above in-terpretations. For example, Positron Annihilation Spectroscopy (PAS) has been used to help interpret themicrostructural changes on aging [47, 72]. By measuring the time for the annihilation of positrons in asample containing defects (e.g. vacancies, grain boundaries and dislocations) relative to the decay time in aperfect crystal one can provide an estimate of the density of these defects [47, 72]. This technique has been16shown to be particularly useful for characterization excess vacancies which can accelerate diffusion [9, 17],and aid in the early stages of clusters [72–74] and GP zones [9]. The complimentary Coincidence Dopplerbroadening (CDB) technique provides information regarding the electronic environment associated with theannihilation process. This has been used in these alloys to estimate the local composition of solute clustersunder the assumption that vacancies (which are annihilation centers) are part of the clusters [72]. The studyof Marceau et al. [47] showed a progressive formation of solute atom clusters around vacancies. This wasfurther supported by showing that the estimated vacancy concentration was of the same order of magnitudeas the number density of detected clusters in their system.Figure 2.14: Solute concentration in precipitation distribution after artificial aging for 80 hrs. at 170◦ in a AA2024 alloy.[63].Deschamps et al.[46], in an effort to obtain results from a more statistically representative technique,employed nuclear magnetic resonance spectroscopy (NMR) and small angle x-ray scattering (SAXS) tostudy a model Al-Cu-Mg system. The NMR results revealed the quick formation of a Cu rich-secondaryphase in the first minutes of aging at 200 ◦C, this signal remaining stable even after the appearance ofadditional signals associated with other transition phases. The SAXS experiments revealed an isotropicspectrum at low scattering angles characteristic of small particles having an ill-defined crystallographicstructure (compared, for example to ordered precipitates). This result supports the interpretation of therapid hardening being a consequence of co-cluster formation at the beginning of aging at 200 ◦C. Furtheraging caused an anisotropic streaking in the diffraction pattern, this being characteristic of features having anaspect ratio greater than one. This observation was interpreted as evidence for the formation of S (or related)phase. Combining the results of NMR and SAXS analysis led to the interpretation that the first phase toprecipitate consisted of particles having a size of 4.5 A˚(∼ 25 atoms) and a composition of approximately35% (±10%) Cu. This Cu concentration agrees with the CDB measurements of Marceau et al. [47], but ishigher than the concentration measured by APT from Sha et al. [63].The interpretation of the characteristics of the previously described co-clusters, as well their associationto the rapid hardening effect, have been challenged by Zahra et al. [75, 76], Reich [50], and more recentlyby Kovarik et al. [8, 49]. These latter studies considered that the APT observations of co-clusters, are infact GPB zones, specifically the 1D-GPB1 structure proposed above (Figure 2.13 A).17Despite these different interpretations, it appears to be widely agreed now that the initial hardening effectis due to the formation of co-clusters [70], while the later hardening arises mainly from a combination ofclusters, GPB zones, and S-phase (Figure 2.14). Finally, it is the evolution of the fractions of these differentphases that gives the peculiar hardening curve shown in Figure 2.12.2.4 Al-Mg-Cu alloysWhile the 2XXX series Al-Cu-Mg alloys described above are well established commercially, there has beenonly exploratory interest in alloys with low Cu to Mg ratios, this dating back to the late 1980’s e.g. [77].For the purposes of this thesis, these Cu lean/Mg rich alloys will be referred to as Al-Mg-Cu alloys so as todistinguish them from the high Cu/low Mg 2XXX series alloys. Specifically, Al-Mg-Cu alloys are definedhere as aluminum alloys containing & 2wt. %Mg and . 1wt. %Cu.As mentioned in the introduction, the original interest in these Al-Mg-Cu alloys was to reduce softeningof wrought 5XXX series Al-Mg alloys, particularly during the automotive paint bake heat treatment (≈185◦C during 30 min [78]). The intent was to use the small Cu additions to trigger precipitation and thus toinduce some combination of precipitation hardening and/or a reduction in recovery [6, 77, 79]. Figure 2.15shows that such small Cu additions can be used to suppress softening, and even lead to hardening duringsimulated paint bake treatments in modified wrought Al-Mg alloys [6, 80]. Despite these results, it is stillnot understood what proportion of the change in strength in these cases arises from precipitation hardeningand what proportion comes from softening due to dislocation recovery.Figure 2.15: Aging behavior of Al-3.35at.%Mg-0.25at.%Cu (Al-3wt.%Mg-0.6 wt.%Cu), Al-3.35at.%Mg-0.08at.%Cu (Al-3wt.%Mg-0.2 wt.%Cu) alloy, and AA5754 system (Al-3.35at.%Mg) at 180 oC, following a pre-strain of 10%. These are conditions similar to thoseexperienced in a paint bake cycle[6]18Like the Cu-rich 2XXX series alloys, Al-Cu-Mg alloys have been shown to also exhibit the ‘rapidhardening response’ upon low temperature aging. Figure 2.16 shows the evolution of tensile yield strengthof a solution treated then aged (180◦C) Al-4.2wt.%Mg-0.6wt%Cu alloy [60]. The initial jump in yieldstrength (∼30 MPa) seen comparable to that seen in the high Cu/low Mg alloys (Fig. 2.12). Unlike the2XXX series alloys, however, the Al-Mg-Cu alloys show a slow and steady increase in yield strength topeak strength, rather than a plateau followed by second hardening peak [8, 60]. Overall, the peak strengthachieved in the Al-Mg-Cu alloys is generally lower than what can be achieved in 2XXX series alloys.Figure 2.16: Al-4.2wt.%Mg-0.6wt%Cu yield stress evolution vs time, aged at 180 ◦C. after[60].Referring back to Figure 2.11, the Al-Mg-Cu alloys as described above fall within the α + T or α +S+ T regions of the phase diagram at 200◦C. The T phase is much less well studied than the S phase[30, 81, 82]. This phase has been reported to be a cubic structure, with a composition Al6CuMg4 [18, 30],or a isomorphous with the T phase in Al-Zn-Mg alloys with high Mg concentration, having a body-centeredcubic structure, a complex unit cell composed by 161 or 162 atoms, and a stoichiometry defined as Mg32(Al,Zn)49 [81]. Surprisingly, considering the established phase diagram, reports of the T phase have only beenmade in Al-Mg-Cu alloys containing additional micro alloying elements e.g. Au [81, 83], after prolongedaging. Rather, TEM and HRTEM observations have revealed the presence of GPB zones and S-phase,similar to long time aged Al-Cu-Mg alloys. [6, 8, 61, 84–86].In comparison to the heavily studied Al-Cu-Mg alloys (see previous section) there have been very fewstudies of the precipitation sequence in Al-Mg-Cu alloys. Based on TEM/HRTEM and DSC analysis (Figure2.17) [8, 60, 61], it has been suggested that the Al-Mg-Cu alloys share the same basic precipitation sequenceas observed in 2XXX series alloys. For example, the experiments and observations used by Kovarik et al.[8, 86], to support GPB zones as being responsible for rapid hardening in 2XXX series alloys, were actuallyperformed on Al-Mg-Cu alloys. Consequently, the same controversies surrounding the nature of soluteclusters/GPB zones, and S-phase variants, exists in the low Cu alloys as do in the Al-Cu-Mg alloys.192.5 The interaction between deformation and precipitation in aluminumalloysIn the prior sections the focus has been on precipitation in a ‘well annealed’ material containing a lowdislocation density. In the case of bake hardening, one has to consider how i) the presence of deformationinduced defects, dislocations and vacancies, influence precipitation and ii) how precipitation can influencethe process of recovery. Recovery and precipitation are highly coupled to one another making interpretationof the evolution of mechanical response in paint baked alloys complex. As noted above, the proportion ofrecovery induced softening and precipitation hardening in the response of the Al-Mg-Cu alloys, shown inFigure 2.15, remains unknown.2.5.1 The effect of deformation on precipitationPre-deformation affects precipitation in two key ways i) it changes the thermodynamic driving force forprecipitation and ii) increases the kinetics of diffusion. These phenomena have been discussed in detail inprevious reviews, the interested reader being pointed to the classic work of Larch [87] and the more recentreview focused on aluminum alloys by Hutchinson [88]. Here, a brief overview of the key ideas will begiven.Dislocations are generally considered to be preferred nucleation sites for precipitates, this being at-tributed to their effect on lowering the energy barrier for nucleation. The original model explaining thiseffect comes from Cahn [89], who envisioned an extra driving force for precipitation due to the relaxationof part of the dislocation’s elastic strain energy within an incoherent precipitate. This was generalized byLarch [9, 87], and the concept has been widely applied in the context of classical nucleation theory (seee.g. [9, 31, 90]). Simplified approaches take the energy barrier to be simply an adjustable fraction of thatrequired for homogeneous precipitation, this fraction being used to obtain correct nucleation kinetics (seee.g. Perrand et al. [91]). When taking this approach, one must also adjust the number density of nucleationsites to make them proportional to the dislocation density [31, 91, 92].A less cited, but potentially important effect of dislocations on precipitation, comes from the fact thatsolute will segregate to dislocations due to the elastic interaction between solute and dislocation stress field[93]. Xiao and Hansen [94, 95] developed a model to explain their observation of preferential precipitation ofNi3Al, on dislocations in Ni based alloys. Using classic thermodynamic arguments, coupled to predicted Alsegregation towards the region surrounding an edge dislocation, they showed how segregation could reducethe critical nucleus size to zero close to the core of the dislocation. This work has been re-investigatedrecently using numerical modeling involving phase field and atomistic models [96–98]Deformation also affects precipitation by accelerating diffusion. This can occur due to the presence ofan excess density of deformation induced vacancies [99–102], and by ’short circuit pipe diffusion’ alongdislocations [14, 22, 103].For aluminum alloys, it is the diffusion of substitutional alloying elements that determines the rate ofnucleation and growth of precipitates. Diffusion in this case is the result of vacancy migration, the rate20of diffusion of the solute elements being proportional to the concentration of vacancies [14]. The processof plastic deformation leads to vacancy formation due to (among other processes) the dragging of jogs ondislocations [104]. Some phenomenological models for vacancy production during deformation have beendeveloped based on such mechanisms [105, 106]. Upon aging, this ‘excess’ density vacancies will decaytowards the equilibrium concentration at the aging temperature, this due to vacancies annihilating on grainboundaries, dislocations, or by the condensation of vacancies into dislocation loops [99, 100, 107–109].Evidence of the importance of vacancies for the formation of precipitates is often cited in the form ofprecipitate free zones around dislocations and grain boundaries, arising from the depletion of vacancies andsolute in the regions around them [110, 111]. Thus, the direct effect of vacancies on accelerating diffusionis usually limited to the early stages of aging before reaching equilibrium [100, 101].So-called ”pipe diffusion” of solute along the core of dislocations [14] has also been cited as a reasonfor accelerated nucleation and growth of precipitates in deformed samples [22, 103, 112]. This faster pathfor solute diffusion is considered to require a lower activation (0.6 to 0.7 of the energy required in bulkdiffusion [113]), having a significant effect at lower temperatures [14]. This diffusive mechanism has beenused to support dynamic strain aging, where large concentration of solute are necessary to justify this effect[114]. The experimental complexity to study this type of diffusion have encouraged the use of computersimulations [113, 114], supporting the need of pipe diffusion as a fast diffusing path, but also showing thepotential need of vacancies for this process to take place [113, 114].The combination of the thermodynamic and kinetic effects described above has observable consequenceson the kinetics of precipitation, precipitate size [34, 115], precipitate size distribution [34, 111] and theprecipitation sequence [103, 111].For Al-Cu-Mg and Al-Mg-Cu alloys, it has been reported that a deformed microstructure leads to thedirect formation of the S-phase along dislocations [60, 116]. The influence of vacancies and dislocationshave also been observed in non-deformed samples, due to dislocation loops formed by quenched-in vacancyagglomeration, these being the sites for rapid and preferential formation of the S-phase [45, 50, 60, 116].Ratchev et al. [84], used DSC to monitor the sequence of precipitation in a Al-4.2 wt.% Mg- 0.6 wt.%Cu alloy that had been solutionized, then deformed in tension to 2% and 5% strain. As can be seen inFigure 2.17, the sharp exothermic peak associated with the precipitation of co-clusters/GPB zones in theas-quenched sample (peak A, Figure 2.17), was observed to broaden and shift to higher temperatures withincreasing deformation. At the same time, the peak attributed to the S-phase was seen to shift towards lowertemperatures. This has strong similarities to DSC results arising from deformed and aged 2XXX seriesalloys [115].The effect of dislocations on solute cluster formation in an Al-3.6 wt.%Cu-1.6 wt.%Mg alloy has alsobeen studied using electrical resistivity and APT measurements [117]. These experiments were performedon samples aged for 96 hours at room temperature after solution treatment and deformation. The results ofboth techniques pointed to an increasing reduction in cluster density with level of deformation. A similarsuppression of clustering due to pre-strain in an Al-Mg-Si alloy has been attributed to the rapid loss ofvacancies to dislocations [118, 119].21Figure 2.17: DSC thermogram of an Al-4.2wt.%Mg - 0.6wt.% Cu alloy system[60].2.5.2 Recovery in the presence of precipitationIt is known that the presence of precipitates can hinder the rate of recovery in precipitation hardenable alloys,either by pinning those dislocations on which precipitates have nucleated heterogeneously [31, 120], or byhindering the glide/climb of dislocations during recovery [120] .In the model developed by Zurob et al. [31] it was assumed that precipitates act to pin dislocationsegments during recovery, the probability of pinning being taken to be,Ppin =N (t)Nc (t)(2.4)where N (t) is the number density of precipitates and Nc (t) ≈ 0.5ρ3/2 is the number density of dislocationnodes. When Ppin > 1 then it was assumed that recovery was completely stopped. Alternatively, whenPpin < 1 then the model developed by Verdier, Equation 2.3 was modified as,σ˙Zurob = σ˙Verdier(1−Ppin) (2.5)In the case of precipitation into a pre-deformed microstructure, Ppin = 0 at t = 0 but increases as precipita-tion takes place, this leading to the halting of recovery. Further aging, however, would lead to precipitatecoarsening and a drop in N and the continuation of recovery.The complex interrelationship between precipitation and recovery when they occur concurrently meansthat verifying the above equation for a variety of systems is difficult. Roumina [120] attempted to separatethe effects of precipitation and recovery experimentally by preparing Al-Mg-Sc alloys containing a stabledistribution of Al3Sc precipitates, followed by deformation then a recovery heat treatment. It was foundthat Zurob’s approach alone was not sufficient to explain the observed recovery kinetics as it over-predicted22the length of the stasis in recovery. In Roumina’s model [120] two parallel processes were considered tocontrol the recovery kinetics: Standard dislocation-dislocation annihilation unaffected by the precipitatesas described by Equation 2.3, and annihilation controlled by dislocations having to circumvent precipitatesby climb. To capture the kinetics of the second process, Roumina adopted a simple climb based kineticequation [121],σ˙Climb =−C 1√ fvb2dpptDvkT(σ˙)2 (2.6)Where dppt is the precipitate diameter, Dv is the vacancy diffusivity, k is the Boltzmann constant, T is theaging temperature, and C is a constant. It was then considered that the total rate of recovery was the sumof the rates of recovery given by equations 2.3 and 2.6 weighted by probability that a moving dislocationwould meet a precipitate during recovery ( f ),σ˙Roumina = (1− f )σ˙Verdier + f σ˙Climb (2.7)Where f was defined as being proportional to the ratio of the dislocation annihilation distance to the precip-itate spacing. An example of the experimental and modeling results, using the previously described model,can be seen in 2.18. Here it is observed how the effect of softening stasis (controlled by the term σ˙Climbabove), due to precipitation, takes place after several hours of recovery at 190 ◦C.Figure 2.18: Yield stress evolution during aging at 190 ◦C, after artificial aging (425 ◦C for 80 minand 8 days) and cold roll (80% reduction)[120]While Roumina’s work provided detailed insight into the process of recovery in the presence of a set ofstable precipitates present prior to deformation, the vast majority of literature on the effect of precipitateson recovery has been on the more practically important situation when precipitation and recovery occur23concurrently. These studies are based on the effects described above, with the main objective of predictingthe evolution of the strength of the material, in which these two phenomena take place during aging. Theoverlapping nature of precipitation and recovery, does not facilitate a clear identification of the relationbetween these two, leading to a multiple modeling strategies [22, 31, 111, 112, 120, 122, 123]. The selectionof a specific strategy is based either on the observations made for the conditions used in the studied alloy andprocessing conditions, or on simplifications needed to deal with the complexity of concurrent recovery andprecipitation. For the case of the Al-Mg-Cu system, under the processing conditions of the pain bake cycle,more studies to understand the relationship between these phenomena are required to develop a successfulmodeling strategy for coupled recovery and precipitation.2.6 Summary1. Small additions of Cu to Al-Mg alloys for the formation of precipitation hardenable alloys from Al-Mg alloys that are conventionally used in the wrought form.2. Significant controversy still exists in the sequence of precipitates formed in Al-Mg-Cu and Al-Cu-Mgalloys with much of our understanding of the behaviour of Al-Mg-Cu alloys coming from studies onAl-Cu-Mg alloys3. Most recent literature seems to point to the decomposition of Al-Mg-Cu alloys as being a gradualtransition from solute clusters to the equilibrium S-phase4. Precipitation into a deformed microstructure in Al-Mg-Cu alloys appears to accelerate the transitiontowards the equilibrium S-phase, with preferential formation of the equilibrium phase on dislocation.5. The relative importance of precipitation hardening versus recovery softening (and how these twoprocesses are related to one another) is still unknown for Al-Mg-Cu alloys subjected to paint bakeoperations.24Chapter 3Scope and ObjectivesIt is clear that Al-Mg-Cu alloys with low Cu:Mg ratios are potentially interesting for applications wherewrought Al-Mg alloys are currently being used. The ability to stop softening during aging would allow forless material usage and higher weight-savings in the automotive industry. Understanding exactly how theprocesses of precipitation and recovery are coupled is necessary if we are to better understand how to designsuch alloys for optimal utilization.The objective of this thesis is to identify how concurrent precipitation and recovery interact in suchalloys, and to relate how these processes determine the time evolution of the material’s yield strength andwork hardening under simulated industrial automotive paint bake cycle conditions.To achieve this objective, an approach combining experiments and models has been utilized. Startingfrom model ternary alloys, mechanical property assessment and the imposition of pre-deformation have beenperformed by uniaxial tensile tests performed at low homologous temperatures. Microstructural characteri-zation has been performed at the macroscopic scale (e.g. via calorimetry and electrical resistivity), and themicroscopic scale (e.g. atom probe tomography, electron microscopy). Phenomenological models for mi-crostructure evolution (i.e. precipitation and recovery) and mechanical response (dislocation and precipitatebased hardening) have then been built based on these observations.In the first part of this thesis, the early stages of precipitation and strengthening in undeformed alloysis explored using experiments and models (Chapter 5). Having obtained an understanding of precipitationin the absence of deformation, the next chapter (Chapter 6) will examine the effect of pre-deformation onprecipitation kinetics and precipitate type. Finally, the work hardening response of deformed, then agedsamples will be assessed experimentally and modelled (Chapter 7). In particular, this section of the thesisaims to separate the contributions of precipitation and forest hardening to the macroscopic yield stress, andto provide guidance for future alloy development strategies.25Chapter 4Experimental ProceduresIn the following section, a description of the methodology and characterization techniques used to accom-plish the previously stated objectives will be provided.4.1 MaterialsFor this study three alloys where used: two Al-Mg-Cu alloys, and a Al-Mg alloy, denominated AA5252.These were provided by Novelis Global Technology Centre, our industrial partner in this project. Thesealloys were produced at Novelis using a Direct Chill Casting method (DC) [124]. For the Al-Mg-Cu alloys,the starting 95 mm thick DC cast material was scalped to a thickness of 77.5 mm. The material was thenhomogenized at 500 ◦C for 2 hrs., using a 50 ◦C/h heating rate, hot rolled (between 250 ◦C and 300 ◦C) to athickness of 5 mm, and finally air cooled to room temperature. The Al-Mg AA5252 alloy was also scalpedto a thickness of 77.5 mm, hot rolled (between 250 ◦C and 300 ◦C) up to 7mm, and cold rolled to 5mmfinal thickness. The previous described processes took place at Novelis and shipped to UBC. The chemicalcomposition of the Al-Mg-Cu and Al-Mg alloys was evaluated by means of Optical Emission Spectrometryat Novelis, and is shown in Table 4.1 for the Al-Mg-Cu alloys, and in Table 4.2 for the Al-Mg alloy.Mg Cu Fe Si Ti Ni Mn Zn Cr0.23 at.%Cu Alloy (at.%) 3.23 0.229 0.048 0.048 0.008 0.003 0.0005 0.00008 0.0005(wt.%) 2.90 0.54 0.1 0.05 0.015 0.007 0.001 0.002 0.0010.12 at.%Cu Alloy (at.%) 3.20 0.115 0.046 0.046 0.007 0.003 0.0005 0.0012 0.0005(wt.%) 2.96 0.28 0.1 0.05 0.014 0.007 0.001 0.003 0.001Table 4.1: Composition obtained by OES of alloys studied. Balance is aluminum.26Mg Cu Fe Si Ti Ni Mn Zn Cr0.23 at.%Cu Alloy (at.%) 2.93 0.0008 0.031 0.044 0.006 0.003 0.002 0.004 0.0005(wt.%) 2.64 0.002 0.065 0.046 0.011 0.007 0.005 0.001 0.001Table 4.2: Composition obtained by OES of high purity AA5252 alloy. Balance is aluminum.4.2 Thermo-Mechanical TreatmentsThe previously described material was further processed at UBC to be suitable for the planned experimentalprocedures. The details of this processing are shown below.4.2.1 Cold RollingThe material received from Novelis was sectioned, and further cold rolled, at constant rolling velocity, usinga laboratory rolling mill with work roll radius of 56 mm. The material was rolled following the rollingdirection of the as-received material, to a final thickness of 1 mm, without lubrication. The reduction stepswhere calculated using Equation 4.1 [125],∆=H f√R(H0−H f )(4.1)where R is the radius of the work roll, H0 is the initial thickness, and H f is the final thickness after the rollingpass. The calculated ∆ parameter should be smaller than one to insure the same strain distribution throughthe sheet thickness. Based on this calculation, 15 steps with a reduction per pass of 10% was used to achievea total reduction of 80%. An average value of ∆=0.5 was calculated.4.2.2 Solution Treatment and RecrystallizationThe cold rolled sheet was subjected to a heat treatment with the dual purpose of recrystallizing the materialand to produce a super saturated solid solution in the Al-Mg-Cu alloys. The solution/recrystallization treat-ment was performed in a salt bath (60% potassium nitrate + 40% sodium nitrite), held at 550 ±2 ◦C, withimmediate quench in water at room temperature (quench rate of ≈190 ◦C/s, measured experimentally witha thermocouple attached to the center of a sample). The solution treatment was selected using Thermocalc(TTAl 6 database), considering the composition of the Al-Mg-Cu system with 0.23 at.% Cu (Table 4.1). Thecalculations revealed Aluminum α matrix and Al3Fe, as the only equilibrium phases present at the chosentemperature. The time for the solution/recrystallization treatment was selected based on a balance betweenattaining the desired solid solution state in the material, and obtaining a fully recrystallized material with agrain size convenient for the further analysis. The solid solution state was verified by resistivity measure-ments (details below), revealing no further increase of resistivity after 10 min of solution treatment, usingthis time for the further solution/recrystallization treatments used in the Al-Mg-Cu systems. Thus, the samesolution treatment has been used previously for a Al-Mg-Cu alloy [8]. The grain size was measured by27Figure 4.1: Geometry of tensile samples used for the reported uniaxial tensile tests. Dimensions areindicated in millimeters.means by line intercept method using optical microscopy, revealing an average grain size of 56 µm in theAl-Mg-Cu alloys. For the case of the AA5252 alloy, the objective of the heat treatment after cold rolling,was to achieve full recrystallization of the alloy, and to achieve the same grain size as that in the Al-Mg-Cualloy. This was done in the same salt bath as described before, holding the material at 500 ◦C for 1 minute,followed by immediate water quench, resulting in an average grain size of 41 µm.4.2.3 Aging treatmentsAll aging treatments were made in a silicone-based open oil bath, coupled to a mechanical stirrer, exceptfor samples where aging was longer than 420 min, where a box furnace was used. The temperature wascontrolled using a k-type thermocouple connected to an electronic controller (PID controller), with a tem-perature variation of± 2 ◦C. After aging treatment, all samples were quenched in water, and stored in liquidnitrogen.4.2.4 Tensile TestUniaxial tensile tests were used as a means to mechanically characterize the material, as well as to applya controlled level of deformation in all samples where pre-deformation was done before aging. Tensilesamples were machined out of the cold rolled material (see above), having the geometry shown in Figure4.1.These tensile samples where further recrystallized/solution treated using the methodology describedabove. Tensile tests were performed using a Instron screw driven machine equipped with a 5 kN load cell.The tests were performed at a constant strain rate of 10−3[1/s], at a temperature of 77K to avoid the effectsof dynamic strain aging [37, 125, 126]. In order to achieve this temperature for the tensile test, the sampleand sample holder arrangement was immersed in liquid nitrogen using a thermal container. The setup wasallowed to equilibrate at 77K for∼5 min, until excessive boiling of the liquid nitrogen ceased. The strain wasmeasured using a MTS extensometer model 63211C-21, directly attached to the sample. The displacement28measurements were converted to strain. The true stress vs true strain was used to calculate yield stress(0.2% strain offset). The work hardening rate was obtained by numerical differentiation (The original datawas smoothed using a Savitzky-Golay filter, using a window of 23 points and 3 degree polynomial, thenumerical derivative was evaluated from this smoothed data).4.3 Characterization4.3.1 Optical microscopyMicrostructural observations where performed using optical microscopy with the objective of measuringgrain size. In order to do this, a standard metallographic procedure was used. First, rough mechanical pol-ishing was done using the following sequence of ANSI grits for grinding papers: 300, 400, 600, 800, 1200.After the last rough mechanical polishing, fine polishing was done using 1 µm diamond based colloidalcompound. The grains were revealed using etching and anodization techniques for the Al-Mg-Cu alloys,and for the Al-Mg alloy respectively. The etching was done by dipping the polished samples in Keller’setchant (2.5 % vol. nitric acid, 1.5 % vol. hydrochloric acid, 1 % Vol. hydrofluoric acid, balance distilledwater) for 35 seconds. The anodization procedure was done using Barker’s anodizing solution (2.5% Vol.fluoroboric acid, balance distilled water), using a direct current source operating at 30 V for 60 to 120 sec-onds and 99.9% purity Al as a cathode. Finally, the observations were done using a light microscope with apolarized light filter.4.3.2 Scanning Transmission Electron Microscopy in Scanning Electron MicroscopeThese observations were possible by using a thin sample, as the type of sample standard for TransmissionElectron Microscopy (TEM), allowing electron transmission through its cross section (Usually using theavailable standard maximum acceleration voltage available in SEM of 30 kV).Sample preparation was done following the same available procedures used to produce TEM samples.This was done by mechanically grinding the sample to a thickness between 20 to 50 µm. This thin samplewas sectioned into 5 mm in diameter discs, using a disc punch device. The resulting samples were furtherelectropolished using a Struers Tenupol-5 twin jet polisher system, operating at 30 V, using 1/3 total volumeof nitric acid (HNO3) with 2/3 methanol (CH3OH) as electrolyte, this at -20 ◦C. Samples were observedusing a FEI Versa dual beam system operating at an acceleration voltage of 30 kV, operating the STEMdetector in bright field mode.4.3.3 Electrical ResistivityElectrical resistivity changes have been used as a mean to track the evolution of microstructure during aging.This is performed by measuring the change in resistivity from the solid solution state, and as a function ofaging time [127]. The electrical resistivity measurements were done by measuring resistance of the materialat 77K in a liquid a nitrogen bath, using a custom made four-point probe resistance bridge with an applied29current of approximately 20 mA, and a reversion frequency of 30 Hz [128].The calibration of the system was verified using a pure (99.99%) aluminum sample. Conversion ofresistance to resistivity was done using the following expression,ρ =ALR (4.2)where A is the cross section area of the sample, and L is the length between the inner electrodes.The resistivity measurements were done directly on the tensile samples describe above, tracking resis-tivity in the different states of the material (i.e. solid solution, aged, pre-deformed, and pre-deformed+aged)taking advantage of the selected geometry of the gauge section, allowing measurements before and afterdeformation, using the results of the tensile test measurements to calculate the change of the cross-sectionarea. The reported measurements were product of the average measurements for samples subjected to thesame conditions. For error calculation, calculation of uncertainty for Equation 4.2 was done, this assumingeach term to be independent [129],δρ =√(∂ρ∂AδA)2+(∂ρ∂LδL)2+(∂ρ∂RδR)2 (4.3)Where the error associated to each independent value (δx), was assumed to be the standard deviationresulting from 12 measurements, this for each independent variable.4.3.4 Differential Scanning CalorimetryDifferential Scanning Calorimetry (DSC) is a classic technique to detect and potentially quantify phasetransformations. This technique relies on a precise measurement of the heat evolving from, or absorbed by,a sample when a phase transformation takes place in it. Formation of a secondary phase will result in theemission of heat out of the sample, while a phase dissolution will absorb heat to take place.For the results shown in this work, a TA Instruments model Q2000 system was used, using a scanningwindow ranging from -50 up to 350 ◦C, at a 5 ◦C/minute heating rate. The studied samples were solutiontreated material, cut in square sections of 5 mm by 5 mm. The material subjected to pre-deformationwas obtained from the gauge section of the pre-deformed tensile sample. Samples were analyzed in highpurity aluminum baskets, using a basket of same characteristics for the reference sample. The baseline wasobtained by performing two scanning cycles as defined above. The second cycle was used as a baseline fromthe first cycle, where the thermal signals associated to precipitation take place, under the assumption that nofurther precipitation occurs after the first thermal cycle. This methodology was adopted after Ivanov [130].4.3.5 Atom Probe TomographySamples studied in this work were aged 20 and 160 minutes at 200 ◦C, this after solution treatment, and after10% pre-strain. The previously described material was sectioned to obtain ”matchsticks”, these consistingof square prisms with a square section of ∼500 µm width, and 45 mm length. These were subjected to a302-stage electrochemical polishing technique employing perchloric acid (HClO4), to produce ”needles” witha section between 50 to 150 nm of diameter [65]. A Cameca LEAP 5000 XS system was used to obtainthe APT data for this work’s analysis. The system was operated at a base temperature of 50K, using apulsing high-voltage at 20% increase of the standing voltage. The DC voltage was progressively adjusted tomaintain a detection rate of 1 ion per 100 pulses.The obtained dataset was analyzed by means of isosurface analysis to reveal fluctuations in concentra-tion that can reveal clusters. the dataset is divided in blocks with an specific composition. These previouslydefined blocks will be single out by a user selected concentration. The addition of adjacent blocks withresult in three dimensional volumes, these called isosorfaces. One-dimensional concentration profiles werealso employed. These consist on using a cylinder or cuboid extended in any selected direction of the re-constructed volume, resulting in a compositional profile along this axis. The 1D profiles were defined inthe cross-section of the identified volumes by isosurface analysis [65]. The estimate of the error for theseprofiles is defined as σ =√ci(1−ci)ni, where ci is the measured concentration of the element i, and ni is thenumber of atoms i detected in the selected bin [131].4.3.6 Summary of Conditions TestedTable 4.2 summarizes all of the conditions tested after solution treatment and aging. Table 4.3 shows allconditions tested after solution treatment, pre-deformation and aging.Figure 4.2: Summary of samples/conditions tested without pre-deformation. The numbers correspondto the number of tensile samples tested per condition.Figure 4.3: Summary of samples/conditions tested following pre-deformation. The numbers corre-spond to the number of tensile samples tested per condition.31Chapter 5Characterization of Al-Mg-Cu SystemDuring Artificial AgingAs shown in Chapter 2, there is relatively little known about the early stages of aging in Al-Mg-Cu alloyshaving a low Cu/Mg ratio. The work reported in this chapter aims to provide a detailed characterizationof the microstructure (clustering and precipitation) evolution during aging of as-solutionized samples fortimes and temperatures relevant to the industrial paint bake cycle. These changes will be linked to the yieldstrength of the material by modelling. This chapter serves as the starting point for further exploration of themore complicated process of aging of pre-deformed samples in subsequent chapters.5.1 Results5.1.1 Optical metallographyThe results of the next sections were obtained from as-recrystallized and solid solution treated materialas described Methodology section (Section 4). The characteristic microstructure is shown in Figure 5.1.It presented equiaxed grains with an average size of 56 µm, this determined by line intercept method.Large coarse particles were also identified, and deemed as constitutive particles commonly denominated asstringers which tend to align along the rolling direction. Regardless of the previously described particles,the obtained microstructure was considered appropriate for the next steps of characterization.5.1.2 Differential Scanning CalorimetryDifferential scanning calorimetry (DSC) measurements have been widely used in the past to identify theformation and dissolution of various phases during the artificial aging of solution treated Al-Mg-Cu andAl-Cu-Mg alloys (cf. Figure 2.17). Though non-isothermal DSC has its limitations [127], it is valuable as afirst, simple, way of identifying temperature ranges were different reactions may take place. Here, DSC isused simply to confirm that distinct reactions can be observed for solute clustering, cluster dissolution and32Figure 5.1: Microstructure of Al-3.23 at.% - 0.23 at.%Cu alloy after solution/recrystallization treat-ment obtained by optical microscopy.equilibrium phase formation [60, 132]. Figure 5.2 shows the thermogram corresponding to starting from asolutionized state1 (Section 4.2.2) with the Al-3.23 at.% - 0.23 at.%Cu alloy, the measurement being madeat a constant heating rate of 5 ◦C/minute. In this figure an exothermic peak is observed in the temperaturerange ≈ 75◦C - 150◦C (peak A in Figure 5.2). This has been previously associated with the formation ofclusters and/or GPB zones in similar alloys [60, 132]. At temperatures above≈ 200◦C, a sharp endothermicpeak (peak B) is observed, this being generally associated with the dissolution of the clusters/GPB zones[60, 132]. Finally, a second exothermic peak (Peak C) is observed at temperatures above 300◦C, this oneconsistent with previous reports of S-phase formation [60, 132]. The endothermic peak at the beginning ofthe thermogram (Peak E), has been associated to an artifact of the measurement and should not be consideredas characteristic of the material. In the sections that follow, the results of isothermal aging at 160◦C and200◦C will be presented for aging times ranging from 2 minutes to several hours. The results in Figure 5.2suggest that we should expect the formation of clusters/GPB zones at short times, with the possibility oftheir dissolution and possible formation of more stable phases upon longer aging time.5.1.3 Mechanical Behaviour of Artificially Aged Al-Mg-Cu AlloysThe decomposition of the solid solution during artificial aging of the Al-Mg-Cu alloys is expected to leadto changes in mechanical response. Figure 5.3a shows how the stress-strain curves measured at 77 K evolvewith aging at 200◦C for the Al-3.23 at.% - 0.23 at.%Cu alloy 2. The results in Figure 5.3a show that theyield strength rises rapidly from 87 MPa to 150 MPa within the first 2 minutes of aging. This is followedby a gradual but continuous increase of the yield strength over the following 18 hours (1100 min). Nearlyidentical results are obtained for aging at 160◦C (Figure 5.3b). For the case of Al-3.2 at.%Mg-0.12 at.%Cualloy, generally lower stress values are observed, compared to the ones of Al-3.23 at.% - 0.23 at.%Cu alloy,for the same aging time and temperature.1Between solution treatment and test, a period of about 1 hour at room temperature took place for sample preparation2Note that only select conditions are shown in Figure 5.3. The full set of data can be found in Appendix A.33Figure 5.2: DSC thermogram corresponding to Al-3.23 at.% - 0.23 at.%Cu alloy. A scanning rate of5 ◦C/minute was used.Figures 5.3a and 5.3c suggest a minor change to the work hardening behaviour of the material, after 180minutes at 200◦C, while the material aged at 160 ◦C (Figure 5.3b), does not show any change, even after420 minutes of artificial aging. This can be seen more clearly if the stress-strain data is plotted as a Kocks-Mecking plot (work hardening rate versus flow stress minus yield stress, Figures 5.4). The lack of changein work hardening rate at early aging times (<160 minutes), in the samples aged at 200◦C (Figure 5.4b and5.4c), and during the whole selected aging period in samples aged at 160◦C, is particularly notable as itsuggests that the hardening phase(s) are predominantly small and shearable, a point that will be discussedin more detail below.Given the lack of strong change in work hardening rate, but rather significant change in yield strength,it is worth investigating the time, temperature and composition dependence of the yield strength evolu-tion more closely. Figure 5.5 presents the 0.2% offset yield strength evolution for the 0.23at.%Cu and0.12at.%Cu alloys, aged at 200◦C, and the 0.23at.%Cu alloy aged at 160◦C. Interestingly, the yield strengthis seen to evolve at a similar rate for all conditions beyond the first 2 minutes of aging. This matches thelinear evolution of yield strength with logarithmic time reported by Court and Lloyd [6] on similar alloystested at room temperature after aging from 30 to 10000 minutes at temperatures between 140 and 200◦C. Moreover, the similarity of the aging response of the 0.23at.%Cu alloy at 160 and 200◦C, agrees withthe results presented for similar alloys by Ratchev et al. [133]. Comparing the behaviour of the 0.12 and0.23at.%Cu alloys, the alloy containing∼50% less Cu is able, after 30 minutes of aging, to provide a similar34(a)(b)(c)Figure 5.3: Stress vs. strain evolution of Al-3.23 at.%-0.23 at.%Cu alloy during artificial aging at a)200 ◦C, and b) 160 ◦C, and Al-3.2 at.%Mg-0.12 at.%Cu alloy, at c) 200 ◦C . All tensile tests weredone at 77K. 35(a)(b)(c)Figure 5.4: Kocks-Mecking plot evolution of Al-3.23 at.%Mg-0.23 at.%Cu alloy during artificial agingat a) 160 ◦C, b) 200 ◦C, and Al-3.2 at.%Mg-0.12 at.%Cu alloy during aging at c) 200 ◦C. Theflow stress has been reduced by the yield stress measured at ε = 0.2% offset. All tensile test weredone at 77K.36Figure 5.5: Yield stress evolution of tested Al-Mg-Cu alloys during artificial aging at 200 ◦C and 160◦Cstrength as the 0.23at.%Cu alloy after 2 minutes of aging.5.1.4 Evolution of Electrical Resistivity on AgingElectrical resistivity has been widely used as a mean-field characterization technique in cluster and precip-itation hardening aluminum alloys [127, 134, 135]. Changes in resistivity reflect both the loss of solutefrom solid solution and, in the case of sufficiently fine clusters/precipitates, an increase in scattering arisingfrom phase interfaces. While disentangling the effects of solid solution and interfaces in these alloys canbe challenging [136], the method gives an independent measurement for comparison against the tensile dataand more local microstructural information obtained from APT or (S)TEM.Figure 5.6 shows the change in electrical resistivity for those samples whose yield strength is shownin Figure 5.5. The higher as-quenched resistivity for the 0.23at.%Cu alloy compared to the 0.12at.%Cualloy reflects the higher overall solute content. Consistent with the ‘rapid hardening’ behaviour illustrated inFigure 5.5, the resistivity also increases rapidly within the first 2 minutes of aging, the magnitude of the jumpbeing much larger in the case of the 0.23at.%Cu alloy compared to the 0.12at.%Cu alloy. This rapid increaseis consistent with the formation of small solute clusters that contribute significantly to conduction electronscattering (cf. results on 2XXX-series alloys [137, 138]). Following the rapid initial resistivity jump, bothalloys exhibit a long period (> 100 min) of nearly constant resistivity, followed by a slow decrease for thecase of samples aged at 200◦C. It is notable that the resistivity evolution of the 0.23at.%Cu alloy, aged at160 and 200◦C, are nearly identical. This observation matches the nearly identical yield strength evolution37shown in Figure 5.5.Figure 5.6: Resistivity evolution for Al-3.23 at.% - 0.23 at.%Cu, Al-3.2 at.% - 0.12 at.%Cu alloyduring artificial aging at 200oC and 160oC.5.1.5 Microstructural ObservationsAtom Probe TomographyTo investigate the microscopic origin of the observed changes in yield strength and resistivity, atom probetomography was performed on samples taken from the 0.23at.%Cu alloy after aging at 200◦C for 20 min(typical paint bake time) and 160 min of aging (end of the resistivity plateau in Figure 5.6). Ideally, onewould like to compliment such local observations with other cluster/GPB zone sensitive techniques suchas HR-TEM, STEM and/or SAXS/SANS to provide better statistics. However, the lack of atomic numbercontrast in these alloys drastically limits the options for complimentary techniques (see for example Section2.3). This has, potentially, been the major stumbling block for previous studies on the early stages ofaging in this alloy system. Figure 5.7a shows an APT volume measured on a sample aged for 20 min.Within this volume, iso-surfaces reveal a distribution of small Mg and Cu enriched particles. The one-dimensional composition plots for the selected particles reveal the particles to contain approximately 80-90at.%Al, 10-15at.%Mg and 1-5at.%Cu. Further aging to 160 min (Figure 5.7b) led to only minor changesin the composition and sizes of the particles based on iso-surface and one-dimensional composition plots.In both cases, the compositions were found to be similar to, but distinct from, those previously reported forclusters/GPB zones in an AA2024 alloy (4.3 wt%Cu, 1.3wt%Mg) [63].38(a)(b)Figure 5.7: Atom probe volumes measured on samples aged for a) 20 min and b) 160 min at 200◦C.In each case, iso-surfaces corresponding to a) 3.13 atoms/nm3 Mg and 0.5 atoms/nm3 Cu, and b)3.5 atoms/nm3 Mg 1.0 atoms/nm3 Cu are plotted to reveal the presence of small Mg and Cu richparticles. One dimensional composition plots are provided along two perpendicular directions,the results being representative of the observations made in the other particles.39Relying on conventional cluster finding algorithms has drawbacks owing to the underlying assumptionsthat one must make [65]. Cluster-finding methods are usually prone to parameter-selection biases [66] inparticular for cases where multiple morphologies of features are present [21]. As an alternative method,a pair correlation based approach has been adopted here to interpret the results in Figure 5.7. This radialdistribution function based method for extracting information on clusters and precipitates [139], and itsdirect relationship to the formalism conventionally used in small angle scattering, has been established[140, 141] and used recently for studying clustering in aluminum alloys by Ivanov et al. [142]. A descriptionof the relationship between the radial distribution function, accessible from the APT datasets, and the paircorrelation function is provided in Appendix C.The pair correlation approach used here has the advantage of providing a self-consistent, parameter freedescription of the solute distribution within the dataset. This can then be interpreted to obtain informationon particle size and composition when combined with a suitable model.A modified definition of the pair correlation function (PCF), compared to the one introduced in [143],has been used. The form used here allows the PCF to be expressed in an equivalent way to the form used insmall angle scattering in the case of an isotropic two-phase system where the composition is uniform withinthe two phases [140, 142, 144, 145]. The pair correlation function has been defined as,γi− j (r) = ci0ci− j (r)− ci0c j0 (5.1)where c j0 is the average concentration of species j in the alloy and ci− j (r) is the concentration of species j ata distance r from an atom of species i averaged over all atoms of species i. γi− j (r) is the correlation betweenthe concentration fluctuations in element i and element j, i.e.〈∆ci∆c j〉. Equation 5.1 can be written in termsof two contributions,γi− j (r) = γi j (0)γ0 (r) (5.2)The function γ0 (r) is a normalized correlation function, such that γ0 (0) = 1 and γ0 (r→ ∞) = 0. Themeaning of γ0 (r) is particularly intuitive in the case of a single object in a (infinitely) large homogeneousvolume. In this case γ0 (r) is the normalized autocorrelation; it is the intersection volume of the object andits ‘ghost’ displaced by a distance r normalized by the object volume. For simple shapes, this function canbe determined analytically. For example, for spherical particles of radius R, γ0 (r) is [146],γsphere0 (r) =1− 3r4R + r316R3 (r ≤ 2R)0(r > 2R)(5.3)In the case of randomly distributed precipitates whose radii are distributed (e.g. following a log-normaldistribution) a volume weighted numerical integration of Equation 5.3 can be performed to obtain γ0 (r).It is important to note that γ0 (r) is a unique function of the size and geometry of the second phase. Theeffect of matrix/particle composition enters entirely through γi− j (0)which is a measure of the compositional40contrast between the phases. In the case of the correlation between atoms of the same type 3,γi−i (0) = fv (1− fv)(cip− cim)2(5.4)while in the case of the correlation between two different types of atoms we obtain,γi− j (0) = fv (1− fv)(cip− cim)(c jp− c jm)(5.5)In the above equations, cp and cm refer to the particle and matrix compositions, c0 to the average com-positions and fv to the volume fraction of particles. It is important to note that if only one type of objectsare present, the 3 PCFs γi−i (r) ,γ j− j (r) and γi− j (r) should all be proportional, the factor of proportionalitybeing related to the fraction of objects and the composition contrast. Moreover, based on the definitionsgiven above,γi− j (0) =√γi−i (0)γ j− j (0) (5.6)In the present case, we have calculated the Mg-Mg, Cu-Cu and Mg-Cu pair correlations (Figure 5.8)from the APT data shown in Figure 5.7. If the particles observed in Figure 5.7 belonged to a single pop-ulation with a uniform composition, then all three pair correlation functions should be proportional to oneanother. Figure 5.9 shows the normalized Mg-Mg, Cu-Cu and Cu-Mg pair correlations revealing that thiscan’t be true as the correlation length for the Cu-Cu and Cu-Mg pair correlations are noticeably longer thanthat for the Mg-Mg pair correlations.The results in Figure 5.8 can be interpreted in terms of particle/matrix compositions and particle sizesif a model for the phases is proposed. Here, it has been assumed that the particles in the APT volumes arespherical, the radii of the particles following a log-normal size distribution. Analysis of the iso-contour datain Figure 5.7 suggests that the aspect ratio of the particles increases on aging from ∼1 at 20 min to closeto 2 at 160 min of aging. Nevertheless, the assumption of spherical particles has been retained, so as tokeep the number of fitting parameters as small as possible. Moreover, the effect of this approximation onthe prediction of yield strength based on particle size presented below, is expected to be nearly insensitiveto this assumption for such small aspect ratios [27].To account for the fact that the pair correlations in Figure 5.8 do not scale with one another, two pop-ulations of particles have been considered to exist, one being richer in Cu, with a larger correlation lengthcompared to the other (see Appendix D, for details). From fitting γMg−Mg (0), γCu−Cu (0) and γCu−Mg (0) itwould be desirable to independently obtain the particle compositions and volume fractions (for the assumedtwo particle types), as well as the matrix composition. In order to do this, one extra piece of informationneeds to be supplied. In the present case it is assumed that the particles contained 80 at% Al, based on theprofiles in Figure 5.7.Under the above assumptions it was possible to obtain two size distributions and particle compositions3The origin of this expression can be consulted in Appendix C.41(a)(b)(c)Figure 5.8: Experimental (symbols) and fit (coloured lines) pair correlation functions for a) Cu-Cupairs, b) Mg-Mg pairs and c) Mg-Cu pairs from the APT datasets shown in Figure 5.7. If allparticles belonged to the same population having a uniform composition, then the three figuresshould simply scale with one another.42(a)(b)Figure 5.9: Normalized pair correlation functions of Cu-Cu, Mg-Mg, and Cu-Mg pairs correspondingto the volume aged a) 20 minutes and b) 160 minutes. If all particles belonged to the samepopulation having a uniform composition, then the three figures should simply scale with oneanother.from the APT volumes (Figure 5.10). The resulting fits to the pair correlations are shown as solid, coloured,lines superimposed on the experimentally determined pair correlations (symbols) in Figure 5.8. The valuesobtained from the fit are also given in Table 5.1. Consistent with the composition profiles shown in Figure5.7, the particles are seen to be systematically richer in Mg than Cu, with the Cu:Mg ratio being highest inthe largest precipitates. With increased aging time, both distributions are seen to shift to larger particle sizes,again qualitatively consistent with the results from the isocomposition plots (Figure 5.7). Interestingly, thevolume fractions of the two populations are observed to remain constant. This would also be consistentwith the resistivity results (Figure 5.6) when interpreted using resistivity models [147, 148] that predict43cluster contributions to the resistivity proportional to volume fraction, and provide also an explanation forthe resistivity decrease at long aging times observed at 200◦C, likely due to the coarsening of the particledistribution.Figure 5.10: The best fit log-normal size distributions corresponding to the pair correlations shown inFigure 5.8. Left: aging for 20 min at 200◦C. Right: aging for 160 min at 200◦C. The green andred areas account for the respective amounts of Cu and Mg in the particles. The results are givenas a volume weighted distribution, or d fvdR .Aging Time Particle 〈R〉 S fv Nv Al (at%) Cu (at%) Mg (at%)20 min Cu Lean Particles 0.73 nm 0.48 0.23% 4.9 × 1023 m−3 80 1 19Cu Rich Particles 2.2 nm 0.4 0.16% 1.8 × 1022 m−3 80 5 15160 min Cu Lean Particles 2.4 nm 0.16 0.23% 3.6 × 1022 m−3 80 2 18Cu Rich Particles 3.2 nm 0.4 0.17% 6.3 × 1021 m−3 80 7 13Table 5.1: The mean particle size (〈R〉) and standard deviation (S) of assumed log-normal particlesize distribution, volume fraction ( fv), number density and composition of particles obtained byfitting to the data in Figure 5.8 assuming two log-normal particle size distributions in each agingcondition. The Al content was fixed at 80 at% based on the composition profiles extracted inFigure 5.7.445.2 DiscussionMechanical Properties and PrecipitationIf the features described in Figure 5.10 are responsible for the evolution in yield strength reported in Figure5.5 it should be possible to use the data to predict the evolution of yield strength with time. Calculating thestrength of such a distribution of precipitates must be done carefully as the way in which one chooses tocalculate the average strength of such an assembly can have a strong influence on the prediction [26, 149].Here, for simplicity, a modified approach to the one originally proposed by Deschamps et al. [111] has beentaken, where the average strength of a distribution of obstacles is calculated as the average of the individualobstacle strengths [149]. It has been shown, by comparing to the results of areal glide simulations, that thisapproach provides a lower limit estimate to the strength of a distribution of obstacles, the predictions beingbetter for narrower and weaker obstacle populations [26].In a first instance, it is assumed that the strength of an individual particle is proportional to the radius ofthe circle (r) formed by the intersection of the spherical particle and the glide plane [150]. The distributionof circle radii ( f (r)) formed by cutting the spherical particles (having a distribution of radii g(R), where Ris the sphere radius) can be calculated from Wicksell’s fundamental integral equation [150, 151],f (r) =rR¯∫ ∞0g(R)dR√R2− r2 (5.7)where R¯ is the mean value of the sphere radii.The contribution of the precipitates to the macroscopic yield stress is defined as,σppt = MGbL¯sτ¯∗ (5.8)where M is the Taylor factor (M=3), G is the shear modulus (G=26 GPa [152]) of aluminum and b is themagnitude of the Burgers vector (b=0.29 [nm] [120]). The average square spacing of precipitates in theglide plane, L¯s, is taken following Ardell [20] as,L¯s =(2pi3 f)1/2R¯ (5.9)The normalized average strength of the ensemble of particles, τ¯∗ is calculated as,τ¯∗ =∫ ∞0τ (r)∗ f (r)dr (5.10)In this expression, τ¯∗ is the strength of a randomly distributed population of particles whose size in theglide plane is r. In the approach originally proposed by [111] the strength of obstacles was assumed to obeyFriedel’s law, this only being strictly valid in the limit of weak obstacles. This approach was generalizedby [149] to include obstacles of all strengths by using the classic result of Foreman and Makin [153] Here,45the same approach has been taken, but an updated relationship between obstacle strength and particle sizearising from computer simulations, has been used[25],τ (r)∗ =0.9(rrc)3/2(1− 16(rrc)5)if r < rc0.75 if r ≥ rc(5.11)The parameter rc in this expression is the critical size at which the particles transition from being shear-able to non-shearable. It was noted, in relation to Figure 5.3 and 5.4, that the minor change in work harden-ing indicates the presence of shearable particles. When considering a distribution of particle sizes one must,however, consider the possibility of sizes that span a range of sizes from below to above rc.The presence of two particle distributions (one lower in Cu, the other higher in Cu) leads to a questionof whether one should use different rc for each distribution. It has been argued, though not proved, thatprecipitation/cluster hardening in Al-Cu-Mg alloys is sensitive to the composition of the phases present [47].Here, a single value of rc has been chosen, so as to minimize the number of adjustable parameters. Evenwith a single value of rc, the two particle distributions (Figure 5.10) lead to two values of σppt accordingto Equation 5.8. Considering that the strengths of these two particle distributions will be similar, the mostappropriate method for their addition is by (see e.g. [154]).σppt =√σ2ppt,1+σ2ppt,2 (5.12)Finally, in order to calculate the total yield strength, the effect of solid solution contribution must beaccounted for. From the particle compositions and volume fractions, we can calculate the remaining Cu andMg in solid solution based on the bulk composition of the alloy. Assuming that the precipitated featureshave the same density as the matrix, the volume fraction of the precipitated features can be considered equalto the atomic fraction. As in the case of the precipitate contribution to the yield strength, the net contributionfrom the two solid solution alloys is expected to follow [26, 154].σss =√σ2ss−Cu+σ2ss−Mg=√(kCuX2/3Cu)2+(kMgX2/3Mg)2 (5.13)where the solid solution hardening coefficients, kCu = 81.8 MPa/at.%2/3 and kMg =27MPa/at.%2/3 are takenfrom [155].Table 5.2 provides the various contributions from precipitates and solid solution to the overall yieldstrength. The relative average precipitate strength is also reported where β = Fm/2Γ where Γ is the dis-location line tension and β = 1 corresponds to the Orowan strength (r = rc). To compute the total yieldstrength, the precipitate and solid solution contributions are summed as in Equation 5.13 and 5.12 owing to46their similar magnitudes. Finally, a constant term, σ0 , has been added to account for the effect of grain size,σys = σ0+(σqss+σqppt)1/q (5.14)Where, assuming clusters and solute both represent weak obstacles, a value of q =2 has been selected:σys = σ0+√σ2ss+σ2ppt (5.15)The value of σ0 was obtained directly by measuring the yield strength of a fully solution treated sampleand subtracting the solid solution contribution calculated from Equation 5.13.Using the above methodology with the particle size distributions from Figure 5.10 there remains onlyone unknown parameter (rc) needed to calculate the yield stress. In order to fit the yield strength measuredafter 20 min of aging at 200◦C (170 MPa), a value of rc = 3.95 nm needs to be used. This is close to theequivalent value (rc = 5 nm) used by Deschamps et al. to describe the precipitation hardening response ofan Al-1.1at%Cu-1.7at%Mg alloy [46].The selection of the q exponent in Equation 5.14 can has been tested by calculating the dislocationreleasing angle from the methodology described in [154]. A calculation of the average size resulting fromthe two particle size distributions results in a value of q= 1.91 for the sample aged 20 minutes, and q= 1.66for the samples aged 160 minutes. These result closer to the used value of q = 2 which has been used tosimplify the calculations.Aging Time σ0 (MPa) σss−Cu (MPa) σss−Mg (MPa) rc (nm) σppt (MPa) β σppt (MPa) β σys (MPa) σys (MPa)at 200◦C (Cu Rich) (Cu Rich) (Cu Lean) (Cu Lean) Predicted Experimental20 min 20 30 58 3.95 104 0.5 87 0.2 170 170160 min 20 29 58 3.95 106 0.7 124 0.5 195 196Table 5.2: Parameters used/calculated in predicting the yield strength of the alloy after aging for 20min and 160 min at 200◦C. The relative strengths of the particles (β = Fm/2Γ) are also reportedHaving established a value for rc one can test the method’s ability to predict the yield stress after agingfor 160 min, the results being shown in Table 5.2. One can see that the predicted value of the yield stress (195MPa) is nearly identical to that measured experimentally (196 MPa). It is important to note that this goodprediction would not have been possible if, in Equation 5.8 the mean radii of the distributions to calculate τ¯∗[149] had been used. Indeed, fitting the yield stress after 20 min of aging would require rc = 3.8 nm leadingto a predicted yield stress of 211 MPa in contrast to the experimental value of 196 MPa.Clustering in Al-Mg-Cu AlloyAs seen in the Literature Review (Section 2), the qualitative similarity of the hardening response of the lowCu alloys studied here and more conventional 2XXX series alloys has been interpreted as evidence of sim-ilar microstructural evolution on aging. Comparison of the observations presented here to those from moreconventional Al-Cu-Mg alloys [47, 63] suggests similarities and differences. In the APT observations re-47ported in [47] and [63], following aging similar to that used here, the dominant feature of the microstructurewas reported as solute clusters. Such clusters were described as roughly spherical solute enriched regionscontaining on average 24 solute atoms [63]. Upon aging up to peak strength (80 hours at 170◦C) threedifferent features were found to dominate; solute clusters (up to 100 atoms in size, < 4 nm in diameter),rod-like GPB zones (< 4nm in diameter and 10-60 nm in length) and large plate like S-phase precipitates.The features seen in Figure 5.7 and quantified via the pair correlation analysis in Figure 5.10 seem tosituate somewhere between the features reported at short aging times and long aging times in the Al-Cu-Mgalloys noted above [47, 63]. The solute clusters reported in [63] after 30 min of aging at 170◦C are similar insize and morphology to the average size of the Cu lean particles in Figure 5.10 after 20 min of aging. At thelonger aging times, the size of the Cu rich particles along with the tendency for more rod-like morphologiessuggests a transition towards more GPB like particles, according to their definition in [47].A significant difference between the clusters/GPB zones reported in [63] and the particles observed hereare the particle chemistries. While the cluster/GPB zones in [63] were found to have Mg:Cu ratios on theorder of 1.1-1.3, here the Mg:Cu ratio was found to range from as high as 16 (in the Cu lean particles at 20min of aging) to as low as 2 (in the Cu rich particles after 160 min of aging). What is consistent with regardto chemistry across both studies, however, is that in all cases the particles are predominantly made up ofAl; ∼ 80 at% in this study and between ∼ 85 and ∼ 90at% in [63]. The enrichment in Mg found here maynot be entirely surprising considering the much higher bulk Mg:Cu ratio (14:1) for the alloy studied herecompared to 0.97:1 in the alloy studied in [63]. This enrichment, combined with the high Al content of theparticles, is a significant factor in the relatively high number density of particles (Nv ≈ 1023 m−3) despitethe low Cu levels employed. It is interesting to note that the behaviour seen here where small amountsof Cu can catalyze precipitation in Al-Mg alloys, qualitatively mirrors the behaviour seen in Al-Cu alloyswhere rapid hardening is only observed when small additions of Mg are made to the alloy [47]. Indeed,the precipitation strengthening observed here is quite comparable to that reported in more conventional Al-Cu-Mg alloys despite a lower number density of particles. For example, an Al-2.5wt%Cu-1.5wt%Mg alloyhas been reported to harden by ∆σ ≈ 80 MPa after 100-200 min of aging at 200◦C [46]. In the case of the0.23at%Cu alloy studied here, ∆σ = 108 MPa evaluated after 160 min of aging at the same temperature. Thestrengthening potential of these clusters/GPB zones may relate to a point made in relation to strengtheningin Al-Cu-Mg alloys [47] where it was argued that particles richer in Mg seemed to be more effective athardening compared to those rich in Cu.The ability of even very small Cu additions to efficiently catalyze the formation of a relatively highnumber density of predominantly Al-Mg strengthening particles at short aging times is emphasized by theresults obtained for the alloy containing only 0.12at%Cu (Figure 5.5). One can double the solutionized yieldstrength of both alloys studied here (∆σ = 90 MPa for 0.23at.%Cu and ∆σ = 67 MPa for 0.12at.%Cu) byaging for 20 min at 200◦C, this despite the fact that one alloy has half as much Cu as the other. Theseresults support those originally reported in [6] where strengthening was achieved for alloys containing aslittle 0.08at%Cu. This is important given the aim of counterbalancing the ∼ 25% loss in strength during thepaint bake cycle [6] with the minimal addition of Cu.48Developing a Simplified Model for Aging KineticsThe above sections provide a detailed overview of the complex microstructure and its relation to the agehardening response in the Al-Mg-Cu alloys studied here. It is clear that a parameter free method for pre-dicting the aging response without direct measurement of the microstructure is not possible yet. It wouldstill be valuable, however, to have a simplified method that can capture the experimentally observed trendsobserved in this work as well as in previous studies. Here, an approach is adopted that follows the spiritof classic process models (e.g. that of Shercliff and Ashby [156]) where the aim is to capture the correctresponse with a minimum number of fitting parameters and experimental evaluations.It is notable that the yield strength varies linearly on a logarithmic time scale (Figure 5.5) for the alloysstudied here. This behaviour has also been reported for similar alloys by Court and Lloyd [6], Ratchev etal. [133] and Kovarik et al. [8]. This does not obey the typical time evolution of yield strength in classicalprecipitation hardening systems where the precipitate size and volume fraction evolution are governed bynucleation and growth [88, 111].Returning to the results of the APT observation, it was pointed out that the volume fraction of theclusters/GPB zones did not appear to evolve with time for the two times observed (within the linear yieldstrength-log(time) regime), though the average size of the features did increase. One possible interpretationof this, is that the growth of the clusters/GPB zones is governed by coarsening within this time/temperaturedomain.Taking the simplest possible approach, let us assume that the average size of the clusters/GPB zonesevolves following a simple coarsening law [156, 157]r¯3− r¯30 =8γDmCmVβ9RTt (5.16)Where r¯ is the average cluster/GPB zone radius, r¯0 is the initial radius, γ is the particle-matrix surfaceenergy, Dm is the diffusivity of the solute, Cm the matrix concentration of solute, Vβ the atomic volume offorming phase β , R the gas constant and T the absolute temperature, and t is the time [157].Next, to simplify the precipitation strengthening model used in the previous section two approximationswill be made. First, it will be assumed that the strength arising from the precipitate distribution can beadequately captured by the average size of the distribution. While this assumption is at odds with thefindings from the previous section (i.e. that knowledge of the full size distribution is important for predictingthe strength accurately), this approach will allow us to write a closed form expression for the yield strengthevolution with time involving a minimum of adjustable parameters. The second assumption is that ratherthan using the full form of equation 5.11 [26], it is assumed that the clusters/GPB zones are can be shearedby dislocations and that the simpler Friedel’s (Section 2.1) approximation can be used [20].With these two approximations we can then write the strength arising from the clusters/GPB zones of49average size r¯ and volume fraction fv as,σppt = M(32pi)1/2 Gbr3/2cf 1/2v r¯1/2 (5.17)where all of the terms have been previously defined in section (Section 2.1). Recall that all but one ofthe parameters in Equation 5.17 are material parameters or are constants (including fv due to the assumedcoarsening response), the only parameter varying with aging time being the average size, r¯.Substituting r¯ from Equation 5.16 into Equation 5.17 allows one to write the time evolution of thecluster/GPB zone contribution to the flow stress as [156]:σppt = A0t1/6 (5.18)with,A0 = M(32pi)1/2 Gbr3/2cf 1/2v (8γDmCmVβ9RT)1/6 [Pas1/6] (5.19)In what follows, A0 is simply used as a fitting parameter, adjusted to fit the data from a given alloy agedat a given temperature.For a given aging temperature and alloy content, one would expect that σppt should vary as approxi-mately t1/6 based on the above argument. Figure 5.11 shows the aging response of the two different Al-Mg-Cu alloys studied here for a variety of aging temperatures all plotted on a log-log graph. In this casethe contribution of clusters/GPB zones to the yield stress was determined from the experimental data asσppt = ((σy.s.−σ0)2−σ2SS)1/2, where the contribution to strength from the solid solution (σSS) is consideredconstant for all cases, based on the finding of the previous section (Section 5.2). When σppt for each agingexperiment is normalized by A0 (Table 5.3) one finds that the data collapses onto a single straight line havinga slope of 1/6, as one would expect from Equation 5.18.Condition(Alloy/Aging temperature)A0 [ Pas1/6 ]0.23at.%Cu - 200◦C 3.95×1070.23at.%Cu - 160◦C 3.88×1070.23at.%Cu - 100◦C 2.83×1070.12at.%Cu - 200◦C 2.69×107Table 5.3: Obtained A0 values used to collapse the data shown in Figure 5.11In the fitting performed for the data in Figure 5.11 the parameter A0 was treated as a simple adjustableparameter for each different aging temperature and alloy composition rather than attempting to calculateits value depending on the parameters in Equation 5.19, requiring more information, particularly the clus-ter/GPB zone volume fraction and its dependence on aging temperature. A evaluation of the expected orderof magnitude can be done by using Equation 5.19 and the data obtained in the past section for the case of50Figure 5.11: Experimentally obtained log σppt vs log time representation, corresponding the agingtemperatures and alloy compositions indicated in the figure. The dashed red line has a slope of1/6, compatible with coarsening kinetics. The experimental values have been normalized by theobtained A0 value for each condition.material aged at 200 ◦C. Using diffusivity data from [158], and assuming an interfacial energy of the orderof 0.3 [J/m] [111], a value of A0 = 2.9× 107 [ Pas1/6 ] was obtained, this in the order of magnitude of thevalues obtained in Table 5.3.Despite the large number of simplifications made in deriving Equation 5.18, the t1/6 evolution lawfor σppt appears to give a good representation of the experimental results for conditions relevant to theindustrial paint bake cycle. The approach fails for very short aging times/low aging temperature (where thecluster/GPB zone volume fraction is likely not constant) or long aging times/high temperatures where thetransition towards the equilibrium S phase is likely to occur and where the assumption of weak obstacles isless valid. The value of such a simplified aging law is that it can be used to predict the aging response witha minimum of experimental measurements. Thus, for other alloys or other aging temperatures, one onlyneeds to determine the value of A0 by means of a minimum of two tensile tests. From a practical point ofview this approach should permit a rapid evaluation of the effect of alloy chemistry and isothermal agingconditions on the age hardening behaviour in an industrial setting. Moving further to the prediction of A051based on alloy chemistry and aging temperature would require a better understanding of the evolution ofthe volume fraction of clusters/GPB zones as a function of aging. This is a challenging proposition giventhe metastability of the clusters/GPB zones and the poor understanding of the chemistry/structure of thesezones.5.3 Summary• Additions of as little as 0.12at.%Cu to a binary Al-Mg alloy can lead to significant precipitation hard-ening, the observed precipitates being similar in size and chemistry to clusters/GPB zones previouslyreported in more conventional 2XXX-series alloys and model Al-Cu-Mg alloys.• Using data extracted directly from APT measurements, the size distribution of particles could be usedto predict the yield strength after aging 160 min at 200◦C following calibration of the shearable/non-shearable radius from data collected after 20 min of aging.• While the strengthening particles share similar size and geometry to clusters/GPB zones in higherCu/lower Mg alloys [63], the chemistry of the particles observed here were much leaner in Cu. Thisobservation helps explain the relatively large number density of clusters/GPB zones despite the lowbulk Cu content.• A highly simplified model has been presented that should allow for a practical prediction of the agingresponse of the studied alloys. This simplified model, when calibrated by a minimum of two tensiletests performed for each alloy/aging temperature should allow for the yield strength evolution to bepredicted for times/temperatures relevant to the industrial paint bake cycle.• Given the appreciable strengthening observed in these low Cu alloys, precipitation hardening in alloyscontaining very low Cu contents should be able to readily compensate for recovery induced softeningin the industrial paint bake cycle.52Chapter 6The Effect of Pre-Deformation on theMicrostructural Evolution in Al-Mg-CuAlloysThe last chapter gave a detailed overview of the correlation between microstructure and yield strength inAl-Mg-Cu alloys, aged starting from the as-solutionized state. For the paint bake cycle, the more relevantsituation is the aging response starting from a pre-deformed microstructure [18, 79, 80]. As noted in the lit-erature review, our understanding of the role of pre-deformation on microstructural and mechanical propertyevolution is poor. In this chapter, the effect of deformation (following solution treatment) on aging will bediscussed for the alloys studied in the previous chapter. This chapter will focus mainly on the microstruc-tural evolution, a detailed discussion of the mechanical response being left for Chapter 5. Owing to thesimilarity of the two alloys studied in the last chapter, the 0.23at.%Cu containing alloy will be focused onin this chapter.6.1 MethodologyA detailed description of the materials and processing path was given in Chapter 4, here only brief reminderis given with a focus on details specific to this chapter. The starting state for the materials studied in thisChapter is the same as that used in the last Chapter (cf. Chapter 4.2.2). The material was cold rolled, thensolution treated, and recrystallized by annealing at 550◦C for 10 minutes. Following this, samples weredeformed in uniaxial tension at 77K to a specific pre-defined flow stress (44 or 174 MPa). Deformation at77k does not represent industrial processing conditions but has been used to avoid effects of dynamic strainaging, simplifying the analysis of coupled precipitation and recovery. Table 6.1 shows the approximateplastic strain value corresponding to the mentioned applied pre-deformation.The samples were then stored in liquid nitrogen until ready to be aged. Aging of the pre-deformedsamples was conducted at 160◦C or 200◦C in a stirred oil bath. Samples were then taken from the gauge53∆σ [MPa] εp44 2 %174 10 %Table 6.1: Selected levels of deformation in terms of increase in work hardening, for the study ofdeformation prior to precipitationsection of these tested tensile samples for further characterization by DSC, electrical resistivity, atom probetomography and electron microscopy.6.2 Results6.2.1 DSC, Electrical Resistivity and Microstructure Evolution on AgingAs noted in the literature review (cf. Section 2.4), prior studies on Al-Mg-Cu alloys [60] have relied onDSC measurements to show the changes in precipitation behaviour following aging of Al-Mg-Cu alloys.Figure 6.1 shows the evolution of the DSC thermograms for Al-3.23 at.% - 0.23 at.%Cu samples havingbeen subjected to a variety of levels of deformation. As noted in Section 5.1.2 (Figure 5.2) Peak A hasbeen previously associated to the formation of co-clusters/GPB zones [60, 132]. Here it is seen to broadenparticularly towards higher temperatures, this effect increasing with the magnitude of pre-deformation. Theendothermic peak B, which is associated with the dissolution of co-clusters/GPB zones [60, 132], is alsobroadened but still retained regardless of the level of deformation. Finally, Peak C associated with theformation of S-phase [60, 132], is seen to become sharper and shifted to lower temperatures with increasingpre-deformation. The broadening effect of the exothermic peak A has been observed by Ratchev et al.[60], using a similar system as the one studied here, uniaxially deformed 2 and 5% strain (their results arepresented in Figure 2.17). In their interpretation, this broad exothermic signal is associated to the earlyformation of what they called S” phase along dislocations. The shift of the exothermic peak C, with furtherdeformation, was also detected by Ratchev et al.[60]. Both effects support an earlier precipitation of S phase,assisted by the presence of dislocations.In contrast to the rather significant changes observed in the DSC response as a function of pre-deformation,the changes in the electrical resistivity are much smaller. Figure 6.2 shows the evolution of the electricalresistivity of samples pre-strained to increase the flow stress by ∆σ = 44 MPa, and ∆σ = 174 MPa, thenaged at 200◦C. These are plotted alongside the results presented in Chapter 5 for samples aged directlyfollowing solution treatment. The first data point on the far left of this plot gives the resistivity of the as-solutionized samples, while the second set of data points present the resistivity following pre-deformation(without aging). The subsequent data points show the resistivity evolution on aging.For the case of material pre-deformed ∆σ = 44 MPa, the behaviour is nearly identically to the as-solutionized case. The only notable difference is an apparent earlier transition to lower resistivity at longtimes. In contrast, pre-deforming to ∆σ = 174 MPa results in a significant resistivity jump following defor-54Figure 6.1: Differential scanning for Al-3.23 at.%Mg - 0.23 at.%Cu deformed to increase the flowstresses by ∆σ= 24 MPa (ε ≈ 0.5%), 34 MPa (ε ≈ 1%), 44 MPa (ε ≈ 2%), 114 MPa (ε ≈8%) and 174 MPa (ε ≈ 10%). The curves have been offset vertically for easier visualization. Ascanning rate of 5 ◦ C/min. was used.mation without aging. Upon subsequent aging, the resistivity does not show the same rapid jump as seenfor the two other cases. In all three cases, the resistivity on aging remains nearly constant and independentof deformation level for times . 100 min. In contrast it is seen that the drop in resistivity seen at times &100 min, does depend on pre-deformation level; the transition from nearly constant to decreasing resistivityhappening earlier the higher the level of pre-deformation. The resistivity measurements, made over samplesartificially aged at 160 ◦C, revealed the same results as for the case of aging at 200 ◦C, with the exceptionthat no transition to a progressively low resistivity values was observed. These results can be consulted inAppendix E. This result is analogous to what it was observed in the previous chapter (Section 5.1.4), onsamples with no deformation before artificial aging at 160 ◦C.The jump in resistivity directly following deformation to ∆σ =174 MPa, raises the possibility that clus-tering occurred during the processing of the material despite the fact that the deformation was performedat 77 K and no artificial aging was conducted. It has, however, been previously shown that deformationin non-precipitation hardenable Al-Mg alloys can also lead to resistivity increases [159–161]. To test this,the AA5252 alloy was subjected to the same solution treatment, pre-deformation and aging schedule as theAl-Mg-Cu alloys. It is important to note that the material was pre-deformed to increment the flow stressby ∆σ =174 MPa, the same as in the case of the Al-Mg-Cu alloy. By choosing the same ∆σ , the aim is toinsure comparable dislocation density. Figure 6.3 shows the resistivity of the as-solutionized material, the55Figure 6.2: Resistivity evolution of Al-3.23 at.% Mg - 0.23 at.%Cu alloy with pre-deformed ∆σ = 44MPa and ∆σ = 174 MPa, aged at 200 ◦C.material after pre-deformation and after three aging times at 200◦C.The first important conclusion from this plot is that deformation can increase the electrical resistivityin the AA5252 alloy by an amount (∆ρ ≈ 0.6 [nΩm]) nearly identical to that seen in the Al-Mg-Cu alloy(∆ρ ≈ 0.65 [nΩm]). Thus, it is likely that the high resistivity following pre-deformation of the Al-Mg-Cualloy is not due to deformation induced dynamic precipitation or to natural aging, rather it is a consequenceof deformation induced defects [162]. The second important conclusion is that, upon aging, the resistivitydrops rapidly back to the value of the as-solutionized material (within 2 minutes of aging). This helps toexplain why all three curves (two different ∆σ and the as-solutionized case) show the same resistivity withinthe plateau (t . 100 min) in Figure 6.2.6.2.2 Yield Stress Evolution on AgingAs seen in the last chapter (Chapter 5), the yield strength evolution in these alloys is also a sensitive macro-scopic measure of the evolution of the microstructure during aging. In the case of pre-deformed samples,there is the additional complexity of separating the effects of softening by recovery, and hardening by pre-cipitation as described in the literature review (section 2.5.2).Figure 6.4 shows the yield strength evolution on aging at 200◦C, for samples pre-deformed to increasethe initial yield stress (before aging) by 44 and 174 MPa. As in Figure 6.2, these are plotted alongside56Figure 6.3: Resistivity evolution corresponding to a AA5252 alloy containing 2.93 at.% Mg, deformed∆σ =174 MPa, aged at 200◦C.the aging response of the as-solutionized material. The first panel shows the yield strengths of the as-solutionized (blue) and pre-deformed (red and green) samples. For material pre-deformed by ∆σ = 44 MPa,the magnitude of the rapid hardening effect is significantly lower than in material with no pre-deformation,measured from the as-deformed value (an increase of≈ 34 MPa vs. ≈ 65 MPa is the non-deformed material).In the case of material pre-deformed 174 MPa, a quick drop in yield stress (≈ 32 MPa) after the first 2minutes of artificial aging can be observed. The yield stress evolution following this initial rapid changeis, in all cases, seen to evolve with the same kinetics; the slopes of the linear portions of the yield stress vslog(time) curves being the same (consistent with σppt ∝ t1/6).The rapid decrease of yield strength in the alloy pre-deformed ∆σ =174 MPa is likely a consequence ofrecovery. This would be consistent with the discussion of the measured evolution of the electrical resistivitypresented above. In that case it was argued that, for this state, the lack of a rapid increase in resistivity was aconsequence of the counterbalancing effects of cluster/GPB zone formation and defect recovery in the firstminute of aging.Interpreting the results in Figure 6.4 is complicated by the fact that the yield strength in these alloysis a result of cluster/GPB zones (σppt), solid solution (σss), and forest dislocations (σ⊥). In Chapter 7 adirect method to separate the these contributions will be proposed. Here, a simpler approach will be adoptedallowing for (at minimum) the identification of the sense of how pre-deformation can affect the cluster/GBP57Figure 6.4: Yield stress evolution of samples with no pre-deformation, and pre-deformed ∆σ = 44MPa and ∆σ = 174 MPa, aged at 200 ◦C.zone hardening relative to the solid solution state studied in Chapter 5.One way to estimate an upper bound value for the rate of recovery in the Al-Mg-Cu alloy is to evaluatethe recovery rate in a Al-Mg binary alloy containing the same Mg content and level of pre-deformation (i.e.the same dislocation density). Recovery in this Al-Mg alloy could be considered to provide an upper boundestimate for the rate of recovery in the Al-Mg-Cu alloy, under the assumption that the main effect of the Cuaddition is to slow recovery by means of precipitation (cf. Section 2.5.2).To evaluate the rate of recovery as described above, a set of experiments were performed on the AA5252alloy (Approximatively a binary Al-Mg alloy), mirroring the experiments presented above for the Al-Mg-Cu alloy. While the AA5252 alloy contains 0.3at%Mg less Mg than the Al-Mg-Cu alloy, such a minordifference in Mg has been shown to have a small effect on the rate of recovery for Al-Mg alloys (See thedata for Al-3wt.% Mg from Barioz et al. reported in [32] vs. the data from Verdier et al. [37] for the case ofAl-2.5wt.% Mg, tested under same processing and aging conditions). The AA5252 alloy was pre-strainedin tension at 77K to increase the flow stress by 44 MPa and 174 MPa. These samples were then annealedfor various times at 200◦C, the yield strength measured after annealing by performing tensile tests at 77K.The results of these tests are shown in Figure 6.5. It can be seen that the results shown in Figure 6.3 andFigure 6.5 are consistent in the sense that both resistivity and yield stress are seen to drop rapidly withinthe first minute of annealing. Moreover, beyond the first minute both resistivity and yield stress are seen58to remain approximately constant for times of up to 420 min. The yield stress evolution shown in 6.5,seems to be at odds with the classically observed linear reduction in a logarithmic time-scale (Section 2.2).Similar results have been reported by Verdier et al. [163] for material with low levels of pre-deformation,as in the experimental conditions used here. Furthermore, pre-deformation at 77K on high purity Al, hasshown faster kinetics of recovery compared to samples deformed at room temperature [35, 164]. Despite thedifference in kinetics of recovery, the magnitude of retained as-deformed flow stress, in the recovered state,is similar to the values reported after stabilization treatment in Al-2.4wt.%Mg alloy [32]. For the purposesof this discussion, it will be assumed that the yield strength of the AA5252 alloy is approximately constantfor aging times of between 2 minutes and 420 minutes.To take this one step further, an attempt can be made to provide an estimate of σppt from the data inFigures 6.4 and 6.5. Following the approach in [154], the general additivity law is defined as,σys = σ0+(σn⊥+(σqss+σqppt)n/q)1/n (6.1)where σ0 is the intrinsic and grain size contribution. Assuming no loss in solid solution, no contributiondue to precipitation, and dislocations to be significantly stronger obstacles compared to solute, the selectedexponent are q = 2 and n = 1 1, allowing to calculate the retained forest strengthening from the data inFigure 6.5 as,σ⊥ = σys−σss−σ0= σys−σrex(6.2)where σrex accounts for the solid solution, grain size and intrinsic strength, and it was taken as the yieldstrength of the fully recrystallized AA5252 alloy. σys is the yield stress plotted in Figure 6.5. The foreststrengthening contribution was estimated as σ⊥ = 41 MPa for the sample pre-deformed to ∆σ = 44 MPaand 106 MPa the sample pre-deformed to ∆σ = 174 MPa. Now, if we assume σ⊥ obtained in this wayas an upper estimate to the degree of softening experienced by recovery in the Al-Mg-Cu alloy, then fromEquation 6.1, we can estimate σppt as,σppt =√(σY.S−σ0−σ⊥)2−σ2ss (6.3)The same q and n exponents have been used, based on the findings in Section 5.2, where the strength ofsolute and clusters/GPB zones are considered similar and, as considered above, dislocation are consideredstronger than the previous two, meaning that a Pythagorean addition law is appropriate. The value σss canbe approximated as constant (σss = 65 MPa), and, as previous Chapter (Chapter 5) a value of σ0 = 20 MPawas used. Substituting the constant value of σ⊥ obtained from the AA5252 alloy then allows for σppt to beestimated.Figure 6.6 shows the values of σppt estimated in this way for the Al-Mg-Cu alloy pre-deformed to ∆σ1Using the method in [154] indicates a value of n = 1.13, here simplified to n = 159Figure 6.5: Yield stress evolution corresponding to the AA5252 alloy, pre-deformed ∆σ =44 MPa,and ∆σ =174 MPa, aged at 200◦C.= 44 MPa and ∆σ = 174 MPa. Also plotted is the value of σppt obtained for the same alloy and agingtemperature in Chapter 5. As we can see, the values of σppt for the pre-deformed samples found in thisway both lie below that of the curve obtained for the material aged from the as-solutionized state. Recallingthat σ⊥ estimated from the AA5252 alloy should represent a lower bound estimate, means that the valuesof σppt for the pre-deformed samples should represent an upper bound estimate. The fact that these upperbound estimates still lie below the value of σppt for the solutionized sample suggests that the effect of pre-deformation is to reduce the number density of clusters/GPB zones. This interpretation also must considerthe fact that the σppt vs log t curves all well fit a t1/6 evolution law, suggesting that beyond the first minuteat 200◦C the evolution of the clusters/GPB zones is very similar in all three cases. A detailed quantitativeanalysis of the previously observed change in mechanical response, will be given in Chapter 7.Finally, while not shown here, the aging response of the pre-deformed materials was also evaluated at160 ◦C. The results of these experiments are shown in Appendix E, the results showing the same trends asfor those reported here.6.2.3 Microstructural ObservationsThe results shown in Figure 6.6 suggest that for the same aging time at 200◦C quite different microstructuralstates should exist, particularly with respect to the clusters/GPB zones. To evaluate this, samples of material60Figure 6.6: Contribution of precipitation to the total strength, considering recovery as measured in theAA5252 alloy.deformed ∆σ =174 MPa and aged at 200 ◦C for 20 and 160 minutes were selected for APT analysis. Thesematch the times/temperatures analyzed by APT in Chapter 5.Figure 6.7 show the reconstructed volume corresponding to Al-3.23 at.% - 0.23 at.%Cu alloy, deformed∆σ =174 MPa, aged at 200 ◦C for 20 minutes. This reconstruction, accounting for a volume of 761484nm3, was analyzed by means of iso-concentration surfaces, and one dimension composition profiles. Theobserved features were defined using a surface with a Mg density of 3.2 atoms/nm3. Comparing this vol-ume to the one shown in Figure 5.7a, corresponding to the same aging time and temperature but withoutdeformation, one sees significant differences. While one can still find some small roughly equiaxed featuressimilar in size to those shown in Figure 5.7a (circled features), the most prominent features are most likelydislocation segments decorated by segregated solute, these indicated by the red lines on the figure, similaras the features reported in [165] as dislocation segments. Examining one-dimensional concentration profilesobtained in the perpendicular direction of these features (cf. profile shown in Figure 6.7), the profile showspeak concentrations of ≈ 12 at. % Mg and ≈ 3.5 at. % Cu along these volumes.Figure 6.8 shows an APT volume extracted from the sample aged for 160 minutes, this reconstructioncomprising an analyzed volume of 1851280 nm3. Here, iso-concentration surfaces were plotted using a Mgdensity of 3.5 atoms/nm3. This volume appears similar to the one shown in Figure 6.7 but very differentfrom the one shown in Figure 5.7b, again the presence of non-equiaxed linear features dominates the volume,61Figure 6.7: Analyzed APT reconstructed volume corresponding to Al-3.23 at.% - 0.23 at.%Cu alloy,deformed ∆σ =174 MPa, aged at 200 ◦C for 20 minutes. The isosuface has been defined using aconcentration of 3.2 atoms/nm3 of Mg.though a few small isolated, roughly equiaxed features can also be found. Enrichment of solute along thelinear features is confirmed by one dimensional chemical composition profiles (see examples shown in 6.8),with Mg enrichment as high as∼ 20% and Cu enrichment as high as∼ 10%. The Mg and Cu compositions,however, vary widely along these features as illustrated by the very large differences in Mg and Cu profilesshown in the one-dimensional profiles.The morphological and chemical complexity of the features seen in Figures 6.7 and 6.8 precludes theuse of the radial distribution analysis from Section 5.1.5, as it requires the assumptions of a simple secondphase shape and uniform composition. In this case a more detailed analysis using iso-surfaces and one-dimensional composition profiles across selected features was performed on the largest analyzed volume;one obtained from the sample aged for 160 minutes (Figure 6.8).Focusing first on the small, isolated, equiaxed features observed at 20 minutes and 160 minutes (e.g.Figure 6.8, particles (i) to (iii)), it was found that they had compositions close to those of the features foundin Figures 5.7a and 5.7b for the undeformed samples. This confirms that the clusters/GPB zones observedin the undeformed samples, and interpreted as being responsible for the hardening response, are present inthe aged, pre-deformed samples. It would appear, however, that these clusters/GPB zones are present inmuch smaller densities in the pre-deformed samples compared to those found in the solutionized and agedsamples. Of course, it is difficult to have good statistics from the limited APT observations reported here,but this observation, would correlate with the slower aging response in the pre-deformed samples (Figure62Figure 6.8: APT reconstructed volume corresponding to Al-3.23 at.% - 0.23 at.%Cu alloy, deformed∆σ =174 MPa, aged at 200 ◦C for 160 minutes.6.6).While it is impossible to identify dislocations in APT volumes, the linear features seen in the two vol-umes shown above, would appear to be consistent with segregation/precipitation on dislocations previouslyreported by other authors on similar systems using APT [165, 166]. It is notable that the maximum solutecontent regions found along these features exhibit a much higher solute concentration compared to the com-position found for the equiaxed particles in Chapter 5. In the case of the sample aged for 160 min segmentswere found with compositions close to those expected for the S phase, i.e. Al2MgCu (Figure 6.8, (iv)).This preferential heterogeneous precipitation on dislocations was observed previously by Ratchev et al.[60] in Al-Mg-Cu alloys, by means of TEM. The phase that was observed was proposed as S” (Al2CuMg),rather than S-phase directly. The observation of preferential precipitation of the S (or S-like) phase ondislocations would be consistent with two of the previous observations reported above. First, it was shownthat increasing the level of pre-deformation shortened the plateau in the electrical resistivity (cf. Figure 6.3).The drop in resistivity in this case would be attributed to the rapid drop in solute in solid solution due to theremoval of the much larger amounts of Mg and Cu required to form the S-phase compared to the low levelsof Mg and (particularly) Cu required to form the clusters/GPB zones. The second observation consistentwith the preferential formation of S-phase induced by the presence of dislocations is the shift to lowertemperatures of the high temperature exotherm (Peak C in Figure 6.1) in DSC experiments, this peak havingbeen associated with S-phase formation. Finally, some additional evidence for the preferential formation63of S-phase on dislocations has been obtained from observations of the microstructures after long aging at200◦C. Figure 6.9 shows a scanning transmission electron microscopy (STEM) image taken from within anSEM on a thin foil prepared from a sample deformed to 10% reduction by rolling at room temperature andthen aged for 1100 min at 200◦C. The retained (un-recovered) dislocation network is apparent in this casewith rod-like precipitates decorating the dislocation network. The precipitates closely resemble (in size andshape) the S-phase precipitates identified by [60, 138].Figure 6.9: STEM in SEM observation of Al-3.23 at.% - 0.23 at.%Cu alloy, deformed by cold rollusing a reduction of ε =10 %, and aged at 200 ◦C for 1100 minutes. The retained dislocationsappear to be decorated by precipitates, most likely S phase.6.3 Rapid Hardening and the Role of Vacancies on Clustering/GPB ZoneFormationThe key point from the results reported above is that pre-deformation leads to a reduction in the density ofhardening clusters/GPB zones and an acceleration of the formation of equilibrium (or near equilibrium) S-phase by heterogeneous precipitation along dislocations. The effect of the pre-deformation on cluster/GPBzone formation appears to be most prominent, however, in the very earliest stages of aging (within the firstminute of aging at 200◦C). The main observation to be explained is the reduction in number density ofclusters/GPB zones, in the case of the pre-deformed samples, and the fact that this appears to be dominated64by processes active during the very initial stages of aging, when the rapid hardening and rapid increase ofresistivity are observed in the un-deformed samples.Figure 6.10 provides a schematic view of the processes occurring during the aging of as-solutionized andas pre-deformed samples. In the as-quenched state the microstructure can be described as being composed ofa random solid solution with a low density dislocations 2. The other important ingredient in the microstruc-ture, essential for the formation of clusters in the early stages of aging, are quenched in (non-equilibrium)vacancies. As mentioned in Section 2.3 and 2.5.1, vacancies play a critical role in cluster/GP(B) zoneformation by i) increasing the diffusivity of solute atoms [9, 17, 100, 101] and ii) by participating in thethermodynamic stabilization of small solute clusters[49, 70, 167]. Changes in vacancy concentration havebeen cited in a variety of aluminum alloys to explain unexpected changes in clustering behaviour dependingon thermo-mechanical processing conditions [47, 111, 118, 119, 168].Upon aging, the quenched in vacancies will allow for accelerated formation of clusters due to accelerateddiffusion of solute, some of these vacancies becoming incorporated into the clusters/GPB zones. Thoseexcess vacancies not captured within clusters/GPB zones may annihilate at other defects (dislocations and/orgrain boundaries) or they may cluster to form dislocation loops [169]. Indeed, STEM observation on non-deformed and aged samples (starting from the as-solutionized state) show evidence of these processes in theform of helical dislocations and small dislocations loops in the Al-Mg-Cu alloys studied here (Figure 6.11).Similar observations have been made in Al-Cu-Mg alloys [138, 158]. The loss of these excess vacancieswould be expected to i) slow the formation/growth of clusters/GPB zones due to the slower solute diffusivityand ii) reduce the nucleation of the clusters/GPB zones if vacancies are required for their stabilization.Thus, one explanation for the rapid initial hardening followed by the observed slow progressive coarseningobserved in Chapter 5 would be the rapid decay of excess vacancies during aging.In the case of the aging of pre-deformed samples a similar schematic picture can be envisioned. In thiscase however, deformation may modify the as-quenched excess vacancy concentration by the processes ofdeformation induced vacancy formation and annihilation. The rate of excess vacancy generation by lowtemperature plastic deformation has been modeled classically as, [105]3dC+exdt= χ∆σΩQ fε˙ (6.4)Where Cex is the excess vacancy concentration, ∆σ is the increase in flow stress due to forest hardening,Ω the atomic volume, Q f the vacancy formation energy, ε˙ the applied strain rate, and χ the vacancy produc-tion efficiency (χ ≈ 0.1[99, 101, 105]). This model has been previously applied to deformation generatedvacancies in aluminum alloys [100, 101].The annihilation of vacancies during deformation has also been previously considered [99] though forhigh temperature deformation where diffusion of vacancies to dislocations and/or vacancies has been con-2Grain boundaries can also be an important microstructural feature but given the rather large grain size of the samples studiedhere, their effect on clustering/GPB zone formation will be ignored3At high homologous temperatures, a second generation term has been proposed due to the contribution of thermal jogs [99, 170]65Figure 6.10: Schematic illustration of the microstructural processes envisioned to occur during aging.Top row: Aging starting from an as-solutionized state with a very low dislocation density Bot-tom row: Aging starting from a pre-deformed sample where significant vacancy annihilationcan occur at forest dislocations.sidered [99]. Given that the models for annihilation depend linearly on the self-diffusion coefficient, whichis very small at 77K, the rate of annihilation for deformation at 77K is negligibly small relative to the rateof production predicted by Equation 6.4.The production of vacancies and dislocations by plastic deformation should lead to an increase in elec-trical resistivity, these being the source of the increase in resistivity with pre-deformation shown in Figure6.3. Figure 6.12 summarizes experiments performed on a number of samples of both the AA5252 alloy andthe Al-3.23at%Mg-0.23at%Cu alloy where samples were pre-strained at 77K to different flow stresses. Theelectrical resistivity of these samples was then measured at 77K directly following deformation. The solidblack line shows the predicted contribution to the electrical resistivity arising from the increasing dislocationdensity. The dislocation contribution to resistivity has been estimated from the measured increase in flowstress ∆σ⊥, via the Taylor equation,∆σ⊥ = MαGb√ρ (6.5)where M is the Talor factor (M=3), α represents the average strength of the forest dislocations (α=0.3), G66Figure 6.11: STEM image of Al-3.23 at.% - 0.23 at.%Cu alloy, aged after quench (No pre-deformation), aged for 2 min at 200 ◦C.is the shear modulus (G=26 GPa [152]) of aluminum, b is the magnitude of the Burgers vector (b=0.29 nm[120]), and ρ the dislocation density.Solving Equation 6.5 for the dislocation density ρ , and multiplying for the resistivity coefficient, K⊥,ρ⊥ = K⊥(∆σMαGb)2 (6.6)The resistivity coefficient, K⊥, for dislocations was taken as 4x10−16nΩm4 following previous work [171,172]. One can see that this prediction underestimates the measured change in resistivity, suggesting that theremaining increase in resistivity could be due to the presence of deformation induced excess vacancies.To test this, Equation 6.4 was used to predict the increase in excess vacancy concentration due to de-formation, the values and sources of the various parameters given in Table 6.2. The contribution of thesevacancies to the resistivity was then obtained as,ρvac = KvacCvac (6.7)where the scattering coefficient Kvac = 25nΩm/at% was taken from [171, 172]. Assuming Matthiessen’srule [134], the observed increase in resistivity can be taken as the sum of the contributions from dislocationand vacancies, this being shown as the red line in Figure 6.12. It can be seen that the sum of these twocontributions matches well with the experimental results up to a flow stress of ≈ 250 MPa.67Figure 6.12: Resistivity contribution of vacancy and dislocation storage during deformation, com-pared to experimentally obtained resistivity measurements from Al-3.23 at.%Mg - 0.23 at.%Cuand AA5252 alloyThe most important conclusion from this result is that the vacancy concentration is not drasticallychanged relative to that expected in the as-quenched material. The equilibrium vacancy site fraction at thesolutionizing temperature (550◦C) was estimated as 0.7× 10−4 using the parameters in [14, 173]. Based onEquation 6.4, increasing the flow stress by ∆σ = 44 MPa would only lead to a small increase (by 6 × 10−6.Increasing the pre-deformation to ∆σ = 174 MPa would lead to an increase of vacancy site fraction to 1 ×10−4.Parameter Value Meaning Source∆σ Increase in flow stress by work hardening Obtained from experimentsε˙ 7.3 × 10−4 s−1 Imposed Strain rate Fixed experimentallyχ 0.1 Vacancy production efficiency [101, 105]Q f 0.67 eV Vacancy formation Energy [174]Ω 1.66 × 10−29 m3 Atomic volume [101]Table 6.2: Numerical values and their origin used in Equation 6.4 to predict vacancy formation duringplastic deformation.The second main difference between the aging of the as-solutionized and the pre-deformed samples isthat a much higher density of sinks, i.e. dislocations, exists for vacancy annihilation in the pre-deformedsample compared to the as-solutionized sample. This is important as during aging there will be a competi-68tion between vacancy annihilation and vacancy incorporation into clusters/GPB zones. The recent work ofFischer et al. [109] has shown the importance of dislocation density on the rate of vacancy annihilation. Intheir model, the rate of annihilation can be written as,dXvdt=−2(2piρhp f)DvXvXv,eqln(XvXv,eq)(6.8)where Xv is the instantaneous vacancy site fraction, Xv,eq is the (temperature dependent) equilibrium vacancysite fraction, Dv is the diffusivity, hp is the density of jogs on dislocations, ρ is the dislocation density and fis a constant (of order 1). One can numerically solve Equation 6.8 to predict the time evolution the vacancysite fraction during quenching from the solutionizing temperature and/or to predict the vacancy site fractionevolution during aging. As shown in [109], for quench rates consistent with those used here (cf. Section4) and for a dislocation density of 1010− 1011 m−2 the as-quenched vacancy concentration is retained towithin a factor of ∼2 of the equilibrium vacancy concentration at the solutionizing temperature (550◦C).More interesting is to examine the effect of the dislocation density on the rate of dislocation annihilationduring aging. Figure 6.13 shows the time evolution of the vacancy site fraction obtained from Equation 6.8,parameterized using the data in Table 6.3. In this case it has been assumed that the material was heated fromroom temperature to 200◦C at 100◦C/s then held isothermally, this being consistent with the experiments(cf. Section 4). In the case of the conditions corresponding to ρ = 1010 - 1013 m−2, the initial vacancyconcentration was taken to be the equilibrium concentration at the solutionizing temperature. In the case ofthe condition having ρ = 1014 m−2 the vacancy site fraction was increased by 1 × 10−4, this being takenfrom the increased vacancy concentration estimated following plastic deformation to ∆σ = 174 MPa byresistivity. Indeed, the conditions corresponding to ρ = 1013 m−2 and ρ = 1014 m−2 resemble the conditionsexpected for ∆σ = 44 MPa and ∆σ = 174 MPa.Parameter Value Meaning SourceD0 1.18 × 10−5 m2/s Pre-exponential for diffusivity [174]Qv 1.28 eV Activation Energy for Self-Diffusion [174]Q f 64.2 kJ/mol Vacancy formation Energy [109]hp 100 Jog density (per unit length) [109]f 0.7815 Geometric Factor for FCC crystals [109]Table 6.3: Numerical values used to predict vacancy annihilation during aging in Equation 6.8.The key take-away from Figure 6.13 is that the excess quenched-in vacancies available in the as-solutionized condition, these samples having expected ρ ≈ 1010− 1011 m−2, will retain a large fractionof their excess vacancy concentration within the first minutes of aging. In contrast, the pre-deformed sam-ples containing ρ ≈ 1013 m−2 (∆σ = 44 MPa) and ρ ≈ 1014 m−2 (∆σ = 174 MPa) will loose their excessvacancies within the first few seconds of aging. The sample with ρ ≈ 1014 m−2 is even predicted to achieve69Figure 6.13: A prediction of vacancy loss during aging in materials containing different dislocationdensities (ρ). In all cases the samples were modelled assuming a heating rate of 100◦C/s from25◦C to 200◦C. In the cases where ρ = 1010-1012 m−2 the initial dislocation density was taken tobe the equilibrium vacancy concentration at 550◦C. In the case of the samples with ρ = 1013 and1014 m−2 an additional excess vacancy concentration was added corresponding to that arisingfrom plastic deformation.[109]the equilibrium fraction of vacancies prior to reaching 200◦C.The analysis shown in Figure 6.13 does not incorporate information on two key factors. First, it doesnot include information on vacancy-cluster/GPB zone interaction. It is expected that if vacancies do playan important role in cluster/GPB zone formation there will be a competition between vacancy trapping insolute clusters and vacancy annihilation at dislocations. This will likely modify the kinetics from thoseshown in Figure 6.13. Qualitatively, however, this picture remains consistent with the aging response shownin Figure 6.6. In this picture, a larger number density of small solute clusters can be formed in the earlystages of aging of the as-solutionized samples owing to the higher density of vacancies that can contributeto cluster/GPB zone formation in the first minutes of aging. In the case of the pre-deformed samples, anearly equal reduction in cluster/GPB zone formation occurs in the early stages of deformation owing toa much larger fraction of vacancies being lost to annihilation on dislocations before they can participate incluster/GPB zone formation.A potentially more significant factor missing from the analysis in Figure 6.13 is the fact that the dis-70location density (in pre-deformed samples) is reduced by the process of recovery during aging. Using therecovery observed in the AA5252 alloy as a measure of the level of recovery observed in the Al-Mg-Cualloy (cf. Figure 6.5) we see that the sample pre-deformed to ∆σ = 44 MPa, retains a large portion of itswork hardening (41 MPa out of 44 MPa) even after holding for > 100 minutes at 200◦C. Using the Taylorequation the retained forest dislocation density can be estimated as ρ = 3 × 1013 m−2. In the case of thesample pre-deformed by ∆σ = 174 MPa, softening occurs to ∆σ ≈ 106 MPa, this corresponding to a re-tained dislocation density of ρ = 2 × 1014 m−2. Thus, although the dislocation density does change due torecovery, the magnitude of dislocations is expected to remain in the 1013-1014 m−2 range for the duration ofaging times of interest here at 200◦C meaning that very fast annihilation of vacancies should be expected.To this point the possible effects of solute segregation (and precipitation) to dislocations may effect theprocesses discussed above. As was shown in Chapter 5, cluster/GPB zone formation occurred with very littlechange in the overall composition of the matrix. Despite the significant amount of segregation/precipitationon dislocations revealed by Figure 6.7 (sample aged for 20 min) it was found that the matrix compositionaway from these features had not changed significantly. This may be partially attributable to the fact thatthe degree of segregation (∼ 20%Mg, < 10%Cu) remained relatively small. This is also consistent with thefact that the resistivity remained relatively constant during aging for times much longer than 20 minutes,suggesting that the solid solution contribution to the resistivity was not dropping drastically. At the longertime examined (Figure 6.8, 160 minutes) much more significant enrichment in Mg and (particularly) Cuwas observed, with compositions approaching those of the S-phase being observed. The larger loss of solutefrom solid solution at these longer aging times would help to explain the drop in resistivity observed at longaging times. The important point, is that no significant change in matrix composition is expected withinthe first minutes of aging where the main effects of pre-deformation are observed on the aging response.Thus, depletion of solute by segregation to dislocations is unlikely to explain the changes in aging responseobserved between the as-solutionized and pre-deformed conditions.If the above explanation for the effect of pre-deformation on aging response is correct, one might expectto find evidence for similar changes in the aging response of Al-Mg-Cu alloys depending on the vacancyconcentration at the start of aging. One simple way to change the initial vacancy concentration withoutpre-deformation would be to change the quench rate and/or the solutionizing temperature. Kovarik et al.[8],noted a slightly higher yield strength for a Al-3wt.%Mg-0.98wt.%Cu solutionized at 550◦C then quenchedand aged compared to the same alloy solution treated at 510◦C then quenched. This was despite the materialhaving the same yield strength in the as-quenched state. It is also interesting to compare the results obtainedin this work with those obtained by Court and Lloyd [6] on a very similar alloy. In [6] samples wereallowed to air cool from the solution treatment temperature, this potentially resulting in a larger loss inexcess vacancy concentration compared to the quenched samples studied here. After aging for 30 minutesat 200◦C Court and Lloyd reported hardening of 66 MPa, compared to 105 MPa measured on the samplesstudied here. It is hard to be confident, however, that this difference has arisen from differences in quenchrate alone. Preparation of the initial alloy, small variations in alloy composition and effects arising fromstorage of samples between solution treatment and aging could all have major effects on the aging response.71Finally, it is useful to reflect on the potential impact of these results on industrial processing conditions.The experimental procedure (low temperature deformation and storage of samples after deformation) cho-sen in this study represent conditions that will lead to promote excess vacancy retention during the earlystages of deformation. In conventional processing performed at room temperature on material that maybe solutionized and slowly cooled and held for significant periods of time at room temperature, lower ex-cess vacancy concentrations may be expected. This will even out differences in the vacancy concentrationsfollowing deformation, leading to less of an effect of pre-deformation on the aging response.6.4 SummaryThe key observations and conclusions from this Chapter can be summarized as follows• Deformation negatively affects the early stages of formation of clusters/GPB zones. Evidence for thiscomes from yield strength measurements, electrical resistivity and DSC observations.• Recovery is not entirely suppressed by clustering/GPB zone formation. Rapid recovery occurs withinthe first seconds of aging at 200◦C.• APT observations reveal significant solute segregation on dislocations. An irregular pattern of seg-regation is observed after 20 minutes of aging, with local regions reaching compositions near thoserequired for S-phase formation. This matches prior work that indirectly suggested rapid formation ofthe S-phase on dislocations.• Despite this segregation, small clusters/GPB zones appear to still be present in the microstructure.• It has been argued that rapid excess vacancy annihilation at dislocations is responsible for the reduc-tion in cluster/GPB zone formation in the pre-deformed samples. This suggests that care must betaken to control the thermo-mechanical processing of samples to ensure reproducible aging response.That being said, the test conditions used here should be expected to give the largest contrast in theas-solutionized and pre-deformed behaviours.72Chapter 7Separating the Effects of Cluster Hardeningand Recovery on the Aging Response ofAl-3.23 at.% - 0.23 at.%Cu: WorkHardening AnalysisThe last Chapter focused on assessing the microstructural changes arising from aging when starting from apre-deformed state. One of the most significant challenges in that analysis was to unambiguously separatethe effects of cluster/GPB zone hardening from recovery induced softening during aging. A simplifiedapproach was presented using the recovery rate of the AA5252 alloy as a proxy for the recovery rate inthe Al-3.23 at.% - 0.23 at.%Cu alloy. In this Chapter, a method for separating the effects of precipitationand recovery is proposed based on a combined analysis of yield strength and work hardening rate. Thismethod provides a method for predicting not only the yield strength but also the overall stress-strain responsefollowing aging.The method presented here is based on observations presented in the Chapter 5. There it was shownthat most of the aging conditions used in this thesis lead to a form of precipitation hardening that increasesthe yield strength without changing the work hardening rate. Recovery, the reduction of dislocation densitythat occurs on aging (as shown in Chapter 6) leads to both a change in yield strength and a change in workhardening rate. Thus, a simple approach to separate the effects of recovery softening and cluster/GPB zonehardening should able to predict both yield strength and work hardening rate from the stress-strain responsefollowing aging of pre-deformed samples.This chapter starts by presenting a more detailed analysis of the stress-strain response of the Al-3.23at.% - 0.23 at.%Cu alloy aged at 160◦C and 200◦C following deformation. A particular focus is made on thework hardening response and its comparison to classic models. Following this, a model is developed thatattempts to account for changes in yield stress and work hardening rate linked to the microstructural changes73described in Chapter 6. Finally, this method is used to separate the contributions of cluster/GPB zonehardening and dislocation based recovery softening, the results being discussed in relation to the conclusionsreached in Chapter 6.7.1 Experimental Results: Work Hardening Response Following AgingThe results presented in this Chapter come from many of the same samples discussed in Chapter 6, withadditional results presented for samples aged at 160◦C as well as for samples taken from the AA5252 alloy.As throughout the rest of this thesis, the tensile tests were all performed at 77K following the procedureoutlined in Chapter 4. Similarly, details on the method used to age the samples can be found in Chapter 4.Figure 7.1 shows the stress-strain response for all of the Al - 3.23 at.% - 0.23 at.%Cu alloy condi-tions studied in this Chapter. The solid black lines in each plot indicate the stress-strain curves of theas-solutionized material. The coloured lines show the stress-strain response of samples that had been pre-deformed to ∆σ = 44 MPa (Figures 7.1a and 7.1b) or ∆σ = 174 MPa (Figures 7.1c and 7.1d). In the caseof the pre-deformed and aged samples, the stress-strain curves have been plotted starting from the level ofpre-strain so as to illustrate the changes in the stress-strain response.Focusing on the samples with ∆σ = 44 MPa (Figures 7.1a and 7.1b) one can see that aging, even for 2minutes, leads to the stress-strain curve jumps above the stress-strain curve of the as-solutionized material,the overall shape of the stress-strain curves all appearing similar. A more drastic effect of aging in seen forthe samples with ∆σ = 174 MPa (Figures 7.1c and 7.1d). In this case, aging leads to a drop in the flow stressfor all but the longest aging times. However, on straining one can see that the work hardening rate (slope ofthe stress-strain curves) is higher for the aged material leading to the stress-strain curves of the aged samplescrossing over the stress-strain curve of the as-solution treated samples (black curve). The insets in Figure7.1 focus on the initial yielding behaviour where it can be seen that, aside from the change in yield stress,all aged samples exhibit a similar low work-hardening rate ‘plateau’ just following yielding.A better way to visualize the evolution of the work hardening behaviour on aging is to re-plot the stress-strain curve as a Kocks-Mecking plot, i.e. to plot the work hardening rate (θ = dσ/dε) versus the flowstress [175]. Figure 7.2 shows the Kocks-Mecking plots for all of the stress-strain curves in Figure 7.1.In all cases the blue curve shows the work hardening response of the as-solution treated sample. The lowwork-hardening regime observed for the aged samples in Figure 7.1 is revealed in the work hardening plotsas a transient at the beginning of each of the work hardening curves. Focusing on the samples pre-deformedto ∆σ = 44 MPa (Figures 7.2a and 7.2b) one sees that the work hardening (beyond the initial transient) lookssimilar to those presented in Figure 5.4 in Chapter 5, the work hardening plots being shifted in stress butsimilar in slope to the work hardening plot for the as-solution treated material. For samples pre-deformedto ∆σ = 174 MPa the similarity between the work hardening behaviour of the aged and as-solution treatedmaterial becomes less clear.Owing to the large number of conditions shown in Figure 7.2, it is difficult to see some of the significantbut subtle differences in the work hardening rates. Figure 7.3 shows only the Kocks-Mecking plots for the74(a) (b)(c) (d)Figure 7.1: Stress vs. strain evolution of Al-3.23 at.% - 0.23 at.%Cu alloy, deformed a) and b) ∆σ=44MPa (εp=2%), during artificial aging at 160 and 200 ◦C respectively, and deformed c) and d)∆σ=174 MPa (εp=10%), during artificial aging at 160 and 200 ◦C respectively. All tensile testswere done at 77K.as-solutionized state (blue curve) and for the materials aged for 2 minutes. These plots show that the Kocks-Mecking plots for the as-solutionized and lightly deformed material (∆σ = 44 MPa) are well approximated asstraight lines, consistent with the classic Kocks-Mecking analysis [175], having practically the same slope.On the other hand, the work hardening behaviour on samples pre-deformed ∆σ = 174 MPa, after 2 minutesof aging, shows an immediate change in the slope of the work hardening evolution. Comparing these plots tothe Kocks-Mecking plots shown in Figure 5.4 in Chapter 5 shows significant differences between the workhardening behaviour following aging of pre-deformed samples compared to the work hardening behaviourfollowing aging of the as-solution treated samples.75(a) (b)(c) (d)Figure 7.2: Kocks-Mecking plots resulting from the stress vs. strain data for Al-3.23 at.% - 0.23at.%Cu alloy pre-deformed to ∆σ= 44 MPa (a and b) and ∆σ= 174 MPa (c and d). The plots onthe left (a and c) show the response on aging at 160 ◦C while the plots on the right (b and d) showthe response upon aging at 200◦C All tensile tests were done at 77K.In Chapter 5 it was argued that for the majority of aging temperatures aging did not fundamentallychange the work hardening behaviour. The differences observed here must come from differences in mi-crostructure on aging of the pre-deformed reported in Chapter 6, e.g. changes in precipitation, segregationand precipitation on dislocations and/or dislocation recovery. To help test whether these effects are dueprimarily to changes in clustering/GPB zone formation in the aged samples, the work hardening behaviourof the AA5252 has been analyzed following the same pre-deformation and aging treatments used for thesamples shown in Figures 7.1 and 7.3. Figure 7.4 shows the stress-strain response of the AA5252 alloy inthe solution treated state as well as after pre-deformation to ∆σ = 44 MPa and 174 MPa and aged at 160◦Cand 200◦C. Figure 7.5 shows the Kocks-Mecking plots produced from the data in Figure 7.4.It can be immediately seen that the AA5252 alloy, which is non-precipitation hardenable, shows the same76(a) (b)(c) (d)Figure 7.3: Kocks-Mecking plots resulting from the stress vs. strain data for Al-3.23 at.% - 0.23at.%Cu alloy deformed a) and b) ∆σ= 44 MPa, during artificial aging at 160 and 200 ◦C respec-tively, and deformed c) and d) ∆σ=174 MPa, during artificial aging at 160 and 200 ◦C respec-tively. All tensile tests were done at 77K.features following pre-deformation and aging as the Al-Mg-Cu alloy, notably, the low initial work hardeningbehaviour followed by a evolution of the work hardening rate over the rest of the tensile test. These plots alsoshow how, even for the lower level of pre-deformation, there is an increase in the non-linearity of the workhardening behaviour following yielding. These results suggest that it is not the process of clustering/GPBzone formation in the early stages of aging that leads to these changes in the work hardening response, ratherit would appear that these changes are due to effects related to aging following pre-deformation in Al-Mgalloys.77(a) (b)(c) (d)Figure 7.4: Stress vs. strain evolution for AA5252 alloy (Al-2.94 at.% Mg) pre-strained a) and b)∆σ=44 MPa (εp=2%), during artificial aging at 160 and 200 ◦C respectively, and deformed c)and d) ∆σ=174 MPa (εp=10%), during artificial aging at 160 and 200 ◦C respectively. All tensiletests were done at 77K.78(a) (b)(c) (d)Figure 7.5: Kocks-Mecking plots resulting from the stress vs. strain data for AA5252 alloy (Al-2.94at.% Mg) pre-strained a) and b) ∆σ= 44 MPa, during artificial aging at 160 and 200 ◦C re-spectively, and pre-strained c) and d) ∆σ=174 MPa, during artificial aging at 160 and 200 ◦Crespectively. All tensile tests were done at 77K.7.2 A Model for the Work Hardening Response of Pre-Deformed and AgedSamplesAt the beginning of this chapter it was proposed to analyze the work hardening response of the Al-Mg-Cusamples to separate the effects of cluster/GPB zone hardening from recovery induced softening. The basicidea proposed was that cluster/GPB zone hardening (as shown in Chapter 5), leads to an increase in yieldstrength but no change in work hardening. Recovery due to the loss of dislocations, on the other hand, shouldlead to both a change in yield strength and work hardening rate. Here, an attempt to perform this separationwill be taken where it is assumed that cluster/GPB zone hardening does not influence the work hardeningrate, and that the effect of recovery can be captured by means of a modified Kocks-Mecking analysis.79The work hardening behaviour of single phase aluminum alloys has been shown to obey the classicKocks-Mecking model for dislocation based work hardening [176, 177]. In this model, a single internal statevariable (the dislocation density, ρ) is used to predict the dislocation evolution of the dislocation density andflow stress during plastic deformation,dρdε p= k1√ρ− k2ρ (7.1)Here, the first term is related to the storage of dislocations with progressive deformation. This storageterm is proportional to the mean distance between dislocations, while the term k1 account for the efficiency ofsuch dislocation generation [175, 178]. The second term accounts for the rate of annihilation of dislocationsby dynamic recovery. Dynamic recovery is assumed in the Kocks-Mecking model to be proportional to thedislocation density. The proportionality factor k2 is sensitive to the deformation temperature, strain rate, andalloy composition [175, 177]. The stress required to move dislocations through a fixed dislocation density,the so-called “forest” strength, is given by the Taylor equation,σ⊥ = MαGb√ρ (7.2)Where α represents the average strength of the forest dislocations (0.3 − 0.5), G the shear modulus, bthe magnitude of the burgers vector, and ρ the dislocation density (line length per unit volume).Combining the Equation 7.2 with Equation 7.1, allows the work hardening response in terms of the flowstress as,θ =dσ⊥dε p= θo(1− σ⊥σv ) (7.3)Whereθo =αGbMk12(7.4)σv =αGbMk1k2(7.5)It can be seen that Equation 7.3 predicts a linear decrease in the work hardening rate from θ0 at the onsetof plastic deformation to zero at a ’saturation stress’, σv 1 The work hardening behaviour of the as-solutiontreated Al-3.23 at.% Mg - 0.23 at.%Cu and AA5252 alloy (Al-2.93 at.% Mg) are well represented by thismodel, the good fit being shown in Figure 7.6. The Al-3.23 at.% Mg - 0.23 at.%Cu alloy fit was obtainedwith a K1=6.55x108 [1/m] and K2=9.97 values, while AA5252 (Al-2.93 at.% Mg) alloy fit was obtained witha K1=5.64x108 [1/m] and K2=9.41 values2.A critical consequence of having a description of the evolution of the work hardening rate of the material,1In reality the work hardening does not go to zero at σv, rather it enters into a stage of deformation with a small but nearlyconstant rate of hardening often referred to as ‘Stage IV’ hardening [175]2The difference in the measured K1 values is coherent with previously reported increase in initial work hardening rate θ0proportional to the Mg content in Al-Mg alloys [152]80Figure 7.6: Experimental and modeled Kocks-Mecking plots.during deformation, is that in principle all states of work hardening during plastic deformation are knownand represented by Equation 7.3 (blue line Figure 7.7). If the same material has been pre-deformed by plasticdeformation to a certain flow stress, corresponding work hardening rate (green square, Figure 7.7), and thensubjected to a process that reduces the dislocation density and, thus, flow stress (e.g. static recovery), theresult will be a correspondingly higher work hardening rate (red square, Fig. 7.7) as described by Equation7.3. Re-loading the material, to continue deformation following this recovery process, should lead to thedeformation continuing on from the reduced/recovered flow stress, following the flow stress/hardening ratelaw as described by Equation 7.3 (blue line Fig. 7.7). If this behaviour were observed experimentally, thenseparating the effects of precipitation and recovery (or the remaining forest hardening), in pre-deformed andaged Al-Mg-Cu samples, would be straight forward; the work hardening at yield would correspond to theforest hardening (dislocation) contribution to the flow stress, this being described by Equation 7.3. Knowingthe dislocation contribution to the flow stress, as well as the other fixed contributions (e.g. solid solution,grain size), the precipitate contribution can be obtained as the remaining contribution to the overall yieldstress, following the same approach taken in Chapter 6 (cf. Equation 6.3).It is clear that this simple interpretation of the Kocks-Mecking model fails to adequately explain thework hardening changes that occur, following pre-deformation and aging in the Al-Mg-Cu and AA5252alloys. This significantly complicates the separation of the cluster/GPB zone, and dislocation contributions,to the yield stress after pre-deformation and aging. Below the origins of these phenomena are discussed,and possible methods for predicting them by modifying the above described Kocks-Mecking model are81Figure 7.7: Schematic work hardening rate evolution. This a reproduction is based on the parametersused for the modeled Al-Mg alloy shown in Figure 7.6.described.The initial low work hardening rate observed in all pre-deformed and aged samples, has been previ-ously reported for FCC materials, including aluminum, tested at temperatures lower than room temperature.This has been reported even for situations where the material has been pre-deformed, unloaded and thenimmediately re-loaded [179]. This effect has been referred to as the “unloading yield point effect” [179]or the “Hassen-Kelly effect” [180]. Different explanations for this behavior have been proposed, includingthe rearrangement of dislocations during unloading [180–182] and jog formation due to dislocation-vacancyinteractions during unloading [179]. Regardless of the details, all of these mechanisms lead to a reduc-tion in dislocations available to continue plastic deformation on re-loading. Few models exist to predictthe mechanical consequences of this effect, Brown presenting a sophisticated mechanistic model for theKelly-Haasen effect based on edge-dislocation dipole stability on unloading [182]. Further complicating theinterpretation of the results presented here is that aging at elevated temperature is conducted in the presentwork. The effect observed here could therefore be described as a form of static strain aging though with-out the appearance of yield point phenomena typical of static strain aging in ferrous alloys [183]. Giventhat both alloys studied here have undergone static recovery, where dislocation rearrangement and soluteredistribution has taken place, the density of dislocations could be significantly reduced by annihilation withother dislocations of opposite sign, or pinned by segregation of solute atoms as clearly shown in Chapter 6for the case of the Al-Mg-Cu alloy (cf Figure 6.8).Kubin et al. [184] have proposed that static strain aging can be described as being due to insufficientmobile dislocations to maintain the imposed plastic strain rate, the relationship between mobile dislocation82density (ρm) and the imposed strain rate ε˙ being given by,ε˙ = Mρmbv (7.6)where v is the average dislocation velocity, which is assumed to be a power law of the applied stress. If ρmis low, then v must increase such that the imposed strain rate is met, this requiring a higher stress than whatwould be required if ρm was large.Expanding Equation 7.6 considering thermally activated plastic deformation aided by the imposed stress,one can re-write it as [185],ε˙ = ε˙0(σσˆ)1/m (7.7)where ε˙0 is proportional to the mobile dislocation density and arrheniusly dependent on the deformationtemperature, σˆ is the limiting flow stress at zero imposed strain rate (or large ρm) and σ is the actual flowstress required to maintain the finite imposed strain rate. Finally, m is the rate sensitivity exponent.In the case of the AA5252 (or any other solid solution strengthened alloy) the total flow stress can bewritten so as to incorporate this rate dependence [177]. The general additivity law can be written as [154],σys = σ0+(σn⊥+(σqss+σqppt)n/q)1/n (7.8)where σ0 is the intrinsic and grain size contribution.Under the same assumptions as described in Section 6.2.2, we can write Equation 7.8 as,σ = σ⊥(ε˙ε˙0)m+σss+σ0 (7.9)where σss is the solid solution contribution to strength, and σ0 is the contribution to the yield stress from thegrain size and intrinsic strength. Moreover, σˆ in this case can be taken as the forest strength given by theTaylor equation σ⊥.Taking the derivative of Equation 7.9 with respect of the strain and using the chain rule gives,θ =dσdε= (ε˙ε˙0)m[dσ⊥dε−mσ⊥ε˙0dε˙0dε] (7.10)Written in this way it can be seen that the work hardening rate is composed of two terms. The first term(dσ⊥/dε) is the work hardening rate obtained in the rate insensitive limit, the one typically considered in theclassic Kocks-Mecking approach. The second term is proportional to -dε˙0/dε , the negative sign indicatingthat it acts to reduce the work hardening rate relative to that obtained in the rate insensitive limit. Recallingthat ε˙0 is proportional to the mobile dislocation density, one can see that this term is related to how rapidlymobile dislocations are produced, in the rate sensitive regime (when ρm is low). In this regime, the flowstress will be reduced as new dislocations are produced, this reducing the macroscopic work hardening rate.In the experiments reported here, one could expect this second term to be responsible for the initial83low work hardening rate following aging. Initially, following aging, the mobile dislocation density is low(owing to recovery and/or solute segregation) but as the material is deformed and dislocation sources beginto operate, the mobile dislocation density will quickly rise back to a level sufficient to satisfy Equation 7.6meaning thatdε˙0dε≈ 0, ε˙0 ≈ ε˙ and so the work hardening rate becomes the classic dσ⊥/dε .The remaining problem is to obtain the evolution law for ε˙0 (or equivalently, ρm). There have beenseveral models proposed which attempt to predict evolution laws separately for the mobile and forest dis-location densities (so-called ‘two internal-state variable’ models) [177, 186]. These models require a largenumber of adjustable parameters, however, to describe the evolution law for both sets of dislocation aswell as their interaction. Here, a much simpler approach is taken, motivated by the fact that the low workhardening regime appears only in the early stages of the deformation. From the picture envisioned here, dis-locations sources will become active once plasticity starts again allowing the lost mobile dislocation densityto be replaced by fresh mobile dislocations and a quick return to nearly rate insensitive behaviour. Here thesimplest, empirical equation (Equation 7.11) is proposed,dε˙0dε= η(1− ε˙0ε˙) (7.11)this expression linearly reduces dε˙0/dε as a function of ε˙0 until ε˙0 is equal to the imposed strain rate, ε˙ .The advantage of such a simple expression is that it adds only two adjustable parameters, η and the initialvalue of ε˙0 = ε˙0i, to describe the evolution of the mobile dislocation density/ε˙0 and thus the transient workhardening behaviour.Figure 7.8 illustrates the results obtained when the work hardening rate is predicted using Equations 7.10and 7.11, with dσ⊥/dε being given by the parameterized Kocks-Mecking model used in Figure 7.6. Whilethis allows for the initial, transient low work hardening behaviour to be explained, it does not provide anexplanation for the higher than expected work hardening rate (and non-linear work hardening rate evolution),observed over the rest of the flow curve (cf. Figure 7.5).In the above discussion, it was assumed that the mobile dislocation density was reduced through theprocesses of recovery and/or solute segregation to dislocations, with segregation to dislocations havingbeen observed for the case of the Al-Mg-Cu alloy in Chapter 6. It has been shown theoretically, for thecase of Al-Mg alloys, that the stress to de-pin a dislocation (edge or screw) from a fully formed soluteatmosphere can be much higher than the flow stresses measured experimentally here [98]. This wouldsuggest that these dislocations are not only immobile during deformation but that they will also be difficultto recover dynamically during plastic deformation. Such segregated forest dislocations should contribute tothe generation of new forest dislocations (the first term in Equation 7.1) but that they will not be availablefor dynamic recovery (the second term in Equation 7.1). This portion of the dislocation density, fixed by thelevel of pre-deformation, the level of recovery and the aging treatment, must be treated separately from theconventional forest dislocation density in Equation 7.1,dρdε p= k1√ρ− k2ρ+ k3ρpinned (7.12)84Figure 7.8: Representation of the modeled deformation accounting for an initial low mobile dislo-cation density, on the work hardening evolution represented by the Kocks-Mecking plot. Thevertical line at the beginning of pre-strain curve represent the end of the elastic segment. Therepresentation was done using k1 = 5.64x108 [1/m], k2 = 9.41 (k1 and k2 as obtained from thecontinuously deformed AA5252 alloy), η =0.08, ε0,i = 1x10−4 and σ⊥,i=200 [MPa]where a separate constant k3 is defined (rather than assuming it to be equal to k2) to reflect the fact thatthe interaction with segregated dislocations may be different from those that are free of segregation. Inthe tests performed in this work, it is expected that ρpinned will be an unknown constant for a given levelof pre-deformation and a given aging condition. Thus we can replace k3ρpinned with a single constant, kDconsidering the prediction of the work-hardening response for a single stress-strain curve. In this case, amodified version of the Kocks-Mecking model can be written,dσ⊥dε p= θo(1− σ⊥σv )+kD(αMGb)22σ⊥(7.13)Its important to note that Equation 7.13 has been commonly used to describe the effect of non-shearableobstacles to dislocation motion in the context of precipitation hardened alloys [187, 188]. In this context,the second term in Equation 7.13 represents the additional storage of geometrically necessary dislocations.The effect of this addition term in the Kocks-Mecking model can be observed in Figure 7.9 whereEquation 7.13 is plotted based on the behaviour of the AA5252 alloy shown in Figure 7.6. Here the bluecurve shows the baseline case (kD = 0 as in Figure 7.9). The black and red curves imagine a situationwhere the material has been pre-deformed to ∆σ = 200 [MPa]. The red line then shows the predicted effect85of continuing to deform but now when kD = 1x1015[1/m2]. It can be seen that the work hardening ratefollowing reloading is higher than what it was at the end of the pre-deformation due to the extra generationof dislocations due to the second term in Equation 7.13, but that the work hardening rate of the red curveapproaches that of the blue curve as the flow stress increases.Figure 7.9: Effect of additional term for the generation of dislocations during plastic deformation,on the work hardening evolution represented by the Kocks-Mecking plot. This curve was con-structed using the following parameters: kD = 1x1015[1/m2], k1 = 5.64x108 [1/m], k2 = 9.41, andσ⊥,i = 200 [MPa]. The vertical lines at the beginning of each plot represent the end of the elasticsegment.Finally, the two models derived here can be used to describe the overall behaviour observed experi-mentally in this chapter. Figure 7.10 shows the results of Equations 7.10 and 7.11 combined with dσ⊥/dεbeing given by Equation 7.13 parameterized as shown in Figure 7.9. One can see that the two deviationsfrom the classic Kocks-Mecking model observed for the Al-Mg-Cu alloy and the AA5252 are qualitativelyreproduced by this modified model. In the following, an attempt is made to compare this modified modelto the experiments and to finally extract from the model the separate effects of cluster/GPB zone hardeningand recovery softening in the Al-Mg-Cu alloy.86Figure 7.10: Effect of additional term for the generation of dislocations, and low initial mobiledislocation density during plastic deformation, on the work hardening evolution representedby the Kocks-Mecking plot. This curve was constructed using the following parameters:kD = 1x1015[1/m2], k1 = 5.64x108 [1/m], k2 = 9.41, η =0.08, ε0,i = 1x10−4, and σ⊥ = 200[MPa] The vertical line at the beginning of the pre-strain plot represent the end of the elasticsegment.7.3 Predicting the Effect of Recovery on Work Hardening for the AA5252AlloyAs a first step towards analyzing the Al-Mg-Cu alloy, the simpler case of describing the work hardeningresponse of the AA5252 alloy using the model developed above is first explored.The full model (Equations 7.10, 7.11 and 7.13) requires knowledge of several parameters, some of whichare constants that can be determined from a single experiment, others which vary with the pre-deformationand aging conditions.The parameters k1 = 5.64 × 108 m−1 and k2 = 9.41 set the work hardening rate of the non-pre-deformedsample, these having been previously determined in Figure 7.6. These parameters are fixed an independentof the pre-deformation/aging conditions.The remaining parameters for the model, all dependent on the pre-deformation and aging conditions are;1. The initial value of ε˙0,i2. The rate of mobile dislocation generation, η873. The work hardening parameter kD4. The initial stress contribution due to work hardening, this due to the retained dislocations after recov-ery, σ⊥,iManually finding the best fit values for these four parameters is made easier by the fact that the first twoonly modify the very initial portion of the work hardening plot (the low work hardening transient), while thethird dominates the shape of the work hardening evolution over most of the rest of the curve, and the fourthdetermines the beginning of the curve.Figure 7.11 shows an example of the model fit to the experimental data for the AA5252 alloy pre-deformed by ∆σ = 174 MPa, and then aged at 200◦C for 2 minutes. The remaining modeled vs. experi-mentally obtained Kocks-Mecking plots can be consulted in Appendix F. One can see that this rather simplemodel is able to successfully predict the shape of the work hardening curve, though it does not perfectlymatch the initial low hardening rate transient. This is likely a consequence of the simplified approach topredicting the evolution of ε˙0.Figure 7.11: Experimental and modeled Kocks-Mecking representation of AA5252 (Al-2.94 at.% Mg)system, pre-deformed ∆σ=174 MPa, aged 2 min at 200 ◦C, and further re-strained.The best fit parameters obtained for all of the aging conditions explored for the AA5252 alloy (i.e.pre-deformation to ∆σ= 44 MPa, and ∆σ= 174 MPa and aging at 160 and 200 ◦C) are given in Table 7.1It was found that it was possible to fit the initial low work hardening rate transient by fixing one of η orε˙0i, and varying the other as a function of the pre-deformation and aging conditions. Here η=0.08 [1/s] was88Aging Time (minutes) 1 2 5 30 420∆σ = 44 MPa, T = 160◦Cσ⊥,i MPa 42 38 42ε˙0i s−1 1.4 × 10−5 9 × 10−5 1.3 × 10−5kD m−2 0.5 × 1015 0.5 × 1015 0.5 × 1015η s−1 0.08 0.08 0.08∆σ = 44 MPa, T = 200◦Cσ⊥,i MPa 40 39 51ε˙0i s−1 1.45 × 10−5 1.6 × 10−5 3.9 × 10−5kD m−2 0.5 × 1015 0.5 × 1015 0.5 × 1015η s−1 0.08 0.08 0.08∆σ = 174 MPa, T = 160◦Cσ⊥,i MPa 123 117 113 108 113ε˙0i s−1 5.5 × 10−5 6 × 10−5 6.5 × 10−5 3 × 10−5 11 × 10−5kD m−2 1.5 × 1015 1.5 × 1015 0.5 × 1015 1.5 × 1015 1.5 × 1015η s−1 0.08 0.08 0.08 0.08 0.08∆σ = 174 MPa, T = 200◦Cσ⊥,i MPa 105 105 104ε˙0i s−1 9.4 × 10−5 10.5 × 10−5 13.0 × 10−5kD m−2 1.5 × 1015 1.5 × 1015 1.5 × 1015η s−1 0.08 0.08 0.08Table 7.1: Numerical values of parameters used in fitting the work hardening model to the work hard-ening response of the AA5252 alloy following pre-deformation and aging. In all cases k1 = 5.64× 108 m−1 and k2 = 9.41.fixed to be constant for all conditions, and the value of ε˙0i was varied as shown in Table 7.1. Owing to thesimplistic nature of the model for the variation of ε˙0, and its inability to perfectly match the experimentallyobserved low work hardening rate transient, it is difficult to infer a physical explanation for the variation ofε˙0i with pre-deformation or aging.In the case of kD, it was found that a good fit to the data was obtained when a single value of kD waschosen for a given level of pre-deformation, the value of kD increasing with the level of pre-deformation. Thefact that kD increases with the level of pre-deformation would be consistent with the model developed abovewhich predicted that kD should be proportional to the density of dislocations pinned by solute segregation.The independence of kD with the aging time and temperature could also be consistent with the fact that evena small amount of segregation is sufficient to increase the stress required for de-pinning [98]. In this case,the immobilized dislocations would be formed within the first few minutes of aging at 160 and 200◦C.897.3.1 Separating the Effects of Cluster/GPB Zone Hardening and Recovery Softening inthe Al-Mg-Cu alloyThe original aim of this analysis was to determine, from the measurement of yield strength and work harden-ing rate alone, the contributions of forest hardening and cluster/GPB zones strengthening in the Al-Mg-Cualloys, and to identify whether it is a reduction in the rate of softening by recovery due to pinning of dis-locations [120], or cluster/GBP zone hardening alone, which allows for this material to retain its strengthduring the paint bake cycle. Here, the model developed above is used to fit the work hardening behaviour ofthe material and to, therefore, allow for this question to be answered.Compared to the analysis of the AA5252 alloy, cluster/GPB zone hardening must be included into theanalysis. This is done by modifying Equation 7.9 to,σ = σˆ(ε˙ε˙0)m+σ0+√σ2ss+σ2ppt (7.14)As described in Section 6.2.2, the key assumption in the use of such an addition law, is that soluteand clusters/GPB zones are assumed to have similar strengths (Chapter 5), while the strength arising fromdislocations is assumed to be considerably larger (6). As a starting point, based on the work in Chapter 5, itis assumed that the clusters/GPB zones contribute only to the yield strength, and not to the work hardeningrate of the alloy. In this case the cluster/GPB zone strength (σppt) is taken as an adjustable parameter in themodel. The contribution of solute in solid solution σss has been considered to be constant, this consistentwith the observation made in Chapter 5.As in the case of the AA5252 alloy, five additional parameters must be fit for each of the aging conditionsstudied (Table 7.2). From the as-solution treated stress-strain curve, the values of k1= 6.55E+08 m−1 andk2=9.97 were fixed (Figure 7.6). As in the case of the AA5252 alloy, it was found that the value of η couldbe fixed to a constant value of 0.08 s−1 for all conditions, while ε˙0i was varied with pre-deformation andaging conditions, the values of this parameter being given in Table 7.2. Although the values of ε˙0i foundfor this alloy are not identical to those found for the AA5252 alloys, they result very similar. This is notsurprising given that the mechanism envisioned does not depend on precipitation, and thus should not bestrongly dependent on the small difference in Cu and Mg content of the alloys.Also consistent with the concept of this model is the fact that the same values of kD, used for the AA5252alloy, could be successfully used here, with kD = 0.5 × 1015 for ∆σ = 44 MPa, and kD = 1.5 × 1015 for ∆σ= 174 MPa.Figure 7.12 shows an example of the model fit to the work hardening response of an Al-3.23 at.% - 0.23at.%Cu alloy sample, pre-deformed to ∆σ = 174 MPa, and aged for 2 minutes at 200◦C. The fits to the othertest conditions are being provided in Appendix F.While nearly all of the tested conditions were found to be adequately fit using the approach describedabove, the samples pre-deformed to ∆σ = 44 and 174 MPa and then aged for 420 min at 200◦C, provideduniquely poor fits. Figure 7.13 shows that, unlike the shorter aging times, the experimental response at thislonger aging time appears to fall back towards the as-solution treated work hardening curve faster. In the90Aging Time (minutes) 2 5 10 30 180 420∆σ = 44 MPa, T = 160◦Cσ⊥,i MPa 42 40 39 39 55σppt MPa 54 67 85 97 112ε˙0i s−1 1,1 × 10−5 1.2 × 10−5 1.4 × 10−5 1.4 × 10−5 3.5 × 10−5kD m−2 0.5 × 1015 0.5 × 1015 0.5 × 1015 0.5 × 1015 0.5 × 1015η s−1 0.08 0.08 0.08 0.08 0.08∆σ = 44 MPa, T = 200◦Cσ⊥,i MPa 43 42 42 54 50σppt MPa 63 80 88 92 115ε˙0i s−1 2.7 × 10−5 3.5 × 10−5 4.5 × 10−5 4.0 × 10−5 8.5 × 10−5kD m−2 0.5 × 1015 0.5 × 1015 0.5 × 1015 0.5 × 1015 0.5 × 1015η s−1 0.08 0.08 0.08 0.08 0.08∆σ = 174 MPa, T = 160◦Cσ⊥,i MPa 115 113 109 101 110σppt MPa 60 65 81 105 117ε˙0i s−1 4.5 × 10−5 5.0 × 10−5 7.0 × 10−5 5.0 × 10−5 6.7 × 10−5kD m−2 1.5 × 1015 1.5 × 1015 1.5 × 1015 1.5 × 1015 1.5 × 1015η s−1 0.08 0.08 0.08 0.08 0.08∆σ = 174 MPa, T = 200◦Cσ⊥,i MPa 100 107 110 110 122σppt MPa 85 91 95 100 130ε˙0i s−1 4.0 × 10−5 5.0 × 10−5 6.0 × 10−5 7.0 × 10−5 10 × 10−5kD m−2 1.5 × 1015 1.5 × 1015 1.5 × 1015 1.5 × 1015 1.5 × 1015η s−1 0.08 0.08 0.08 0.08 0.08Table 7.2: Numerical values of parameters used in fitting the work hardening model to the work hard-ening response of the Al-3.23 at.% - 0.23 at.%Cu alloy following pre-deformation and aging. Inall cases k1= 6.55× 108 m−1 and k2=9.97. Note that the fit obtained for both conditions aged for420 minutes at 200◦C gave less satisfactory fits to the model compared to the other conditions.case of the sample pre-deformed to ∆σ = 174 MPa, it even appears that the work hardening curve wouldcross that of the non-pre-deformed sample at higher stresses (if necking did not intervene). Reflecting backon Chapter 5, Figure 5.4, it was noted that deviations in the work hardening behaviour started to appear atlonger aging times. There it was suggested that, at these longer aging times, the clusters/GPB zones may startto transition towards larger, non-shearable precipitates (e.g. S” or S-phase) that could influence the workhardening rate (see e.g. [149]). In this case, the assumptions regarding the lack of effect of clusters/GBPzones/precipitates, on the work hardening rate, will no longer be valid. Moreover, the assumption made inconstructing Equation 7.14, i.e. that the precipitates are weak obstacles to dislocation motion, would nolonger be valid. To avoid the additional complexity (and parameters) needed to account for these additionalfactors, the data for samples aged for 420 minutes at 200◦C will not be considered further.In fitting the above model, it was possible to obtain the value of σppt and the value of σ⊥,i, at the onset of91Figure 7.12: Experimental and modeled Kocks-Mecking representation of Al-3.23 at.% - 0.23 at.%Cualloy system, deformed ∆σ=174 MPa, aged 2 min at 200 ◦C.(a) (b)Figure 7.13: Kocks-Mecking plot for Al-3.23 at.% - 0.23 at.%Cu aged at 200 ◦C, pre-deformed a)∆σ=44 MPa, and b) ∆σ=174 MPa.yielding (σ ). The former is the cluster/GPB zone strength, while the latter is the remaining forest hardeningfollowing recovery. Starting with the variation of σˆ0 (Figure 7.14), it is seen that it remains (to with theaccuracy obtainable from the fits to the model) constant and independent of aging time. Also plotted inFigure 7.14 is the data obtained directly from the AA5252 alloy. This is the same data used to approximate92the recovery rate of the Al-Mg-Cu alloy in the analysis performed in Chapter 6. It can be seen that theapproximation is good, with the forest contribution to the flow stress in the two alloys being nearly identicalfor both levels of pre-strain and for both aging temperatures. The observed recovery in Al-Mg-Cu exhibitsthe same quick drop, showing no further evolution as seen in AA5252 alloy and can be rationalized as donein Section 6.2.2.The similarity in the forest contribution to the flow stress for the Al-Mg-Cu and AA5252 alloy suggeststhat the analysis performed here should give very similar predictions for the contribution of σppt to the yieldstrength of the aged samples as well. Indeed, as shown in Figure 7.15 the results obtained through theapplication of the model proposed here give nearly identical results to those presented via the much simpleranalysis performed in Chapter 6 (cf. Figure 6.6). Importantly it is found here that for aging at 160◦C and200◦C the initial cluster/GPB zone contribution to the strength is lower than what it would be for agingof the as-solutionized sample. Moreover, it is seen (for both aging temperatures) that the magnitude of thepre-deformation has little effect on the aging response. Finally, it is noted that while the overall, contributionof σppt is lower for the pre-deformed samples, the rate of increase in σppt is the same in all cases.One of the key questions posed at the outset of this thesis was whether the observed suppression ofsoftening of AA5XXX alloys during the paint bake cycle due to the minor addition of Cu was due to aretardation of recovery (owing to pinning of dislocations) or due to cluster/GPB zone hardening. The resultspresented in this Chapter (as well as the one before it) provide strong evidence that recovery is affectedvery little by the addition of Cu and that the improved performance in the paint bake cycle arises fromcluster/GPB zone induced hardening that can more than counterbalance the loss in strength arising from therecovery. The fact that there is only a minor coupling between the process of clusters/GPB zone formationand recovery makes alloy design and selection significantly easier. Though pre-deformation may lower theeffect of cluster hardening relative to what is achievable in the aging of the as-solutionized material, theremay be ways to modify this (as explained in Chapter 6) by modifying the processing conditions to controlthe excess vacancy concentration. Moreover, while the exact mechanism leading to the linear dependenceof σppt with the logarithm of aging time remains only hypothesized, this observation provides a way ofpredicting the hardening response of other, similar, alloys with a minimum number of experiments.7.4 SummaryThe key observations and conclusions from this Chapter can be summarized as follows• In this chapter the mechanical response of the Al-3.23 at.% - 0.23 at.%Cu and AA5252 alloys wereanalyzed using a modified version of the Kocks-Mecking model with the aim of independently verify-ing the separate contributions of forest hardening and cluster/GBP zone strength in the pre-deformedand aged Al-3.23 at.% - 0.23 at.%Cu alloy.• It was found that a simple application of the Kocks-Mecking analysis failed to predict the basic workhardening behaviour of either alloy following pre-deformation and aging.93• Two modifications were made to the classic Kocks-Mecking analysis, so as to account for the effectsof solute segregation to dislocations, these acting to modify the available mobile dislocation density atthe onset of yielding and to provide additional dislocation obstacles throughout the entire stress-straincurve.• Using the previously mentioned approach, the work hardening behaviour for both alloys was success-fully modelled. The results of this model were used to estimate the cluster/GPB zone and dislocationforest contributions to the yield strength, the results obtained here independently confirming thosehypothesized in the previous chapter.• Importantly, it is confirmed through this analysis that i) recovery is negligibly affected by the clus-ter/GPB zone formation and that ii) pre-deformation suppresses a portion of the rapid initial clusterhardening that is observed in aging of the as-solution treated samples.94(a)(b)Figure 7.14: Forest strength from conversion of extracted dislocation density for Al-3.23 at.% - 0.23at.%Cu aged at a) 160 ◦C and b) 200 ◦C, pre-strained ∆σ=44 MPa, and ∆σ=174 MPa.95(a)(b)Figure 7.15: Precipitation contribution to the total strength for Al-3.23 at.% - 0.23 at.%Cu aged ata) 160 ◦C and b) 200 ◦C, pre-strained ∆σ=44 MPa, and ∆σ=174 MPa. These results havebeen plotted along the precipitation contribution for material without any pre-deformation ascalculated in Section 6.2.2.96Chapter 8Summary and ConclusionsIn this thesis, the relation between concurrent recovery and precipitation in a pre-deformed Al-Mg-Cu alloywas studied with the aim of identifying how these processes affect the material’s yield strength duringconditions compatible with the industrial automotive paint bake cycle. While it had been previously shownthat small additions of Cu could reduce softening of AA5XXX series alloys during simulated paint bakeprocesses, the origins of this phenomenon remained unexplored.Due to the limited body of literature dedicated to low Cu Al-Mg-Cu system, it was necessary to firstcharacterize the precipitation process taking place after solution treatment. Chapter 5 was dedicated to thispurpose, using macroscopic characterization techniques, specifically, electrical resistivity, DSC and detaileduniaxial tensile tests. Furthermore, microscopic characterization of the precipitation process was possibleby using Atom Probe Tomography (APT). The use of APT revealed that, under the times and temperaturesrelevant to the paint bake cycle, the age hardening observed during artificial aging is the result of soluteclusters/GPB zones. The presence of these clusters/GPB zones was shown to be consistent with the observedchanges in electrical resistivity and DSC.A new cluster analysis technique for interpreting APT data, based on pair correlation functions, wasused to obtain quantitative information about clusters/GPB zones. The output of this analysis was then usedas input to a detailed yield strength model, showing that the age hardening response is due to a bimodaldistribution of features which evolve differently during aging. While it has been previously hypothesizedthat the clusters/GPB zones found in low Cu:Mg alloys are the same as those found in more conventionalAA2XXX alloys, here it was shown that the clusters/GPB zones contained very little Cu, with the twomajority species being Al (∼ 80%) and Mg (∼15-20%). This helps to explain how efficient the very smalladditions of Cu are in producing age hardening comparable to that found in much more Cu rich AA2XXXalloys.The particular age hardening kinetics observed in these alloys was hypothesized to be a result of coars-ening. While a detailed model of cluster/GBP zone growth would require more detailed information aboutthe thermodynamics and crystallography of these features, a simple phenomenological model was proposedthat can be used (upon parameterization) to predict the age hardening response. This analysis could be97useful for future rapid alloy design experiments.With this understanding of the age hardening response in solution treated materials, Chapter 6 focusedon the more industrially relevant processes involved in aging of samples that had be pre-deformed plastically.The key finding from in this Chapter was that pre-deformation reduced the immediate jump in yield strengthexperienced during the first 1-2 minutes of aging. The kinetics of aging following this, however, were seento be unaffected by pre-deformation. Microstructure characterization, though much more difficult in thesesamples, revealed a reduction in the presence of small clusters/GPB zones compared to the microstructureof the as-solution treated material aged for the same time. Prominent in APT observations was segregationinterpreted as segregation along dislocations. It was proposed that the reduction in age hardening responseat short times was due to the rapid annihilation of excess vacancies to dislocations, vacancies being animportant contributor to the formation and growth of clusters/GPB zones. A simple model was used toillustrate the importance of dislocations on the rate of loss of vacancies.In the final Chapter, a method was proposed to separate the effects of cluster/GPB zone hardeningand recovery induced softening by an analysis of the work hardening response of pre-deformed and agedsamples. It was shown that a simple application of the Kocks-Mecking model was insufficient to explain theshape of the stress-strain curve (work hardening behaviour) following aging of the pre-deformed material.For this reason, two new ingredients were added, one dealing with the loss of mobile dislocations duringaging and the second considering dislocations pinned by solute (as revealed in APT observations) as fixedobstacles during subsequent deformation. Using this revised model, it was possible to show that recoveryproceeds very rapidly for the aging conditions examined such that there is no strong coupling betweenrecovery and cluster/GPB zone formation. This analysis also confirmed the approximate analysis performedin the previous chapter showing that the cluster/GPB zone hardening in the pre-deformed samples is reducedduring the first minutes of aging. The application of the methodology developed in this chapter to separatingthe effects of age hardening and recovery softening should be valuable for the analysis of other alloys whereprecipitation and recovery are coupled.8.1 Future workThe results of this thesis raise many new possible directions for future research. Below, four are suggested.Identification of the Structure and Thermodynamics Governing the Clusters/GPB zonesThe study of the detailed structure and thermodynamics of the clusters/GPB zones observed here wasoutside the scope of this work. Further work, however, requires more detailed experimental and theoreticalstudy of the structure and composition of these ‘phases’. The experimental results presented here suggestthat the composition of these ‘phases’ is much higher in Al than previous studies have shown. This presentsa challenge for electron microscope characterization but with improvements in techniques it has been sug-gested that this might be possible. Quantum mechanical calculations able to assess the stability of a largenumber of structures in the composition range observed here would also be very valuable.Characterization and Modelling of the Kinetics of Aging:98It has been hypothesized here that the aging kinetics are controlled by a coarsening-like process. Giventhe complexity of the microstructure of these alloys this requires further exploration with the aim of provid-ing a more physical explanation of the aging kinetics. This analysis would greatly benefit from measurementof the volume fraction, size and composition of the clusters/GPB zones for a wide range of different agingtemperatures and times. While detailed APT analysis could provide this data, the cost (in time) would bevery high and statistics would be a question. New developments in small angle x-ray scattering analysiscould also provide a route for a more rapid method to perform this sort of analysis despite the low chemicalcontrast between Al and Mg.Effect of Excess Vacancy Concentration on Aging:It has been proposed that the aging of the Al-Mg-Cu alloy is highly sensitive to the vacancy concentra-tion, particularly in the first seconds of aging. This should be further studied by varying the excess vacancyconcentration at the beginning of aging. This could be achieved by adopting different solution treatmenttemperatures and/or quenching rates. If results show a clear sensitivity to the change in vacancy density, in-dustrial strategies to induce a higher strengthening response in these alloys could be envisioned. These couldinclude the addition of solute atoms that can trap vacancies or by the recent cyclic deformation mechanism[189].Application of Work Hardening Model to Other Conditions:The modeling strategy developed in the final chapter was shown to allow for the separation and quan-tification of the effects of retained work hardening and clustering. This approach should be tested againsta range of other alloys/test conditions to evaluate the breadth of its applicability. For example, it couldbe applied to samples pre-deformed at room temperature, this being closer to the condition experienced inindustry.99Bibliography[1] IEA. CO2 Emissions from Fuel Combustion 2017 - Highlights. Technical report, InternationalEnergy Agency, 2017. → pages 1[2] Elaheh Ghassemieh. Materials in Automotive Application, State of the Art and Prospects. InMarcello Chiaberge, editor, New Trends and Developments in Automotive Industry. InTech, January2011. → pages 1[3] Richard Roth, Joel Clark, and Ashish Kelkar. Automobile bodies: Can aluminum be an economicalalternative to steel? JOM, 53(8):28–32, August 2001. → pages 1[4] Ducker Worldwide. Aluminum Content in Cars - Summary report. Technical report, DuckerWorldwide, July 2017. → pages 1[5] J. C. Benedyk. Aluminum alloys for lightweight automotive structures. In P. K. Mallick, editor,Materials, Design and Manufacturing for Lightweight Vehicles, Woodhead Publishing Series inComposites Science and Engineering, pages 79–113. Woodhead Publishing, 2010. → pages 1[6] S.A. Court, K.P. Hicklin, and David J. Lloyd. The Ageing and Thermal Recovery Behaviour ofAl-Mg-Cu Alloys. Materials Science Forum, 396-402:1031–1036, 2002. → pages 2, 18, 19, 34, 48,49, 71[7] Gene Mathers. Strength Loss Due to Welding. In Welding of Aluminium and Its Alloys, pages24–32. Woodhead Publishing, 2002. → pages 2[8] L. Kovarik, S.A. Court, H.L. Fraser, and M.J. Mills. GPB zones and composite GPB/GPBII zones inAlCuMg alloys. Acta Materialia, 56(17):4804–4815, October 2008. → pages 2, 15, 17, 19, 27, 49,71[9] Hubert I. Aaronson, Masato Enomoto, and Jong K. Lee. Mechanisms of diffusional phasetransformations in metals and alloys. CRC Press, Boca Raton, 2010. → pages 2, 4, 5, 17, 20, 65[10] Paul Dyer Merica, R.G. Waltenberg, and J.R. Freeman. Constitution and metallography ofaluminum and its light alloys with copper and with magnesium, volume 15. Sci. Pap. Bur. Stand.,1919. → pages 3[11] Aniruddha Biswas, Donald J. Siegel, C. Wolverton, and David N. Seidman. Precipitates in AlCualloys revisited: Atom-probe tomographic experiments and first-principles calculations ofcompositional evolution and interfacial segregation. Acta Materialia, 59(15):6187–6204, September2011. → pages 3, 4, 5, 7, 8100[12] S. K. Son, M. Takeda, M. Mitome, Y. Bando, and T. Endo. Precipitation behavior of an AlCu alloyduring isothermal aging at low temperatures. Materials Letters, 59(6):629–632, March 2005.→ pages 5[13] Tatsuo Sato and Akihiko Kamio. High resolution electron microscopy of phase decompositionmicrostructures in aluminium-based alloys. Materials Science and Engineering: A, 146(1):161–180,October 1991. → pages 3, 11, 12[14] K. E. D. A. Porter, Easterling. Phase transformations in metals and alloys. Nelson Thornes,London, 1992. → pages 4, 20, 21, 68[15] H. K. Hardy and T. J. Heal. Report on precipitation. Progress in Metal Physics, 5:143–278, January1954. → pages 4[16] W Desorbo, H. N Treaftis, and D Turnbull. Rate of clustering in Al-Cu alloys at low temperatures.Acta Metallurgica, 6(6):401–413, June 1958. → pages 4[17] Anthony Kelly. Precipitation hardening. Progress in Materials Science, 10:151–391, January 1963.→ pages 4, 17, 65[18] Ian Polmear, David StJohn, Jian-Feng Nie, and Ma Qian. 2 - Physical Metallurgy of AluminiumAlloys. In Light Alloys (Fifth Edition), pages 31–107. Butterworth-Heinemann, Boston, 2017.→ pages 4, 7, 8, 12, 13, 19, 53[19] M. Karlk, A. Bigot, B. Jouffrey, P. Auger, and S. Belliot. HREM, FIM and tomographic atom probeinvestigation of GuinierPreston zones in an Al1.54 at% Cu alloy. Ultramicroscopy, 98(24):219–230,January 2004. → pages 4[20] A. J. Ardell. Precipitation hardening. Metallurgical Transactions A, 16(12):2131–2165, December1985. → pages 5, 6, 7, 45, 49[21] R. K. W. Marceau, L. T. Stephenson, C. R. Hutchinson, and S. P. Ringer. Quantitative atom probeanalysis of nanostructure containing clusters and precipitates with multiple length scales.Ultramicroscopy, 111(6):738–742, May 2011. → pages 6, 40[22] W. J. Poole, J. A. S\a eter, S. Skjervold, and G. Waterloo. A model for predicting the effect ofdeformation after solution treatment on the subsequent artificial aging behavior of AA7030 andAA7108 alloys. Metallurgical and Materials Transactions A, 31(9):2327–2338, 2000. → pages 6,20, 21, 24[23] Michael F. Ashby and David R.H. Jones. 11.3 Age (Precipitation) Hardening. In EngineeringMaterials 2 - An Introduction to Microstructures and Processing, page 198. Elsevier, 4th editionedition, 2013. → pages 6[24] R.E. Smallman and R.J. Bishop. Mechanisms of Precipitation-Hardening. In Modern PhysicalMetallurgy and Materials Engineering - Science, Process, Applications, page 266. Elsevier, 6thedition edition, 1999. → pages 7[25] A. de Vaucorbeil, C. W. Sinclair, and W. J. Poole. Dislocation glide through non-randomlydistributed point obstacles. Philosophical Magazine, 93(27):3664–3679, September 2013. → pages7, 46101[26] A. de Vaucorbeil, Warren J. Poole, and Chadwick W. Sinclair. The Effect of Obstacle StrengthDistribution on the Critical Resolved Shear Stress of Engineering Alloys. Materials Science Forum,794-796:449–454, 2014. → pages 7, 45, 46, 49[27] J. F. Nie and B. C. Muddle. Microstructural design of high-strength aluminum alloys. Journal ofPhase Equilibria, 19(6):543, December 1998. → pages 7, 41[28] J. da Costa Teixeira, D. G. Cram, L. Bourgeois, T. J. Bastow, A. J. Hill, and C. R. Hutchinson. Onthe strengthening response of aluminum alloys containing shear-resistant plate-shaped precipitates.Acta Materialia, 56(20):6109–6122, December 2008. → pages 7[29] Laure Bourgeois, Christian Dwyer, Matthew Weyland, Jian-Feng Nie, and Barrington C. Muddle.The magic thicknesses of precipitates in Sn-microalloyed AlCu. Acta Materialia, 60(2):633–644,January 2012. → pages 7[30] S. P. Ringer and K. Hono. Microstructural Evolution and Age Hardening in Aluminium Alloys:Atom Probe Field-Ion Microscopy and Transmission Electron Microscopy Studies. MaterialsCharacterization, 44(1):101–131, January 2000. → pages 7, 13, 19[31] H. S. Zurob, C. R. Hutchinson, Y. Brechet, and G. Purdy. Modeling recrystallization ofmicroalloyed austenite: effect of coupling recovery, precipitation and recrystallization. Actamaterialia, 50(12):3077–3094, 2002. → pages 8, 20, 22, 24[32] E. Nes. Recovery revisited. Acta Metallurgica et Materialia, 43(6):2189–2207, June 1995. → pages8, 9, 10, 11, 58, 59[33] F. J. Humphreys and M. Hatherly. Chapter 2 - The Deformed State. In F. J. Humphreys andM. Hatherly, editors, Recrystallization and Related Annealing Phenomena (Second Edition), pages11–II. Elsevier, Oxford, 2004. → pages 8, 9, 10[34] W. J. Poole, M. Militzer, and M. A. Wells. Modelling recovery and recrystallisation duringannealing of AA 5754 aluminium alloy. Materials Science & Technology, 19(10):1361–1368,October 2003. → pages 8, 9, 11, 21[35] F. J. Humphreys and M. Hatherly. Recrystallization and Related Annealing Phenomena. Pergamon,Amsterdam, NLD, 2004. → pages 8, 10, 59[36] Ole Runar Myhr, ystein Grong, and Ketill Olav Pedersen. A Combined Precipitation, YieldStrength, and Work Hardening Model for Al-Mg-Si Alloys. Metallurgical and MaterialsTransactions A, 41(9):2276–2289, September 2010. → pages 11[37] M. Verdier, Y. Brechet, and P. Guyot. Recovery of AlMg alloys: flow stress and strain-hardeningproperties. Acta materialia, 47(1):127–134, 1998. → pages 11, 28, 58[38] Gaosong Yi, David A. Cullen, Kenneth C. Littrell, William Golumbfskie, Erik Sundberg, andMichael L. Free. Characterization of Al-Mg Alloy Aged at Low Temperatures. Metallurgical andMaterials Transactions A, 48(4):2040–2050, April 2017. → pages 11[39] M. J. Starink and A.-M. Zahra. Low-temperature decomposition of Al-Mg alloys: Guinier-Prestonzones and L12 ordered precipitates. Philosophical Magazine A, 76(3):701–714, September 1997.→ pages 11, 12102[40] T. Sato, Y. Kojima, and T. Takahashi. Modulated structures and GP Zones in Al-Mg Alloys.Metallurgical Transactions A, 13(8):1373–1378, August 1982. → pages 11, 12[41] Kozo Osamura and Tetsuzo Ogura. Metastable phases in the early stage of precipitation in Al-Mgalloys. Metallurgical Transactions A, 15(5):835–842, May 1984. → pages 11[42] M. Roth and J. M. Raynal. Small-angle neutron scattering by GuinierPreston zones in AlMg alloys.Journal of Applied Crystallography, 7(2):219–221, April 1974. → pages 11[43] Gaosong Yi, Weizhi Zeng, Jonathan D. Poplawsky, David A. Cullen, Zhifen Wang, and Michael L.Free. Characterizing and modeling the precipitation of Mg-rich phases in Al 5xxx alloys aged at lowtemperatures. Journal of Materials Science & Technology, February 2017. → pages 12[44] Paul Dyer Merica, Alfred Nelson Finn, and Romaine George Waltenberg. Mechanical propertiesand resistance to corrosion of rolled light alloys of aluminum and magnesium with copper, withnickel, and with manganese, volume 132. Washington, D.C. : U.S. Dept. of Commerce, Bureau ofStandards, United States, 1919. → pages 12[45] M. J. Styles, C. R. Hutchinson, Y. Chen, A. Deschamps, and T. J. Bastow. The coexistence of two S(Al2cumg) phases in AlCuMg alloys. Acta Materialia, 60(20):6940–6951, December 2012.→ pages 13, 14, 21[46] A. Deschamps, T.J. Bastow, F. de Geuser, A.J. Hill, and C.R. Hutchinson. In situ evaluation of themicrostructure evolution during rapid hardening of an Al2.5cu1.5mg (wt.%) alloy. Acta Materialia,59(8):2918–2927, May 2011. → pages 13, 17, 47, 48[47] R.K.W. Marceau, G. Sha, R. Ferragut, A. Dupasquier, and S.P. Ringer. Solute clustering in AlCuMgalloys during the early stages of elevated temperature ageing. Acta Materialia, 58(15):4923–4939,September 2010. → pages 13, 14, 16, 17, 46, 47, 48, 65[48] I. J. Polmear. Aluminum Alloys - A Century of Age Hardening. Materials Forum, 28:1–14, 2004.→ pages 13[49] L. Kovarik and M. J. Mills. Ab initio analysis of GuinierPrestonBagaryatsky zone nucleation inAlCuMg alloys. Acta Materialia, 60(9):3861–3872, May 2012. → pages 15, 16, 17, 65[50] L. Reich, S.P. Ringer, and K. Hono. Origin of the initial rapid age hardening in an Al-1.7 at.%Mg-1.1 at.% Cu alloy. Philosophical Magazine Letters, 79(9):639–648, 1999. → pages 17, 21[51] Y. Nagai, M. Murayama, Z. Tang, T. Nonaka, K. Hono, and M. Hasegawa. Role of vacancysolutecomplex in the initial rapid age hardening in an AlCuMg alloy. Acta materialia, 49(5):913–920,2001. → pages[52] A. Somoza, M. Petkov, K. Lynn, and A. Dupasquier. Stability of vacancies during solute clusteringin Al-Cu-based alloys. Physical Review B, 65(9), February 2002. → pages 13[53] Y. Bagaryatsky. Doklady Akademii SSSR, 87:559–562, 1952. → pages 13[54] J.M. Silcock. The structural ageing characteristics of aluminum-copper-lithium alloys. J. Inst.Metals, 88:203 – 214, 1960. → pages 13, 14, 15103[55] G. B. Winkelman, K. Raviprasad, and B. C. Muddle. Orientation relationships and lattice matchingfor the S phase in AlCuMg alloys. Acta Materialia, 55(9):3213–3228, May 2007. → pages 14[56] S.C. Wang and M.J. Starink. Two types of S phase precipitates in AlCuMg alloys. Acta Materialia,55(3):933–941, February 2007. → pages[57] L. Kovarik, M. K. Miller, S. A. Court, and M. J. Mills. Origin of the modified orientationrelationship for S(S)-phase in AlMgCu alloys. Acta Materialia, 54(7):1731–1740, April 2006.→ pages 14, 15[58] S. C. Wang and M. J. Starink. The assessment of GPB2/S structures in AlCuMg alloys. MaterialsScience and Engineering: A, 386(1):156–163, November 2004. → pages 14[59] S.C. Wang, M.J. Starink, and N. Gao. Precipitation hardening in AlCuMg alloys revisited. ScriptaMaterialia, 54(2):287–291, January 2006. → pages 14[60] Petar Ratchev, Bert Verlinden, Peter De Smet, and Paul Van Houtte. Precipitation hardening of anAl4.2 wt% Mg0.6 wt% Cu alloy. Acta materialia, 46(10):3523–3533, 1998. → pages 15, 19, 21, 22,33, 54, 63, 64[61] L. Kovarik, P. I. Gouma, C. Kisielowski, S. A. Court, and M. J. Mills. A HRTEM study ofmetastable phase formation in AlMgCu alloys during artificial aging. Acta Materialia,52(9):2509–2520, May 2004. → pages 15, 19[62] A. Charai, T. Walther, C. Alfonso, A. M. Zahra, and C. Y. Zahra. Coexistence of clusters, GPBzones, S-, S- and S-phases in an Al0.9% Cu1.4% Mg alloy. Acta Materialia, 48(10):2751–2764,June 2000. → pages 15, 16[63] G. Sha, R.K.W. Marceau, X. Gao, B.C. Muddle, and S.P. Ringer. Nanostructure of aluminium alloy2024: Segregation, clustering and precipitation processes. Acta Materialia, 59(4):1659–1670,February 2011. → pages 15, 16, 17, 38, 47, 48, 52[64] L. Kovarik and M. J. Mills. Structural relationship between one-dimensional crystals ofGuinierPrestonBagaryatsky zones in AlCuMg alloys. Scripta Materialia, 64(11):999–1002, June2011. → pages 15[65] Baptiste Gault, Michael P. Moody, Julie M. Cairney, and Simon P. Ringer. Atom Probe Microscopy,volume 160 of Springer Series in Materials Science. Springer New York, New York, NY, 2012.→ pages 15, 31, 40[66] Emmanuelle A. Marquis and Jonathan M. Hyde. Applications of atom-probe tomography to thecharacterisation of solute behaviours. Materials Science and Engineering: R: Reports, 69(4):37–62,July 2010. → pages 15, 40[67] Simon P. Ringer, Kazuhiro Hono, Toshio Sakurai, and Ian J. Polmear. Cluster hardening in an agedAl-Cu-Mg alloy. Scripta Materialia, 36(5):517–521, March 1997. → pages 15[68] S. P. Ringer, T. Sakurai, and I. J. Polmear. Origins of hardening in aged AlGuMg(Ag) alloys. ActaMaterialia, 45(9):3731–3744, September 1997. → pages 16104[69] R.K.W. Marceau, G. Sha, R.N. Lumley, and S.P. Ringer. Evolution of solute clustering in AlCuMgalloys during secondary ageing. Acta Materialia, 58(5):1795–1805, March 2010. → pages 16[70] Baptiste Gault, Xiang Yuan Cui, Michael P. Moody, Anna V. Ceguerra, Andrew J. Breen, RossK. W. Marceau, and Simon P. Ringer. A nexus between 3d atomistic data hybrids derived from atomprobe microscopy and computational materials science: A new analysis of solute clustering inAl-alloys. Scripta Materialia, 131:93–97, April 2017. → pages 18, 65[71] M. J. Starink *, N. Gao, L. Davin, J. Yan, and A. Cerezo. Room temperature precipitation inquenched AlCuMg alloys: a model for the reaction kinetics and yield strength development.Philosophical Magazine, 85(13):1395–1417, May 2005. → pages 16[72] A. Dupasquier, G. Kgel, and A. Somoza. Studies of light alloys by positron annihilation techniques.Acta Materialia, 52(16):4707–4726, September 2004. → pages 16, 17[73] M. D. H. Lay, H. S. Zurob, C. R. Hutchinson, T. J. Bastow, and A. J. Hill. Vacancy Behavior andSolute Cluster Growth During Natural Aging of an Al-Mg-Si Alloy. Metallurgical and MaterialsTransactions A, 43(12):4507–4513, December 2012. → pages[74] Hossein Seyedrezai, Dmitrij Grebennikov, Peter Mascher, and Hatem S. Zurob. Study of the earlystages of clustering in AlMgSi alloys using the electrical resistivity measurements. MaterialsScience and Engineering: A, 525(12):186–191, November 2009. → pages 17[75] A. M Zahra, C. Y Zahra, C Alfonso, and A Chara. Comments on cluster hardening in an agedAl-Cu-Mg alloy. Scripta Materialia, 39(11):1553–1558, November 1998. → pages 17[76] A.-M. Zahra, C. Y. Zahra, and B. Verlinden. Comments on Room-temperature precipitation inquenched AlCuMg alloys: a model for the reaction kinetics and yield-strength development.Philosophical Magazine Letters, 86(4):235–242, April 2006. → pages 17[77] T. Komatsubara, T. Muramatsu, and M. Matsuo. Production process for aluminium alloy rolledsheet, May 1990. Skyaluminium Co Ltd EP Patent App. EP19,870,112,409. → pages 18[78] Mohammed A. Omar. Automotive Painting. In The Automotive Body Manufacturing Systems andProcesses, pages 177–226. John Wiley & Sons, Ltd, 2011. → pages 18[79] Olaf Engler, Calin D. Marioara, Thomas Hentschel, and Henk-Jan Brinkman. Influence of copperadditions on materials properties and corrosion behaviour of AlMg alloy sheet. Journal of Alloysand Compounds, 710:650–662, July 2017. → pages 18, 53[80] G. B. Burger, A. K. Gupta, P. W. Jeffrey, and D. J. Lloyd. Microstructural control of aluminum sheetused in automotive applications. Materials Characterization, 35(1):23–39, July 1995. → pages 18,53[81] Mami Mihara, Calin D. Marioara, Sigmund J. Andersen, Randi Holmestad, Equo Kobayashi, andTatsuo Sato. Precipitation in an AlMgCu alloy and the effect of a low amount of Ag. MaterialsScience and Engineering: A, 658:91–98, March 2016. → pages 19[82] C. Macchi, A. Tolley, R. Giovachini, I. J. Polmear, and A. Somoza. Influence of a microalloyingaddition of Ag on the precipitation kinetics of an AlCuMg alloy with high Mg:Cu ratio. ActaMaterialia, 98:275–287, October 2015. → pages 19105[83] J. H. Auld, J. T. Vietz, and I. J. Polmear. T-phase Precipitation induced by the Addition of Silver toan AluminiumCopperMagnesium Alloy. Nature, 209(5024):703–704, February 1966. → pages 19[84] P Ratchev, B Verlinden, P De Smet, and P Van Houtte. Effect of Cooling Rate and Predeformationon the Precipitation Hardening of an Al-4.2wt.%Mg-0.6wt.%Cu Alloy. Scripta Materialia,38(8):1195–1201, March 1998. → pages 19, 21[85] P. I Gouma, D. J Lloyd, and M. J Mills. Precipitation processes in AlMgCu alloys. MaterialsScience and Engineering: A, 319321:439–442, December 2001. → pages[86] L. Kovarik, P. I. Gouma, C. Kisielowski, S. A. Court, and M. J. Mills. Decomposition of an AlMgCualloya high resolution transmission electron microscopy investigation. Materials Science andEngineering: A, 387389:326–330, December 2004. → pages 19[87] F. C. Larch. Nucleation and Precipitation on Dislocations. In F. R. N. Nabarro, editor, Dislocationsin solids, volume 4, pages 134–153. North-Holland Pub. Co. ; sole distributors for the USA andCanada, Elsevier North-Holland, Amsterdam ; New York : New York, 1979. → pages 20[88] Christopher Hutchinson. Modeling the kinetics of precipitation processes in aluminium alloys. InRoger Lumley, editor, Fundamentals of aluminium metallurgy: Production, processing andapplications, pages 422–467. Woodhead Publishing Limited, UK, 2010. → pages 20, 49[89] John W. Cahn. Nucleation on dislocations. Acta Metallurgica, 5(3):169 – 172, 1957. → pages 20[90] Z. M. Wang and G. J. Shiflet. Heterogeneous nucleation of on dislocations in a dilutealuminum-lithium alloy. Metallurgical and Materials Transactions A, 27(6):1599–1609, June 1996.→ pages 20[91] F. Perrard, A. Deschamps, and P. Maugis. Modelling the precipitation of NbC on dislocations in -Fe.Acta Materialia, 55(4):1255–1266, February 2007. → pages 20[92] J. D. Robson, M. J. Jones, and P. B. Prangnell. Extension of the N-model to predict competinghomogeneous and heterogeneous precipitation in Al-Sc alloys. Acta Materialia, 51(5):1453–1468,March 2003. → pages 20[93] A. H. Cottrell and B. A. Bilby. Dislocation Theory of Yielding and Strain Ageing of Iron.Proceedings of the Physical Society. Section A, 62(1):49, 1949. → pages 20[94] S. Q. Xiao and P. Haasen. A model for the nucleation of a spherical coherent precipitate near anedge dislocation. Scripta Metallurgica, 23(3):365–370, March 1989. → pages 20[95] S. Q. Xiao, P. J. Wilbrandt, and P. Haasen. HREM observation of the nucleation of -precipitates atdislocations in a Ni-12at%Al alloy. Scripta Metallurgica, 23(3):295–300, March 1989. → pages 20[96] Vahid Fallah, Jonathan Stolle, Nana Ofori-Opoku, Shahrzad Esmaeili, and Nikolas Provatas.Phase-field crystal modeling of early stage clustering and precipitation in metal alloys. PhysicalReview B, 86(13):134112, October 2012. → pages 20[97] S. Y. Hu and L. Q. Chen. Solute segregation and coherent nucleation and growth near a dislocationaphase-field model integrating defect and phase microstructures. Acta Materialia, 49(3):463–472,February 2001. → pages106[98] E. Dontsova, J. Rottler, and C. W. Sinclair. Solute segregation kinetics and dislocation depinning ina binary alloy. Physical Review B, 91(22):224103, June 2015. → pages 20, 84, 89[99] M. Militzer, W. P. Sun, and J. J. Jonas. Modelling the effect of deformation-induced vacancies onsegregation and precipitation. Acta Metallurgica et Materialia, 42(1):133–141, January 1994.→ pages 20, 21, 65, 66[100] A. Deschamps, G. Fribourg, Y. Brchet, J.L. Chemin, and C.R. Hutchinson. In situ evaluation ofdynamic precipitation during plastic straining of an AlZnMgCu alloy. Acta Materialia,60(5):1905–1916, March 2012. → pages 21, 65[101] C. R. Hutchinson, F. de Geuser, Y. Chen, and A. Deschamps. Quantitative measurements ofdynamic precipitation during fatigue of an AlZnMg(Cu) alloy using small-angle X-ray scattering.Acta Materialia, 74:96–109, August 2014. → pages 21, 65, 68[102] W. Z. Han, Y. Chen, A. Vinogradov, and C. R. Hutchinson. Dynamic precipitation during cyclicdeformation of an underaged AlCu alloy. Materials Science and Engineering: A,528(24):7410–7416, September 2011. → pages 20[103] Z. M. Wang and G. J. Shiflet. Growth of on dislocations in a dilute Al-Li alloy. Metallurgical andMaterials Transactions A, 29(8):2073–2085, August 1998. → pages 20, 21[104] Derek Hull and D. J. Bacon. Introduction to dislocations. Butterworth-Heinemann, Oxford ;Burlington, MA, 5th ed edition, 2011. OCLC: ocn704891549. → pages 21[105] H. Mecking and Y. Estrin. The effect of vacancy generation on plastic deformation. ScriptaMetallurgica, 14(7):815–819, July 1980. → pages 21, 65, 68[106] R. W. Balluffi and A. L. Ruoff. On Strain-Enhanced Diffusion in Metals. I. Point Defect Models.Journal of Applied Physics, 34(6):1634, 1963. → pages 21[107] R. Bullough and R. C. Newman. The kinetics of migration of point defects to dislocations. Reportson Progress in Physics, 33(1):101, 1970. → pages 21[108] Emmanuel Clouet. The vacancyedge dislocation interaction in fcc metals: A comparison betweenatomic simulations and elasticity theory. Acta Materialia, 54(13):3543–3552, August 2006.→ pages[109] F. D. Fischer, J. Svoboda, F. Appel, and E. Kozeschnik. Modeling of excess vacancy annihilation atdifferent types of sinks. Acta Materialia, 59(9):3463–3472, May 2011. → pages 21, 69, 70[110] J. D Embury and R. B Nicholson. The nucleation of precipitates: The system Al-Zn-Mg. ActaMetallurgica, 13(4):403–417, April 1965. → pages 21[111] A. Deschamps, F. Livet, and Y. Brchet. Influence of predeformation on ageing in an AlZnMg alloyI.Microstructure evolution and mechanical properties. Acta Materialia, 47(1):281–292, December1998. → pages 21, 24, 45, 49, 51, 65[112] Ole Runar Myhr, ystein Grong, and Carmen Schfer. An Extended Age-Hardening Model forAl-Mg-Si Alloys Incorporating the Room-Temperature Storage and Cold Deformation ProcessStages. Metallurgical and Materials Transactions A, 46(12):6018–6039, December 2015. → pages21, 24107[113] G. P. Purja Pun and Y. Mishin. A molecular dynamics study of self-diffusion in the cores of screwand edge dislocations in aluminum. Acta Materialia, 57(18):5531–5542, October 2009. → pages 21[114] Z. Xu and R. C. Picu. Dislocationsolute cluster interaction in AlMg binary alloys. Modelling andSimulation in Materials Science and Engineering, 14(2):195, 2006. → pages 21[115] Ccile Genevois, Damien Fabrgue, Alexis Deschamps, and Warren J. Poole. On the coupling betweenprecipitation and plastic deformation in relation with friction stir welding of AA2024 T3 aluminiumalloy. Materials Science and Engineering: A, 441(12):39–48, December 2006. → pages 21[116] R. N Wilson and P. G Partridge. The nucleation and growth of S’ precipitates in an aluminium-2.5%copper-1.2% magnesium alloy. Acta Metallurgica, 13(12):1321–1327, December 1965. → pages 21[117] D. Shao, P. Zhang, J. Y. Zhang, G. Liu, R. H. Wang, W. Q. Liu, G. Sha, and J. Sun. Effect ofPre-strain on the Solute Clustering, Mechanical Properties, and Work-Hardening of a NaturallyAged Al-Cu-Mg Alloy. Metallurgical and Materials Transactions A, 48(9):4121–4134, September2017. → pages 21[118] A. Serizawa, T. Sato, and M. K. Miller. Effect of cold rolling on the formation and distribution ofnanoclusters during pre-aging in an AlMgSi alloy. Materials Science and Engineering: A,561:492–497, January 2013. → pages 21, 65[119] K. Teichmann, C.d. Marioara, S.j. Andersen, K.o. Pedersen, S. Gulbrandsen-Dahl, M. Kolar,R. Holmestad, and K. Marthinsen. HRTEM study of the effect of deformation on the earlyprecipitation behaviour in an AA6060 AlMgSi alloy. Philosophical Magazine, 91(28):3744–3754,October 2011. → pages 21, 65[120] R. Roumina and C. W. Sinclair. Recovery kinetics in the presence of precipitates: The softeningresponse of an AlMgSc alloy. Acta Materialia, 58(1):111–121, January 2010. → pages 22, 23, 24,45, 67, 90[121] J. Rsler and E. Arzt. The kinetics of dislocation climb over hard particlesI. Climb without attractiveparticle-dislocation interaction. Acta Metallurgica, 36(4):1043–1051, April 1988. → pages 23[122] Z. Zhu and M.J. Starink. Age hardening and softening in cold-rolled AlMgMn alloys with up to0.4wt% Cu. Materials Science and Engineering: A, 489(1-2):138–149, August 2008. → pages 24[123] Katharina Teichmann, Calin D. Marioara, Sigmund J. Andersen, and Knut Marthinsen. The Effectof Preaging Deformation on the Precipitation Behavior of an Al-Mg-Si Alloy. Metallurgical andMaterials Transactions A, 43(11):4006–4014, November 2012. → pages 24[124] Mojan Sohi. Aging behavior of flexcast Al-Mg alloys with Sc and Zr additions. PhD thesis, TheUniversity of British Columbia, Vancouver, British Columbia, Canada, 2012. Graduate. → pages 26[125] R. Roumina and C. W. Sinclair. The Work Hardening Rate of an Aged and Recovered Al-Mg-ScAlloy. Metallurgical and Materials Transactions A, 42(2):473–487, February 2011. → pages 27, 28[126] Zhijie Xu and R. C. Picu. Effect of residual and pre-existing solute clusters on dynamic strainageing in dilute solid solutions. Modelling and Simulation in Materials Science and Engineering,15(5):385, July 2007. → pages 28108[127] Alexis Deschamps. Analytical Techniques for Aluminum. In Handbook of Aluminum. CRC Press,April 2003. → pages 29, 32, 37, 117[128] Shahrzad Esmaeili. Precipitation hardening behaviour of AA6111. PhD thesis, University of BritishColumbia, 2002. → pages 30[129] John R. Taylor. An introduction to error analysis: the study of uncertainties in physicalmeasurements. Series of books in physics. University Science Books, Mill Valley, Calif, 1982.→ pages 30[130] Rosen Ivanov. Solute clustering in multi-component aluminium alloys. phdthesis, UniversitGrenoble Alpes, February 2017. → pages 30[131] M. K. Miller. Atom Probe Tomography. Springer US, Boston, MA, 2000. → pages 31[132] Mami Mihara, Equo Kobayashi, and Tatsuo Sato. Effects of the Pre-Aging Period on the FormationBehavior of Nanoclusters in an Al-Mg-Cu Alloy. Materials Transactions, 56(4):500–506, 2015.→ pages 33, 54[133] Peter Ratchev, Bert Verlinden, Peter De Smet, and Paul Van Houtte. Artificial Ageing of Al-Mg-CuAlloys. Materials Transactions, JIM, 40(1):34–41, 1999. → pages 34, 49[134] B. Raeisinia, W. J. Poole, and D. J. Lloyd. Examination of precipitation in the aluminum alloyAA6111 using electrical resistivity measurements. Materials Science and Engineering: A,420(12):245–249, March 2006. → pages 37, 67, 117[135] S. Esmaeili, D. Vaumousse, M. W. Zandbergen, W. J. Poole, A. Cerezo, and D. J. Lloyd. A study onthe early-stage decomposition in the AlMgSiCu alloy AA6111 by electrical resistivity andthree-dimensional atom probe. Philosophical Magazine, 87(25):3797–3816, 2007. → pages 37[136] A. J. Hillel and P. L. Rossiter. Resistivity mechanisms during clustering in alloys. PhilosophicalMagazine B, 44(3):383–388, September 1981. → pages 37[137] M. Rosen, E. Horowitz, L. Swartzendruber, S. Fick, and R. Mehrabian. The aging process inaluminum alloy 2024 studied by means of eddy currents. Materials Science and Engineering,53(2):191–198, May 1982. → pages 37[138] Han-Cheng Shih, New-Jin Ho, and J. C. Huang. Precipitation behaviors in Al-Cu-Mg and 2024aluminum alloys. Metallurgical and Materials Transactions A, 27(9):2479–2494, 1996. → pages37, 64, 65[139] T. Philippe, S. Duguay, and D. Blavette. Clustering and pair correlation function in atom probetomography. Ultramicroscopy, 110(7):862–865, June 2010. → pages 40[140] Laurent Couturier, Frdric De Geuser, and Alexis Deschamps. Direct comparison of Fe-Cr unmixingcharacterization by atom probe tomography and small angle scattering. Materials Characterization,121:61–67, November 2016. → pages 40[141] Huan Zhao, Baptiste Gault, Dirk Ponge, Dierk Raabe, and Frdric De Geuser. Parameter freequantitative analysis of atom probe data by correlation functions: Application to the precipitation inAl-Zn-Mg-Cu. Scripta Materialia, 154:106–110, September 2018. → pages 40109[142] R. Ivanov, A. Deschamps, and F. De Geuser. A combined characterization of clusters in naturallyaged AlCu(Li, Mg) alloys using small-angle neutron and X-ray scattering and atom probetomography. Journal of Applied Crystallography, 50(6):1725–1734, December 2017. → pages 40[143] F. De Geuser, W. Lefebvre, and D. Blavette. 3d atom probe study of solute atoms clustering duringnatural ageing and pre-ageing of an Al-Mg-Si alloy. Philosophical Magazine Letters,86(4):227–234, April 2006. → pages 40[144] P. Debye and A. M. Bueche. Scattering by an Inhomogeneous Solid. Journal of Applied Physics,20(6):518–525, June 1949. → pages 40[145] O. Glatter and O. Kratky, editors. Small angle x-ray scattering. Academic Press, London ; NewYork, 1982. → pages 40[146] Andr Guinier and Grard Fournet. Small-angle scattering of X-rays. Structure of matter. Wiley, NewYork, 1955. → pages 40[147] Kozo Osamura, Naotaka Otsuka, and Yotaro Murakami. Resistivity maximum duringGuinier-Preston zone formation in an Al-4 wt% Cu alloy. Philosophical Magazine B,45(6):583–599, June 1982. → pages 43[148] Shoichi Hirosawa, Tatsuo Sato, Junichi Yokota, and Akihiko Kamio. Comparison betweenResistivity Changes and Monte Carlo Simulation for GP Zone Formation in Al&ndash;Cu BaseTernary Alloys. Materials Transactions, JIM, 39(1):139–146, 1998. → pages 43[149] F. Fazeli, W. J. Poole, and C. W. Sinclair. Modeling the effect of Al3sc precipitates on the yieldstress and work hardening of an AlMgSc alloy. Acta Materialia, 56(9):1909–1918, May 2008.→ pages 45, 47, 91[150] R. K. W. Marceau, A. de Vaucorbeil, G. Sha, S. P. Ringer, and W. J. Poole. Analysis ofstrengthening in AA6111 during the early stages of aging: Atom probe tomography and yield stressmodelling. Acta Materialia, 61(19):7285–7303, November 2013. → pages 45[151] Adrian Baddeley and Eva B. Vedel Jensen. Stereology for Statisticians. CRC Press, November2004. → pages 45[152] M. Jobba, R. K. Mishra, and M. Niewczas. Flow stress and work-hardening behaviour of AlMgbinary alloys. International Journal of Plasticity, 65:43–60, February 2015. → pages 45, 67, 80[153] L.M. Brown and R.K. Ham. Dislocationparticle interactions. In A. Kelly and Robin Nicholson,editors, Strengthening methods in crystals, Elsevier materials science series, pages 12–135. JohnWiley, Amsterdam, New York, 1971. OCLC: ocm258398. → pages 45[154] A. de Vaucorbeil, W. J. Poole, and C. W. Sinclair. The superposition of strengthening contributionsin engineering alloys. Materials Science and Engineering: A, 582:147–154, October 2013. → pages46, 47, 59, 83[155] O. R Myhr, Grong, and S. J Andersen. Modelling of the age hardening behaviour of AlMgSi alloys.Acta Materialia, 49(1):65–75, January 2001. → pages 46110[156] H. R. Shercliff and M. F. Ashby. A process model for age hardening of aluminium alloysI. Themodel. Acta Metallurgica et Materialia, 38(10):1789–1802, October 1990. → pages 49, 50[157] Richard Wagner, Reinhard Kampmann, and Peter W. Voorhees. Homogeneous Second-PhasePrecipitation. In Phase Transformations in Materials, pages 309–407. Wiley-VCH Verlag GmbH &Co. KGaA, 2005. → pages 49[158] R.K.W. Marceau, N. Tsafnat, D. Haley, and S.P. Ringer. Solute Diffusion Characteristics of a RapidHardening Al-Cu-Mg Alloy during the Early Stages of Age Hardening. Metallurgical and MaterialsTransactions A, 41(8):1887–1890, August 2010. → pages 51, 65[159] S. Sarkar, M.A. Wells, and W.J. Poole. Softening behaviour of cold rolled continuous cast and ingotcast aluminum alloy AA5754. Materials Science and Engineering: A, 421(1-2):276–285, April2006. → pages 55[160] Miljana Popovi and Endre Romhanji. Characterization of microstructural changes in an Al-6.8wt.%Mg alloy by electrical resistivity measurements. Materials Science and Engineering: A,492(1):460–467, September 2008. → pages[161] B. Raeisinia and Warren J. Poole. Electrical Resistivity Measurements: A Sensitive Tool forStudying Aluminium Alloys. Materials Science Forum, 519-521:1391–1396, 2006. → pages 55[162] M. Verdier, I. Groma, L. Flandin, J. Lendvai, Y. Brchet, and P. Guyot. Dislocation densities andstored energy after cold rolling of Al-Mg alloys: Investigations by resistivity and differentialscanning calorimetry. Scripta Materialia, 37(4):449–454, August 1997. → pages 56[163] M. Verdier, M. Janecek, Y. Brchet, and P. Guyot. Microstructural evolution during recovery inAl2.5%Mg alloys. Materials Science and Engineering: A, 248(12):187–197, June 1998. → pages 59[164] J. Schmidt and F. Haener. Stage III-recovery of cold worked high-purity aluminium determined witha low-temperature calorimeter. Zeitschrift fr Physik B Condensed Matter, 81(2):215–222, June1990. → pages 59[165] Vicente Araullo-Peters, Baptiste Gault, Frederic de Geuser, Alexis Deschamps, and Julie M.Cairney. Microstructural evolution during ageing of AlCuLix alloys. Acta Materialia, 66:199–208,March 2014. → pages 61, 63[166] H. Aboulfadl, J. Deges, P. Choi, and D. Raabe. Dynamic strain aging studied at the atomic scale.Acta Materialia, 86:34–42, March 2015. → pages 63[167] H.S. Zurob and H. Seyedrezai. A model for the growth of solute clusters based on vacancy trapping.Scripta Materialia, 61(2):141–144, July 2009. → pages 65[168] S. Pogatscher, H. Antrekowitsch, H. Leitner, T. Ebner, and P. J. Uggowitzer. Mechanisms controllingthe artificial aging of AlMgSi Alloys. Acta Materialia, 59(9):3352–3363, May 2011. → pages 65[169] G.F. Bolling and D Fainstein. Vacancy condensation and origin of dislocations in growth from melt.PHILOSOPHICAL MAGAZINE, 25(1):45–45, January 1972. → pages 65[170] Wilfried Witzel. Vacancy production by thermal jogs during plastic deformation. WAA TranslationFrom- Z. Metallkd., 64(8):11, 1973. → pages 65111[171] F. R. Fickett. Aluminum1. A review of resistive mechanisms in aluminum. Cryogenics,11(5):349–367, October 1971. → pages 67[172] A. Deschamps, L. Le Sinq, Y. Brchet, J. D. Embury, and M. Niewczas. Anomalous strain hardeningbehaviour of a supersaturated Al-Zn-Mg alloy. Materials Science and Engineering: A,234236:477–480, August 1997. → pages 67[173] R. O. Simmons and R. W. Balluffi. Measurements of equilibrium vacancy concentrations inaluminum. Physical Review, 117(1):52, 1960. → pages 68[174] Dan Mordehai, Emmanuel Clouet, Marc Fivel, and Marc Verdier. Introducing dislocation climb bybulk diffusion in discrete dislocation dynamics. Philosophical Magazine, 88(6):899–925, February2008. → pages 68, 69[175] U. F. Kocks and H. Mecking. Physics and phenomenology of strain hardening: the FCC case.Progress in Materials Science, 48(3):171–273, 2003. → pages 74, 75, 80[176] U. F. Kocks. Laws for Work-Hardening and Low-Temperature Creep. Journal of EngineeringMaterials and Technology, 98(1):76–85, January 1976. → pages 80[177] A. S. Krausz and K. Krausz, editors. Unified constitutive laws of plastic deformation. AcademicPress, San Diego, 1996. → pages 80, 83, 84[178] L. M. Cheng, W. J. Poole, J. D. Embury, and D. J. Lloyd. The influence of precipitation on thework-hardening behavior of the aluminum alloys AA6111 and AA7030. Metallurgical andMaterials Transactions A, 34(11):2473–2481, November 2003. → pages 80[179] E. O. Hall. Aluminium and Its Alloys. In Yield Point Phenomena in Metals and Alloys, pages171–200. Springer, Boston, MA, 1970. → pages 82[180] P Haasen and A Kelly. A yield phenomenon in face-centered cubic single crystals. ActaMetallurgica, 5(4):192–199, April 1957. → pages 82[181] M. J. Makin. Unloading Effects in Copper Single Crystals. Nature, 180(4600):1476, December1957. → pages[182] L.M. Brown. An interpretation of the HaasenKelly effect. Philosophical Magazine,90(31-32):4147–4152, November 2010. → pages 82[183] J. D. Baird. The effects of strain-ageing due to interstitial solutes on the mechanical properties ofmetals. Metallurgical Reviews, 16(1):1–18, January 1971. → pages 82[184] L. P. Kubin, Y. Estrin, and C. Perrier. On static strain ageing. Acta Metallurgica et Materialia,40(5):1037–1044, May 1992. → pages 82[185] H. J. Frost and M. F. Ashby. Deformation-mechanism maps. Pergamon Press, Oxford [Oxfordshire]; New York, 1st ed. – edition, 1982. → pages 83[186] L. P. Kubin and Y. Estrin. Evolution of dislocation densities and the critical conditions for thePortevin-Le Chtelier effect. Acta Metallurgica et Materialia, 38(5):697–708, May 1990. → pages 84112[187] M. F. Ashby. The deformation of plastically non-homogeneous materials. The PhilosophicalMagazine: A Journal of Theoretical Experimental and Applied Physics, 21(170):399–424, February1970. → pages 85[188] A. Kelly and Robin Nicholson. Strengthening methods in crystals. Elsevier materials science series.Elsevier Pub. Co, Amsterdam, New York, 1971. OCLC: ocm258398. → pages 85[189] C. R. Hutchinson. Modeling the kinetics of precipitation in aluminium alloys. In Roger Lumley,editor, Fundamentals of Aluminium Metallurgy, Woodhead Publishing Series in Metals and SurfaceEngineering, pages 422–467. Woodhead Publishing, 2011. → pages 99[190] Katsuya Matsumoto, Shin-ya Komatsu, Masahiko Ikeda, Bert Verlinden, and Pieter Ratchev.Quantification of Volume Fraction of Precipitates in an Aged Al-1.0 mass%Mg2si Alloy. MaterialsTransactions, JIM, 41(10):1275–1281, 2000. → pages 117[191] F. De Geuser and W. Lefebvre. Determination of matrix composition based on solute-solutenearest-neighbor distances in atom probe tomography. Microscopy Research and Technique,74(3):257–263, February 2011. → pages 122113Appendix ANo Deformed Al-Mg-Cu alloy:Complementary MechanicalCharacterization DataThe full set of stress vs. strain and Kocks-Mecking plots, corresponding to the Al-3.23 at.%-0.23 at.%Cualloy, aged at 200 and 160 ◦C, are shown next.Figure A.1: Stress vs. strain evolution of Al-3.23 at.%-0.23 at.%Cu alloy during artificial aging at200 oC,114Figure A.2: Kocks-Mecking plot evolution of Al-3.23 at.%-0.23 at.%Cu alloy during artificial agingat a) 200 oC,Figure A.3: Stress vs. strain evolution of Al-3.23 at.%-0.23 at.%Cu alloy during artificial aging at160 oC,115Figure A.4: Kocks-Mecking plot evolution of Al-3.23 at.%-0.23 at.%Cu alloy during artificial agingat a) 200 oC,116Appendix BResistivity in Solid Solution StateResistivity measurements after solid solution treatment were analyzed using the reported coefficients foralloying elements in solid solution in Al measured at 77K as the measurements performed in this thesiswork [190], assuming a resistivity behaviour as given by the Matthiessen’s rule [127], measured in theconditions and over the material described in the Methodology (Chapter 4). The same coefficients havebeen used in previous research performed in the same instrumentation as used in this work [134].The theoretical values are consistent with the experimentally obtained values (Table B.4), when no Fecontribution is accounted in solid solution. This is compatible with the presence of Fe rich constitutiveparticles (e.g. Al3Fe).Solute Concentration [at.%] Coefficient [nΩ m/at.%] Resistivity contribution [nΩ m]Mg 3.23 5.27 17.05Cu 0.229 7.98 1.83Fe 0.048 79.06 3.82Si 0.048 6.55 0.31Ti 0.008 55.63 0.47Ni - - -Mn - - -Zn - - -Cr - - -Al Balance - 2.29Total - Fe included 25.83Total - No Fe included 21.97Table B.1: Resistivity contributions from solute elements in solid solution in Al-3.23 at.% Mg-0.23at.%Cu alloy. The contribution of minor alloying elements is not considered.117Solute Concentration [at.%] Coefficient [nΩ m/at.%] Resistivity contribution [nΩ m]Mg 3.2 5.27 16.9Cu 0.115 7.98 0.92Fe 0.046 79.06 3.71Si 0.046 6.55 0.42Ti 0.007 55.63 0.42Ni - - -Mn - - -Zn - - -Cr - - -Al Balance - 2.29Total - Fe included 24.54Total - No Fe included 20.83Table B.2: Resistivity contributions from solute elements in solid solution in Al-3.2 at.% Mg - 0.12at.%Cu alloy. The contribution of minor alloying elements is not considered.Solute Concentration [at.%] Coefficient [nΩ m/at.%] Resistivity contribution [nΩ m]Mg 2.93 5.27 15.48Cu 0.0008 7.98 0.006Fe 0.031 79.06 2.47Si 0.044 6.55 0.28Ti 0.006 55.63 0.34Ni - - -Mn - - -Zn - - -Cr - - -Al Balance - 2.29Total - Fe included 20.89Total - No Fe included 18.42Table B.3: Resistivity contributions from solute elements in solid solution in Al-2.9 at.% Mg alloy.The contribution of minor alloying elements is not considered.118Alloy Mean Resistivity [nΩ m]Al -3.35 at.% Mg0.23 at.% Cu22.1 ± 0.18Al -3.2 at.% Mg0.12 at.% Cu21.4 ± 0.18Al -2.9 at.% Mg18.1 ± 0.19Table B.4: Average resistivity values experimentally obtained after solid solution treatment.119Appendix CRadial Distribution Function and PairCorrelation Function (PFC)The Radial Distribution Function (RDF) can be obtained directly from APT dataset, this function is definedas:gi j(r) =Ci j(r)C0, j(C.1)where Ci j is the average concentration of ”j” atoms located at a distance ”r” from a ”i” atom, and C0, j is theaverage concentration of ”j” atoms in the material. From here we will assume an isotropic system.From the definition of PCF given in Chapter 5 (Equation 5.1), we can appreciate the relationship betweenthe RDF and the PCF as,γi j (r) =C0,iCi j (r)−C0,iC0, j=gi j (r)c0, j−1(C.2)Furthermore, from Eq. 5.2, we can separate the composition and volume fraction contribution from thegeometrical contributions. Assuming that the RDF function is constructed from B solute atoms from thenearest neighbors (binary A-B system) contained in a volume dV (r ≈ 0), we can rewrite,γii (0) = γii (0) =gii (0)ci0−1 (C.3)Where gii (0) is only function of the local concentration and volume fraction. We can further define this,based on the weighted contribution of concentration contribution in dV as,giidVci0=p(β )CβdV + p(α)CαdVci0(C.4)Where p(β ) and p(α) are the probability of the volume dV of be located in the β phase and α phase,120respectively. These probabilities can be defined as,p(k) =NkBNB,k = (α,β ) (C.5)Where NkB is total number of B atoms in the k phase, and NB is the total number of B atoms in thematerial. We can express these probabilities in terms of the volume fraction as,p(k) =NkBNB=f kv CkNBC0, k = (α,β ) (C.6)Substituting in Eq. C.4 results in,giiCi0=( f βv C2β + fαv C2α)C20(C.7)From the definition given in Eq. C.3,γi−i (0) =giici0−1 =( f βv C2β + fαv C2α)C20−C20C20(C.8)This expression can be further simplified by taking advantage of the fact that C0 =Cβ fβv +Cα f αv , result-ing in:γi−i (0) =f βv f αv (Cβ −Cα)2C20(C.9)Which is Eq. 5.4, used in Section 5.1.5. The previous rationale can be extended for two solute compo-nents, giving origin to Eq.5.5 in the previously mentioned Section.121Appendix DPair Correlation Function FitAs mentioned in Section 5.1.5, the experimentally obtained pair correlation functions do not result pro-portional to each other, this compatible with the idea of different distributions of clusters contribution tothe constructed PCF’s. To tackle this problem, two PCF’s are proposed to be represent the experimentallyobtained PCF’s. Taking advantage of the capacity to separate the geometrical contribution γ0 (r), and thechemical contribution γi j (0), to the total PCF (Eq. 5.2), we can perform two separated fitting procedures.For the first case, the chemical contributions (γi j (0)), we propose a system of equations associated to eachexperimentally obtained γi j (r) as,γTotCuCu (0) = γD1CuCu (0)+ γD2CuCu (0)γTotMgMg (0) = γD1MgMg (0)+ γD2MgMg (0)γTotCuMg (0) = γD1CuMg (0)+ γD2CuMg (0)(D.1)Where D1 and D2 indicates distribution 1 and 2, respectively, and each γi j (0) is given by either Eq.5.4or Eq.5.4. The local matrix composition has been obtained from the APT datasets using the DIAM protocol[191], for both aging times.Each distribution is assumed to fulfill the mass balance within each proposed distribution, namely,1 = 0.8+CD1Cu +CD1Mg1 = 0.8+CD2Cu +CD2Mg(D.2)Where the assumption of a 80at.% concentration of Al in the cluster has been preserved.And, finally, from Eq. 5.6,γTotCuMg (0) =√γTotCuCu (0)γTotMgMg (0) (D.3)This proposed non-linear system of equations can be solved using a numerical equation solver routine.From this strategy, we are able to obtain the volume fraction and mean solute concentration of each proposedparticle size distribution.Regarding the geometrical contribution γ0 (r), a solution is obtained by simultaneously fitting the pair122correlation function obtained from the Cu-Cu, Mg-Mg, and Cu-Mg pairs, and using the previously obtainedγi j (0) values. This has been done by assuming a linear addition of the contribution of the two distributionas,γTot0CuCu (r) = γD1CuCu (0)γD10CuCu (r)+ γD2CuCu (0)γD20CuCu (r)γTot0MgMg (r) = γD1MgMg (0)γD10MgMg (r)+ γD2MgMg (0)γD20MgMg (r)γTot0CuMg (r) = γD1CuMg (0)γD10CuMg (r)+ γD2CuMg (0)γD20CuMg (r)(D.4)Where each population has considered to have a log-normal distribution as,γD(k)0i j (r) =∫ ∞0γD(k)0i j (r,R) f (R)dR (D.5)Where γD(k)0i j is given by Eq. 5.3 and f (R) is defined as,f (R) =1(2pi)1/2σRexp{−12(ln(R/Rm)σ)2} (D.6)From this general strategy, the median radius and the with of the two proposed distributions, can beobtained.123Appendix EResults of Al-Mg-Cu Alloy Pre-DeformedMaterial During Aging at 160 ◦CIn this appendix the resistivity and mechanical strength results, pertaining to the Al-3.23 at.% - 0.23 at.%Cusystem processed as in Chapter 6, and aged 160◦C, will be shown.The resistivity results for material with previous deformation are shown in Fig. E.1, these plotted along-side the aging response of the material starting from the as-solutionized state (figure E.1). As already notedfor the as-solutionized case, the aging times investigated where not sufficient to see the expected drop inresistivity at long times. Rather, one sees that all three conditions reach approximately the same level ofresistivity and remain nearly constant for the full length of aging, this being consistent with the behaviourshown above for 200◦C at times < 100 min (Fig. 6.2).Figure E.1: Resistivity evolution of Al-3.23 at.% - 0.23 at.%Cu alloy, artificially aged at 160 ◦C.124Figure E.2 shows the yield stress evolution of the pre-deformed material along with material where notlevel of level of pre-deformation has been applied. The results are analogous to the material artificiallyaged at 200C◦ (Fig. 6.4), namely, for material pre-deformed 44 MPa, the magnitude of the rapid hardeningeffect is significantly lower than in material with no pre-deformation, measured from the as-deformed value,while for the case of material pre-deformed 174 MPa, a quick drop in yield stress after the first 2 minutesof artificial aging can be observed. As in the case of material artificially aged at 200 ◦C, the yield stressevolution, during artificial aging, is plotted with parallel dashed lines for each of the aging curves, the slopeof these lines have been taken from the best fit to the as-solutionized material’s aging response. This revealsthat, despite the applied levels of pre-deformation, similar kinetics control the strengthening during aging.Figure E.2: Yield stress evolution of Al-3.23 at.% - 0.23 at.%Cu alloy, artificially aged at 160 ◦C.125Appendix FMechanical Analysis of Al-Mg-Cu System:Complementary ResultsIn this Appendix, the comparison between the experimentally obtained evolution of pre-deformed materialcompared to the modeled ones will be shown. The first section shows the.F.1 AA5252 alloy resultsIn this section results from the AA5252 alloy subjected to pre-deformation and later artificially aged will beshown126(a) (b)(c)Figure F.1: Experimental and modeled Kocks-Mecking representation of AA5252 (Al-2.94 at.% Mg)system, pre-deformed ∆σ= 44 MPa , during artificial aging at 160 ◦C.127(a) (b)(c)Figure F.2: Experimental and modeled Kocks-Mecking representation of AA5252 (Al-2.94 at.% Mg)system, pre-deformed ∆σ= 44 MPa , during artificial aging at 160 ◦C.128(a) (b)(c) (d)(e)Figure F.3: Experimental and modeled Kocks-Mecking representation of AA5252 (Al-2.94 at.% Mg)system, pre-deformed ∆σ= 44 MPa , during artificial aging at 160 ◦C.129(a) (b)(c)Figure F.4: Experimental and modeled Kocks-Mecking representation of AA5252 (Al-2.94 at.% Mg)system, pre-deformed ∆σ= 44 MPa , during artificial aging at 160 ◦C.130F.2 Al-3.23 at.% - 0.23 at.%Cu alloy resultsIn this section results from the Al-Mg-Cu alloys subjected to pre-deformation and later artificially aged willbe shown.(a) (b)(c) (d)(e)Figure F.5: Experimental vs modeled Kocks-Mecking plots resulting from the stress vs. strain data forAl-3.23 at.% - 0.23 at.%Cu alloy deformed ∆σ= 44 MPa (ε =2%), during artificial aging at 160◦C.131(a) (b)(c) (d)(e) (f)Figure F.6: Experimental vs modeled Kocks-Mecking plots resulting from the stress vs. strain data forAl-3.23 at.% - 0.23 at.%Cu alloy deformed ∆σ= 44 MPa (ε =2%), during artificial aging at 200◦C.132(a) (b)(c) (d)(e)Figure F.7: Experimental vs modeled Kocks-Mecking plots resulting from the stress vs. strain data forAl-3.23 at.% - 0.23 at.%Cu alloy deformed ∆σ= 174 MPa (ε =10%), during artificial aging at160 ◦C.133(a) (b)(c) (d)(e) (f)Figure F.8: Experimental vs modeled Kocks-Mecking plots resulting from the stress vs. strain data forAl-3.23 at.% - 0.23 at.%Cu alloy deformed ∆σ= 174 MPa (ε =10%), during artificial aging at200 ◦C.134

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