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Co-deformation of an aluminum zinc alloy Breakey, J.W. Matthew 2007

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Co-deformation of an Aluminum Zinc Alloy Processing and Mechanical Testing by J. W. Matthew Breakey B.Sc., University of Alberta, 2005 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF Master of Applied Science in The Faculty of Graduate Studies (Materials Engineering) The University Of British Columbia October, 2007 © J. W. Matthew Breakey 2007 Abstract In some systems, including copper niobium, it has been found that as the scale of the two phases decreases, there is an anomalous increase in strength. Mechanisms of this strengthening have been postulated, but a general theory has yet to be developed. A model system to study the co-deformation of fine scale materials was developed and characterized. An aluminum 18.5at.% zinc alloy was selected and discontinuously precipitated to produce 100% transformation and an interlamellar spacing of 240nm. The material was tested using strain rate jump tests to determine the temperature sensitivity, tensile tested to determine work hardening and the temperature sensitiv- ity, wire drawn to study the effect of large plastic deformation and finally tension compression tested to determine internal stresses. The bulk properties of the two phases are well known allowing for a detailed analysis of the composite properties when combined with the mechanical results. The material showed increased strength above the rule of mixture prediction from bulk properties due to a fine scale mi- crostructure . Although the lamellar material had a much higher strength than the rule of mixtures would predict, the overall strength of the alloy did not approach that of more conventional high strength aluminum alloys. The material was found to be temperature and rate dependent, with an increased work hardening rate as the temperature was decreased. Temperature was found to play a key role in the stress partitioning between the two phases. Temperature dependent relaxation processes lowered the stress partitioning between the hard and soft phases as the tempera- ture was increased. Therefore, stress relaxation must be minimized to maximize the strengthening found in fine scale materials. 1 1 Table of Contents Abstract  ^ii Table of Contents ^  iii List of Tables  vi List of Figures ^  vii Acknowledgments  x 1 Introduction  ^1 2 Literature Review ^ 4 2.1 Introduction ^ 4 2.2 Properties of Bulk Aluminum and Zinc ^ 5 2.2.1 Physical Properties of Zinc and Aluminum ^ 5 2.2.2 Deformation and Plasticity of Zinc ^ 6 2.2.3 Deformation and Plasticity of Aluminum ^ 7 2.2.4 Chemical Properties of the Aluminum Zinc System ^ 8 2.3 Discontinuous Precipitation in the Aluminum Zinc System ^ 8 2.3.1 Discontinuous Precipitation Mechanism ^s 2.3.2 Discontinuous Precipitation Kinetics ^  13 2.3.3 Experimental Observations on Discontinuous Precipitation in the Aluminum Zinc System ^  16 2.4 Strengthening of Co-deforming Two Phase Materials ^ 17 2.4.1 Theoretical Strength of Materials  18 2.4.2 Strengthening by Scale Refinement ^  19 2.4.3 Strengthening Mechanisms ^  19 2.5 Models of Strengthening Mechanisms  20 2.5.1 Hall-Fetch Relation^ 20 2.5.2 Dislocation Pile-up Model ^  21 2.5.3 Dislocation Source Model: Spitzig's Variation ^ 22 2.5.4 Strengthening by GNDs: Courtney et al. Variation ^ 23 2.5.5 Orowan Model ^  26 2.6 Internal Stresses in In-Situ Composite Materials^ 26 2.6.1 Elastic-Plastic Masing Model ^  27 2.6.2 Bauschinger Effect ^  29 iii Table of Contents 3 4 2.7^Summary ^ Scope and Objectives ^ Experimental Procedure 31 32 34 4.1 Introduction ^ 34 4.2 Material Fabrication ^ 34 4.2.1^Casting 34 4.2.2^Preparation of Aluminum Zinc Sheet ^ 35 4.2.3^Preparation of Aluminum Zinc Rod 37 4.2.4^Wire Drawing ^ 38 4.3 Material Characterization 38 4.3.1^Polishing and Etching ^ 38 4.3.2^Scanning and Transmission Electron Microscopy Sample Prepa- ration ^ 38 4.3.3^Metallography ^ 40 4.3.4^X-Ray Diffraction Analysis ^ 41 4.4 Mechanical Characterization 41 4.4.1^Sample Geometry ^ 41 4.4.2^Monotonic Tensile Tests 43 4.4.3^Tension Compression Tests ^ 43 4.4.4^Strain Rate Jump Tests 46 5 Results 47 5.1 The Discontinuous Precipitation Reaction ^ 47 5.1.1^Cast Microstructure ^ 47 5.1.2^Solutionization and Recrystallization 49 5.1.3^Kinetics of Transformation ^ 51 5.1.4^Microstructure and Lamellar Spacing ^ 51 5.1.5^Solute Content and Precipitate Volume Fraction ^ 55 5.2 Mechanical Properties ^ 57 5.2.1^Monotonic Tensile Tests ^ 57 5.2.2^Tension Compression Tests 61 5.2.3^Wire Drawing ^ 65 5.3 TEM Analysis of A1-18.5at.%Zn ^ 65 6 Discussion ^ 74 6.1 The Discontinuous Precipitation Reaction ^ 74 6.1.1^Kinetics and Diffusion Rate ^ 76 6.1.2^The Solute Content of the a Phase 79 6.2 Deformation Behavior of DP A1-18.5at.%Zn ^ 80 6.2.1^Monotonic Tensile Tests ^ 82 6.2.2^Composite Behavior: The In-Situ Matrix Stress ^ 85 iv Table of Contents 6.2.3 Composite Behavior: The Predicted Yield Stress of Fine-Scale Zinc ^  90 6.2.4 Strain Rate Jump Tests ^  94 6.2.5 Wire Drawing ^  98 6.3 Stability of the Deformed Microstructure ^  99 7 Conclusion ^  104 7.1 Future Work  105 Bibliography ^  106 Appendix A: Calculations ^  111 List of Tables 2.1 Summary of the general properties of zinc and aluminum  ^5 2.2 The Arrenhius coefficients used to estimate 6DB for A1-20at.%Zn alloy [1]^ 17 2.3 Theoretical versus measured strengths of materials ^ 19 4.1 Etchants selected for use on aluminum zinc alloys  38 5.1 The composition of A1-18.5at.%Zn measured by Novelis Inc. The zinc concentration was outside of the calibration range. ^ 47 5.2 The atomic percent zinc in an aluminum zinc alloy measured by EDX ^ EDX could not detect any impurities besides oxygen. The balance is aluminum ^  48 5.3 Experimentally measured transformation velocity of A1-18.5at.%Zn ^ 51 5.4 Lattice parameter of the FCC matrix calculated by GSAS and the corresponding dissolved zinc content ^  56 5.5 Yield stress of the composite and A1-2.0at.%Zn at varied temperatures 60 6.1 Boundary diffusion constants^  78 6.2 Estimations and experimental values of the Orowan stress for alu- minum and zinc in a DP alloy  89 6.3 The Haasen slope and intercept for DP A1-18.5at.%Zn material at 25 °C, -75 °C, and -196 °C ^  97 6.4 The Haasen slope and intercept for DP A1-2.0at.%Zn material at 25 °C, -75 °C, and -196 °C  97 6.5 The Haasen slope and intercept for pure zinc at 20 °C, -95 °C, and -120°C as measured by Risebrough [2] ^  97 vi List of Figures 2.1 Stress strain curve of 99.999% pure zinc at varied temperature . . . .^7 2.2 The binary equilibrium phase diagram of aluminum zinc produced by Thermocalc [3]^ 9 2.3 An SEM image of the microstructure of discontinuously precipitated A1-18.5at.%Zn prepared as part of this study (see section 5.1.4).^. .^10 2.4 Discontinuous precipitation "pucker" mechanism proposed by Tu and Turnbull ^  12 2.5 Discontinuous precipitation mechanism proposed by Fournelle and Clark 13 2.6 The Zener and Turnbull models for reaction front velocity. Zener uses volume diffusion as Turnbull uses boundary diffusion.^14 2.7 The interlamellar spacing produced by the discontinuous precipitation reaction^ 16 2.8 The boundary velocity for an A1-20at.%Zn alloy [1] ^ 17 2.9 Strength of a laminar copper niobium composite, pure copper, pure niobium and a rule of mixtures prediction for the laminar copper nio- bium composite [4] ^  20 2.10 Diagram of a square particle in a matrix, an elastic shear on the same particle, and the formation of GNDs around the particle.^24 2.11 The Masing Model ^  28 2.12 A typical Bauschinger curve. Tensile data is the solid line, compres- sion data is the dashed line. Imporant points are forward yield (o-,), compressive yield (cr,), the flow stress (o-f) and the backstress (0-b)• •^30 4.1 Comparison of the aluminum zinc phase diagram (left) to the heat treatment path (right) used for rolled material^ 36 4.2 Comparison of the aluminum zinc phase diagram (left) to the heat treatment path (right) used for swagged material  37 4.3 Electro-chemical etch set-up ^  39 4.4 Flat tensile specimen geometry (dimensions in mm) ^ 42 4.5 Tension compression specimen geometry (dimensions in mm), threads are M-20 ^  42 4.6 Cold temperature tensile set-up ^  44 4.7 Set-up used for the tension compression tests ^ 45 4.8 Measurement of a strain rate jump  46 vii List of Figures 5.1 As-cast microstruture of a round, A1-18.5%Zn ingot: left) as-cast right) homogenized at 400 °C for 24 hours. ^  48 5.2 Recrystallization microstructure of A1-18.5%Zn samples aged at 350°C for: a) as-swagged b) 2 min c) 10 min d) 60 min  50 5.3 Grain size of rolled A1-18.5%Zn annealed at 350°C for various time. ^ 50 5.4 Optical images of rolled DP A1-18.5%Zn annealed at 160°C for: a) 1/2hr b) 2hr c) 5hr d) 50hr ^  52 5.5 Fraction of DP microstructure versus aging time at 160°C for rolled A1-18.5%Zn. ^  52 5.6 The measured lamella spacing of a rolled DP A1-18.5%Zn alloy . . ^ 53 5.7 SEM micrographs of rolled DP A1-18.5%Zn transformed for 30 minutes at 160°C ^  53 5.8 SEM micrographs of rolled and fully transformed at 160°C DP Al- 18.5%Zn  54 5.9 Measured, calculated and difference curve for swagged material trans- formed at 160°C ^  55 5.10 Monotonic tensile test of A1-18.5%Zn at varied temperature ^ 58 5.11 Two tensile curves showing typical difference between two tests con- ducted at -196°Cand 25 °C. ^  58 5.12 Strain hardening rate at varied temperature of A1-18.5%Zn ^ 59 5.13 Stress strain curves of the matrix material (A1-2.0at.%Zn) tested in monotonic tension at varied temperature ^  60 5.14 Strain hardening curves of the matrix at varied temperature.^60 5.15 Strain rate jumps of DP A1-18.5at.%Zn  61 5.16 Bauschinger tests of DP A1-18.5at.%Zn at 25°C ^ 62 5.17 Bauschinger tests of DP A1-18.5at.%Zn at -196°C  63 5.18 Creating a tension compression curve from the raw data to better represent the Bauschinger effect. ^  64 5.19 Tensile curves of DP A1-18.5%Zn wire drawn to different true strains 66 5.20 The UTS of A1-18.5at.%Zn wire drawn to different true strains . . . 66 5.21 TEM micrograph of A1-18.5at.%Zn in the as-transformed state. The top image shows discontinuous precipitation and the bottom image shows continuous precipitation. ^  68 5.22 TEM micrograph of A1-18.5at.%Zn in the as-transformed state. . . ^ 69 5.23 Bright field, TEM images of A1-18.5at.%Zn strained to 5% at 25°C . ^ 70 5.24 Dark field, TEM images of A1-18.5at.%Zn strained to 5% at -196°C ^ 71 5.25 TEM micrograph comparison of as-transformed material (a) compared to wire drawn to eTrue - 2.7 (b) ^  72 5.26 TEM micrographs showing DP A1-18.5at.%Zn material wire drawn to ETrue = 4.9. Image a) shows the equiaxed precipitates and image b) shows the lamellar structure.   73 6.1 The lamella spacing of both A1-18.5at.% and A1-30.0at.% alloys as a function of temperature compared to literature values ^ 75 viii List of Figures 6.2 The transformation velocity of an A1-18.5at.% as a function of tem- perature compared to Yang et al [1]^ 76 6.3 Example calculation of the chemical free energy (AGcDp) at 300K for the transformation from supersaturated FCC aluminum (a') to FCC aluminum and HCP zinc (a + /3) from Thermocalc data for a sample with a composition of A1-18.5at%Zn. ^  77 6.4 The chemical free energy (AGc), surface free energy (AG') and overall free energy (SG) of an A1-18.5at.% alloy as a function of temperature 78 6.5 An Arrenhius plot for the boundary diffusion of an A1-18.5at.% alloy 79 6.6 The measured and literature zinc content of the matrix on the phase diagram. The transformation temperature and the alloy composition are marked. ^  81 6.7 The stress strain curve for A1-18.5at.%Zn at -196°C with a microstruc- ture corresponding to that shown in figure 5.8 in the results.^. 83 ^ 6.8 The work hardening curve for A1-18.5at.%Zn at -196°C   83 6.9 Fracture surface of A1-18.5at.%Zn strained until failure at 25°C. . . ^ 84 6.10 A dark field TEM image of A1-18.5at.%Zn showing dislocations 'bow- ing' between lamella after 5% tensile deformation. No clear evidence of dislocations could be found in the zinc phase. ^ 86 6.11 How to calculate the matrix yield stress from a Bauschinger test. . ^ 87 6.12 The room temperature behavior of the composite, matrix and, matrix with Orowan stress. The open circles represent an estimate of the matrix flow stress from tension compression tests. 88 6.13 The -196°C behavior of the composite, matrix, and matrix with Orowan stress. The open circles represent an estimate of the matrix flow stress from tension compression tests.   88 6.14 Stress strain curve of the matrix, composite and predicted precipitate at -196 °C.  ^91 6.15 Stress strain curve of the matrix, composite and predicted precipitate at 25 °C^ 91 6.16 The back stress of DP A1-18.5at.%Zn at -196°C. ^ 92 6.17 The predicted strength of the zinc at both 25 °C and -196 °C.^93 6.18 Haasen plot of DP A1-18.5at.%Zn at varied temperature  96 6.19 Haasen plot of A1-2.0at.%Zn at varied temperature ^ 96 6.20 Haasen plot for the Composite, A1-2.0at.%Zn and pure zinc at varied temperature ^  97 6.21 The theoretical and measured strength of a DP A1-18.5at.%Zn alloy 99 6.22 Free energy of the aluminum zinc system at varied temperature . . . 100 6.23 The aluminum zinc phase diagram corrected for the Gibbs-Thompson free energy. ^  101 6.24 The estimated diffusion distance of an A1-18.5at.% alloy at room tem- perature  102 ix Acknowledgments I would like to thank all those who have helped me throughout my tenure at UBC. I would like to especially thank my supervisor, Chad Sinclair, for his instruction, guidance, and enthusiasm. I am thankful to my peers for showing me the ropes and helping me sort out technical problems as they arose. Babak Raeisinia, Henry Proudon and Reza Roumina were particularly helpful with everything from training me to use the swagger to trouble shooting the tensile machine. I would like to thank Mary Mager for her patience and instruction on the XRD, multiple SEMs and the STEM. The materials machine shop -Ross McLeod, Carl Ng and David Torok- deserves recognition for their craftsmanship. Mati Raudsepp was helpful analyzing my XRD results using the Rietveld method and his expertise in this area is second to none. x Chapter 1 Introduction Refinement of microstructural scale is an important technique for improving the strength of materials. An example of obtaining high strengths in this way is to use two phase microstructures with microstructural spacings as small as a few tens of nanometers. Scale refinement has allowed material engineers to design materials that combine high strength with desirable physical properties. An important exam- ple of using scale refinement to achieve maximized failure stresses can be found in cold drawn pearlite wire where strengths approaching the theoretical limit have been obtained [5] [6]. The same concept of phase refinement has been applied to copper niobium (Cu-Nb) composites for high field magnet design. In this case, the high strengths obtained in the fine scale in-situ copper niobium composites are combined with high electrical conductivity, illustrating the potential for designing materials with combinations of mechanical and functional properties. The application of fine scale two phase microstructures similar to those found in pearlite and Cu-Nb alloys to aluminum alloys has not been as actively explored. However, the use of these same design strategies to the development of high strength aluminum conductors could have significant practical application in, for example, overhead transmission lines or other applications where low cost and low density conductors are important. Aside from the practical aspects of the design of materials with these specific prop- erties, there are also fundamental questions about co-deformation in materials with very different mechanical properties and under conditions where the microstructure is on the nanometer lengthscale. In this thesis, a two phase aluminum zinc alloy has been studied with a specific emphasis on its strengthening during deformation. The goal of this study was to: • examine the potential for making very high strength, fine scale materials based on this system • examine the plastic co-deformation behavior of a fine scale system and the resulting strengthening. 1 Chapter 1. Introduction There are a number of reasons why the aluminum zinc system was chosen for this study. First, it is known that in this system it is possible to obtain a fine scale two phase FCC/HCP microstructure containing a low dislocation density and small residual stresses via phase transformation. The application of phase transformations to achieve fine scale materials has a number of advantages over other techniques such as accumulated roll bonding and bundle drawing as will be discussed within this thesis. Another interesting aspect of this material is that it contains a mixture of phases with very different mechanical properties (FCC versus HCP). This combined with the fine scale of the microstructure raises questions about whether the zinc phase (for example) will be able to deform under similar conditions observed in bulk, e.g. will twinning occur? Finally, the aluminum zinc system can be processed to obtain a large volume fraction of second phase, facilitating further analysis. The attainment of a fine scale two phase microstructure in the aluminum zinc system can be obtained by processing to produce a discontinuously precipitated (DP) microstructure. The DP microstructure is a fine scale lamellar structure similar to the microstructure of pearlite in steels. The discontinuous precipitate structure is ideal for this study because: • The two phases are highly constrained and must co-deform or fracture. • The material contains a large ratio of interfacial area per unit volume. • The geometry of the phases is relatively simple. • The DP transformation fills the entire microstructure. This study commenced by seeking an optimal processing route for obtaining a fully DP microstructure under accessible annealing conditions. Once obtained, the DP material was mechanically tested to develop a picture of the deformation mech- anisms in the two phases. The material was tested using strain rate jump tests to determine the rate sensitivity, monotonic tensile tested to determine the work hard- ening rate and finally compression-tension tested to determine the internal stresses, all at varied temperature. The material was also analyzed using XRD, TEM and SEM at intermediate stages of the processing to determine the microstructural evo- lution during deformation. Finally, large strains have been imparted by wire drawing in order to study the stability and strength of the heavily deformed material. The results of these tests have been compared to existing models for strengthening in an 2 Chapter 1. Introduction attempt to better understand the behavior of this material. The effect of temper- ature and internal stresses can then be related to the mechanism of strengthening. An understanding of strengthening allows for the optimization of strengthening in exhisting materials and aids in the development of new, high strength alloys. This thesis commences with an overview of literature related to the aluminum-zinc system and to co-deformation in two phase materials in general. This is followed by a description of the experimental techniques employed. Next, the results of charac- terization of the DP microstructure and mechanical properties are presented followed by a discussion of the results. 3 Chapter 2 Literature Review 2.1 Introduction Fine scale in-situ composite materials have been demonstrated to have extremely high strengths approaching the theoretical shear strength while remaining ductile. Much of the interest in these materials has arisen from the fact that these high strengths can be combined with other functional properties (e.g. electrical conductivity) not found in other systems [7]. While there are a number of fine scale two phase materials that have been shown to exhibit high strengths including pearlite, Cu-Nb, Cu-Cr and Fe-Ag [8], little is understood about the way in which these high strengths are achieved. Understanding how strength and ductility can be controlled in these materials is important for obtaining engineering materials with a desirable combinations of these properties. In particular, more knowledge is needed about how the individual phases in these two phase materials deform to better be able to understand the strengthening mechanism. It is interesting to explore the strengthening mechanisms in fine scale two phase alloys based on the aluminum zinc system. This system can be processed to form a fine scale lamellar microstructure via phase transformation with a high volume fraction of the precipitate phase. In comparison with materials processed to have a fine scale two phase microstructure by deformation processing (e.g. bundling and drawing or accumulated roll bonding [1, 9, 7]) the aluminum zinc system processed via phase transformation contains low residual stresses and a low starting dislocation content which makes interpretation of the behavior easier. Similar to previously studied systems (e.g. Cu-Cr, Cu-Nb, Cu-Ag) the aluminum and zinc rich phases have low mutual solid solubility at equilibrium. While most previous studies have focused on materials having a combination of cubic metals, the zinc rich phase is HCP. This raises interesting questions about the way in which co-deformation occurs since the deformation behavior of zinc is significantly different from that of the aluminum matrix. To the author's knowledge, there have been no previous in-depth studies of the co-deformation behavior of FCC/HCP in-situ composites. 4 Chapter 2. Literature Review The goal of this literature review will be to provide the background necessary to understand the observations made on the aluminum zinc system studied here. First, the mechanical behavior of bulk aluminum and zinc will be described. This is fol- lowed by a discussion of precipitation, in particular discontinuous precipitation, in aluminum zinc alloys. This is followed by a discussion of the strengthening mecha- nisms in fine scale two phase materials, including a discussion of internal stresses and their importance in these materials. 2.2 Properties of Bulk Aluminum and Zinc 2.2.1 Physical Properties of Zinc and Aluminum The starting point for understanding the behavior of the individual phases in an in- situ composite is to understand the behavior of similar materials in bulk form. Several physical properties of bulk aluminum and zinc are given in table 2.1 [10] [11] where the T  temperature dependent shear modulus is calculated via, ,u = pc, (1 + (T-3oo . One important point that impacts on the behavior of aluminum zinc alloys is that room temperature is a high homologous temperature (TH) for both aluminum (TH :,--- 0.32) and zinc (TH P.--., 0.43). This has consequences for how the materials must be handled. For example, supersaturated aluminum zinc alloys have been known to form precipitates at room temperature by natural aging [12]. Material Property Zinc Aluminum Atomic weight (g/mol) 65.409 26.982 p (g I cm3) 6.51 2.71 Atomic structure HCP FCC Melting point (C) 420 660.4 E (GPa) 96.5 68 Shear Modulus (GPa) 49.3 25.4 Tm diz -0.50 -0.50pocIT Vapor Pressure (Pa) 19.2 © 419.75°C 2.42 x 10-6 © 419.75°C Atomic Volume (m3) 1.52-28 1.66-29 Burger's Vector (m) 2.67'9 2.86-19 Table 2.1: Summary of the general properties of zinc and aluminum The two phases -FCC aluminum and HCP zinc- have very different deformation properties. The difference in properties between aluminum and zinc makes predicting 5 Chapter 2. Literature Review the co-deformation behavior of an aluminum zinc composite difficult. The bulk phase deformation properties of aluminum and zinc will be reviewed in the following two sections with the bulk phase deformation properties used as a starting point in the analysis of the composite material. 2.2.2 Deformation and Plasticity of Zinc Zinc deforms by slip predominately on the basal system (0001) < 1120 >. Von Mises showed that a minimum of 5 independent slip systems are required to obtain an arbitrary shape change [13]. The basal slip system only has 2 independent slip systems and therefore does not satisfy the Von Mises criterion. Another deformation mechanism, such as twinning, an additional slip system, or kink banding, is required for zinc to plastically deform [2]. Zinc has been shown to undergo second order pyramidal slip on the system (1122) < 1123 > and slip on this system increases in frequency with a decrease in grain size [2]. Zinc also twins on the (1012) < 1011 > system [2]. The occurrence of twinning was found to be reduced as the scale of the material decreased [14]. In zinc with a grain size smaller than 1pm, no twinning was observed during tensile tests at room temperature [14]. The frequency of twinning was found to be temperature independent except at high homologous temperatures where boundary migration was found to reduce twinning because it removed stress concentration sites required for the nucleation of twins [2]. Twins were observed to become finer as the temperature was decreased [2]. The stress strain curve of pure polycrystalline zinc at different temperatures is shown in figure 2.1 and was taken from the study by Risebrough [2]. The ultimate ten- sile strength increases with decreasing temperature while the material was observed to strain soften at temperatures greater than TH ';.--2, 0.26 due to dynamic recrystalliza- tion. Deformation at room temperature induces partially dynamic recrystallization up to 50% of the microstructure. At temperatures below -95 °C, the material fails in a brittle, intergranular fashion with little evidence of plasticity. In Risebrough's work, it was found that both the strength and maximum ductility could be improved by a factor of two if the grain size was reduced from 400/im to 20tim. In a recent review, Conrad and Narayan [14] report the scale dependent defor- mation behavior of polycrystalline zinc. Of particular interest are experiments which reveal that pure zinc with a grain size between 10-8 — 10-6m deform differently than zinc with larger grain sizes. The Hall-Fetch slope for pure zinc with a grain size between 10-8 — 10-6m is 34/11N/m3/2 and is much lower than zinc with a grain 6 160 -120°C^-30°C Strain Rate = 4.0 x 10^4 1/s 140 15° 13 120 20°C Grain Diameter = 20pm 2 in 100In 80 a) it 60- 40 20 87°C Chapter 2. Literature Review 0^10^20^30^40^50 ^ 60 ^ 70 True Strain % Figure 2.1: Stress strain curve of 99.999% pure zinc at varied temperature size in the range of 3 x 10-5 — 4 x 10-4m. However, the Hall-Petch slope for Zinc is larger than that of pure aluminum, which is 1.6MN/m3/2. Fine scale zinc did not twin [15], did not form dislocation cells and contained a low dislocation density as measured by transmission electron microscopy at room temperature. The rate controlling mechanism associated with plasticity was found to be the intersection of forest dislocations. 2.2.3 Deformation and Plasticity of Aluminum In contrast with pure zinc, pure aluminum contains a large number of active slip systems. The ASM handbook [16] reports for pure aluminum a yield stress of 10- 20MPa, an ultimate tensile strength (UTS) of 50-70 MPa and the strengthening effect of zinc in solid solution of 4.8 MPa/at% on the yield stress and 20.0 MPa/at% on the UTS [17]. The grain size dependence of the yield stress and the rate hardening of pure aluminum are shown in equation 2.1 and 2.2 [18]. cro = 5.1 + 1.6/N/d (M Pa)^ (2.1) 7 Chapter 2. Literature Review 60 =- 633 + 358/id (MPa)^ (2.2) Pure aluminum is observed to have a low strain rate sensitivity. Chinh et al [19] measured the strain rate sensitivity (m) to be 0.03 at room temperature. 2.2.4 Chemical Properties of the Aluminum Zinc System The binary aluminum zinc phase diagram is shown in figure 2.2. The equilibrium HCP phase (0) formed during both discontinuous and continuous precipitation has a negligible solubility of aluminum at room temperature while the FCC phase (a) has a solubility of — 2at.% zinc at room temperature. Above 277°C the solubility of zinc in the a phase rises rapidly which allows for the dissolution of up to 70at.% zinc. Although the phase diagram is relatively simple with no intermediate phases, the system exhibits a large number of metastable and precursor phases not present in figure 2.2. Supersaturated a aluminum has also been found to form Guinier- Preston (GP) zones at temperatures near room temperature [12]. The GP zones have been measured in the range of 1-4nm and may further decompose into more stable phases. A slowly cooled Al-15at.%Zn alloy was found to form GP zones that directly transformed into ,3 zinc, the equilibrium phase, at room temperature [12]. The room temperature decomposition of supersaturated zinc implies that the material must be carefully processed when supersaturated to produce a consistant final microstructure. The aluminum zinc system undergos discontinuous precipitation in the tempera- ture and composition ranges of 10.3at.% — 59.5at.% zinc and 323K — 527K [1]. This reaction produces a lamella structure similar in microstructure to that of pearlite. An example micrograph of discontinuously precipitated aluminum zinc is shown in figure 2.3. This transformation will be discussed in more detail in the following section. 2.3 Discontinuous Precipitation in the Aluminum Zinc System 2.3.1 Discontinuous Precipitation Mechanism The discontinuous precipitation (DP) reaction, otherwise know as cellular precipi- tation [20], is defined as the formation of a lamellar structure by a partitioning of a supersaturated matrix (a') into a solute-depleted phase (a) and a solute enriched 8 100- 04+ j3 G. 500- a)L- 400-=4-1 (13 '45 300 - o_ w 200 - I-- 0.2^0.4^0.6^0.8 Zn (atomic fraction) 10 Figure 2.2: The binary equilibrium phase diagram of aluminum zinc produced by Thermocalc [3] Chapter 2. Literature Review 9 Chapter 2. Literature Review Figure 2.3: An SEM image of the microstructure of discontinuously precipitated A1-18.5at.%Zn prepared as part of this study (see section 5.1.4). phase (,3) by a transformation reaction behind a mobile interface [21]. The main difference with other cellular precipitation reactions such as the eutectoid reaction is that the discontinuous precipitation reaction produces one phase that is the same crystal structure as the parent phase, but with a lower solute content: discontinuous reaction : a' -+ a + eutectaid reaction : -y^a + 13 Grain boundaries facilitate the reaction by providing a fast diffusion path at temperatures that are too low for significant volume diffusion [12]. In aluminum zinc alloys, the reaction results in alternating plates of FCC aluminum and HCP zinc that will fill the entire microstructure. The reaction is called discontinuous because the solute concentration is discontinuous across the reaction front from a to a'. For the aluminum zinc system, the supersaturated matrix has been found to decompose in stages where the final structure is produced by the discontinuous pre- cipitation reaction. A supersaturated aluminum zinc has been proposed to break down by the following steps [22): 10 Chapter 2. Literature Review a' —> GP Zones —> aR —> 0 + a To initiation of the discontinuous reaction usually requires the full dissolution of zinc into the FCC aluminum matrix producing a supersaturated a' matrix after the material is cooled below the solvus line. The supersaturated a' matrix breaks down into coherent GP zones. The quench conditions greatly affect the GP zones and therefore the subsequent discontinuous precipitation reaction. The GP zones then decompose into more stable phases, such as the rhombohedral distorted FCC structure (ce'R) that contains a higher than equilibrium fraction of zinc [12]. The zinc concentration of the alloy, quench conditions and transformation temperature deter- mine the intermediate phases that are produced [12]. The discontinuous reaction then occurs producing alternating lamella of a aluminum and 13 zinc. The discontinuously precipitated aluminum phase (a) has been found to contain more dissolved zinc than the phase diagram would predict depending on the overall zinc content of the alloy and the transformation temperature [1] [12]. The discontinuous precipitates are known to coarsen by the same mechanism where the discontinuous precipitates undergo a second discontinuous reaction directly over the first. This discontinuous coarsening reaction produces a microstructure similar to the original discontinuously precipitated microstructure, but with an order of magnitude larger lamella spacing and a phase composition closer to equilibrium. The driving force for discontinuous coarsening is to reduce the total amount of free energy by decreasing the amount of interface and supersaturation in the material [23] There are a number of different theories on the mechanisms of discontinuous precipitation, a detailed review of these mechanisms has been recently compiled by Purdy [24]. One of the original theories is attributable to Tu and Turnbull [21]. This work involved studies on the Pb-Sn system in which, 0 tin platlets precipitate on a grain boundary between two supersaturated a' grains. The platlets have a semi-coherent, low energy boundary with one grain, and a high energy, incoherent boundary with the other grain. The driving force for the migration of the grain boundary is the replacement of the high energy phase boundary with the low energy phase boundary by a 'puckering' mechanism as shown in figure 2.4. The grain boundary continues to migrate through the material, trailing lamellar precipitates. This mechanism as- sumes a habit plane, and there is strong texture due to the initial orientation of the 11 Grain Boundary Coherent^Incoherent Boundary^Boundary Precipitate New Precipitate Chapter 2. Literature Review Figure 2.4: Discontinuous precipitation "pucker" mechanism proposed by Tu and Turnbull precipitate and the preferred crystallographic growth direction. There are a number of discontinuous systems that do not show strong texture including Fe-Zn, Cu-In, and Mg-Al, which implies that this mechanism is not general enough to describe all discontinuous systems [25]. A second mechanism proposed by Fournelle and Clark [25] does not require a strong texture and proposes a different driving mechanism than the To and Turnbull model. To start, a large number of allotriomorphs nucleate simultaneously on the grain boundary. These allotriomorphs have no strong crystallographic relationship with either grain. The grain boundary then bows out between the precipitates, depleting the matrix of solute. The solute diffuses along the grain boundary and deposits on the allotriomorphs which act as solute sinks. The interface continues to migrate through the unstable matrix and trails precipitates. The driving force is the depletion of solute in the unstable matrix which reduces the overall free energy of the system. As the interface migrates, the lamella can branch and new lamella can precipitate until a steady-state structure is obtained [25]. A schematic diagram of the process is shown in figure 2.5 The third mechanism proposed by Purdy [24] is based on chemically induced grain bounday motion (CIGM). CIGM is very similar in nature to the Fournelle and Clark mechanism, but is more general in its treatment. CIGM is diffusion induced 12 Aging Time Grain Boundary Chapter 2. Literature Review Figure 2.5: Discontinuous precipitation mechanism proposed by Fournelle and Clark grain boundary motion by the sweeping of solute by the grain boundary to or from a solute sink or source. The moving grain boundary is subject to a number of forces including capillary, chemical, mechanical (elastic) and frictional. The balance of these forces causes the grain boundary to migrate. No nucleation event is required for the initiation of CIGM and in the case of DP the grain boundary sweeps zinc from the supersaturated aluminum to alternating plates of 0 zinc and aluminum. 2.3.2 Discontinuous Precipitation Kinetics The boundary velocity during a cellular transformation was first estimated by Zener using a volume diffusion controlled model [26]. Turnbull [26] modified the Zener model and replaced volume diffusion with boundary diffusion to more accurately mimic the reaction mechanism. Subsequently, the Petermann and Hornbogen [27] model was proposed with a few minor modifications to the Turnbull model. The Petermann and Hornbogen model has been used for the aluminum zinc system in the literature [1]. All three models assume that the velocity of the grain boundary has reached a constant rate for a given temperature and composition. Also, the discontinuous reaction usually continues until it fills the entire microstructure [25]. Zener based his model on a conservation of mass such that the flux (J) of solute swept by the interface 13 Chapter 2. Literature Review Zener ^Turnbull  A P A A 1 0 cx 1 cx Figure 2.6: The Zener and Turnbull models for reaction front velocity. Zener uses volume diffusion as Turnbull uses boundary diffusion. must equal the solute transported by volume diffusion to the precipitate(equation 2.3). The Zener process is illustrated in figure 2.6 and is compared to the Turnbull model, which replaces volume diffusion for boundary diffusion. viC = J = —D— dC —D AC (2.3) dx^Ax Where vi is the velocity of the migrating boundary assuming that all solute is depleted from the a phase. From figure 2.6; C xo, AC (x, — xe), and Ax = 1/2. Therefore: (x, — xe) 2Dvi^ (2.4) x,^1 Turnbull then replaced the volume diffusion in the Zener model with boundary diffusion and produced the more general equation 2.5: 14 Chapter 2. Literature Review (xo — xe) 6=  ^ (2.5) x,^t Where 8 is the grain boundary thickness. The characteristic diffusion time (t) can be estimated from x = VDBt, which can be modified for a lamellar system to equal t A, where DB is the grain boundary diffusivity for zinc along a a - a' boundary. The Turnbull estimation for the steady state boundary diffusion becomes: (x, — xe) 6.DB v, =  ^ (2.6) X0^/2 The Petermann and Hornbogen [27] equation modifies the Turnbull model to give: —AG, 8DB vi = 8  ^ (2.7) RT 12 Where AG, is the net free energy change of the transformation. According to the Fournelle and Clark mechanism, the discontinuous reaction is controlled by diffusion at the reaction front and progresses into one grain only. The chemical free energy change associated with the formation of the equilibrium phases drives the precipitation reaction while the energy consumed by the formation of new interfaces reduces this driving force. Equation 2.8 shows how the overall free energy is calculated and is simply a balance of the chemical free energy of the precipitation reaction and the formation of new interface boundary. Equation 2.9 shows that the interlamella spacing (ADP) is inversely proportional to the change in free energy AG. AG = AGcDp + AG'Dp^ (2.8) 2o-14, AG = AGeDp + ^ (2.9) ADP The discontinuous coarsening (DC) reaction appears to follow a similar process as the DP reaction. However, the driving force for discontinuous coarsening is the replacement of a large interfacial area with a smaller interfacial area by coarsening of the two phase microstructure, where ADC >> ADP: AG = AGDC ADP 2o-Vn, ± ADC 2o-V,„ (2.10) 15 500- 400- c . cr) .g- 300-UCDa Li) fa 200 Tu E 2 100- ....................................................................... 0- 80^10^-0 126 - .1;10 - 160^180^200^220 Precipitation Temperature (C) Chapter 2. Literature Review Figure 2.7: The interlamellar spacing produced by the discontinuous precipitation reaction. 2.3.3 Experimental Observations on Discontinuous Precipitation in the Aluminum Zinc System Yang et al [1] reported that as the solute content increases, the net free energy change associated with the transformation becomes more negative and the reaction velocity increases. Interlamellar spacing has been shown to be inversely proportional to the reaction rate [26]. Therefore, as the solute content increases, the interlamella spacing decreases. The lamella spacing in the aluminum zinc system has been experimentally shown to change with temperature as shown in figure 2.7. The interlamellar spacing is measured as the perpendicular thickness of one zinc and one aluminum plate [1]. The effect of temperature on reaction front velocity is more difficult to capture as it is dependent on the free energy change, diffusion rate, and temperature (see equation 2.7), with the free energy change and the diffusivity both strongly dependent on temperature. Experimental results by Yang et al. [1] for the boundary velocity are shown in figure 2.8. The product of the grain boundary diffusion and the grain boundary thickness ((MB) has been calculated by Yang et al. [1] for a number of different aluminum zinc alloys. The reported results for an alloy (A1-20at.%Zn) close to the one used in this 16 1-1-1--C. l^-e-08 E P0 o 'Tv le-09> 7 Chapter 2. Literature Review le-077 le-10-.^• 300^3k^400^450 Temperature (K)  •^•^. 500 Figure 2.8: The boundary velocity for an A1-20at.%Zn alloy [1] Material (6D)0 (m3)/ s Q0 KJ/mol A1-20.0at.%Zn 3.58 x 10-14 57.8 Table 2.2: The Arrenhius coefficients used to estimate 8DB for A1-20at.%Zn alloy [1]. study is shown in table 2.2 where the behaviour was observed to follow an Arrenhius equation: 6DB = (6DB)0e R'^ (2.11) 2.4 Strengthening of Co-deforming Two Phase Materials There are two main goals of studying fine scale, two phase materials. The first is to manufacture a material with strengths approaching the theoretical limit. The second is to better understand how the scale of a material alters the deformation behavior. In this section, a description of the upper limit of strengthening will be 17 Chapter 2. Literature Review described to show how much strengthening is theoretically possible. Then, a number of strengthening theories will be outlined and the pros and cons of each model will be discussed. Although there are a number of proposed strengthening mechanisms, no one model can describe all phenomena including the effect of deformation history on strength, the Bauschinger effect and dislocation density. 2.4.1 Theoretical Strength of Materials The theoretical maximum strength of materials can be predicted using Frenkel's method [28]. The Frenkel method is an order of magnitude approximation of the maximum strength of ductile materials based on the assumption that the theoret- ical maximum strength is achieved when one plane of atoms shears over another. The shear stress variation associated with this process can be approximated using a sinusoidal function 2.12. 271X 7 = k • sin(-21-x )-,-:.,- k^ (2.12) d^d Near the origin, the sinusoidal curve can be approximated as linear using the shear modulus (p). Hooke's law 7 = ? can be solved for displacement (x) and back substituted into equation 2.12 to solve for k. The plane spacing (a) and the displace- ment distance (d) are approximately equal and the critical displacement distance that would result in movement of the planes is x = d/4. The result is equation 2.13 which is the theoretical maximum shear strength (7) [28]. liT = -^ (2.13) 27r When a more realistic force displacement curve is used, the theoretical shear stress can be further reduced to T = fo- [28]. The theoretical strength is generally much larger (of an order of magnitude higher) than the observed strength of alloys. Table 2.3 compares the estimated theoretical strengths of various materials to ex- perimentally measured strengths. The stress was estimated from the shear using the Tresca criteria (7 = a/2). Fine scale materials are the only materials in this table to approach the theoretical strength to within a factor of two. The difference in theoretical versus measured strength is due to slip by the motion of dislocations. The motion of dislocations results in lower stresses since the displace- ments associated with moving one plane of atoms over another can be reduced to only the atoms surrounding the dislocation core. Finding ways to reduce the ease with 18 Chapter 2. Literature Review Material E (GPa) Theoretical Strength (MPa) UTS (MPa) (4s Al (6061) 69 2300 124-310 7-19 Fe (4140) 207 6900 655-1020 7-11 Pearlite 206 6867 4247 1.6 Cu-Nb 115 3833 1900 2.02 Table 2.3: Theoretical versus measured strengths of materials which dislocation glide occurs can therefore be used to control the strength of ductile materials. 2.4.2 Strengthening by Scale Refinement A promising technique to improve the strength of materials is by refining the mi- crostructural scale by introducing a high density of interfaces. The concept of mi- crostructural scale refinement for high strength is illustrated very well by the com- posites used for high field magnet design. The wire drawn copper niobium system is a classic example. Deformation processed in-situ copper niobium composites are comprised of almost pure copper and pure niobium. On this basis, it would seem log- ical to use a rule of mixtures (ROM), i.e. a composite = (1 — f)orcu + f a Nb, to predict the composite strength based on the strengths of bulk copper and niobium (o-cu and o-Nb respectively where f is the volume fraction of niobium). Figure 2.9 shows the bulk strength of pure copper and pure niobium and the predicted ROM strength of a Cu-20 vol.%Nb composite versus wire drawning strain. Also shown in figure 2.9 is the experimentally measured strength of a Cu-20 vol.%Nb composite manufactured by wire (bundle) drawing. The composite strength is far higher than the ROM estimate based on the bulk behavior of copper and niobium. In fact, the experimentally determined composite strength is higher than that obtained in either of the bulk materials [4]. The observed strength of the real composite versus the predicted strength is attributed to the scale refinement of the composite as it is wire drawn, a feature which is not accounted for in the rule of mixtures estimate. 2.4.3 Strengthening Mechanisms A number of mechanisms that describe aspects of scale refinement strengthening have been postulated, but general agreement has yet to be attained. A detailed under- standing of the strengthening mechanism would facilitate the application of phase 19 20007 • Chapter 2. Literature Review A Bulk Copper O Bulk Niobium — Rule of Mixtures • 20%Nb-Cu Composite • •• o• 0 • 0 o o ^ A^A A^A^A o ^0-^ ^ 0 2^4^6^8^10^12 Wire Drawing Strain Figure 2.9: Strength of a laminar copper niobium composite, pure copper, pure niobium and a rule of mixtures prediction for the laminar copper niobium composite [4] refinement to other materials and the optimization of existing systems. Funkenbusch and Courtney [29] have suggested that geometrically necessary dislocation (GND) formation is the mechanism of strengthening while Spitzig et al [7] have promoted a barrier model. Sevillano [30] and Embury and Hirth [31[ have proposed a third model based on Orowan type strengthening. The first two mechanisms predict Hall-Fetch type strengthening and can be adapted for the anomalous acceleration of hardening at high strains. Each of these models have strengths and weaknesses compared to their ability to predict the response of fine scale two phase materials. In the following sections, these models will be compared and discussed. 2.5 Models of Strengthening Mechanisms 2.5.1 Hall-Petch Relation The grain size was originally shown to influence the strength of steels by Hall [32] and Petch [33]. Hall and Petch found that the strength was proportional to the inverse 20 Chapter 2. Literature Review square root of the grain diameter (d) (equation 2.14) [34]. a = go + ^ (2.14) id In in-situ composites, it is the interfaces between phases that have been shown to strengthen a material similar to that observed for grain boundaries [9]. Fisher and Embury [6] have modified the Hall-Petch relation for laminar pearlite to account for the change in microstructure due to heavy deformation. Embury and Fisher proposed that the barrier spacing (A,) could be described as a function of strain as: 1^1 T, — -AT, • "P (-2 c ) (2.15) assuming that the change in macroscopic geometry is identical to the change in microscopic geometry. Substituting equation 2.15 into the Hall-Petch relation by replacing d with A, results in equation 2.16. Equation 2.16 has been successfully used to explain the strengthening trends in a number of deformation processed systems, e.g. [6] [7]. k^/E ) \ 01 = Grid— .07o "P U-^ (2.16) Most materials strengthen by cold working such that the material strain hardens most rapidly at yield and approaches a saturation of the flow stress as more deforma- tion is imposed. Fine-scale, two phase materials actually undergo an acceleration of work hardening as more deformation is imposed as demonstrated by equation 2.16. The Embury-Fischer model is semi-empirical and does not define a particular mechanism to explain the strengthening. Although the Hall-Petch relation has been experimentally proven to be capable of predicting the scale dependence of strength for a wide range of materials and scales, it does not explain what is causing the strengthening. 2.5.2 Dislocation Pile-up Model Eshelby et al [35] proposed that the Hall-Fetch effect could be caused by dislocation pile-up at the grain boundaries. The number of dislocations (n) that can be stored on a slip plane with length (L) and a resolved shear stress of Ts is given by, aT,sd 71=  ^ (2.17) ktb KHp 21 Ter = pb which simplifies to the Hall-Petch equation, aer — ri)2d (2.19) Chapter 2. Literature Review The grain boundary can resist a critical shear stress 're. The critical shear stress is reached when the cumulation of the shear caused by n dislocations exceeds the critical shear represented by, ay2d (2.18)Ter n • Ts = ŝ pb Since the resolved shear stress is equal to the applied stress minus the frictional stress, equation 2.18 can be rewritten as equation, ky T = — (2.20) The greatest weakness of the dislocation pile-up model is that dislocation pile-ups are not generally observed using TEM in fine scale co-deformed two phase systems [36]. The fact that dislocation pile-ups have not been documented by TEM is not proof that this model is incorrect. However, if dislocation pile-ups did occur, it is very likely that they would be visible as much smaller dislocation structures have been documented by TEM such as active Frank-Read sources. One of the advantages of the dislocation pile-up model is that it can be adapted to explain the transient part of the Bauschinger effect. Orowan [37] proposed that the Bauschinger effect, although partial due to backstress, was also caused by the directionality of slip. If dislocations moved through a structure and were stopped by a barrier such as a phase boundary, it would take a smaller shear strain to reverse that same dislocations motion than to force it through the barrier. Thus, when the stress is reversed, dislocations that had been stopped by a barrier would reverse their path along a slip plane that they were able to cross at a lower stress. 2.5.3 Dislocation Source Model: Spitzig's Variation Spitzig et al [4] proposed an interface dislocation source model. Spitzig et al. assumed that the dislocation density (p) is dependent on the density of dislocation sources in the interface (m) multiplied by the surface area to volume ratio of the phase (S„), this is represented by equation 2.21. 22 Chapter 2. Literature Review p = rn • Sy^ (2.21) The surface area to volume ratio is proportional to the inverse of the interlamellar spacing (St, = The flow stress of materials that are strengthened by forest hardening is found to vary with dislocation density by: a = an+ aiMpyTo^ (2.22) The constant a and material properties of shear modulus (A), yield stress (an), Taylor factor (M) and Burgers vector (b) are fixed. The dislocation density p varies with processing history and material type The strength can then be predicted using, 1 a = ao + a2Mtlb^ (2.23) The constant a changes depending on how the surface to volume ratio is cal- culated. The interlamellar spacing can then be correlated for deformation using equation 2.15. The most significant flaw with the Spitzig model is that it does not account for deformation history and assumes that the strengthening is dependent only on the interlamellar spacing [38]. Work done by Everett [39] has shown that the strength of a DPCMs is strongly dependent on the processing history, even for identical inter- phase spacing. The most convincing work against the barrier model was completed by Spitzig [40] himself. He showed that the initial interphase spacing of a Cu-Nb DPCM changed the flow stress after drawing to identical interphase spacing. Since the Spitzig barrier model does not account for deformation history, it can not predict the Bauschinger effect, which implies that it is not a complete model that can explain general strengthening 2.5.4 Strengthening by GNDs: Courtney et al. Variation As a composite plastically deforms, there becomes a mismatch in deformation between the hard and soft phases. If the applied stress is in tension, upon release of load the phase mismatch will result in elastic compressive stresses in the soft phase and residual tension in the hard phases. Residual stresses result in stored elastic energy 23 Initial Partical Shape d Sheared Partical Shape Shear Mode GND _ Chapter 2. Literature Review Figure 2.10: Diagram of a square particle in a matrix, an elastic shear on the same particle, and the formation of GNDs around the particle. in the material [41]. The stored elastic energy could be relaxed by the formation of geometrically necessary dislocations (GNDs). Ashby [42] describes a simple case of the formation of GNDs around an elastically stressed, square particle as shown in figure 2.10. The density of the GNDs is related to the gradient of plastic deformation induced by non-homogenous flow in a composite. GNDs form around the particle such that nowhere does the local stress field around the particle exceed the local yield stress. If the local stress is less than the local yield stress, the stress to fracture the particle or the stress to nucleate dislocations from the phase boundary, the system is stable. However, if the local stress field exceeds the local yield stress, an array of GNDs are created to lower the energy. The new array of dislocations then lowers the local stress field around the particle below the local yield stress and the system reaches a new stable state with new GNDs around the particle. Courtney et al [38] proposed that the change of dislocation density with strain for each phase was found to obey the Kocks-Mecking equation which includes a geometrically necessary dislocation term. The rate of dislocation storage within each of the phases can be written as, dpi = [C1fp7i — C2pi+ -13i1dc^ Vi Ai (2.24) Where i is the phase. The first term accounts for the accumulation of dislocations during deformation. The second term is the dynamic recovery of the dislocations and is temperature sen- sitive [43]. The third term arises from geometrically necessary dislocations. The constant K is a compatibility constant that is dependent on the difference in defor- mation between the phases. The constant P is the partitioning coefficient and must 24 Chapter 2. Literature Review always sum to unity for all of the phases. A can be predicted using equation 2.15 The above equations must be solved, usually numerically. There are 8 constants that must be determined: o-o, C1 and C2 for both a and i3 phases and K and P, (P, + P = 1). If one assumes that the basic mechanisms of deformation for the phases are unchanged relative to the bulk materials then cro, C1 and C2 can be determined from tensile tests on bulk materials. The constants K and P then be determined by fitting equation 2.24 coupled by a = faaa + foao (2.25) to stress strain curves [29] where f, and fo are the volume fraction of the a and phase respectively. This model has been found to work for the Ag-Fe and Cu-Nb systems but was found to be poor at predicting the strength for more complicated systems such as Cu-Fe. It has been argued that this was due to precipitates that alter the flow stress of individual phases [29]. Arguments have been made against the Funkenbusch et al. [29] strengthening model primarily based on the fact that it predicts dislocation densities much higher than those observed by TEM [36]. Moreover, the basic assumption that the param- eters a0, C1 and C2 can be determined from bulk stress-strain curves is questionable since it might be expected that dynamic recovery may be strongly affected in the presence of a large density of phase interfaces. Since the Funkenbusch model predicts the individual stress strain behavior of the two phases, one way to test its validity would be to compare against measured internal stresses and the Bauschinger effect. Since these effects arise directly due to the difference in the behavior of the two phases, this along with the bulk stress- strain curve should provide a sensitive way to test the model. Unfortunately, the Funkenbusch model has never been compared against experimental data in this way. Finally, this model uses 8 fitting parameters, and does not obtain a significantly better fit than simpler models such as the Embury and Fisher model, which uses 3 fitting parameters. It is hard to justify the more complex model unless it obtains better reliability, or provides a more accurate physical picture. Importantly, the values of the partitioning coefficients (P, & R3) are simply used as fitting parameters and thus do not add to our physical understanding of the problem. 25 Chapter 2. Literature Review 2.5.5 Orowan Model A third theory of fine scale hardening has been proposed which is related to the Hall- Fetch type models above. Since the phase interfaces act to pin dislocation movement, extra stress is required to bow dislocations between the channels/plates formed by the phases. The Orowan stress is the increase in shear stress required to bow a dislocation to the critical configuration such that plastic deformation can occur, i.e. aM pb (A) a = (70 +^ln -7-27A \ b ) (2.26) The coefficient a is usually reported as 1.2 and the Taylor factor (M) has been calculated to be 3 in FCC metals [44] There are several examples of such dislocation bowing in fine scale composites. Thilly et al [44] completed in-situ tensile tests in a TEM on bundle drawn Cu- Nb. These experiments have shown that deformation occurs by the bowing of single dislocation loops on finely spaced slip planes. The dislocation loops originate at the interface and cross the entire lamella [30]. The Orowan model, unlike the Hall-Petch/Embury Fischer models provides a physical picture for explaining how the scale induced strengthening occurs. However, like these models, it is strictly a yield strength model which does not account for the sort of work hardening processes such as those described in the GND models described above. Moreover, the model is often used to explain the point at which yielding occurs in one phase and not the strengthening when both phases are deforming plastically. In this sense, it is not clear how the model should be used to describe the large strain strengthening behavior of the material. It also fails to account for internal stresses observed in these materials, a topic which will be discussed next. 2.6 Internal Stresses in In-Situ Composite Materials Internal stresses develop in composite materials upon plastic deformation and are the cause of certain aspects of a composite stress strain curve including rounding of the yield point [45] and the Bauschinger effect [46]. Internal stresses have been directly measured in composite materials by diffraction experiments [47] [48]. Diffraction allows for the measurement of plane spacing of a specific crystallographic orientation or phase in a crystalline material. As a crystal is elastically strained, the lattice 26 Chapter 2. Literature Review spacing changes, causing peak shift in the diffraction pattern. The peak shift can be measured and can be related to a lattice spacing by Bragg's law. The lattice spacing can be related to strain by equation 2.27 where dhki is the strained plane spacing of plane hkl and d4/ is the unstrained plane spacing. dhkl — dh,k1 elastic — (2.27) dcl-ekl The local lattice strain can be related to the internal stress by the Young's modulus of the phase. Diffraction can be used to measure the average internal stress in a specific phase or crystallographic orientation, but can not be used to measure the stress in a specific crystal or grain. 2.6.1 Elastic-Plastic Masing Model A heterogenous material made up of two phases with a random orientation will have varied microscopic deformation behavior. Grains with favorable slip orientations composed of the softest phase will yield first. Grains with the least favorable orienta- tion to slip composed of the hardest phase will yield last. The difference in yielding results in the build up of internal stresses. One of the more simple models used to envision the build up of internal stresses and corresponding Bauschinger behavior is the Masing model [45]. The Masing model (cited by [45]) assumes isostrain and elastic perfectly plastic behavior for two phases. However, the model can be adapted to incorporate strain hardening and the original model used multiple phases. Figure 2.11 shows the ide- alized material and the predicted stress strain curve for a two phase, elastic-plastic material. The curves can be broken up into three regions. • Region I: All phases are elastic. In this case, all phases were assumed to have the same modulus of elasticity for simplicity. • Region II: The region starts where the softest phase yields, which is phase I at point A. Region II ends were the hardest phase starts to yield at point B. Region II results in the largest build up of internal stresses because phase I is deforming plastically while phase II is deforming elastically. A shape mismatch will develop between the two phases where phase I will be elongated in the tensile direction and phase II will maintain its original shape. 27 Phase I *-Phase II * (-) Stress Stress 44^ (+) Composite III^Strain Phase II Chapter 2. Literature Review Figure 2.11: The Masing Model There are two approaches to analysing the internal stresses: the backstress concept and composite hardening. While the starting point for these methods is different, the physical interpretation is the same. Here, the backstress approach will be adopted. The backstress is a result of the stress partitioning between phase I and II. The backstress (ab) is defined as the difference in the macroscopic flow stress and the flow stress of the matrix, i.e. equation 2.28. ab — 0-composite — 07 (2.28) The stress in phase I or II can be calculated from equation 2.28 and ROM giving cri = 0-composite + ( liff) ab and all = CI composite ± cif • • Phase III: Both phases are deforming plastically and the amount of internal stress or backstress becomes constant in this case because both phases do not work harden. If the two phases have different work hardening rates, the internal stresses would generally continue to accumulate in a slower manner than region II. The same equations for the backstress and the stress in the two phases given above apply here also. • Compression: At point C, the strain rate reverses direction. The composite yield stress in compression (point D) is less than the forward yield stress (point 28 Chapter 2. Literature Review C). This is due to the internal stresses that develop between phase I and phase II. If phase I yields at the same absolute value in compression as it does in tension, phase I should yield at a value 2 x o-i less than the composite yield stress in tension. The reverse yield stress is related to the backstress by equation 2.28. 2.6.2 Bauschinger Effect The Bauschinger effect is defined as a deformation anisotropy resulting from pre- straining and is a direct result of the presence of internal stresses as described above. In a typical tension compression test, the anisotropy results in an apparent softening of the compressive yield stress when compared to the tensile yield stress [37]. There are two regions associated with the Bauschinger effect: transient and perment soft- ening. Transient softening is the initial, rounded region of the compression curve. The permenant softening region is the part of the compression curve that is parallel and smaller in magnitude to the tensile curve. From figure 2.11, one can see that the forward yield stress (point C) is larger in magnitude than the reverse yield stress (point D). If one superimposes a large number of grains with slightly different me- chanical properties, one could see that the resulting additive curve would be rounded and lower than the reverse yield curve. This phenomena directly leads to transient softening. The forward flow stress (point C) is larger than the reverse flow stress (point E) and the absolute difference is the backstress. Bauschinger data is usually replotted from the raw stress strain data such that the strain is the forward strain and the stress is made absolute. The forward strain is calculated such that each increment of strain of a negative stress value is made positive and added to the last increment of strain. A typical replotted Bauschinger curve is shown in figure 2.12 Important information that can be measured from figure 2.12 is: the value of the backstress that is a measure of the internal stresses, the compressive yield stress at a corresponding flow stress which can be used to measure the yield stress of the softest phase by equation 2.29, and the degree of transient softening which is indicative of how anisotropic a material is. (uf — crc) 0-matrix =^2 (2.29) 29 .... 0.0. .., ." Stress Tension / / / Compression Chapter 2. Literature Review Strain Figure 2.12: A typical Bauschinger curve. Tensile data is the solid line, compression data is the dashed line. Imporant points are forward yield (o-0), compressive yield (at), the flow stress (of) and the backstress (o-b). 30 Chapter 2. Literature Review 2.7 Summary In this literature review three main areas were covered; discontinuous precipitation in the aluminum zinc system, strengthening of fine scale, two phase materials and internal stresses associated with these materials. This provides the background nec- essary to understand the results of the experiments performed in this thesis. In the following chapter the results of experiments on the production and deformation of discontinuously precipitated aluminum zinc alloys will be presented. 31 Chapter 3 Scope and Objectives Scale refinement of two phase materials has been shown to produce large yield stresses approaching the theoretical limit. A number of models have been proposed to explain the strengthening mechanism, but each of the models have fallen short in some aspect. For example, none of the existing models outlined in the literature review take into account internal stresses or temperature. Recently, there has been interest in the role that internal stresses play in the strengthening of materials. Work by Thilley et al. [44] and Matt Killick at UBC [49] involved the a study of the strengthening of a fine scale copper niobium composite with special emphasis on the effect of internal stresses. However, the effect that temperature plays in strengthening fine scale materials has largely been ignored. The goal of this thesis was to take these works one step further and look at the effect of temperature on internal stresses and the role that both temperature and internal stresses play in the strengthening of fine scale materials. For this thesis, an aluminum zinc system was selected as a model system. Al- though the aluminum zinc system has been studied extensively for phase transfor- mations, very little work has been completed on its fine scale mechanical properties. An alloy composition and processing path had to be developed to produce a material with the required composite properties similar to that of fine scale copper niobium. A series of experiments were completed to develop a suitable processing path to produce a desirable microstructure. One alloy composition and processing path was selected. The material was then mechanically tested including: monotonic ten- sile tests to determine temperature sensitivity and work hardening behavior, tension compression tests to measure internal stresses and strain rate jump tests to determine the rate sensitivity. The model system was useful for investigating the feasibility of using an alu- minum zinc alloy as a high strength, low density in-situ composite modeled after copper niobium DMMCs. The data obtained on this system could then be used for further analysis. Once the strength over a wide range of homologous temperatures has been related to the material parameters including internal stresses, hardening 32 Chapter 3. Scope and Objectives rate, and TEM micrographs, a picture of the deformation can be developed. An un- derstanding of the deformation mechanism allows a focused approach in controlling the deformation and increasing the strength. The deformation can then be optimized in existing materials and to aid in the development of new high strength materials. 33 Chapter 4 Experimental Procedure 4.1 Introduction The three main experimental steps of the thesis were to: 1) produce the aluminum zinc alloy, 2) to characterize the microstructure and 3) to probe the alloy's mechanical properties with particular emphasis on the generation of internal stresses. Prelim- inary experiments first focused on identifying transformation conditions leading to the sought after fine scale two phase microstructure. The effects of zinc composti- tion, homogenization temperature, aging time and aging temperature were tested to determine the best processing path for this study. After an alloy and processing path were selected, the microstructure was characterized to identify interlamellar spacing, phases present, microstructure, degree of transformation, volume fraction and com- postition of the constituents. Finally, the characterized material was mechanically tested using strain rate jump tests, tension compression tests and monotonic tensile tests. The procedures used in these experiments will be described here. 4.2 Material Fabrication 4.2.1 Casting The aluminum zinc alloys used in this study were cast in-house as part of this work. High purity aluminum (99.99%) and zinc (99.99%) were weighed to give the desired bulk composition of the alloy (see Appendix A for a detailed description of how the weights were calculated) based on a total casting size of 400g. The aluminum was cut into strips 1x2x5 cm using a band saw and the zinc rod was cut into lcm diameter x lcm long buttons. The aluminum and zinc were ultrasonically cleaned in denatured ethanol. The aluminum was etched in a 10% sodium hydroxide in water solution for 60 seconds while the zinc was etched in a 10% nitric acid in water solution for 60 seconds in order to chemically clean their surfaces. Two different casting geometries were used. A 42mm diameter mold was used to 34 Chapter 4. Experimental Procedure make castings that were subsequently hot and cold rolled to form sheet material. A 20mm diameter mold was used to make castings that were subsequently swagged to form rods. Approximately 7 trial castings were prepared to identify a suitable composition and processing method. Alloy compositions of A1-14.0at.%Zn, A1-2.0at.%Zn, Al- 18.5at.%Zn and A1-30.0at.%Zn were tested. The weighed aluminum was placed in a graphite crucible inside of a box furnace at room temperature. The furnace was then heated to 700°C in air. The aluminum was allowed to fully melt over 2-3 hours. Following this, the zinc was added every 10 minutes to the aluminum in 30g increments. Once all of the zinc had been added, the melt was stirred two additional times before casting. To stir, the crucible was removed from the furnace, the oxide layer skimmed with a graphite coated stainless steel rod, stirred with a graphite rod, and placed back into the furnace. The furnace was allowed to return to temperature before repeating the stirring process. After homogenization of the alloyed melt, casting was conducted in one of the two molds. A 42mm diameter stainless steel mold pre-coated with graphite was pre-heated to 200 °C prior to casting. Similarly, a 20 mm diameter stainless steel mold coated in graphite was pre-heated to 300°C prior to casting. The pre-heating of the molds was required to prevent cold-shut. It was found through experimentation that the smaller of the two molds required a higher pre-heating temperature because at 200 °C a poor surface was obtained. Casting involved removing the melt from the furnace, skimming the oxide film with the stainless steel rod and stirring with a graphite rod. The melt was then quickly poured into the mold and allowed to solidify. The ingot was removed from the mold after it had cooled. 4.2.2 Preparation of Aluminum Zinc Sheet The total thermo-mechanical treatment path for the rolled aluminum zinc sheet is shown in figure 4.1. Between 8-16 dog bone tensile samples could be prepared from each cast ingot. The 42 mm diameter ingot was cut into two 14 x 30 x 70 mm slabs. Homogeniza- tion was then performed by heating the material to 400°C and holding for 24 hours. This combination of time and temperature allowed the material to be easily hot rolled without any evidence of edge cracking. These slabs were hot rolled from a thickness of 14 mm to 2mm using 15% deformation per pass. The rolling mill was cleaned with sodium hydroxide and lubricated with a graphite spray prior to rolling. A furnace 35 Chapter 4. Experimental Procedure 700 100 1 0 1̂ ^ 0^0.2^0.4 Casting Homogenization Storage^REX^Aging Zn (mol/mol) Time (h) Figure 4.1: Comparison of the aluminum zinc phase diagram (left) to the heat treat- ment path (right) used for rolled material was positioned beside the rolling mill and the two slabs were pre-heated to 400°C for 30 minutes prior to rolling. Subsequently, the material was put into the furnace for 5 minutes between each rolling pass. A metal guide was set-up on the rolling mill to make sure the slabs were directed into the rolls in a perpendicular manner. The rolling direction was kept constant, but the top rolling face was alternated between passes. After hot rolling the material was stored in the homogenized state in a freezer at -18°C until required. The rolled material was next solutionized at 350°C for 2 hours before being quenched in ice water. This step was intended to dissolve any precipitates, regardless of storage conditions and times. The sheet was then cold rolled from a thickness of 2 mm to 1 mm with 10% reduction per pass. The sheet was then recrystallized at 350°C in a salt bath for 30 minutes followed by a quench into ice water. The re- crystallization procedure was also a final solution anneal. The quench condition had to be kept consistent because of GP zone formation on cooling that could influence subsequent transformations. Also, consistency of grain size was important because discontinuous precipitates nucleate on the grain boundaries. Once the material has been recrystallized/solutionized, the material was imme- diately aged from 12 minutes to 120 hours at temperatures between 120°C to 200°C. 600 - 500 - 0 I- 300 - 200 - liq oc+ liq CX cx11-oe - 2hr 400C 24h r --1/--- 2hr 1/2hr - 300C 160C 36 lip cc+ jig 18 . 59sZn Chapter 4. Experimental Procedure 2hr 1/2hr 380C 160C 700 600 500 400 300 200 100 0^0.2^0.4 Ca sting 11-lomogeni zation Storage^REX^Aging Zn (mol/mol) Time (h) Figure 4.2: Comparison of the aluminum zinc phase diagram (left) to the heat treat- ment path (right) used for swagged material The material was cooled to room temperature by quenching in room temperature water. 4.2.3 Preparation of Aluminum Zinc Rod The preparation of rods of the aluminum zinc alloy followed a very similar process to that for the rolled materials, the overall flow of the processing route being shown in figure 4.2. Two hourglass specimens could be prepared from each ingot. How- ever, multiple ingots were made from each casting by pouring the melt into multiple moulds. While most of the steps for preparing the rods were the same as for the sheets a few significant differences did exist. The preparation of the rod material started from the 20mm diameter ingots, which were directly homogenized at 400°C for 24 hours. No hot deformation was performed on these materials. Swagging was conducted directly on the homogenized 20mm diameter ingot. The surface of the casting was removed and the material was subsequently reduced from a diameter of 19.1mm to 11.1mm with 25% reduction per pass. The rods were then recrystallized in a salt bath at 350°C for 30 minutes, following the same proceedure as that used for the sheet material. Similarly, the precipitation 0 24h F/^490C 37 Chapter 4. Experimental Procedure Keller's Reagent Modified Keller's Reagent 2m1 HF (40%) 2m1 HF (40%) 3m1 HC1 (38%) 3m1 HC1 (38%) 5m1 HNO3 (70%) 20m1 HNO3 (70%) 190m1 H20 175m1 1120 Table 4.1: Etchants selected for use on aluminum zinc alloys temperatures/times were the same as those given above. 4.2.4 Wire Drawing The swagged material was transformed at 160°C for 50 hours. The material was then wire drawn at room temperature to a diameter of lmm at room temperature from an ingot with an initial diameter of 11 6mm and a length of 100mm. Kerosene was used as the lubricant. Each wire drawing step introduced a strain of 10%. The tip of the wire was reduced either by swagging for wire larger than 3.2mm, or a hardened steel file and sand paper for smaller diameter material. The true strain was calculated as ETrue = 171/14 and the maximum total true strain after the final die was 4.9. 4.3 Material Characterization 4.3.1 Polishing and Etching Specimens from the 42 mm diameter ingot were cut into 10x1Omm squares and polished to 6pm with diamond paste before being etched with a modified Keller's agent. Similarly, the 20 mm diameter ingot was cut into buttons that were 3mm deep and polished to 6pm. The etchants used are shown in table 4.1 Etching involved submerging the sample for 10-60 seconds at room temperature before rinsing the sample in a warm stream of water. Thirty seconds produces a deep etch. This reagent worked best for exposing grain structure. 4.3.2 Scanning and Transmission Electron Microscopy Sample Preparation The discontinuous precipitation microstructure is much finer than the grain size and thus required higher resolution than obtained by optical microscopy. Scanning elec- 38 thermometer SS beaker funnel ethanol (-23C) Chapter 4. Experimental Procedure stand Figure 4.3: Electro-chemical etch set-up tron microscope (SEM) samples were mechanically ground and polished to lpm di- amond paste before being electrochemically polished using 110m1 of perchloric acid in 550m1 of ethanol. The applied voltage was between 30-60V where 35-40V seemed to produce a satisfactory result. The current density was 0.3A/cm2. The set-up for the electro-chemical polish is shown in figure 4.3. The ethanol bath temperature was kept at -23°C to -27°C. Foils for the transmission electron microscope (TEM) were ground to a thickness of 90pm to 110pm using 1200 grit paper. The samples were then punched to produce disks 3 mm in diameter. The TEM foils were then electro- jet polished in a Tenupol-2 jet polishing unit using the same electrolyte, temperature and voltage as the SEM samples. Preparing TEM samples of material that had undergone a true strain greater than ,-- 3 was problematic. The TEM required samples that were 3mm in diameter and drawing strains larger than '- reduced the diameter of the wire to less than 3mm. To prepare TEM foils of material drawn to a true strain of --, 5, a hole was drilled down the middle of a 4mm diameter DP A1-18.5at.%Zn wire and a 1.5mm DP-Al- 18.5at.%Zn wire was inserted into the hole. The thin wire was cleaned with sandpaper and acetone before insertion. The bundle was then wire drawn as outlined above until the outside diameter was 3mm. The wire was then sliced and electropolished as 39 Chapter 4. Experimental Procedure outlined above to produce 3mm TEM foils. The samples had to be handled carefully because the center would often fall out after electropolishing even if the bond between the two wires was strong before electropolishing. The large and small diameter wires used in the bundle had to be made from the same material to prevent preferential etching during electropolishing. Two different SEMs were used, a Hitachi S-2300 for low resolution images and and a Hitachi S-3000N for high resolution images. The TEM was a Hitachi H800. The EDX measurements were made by taking an average of three random mea- surements over the sample surface. The surface was prepared by polishing to 6pm diamond paste and no etchant was used. EDX measurements are calculated by Quartz software [50] that: 1) accounts for spurious peaks 2) identifies the elements present 3) fits and removes the background 4) resolves the spectral peaks 5) calculates the element concentration by integrating the peak height and adjusts the results using a ZAF correction until the final result converges [51]. 4.3.3 Metallography The lamella spacing was calculated by locating a region of finest lamella spacing in either a TEM or SEM micrograph, drawing a line perpendicular across a known number of lamella and then measuring the line length. The lamella spacing (A) was then equal to the line length divided by the number of lamella. The lamella spacing was defined as the average thickness of one plate of a and one plate of [3 . The lamella spacing was calculated in the same way as by Yang et al. [1] The fraction of the microstructure transformed by precipitation was measured by superimposing a grid over the micrograph and counting the number of intersections that landed inside transformed grains divided by the total number of intersections [52]. The reaction front velocity was measured from optical micrographs of partially transformed material and was calculated as the longest chord in the micrograph divided by the aging time [53]. The grain size was measured from the optical micrographs by drawing a number of random lines over the micrograph. The inverse of the number of intersections per unit length multiplied by 1.5 was the reported grain size [52]. 40 Chapter 4. Experimental Procedure 4.3.4 X-Ray Diffraction Analysis Specimens were analyzed using a Rigaku X-ray diffractometer using 1/2° diffraction and scattering slits with a 0.3mm receiving slit. The X-ray source was Cu — Ka. The beam voltage was set at 40KV and the beam current was set at 20mA The samples were analyzed from 30°-90° 26. The raw files were then analyzed using Jade [54] to remove the background and K„ peaks. Jade was also used to determine the peak position, interatomic spacing, width at half maximum, integrated peak area and peak height. GSAS [55] was used for Rietveld analysis. Jade fit the background using a parabolic function. The peaks were determined by finding the summit using a 5-point centroid fit. The peaks were curve fit using a Pseudo-Voigt curve which was used to separate peaks that were overlapping. The integrated peak height (area of the peak) was the area under the fit curve and above the background. The X-ray diffraction (XRD) spectra were fit using GSAS. The starting lattice parameter of the FCC phase was 4.0496A and the lattice parameter of the HCP phase was a=-2.6591A c=.4.9353A. The Rietveld method is iterative and one parameter at a time was refined. The parameters that were refined in order are the background (6 term shifted Chebyschev), scale factor, phase fraction (for both phases), the zero position, the lattice parameter (for both phases), the peak width and the spherical harmonic using 6 to 12 terms. 4.4 Mechanical Characterization 4.4.1 Sample Geometry Three different sample types were used in mechanical testing. The first set of samples were prepared by punching tensile samples from the cold rolled sheet (thickness lmm). The geometry of these samples is shown in figure 4.4. The swagged material was made into hourglass tensile samples. Unthreaded sam- ples were used for monotonic tensile and tension compression tests at room temper- ature. The heads of some samples were threaded for monotonic tensile and tension compression tests performed at -75°C and -196°C. The round sample geometry is shown in figure 4.5 41 e5 CD C■.1 75 32 Chapter 4. Experimental Procedure Figure 4.4: Flat tensile specimen geometry (dimensions in mm) 95 19 38 11111111111111111111111  11111111111111111111 Figure 4.5: Tension compression specimen geometry (dimensions in mm), threads are M-20 42 Chapter 4. Experimental Procedure 4.4.2 Monotonic Tensile Tests The monotonic tensile set-up is shown in figure 4.6. A ±3.75mm travel MTS exten- someter (25 mm gauge length) was directly attached to the sample and was used for strain measurements at all temperatures. The temperature was controlled by either testing the samples in ambient air (25°C), adding ethanol cooled to -75°C with dry ice, or adding liquid nitrogen (-196°C). The temperature was measured using a K type thermocouple for ambient and -75°C tests. The temperature of the liquid nitrogen bath was not measured. When cooling the specimen, the sample temperature was allowed to homogenize by allowing the sample to sit for 5 minutes prior to testing. Samples were tested at a cross head speed of 0.025mm/s, approximately equivalent to a strain rate of e = 0.001s-1. The Instron was controlled using Wavemaker-Editor 7.1.0 software [56]. 4.4.3 Tension Compression Tests Tension compression tests were conducted at 25°C and -196°C. The test apparatus used is shown in figure 4.7. The apparatus was carefully aligned to prevent buckling on compressive loading. An alignment specimen was made by precisely cutting a specimen in half on a plane perpendicular to the loading direction. The lower cross- head was then manipulated until there was no visible mis-alignment between the two specimen halves. The samples were tested at a forward and reverse strain rate of 0.001s-1. The samples were either tested under ambient conditions (25°C) or in liquid nitrogen (-196°C). Wavemaker-Editor 7.1.0 [56] was used to determine when to reverse the strain direction of the Instron 8872 . A ±1.00mm MTS extensometer with a lOmm gauge length was used at both temperatures. 43 Foam Container ExtensemEterIMI N., ---1^ mple I Bottom Piston Load IelL Chapter 4. Experimental Procedure Figure 4.6: Cold temperature tensile set-up 44 Top Piston Foam Container Bottom Piston Chapter 4. Experimental Procedure Figure 4.7: Set-up used for the tension compression tests 45 Chapter 4. Experimental Procedure True Strain Figure 4.8: Measurement of a strain rate jump 4.4.4 Strain Rate Jump Tests Tensile tests were conducted on the fully transformed Al-18.5at.%Zn and solutionized Al-2.0at.%Zn with strain rate jumps. The strain rate was alternated from 0.01s-1 to 0.001s-1 at 0.5% strain increments until the test was stopped. The magnitude of the stress jump response was measured by extrapolating the steady state curves and measuring the vertical distance (Acr) between the two strain rates. The change in stress was always measured from the stress jump caused by decreasing the strain rate. The change in stress was then plotted versus the stress of the higher of the two curves at the strain rate jump. The strain rate jumps were measured as shown in figure 4.8 46 Chapter 5 Results Results of experiments performed as part of this thesis will be presented by first describing the microstructures developed through the thermomechanical treatments described in the previous chapter. Subsequently, the mechanical properties and mi- crostructures associated with the deformation of the sheet and rod materials will be presented. 5.1 The Discontinuous Precipitation Reaction 5.1.1 Cast Microstructure After sectioning the castings, the cross section was observed using optical and SEM microscopy. The microstructure of the castings was found to be dendritic with no distinctive equiaxed zone. Some gas porosity between dendrites was visible and oc- curred mostly in the top and middle of the casting. The 20mm diameter ingot showed greater porosity than the 42mm diameter ingot. EDX was completed on the center line of the ingot and no micro-segregation was observed in the homogenized sample. The homogenization caused recrystallization of the microstructure with no apprecia- ble grain growth as shown in figure 5.1. The chemical composition of the castings were estimated by means of EDX in the SEM. The impurity composition of the A1-18.5at.%Zn alloy was found to be below the detection limit of EDX for all impurities except oxygen and was verified by Novelis Inc. using ICP mass spectroscopy and the results are shown in table 5.1. Cr Cu Fe Mg Mn Ni Si Ti V < 0.001 0.001 0.034 0.002 <0.001 < 0.001 0.025 0.003 0.008 Table 5.1: The composition of A1-18.5at.%Zn measured by Novelis Inc. The zinc concentration was outside of the calibration range. Composition measurements made by EDX on samples that were prepared to have 47 Chapter 5. Results Figure 5.1: As-cast microstruture of a round, Al-18.5%Zn ingot: left) as-cast right) homogenized at 400 °C for 24 hours. a nominal composition of 18.5at% zinc are shown in table 5.2. The values given in this table reflect two separate castings made at three random measurement points over the sample surface of each ingot. Material Zn (at.%) of Sample Mean Zn (at.%) 1 2 3 4 5 6 Rolled 19.8 21.6 19.5 20.7 21.0 20.9 20.6 Swagged 16.7 19.2 19.8 22.1 20.6 21.5 20.0 Table 5.2: The atomic percent zinc in an aluminum zinc alloy measured by EDX. EDX could not detect any impurities besides oxygen. The balance is aluminum There are three points that can be made from the EDX results: • The swagged material has a larger deviation than the rolled material. The swagged material was not hot rolled and thus was not homogenized as well as the rolled material, which explains the greater variability of the swagged material. • There was a significant scatter in the composition of the castings (±2at.%). • The castings all ended up with slightly more zinc than expected. A composition of 1-2at.%Zn larger than the expected value changes the analysis very little. The composition is used to calculate the volume fraction of precipitates and the change in molar free energy. A one percent difference in actual zinc content 48 Chapter 5. Results results in a 1% change in the volume percent. The Gibbs free energy change obtained from Thermocalc is modified by less than 0.05KJ/mol for a 1% change in zinc com- position, which is relatively small compared to the total change in free energy due to the precipitation reaction. Based on this small variation, for consistency relative to the previous sections these castings will continue to be referred to as A1-18.5at.%Zn. To minimize the effect of the error arising from the variation in compositions be- tween castings, a single casting was used for each type of experiment. The following results were made from a single casting: strain rate jump tests for the A1-18.5at.%Zn, strain rate jump tests for the A1-2.0at.%Zn, tension compression test at -196°C, ten- sion compression test at 25°C, swagged microstructure, rolled microstructure, and monotonic tensile tests. Casting compositions of A1-14at.%Zn could not be discon- tinuously precipitated from temperatures ranging from 120°C to 200°C. A1-30.0at%Zn could not be fully transformed to produce either homogeneous DP or discontinuously coarsened microstructures from temperatures ranging from 120°C to 200°Cin under 1 week of aging. 5.1.2 Solutionization and Recrystallization The grain size after the solutionization/recrystallization treatment was , 70pm for both types of casting. The grain size of both the sheet material and rod material after cold rolling/swagging and annealing was between 30-35pm for anneal times between 10-30 minutes. Figure 5.2 shows the microstructure of swagged and annealed materials after different annealing times. Picture a) shows a complex etching pattern resulting from deformation and grain boundaries. Image b) shows nucleation of new grains on prior grain boundaries. Images c) and d) show fully recrystallized and equiaxed grain structure where the grains are slightly coarser in image d). The recrystallization kinetics were followed by measuring the grain size as a func- tion of time and are shown in figure 5.3. The smallest grain size was obtained by recrystallizing between 5 to 10 minutes to obtain a grain size of 25pm. The 2 minute sample shows large areas of non-recrystallized material. The sample appears to have fully recrystallized by 5 minutes. The grains coarsened up to a recrystallization time of 10 minutes where the grain size appears to become stable. The recrystallization process was also a solutionization step. Since there was only a small difference in grain size between about 10-30min, a solution treatment of about 30 minutes was selected to ensure that all precipitates were dissolved and to fully recrystallize the microstructure. 49 1000m Chapter 5. Results Figure 5.2: Recrystallization microstructure of A1-18.5%Zn samples aged at 350°C for: a) as-swagged b) 2 min c) 10 min d) 60 min 40: --E-' 35: 30:a)^. E^. 03 5 25- 'I.% 5 20 5^10^15^20^25^30 Anneal Time @ 350°C Figure 5.3: Grain size of rolled A1-18.5%Zn annealed at 350°C for various time. 50 Chapter 5. Results Temperature (°C) Time (min) Velocity (pm/s) 160 31 0.010 160 12 0.0094 160 60 0.0141 200 60 0.0072 120 60 0.0075 Table 5.3: Experimentally measured transformation velocity of A1-18.5at.%Zn 5.1.3 Kinetics of Transformation The material after the different precipitation treatments was analyzed using SEM and optical microscopy. Optical microscopy worked well for determining fraction trans- formed, transformation velocity and grain size. Figure 5.4 are optical micrographs showing the change in microstructure with aging time. The dark areas are DP cells and grow from the grain boundary into the interior of the grain. As time increases, the amount of DP material increases until it fills the entire microstructure. Figure 5.5 shows the fraction of DP material transformed versus time. The material was fully transformed by about 60 minutes. The reaction front velocity was measured using the method outlined in section 4.3.3 and the results are shown in table 5.3. 5.1.4 Microstructure and Lamellar Spacing The SEM in secondary electron mode worked well for imaging the precipitate mi- crostructure. Images at varying stages of precipitation where taken of the rolled material. The temperature was varied from 120°C to 200°C and the time from 0 to 120hr. The measured lamella spacing is shown in figure 5.6. The lamella spacing for aging at 160°C is 240nm. The microstructure of partially transformed material is shown in figure 5.7 where the DP grain can be seen growing from the grain bound- ary into the grain in image b) and impinging on other DP grains in image a). The fully transformed material is shown in figure 5.8 where image a) shows a number of randomly oriented grains. The lamella spacing appears to change due to orientation of the lamella. The greater the angle of the lamella to the viewing plane, the greater the lamella spacing appears to be. Image b) of figure 5.8 is a zoom in of the DP microstructure and shows branching of the lamella. The light phase is the aluminum and the dark phase is the zinc. The aluminum lamella are much thicker than the zinc lamella. 51 10 ^ leo Chapter 5. Results Figure 5.4: Optical images of rolled DP Al-18.5%Zn annealed at 160°C for: a) 1/2hr b) 2hr c) 5hr d) 50hr Time (min) Figure 5.5: Fraction of DP microstructure versus aging time at 160°C for rolled Al- 18.5%Zn. 52 Chapter 5. Results 400- o AI-18.5at.%Zn A AI-30.0at.%Zn350- E- 300- 7.13250- fa a Ln 200- it; E 150; tei^. -1 - 100: 50- ^ .^•^•^.^•^- 120 140^160 180 200 Anneal Temperature (C) for 50hr Figure 5.6: The measured lamella spacing of a rolled DP Al-18.5%Zn alloy Figure 5.7: SEM micrographs of rolled DP Al-18.5%Zn transformed for 30 minutes at 160°C 53 Figure 5.8: SEM micrographs of rolled and fully transformed at 160°C DP Al-18.5%Zn  Measured Rietveld Calculation A1(220) Zn(101) Al(200) Al(311) Zn(103) Z Zn(112) n(110) Zn(201) Zn(002) ^ Zn(102) Al(111) Zn(100) Al(311) A1(222)  Chapter 5. Results 20000- 30^40^50 ^ 60 ^ 70 ^ 80 ^ 90 20 Figure 5.9: Measured, calculated and difference curve for swagged material trans- formed at 160°C 5.1.5 Solute Content and Precipitate Volume Fraction XRD data were used to determine the phases present, presence of preferred orien- tation, and the amount of zinc dissolved in the a matrix for different precipitation conditions of the aluminum zinc alloys. It was found that the transformed material contained FCC aluminum and HCP zinc and no other phases were present in de- tectable quantities. A measured XRD profile fit by Rietveld analysis illustrates this in figure 5.9. Rietveld analysis using GSAS was conducted to determine the phase fraction of zinc precipitates. The samples tested include: rolled and transformed, swagged and transformed, transformed and wire drawn to a true strain of 3.1 and transformed and wire drawn to a true strain of 4.9. An example of a Rietveld fit is shown in figure 5.9 with the calculated Rietveld, measured and difference curves. The closer the difference curve is to a straight line, the better the Rietveld fit. The lattice parameter of the FCC phase calculated by GSAS is shown in table 5.4 as is the corresponding dissolved zinc content. The dissolved zinc content is used to calculate the volume fraction of the precipitate and to create a bulk material rep- resentative of the aluminum lamella. A zinc content of 2.0at.% zinc was selected to 55 Chapter 5. Results represent the aluminum lamella. A zinc content of 2.0at.% zinc is lower than the expected value of 3.6at.%, but was selected because it was closer to the equilibrium concentration of zinc at room temperature and thus mitigated the risk of room tem- perature precipitation. This difference in zinc content would result in less than 8MPa [16] difference in yield strength. Material Matrix Lattice Parameter (À) Zinc in Matrix Transformed CTrue = 4.9 4.043793 7.0 Transformed ETrue = 3.1 4.046630 3.6 Swagged and Transformed 4.046667 3.6 Rolled and Transformed 4.047898 2.1 Table 5.4: Lattice parameter of the FCC matrix calculated by GSAS and the corre- sponding dissolved zinc content The volume fraction of 0 precipitate was calculated by measuring the zinc content in the a phase and then calculating the amount of f3 by stoichiometry assuming 100% zinc in the /3 phase. The lattice parameter was obtained by the Rietveld method calculated by GSAS software. The lattice parameter (a) can then be related to the amount of dissolved zinc in the a phase (4) by equation 5.1 [57]. a = 0.04084784„ H- 2.69547^ (5.1) The calculation used to determine the volume fraction is as follows: c * Mzn/Pzn C * M Zn / P Zn + (1 — C) * Mmatrix / Pmatrix Where (XT — X aZn) (x oZn _ xZn) a With the fraction of dissolved zinc xazn in the a phase calculated and assuming no solubility of aluminum in the 0 phase (472 = 1) [1], the volume fraction of precipitate zinc (f) can be calculated using the overall zinc molar fraction (xi, = 0.185). The volume fraction of precipitate zinc was calculated to be 14.9%. The volume fraction is used in the mechanical analysis. f = C = (5.2) (5.3) 56 Chapter 5. Results 5.2 Mechanical Properties From the range of experiments conducted on different aluminum zinc alloys above, an alloy of A1-18.5at.%Zn was selected for further mechanical characterization. This alloy was selected because it was found that it allowed for the preparation of consistent and reproduceable lamellar microstructures where as A1-14at.%Zn and A1-30at.%Zn did not. Based on the XRD analysis of solute content in the aluminum rich lamella of this alloy, a new casting with a composition of A1-2.0at.%Zn was processed in a similar way as the A1-18.5at.%Zn alloy so as to give an independent measure of the mechanical properties of the aluminum lamella. Instead of being artificially aged, the A1-2.0at.%Zn alloy was directly quenched from the recrystallization temperature. Both discontinuously precipitated A1-18.5at.%Zn and solid solution A1-2.0at.%Zn alloys were mechanically tested. From the mechanical tests of the composite and having the bulk properties of both constituents of the composite, a detailed analysis can be completed. It was found that the storage was important to the mechanical properties of the A1-2.0at.%Zn . The final solutionization quench and storage conditions both had an influence on the final mechanical results of the A1-18.5at.%Zn. It was found that treating each batch in an identical manner and testing specimens in as short a time frame as possible maximized consistency. Moreover, because of the differences in the actual cast compositions of the alloys, all tests of a given type were made from a single casting (e.g. all tension compression tests at 25°C were performed on A1-18.5at.%Zn samples from the same casting). 5.2.1 Monotonic Tensile Tests The DP A1-18.5at.%Zn and A1-2.0at.%Zn alloys were monotonically tensile tested at three temperatures; 25°C, -75°C, and -196°C. Discontinuously Precipitated Al- 18.5at.%Zn The stress strain curves of the DP A1-18.5at.%Zn are shown in figure 5.10. In each case the reproducibility of the tests were checked by making at least two tests under the same test conditions. Figure 5.11 shows two tensile curves and typical error. There are three areas of interest in figure 5.10; a rounded yield section, an increase in the maximum elongation with a decrease in temperature, and an increase in the work hardening as the temperature decreased. 57 400- -196°C 350 (-3300 a^: 2 250- in Ful 200 -75°C 25°C in 0 150 2 1— 100 50 o^0.05^0.1^0.15^• • 0:2 True Strain (MPa) o -196°C 25°C Chapter 5. Results Figure 5.10: Monotonic tensile test of A1-18.5%Zn at varied temperature 400: 350:. *3 300 2^•-- 250: 4V200: tri^.,a) 150: = I—. 100 50 0 0 0:05 ^ 0.1 ^ 0.15 ^ 0 '' 2 True Strain Figure 5.11: Two tensile curves showing typical difference between two tests con- ducted at -196°Cand 25 °C. 58 • .200. .^250^300 • •^I^• Stress (M Pa) Chapter 5. Results Figure 5.12: Strain hardening rate at varied temperature of A1-18.5%Zn The strain hardening rate is shown in figure 5.12. The initial work hardening rate was observed to be higher than that expected for an aluminum alloy (;--- p/20) before saturating out at more typical values. Also interesting is the fact that the hardening rate increased as the temperature decreased. Solid Solution Al-2.0at.%Zn Alloy The stress strain curve of the A1-2.0at%Zn alloy is shown in figure 5.13 and the corresponding work hardening curve is shown in figure 5.14. The A1-2.0at.%Zn be- haved in the same way as most aluminum alloys. Temperature had little effect on the yield stress, but did influence the strain hardening rate that resulted in an in- creased ultimate tensile strength as the temperature decreased. The yield portion of the A1-2.0at.%Zn curve was much sharper than the composite. A summary of the yield stresses, measured based on a 0.2% offset, for the DP A1-18.5at.%Zn and A1-2.0at.%Zn materials, is shown in table 5.5. The expected error is in the range of ±10MPa. Strain Rate Jump Tests Strain rate jump tests were conducted at 25°C, -75°C, and -196°C for both the DP Al- 18.5at.%Zn and solid solution A1-2.0at.%Zn. The strain rate jumps were measured 59 200 25050^100^150 Stress (MPa) Figure 5.13: Stress strain curves of the matrix material (A1-2.0at.%Zn) tested in monotonic tension at varied temperature 3000- 2500- 2000- -196°C - 500- Chapter 5. Results 250- 0.02^0.04^0.06^0.08^0.1^0.12 ^ 0.14 True Strain Figure 5.14: Strain hardening curves of the matrix at varied temperature. Material a, © 25 °C (MPa) a„ A -75 °C (MPa) a, © -196 °C (MPa) Composite Matrix 144.9 32.5 151.1 36.8 166.9 36.8 Table 5.5: Yield stress of the composite and A1-2.0at.%Zn at varied temperatures 60 Chapter 5. Results 400: 350: 1,3300: CL^: Z^'—250: in II?) 200: i'lltu 150:: z I— 100: 50: 0 o 0.02^0.04^0.06^0.08^0. 1 True Strain Figure 5.15: Strain rate jumps of DP A1-18.5at.%Zn as outlined in section 4.4.3. The strain rate jumps will be analyzed in section 6.2.4 of the discussion for estimating the strain rate sensitivity using Haasen curves. The raw stress strain data for the DP material is shown in figure 5.15 where two curves for each condition are plotted to show typical error. The noise in figure 5.15 was in the range of 1MPa. Some of the strain jumps of the A1-2.0at.%Zn material at low strains were of the magnitude of the noise making measurements difficult. 5.2.2 Tension Compression Tests The tension compression data is shown in figures 5.16 and 5.17 for 25°C and -196 °C respectively. The plots are created as done in Abel [37] and the procedure used is shown in figure 5.18. The data is presented in this way to better represent the transient and permanent softening of the Bauschinger effect. Image a) of figure 5.18 shows the raw stress strain data for a tension compression test where the compression part of the curve begins at 6% forward strain. Image b) shows how the compression part of the tension compression curve is mirrored about the unloading line and then the x-axis to produce the thick black line. The rotation is calculated by plotting the cumulative strain starting at the last point of forward strain minus 2-i and reversing the sign of the stress. Image c) is simply image b) with a monotonic tension test included for comparison. 61 300- 200- -200 -300-^ -0 06 -.0.04 -0.02 O^0:02 0.04 0:06 6:08 0.1 Strain 300- 200- 100- 0- (1) p -100 - -200- -300-  . -002 ,^.... 0^0.02^0.04^0.06^0.08^0.1 True Strain 300 200 -200- 0.02 0.04 0.06 0.08^011^0.12 True Strain -300-, ^ -0.02 Chapter 5. Results Figure 5.16: Bauschinger tests of DP A1-18.5at.%Zn at 25°C. 62 0.05 True Strain 0.10.1 0.05 True Strain 400 300 200 100 i% 0 'F.: -100- -200- -300- 0.05^0:1^0.15 True Strain -005 Figure 5.17: Bauschinger tests of DP A1-18.5at.%Zn at -196°C. 0.1 0.150.05 True Strain 400 300- 200 - X • 100-a) g 0 a, if -100- -200- -300- -005 400- 300- F!• 200- -100- -0 02 0^0.02 0.04 0.06 0.08 0.1 0.12 0.14 True Strain 400 ea 200 a. 2 100 E 027, -100 4 -200 0 0.02 0.04 0.06 0.08 True Strain 0.1 0.12 0.14 400- 300- - • 200 • 100 La ID_^0 w -100 4 -200 -300- -400- Chapter 5. Results 63 400 c) 300 200 a. 2 100- 0.12 0.140.02^0.04^0.06^0.08^0.1 Cumulative Strain 300 b) 400 recalculated compression curve -400 0 200 a. 2 100 0 ir) A-100 -200- -300- -400 -002^0^0.02 0.04 0.06 0.08 Cumulative Strain 1— -200 -300 0.1^0.12^0.14 a) 400 300 200 40a_ 2 100 g -100 -200 -300 -400 ^ 0 0.02^0.04^0.06^0.08^011 True Strain Chapter 5. Results Figure 5.18: Creating a tension compression curve from the raw data to better rep- resent the Bauschinger effect. 64 Chapter 5. Results The Bauschinger results show that both temperatures produce strong transient softening behavior that increases with the degree of forward strain. The backstress is larger in the tests conducted at -196°C than at room temperature. The room temperature tests do not show a significant backstress. The forward stress was measured as the stress at the point that the strain was reversed. The reverse stress was measured using a 0.2% offset and the back stress (0" f or w ar d-21,7* e,,e, 8.1) .was calculated using aback — Buckling of the Bauschinger samples became an issue in compression. About 4% reverse strain could be obtained before buckling was initiated as determined by differ- ences in two strain gauges mounted at different angles at room temperature. Careful alignment of the machine delayed the onset of buckling, but could not eliminate it. Buckling was worse for the cold temperature set-up than for the room temperature set-up. 5.2.3 Wire Drawing Figure 5.19 shows the stress strain curves and figure 5.20 shows the change in ultimate tensile stress with wire drawing strain. A linear fit to the data in 5.20 shows that little work hardening occurs at large strains, 6 t--.--, 20MPa. The elongation to failure decreased and UTS increased as the amount of wire drawing increased as expected, but the material did not become brittle. The noise of the tensile curves increases as the amount of wire drawing increased. 5.3 TEM Analysis of A1-18.5at.%Zn The microstructure of the DP A1-18.5at.%Zn was analyzed using a transmission elec- tron microscope to determine the microstructural effect of temperature and deforma- tion. A number of conditions were analyzed including the as-transformed material, material strained to 5% at 25°C and -196°C, and material wire drawn to a true strain of 3.1 and 4.9. A strain of 5% was selected because that was the value that the Bauschinger backstress curves had saturate for both temperatures tested. The as-transformed material is shown in figure 5.21; image a) shows a typical DP microstructure as image b) shows continuous precipitation microstructure that oc- curred in isolated pockets. Although the material did contain continuous precipitates, the vast majority of the microstructure was discontinuously precipitated. Unfortu- nately, neither optical or scanning electron microscopy could resolve the difference 65 320- Chapter 5. Results 3501 300.: --ti3 2 5 0 a in 200-v) 2u; 150-. a, 2 100-1-^• 50 0 0 E = 1 . 9 ^- E=0 0.02 0.04 0.06 0.08^0.1^0.12 True Strain Figure 5.19: Tensile curves of DP A1-18.5%Zn wire drawn to different true strains 340- aurs=20E+234^ --- R2=0.9986 ....-- 9-' o --- --',-- )>" ----- ...-' ---0--,,,,,,, ---- S. 7-- -' . • . " ' . . 0 240 220- 0 1 ^ 2^3 ^ 4 ^ 5 E= I n(Ao/A) Figure 5.20: The UTS of A1-18.5at.%Zn wire drawn to different true strains 66 Chapter 5. Results between DP and continuous precipitates because the continuous precipitation tended to occur in small areas at the edges of of discontinuously precipitated areas. Thus, the total transformation calculations included both continuous and discontinuous precip- itates. The error should be small because the relative fraction of continuous to DP microstructure was small. The interlamellar spacing was measured from TEM images to be 263nm and the volume fraction of precipitate to be 0.15. The interlamellar spacing and volume fraction of precipitate is dependent on finding plates that are edge on to the camera. Figure 5.22 shows precipitation defects that look like fractured lamella in material that had not been deformed. Also, no voids were observed after deformation in front of the fractures. Therefore, the areas that look like fractured lamella (marked by arrows) are probable precipitation defects. Tensile samples tested at both room temperature and in liquid nitrogen were strained to 5%. TEM foils were then prepared from the gauge section and a number of dark and bright field images were taken. The dislocation structure can be seen in figures 5.23 and 5.24. The dislocations appear to be lines crossing lamella channels and are very similar to Orowan type loops reported by Embury and Hirth [31], and Thilly [44]. The dislocation structure in the zinc could not be resolved. No twinning was observed in the zinc at either temperature. Twins would appear as discontinuities at the edge of the zinc lamella. 67 Chapter 5. Results Figure 5.21: TEM micrograph of A1-18.5at.%Zn in the as-transformed state. The top image shows discontinuous precipitation and the bottom image shows continuous precipitation. 68 Chapter 5. Results Figure 5.22: TEM micrograph of A1-18.5at.%Zn in the as-transformed state. 69 Chapter 5. Results Figure 5.23: Bright field, TEM images of Al-18.5at.%Zn strained to 5% at 25°C 70 Chapter 5. Results Figure 5.24: Dark field. TEM images of Al-18.5at.%Zn strained to 5% at -196°C 71 Chapter 5. Results Figure 5.25: TEM micrograph comparison of as-transformed material (a) compared to wire drawn to ETrue =- 2.7 (b) TEM micrographs were taken of the as-transformed material that had been wire drawn to a true strain of 3 and — 5 to show the effect of large deformation. Figure 5.25 shows the difference between as-transformed DP Al-18.5at.%Zn (image a) and wire drawn DP Al-18.5at.%Zn to a true strain of 2.7 (image b). The lamella are more uniform and linear in the as-transformed material compared to the wire drawn material and the lamella spacing decreases as the strain increases. The lamella spacing was measured to be 166nm in the material wire drawn to ET, 2.7. The structure of the material wire drawn to ETrue = 4.9 is shown in figure 5.26. The microstructure is considerably different than that of the as-transformed material. The majority of the microstructure shows equiaxed precipitates with scattered and isolated regions of very fine lamellar precipitates with a lamellar spacing of 32nm. 72 Chapter 5. Results Figure 5.26: TEM micrographs showing DP Al-18.5at.%Zn material wire drawn to ETr ue =----  4.9. Image a) shows the equiaxed precipitates and image b) shows the lamellar structure. 73 Chapter 6 Discussion Based on the results presented in the previous section, there are three main areas to be discussed: the discontinuous precipitation reaction, the mechanical properties, and the microstructural stability of the material after large strain. In the first section, the discontinuous precipitation results (including interlamellar spacing, transformation velocity, and microstructure) will be compared to previous results in the literature for similar systems. The second section will discuss the analysis of the mechanical results. The mechanical properties -yield strength, work hardening, and Bauschinger effect- will be compared with existing deformation models, and mechanisms of deformation and strengthening will be discussed. Finally, the stability of the microstructure after deformation at room temperature will be discussed. Possible mechanisms for the observed destabilization will be developed. 6.1 The Discontinuous Precipitation Reaction Figure 6.1 compares the results obtained in this study with those of Yang et al [1]. These authors compiled an extensive review of the kinetics and microstructures due to discontinuous precipitation in aluminum zinc alloys. The observed interlamellar spacing for samples with 18.5at.%Zn were found to agree closely with results reported by Yang et al [1] although there was a small difference between the results obtained for Al-30at.%Zn. While the data at 18.5at.%Zn compares very well to the literature data, the interlamellar spacings observed for samples with 30at.%Zn appear higher than those observed by Yang et al. The small discrepancy between the results obtained here and those in the literature is most likely attributable to the fact that the composition is not precisely the same between the two. It was found that the microstructure of the Al-30at.%Zn material was difficult to control. It was difficult to obtain material that was fully transformed with a uniform microstructure, thus no further work went into developing this material for mechanical testing. Although the Al-18.5at.%Zn material was found to transform fully, TEM analysis 74 Chapter 6. Discussion 5007 . 450- -E'c 400- CY1c 350- -0 ra0300: V')^: n 250:: T.) E200.: (0^._1 . 150: 100 80 o Al-18.5at.%Zn A Al-30.0at.%Zn --- Yang et al Al-20.0at.%Zn Yang et al Al-28.4at.%Zn 0^.. ..,- A A^ A .............................................. ................... ....... ....... ...... ......... , A o -^.^•^-^•^.^-^..... 100^120 140 160^180 200 220 Anneal Temperature (C) for 50hr Figure 6.1: The lamella spacing of both Al-18.5at.% and Al-30.0at.% alloys as a function of temperature compared to literature values showed that there were scattered areas of continuous precipitation in the predomi- nantly discontinuously precipitated microstructure. Figure 5.21 in the results section shows an example of this. The amount of continuous versus discontinuous precipi- tation was not quantitatively measured in this study because both SEM and optical metallography lacked the resolution to distinguish between continuous and discontin- uous precipitation while from TEM observations it was difficult to obtain statistically significant results. Qualitatively, it was observed that the amount of discontinuous precipitation was much larger than the continuous precipitation for the samples ob- served. The transformation velocity was found to compare within a factor of two to the results reported by Yang et al. [1]. Figure 6.2 summarizes the experimental and literature boundary velocity results. The error is reasonable considering that different processing conditions were used compared to those used by Yang et al; the results reported by Yang et al. are for 20at.% zinc, but 18.5at% zinc was used in the experiment. The results are consistent with the difference in zinc content because the boundary velocity should be higher for higher zinc contents because of a higher driving force for the precipitation reaction. 75 Yang et al 7  o Measured 0 Chapter 6. Discussion le-077 le-10-^ .^- 300 350400^450 Temperature (K) •^•^5 500 Figure 6.2: The transformation velocity of an Al-18.5at.% as a function of tempera- ture compared to Yang et al [1] 6.1.1 Kinetics and Diffusion Rate The boundary diffusion constants were calculated to further compare with the litera- ture and also for use later in the discussion of microstructural stability. The dominant diffusion rate is reported to be boundary diffusion over volume diffusion for the Al- 2lat.%Zn system [58]. The product of the boundary diffusion constant (DB) can be estimated from the transformation velocity and interlamellar spacing using the Petermann and Hornbogen equation 2.7, which requires an estimation of the Gibbs free energy. The net Gibbs free energy can be calculated from equation 6.1. 2o-V„AG -- AGcDp + ,^ (6.1) ADP Where AGeDp was obtained from Thermocalc [3] as shown in figure 6.3. The interface energy was taken from Cheetham and Sale (a = 0.72 — 0.00066T J/m2) [59], A was interpolated from figure 6.1 and the molar volume was calculated to be V, = 9.97 x 10-6m3/mo/. A plot of the calculated free energy (figure 6.4) shows the chemical free energy, surface energy and overall free energy for an A1-18.5at.% alloy as a function of temperature. Note that the surface energy is positive, the chemical free energy is negative and 76 _____-----TIEGI—T: 1 o3 Chapter 6. Discussion 1 5 AI-18.5at.%Zn ^ - C< 1 i 1  I^I^I^I 0.2^0.4^0.6^0.8^1 0 MOLE_FRACTION ZN Figure 6.3: Example calculation of the chemical free energy (AGeDp) at 300K for the transformation from supersaturated FCC aluminum (a') to FCC aluminum and HCP zinc (a -FM from Thermocalc data for a sample with a composition of A1-18.5at%Zn. 77 Chapter 6. Discussion 200- AGcr F200--200- 0 -400- ^ AG AGc -600- -800-  ^ • •^• 300^350^460 • • • • 450 •^500 T (°K) Figure 6.4: The chemical free energy (AG'), surface free energy (AG') and overall free energy (AG) of an Al-18.5at.% alloy as a function of temperature Material Source (8DB)0 (m3)/s Q KJ/mol Al-18.5at.%Zn Al-20.0at.%Zn This work Yang 3.16 x 10-17 3.58 x 10-14 29.7 57.8 Table 6.1: Boundary diffusion constants the overall free energy is negative for temperatures below the monotectoid. With the free energy, transformation velocity, and interlamellar spacing, the value ODB (boundary thickness multiplied by the boundary diffusion) can be evaluated using the Petermann and Hornbogen equation (equation 2.7 in the literature review) and compared to the literature using an Arrenhius equation 6.2. An Arrenhius plot was created and is shown in figure 6.5. The Arrenhius constants are reported in table 6.1 and are compared to results reported by Yang et al. [1] 6DB = (8DB)0eRT ^ (6. 2) The measured activation energy is consistent with that of stationary boundaries, 22.2-49.8 KJ/mol [1]. There is a difference between measured and literature values for the activation energy and diffusion constant, the measured values correspond more 78 -100: -200- -ö -300- E • 7_—...-400 - <61-500 -600 Chapter 6. Discussion Figure 6.5: An Arrenhius plot for the boundary diffusion of an A1-18.5at.% alloy closely to the trends obtained for different zinc compositions in the literature. The activation energy reported for A1-39.3at.%Zn was 48.2KJ/mol and for A1-59.9at.%Zn was 74.6KJ/mol [1]. One would expect a smaller activation energy than 48.2KJ/mol rather than larger if the trend for A1-39.3at.%Zn and A1-59.9at.%Zn is followed. 6.1.2 The Solute Content of the a Phase The Rietveld method was used to determine the volume fraction and solute content of phases in the material. The Rietveld method works best for materials with a random texture, usually powder samples. In the present study, rolled or swagged material have been used and have crystalline texture. While texture present in these samples decreases the accuracy of the Rietveld method, there is good agreement between TEM micrographs and the volume fraction measured in this way. The literature [1] reports 8.2at.% zinc in the matrix phase after the transformation at 160°C while it has been found here that the zinc content is 3at.%. The difference between zinc content of Yang et al. and the measured results could be due to differences in the processing paths used and in the measurement procedure. Yang et al. calculated the lattice parameter from a single peak where as whole spectrum fitting was used in this report. The material was aged for longer than required for transformation, and it is possible that the material may have shifted closer to equilibrium during that time by local 79 Chapter 6. Discussion precipitation. It is unlikely that the material discontinuously coarsened because the lamella spacing agreed closely with the discontinuous precipitation spacing described in the literature. The measured solute content of the matrix phase should be equal to the Gibbs- Thompson corrected equilibrium concentration at the transformation temperature of 160°C because the reaction is controlled by boundary diffusion. The boundary has passed once the matrix has cooled to room temperature and the solute is functionally trapped in the matrix. The equilibrium solute content at 160°C is 3.3% measured from a phase diagram produced by Thermocalc [3]. The Gibbs-Thompson surface energy is relatively small (AG = 18J/mol) compared to the total change in free energy, thus does not significantly change the equilibrium solute content. Therefore, the matrix should contain close to the equilibrium concentration of zinc at 160°C, which agrees closely with the experimentally calculated value. Figure 6.6 shows the measured and literature matrix solute content [1] on the phase diagram. Some preliminary atom probe experiments conducted during the process of this work support a solubility of 3% zinc in the matrix phase [60]. An A1-2.0at.%Zn alloy was selected to represent the matrix because it was im- portant to avoid strengthening by precipitation. A1-3.6at%Zn is supersaturated at room temperature and could produce some precipitates. The difference in strength between A1-2.0at.%Zn and A1-3.6at.%Zn is small and should be in the range of 8MPa if precipitation is avoided, and could be much larger if precipitation occurred [16]. One way to check the consistency of the above measurements is to compare the observed lamellar spacings (lamella viewed edge on) from TEM micrographs. The ratio of the lamella thickness should be equal to the ratio of the volume fraction of the phases. A TEM micrograph with the smallest lamella thickness was selected to coincide with an `edge-on' condition and an average measure of lamella thickness was made using ImageJ [61] software. Based on these images an average volume fraction of 15.0% was found, agreeing closely with the Rietveld method. 6.2 Deformation Behavior of DP A1-18.5at.%Zn Two sets of tensile and strain rate data were produced - A1-18.5at.%Zn (also called the composite) and A1-2.0at.%Zn (to represent the bulk properties of the aluminum lamella). The bulk tensile and strain rate data for the precipitate (zinc phase) were referenced from the literature for pure zinc. From the mechanical properties of the 80 700 Alloy Compostition (18.5at.%Zn) 600 - —I 500 -a) 3 400 - rt CD CI - ) C 300 - n 200 - 100 - lig 0C-1- OC DO- j3 Yang et al Zn in Matrix Transformation Temperature oc+ J3 Measured Zn in Matrix 0.2^0.4^0.6^0.8 Zn (atomic fraction) 10 Chapter 6. Discussion Figure 6.6: The measured and literature zinc content of the matrix on the phase diagram. The transformation temperature and the alloy composition are marked. 81 Chapter 6. Discussion composite and the bulk properties of its two constituents, an analysis of the defor- mation behavior could be completed. In this case, an Orowan based model is applied because TEM micrographs show dislocation loops similar to that reported by Thilly et al [44] and Embury and Hirth [31]. Strain rate data is then used to further analyze the deformation of the composite and account for rate dependent phenomena. 6.2.1 Monotonic Tensile Tests There are three main points that can be drawn from the composite stress strain and strain hardening curve: • Rounding of the yield curve • Ductility at all temperatures • An increase in the strain hardening rate as the temperature decreases To clarify these points, figures 6.7 and 6.8 will be used. These two plots are broken up into three regimes. Regime I is elastic-elastic deformation of the matrix and precipitate. Regime II is elastic-plastic deformation of the precipitate and matrix respectively. Regime III is plastic-plastic deformation of both phases. The stress strain curve starts with elastic-elastic deformation (region I) where both the precipitate and matrix deform elastically. The tangent modulus in region I is equal to the Young's modulus. Region II is defined after yielding occurs and is comprised of a rounded yielding zone indicative of heterogeneous deformation. Phase II has a much higher strain hardening rate than typical aluminum alloys. A typical aluminum alloy has a strain hardening rate of /2/20 at yielding or about 1300MPa. The strain hardening rate of the composite is initially much higher than this and increases with decreasing temperature. The high work hardening is attributed to composite hardening where the stress is partitioned from the soft to the hard phase. In region III, both phases deform plastically and the work hardening drops to a level expected for more homogeneous aluminum alloys. The composite shows a large degree of ductility at low temperatures. At liquid nitrogen temperatures, bulk zinc is brittle, yet Al-18.5at.%Zn deforms plastically up to a strain of — 18% before necking. The large degree of elongation is evidence that fine scale zinc deforms plastically at all temperatures. Figure 6.9 shows a micrograph of a composite material strained to failure and depicts typical ductile fracture. 82 400- 3507. I 73300: M 250- in r_.) 200= C) 150: 2 I 100 - 50 0 0 0.05^0.1^0.15 • True Strain (MPa) IIIII 0.2 Chapter 6. Discussion Figure 6.7: The stress strain curve for A1-18.5at.%Zn at -196°C with a microstructure corresponding to that shown in figure 5.8 in the results. 70000- 60000- 50000- 13'40000-a. o 30000- 20000- 10000- 0-o .^ ,^. ^. 50^100^150 200 250 Stress (MPa) 300 350 400 Figure 6.8: The work hardening curve for A1-18.5at.%Zn at -196°C. 83 Chapter 6. Discussion Figure 6.9: Fracture surface of A1-18.5at.%Zn strained until failure at 25°C. There is no evidence that the zinc twins or fractures during deformation. Fracture usually results in the formation of micro-voids that are not seen around breaks in the lamella [9]. The breaks in the zinc lamella viewed by TEM are observed in the as-transformed material as well and are probably formed during precipitation. Also, pure zinc has been shown to fracture by brittle, intergranular crack propagation at low temperatures and to recrystallize at warmer temperatures [2]. The lamellar zinc lacks the grain boundaries to fracture in an intergranular manner and recrystallization of the zinc structure is inhibited by the aluminum lamella. The fine scale of the zinc changes the deformation behavior and prevents the deformation mechanisms that contribute to zinc's low yield stress. Although it was not possible to directly image dislocation activity within the zinc phase, the above points would tend to suggest that some dislocation activity does occur in the zinc lamella, leading to co-deformation between the two phases. Finally, there was a strong temperature dependence of the work hardening rate although the yield stress was similar for all three temperatures tested. Both the ultimate tensile stress and the strain hardening rate increases with decreasing tem- perature. As the strain hardening rate increases, the onset of necking is delayed as more deformation is required to meet the Considere criteria of necking (a = 0 for monotonic tensile tests). Therefore, it is logical that the coldest temperature shows 84 Chapter 6. Discussion the largest elongation at necking because it has the highest work hardening rate. The A1-2.0at.%Zn material behaved very similarly to solid solution strengthened aluminum alloys. The yield stress was insensitive to temperature (within error). The yield stress can be predicted from the data reported in the ASM handbook [17] to be between 20-30 MPa which is close to a yield of 32.5MPa for the A1-2.0at.%Zn material tested at room temperature. The yield portion of the stress strain curve was much sharper than the composite and the strain hardening rate was much lower and closer to the typical value of ///20. 6.2.2 Composite Behavior: The In-Situ Matrix Stress The basic aim here is to try to understand the composite stress strain behavior in relation to the mechanical properties of the individual phases. In this case, it is interesting to try to use the experimental results to assess the stress-strain response of the individual phases and then to compare them against the expected response of the bulk materials. TEM micrographs (figure 6.10) show dislocations bowing in the aluminum be- tween lamella consistent with the section "Orowan Backstress Model" of the liter- ature review. This Orowan stress would be expected to increase the yield strength of the aluminum above that observed in Al-2.0at.%Zn. Thus, the Orowan model applied alone, would predict the same response of the aluminum lamella as that for A1-2.0at.%Zn, but with an increased yield stress due to the extra shear stress required to bow a dislocation between the lamella. The Orowan stress can be calculated using equation 6.3. 0- --=-- °o + aM,ub ( A ) 27 A ln b ) (6.3) The in-situ matrix flow curve can be estimated from tension compression tests [49]. Figure 6.11 schematically illustrates the Masing model discussed in section 'Elastic-Plastic Masing Model' of the literature review. The Masing model predicts the stress of a composite material from the deformation behavior of a matrix and precipitate phase assuming equal strain conditions and equal moduli. The softest phase, assumed to be the matrix, will be the first phase to yield in both tension and compression. The bulk matrix curve yields in tension at Umatrix and yields in compression at a— - matrix with a difference in stress between the forward and reverse yield stress of 20-matrix • The composite yields in tension at af and in compression at 85 1 u m Chapter 6. Discussion Figure 6.10: A dark field TEM image of A1-18.5at.%Zn showing dislocations 'bowing' between lamella after 5% tensile defoi illation. No clear evidence of dislocations could be found in the zinc phase. 86 Chapter 6. Discussion ,401. Am/Earwirr Crecipitate Figure 6.11: How to calculate the matrix yield stress from a Bauschinger test. a,. If the matrix is the softest phase, it should start to yield in compression first at a stress 2n-- matrzx lower than a f . The matrix yield stress for a given forward strain should then be half the difference between the forward and reverse yield stresses. From the results of the tension compression tests, the yield stress of the aluminum lamella has been estimated as described above, the results being presented in figures 6.12 and 6.13 as open cirles alongside the bulk stress strain curve of A1-2.0at.%Zn, A1-18.5at.%Zn. On both charts, the bulk stress strain curve of the A1-2.0at.%Zn has been shifted up to best match the estimated aluminum lamella stress (open cirles) and the magnitude of the shift to produce the best fit is indicated on the plots. From figures 6.12 and 6.13, the estimated values of the flow stress for the aluminum lamella fit well to the stress strain curves of the bulk A1-2.0at.%Zn stress strain curves adjusted for the increase in the yield strength due to scale. The yield stress increments calculated as the difference between the estimated lamella stress minus the bulk A1-2.0at.%Zn stress can be calculated from equation 6.3. This comparison is shown in table 6.2. The Orowan stress, as defined by equation 6.3, is temperature dependent only through the temperature dependence of the shear modulus. However, the experimentally observed increase in the yield strength does not appear to be temperature dependent. The difference between the apparent aluminum lamella yield strength at 77K and room temperature is 9 MPa, a value smaller than the scatter Tension Stress Compression —C37natrix Strain Crmatrix 073recipitate 20;.trix 207.trix= 01 + 87 2501 CYAI-18.5%Zn 79 MPa CrAI-2.0%Zn aAI-2.0%Zn Obrow an 50- Chapter 6. Discussion 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 True Strain Figure 6.12: The room temperature behavior of the composite, matrix and, matrix with Orowan stress. The open circles represent an estimate of the matrix flow stress from tension compression tests. 400 350 73300 o_ 250 2.'1200 co 150 2 1• 100 50 0.05 ^ 0.1 ^ 0.15 ^ 0.2 True Strain Figure 6.13: The -196°C behavior of the composite, matrix, and matrix with Orowan stress. The open circles represent an estimate of the matrix flow stress from tension compression tests. 88 Chapter 6. Discussion Temperature (V) 0.0rowan (mPa) Measured oli°' (MPa) cr(Aowan (m pa) 25 134 79 1088 -75 142 N/A 1165 -196 150 70 1260 Table 6.2: Estimations and experimental values of the Orowan stress for aluminum and zinc in a DP alloy of the tensile curves. The increase in yield strength required to fit the A1-2.0at.%Zn curve to the points estimated from the Bauschinger tests is consistently lower than the calculated Orowan stress. This is probably due to the method used to estimate the matrix yield from the Bauschinger curves; It was based on a 0.2% offset which is close to the first point of yielding. The material with the largest lamella in the most favorable orientation for slip or the continuously precipitated areas will yield first. However, the Orowan stress was calculated using the average lamella spacing for grains with the average yield stress due to orientation. It is expected that the actual matrix yield stress should be significantly larger than the estimation of the Bauschinger matrix yield stress. There is no obvious way to estimate the average matrix yield stress from a Bauschinger curve as the yield section is rounded and it is not certain where the 0 phase starts to yield. Moreover, this method assumes equal strains in the two phases and that the elastic moduli are the same for the two phases. The assumption that the elastic moduli are the same when in reality the modulus of zinc is approximately twice the modulus of aluminum (see table 2.1) tends to over predict the stress in the aluminum lamella. This is due to the assumption of equal strain in each phase. The stress in the zinc lamella changes twice as fast as the stress in the aluminum lamella for the same change in strain. However, the difference in overall elastic modulus as seen in region I of figure 6.8 is very close to the elastic modulus of the aluminum lamella and this effect should be small. It is interesting to note that the strain hardening rate of the aluminum lamella estimated from the Bauschinger tests is very similar to that of the A1-2.0at.%Zn material for the liquid nitrogen test and agrees within error for the room temperature test. More room temperature data points would be required to verify the strain hardening rate at that temperature. The third room temperature Bauschinger point was very close to necking and is expected to be less reliable than the first two. Since the strain hardening rate for the aluminum lamella was the same as A1-2.0at.%Zn, it is unlikely that GNDs or dislocations from an interface play a significant role in the 89 Chapter 6. Discussion strain hardening of the in-situ matrix material. Thus, it is sufficient to explain the only modification of the mechanical response of the a phase as being due to the scale induced increase in yield strength. Both the GND and grain boundary source model are dependent on changing the strain hardening rate by influencing the dislocation density. If the strain hardening rate of the matrix is the same as the bulk, neither the GND or grain boundary source mechanism would apply to the DP A1-18.5at.%Zn system. In figures 6.13 and 6.12, three aspects are worthy of further comment. Firstly, the flow stress of the composite is significantly higher than that of the matrix. Secondly the work hardening rate after the first 5% strain all become about the same. Lastly, the difference in flow stress is higher between the matrix and 0 phase at -196°C than at room temperature. This indicates that the /beta phase must be carrying a very large stress and this observation will be investigated below. 6.2.3 Composite Behavior: The Predicted Yield Stress of Fine-Scale Zinc There are two main ways to calculate the stress in the in-situ precipitates. The first method requires the A1-18.5at.%Zn stress strain curve, the A1-2.0at.%Zn stress strain curve corrected for phase scale and the volume fraction of precipitate. If equal strain is assumed in all phases, the rule of mixtures can be applied and the precipitate yield stress can be calculated using equation 6.4. The predicted stress strain curve of the zinc for room and liquid nitrogen temperatures are shown in figure 6.14 and 6.15. acomposite — (1 — f )crmatrix (6.4)azinc — f A plot of the back stress versus the forward strain for both temperatures is shown in figure 6.16. Plot 6.16 shows that the internal stresses saturate at room temperature after a forward strain of approximately 1%, but do not saturate until 3-4% at -196°C. The build up of internal stresses is higher at -196°C than at room temperature. The backstress builds up most rapidly in the rounded zone of the stress strain curve (phase II) and seems to saturate in phase III for both temperatures. The second method for estimating the stress carried by the zinc is through the Bauschinger backstress and the aluminum lamella strength estimated above. The rule of mixtures (n-\-- composite — f aprecipitate + (1 — f)Crmatrix) and the backstress (o-b = a composite — gm) can be combined and rearranged to produced equation 6.5. The stress 90 aprecipitate o (of+a,)/2 500- 713 °- 400-M 300- Y)^• 01z 200- 100- 0.1^0.15 True Strain Figure 6.14: Stress strain curve of the matrix, composite and predicted precipitate at -196 °C. 600- 0.04^0.06 True Strain 0.02 0. 10.08 crAI-18.5at.%Zn Chapter 6. Discussion Figure 6.15: Stress strain curve of the matrix, composite and predicted precipitate at 25 °C. 91 Chapter 6. Discussion 120- o 0.01^0.02^0.03^0.04^0.05 0.06^0.07 Forward Strain Figure 6.16: The back stress of DP Al-18.5at.%Zn at -196°C. strain curve for the precipitate can then be calculated. gb i Cr zzric — 7 ,- go, The Bauschinger stress used to predict the precipitate strength is based on the offset used to calculate o-b. The offset used by Moan and Embury [62] is 0.1%, whilst Proudhon and Poole [63] use an offset of 2%. An intermediate offset of 0.2% is used in this thesis. The most appropriate value of offset to use in estimating the values of the internal stresses is still a question under active debate, thus three offsets are plotted in figure 6.16. Regardless of the offset used, the backstresses saturate at approximately the same strain values and have comparable shapes. Thus, while the offset used will change the magnitudes of the predicted stresses, similar trends should be obtained regardless of the offset used. The estimation for the precipitate stress is plotted in figures 6.17. The predicted precipitate stress from equation 6.4 is also plotted for comparison. The agreement between the two different methods is close considering that the precipitate yield stress should be lower for equation 6.4. The error is smaller for -196°C than for room temperature, this is probably due to thermally activated processes that become active at room temperature as will be seen later in the discussion. Also, equal strain was assumed in the material. Equal strain is a reasonable assumption because the lamella (6.5) 92 1000: 800: 600-Ln L/) 400-a) 200- (1) aprecipitate=(CFAI-18.5at%Zri-(1-f)aA1-2.0at%Zn)if (2) aprecipitate=ab/f+00 ••1'^•^•^•I••^•^I••^•^1••^•^I0-. ^ Chapter 6. Discussion 0.02 0.04^0.06^0.08^0.1 True Strain Figure 6.17: The predicted strength of the zinc at both 25 °C and -196 °C. are so closely constrained, but the true deformation will be somewhere in between the equal stress and the equal strain cases. Both the zinc and aluminum will have some anisotropy, which causes rounding of the stress strain curve and makes it more difficult to predict the average properties of both the precipitate and the matrix. The predicted stress carried by the zinc lamella is significantly higher than the bulk flow stress for pure zinc, which is reported to be between 160-390MPa at 300K for similar grain sizes in pure bulk zinc [14]. The calculated Orowan stress based on the thickness of the zinc lamella and using equation 6.3 is much larger than that predicted above, and much larger than that predicted for the aluminum lamella since the zinc lamella are much finer. As in the case of the aluminum lamella, the Orowan prediction of the flow stress is expected to be an upper limit estimate for the flow stress owing to the basic assumptions of equal strain and uniform lamella size and orientation used to back-estimate its value. It is important to note that the back estimated stresses carried by the zinc are much larger for samples tested at -196°C than at 25°C. This, combined with the observation of the saturation of the Bauschinger effect at relatively small backstresses at room temperature suggest that temperature dependent processes are capable of relaxing some of the plastic misfit between the two phases. It would appear that these processes are less effective at liquid nitrogen temperatures. A similar observation has 93 Chapter 6. Discussion been made in the copper chromium system [64]. The above estimates of the stresses in the two phases require a large number of important assumptions about lamellar morphology, spacing and orientation relative to the loading axis. This results in uncertainties in the estimated flow stresses. The matrix yield stress is probably underestimated because it is based on minimum versus average reverse yield stress in the composite. A minimum estimation for the matrix stress results in an maximum for the precipitate stress. Also, the error is magnified by a factor of 1/f. Therefore, a small change in the matrix stress results in a much larger change in the predicted zinc stress. The stress in the zinc at liquid nitrogen temperatures has a UTS of 885MPa, which is within a factor of two of the theoretical strength of zinc (t 1600MPa). As has been discussed earlier, the fine scale structure inhibits deformation in the zinc lamella by preventing twinning, fracture, intergranular cracking and recrystallization. The high strength observed in the zinc is consistent with a change in mechanism due to the reduced scale. 6.2.4 Strain Rate Jump Tests The composite stress-strain curve of the Al-18.5at.%Zn material appears to be ex- plainable by considering that the aluminum lamella behave similarly to bulk alu- minum but with an increased yield strength and that large internal stresses develop due to the presence of the constrained zinc lamella. As noted above, the develop- ment of internal stresses appear to be strongly temperature dependent indicating the presence of thermally assisted relaxation processes. Strain rate jump tests have been used to confirm the presence of such processes. Linear Superposition Theory It is often assumed that the individual components of strengthening can be linearly added to estimate the flow stress and has been found to be accurate in a surprising number of cases [65]. The flow stress (TO can be broken up into two components: one part independent of deformation (Ty) and the other part dependent on deformation (TD). The total flow stress of the material is thus given by the linear addition of theses two components to produce equation 6.6 [65] and is true when the controlling mechanism for the two components are on different length scales. Ti = TY ± TD^ (6.6) 94 Chapter 6. Discussion When equation 6.6 is differentiated in terms of dln(e) at constant temperature and substructure, equation 6.7 results and can be simplified to 6.8. dyi^dlnry^dlwro I = TY •^• TI ±(Ti Ty) •̂ T Pdine T'P ding dlnE I ' dy, dine IT 'p— TY • (MY MD) ± T • MD From a strain rate jump test, a Haasen plot can be created by plotting didn(f) versus a. The curve should be linear with a slope of MD (where MD = dine ) and an intercept of cry • (My — MD). MD and My are conventionally referred to as the rate sensitivity. The slope MD can be integrated to produce equation 6.9 that shows the depen- dence of the stress on strain rate. The larger the value of MD the larger the effect of strain rate on the stress. = C • emp (6.9) The intercept of the Haasen plot is equal to Ty • (My — MD) and indicates how temperature and rate sensitive the contributions to the yield strength are. A positive intercept indicates thermal obstacles (i.e high rate sensitivity) such as solute pinning. A negative intercept indicates strengthening by athermal obstacles (i.e. low rate sensitivity). An intercept of zero is indicative of pure crystals that strengthen solely because of dislocations. The slope of the Haasen plot indicates the rate sensitivity of the obstacles leading to work hardening of the material. Haasen plots were created for both the composite and matrix material at 25°C, - 75°C, and -196°C (figures 6.18 and 6.19). The Haasen plot for bulk zinc was calculated from rate jump experiments conducted by Risebrough [2]. A summary of the slopes for each temperature calculated by linear regression of the composite, matrix and precipitate are shown in tables 6.3, 6.4, and 6.5 respectively. A plot of all the Haasen data for all three materials at all three temperatures is shown in figure 6.20 The intercept of both the matrix and precipitate material are close to zero within error. The Haasen slope of all three test temperatures for the Al-2.0at.%Zn, the two coldest temperatures for the pure zinc and the two coldest conditions for the composite material are similar within error. Similar slopes suggest a similar defor- mation mechanism. Al-2.0at.%Zn and pure zinc contain a much smaller surface to volume ratio than the composite material. Therefore, since the composite has a sim- (6.7) (6.8) 95 iia_ 2 0.08 - •-•-. -z•-_, 0.06- ■-..^• W . 1:30 ' 04 -*-c-^• P-0.02- Chapter 6. Discussion 6^8^10 ^ 12 arrue/p (1/1000) Figure 6.18. Haasen plot of DP A1-18.5at.%Zn at varied temperature i -^•^•^•^-^•2 3 4 crTrue/p (MPa) a Figure 6.19: Haasen plot of A1-2.0at.%Zn at varied temperature 96 Chapter 6. Discussion Temperature (°C) m b 25 °C 0.027 -0.000319 -75 °C 0.031 -0.000129 -196 °C 0.069 -0.000124 Table 6.3: The Haasen slope and intercept for DP A1-18.5at.%Zn material at 25 °C, -75 °C, and -196 °C Temperature (°C) m b 25 °C 0.0335 -0.0000424 -75 °C 0.0190 -0.00000517 -196 °C 0.0137 0.0000102 Table 6.4: The Haasen slope and intercept for DP A1-2.0at.%Zn material at 25 °C, -75 °C, and -196 °C Temperature (°C) m b 20°C 0.13 -0.0260662 -95 °C -0.0042 0.0382865 -120 °C 0 0.0215861 Table 6.5: The Haasen slope and intercept for pure zinc at 20 °C, -95 °C, and -120°C as measured by Risebrough [2] Figure 6.20: Haasen plot for the Composite, A1-2.0at.%Zn and pure zinc at varied temperature 97 Chapter 6. Discussion ilar strain rate sensitivity as the A1-2.0at.%Zn and pure zinc at -95°C and -120°C, the rate limiting deformation mechanism can not be related to the interface. However, the Haasen slope is elevated for the room temperature composite test indicating a change of mechanism to a more thermal process such as grain boundary sliding or cobble creep. The Haasen slope for the bulk zinc is also elevated at room temperature. This is consistant with the evolution of the zinc microstructure as it deforms, which has been shown to recrystallize - a thermally activated process. TEM micrographs of 5% deformed composite material at room temperature show that the lamella are intact, thus not recrystallized and the same mechanism that causes an increase in the Haasen slope for the bulk zinc probably does not operate in the composite. In this case, it is more likely that the high rate sensitivity indicates the presence of thermally activated processes that allow for the relaxation of the plastic misfit between the alu- minum and zinc lamella. At room temperature this process is active and allows for most of the internal stresses to be relaxed (i.e. the efficiency of load transfer to the zinc is low). At -196°C the effectiveness of this process is significantly reduced and the efficiency of load transfer to the zinc is increased. This leads to the generation of much larger stresses in the zinc, much larger internal stresses and larger overall composite flow stresses and better work hardening rate. 6.2.5 Wire Drawing The deformation of pearlite as well as other co-deforming two-phase materials by wire drawing has been shown to result in decreasing lamella spacing according to equation 6.10 [6]. 1 1 ( € A, A, • exP 2) (6.10) Using equation 6.10, the interlamellar spacing should be 54nm for DP A1-18.5at.%Zn wire drawn to a true strain of 3 and 20nm for material wire drawn to a true strain of 5. The measured interlamella spacing for DP A1-18.5at.%Zn wire drawn to a true strain of 3.1 is 166nm and 37nm for material wire drawn to a true strain of 5. Several reasons could be used to explain why the measured interlamella spacing are larger than the calculated interlamella spacing. Perhaps most importantly, the initially randomly orientated microstructure must arrange to become aligned parallel to the wire drawing axis. During this period, the reduction of the lamellar spacing is less efficient [66]. 98 Measured :4 5 1800 ^ 1600 1400 1 1200 Theoretical 200 ^ 0 c=ln(A./A) .- 800 600 400 Chapter 6. Discussion Figure 6.21: The theoretical and measured strength of a DP Al-18.5at.%Zn alloy The material wire drawn at room temperature was found to have a much lower strength than predicted. The theoretical strength can be calculated by first deter- mining the lamella spacing using equation 2.15 and then the stress using the Orowan equation 6.3 for both phases and the overall stress using the rule of mixtures. Figure 6.21 compares the theoretical to the measured strength of DP Al-18.5at.%Zn wires. The measured strength is lower than the predicted strength because of the breakdown of the lamella structure. 6.3 Stability of the Deformed Microstructure The free energy diagram (figure 6.22) predicts a decomposition of the solid solution into a aluminum and zinc that is generally followed during the discontinuous pre- cipitation. However, the phase diagram ignores the effect of interface energy that becomes large due to the fine scale lamella structure. Experiments have shown that pearlite will dissolve if enough deformation is put into the material [5]. As the material is deformed, the lamella become finer which reduces the effective radius and increases the Gibbs-Thompson free energy of the lamella phase. Using the Gibbs-Thompson relation and the free energy diagram, the critical lamella thickness that will result in the dissolution of the precipitate can be calculated and the required strain to produce the critical lamella thickness backed 99 14 12- - - FCC: 300K 400K 450K 500K HCP: 300K 400K _ 450K 500K I^I^I^1 0.2^0.4^0.6^0.8 ^ 1.0 MOLE_FRACTION ZN Figure 6.22: Free energy of the aluminum zinc system at varied temperature _ Chapter 6. Discussion out. To start, the free energy diagram of the system is required and is displayed in fig- ure 6.22. At the material composition of 18.5at.%Zn, the most stable microstructure is almost pure FCC aluminum and HCP zinc. However, as the temperature increases, the change in free energy due to decomposition decreases. The 18.5at.%Zn compo- sition is close to the inflection point, and thus is close to the spontaneous spinodal zone. The Gibbs-Thompson relation is shown as equation 6.11. The critical radius will be located at the edges of the plates where the radius will be the smallest. The critical radius will then be equal to half the precipitate lamella thickness. The measured A is equal to the thickness of one FCC plate and one HCP plate. The volume fraction of the HCP phase is about --, 15%. Therefore, k can be estimated by k = where r = 0. 15A . AG = o-Vmk^ (6.11) 100 Chapter 6. Discussion 14 12- a.)^6-c L.L.1 O 4 -sasa._CD 2-^X. _.---------0^-------- 1------- - - - - _ i AGPGibbs-Thompsol 103 2 ,^I^I 1 A ^ 0^0.2^0.4^0.6^0.8^1 0 Mol Fraction Z Figure 6.23: The aluminum zinc phase diagram corrected for the Gibbs-Thompson free energy. The phase diagram can then be corrected for the Gibbs-Thompson effect as shown in figure 6.23. In this case, the Gibbs-Thompson effect does not cause an appreciable change in the mutual solubility until full dissolution at room temperature because of the shape of both curves. The molar volumes of both zinc and aluminum are very close; Thus, the change in free energy caused by the Gibbs-Thompson effect is similar for both the a and 0 phases and the 0 curve can be corrected by the value of the Gibbs-Thompson effect for the 0 phase at all compositions. Equation 6.11 can be solved using lin, = 1.005 x 10 and amp = 0.522 6 [59]. The resulting critical lamella size is A7.00K = 20nm and noic = 56nm. As the temperature increases, the change in free energy decreases, increasing the critical lamella size required for dissolution. The required true strain to cause dissolution of the lamella is ET.00K = 5.0 and Eci(.0K- = 2.9. The measured lamella spacing after a true strain of 5 is 37nm which is reasonably close to the value of 20nm considering only lamella with a spacing larger than the critical value will be left after deformation and are the only lamella measured. 101 14 164^6^8^10^12 Time (s x 1000) 70: E^60:  . (3) 50: 2 4 0 -n 5 7030- 0 0- 0 Chapter 6. Discussion Figure 6.24: The estimated diffusion distance of an Al-18.5at.% alloy at room tem- perature An estimation of the boundary diffusion constant can be made using the boundary diffusion calculated in the first section of the discussion. This diffusion constant calculated from experimental results in not exactly the same as that required for this section. The measured diffusion constant is for diffusion along the mobile boundary as coarsening would occur along the lamella. However, the boundaries are similar in nature and the diffusion constants for the mobile interface should be closer to the diffusion constants along the lamella than using an estimate based on a rule of mixtures approximation from pure phases. The diffusion distance (x) was estimated using equation 6.12 and a plot of diffusion distances follows: x = VD time (6.12) The diffusion distance at the transformation temperature (160°C) is large com- pared to the grain size (— 35pm). It is possible for solute to diffuse one quarter the grain length in under an hour at 40°C. TEM images show that the lamellar mi- crostructure is relatively stable, even after weeks at room temperature. All tensile samples were stored at -20°C, but TEM foils had to be kept at room temperature to avoid condensation if they were removed from a freezer. Figure 6.24 shows that boundary diffusion is rapid and could play a dominate role in transformations if they 102 Chapter 6. Discussion occur. The TEM micrographs show that the microstructure of material deformed to a true strain of '- ^contains mostly equiaxed precipitates and little lamellar structure, but the material strained to '- ^is still mostly laminar. This can be explained by the Gibbs-Thompson surface energy. As the material is heavily deformed, the lamella dissolve because the lamella become finer than the critical radius. This results in a non-equilibrium state, and boundary diffusion allows the supersaturated solute to form the equiaxed precipitates. However, there is no coarsening in material that has been deformed less because the material is close to equilibrium and relatively sta- ble. The reprecipitation of the material strained to — 5 would explain the lack of significant supersaturation of the FCC phase measured by XRD. 103 Chapter 7 Conclusion An aluminum 18.5at.% zinc alloy was selected for a study of strengthening by scale refinement. To start, a processing method to produce a discontinuously precipitated microstructure with close to 100% transformation and an interlamellar spacing of 240nm was developed. The microstructure was characterized and the results agreed closely with the literature. The combination of tension compression tests, the com- posite stress strain curve and the bulk stress strain curve of the composite constituents were used to analyse the deformation. The in-situ matrix and precipitate stress strain curves were then calculated. The in-situ stress strain curves differed from the bulk stress strain curves because of the scale of the material and the resulting Orowan stress from the bowing of dislocation in the lamella channels. An Orowan model accounting for the internal stresses was applied to the system and could be used to explain the strengthening. It was found that only the Orowan stress contributed to the strengthening of the yield stress and neither GNDs or interfaces as a dislocation source played a role. The temperature was found to affected the build up of internal stresses, the work hardening rate and the final strength. At high homologous temperatures, stress relaxation processes decreased the stress partioning between the hard and soft phases resulting in a lower strain hardening rate and a lower yield stress. The system shows the importance of temperature in the strengthening of DMMCs and that temperature is an important parameter for future study in this field. Although the lamellar material had a much higher strength than the rule of mix- tures would predict, the overall strength of the alloy was lower than that of more conventional high strength aluminum alloys. However, the cause of the low strength was identified as the stress relaxation between the hard and soft phases. If the stress relaxation could be controlled, much higher strengths should be attainable. 104 Chapter 7. Conclusion 7.1 Future Work There are a few areas of this project that would be interesting to pursue further: • From theory and the experimental evidence gathered in this study, high strengths should be obtained if the material is wire drawn at liquid nitrogen tempera- tures. Unfortunately, UBC does not have a reliable way to wire draw at liquid nitrogen temperatures. A process would have to be developed on campus or samples prepared by a third party to test this hypothesis. • The dislocation structure of the zinc was not analyzed. Conditions could not be found to image dislocations in the zinc lamella, but it would be useful to do so to better understand how zinc deforms on a fine scale, especially at liquid nitrogen temperatures. • A solutionized A1-18.5at.%Zn alloy was produced and preliminary tests were conducted at room and liquid nitrogen temperatures. High strengths in the range of 500MPa were obtained. The cause of this strengthening was unknown, but it is believed to originate from clustering of the zinc. • The effect of changing either the lamella spacing or volume fraction of phases would help our understanding of the deformation mechanism and the applica- tion of the Orowan model to this system. The discontinuous coarsening reaction might be a possible way to vary interlamellar spacing to a large enough degree to produce significant change in the yield stress. However, producing a consis- tent discontinuous coarsened structure is more difficult than aging for a longer period of time. Tests failed to produce a mostly DC material using compo- sitions between 14at.%Zn to 30at.%Zn, transformation temperatures between 120°C to 200°C and aging times up to 5 days. 105 Bibliography [1] C. F. Yang, Sarkar G, and R. A. Fournelle. Discontinuous precipitation and coarsening in al-zn alloys. Acta Metallurgica, 36(6):1511-1520, 1988. [2] N. 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Materials Science Division, Argonee National Laboratory. [66] D. Raabe, F.Heringhaus, U. Hangen, and G. Gottstein. Investigation of a cu- 20 massmicrostructure and mechanical properties. Zeitschrift fur Metallkunde, 1995. 110 Appendix A: Calculations The procedure used to calculate the mass of zinc and aluminum required to produce an 18.5 atomic percent zinc melt was as follows. The total mass (Int) was determined from the size of the mold. The aluminum was measured first with in a close approxi- mation. The amount of zinc was then calculated from the previously measured mass of aluminum and carefully measured out. This method saved time because the zinc was far easier to divide into smaller portions than the aluminium. int = mai + mzn mai = 26.98(1 — X)C rnzn = 65.409(X)C mt = (26.98(1 — x) ± 65.409x) x C^ (7.1) Equation 7.1 was solved for x=0.185 and the mass of zinc and aluminum were calculated using equation 7.2 nizn = 0.550mai ^ (7.2) 111

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