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Recovery and recrystallization behaviour of AA5754 and IF-Boron steel during annealing Go, Johnson 2001

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R E C O V E R Y AND R E C R Y S T A L L I Z A T I O N BEHAVIOUR O F AA5754 AND IF-BORON S T E E L DURING ANNEALING by J O H N S O N G O Bachelor of Applied Science, The University of British Columbia, Canada, 1998. A THESIS S U B M I T T E D IN P A R T I A L F U F E L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F M A S T E R O F A P P L I E D S C I E N C E in T H E F A C U L T Y O F G R A D A U T E STUDIES ( D E P A R T M E N T O F M E T A L S A N D M A T E R I A L S E N G I N E E R I N G ) We accept this thesis as conforming to the required standard T H E U N I V E R S I T Y O F BRITISH C O L U M B I A O C T O B E R 2001 © Johnson Go, 2001 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Hrf^f qwi ^tfvhll E K j * * ^ The University of British Columbia Vancouver, Canada Date Oct U , -^<N) f DE-6 (2/88) A B S T R A C T A microstructure model to predict the mechanical properties during annealing has been developed for two important classifications of industrial processed automotive alloys: aluminum-magnesium AA5754 alloy and boron-containing interstitial free steel. The model adopts a rule of mixture to capture the overall softening due to recovery and recrystallization based on the assumption that these two processes proceed independently. The internal state variable approach is employed in the mathematical formulation of the model. The Kuhlmann and Cottrell/Aytekin recovery model and the J M A K recrystallization model are used to capture the time evolution of dislocation density and fraction recrystallized, respectively. The required kinetic parameters are determined from isothermal tests. Isothermal annealing models are developed and validated against data obtained from continuous heating experiments. Experimentally, tensile and hardness tests are carried out in conjunction with quantitative metallography to quantify the kinetics of recovery and recrystallization. The model accurately predicts the microstructural and yield stress evolution in AA5754 under isothermal and non-isothermal annealing conditions. For IF-boron steel, however, the current modelling approach is too simple to capture the complexity involved in the recrystallization process. Consequently, the model for IF-boron steel is considered as purely empirical in nature. ii T A B L E OF CONTENTS ABSTRACT ii LIST OF TABLES v LIST OF FIGURES vi LIST OF SYMBOLS xi ACKNOWLEDGEMENTS xiii CHAPTER 1 INTRODUCTION 1 1.1 Advanced Automotive Materials 2 1.2 Continuous Annealing Technology 7 1.3 Motivation for Research 9 1.4 Scope and Objectives 10 CHAPTER 2 LITERATURE REVIEW 12 2.1 Introduction 12 2.2 Recovery - General Observations 13 2.2.1 Recovery Behaviour of A l - M g Alloys 14 2.2.1.1 Determination of Microstructural Parameter 16 2.2.1.2 Kinetic Models for Recovery 21 2.2.2 Recovery Behaviour of Interstitial Free Steel 27 2.3 Recrystallization - General Observations 29 2.3.1 Kinetic Models for Recrystallization 30 2.3.1.1 Application of J M A K Theory to Model Recrystallization Kinetics 31 2.3.2 Recrystallization Behaviour of A l - M g Alloys 35 2.3.2.1 The Effect of Solute M g 35 2.3.2.2 The Effect of Heating Rate 40 2.3.3 Recrystallization Behaviour of Interstitial Free steel 42 2.3.3.1 The Effect of Microalloying Elements 42 2.3.3.2 The Effect of Heating Rate 48 CHAPTER 3 EXPERIMENTAL PROGRAM 52 3.1 Materials 52 3.2 Isothermal Annealing 53 3.2.1 AA5754 53 3.2.2 IF-Boron Steel 54 3.3 Continuous Heating Using Gleeble 56 3.4 Tensile and Hardness Measurements 60 3.5 Quantitative Metallography 61 iii CHAPTER 4 RESULTS AND DISCUSSION 63 4.1 AA5754 63 4.1.1 Characterization of As-received Materials 63 4.1.2 Isothermal Annealing - Tensile Measurements 65 4.1.3 Isothermal Annealing - Microstructural Analysis 67 4.2 IF-Boron Steel 74 4.2.1 Characterization of As-received Materials 74 4.2.2 Isothermal Annealing - Hardness Measurements 78 4.2.3 Isothermal Annealing - Microstructural Analysis 81 CHAPTER 5 MODEL DEVELOPMENT 91 5.1 The Internal State Variable Approach 91 5.1.1 Single State Variable Formulation for Recovery and Recrystallization 93 5.1.2 Material Response Equation for Recovery and Recrystallization 94 5.2 Isothermal Annealing Model for AA5754 95 5.3 Isothermal Annealing Model for IF-Boron Steel 104 CHAPTER 6 MODEL VALIDATION 109 CHAPTER 7 SUMMARY AND CONCLUSIONS 116 7.1 Summary 116 7.2 Future work 119 REFERENCES 120 iv LIST OF T A B L E S Table 2.1. Summary of proposed rate controlling mechanisms for recovery. 21 Table 2.2. Fitting parameters for the softening curves in Figure 2.7. 24 Table 2.3. Ideal J M A K exponents. 31 Table 2.4. Thermal cycle employed by Simielli et al. to study the effect of heating time on the recrystallization behaviour of an Al-0.5%Mg alloy. 40 Table 3.1. Chemical composition of as-received AA5754. 52 Table 3.2. Chemical composition of as-received IF-boron steel. 52 Table 3.3. Processing routes of as-received materials. 52 Table 3.4. Etching methods for AA5754 and IF-boron steel. 61 Table 4.1. Mechanical properties of as-received cold rolled AA5754. 64 Table 4.2. Summary of isothermal recrystallization start and finish time for AA5754. 71 Table 4.3. Mechanical properties of as-received cold rolled IF-boron steel. 75 Table 4.4. Summary of isothermal recrystallization start and finish time for IF-boron steel. 90 Table 5.1. Fitting parameters for the isothermal recovery and recrystallization models for AA5754. 96 Table 5.2. Fitting parameters for the isothermal recovery and recrystallization models for IF-boron steel. 105 Table 6.1. Recrystallization start and finish temperatures during continuous heating. 113 v LIST O F FIGURES Figure 1.1. Requirements for a new generation of automotive materials. 3 Figure 1.2. Properties of advanced cold rolled high strength steels. 4 Figure 1.3. Comparison of the current and future development of aluminum and steel sheet alloys. 6 Figure 1.4. Typical thermal cycle of C A L for steel and aluminum alloys. 8 Figure 1.5. Processing-microstructure-properties relation. 9 Figure 2.1. Microstructural evolution during recovery of a plastically deformed material. 14 Figure 2.2. Yield stress evolution as a function of time at room temperature for A l - M g alloys. 15 Figure 2.3. Correlation between yield stress and dislocation density according to the forest work hardening theory. 17 Figure 2.4. Changes in resistivity in A l - M g alloys after 10 min heat treatment at temperatures between 100 and 5 0 0 ° C . 18 Figure 2.5. The linear relationship between oys-o0 and pm. 19 Figure 2.6. Evolution of yield stress during static recovery at 160 and 2 2 0 ° C for 90% cold rolled A l - M g alloys. 20 Figure 2.7. Recovery kinetics of a 90% cold rolled A l - 3 M g alloy. 23 Figure 2.8. The time dependence of the softening behaviour of AA5182 at 1 7 7 ° C 24 Figure 2.9. Fitting of Equation 2.7 to the in-situ Rj measurements of recovery in an IF steel at temperatures ranging from 500 to 6 2 5 ° C . 28 Figure 2.10. Experimental isothermal recrystallization kinetics of a 80% cold rolled Ti+Nb stabilized IF steel. 34 Figure 2.11. The effect of M g content on the recrystallization kinetics of 95% cold rolled A l - M g alloys. 36 vi Figure 2.12. The effect of M g content on the temperature at which 50% recrystallization occurred in A l - M g alloys. 36 Figure 2.13. Variations in activation energy with progress of recrystallization and the effect of M g content in A l - M g alloys. 38 Figure 2.14. Recrystallization kinetics in 80% cold rolled commercial purity A l and Al -5%Mg alloy. 39 Figure 2.15. Effect of heating time on the isothermal recrystallization kinetics of a 30% cold rolled Al-0.5%Mg alloy. 41 Figure 2.16. T T R diagram for T i stabilized, Al-killed steel, and rimmed steel. 43 Figure 2.17. Recrystallization curves for a series of IF steels isothermally annealed at 7 0 0 ° C . 44 Figure 2.18. Effect of boron content on recrystallization starting and finishing temperatures in IF steels. 46 Figure 2.19. Recrystallization activation energy for different cold rolled steel grade. 48 Figure 2.20. Effect of heating rate on Tso% in 70% cold rolled steel with varying amount of carbon content. 49 Figure 2.21. Schematic diagram illustrating the application of principle of additivity to continuous heating kinetics. 50 Figure 2.22. Effect of heating rate on continuous heating recrystallization kinetics of a 80% cold rolled Ti+Nb stabilized IF steel. 51 Figure 3.1. Thermal cycle of heating a sample in a salt bath set at 2 5 0 ° C . 55 Figure 3.2. Strip annealing in Gleeble 1500 thermomechanical simulator. 56 Figure 3.3. Schematic of a sheet sample used in Gleeble experiments. 57 Figure 3.4. Typical thermal cycle of continuous heating tests with l ° C / s heating rate. 58 Figure 3.5. Schematic of a Gleeble isothermal annealing sample for IF-boron steel. 59 Figure 3.6. Definition of transverse plane in samples. 60 vii Figure 4.1. Typical loading response of cold rolled AA5754 in the rolling direction. 64 Figure 4.2. Microstructure of a 40% cold rolled AA5754 sample. 64 Figure 4.3. Isothermal recovery kinetics of AA5754. 66 Figure 4.4. Isothermal recovery and recrystallization kinetics of AA5754. 66 Figure 4.5. Recovered microstructure of a AA5754 sample. 68 Figure 4.6. Microstructure showing the initiation of recrystallization in AA5754. 68 Figure 4.7. Partially recrystallized structure of a AA5754 sample. 69 Figure 4.8. Fully recrystallized structure of a AA5754 sample. 69 Figure 4.9. Averaged recrystallized grain sizes as a function of recrystallization temperatures for AA5754. 70 Figure 4.10. Through thickness variation of fraction recrystallized for AA5754. 72 Figure 4.11. Isothermal recrystallization kinetics of AA5754 at 325 and 3 5 0 ° C determined by quantitative metallography. 74 Figure 4.12. Engineering stress-strain curve for cold rolled IF-boron steel. 75 Figure 4.13. Poorly etched as-received microstructure of IF-boron steel. 77 Figure 4.14. Photomicrograph showing the elongated ferrite grains in a slightly recovered IF-boron steel sample. 77 Figure 4.15. Isothermal softening curves obtained from salt bath annealing experiments for IF-boron steel. 78 Figure 4.16. Microstructure of a carburised IF-boron steel sample. 80 Figure 4.17. Isothermal softening curves obtained from Gleeble annealing experiments for IF-boron steel. 81 Figure 4.18. Initiation of recrystallization in a IF-boron steel sample 83 Figure 4.19. Coarsening of recrystallized grains in a IF-boron steel sample 83 viii Figure 4.20. Microstructure of a 60% recrystallized EF-boron steel sample. 84 Figure 4.21. Fully recrystallized structure of a IF-boron steel sample. 84 Figure 4.22. Volume fraction of recrystallized grains of IF-boron steel after annealing at 7 1 7 ° C for various lengths of times. 87 Figure 4.23. Averaged recrystallized grain sizes as a function of recrystallization temperatures for IF-boron steel. 90 Figure 5.1. Schematic representations of the composite model of the structure in a partially recrystallized sample. 94 Figure 5.2. Isothermal recovery model for AA5754. 96 Figure 5.3. J M A K plot of the isothermal recrystallization kinetics of AA5754. 98 Figure 5.4. Arrhenius plot of the t50% for recrystallization as a function of temperature. 100 Figure 5.5. Isothermal recrystallization kinetics of AA5754. 100 Figure 5.6. Comparison of volume fraction recrystallized in AA5754 calculated from quantitative metallography, rule of mixture and the J M A K model. 101 Figure 5.7. Yield stress evolution of AA5754 during isothermal annealing. 102 Figure 5.8. Empirically derived iso-yield diagram for isothermal recovery and recrystallization of cold rolled AA5754. 103 Figure 5.9. Hardness evolution of IF-boron steel during isothermal annealing. 104 Figure 5.10. Comparison of volume fraction recrystallized in IF-boron steel calculated from quantitative metallography, rule of mixture and the J M A K model. 107 Figure 6.1. The effect of holding time at peak temperature during continuous heating of a AA5754 sample. 110 Figure 6.2. Comparison between the model predictions and continuous heating experimental data for AA5754. 112 Figure 6.3. Comparison between the model predictions and continuous heating experimental data for IF-boron steel. 112 ix Figure 6.4. Non-isothermal recrystallization kinetics as a function of homologous temperatures for AA5754 and JJF-boron steel. 114 Figure 6.5. Measured recrystallized grain sizes after annealing with different heating rates for AA5754 and IF-boron steel. 115 x LIST O F SYMBOLS A pre-exponential factor in Equation 5.9 At interfacial area per unit volume separating the recrystallized grains from the unrecrystallized matrix Ag mean grain area b temperature dependant constant in J M A K model Ci, C2 constants used in recovery model Cj concentration of dislocation jogs Ds coefficient of self-diffusion d-A averaged grain size F driving force G shear modulus G growth rate G average interfacial growth rate k temperature dependant constant in Speich/Fisher model ky constant in Hall-Petch equation M Taylor factor m Speich/Fisher exponent N nucleation rate n J M A K exponent Qu activation energy for recrystallization Qo activation energy for recovery R gas constant (8.314 J/mol-K) xi Ri X-ray peaks ratio Sj,S2--- Si instantaneous values of internal state variables T temperature Tf recrystallization finish temperature Ts recrystallization start temperature t time to constant used in Equation 2.4 tso% time taken to complete 50% recrystallization X volume fraction of recrystallized grains OyS yield stress Ob, <?Rx yield stress of fully recrystallized material <Ji initial yield stress <7RC recovered yield stress predicted by the recovery model a constant in Taylor work hardening model p dislocation density Pi initial dislocation density PR resistivity Vd climb velocity of dislocations 0Cj, 0C2 constants used in Equation 2.8 8 cell/subgrain size xii ACKNOWLEDGEMENTS First and foremost, I would like to express my heartfelt gratitude to my supervisors: Profs. Mary Wells and Matthias Militzer. I am very grateful to Prof. Warren Poole for his professional guidance throughout the course of this project. I have been extremely fortunate to be able to take advantage of their specific expertise in various aspects of this project. Special thanks are extended to Prof. Matthias Militzer who first offered me the opportunity to work on this research project. Financial support from the Natural Sciences and Engineering Research Council of Canada is gratefully acknowledged. I would also like to acknowledge the support provided by many people in the Department of Metals and Materials Engineering at U B C . In particular, I would like to thank Mr. Gary Lockhart and Mr. Binh Chau for helping me to conduct all the experiments. A special note of thanks to Fateh Fazeli, Leon Cheng, Taryn Biggs for their stimulating discussion and suggestions. This thesis is dedicated to the memory of my father. The generous tolerance and constant encouragement shown by Lee Leng are deeply appreciated. xiii C H A P T E R 1 INTRODUCTION Cold rolling is a common industrial process utilized extensively to reduce the thickness of sheet metals. But very often due to the structural changes introduced during the rolling process, the strength levels of the sheets are increased to several folds higher than in their original state. The sheets become so hard to the extent that any shape forming operations after that will become impractical. Annealing is a process applied to soften the materials and usually is the final step prior to shipping to customers. Hence, the ability to control the final properties of the sheets largely depends on the efficiency in the operation of the annealing process. The automotive industry has been the single largest driving force for the efficient thermal processing of advanced sheet alloys. The properties of sheet metals produced nowadays for automotive applications must be tailored to satisfy the increased demands from car buyers. In order to meet these targets, both aluminum and steel sheet metal producers are required to be innovative in process improvements, especially in downstream operations so that highly sophisticated end products can be mass-produced in a cost effective way. One clear example of this trend in recent years is the widespread use of continuous annealing technology to process a broad range of advanced aluminum and steel sheet alloys. In the following, current trends in the application of advanced sheet metals to manufacture vehicles are reviewed with an emphasis on the fierce competition between 1 advanced aluminum and steel sheet alloys. The continuous annealing process is briefly described and finally, the rationale for the present research project is delineated. 1.1 Advanced Automotive Materials The automotive industry is a consumer-driven industry. Since the oil crisis in 1973, the car industry is compelled to reduce the weight of new vehicles in order to boost fuel efficiency. Tightening environmental regulations on C O 2 emissions, which can only be cut by using less fuels, have also pushed automotive engineers to consider lightweight design seriously. From a marketing point of view, due to escalating public's awareness of environmental issues, "ultra-low-emission-vehicle ( U L E V ) " is becoming a popular choice among consumers. In short, new generation of automotive materials have to satisfy at least five equally important requirements: costs, production, physical qualities, environmental impact, and styling, as shown in Figure 1.1 [Bleck, 1996]. On the other hand, weight saving targets must be achieved without compromising safety performance and passenger comfort. For instance, lightweight can be attained by reducing the size of the vehicles but this method is not preferred because customers usually demand more room and there is a battery of accessories that can be installed if cars are bigger. Hence, the most direct route to vehicle weight reduction is to make the structural components and exterior panels, i.e., the body-in-white (BIW) lighter. This can be achieved by the following two methods: 2 1. Replace conventional low carbon steel sheets with higher strength steel, therefore allowing the thickness of structural members to be reduced and at the same time maintaining the structural strength of the body. 2. Replace conventional materials with lower density materials, for example, with aluminum or plastics and composites. Figure 1.1. Requirements for a new generation of automotive materials [Bleck, 1996]. The steel industry, still mindful of the defeat by aluminum in the beverage can wars in the 70's, has responded with a new and impressive range of advanced cold rolled high-strength steels (HSS) with tensile strengths of at least 340 M P a [Kishida, 2000]. 3 Figure 1.2 shows the mechanical properties of different grades of advanced cold rolled HSS along with their respective strengthening mechanisms. i u S 1 (2 2.5 2.0 1.5 1.0 0.5 0 50 40 30 20 10 0 1,200 1,100 1,000 900 800 700 600 500 400 300 200 Precipitation hardened steel (Cu precipitation) Bainitic-martensitic steel Solid solution hardened steel (IF) (with precipitation hardening) Retained-austenite steel Martensitic steel T Solid solution hardened steel (IF) t-Retained-austenite steel Precipitation "hardened Dual-phase steel Bainitic-martensitic steel (with precipitation lhardenini Martensitic _ steel" Bainitic-martensitic steel (with precipitation hardening)^ Solid solution hardened steel (IF) Precipitation hardened steel Yield ratio = 50% 800 1,000 1.200 Tensile strength (MPa) Figure 1.2. Properties of advanced cold rolled high strength steels [Akisue and Usuda, 1993]. Among all the advanced high strength steels, the developments of interstitial free (IF) grades have received a considerable amount of attention in the past decade due to advancement in the steelmaking processes to produce cleaner steels. JJF steels are a type of steels with very low carbon and nitrogen level equal to or less than 0.003wt% 4 [Gladman, 1997]. Interstitial elements are tied up by addition of strong nitride and carbide forming elements such as titanium and niobium. IF steel sheets are characterized by their superior formability and non-aging properties. From Figure 1.2, it can be seen that the mean r-value of solid solution hardened IF steel can be as high as 2.5 while maintaining tensile strength of nearly 400 MPa. Not to be outdone, the aluminum industry has been intensifying its effort to gain its share in the construction of BIW structure [Sherman, 2000]. To date, the aluminum industry has already penetrated more than 50% of the markets in powertrain components such as engine blocks with usage primarily restricted to castings. According to aluminum sheet metal producers, there are three principal advantages associate with the use of aluminum [Warren, 1991]: 1. Up to 50% mass saving in the BIW compared to spot welded steel. 2. Excellent long life corrosion resistance. 3. Economically recyclable automotive sheets, permitting significant energy savings. Three important classifications of aluminum sheet alloys have found applications for different automobile panels: the non-heat-treatable A l - M g alloys of the 5000 series, and the heat-treatable A l - C u , A l -Mg-S i -Cu, and A l - M g - S i alloys of the 2000 and 6000 series [Burger et al., 1995]. The most important technological basis for the 5000 series A l - M g alloys is their high capacity for strain hardening. Yield stress can be more than tripled by cold rolling reductions typical of commercial sheet productions. 5 It is interesting to compare the strength and formability of advanced steel and aluminum sheet alloys, as shown in Figure 1.3. Steel has a distinct advantage over aluminum because it provides the automotive manufacturer a wide choice of grades in terms of applications. For example, IF steel sheets are frequently selected for parts that require deep drawing operations while dual phase and transformation-induced plasticity (TRIP) steels are particularly suited for structural applications. By comparison, the 5000 and 6000 series aluminum alloys currently available fall within a narrow spectrum and their properties are inferior to steel. Hence due to the rapid technological innovation in steel products, it is likely that steel will remain the dominant automotive material in the future. 0 H 1 1 1 , T , 1 200 300 400 500 600 700 800 900 Tensile Strength (N/mm 2) Figure 1.3. Comparison of the current state and future development of aluminum and steel sheet alloys [Hewitt, 1996]. 6 1.2 Continuous Annealing Technology Japan has pioneered the research and development of continuous annealing technology for many years. The world's first continuous annealing line ( C A L ) to commercially produce deep drawing sheets started operation at Kimitsu Works of Nippon Steel in 1972. Since then, 50 similar C A L have been constructed worldwide, mostly in Japan and Europe [Takechi, 1995]. In traditional batch annealing processes, coils which weigh up to several tonnes are heated to the annealing temperature in bell type or tunnel furnaces. Due to the different heating and cooling rates experienced in the coil centre and surface, property variations could be found between the outside and inside laps of the coiled strip. Such inconsistency of properties is no longer acceptable in modern production facilities. For the same reason, rapid heating and cooling cannot be accomplished and this restricts the range of sheet metals it can produce. By contrast, in continuous annealing processes, the coils are unwound and continuously fed through the furnace hot zone in strip form before being recoiled. In this case, the thermal profiles in the strips are dictated by the furnace temperature and strip thickness rather than coil sizes. This eliminates the property variation problem and therefore greatly improves uniformity of quality in the products. In addition, high temperature annealing can be applied because there is no sticking problem since the sheets are annealed in strip form. 7 One of the most attractive features of continuous annealing technology is its capability to combine several processes such as electrolytic cleaning, annealing, cooling, temper rolling, galvanizing into a single line. This leads to significant reduction in processing time and thus operating cost. Annealing time is greatly shortened from several days in batch annealing to a matter of minutes in continuous annealing. Typical annealing cycles are characterized by very rapid heating to soaking temperature, hold for a very short period of time, and then by employing different cooling strategies to achieve desired end properties in the sheets. Figure 1.4 schematically illustrates the thermal cycle typical of modern continuous lines for aluminum or steel and metallurgical features associate with each stage. Rapid heating 10-100°C/s Soaking 10-600 seconds Al alloys: 500-560°C Steels: 750-850°C Forced air or water quenching 10-150°C/s Time Recovery, recrystallization, grain growth and dissolution of precipitates Precipitation Figure 1.4. Typical thermal cycle of CAL for steel or aluminum alloys. 8 1.3 Motivation for Research The essence of the present project is to develop a microstructure model for continuous annealing and it is driven by two factors. First, the properties of engineering alloys are largely determined by their microstructure, and the microstructure of a material is determined by its composition and can be modified by changing the processing conditions it has received. Because the processing-properties relation is indirect, microstructure models become a valuable tool to provide the direct link to quantify the associate changes in final properties brought upon by any changes in processing conditions. This concept is illustrated in Figure 1.5. Indirect relation Processing conditions input Microstructure model output Final properties Figure 1.5. Processing-microstructure-properties relation. Second, a microstructure model developed based on scientific understanding of the underlying metallurgical phenomena is a more generic approach to explore the complex interactions between processing conditions and product properties as compared to the traditional trial and error approach. In the past, in order to optimize process efficiency and product quality, plant trials were carried out to find the best 9 combination of process parameters for a given set of desired final properties for a specific type of alloy. These plant trials are not only expensive and time consuming but the results are often ambiguous and statistically irrelevant because the amount of data collected is limited by allowable number of trials [Hirsch, et al., 2000]. Nowadays, sophisticated process models are available for hot rolling of aluminum and steel [Militzer et al., 2000, Hodgson et al., 1992, Sellars, 1997, Wells et al., 1998]. Despite the crucial role continuous annealing plays in determining the magnitude and variation of properties in the final products, the development of a comprehensive model for continuous annealing is still in its infancy. This is probably due to the fact that the extremely non-isothermal nature of the process is difficult to characterize even though the metallurgical features involved, for instance, recrystallization, precipitation and grain growth, have been extensively studied over the years. 1.4 Scope and Objectives The present project is part of an ongoing strategic project aimed at developing a mathematical model to predict the properties of continuously annealed advanced cold rolled sheet metals. The objective of the overall research is to develop a microstructure model that provides the quantitative linkage between processing conditions and mechanical properties. The present work is devoted to developing sub-models for the two principal metallurgical phenomena, namely recovery and recrystallization that occur during continuous annealing. 10 To date, very few systematic studies have been carried out to produce a model that links these two processes together. One important aspect of the current work is to combine and extend the currently available fundamental models to predict the kinetics of recovery and recrystallization under extremely non-isothermal heating conditions. To accomplish this task, an isothermal annealing model will be developed and validated against experimental data obtained from continuous heating tests by using an appropriate mathematical procedure. The internal state variable approach will be adapted in the mathematical formulation of the model. Experimentally, the kinetics of recovery and recrystallization will be characterized by softening measurements in conjunction with quantitative metallography. Two important classifications of industrial processed automotive alloys are selected for this study: aluminum-magnesium alloy AA5754 and boron-containing interstitial free steel. 11 C H A P T E R 2 L I T E R A T U R E REVIEW 2.1 Introduction Recovery and recrystallization are the two fundamental processes that control the degradation of mechanical properties during the annealing of plastically deformed materials. Although many fundamental studies have been carried out in the past to study the nature of their underlying mechanisms, particularly for recrystallization, current understanding of many aspects of the two processes is still incomplete. This is mainly due to lack of in depth understanding of the deformed state which sets the stage for recovery and recrystallization. A n excellent review of the discrepancies between current state of knowledge of the deformation process and the requirements for the understanding of annealing has been recently provided by Humphreys and Hurley (2001). Therefore, it must be recognized that any attempt including the present one to review the literature concerning the topics of recovery and recrystallization can only be seen as a snapshot of an evolving subject. The aim of this chapter is not to provide a comprehensive review on the fundamental theories or micromechanisms involved in the recovery and recrystallization processes. Rather, a mixture of fundamental principles, experimental observations, and kinetic models with reasonable assumptions is presented to illustrate the complexity involved in modelling the kinetics of the two processes. Emphasis is placed on the two important classifications of automotive alloys, namely A l - M g alloys and IF steels. 12 2.2 Recovery - General Observations When a metal is plastically deformed by cold rolling, 99% of the mechanical energy utilized is converted into heat and only about 1% is stored in the metal in the form of various types of imperfections; the most important type being dislocations [Humphreys and Hatherly, 1995]. Both recovery and recrystallization are driven by the same stored energy of the deformed state and therefore can be seen as two competing processes. Recovery refers to a process that occurs prior to recrystallization and does not involve the sweeping of the deformed microstructure by migrating grain boundaries. Although the order of the occurrences of recovery and recrystallization can be treated as sequential, it is often difficult if not impossible to separate recovery from recrystallization. It is now well established that rearrangement and annihilation of dislocations into lower energy configurations are the two primary processes that control recovery [Humphreys and Hatherly, 1995]. However, the rate controlling mechanism for these dislocation processes remains unclear. A series of micromechanisms involved in the process of recovery is schematically shown in Figure 2.1. The most apparent feature of Figure 2.1 is the significant reduction in dislocation density due to the formation of cell/subgrain structures at the end of the recovery process. As a result, the properties, particularly mechanical properties, of the deformed materials are partially restored to their values before deformation. 13 (a) Dislocation tangles (b) Cel l formation (c) Annihilation of dislocations within cells (d) Subgrain formation (e) Subgrain growth Figure 2.1. Microstructural evolution during recovery of a plastically deformed material [Humphreys and Hatherly, 1995]. 2.2.1 Recovery Behaviour of Al-Mg Alloys The recovery kinetics of A l - M g alloys has been extensively studied over the past two decades because recovery has a much more profound softening effect in strain hardened A l - M g alloys than other wrought aluminum alloys. M g atoms are known to pin dislocations due to their high diffusivity during deformation, and therefore severely retard dynamic recovery [Lloyd, 1980, Burger et al., 1995, Humphreys and Hatherly, 1995]. The resultant high stored energy provides a large driving force for static recovery. On the other hand, at elevated temperatures, this high diffusivity allows easy dislocation movements and thus increases the degree of softening. Recovery can even 14 be followed at room temperature in A l - M g alloys. Figure 2.2 shows the results obtained from a series of recovery annealing experiments performed at room temperature for 17 years by Alcoa laboratory [Sanders et al., 1986]. Experimentally, recovery kinetics is often followed indirectly by the changes in some physical or mechanical properties such as hardness, yield stress, resistivity or heat evolution because no evident changes in the microstructures can be observed by optical microscopy. Alteration in dislocation structures can only be seen in transmission electron microscope (TEM). Hence, in order to develop a realistic physical model to capture the evolution of the material properties during annealing, it is essential to first identify the microstructural parameter that controls the recovery process. 150 h 100 I 1 l l I 1 104 105 105 107 108 109 TIME AT ROOM TEMPERATURE [S] Figure 2.2. Yield stress evolution as a function of time at room temperature for the Al-Mg alloys indicated [Sanders et ai, 1986]. 15 2.2.1.1 Determination of Microstructural Parameter As illustrated in Figure 2.1, the evolution of dislocation density plays a decisive role in determining the kinetics of recovery and thus the softening response of a material. According to the classical forest work hardening theory, the relationship between the dislocation density, p and the yield stress of a deformed material ays can be given as [Taylor, 1934]: ays = <r0 + aMGb-Jp (2.1) where Go is the sum of the intrinsic flow stress and contribution from solid solution hardening, M is the Taylor factor, a is a constant of order 0.3, G is the shear modulus, and b the magnitude of the Burgers vector. Figure 2.3 shows such a correlation for plastically deformed high purity A l , Al -3%Mg, and Al -5%Mg [Guyot and Raynaud, 1991]. The unique linear relationship between crys and pm as expressed by Equation 2.1 is perfectly followed by the two A l - M g alloys and valid over the entire strain range tested. It is interesting to note that for high purity aluminum (Al), OQ ~ 0 implying that the intrinsic flow stress is insignificant. The straight lines shown in Figure 2.3 indicate that the increase in yield stress during cold deformation can be followed by a single internal state variable, i.e. the dislocation density. However, it is not a priori obvious that the reduction of dislocation density in subsequent heat treatment will also follow the single variable theory. In other words, 16 will the yield stress evolution during recovery be sufficiently described by dislocation density alone or other structural parameters need to be incorporated? 500 400 o 300 Q-s ~b 2 0 0 100 0 2 x 1 0 5 4 x 1 0 5 6 x 1 0 5 8 x 1 0 5 v^(cm"1) Figure 2.3. Correlation between yield stress and dislocation density according to forest work hardening theory for Al, Al-3%Mg and Al-5%Mg alloys [Guyot and Raynaud, 1991]. In an effort to answer this question, Verdier et al., (1997) investigated the stored energy after cold rolling of a high purity 1199 aluminum alloyed with 2.5wt% of magnesium. Isochronal (10 min) heat treatments at temperatures between 100 and 5 0 0 ° C were performed. Hardness and tensile tests, resistivity measurements and Differential Scanning Calorimetry (DSC) were carried out to characterize the annealed samples. 17 Figure 2.4 shows the decrease in resistivity for 90% cold rolled samples as obtained from isochronal tests. Dislocation density was calculated from the resistivity data according to the relationship provided by Friedel (1964) by assuming the decrease in the resistivity reflects mainly the changes in the dislocation density. o X CL "as Q_ : • j j V : j • 1 TS. i • j • . . . . . . . : 0 100 200 300 400 500 Temperature ( ° C ) Figure 2.4. Changes in resistivity after 10 min heat treatments at temperatures between 100 and 500°Cfor 90% cold rolled 1199-2.5%Mg alloy [Verdier et ai, 1997]. The underlying hypothesis is that if dislocation density is indeed the single structural parameter to describe the yield stress evolution, the plot of crys-cr0 vs. pin should yield a straight line with a linear slope equals to aMGb. oa in this case refers to the yield stress in the fully recrystallized material. Figure 2.5 shows the plot of the correlation between oys-o0 vs. p'/2 which indeed shows a straight line. 18 Verdier et al., (1996, 1998) further examined the isothermal recovery behaviour of two cold rolled Al-2.5%Mg alloys: high purity 1199 and commercial purity 1070 alloy. The basic difference between these two alloys is the small amount of A ^ F e and (Al,Mg,Si) precipitates in the latter. Isothermal annealing experiments were conducted in an oil bath at 160 and 2 2 0 ° C for various lengths of time. The results are summarized in Figure 2.6 where the amount of softening is given by Ob.2(t) - OQR (CT0.2 = 0.2% yield stress and OCR - cold rolled yield stress). Optical metallography was used to check the occurrence of recrystallization. Figure 2.6 clearly shows that the recovery kinetics is identical for the two alloys. This indicates that the small amount of precipitation in the commercial purity 1070+2.5%Mg alloy did not influence the rate of recovery. Furthermore, based on 19 their T E M studies, they found that there were two microscopic stages involved in the recovery event, namely elimination of dislocations and subgrain growth. However, they found no evidence of any change in the yield stress evolution that corresponds to this strong change of microscopic mechanism. In other words, the recovery of yield stress remains logarithmic irrespectively of the regime of the rnicrostructural evolution. 50 0-U b © 0 -50 -100 •150 h -200 + 160°C-1070+2.5Mg A3 cold • rolled e 160°G- 1199+2.5Mg — \\m i n !|[ X 220°C- 1070+2.5Mg \ Hill I! illiil t "riiijli 1 llfl 0 220°C- 1199+2.5Mg - \W\\ - o X °q jjii! -Miiiiii \ wm i X 0,01 0,1 1 10 100 1000 10000 100000 Time (min) Figure 2.6. Evolution of yield stress during static recovery at 160 and 220° C for 90% cold rolled (1070+2.5%Mg) and (1199+2.5%Mg) [Verdier et al, 1998]. A l l of the above experimental observations strongly suggested that as far as yield stress is concerned a single variable description of recovery kinetics in terms of dislocation density is sufficient. The spatial distribution of dislocations does not seem to have any effect on the static recovery kinetics. This lack of influence of the dislocation 20 arrangements on the yield stress justifies the use of a single internal state variable, i.e., the total dislocation density to model the recovery kinetics in A l - M g alloys. Kinetic models that have been developed to account for the logarithmic time dependence of yield stress are introduced in the next section. 2.2.1.2 Kinetic Models for Recovery The logarithmic time decay of yield stress shown in Figures 2.2 and 2.6 is the most notable characteristics of recovery kinetics in many deformed metals whether single or polycrystals. Table 2.1 summarizes the possible rate controlling mechanisms for the recovery process proposed by various authors. Table 2.1. Summary of proposed rate controlling mechanisms for recovery. Paper Rate controlling mechanism Materials Studied Cottrell/Aytekin (1950, 1953) Cross slip Single/poly crystal of pure Zn Friedel (1964) Cross slip A l , Cu , A g Prinz et al. (1982) Climb Single crystal of C u and N i Nes (1995) Glide or solute drag Fe, A l , A l - M g alloys Kuhlmann (1947, 1951) Glide Pure A l , A l - M g alloys 21 The formal theory developed by Kuhlmann (1947, 1951) and Cottrell/Aytekin (1950) is explained in detail in the following since it has successfully been applied to A l - M g alloys [Barioz et al., 1992, Burger et al., 1995]. In this theory, the rate of recovery is assumed to be controlled by thermally activated glide or cross-slip of dislocations. Recent theoretical treatment by Kuhlmann-Wilsdorf (2000), however, has strongly suggested that A l - M g alloys are of planar glide type in spite of their high stacking fault energy and thus corresponding ease of cross-slip. If the activation energy Q is assumed to be a function of the yield stress <Tys then the rate of recovery is [Cottrell, 1953] They further suggested that over small ranges of CT^ , the function Q(oys) decreases linearly with the yield stress in the material. Equation 2.2 can then be rewritten as follows: (2.2) do. ys = - C , exp -(Qo-C2oys)] (2.3) dt RT where C / and C2 are constants, T the temperature, and R the gas constant. Upon integration Equation 2.3 becomes 22 RTj, . t Gys = t r ( - 7 ^ l n | 1 + f ( 2 - 4 ) where cr, is the initial yield stress at time / = 0 and to is defined by the relation: . _ RT ' ° " C A e x \ RT (2.5) Figure 2.7 shows the validity of this model for a 90% cold rolled Al -3%Mg alloy isothermally annealed at three different temperatures using the fitting parameters given in Table 2.2 [Barioz et al., 1992]. Different parameters have also been calculated for other A l - M g alloys with varying amount of M g content. The activation energy was seen to decrease from 277 kJ/mol for an A l - l % M g alloy to 231 kJ/mol for an A l -5%Mg alloy. 310 o CL 290 w 270 | 250 J 230 8 210 £ "o 150 190°C - — A A • - - » 10 100 Annealing time (min) 1000 Figure 2.7. Recovery kinetics of a 90% cold rolled Al-3Mg alloy. Solid lines indicate fitting of Equation 2.4 using parameters given in Table 2.2 [Barioz et al, 1992]. 23 Table 2.2. Fitting parameters for the softening curves in Figure 2.7 [Barioz et al., 1992]. at (MPa) Qo (kj/mol) d (MPa/s) C2 (J/mol/MPa) 305 241 2.8 x 10 1 5 378 Burger et al. (1995) also found that the softening response of automotive alloy AA5184 (Al-4.5%Mg) during paint bake cycle closely follows the kinetics predicted by Equation 2.4. Their results are shown in Figure 2.8. However, the fitting parameters were not given in the paper. 0 200 400 600 800 1000 1200 1400 1600 1800 TIME (s) at 177*C Figure 2.8. The time dependence of the softening behaviour of AAS 182 at 177° C. Solid line indicates fitting of Equation 2.4 to experimental data [Burger et al., 1995]. 24 A rigorous treatment to refine Equation 2.4 was recently provided by Verdier et al. (1999). The improved model was derived by assuming the relaxation effect caused by recovery is equivalent to the application of an inverse stress. This assumption allows incorporation of a plastic relaxation strain rate into Equation 2.4. The modelling results have also been found to agree reasonably well with the experimental results obtained from A l - M g alloys. Humphreys and Hatherly (1995) developed a recovery model by considering dislocation climb as rate controlling. They assumed that the dislocation structure is in the form of a 3-D network of mesh size R. The rate of coarsening of this network dR/dt induced by a small driving force F (F = Gb2/R) is assumed to be equal to the climb velocity of dislocations Vd-d R DsGb*Cj i V d = ^ = ^ f - R ( 2 - 6 ) where Ds is the coefficient of self-diffusion, c, is the concentration of jogs, b the Burger's vector and G the shear modulus. The integration of Equation 2.6 can be written in terms of dislocation density by assuming p is related to the network size by p ~ R'2: 1 i 2DsGb\l 25 Using the forest work hardening equation and by considering only dislocation hardening, Equation 2.7 can be expressed in terms of flow stress as 1 2 1 _ 2DsCjt a2 a2GbkT (2.8) The two models described so far were derived based on the internal stress generated by dislocations. In a recent approach by Nes and Saeter (1995), a response equation which is in a similar form to the work hardening equation was adapted to account for the recovery of yield stress in iron, aluminum and A l - M g alloys. The response equation comprises of two independent microstructural parameters: the dislocation density p within the subgrains and cell/subgrain size 8. The logarithmic time dependence of flow stress is obtained by adding the time dependent contributions due to subgrain growth and dislocation network growth: where cti and 0:2 are constants. According to Nes (1995) the rate controlling mechanism for the recovery process in A l - M g alloys was determined to be either thermally activated glide or solute drag. Hence, it can be seen that by assuming different rate controlling mechanisms, different equations can be derived to describe the flow stress evolution during static recovery. a(t) = cr, + a, (2.9) 26 However, with the current modelling objective in mind, it is preferable to formulate the model base on simple but physically sound principles which use a minimum of adjustable microstructural parameters. In this respect, the models developed based on internal stress seem to be the most favourable since the yield stress evolution can be readily described by a single internal state variable, the dislocation density. 2.2.2 Recovery Behaviour of Interstitial Free Steel To the best of the author's knowledge, very little work has been done to study the recovery behaviour of IF steel. As a result, there is hardly any publications on this subject in the literature. The only systematic study that has been carried out to model the kinetics of recovery in IF steel was conducted by Mukunthan and Hawbolt (1996). They studied the isothermal recovery kinetics in an 80% cold rolled Ti -Nb stabilized IF steel by means of in situ X-ray peak resolution measurements. Recovery was characterized by measuring the ratio of the heights of diffraction peaks in the temperature range of 500 to 6 0 0 ° C . Occurrence of recrystallization was checked by using optical microscopy. The isothermal recovery kinetics was assumed to be proportional to the X-ray peaks ratio, Ri, and the following logarithmic relationship was proposed: R,=b-a\nt (2.10) where Ri is the X-ray ratio at time t, and b and a are constants for a given temperature. 27 The fitting of Equation 2.7 to their experimental data is shown in Figure 2.9. The values for recovery activation energy were obtained by assuming Arrhenius rate behaviour: dR/dt <*= exp(-Q/RT). By plotting ln(-dR/dt) at fixed fractions of recovery (at constant Rj value) versus the inverse absolute temperature 1/T, the activation energy Q was found to increase from 173 kJ/mole at Ri = 0.60 to 312 kJ/mole at R/ = 0.15. They further suggested that the high values of activation energy can be attributed to the hindering of recovery process by the presence of the excess solute T i and Nb in solid solutions and/or the fine stabilizing precipitates of T i and Nb nitrides and carbides. at >^  X 0.6 0.5 0.4 0.3 0.2 \ - 4 + o ^ \ Isothermal Recovery + 500 fc o 550 fc * 600fc * 625fc Best Fit 10" 10' 10 10J Time (s) 10M 10" Figure 2.9. Fitting of Equation 2.7 to the in-situ Ri measurements of recovery at temperatures indicated [Mukunthan, 1994]. 28 2.3 Recrystallization - General Observations Recrystallization can be seen as a further restoration process that occurs after recovery in which new dislocation-free grains grow and consume the deformed or recovered structure. This process is accomplished by the migration of high angle boundaries driven by the same stored energy that drives recovery. In an earliest attempt to rationalize the recrystallization process, Burke and Turnbull (1952) formulated a series of laws concerning many of the factors that can effect recrystallization. These quantitative statements were devised based on a large body of experimental work on a wide variety of materials. Although newer research has shown that recrystallization is in fact a much more complex process [Doherty et al, 1997], they still provide a useful guide to the overall recrystallization behaviour of many metallic materials. (1) The initiation of recrystallization requires a minimum amount of deformation. (2) The smaller the amount of deformation, the higher is the temperature required to cause recrystallization. (3) Increasing the annealing time decreases the temperature necessary to cause recrystallization. (4) The recrystallized grain size depends mainly upon the degree of deformation, being smaller the greater the degree of deformation. (5) For a given amount of deformation the recrystallization temperature will be increased by a larger initial grain size. 29 2.3.1 Kinetic Models for Recrystallization The most commonly used analytical approach to model recrystallization kinetics follows the theory developed independently by Johnson and Mehl (1939), Avrami (1939) and Kolmogorov (1937), which has been frequently referred to as the J M A K model. In this theory, recrystallization is treated as a thermally activated process comprising two events: nucleation and growth, similar to the classical phase transformations. However, it has now been generally recognized that the nucleation of new dislocation-free grains is not accomplished by thermal fluctuations as in the classical phase transformation process. Rather, nuclei from which recrystallization originates are formed at small volumes which pre-exist in the deformed microstructure [Humphreys and Hatherly, 1995, Doherty et al., 1997]. Based on the J M A K model, the volume fraction of material recrystallized X in time t is given by X=l -exp ( - fe") (2.11) where b is a function of the nucleation rate, N, and the growth rate, G. The constant n which is commonly known as the J M A K exponent characterizes nucleation conditions and growth geometries. Recrystallization kinetics data are usually plotted in the form of lnln[l/(l-X)] versus ln(t) which is generally known as the J M A K plot. 30 Table 3 shows the variation of ideal J M A K exponent with respect to growth dimensionality and nucleation condition [Humphreys and Hatherly, 1995]. Table 2.3. Ideal JMAK exponents [Humphreys and Hatherly, 1995]. Growth dimensionality Site saturation Constant nucleation rate 3-d 3 4 2-d 2 3 1-d 1 2 Ideal J M A K model assumes: (1) Random distribution of recrystallized nuclei in the microstructure. (2) N and G remain constant during recrystallization. (3) The growth of recrystallized nuclei is isotropic. 2.3.1.1 Application of JMAK Theory to Model Recrystallization Kinetics There are two main inconsistencies when the J M A K model is applied to interpret recrystallization kinetics data. First, if the three assumptions of the J M A K model are strictly adhered to, the J M A K plot should yield curves that are linear. On the contrary, negative deviations from linearity are often observed towards the end of recrystallization [Vandermeer and Gordon, 1962, Rosen et al., 1964, Wilshynsky et al., 1992]. In such a case, the J M A K exponent (slope of the J M A K plot) may be seen to 31 decrease as recrystallization proceeds. Second, when new recrystallized grains are growing three dimensionally, then a J M A K exponent of 3 or greater is expected. However, most of the recrystallization studies have reported J M A K exponents of less than 3. Experimental n-values are usually below 2 [Vandermeer, 2001]. Although many theories have been proposed to explain these two inconsistencies, both can be readily explained by the inhomogeneity of the deformed microstructure [Humphreys and Hatherly, 1995]. Due to non-uniform distribution of stored energy in the structure, the assumption of random distribution of recrystallization nuclei is not expected to hold [Vandermeer, 1992]. Srolovitz et al. (1988), Rollett et al., (1989), Marthinsen et al., (1989), Hesselbarth and Gobel, (1991) and Hayakawa and Szpunar, (1996) have elegantly demonstrated, by means of computer simulation, that the J M A K exponent in a non-uniformly deformed metals is typically smaller than 3. Non-uniform distribution of stored energy can also lead to decreasing growth rate towards the end of recrystallization which leads to the deviation from linearity in the J M A K plot [Hutchinson et al., 1989, Furu et al., 1990]. According to Furu et al. (1990), the deviations can also be explained by the effect of simultaneous recovery. As an alternative to the J M A K model, Speich and Fisher (1966) have developed a recrystallization model (SF) which takes the following form: T^X = ktm (2.12) 32 where k is a constant which is a function of temperature and m is a constant which is independent of temperature. In this model, the average growth rate G was assumed to be inversely proportional to time. Vandermeer and Rath (1990) have made a significant improvement on the J M A K theory using the concept of Microstructural Path Methodology (MPM). The essential idea behind M P M is to expand the number of parameters that are used to characterize the microstructure of a material undergoing recrystallization. In addition to volume fraction recrystallized X, the interfacial area per unit volume A,, separating the recrystallized grains from the unrecrystallized matrix is considered. The microstructural path function is obtained by relating A, to X using a semi-empirical equation proposed by Rath [1982]. The interfacial average growth rate G which is a function of temperature and time can then be estimated from A, by using the Cahn-Hagel formulation (dX/dt = A , G ) [Mukunthan and Hawbolt, 1996]. Finally, the kinetics of recrystallization is described by combining the path function of A, and the kinetic function of G . However, it must be emphasized that although the two improved models (SF and M P M ) have considered growth rates as a decreasing function of time, they are still based on the assumption that the spatial distribution of nuclei is random. This is a major hurdle in employing these and the J M A K approaches in modelling recrystallization kinetics because recrystallization in general occurs heterogeneously as described above. 33 Despite the shortcomings of the J M A K theory, its predictive power to describe the frequently observed sigmoidal kinetic behaviour of recrystallization should not be neglected. In fact, J M A K model has long been adapted by many researchers as a semi-empirical tool to develop simple models for the recrystallization process. For instance, Figure 2.10 shows the application of the J M A K model to the isothermal recrystallization kinetics in a 80% cold rolled Ti+Nb stabilized IF steel [Mukunthan and Hawbolt, 1996]. The volume fraction recrystallized was determined by A S T M standard point counting method. The average J M A K exponent obtained for all the curves is equal to 0.73. It can be seen that the J M A K approach provides a good description of the recrystallization kinetics for a wide range of temperatures despite the low value of n. The J M A K exponent in this case is basically treated as a fitting parameter independent of temperature. *0 (b) Figure 2.10. Experimental isothermal recrystallization kinetics of a 80% cold rolled Ti+Nb stabilized IF steel obtained at (a) 600-625°C, and (b) 700-760°C, as described by the JMAK equation [Mukunthan and Hawbolt, 1996]. 34 2.3.2 Recrystallization Behaviour of Al-Mg Alloys 2.3.2.1 The Effect of Solute Mg The presence of M g atoms in solution can strongly influence the recrystallization behaviour of A l - M g alloys in two ways. First, during deformation at room temperature, M g is known to retard dynamic recovery and, as a result a large, driving force is preserved to drive the subsequent recrystallization process. On the other hand, due to the larger size of M g atoms (about 12% larger than that of A l in terms of atomic radius), those present in the solution can strongly interact with the migration of high angle grain boundaries during recrystallization. This is commonly known as the solute drag effect [Cahn, 1962, Suehiro et al., 1998]. In a recent attempt to clarify the effect of M g atoms on the recrystallization kinetics of A l - M g alloys, Koizumi et al. (2000) found that there is a critical solute content, at which the increase in driving force for recrystallization counterbalances the solute drag effect. By studying the isothermal annealing kinetics of 95% cold rolled high purity A l - M g alloy with various amounts of M g contents, they showed that recrystallization was most strongly retarded in specimens containing lwt% M g . With increasing M g concentration up to 5wt%, recrystallization was accelerated remarkably. Figure 2.11 shows the effect of M g content on the recrystallization kinetics after 5 minutes of annealing at each temperature. If the temperature at which 50% recrystallization occurred is plotted against the M g content, it is evident that the critical solute content 35 lies at about lwt% M g and the recrystallization temperature decreases linearly with increasing M g content. This is shown in Figure 2.12. 200 225 250 275 300 325 350 Temperature (*C) Figure 2.11. The effect ofMg content on the recrystallization kinetics of 95% cold rolled Al-Mg alloys annealed for 5 minutes at each temperature [Koizumi et al, 2000]. 1 4 Mg (%) Figure 2.12. The effect ofMg content on the temperature at which 50% recrystallization occurred in Al-Mg alloys [Koizumi et al, 2000]. 36 According to Koizumi et al. (2000), the nucleation and growth rate of recrystallized grains were significantly reduced due to solute drag with increasing solute content up to the critical concentration (1%). Further addition of the solute element results in a significant increase in stored energy which acts to counteract the effect of solute drag and consequently enhances the nucleation and growth of recrystallized grains. The increase in stored energy is the outcome of the suppression of both dynamic recovery during cold rolling and concurrent recovery during recrystallization. T E M observations of the cold deformed structure of the Al-5wt%Mg alloy which shows the fastest recrystallization kinetics reveal the development of ill-defined very small cells/subgrains with high dislocation densities. Another interesting finding of their study is that the activation energy for recrystallization obtained based on an Arrhenius analysis decreases with the progress of recrystallization. This effect is schematically illustrated in Figure 2.13 which also shows the activation energy as a function of M g content. At 20% recrystallization, the activation energy saturates at a M g content above 3%, giving an almost constant value of 54.4 kcal/mol. With the exception of Al-0.5wt% M g alloy, the values for activation energy at 40% recrystallization is generally lower than those values obtained at 20% recrystallization. A similar effect of M g content on activation energy was also observed by Perryman (1955) in a 20% cold rolled A l - M g alloys with varying amount of M g content, as indicated in Figure 2.13. 37 Mg <%) Figure 2.13. Variation in activation energy with progress of recrystallization and the effect of Mg content [Koizumi et al., 2000]. The effect of M g atoms on the overall recrystallization kinetics of A l - M g alloys was also investigated by Ryum and Embury (1982). They compared the kinetics of recrystallization of commercial purity A l and an Al-5wt% M g subject to 80% deformation by cold rolling. They found that the overall kinetics of recrystallization processes were similar in the two materials. In other words, both materials achieved complete recrystallization within the same amount of time as shown in Figure 2.14. It is interesting to compare the results of Ryum and Embury with the already discussed experimental observations provided by Koizumi et al. As proposed by Koizumi et al., if the concentration of M g atoms is higher than lwt%, i.e. the critical concentration, M g atoms will act to promote recrystallization by increasing the stored energy in the deformed structure. Hence, the recrystallization kinetics of the Al-5wt%Mg shown in 38 Figure 2.14 is in fact the superposition of the two simultaneous effects due to the M g in solid solution. The retarding effect of M g atoms due to solute drag of boundary migration is exactly counterbalanced by the effect of increased driving force. Consequently, the recrystallization in Al-5wt%Mg proceeds in a way as i f there is no M g atom in the solution, which is precisely the behaviour shown in Figure 2.14. The other important results that can be extracted from Figure 2.14 is that the effect of a recovery anneal at 1 8 0 ° C for 30 minutes prior to recrystallization has a negligible effect on the overall recrystallization kinetics. This gives strong indication that in the A l - M g system, the nuclei are already present in the deformed structure. The nucleation mechanisms via subgrain coalescence during recovery proposed by Humphreys and Hatherly (1995) do not seem to apply to A l - M g alloys. X 0.5 280 O Al A Al-Mg • Al-recov A Al-Mg-recov 290 300 - * - T # C 310 Figure 2.14. Recrystallization kinetics in 80% cold rolled commercial purity Al and Al-5%Mg alloy [Ryum and Embury, 1982]. 39 2.3.2.2 The Effect of Heating Rate The effect of heating rate on the recrystallization behaviour of A l - M g alloys has not been widely studied despite its important role in continuous annealing. Simielli et al. (1987) studied the influence of heating time on the recrystallization kinetics of an A l -0.5wt%Mg alloy cold deformed 25%. The cold rolled samples were heat treated to various temperatures with three different heating times: 5, 150 and 300 seconds. The total time (heating + soaking) for heat treatment has been maintained constant at 300 seconds for the three cases. For example, the heating rates employed to reach three annealing temperatures and the soaking time for each heating condition is shown in Table 2.4. Figure 2.15 shows the recrystallization kinetics as characterized by hardness measurements. Table 2.4. Thermal cycle employed by Simielli et al. to study the effect of heating time on the recrystallization behaviour of an Al-0.5wt%Mg alloy. Heating time (s) Soaking time (s) Heating rate (°C/s) to reach 200°C 300°C 400°C 5 295 40 60 80 150 150 1.33 2 2.67 300 0 0.67 1 L33 40 40 35 30 25 20 Al - Mg a 300 s o 150s A 5s XA (50% softening) 50 y 200 250 300 350 400 450 . T( C) Figure 2.15. Effect of heating time on the isothermal recrystallization kinetics of a 30% cold rolled Al-0.5wt%Mg alloy [Simielli et al., 1987]. Figure 2.15 may indicate that taking 50% softening level as reference that the recrystallization kinetics of the specimens with slow heating rates are more sluggish than the kinetics observed in the specimens that were rapidly heated to soaking temperature. However, it must be noted that the effective holding time was longer in samples with short heating time. Hence, the increase in softening for samples with high heating rates is most likely caused by the increase in holding time at soaking temperatures. 41 2.3.3 Recrystallization Behaviour of IF Steel 2.3.3.1 The Effect of Microalloying Elements One of the earliest studies on recrystallization behaviour of cold rolled titanium stabilized low-C steels (0.01 IC + 0.19Ti) was carried out by Goodenow and Held (1970). They found that the isothermal recrystallization kinetics followed a normal sigmoidal shaped curve at all temperatures but the rate of recrystallization was significantly slower as compared to Al-killed and rimmed steel. Figure 2.16 shows the time-temperature-recrystallization (TTR) diagram for specimens cold rolled to 50% reduction. It can be seen that both the temperature required to initiate recrystallization and the time to complete recrystallization for the Ti-stabilized low carbon steel were considerably larger than for other steels. They attributed the sluggish recrystallization kinetics as a result of T i in solution and to a lesser degree because of the presence of stable fine Ti(C,N) precipitates since no precipitation was observed during recovery prior to recrystallization to alter the recrystallization kinetics. More recently, Wilshynsky et al. (1990, 1992) have also found that the recrystallization in IF steel were severely retarded by the addition of stabilizing element such as titanium and niobium. They compared the recrystallization kinetics of 75% and 90% cold rolled IF steels stabilized with Ti-only (0.087Ti), Ti+Nb (0.035Ti+0.049Nb), or Nb-only (0.045Nb) with an unstabilized ultra-low carbon (ULC) steel of the same base composition at temperatures ranging from 5 0 0 - 8 1 5 ° C . The carbon content of all the 42 steels was kept at 0.004wt%. Figure 2.17 shows the results in the form of fraction recrystallized versus annealing time at 7 0 0 ° C for the 75% cold rolled specimens. Volume fraction recrystallized was determined by point counting in accordance with A S T M E562-83. ae 3 < ae 1700 1600 1500 1400 1300h ^ 1200 ui H 1100 1000 900 800 Ti Stabilized, T6 Aluminum Kiled Rimmed 50% Reduction End Of Recrytelzetion UStert Of Recry»t»lizition V ""<•. * ~ ~ r — ~"»— 0.1 1.0 10 100 TIME AT TEMPERATURE. MIN. 1000 Figure 2.16. Time-temperature-recrystallization diagram for the Ti stabilized steel and for rimmed and Al-killed steel annealed in salt [Goodenow and Held, 1970]. Clearly, the recrystallization of the unstabilized U L C specimens (denoted as A K in Figure 2.17) is much more rapid than that of the stabilized IF steels. This behaviour was consistent at all temperatures as well as for samples with different amount of cold reduction. The Nb-only, and Ti+Nb stabilized specimens recrystallized the slowest. In fact, by comparing the kinetics at 6 5 0 ° C , they determined that the minimum temperature for recrystallization to occur in the Ti+Nb stabilized steels is 7 0 0 ° C 43 whereas 100% recrystallization can be achieved in the U L C specimens at temperature as low as 5 0 0 ° C . 100 U N ed •+-» b so r o - Tcoil=5S5 C, cold reduction=75x, Tannoal=700 C • r x r ° ^ • 1 • A K / • Ti A T i - N b • x Nb • 10° 101 10 103 10* tlma (saconds) Figure 2.17. Recrystallization curves for the series of IF steels isothermally annealed at 700°C [Wilshynsky et al, 1992]. B y means of T E M , Wilshynsky et al. (1990, 1992) discovered that the majority of precipitates found in the Ti+Nb stabilized steels consist of fine spherical precipitates although a few large cubic T i N precipitates were observed. Therefore they concluded that the grain boundaries were pinned by these fine precipitates during recrystallization resulting in slower recrystallization kinetics. Retardation of recrystallization due to pinning of grain boundaries by fine precipitates is in fact a common behaviour observed in IF steel [Lotter et a l , 1980, Bleck et al., 1988, Fonstein and Girina 1994, Takechi, 1995, Mukunthan and Hawbolt, 1995, Huang et al., 2000]. 44 Boron is one of the most important trace elements in IF steel because it has been widely recognized as an effective element to suppress secondary-cold-work-embrittlement during press forming of IF steel sheets [Yasuhara et al., 1994]. However, the mechanism of the suppression of recrystallization by boron addition has not been clarified until recently. Haga et al. (1998) compared the isothermal recovery and recrystallization kinetics of T i (~0.0049wt%)-added IF steels containing different amounts of boron. The carbon content of the steels was in the range of 0.0026 to 0.003 lwt%. Figure 2.18 shows the effect of boron on the recrystallization starting and finishing temperature. Recrystallization starting temperatures were derived from hardness curves at the point where a sudden increase in softening was observed. It can be seen from Figure 2.18 that both Ts and 7} rose drastically with increasing boron content indicating that both nucleation and growth rates of recrystallized grains decreased with increasing boron content. Similar behaviour of boron in retarding recrystallization of IF steel was also seen by Hoydick and Osman (1998). Other studies have confirmed that a significant number of boron atoms can segregate to grain boundaries during heat-treatment [Yasuhara et al., 1994, Seto et al., 1999]. It is believed that segregation of boron atoms to grain boundaries hinder the mobility of the boundaries and as a result, retards recrystallization. 45 B content (ppm) Figure 2.18. Effect of boron content on recrystallization starting and finishing temperatures in IF steel [Haga et ai, 1998]. The most convenient way to illustrate the sluggish recrystallization kinetics in IF steel grades is to compare their activation energies for recrystallization with the values obtained in Al-killed and rimmed steels. Figure 2.19 summarizes the activation energies for a variety of steel grades. The histogram was constructed based on data provided by Bleck et al. (1990). The recrystallization activation energy QR was calculated by assuming that the temperature dependence of the kinetics follows the Arrhenius rate behaviour: (2.13) 46 where tR is the time taken to complete a certain fraction of recrystallization (e.g. 50%) and A is a pre-exponential constant. The isothermal recrystallization kinetics for different unalloyed and microalloyed steels was evaluated by using the J M A K equation. The recrystallization volume fraction, X at a given annealing time t was assumed to be directly proportional to the relative drop in the hardness of annealed specimens. The data presented in Figure 2.19 are in close agreement with the values obtained by Wilshynsky et al. (1992) and Meyer et al. (1994). JP steel microalloyed with Ti+Nb exhibits the highest activation energy. Mukunthan and Hawbolt (1996) have reported an even higher activation energy for Ti+Nb stabilized IF steel, 502 kJ/mol. Nevertheless, all of the activation energies for IF steels are significantly higher than those for unalloyed steels. Bleck et al. further pointed out that activation energies less than 200 kJ/mol can be associated with self-diffusion phenomena in iron and hence the recrystallization process in unalloyed steel is achieved by short-range diffusion of iron atoms from the unrecrystallized portion to the recrystallized portion. The high activation energies of IF steels represent the effect of pinning by fine precipitates and/or solute drag by atoms present in solid solution [Wilshynsky et al., 1992]. In summary, the recrystallization kinetics of different grades of steels can be ranked in order of increasing time as follows: (1) unstabilized (aluminum killed or rimmed steel), (2) Ti-stabilized, (3) Nb-stabilized, and (4) Ti+P or Nb+P stabilized (4) Ti+Nb or Nb+B stabilized. 47 450 400 o 350 E 3 300 >. o? 250 * 200 o ro 150 < 100 50 H H H H H m i • i E •killed • be < 9 - I 2 -U . I L L r i 11 il" ! 2 I C D + z z Steel Grade Figure 2.19. Recrystallization activation energy for different cold rolled steel grade [Blecketal., 1990]. 2.3.3.2 The Effect of Heating Rate Ferry et al. (1999) investigated the influence of heating rate on the recrystallization kinetics in 70% cold rolled low and ultra-low carbon (ULC) steels. Electrical resistance annealing using a Gleeble 3500 was employed to simulate the effect of heating rate ranging from 50 to 1000°C/ s to peak temperatures in the range of 600 to 9 0 0 ° C . A l l samples were water quenched within 0.05 seconds of reaching the peak temperatures. Volume fraction of recrystallized grains was determined by quantitative metallography. Figure 2.20 shows the effect of heating rate on the temperature to complete 50% recrystallization (Jo.s) in the three grades of steel that contain different amounts of carbon. It can be seen that To.s increases with heating rate, i.e., the faster 48 the heating rate, the higher the temperature is required to complete 50% recrystallization. The U L C steel was found to recrystallize in a higher temperature range than the other two low carbon steels. 850 H 0.003%C 800-1 o a 750' 0.02%C (-0.05%C 700-1 650' 10 100 1000 10000 Heating Rate (°C/s) Figure 2.20. Effect of heating rate on Tso% in 70% cold rolled steel with varying amount of carbon content [Ferry et al., 1999]. Mukunthan and Hawbolt (1996) developed a model to predict the volume fraction of recrystallized grains during continuous heating. The essential feature of this model is that the recrystallization process was assumed to be additive. In this approach, the heating cycle was described as a series of isothermal steps, as shown in Figure 2.21. By applying the principle of additivity, the fraction recrystallized calculated at each time step can be summed to predict the kinetics during continuous heating. 49 Recrystallization Recovery & Recrystallization Start Temperature Recovery I / \ Only 7 Time Figure 2.21. Schematic diagram illustrating the application of principle of additivity to continuous heating kinetics. Figure 2.22 shows the modelling results of the continuous recrystallization kinetics of a 80% cold rolled Ti+Nb stabilized IF steel. It can be seen that the application of additivity rule in conjunction with the J M A K model adequately captured the increase in fraction recrystallized with increasing annealing time. The same approach has also been successfully applied to model continuous recrystallization kinetics in a cold rolled low carbon steel [Muljono et al., 1999]. 50 Temperature (*C) Figure 2.22. Effect of heating rate on continuous heating recrystallization kinetics of a 80% cold rolled Ti+Nb stabilized IF steel [Mukunthan and Hawbolt, 1996]. 51 CHAPTER 3 EXPERIMENTAL PROGRAM 3.1 Materials The chemical compositions of the as-received industrial cold rolled AA5754 and IF-boron steel sheets are listed in Tables 3.1 and 3.2, respectively. Table 3.3 shows the processing histories of both materials. The aluminum and steel sheets were supplied by Alcan and Stelco Inc., respectively. Table 3.1. Chemical composition of 'AA5754 provided by Alcan (in wt%). Mg Mn Fe Si Cr Cu Ti Zn V Ni A l 3.07 0.24 0.17 0.057 0.034 0.008 0.006 0.004 0.004 0.002 96.41 Table 3.2. Chemical composition of IF-boron steel provided by Stelco (in wt%). C Mn Ti Cu Cr Ni P Nb S N B Fe 0.0026 0.16 0.068 0.046 0.041 0.012 0.011 0.009 0.008 0.003 0.0005 99.64 Table 3.3. Processing histories of as-received materials. Materials Production route Hot rolled gauge (mm) Cold rolled gauge (mm) % Cold reduction AA5754 Ingot cast 3.0 1.8 40 IF-boron steel Continuous cast 2.9 0.6 80 52 3.2 Isothermal Annealing 3.2.1 AA5754 The first series of annealing experiments were designed to study the isothermal recovery and recrystallization behaviour of the cold rolled materials. Small square coupons measuring 20 x 20 mm were cut from strips sectioned from the centre of the as-received sheets. Some smaller samples (10 x 10 mm) were also prepared. In addition, strips in rectangular shape (105 x 19 mm) were sheared with the longitudinal direction parallel to the rolling direction of the sheets. Tensile samples with 40 mm long reduced section were subsequently punched out from these rectangular strips using a manual die. A l l isothermal heat-treatment tests were conducted using two low temperature salt baths (60% potassium nitrate + 40% sodium nitrite) with the exception of tests at 1 7 5 ° C where an oil bath was used. Both the oil and salt baths were equipped with Omega CN9000A auto-tune temperature controllers. The temperatures of the salt baths were regularly checked by using a Fluke K-type thermometer before and after immersion of samples into the baths. Differences between the thermometer and controller readings were typically within ± 4 ° C . Isothermal annealing experiments were performed between 175 and 4 0 0 ° C for holding times ranging from 15 seconds to 17 hours. A l l holding times were measured using a 53 stopwatch from the first immersion in the oil/salt baths and include the time to reach temperature. Samples were immersed into the melted salt solution in small steel baskets and positioned near the tip of the temperature controller's thermocouple for the entire period of heat-treatment. The thermal history of heating a sample in a salt bath was obtained in the following way: a thermocouple was inserted in the core of a sample and then the sample was immersed into a salt bath set at a particular temperature. Time-temperature data was collected in real time using a data acquisition system connected to the thermocouple. A typical heating cycle of the sample in the salt bath is shown in Figure 3.1. It can be seen that it took about 10 seconds for the sample to reach and stabilize at the bath temperature. This time varies slightly when the salt bath was set at different temperatures but it was determined that 10 seconds is a reasonable average. Upon completion of the heat-treatment, samples were quenched in water. A n electronic engraver was used to label the samples accordingly. 3.2.2 IF-Boron Steel The first series of isothermal annealing experiments was conducted using a high temperature salt bath (70% barium chloride + 30% sodium chloride). Small square samples measuring 1 5 x 1 5 mm sheared from the centre of the as-received sheets were used in these tests. Tensile samples similar to the ones used for AA5754 were prepared only to measure the cold rolled mechanical properties. No tensile samples 54 were prepared for the annealing experiments because the size of a tensile sample was too big for the high temperature salt bath. The heat-treatment procedure follows the one described for AA5754. The annealing temperatures were varied between 550 to 7 0 0 ° C for holding times ranging from 5 to 600 minutes. However, subsequent hardness measurements show that the samples were contaminated by the melted salt solution. Hence, a second series of isothermal annealing was carried out in a Gleeble 1500 thermomechanical simulator. Details of the Gleeble experiments are presented in the following section. Figure 3.1. Thermal cycle of heating a sample in a salt bath set at 250°C. 55 3.3 Continuous Heating Using Gleeble The Gleeble 1500 thermomechanical simulator equipped with a strip annealing system provides a unique method for physical simulation of the continuous annealing process. Using the experimental set up shown in Figure 3.2, different combinations of heating and cooling rates can be applied to simulate the thermal cycle typical of industrial continuous annealing lines. Figure 3.2. Strip annealing in Gleeble 1500 thermomechanical simulator. In this system, the sheet samples were subjected to a computer programmed thermal cycle by the use of resistance heating. The original configurations of the pair of jaws 56 were modified in order to provide a firmer contact between the samples and the jaws. This was done to prevent any movements and vibrations of the samples from happening during rapid heating and quenching. A ir ram was applied to hold the samples in place during heating. Prior to heating, the specimen chamber was held in high vacuum and then backfilled with argon in order to avoid oxidation of samples which can in turn cause the detachment of thermocouples. The heating and cooling were controlled through a closed loop feedback system. The temperatures were continuously monitored by the two C r - A l thermocouples (TC and TC4) spot-welded on the samples. Figure 3.3 shows the locations of the two thermocouples along with the dimensions of the sheet samples. A uniform temperature zone ( ± 1 0 ° C ) of 5 x 4 cm was maintained in the middle section of the specimens as indicated in Figure 3.3. Rapid quenching was achieved by the use of atomizing spray nozzles positioned directly above the sample (Figure 3.2). A mixture of helium and water was used as quenching medium. The jaw design angles the sheet 4 5 ° from horizontal so as to allow water to drain off the specimen and reduce the polling effect. Metallography and hardness sample (2x2cm) Tensile sample (10.5x1 cm) • Rolling Uniform temp, zone (~5x4cm) 12.70cm 2.54cm 8.89cm 1.27cm Figure 3.3. Schematic of a sheet sample used in Gleeble experiments. 57 Two series of continuous heating tests were conducted with heating rates of 1 and 26°C/s, respectively. Heating cycle was interrupted at various stages of annealing by rapid quenching to room temperature with cooling rates typically in excess of 100°C/s. However, an average delay of approximately 0.6 seconds was observed at peak temperatures. The effect of this short holding time is significant and will be further discussed in Chapter 6. A typical thermal cycle with 1 °C/s heating rate is shown in Figure 3.4. It can be seen that T C 4 closely followed the temperature at the control thermocouple T C . However, at high heating rates, the differences between T C and T C 4 can increase up to 10°C. A n Omega type-K thermocouple simulator was used to check the accuracy of the temperature readings given by T C and T C 4 . The averaged error was ± 2 . 4 % in degrees Celsius within the temperature range of 100 to 8 0 0 ° C for both thermocouples. 400 0 50 100 150 200 250 300 350 400 450 Time (s) Figure 3.4. Typical thermal cycle of continuous heating tests with l°C/s heating rate. 58 A Temppress 602 diamond cutter was utilized to slowly cut the annealed samples to ensure no undesired deformation was introduced during sample preparation. Tensile and metallography/hardness samples were obtained from different areas in the annealed specimens, as shown in Figure 3.3. Isothermal annealing of IF-boron steel was carried out using a similar set up but on a smaller scale so that samples with reduced dimensions (Figure 3.5) can be used. The reason of using smaller samples is to avoid severe vibrations of the samples during rapid heating to achieve isothermal annealing conditions. It was determined that 5 0 ° C / s is the optimum heating rate to be applied. Samples were heated to temperatures ranging from 667 to 7 6 6 ° C and the holding times were varied from 1 to 720 seconds. Operating procedures were basically the same as described above except that only helium was used as quenching medium in these tests. • Rolling Figure 3.5. Schematic of a Gleeble isothermal annealing sample for IF-boron steel. 59 3.4 Tensile and Hardness Measurements The kinetics of recovery and recrystallization are primarily characterized by following the changes in mechanical properties. Softening in yield stress and hardness were chosen to characterize the kinetics for AA5754 and IF-boron steel, respectively. Tensile tests were conducted at a strain rate of 0.002 s"1 on a M T S 8500R tensile machine. A n extensometer with gauge length of 40 mm was attached to the samples to measure the elongation of the samples during deformation. The values for yield stress were derived from the resulting engineering stress strain curve according to the standard 0.2% offset method. A l l hardness specimens were cut at the thermocouple position. Measurements were taken along the centre line on the transverse plane (Figure 3.6). Prior to measuring the hardness, the surface was progressively ground to 600 grit finish in order to reduce surface roughness. The load and dwell time for the Micromet® 3 micro hardness tester were set at 1 kg and 10 seconds, respectively. A minimum of six measurements was taken for each sample to obtain the average hardness of the samples. Figure 3.6. Definition of transverse plane in samples. 60 3.5 Quantitative Metallography After annealing, AA5754 samples were cold mounted in an acrylic resin and JJF-boron steel samples were hot mounted in bakelite. The surface of interest i.e., the transverse plane, of the specimens was subsequently polished using a Phoenix 4000 automatic polisher to a 0.05 iim finish. Table 3.4 lists the two etching methods used to reveal the microstructures of the two materials. Photomicrographs of all the microstructures were taken using a Nikon EPIPHOT 300 series inverted metallurgical microscope equipped with a digital camera. Table 3.4. Etching methods for AA5754 and IF-boron steel. Materials Etchants Conditions AA5754 Baker's reagent: 200 ml distilled H 2 0 + 5 ml H B F 4 (48wt% solution) Electrolytic: pure A l as cathode and specimen as anode. 30 V dc for 1-1.5 minutes. Use cross-polarizers in microscope. IF-boron steel 10 g sodium doceyl benzene sulfonate + 0.1 g oxalic acid + 5 g picric acid + 2 ml hydrochloric acid + 0.3 g iron + 100 ml distilled H 2 0 Ultrasonic clean specimen in advance, dipped into etchant at about 5 0 ° C for 1-1 .5 minutes. The volume fractions of recrystallized grains were determined according to A S T M E562-89 standard point counting method. In this method, a grid with a number of regularly arrayed points was placed over the micrographs. The number of points falling within the recrystallized grains was counted and averaged for a selected number 61 of fields. This average number of points expressed as a percentage of the total number of points in the array is assumed to be an unbiased statistical estimation of the volume percent recrystallized grains. Recrystallized grains were selected solely based on their shape. A l l equiaxed and round grains were considered recrystallized grains. For every sample, two micrographs were taken at different locations and a minimum of 24 fields was measured (12 fields/micrograph). The magnifications used for AA5754 and IF-boron steel were 380x and 1900x respectively. The recrystallized grain sizes were estimated according to A S T M E l 12-88 standard employing Jeffries' method. The sum of all the grains included within a micrograph plus one half the number of grains intersected by the perimeter of the area of the micrograph gives the total number of grains. The mean grain area, Ag was obtained by dividing the total area of the micrograph by the total number of grains. The average grain sizes, d&, were then calculated as equivalent area diameter, i.e. (3.1) A minimum number of 250 grains were counted for each analysis. 62 C H A P T E R 4 R E S U L T S A N D DISCUSSION 4.1 AA5754 4.1.1 Characterization of As-received Material It is imperative to characterize the starting conditions of the as-received cold rolled sheets in order to provide a basis for subsequent softening measurements. The cold rolled yield stress was measured in three directions: along the rolling direction, 4 5 ° to the rolling direction, and 9 0 ° to the rolling direction. The results are given in Table 4.1 along with the ultimate tensile strength and hardness values. A typical engineering stress-strain curve for this alloy is plotted in Figure 4.1. The serrated flow which is characteristic of A l - M g alloys is caused by the pinning of dislocations by M g atoms during deformation. [Lloyd, 1980, Inagaki and Komatsubara, 2000]. A n optical micrograph of the cold rolled microstructure taken in the centre of the transverse plane is shown in Figure 4.2. The structure mainly consists of bands of deformed grains elongated in the direction of rolling although a small number of grains remain essentially equiaxed. This type of microstructure is consistent with the cold deformed microstructure found in other 5000 series alloys [Lloyd et al., 1982, Lloyd, 1985]. 63 Table 4.1. Mechanical properties of as-received cold rolled AA5754. (MPa) (MPa) 0"y, 90° (MPa) UTS0° (MPa) Vickers Hardness (500g load, dwell time = 10s) 245 235 233 284 91 CL in m 0) CO 0.00 0.01 0.02 0.03 0.04 Strain 0.05 0.06 0.07 Figure 4.1. Typical loading response of cold rolled AA5754 in the rolling direction. Figure 4.2. Microstructure of a 40% cold rolled AA5754 sample. 64 4.1.2 Isothermal Annealing - Tensile Measurements In order to first study the isothermal recovery behaviour, a series of low to medium temperature annealing experiments were carried out. Figure 4.3 shows the isothermal recovery kinetics in terms of yield stress vs. time relationships in the temperature range from 175 to 2 7 5 ° C for holding times up to 2 hours. Holding times do not include the time spent on heating the samples to temperature. The logarithmic time decay of yield stress as illustrated in Figure 4.3 indicates that recovery is the only softening mechanism under these experimental conditions. No recrystallized grains were detected in these samples by optical microscopy even after 2 hours at 2 5 0 ° C . However, for long annealing times a plateau in the yield stress curves is observed for all the temperatures except at 2 7 5 ° C . Similar behaviour has also been reported by Tietz et al. (1962) and Verdier et al. (1996) in other type of A l - M g alloys. In Figure 4.4, the annealing temperature was increased up to 4 0 0 ° C . It can be clearly seen from the softening curves that two processes, i.e., recovery and recrystallization have taken place during the annealing. Recrystallization was found to start at a yield stress of approximately 170 M P a for all the temperatures as indicated by the arrows in Figure 4.4. The occurrence of recrystallization was confirmed by microstructural analysis using optical microscopy. The yield stress of a fully recrystallized sample is around 90 MPa. Hence, approximately 50% of the total softening can be attributed to recovery. At 375 and 4 0 0 ° C , recrystallization is so rapid that complete softening is achieved within 40 seconds. 65 260 60 A— — — — — 1 10° 101 102 103 104 105 Time (s) ure 4.4. Isothermal recovery and recrystallization kinetics of 'AA5754. Arrows indicate start of recrystallization determined by optical microscopy. 66 It is worth noting from Figure 4.4 that a slow down of the recrystallization kinetics is observed at 275 and 3 0 0 ° C leading to plateaus in the softening curves. This behaviour is especially apparent for the curve obtained at 2 7 5 ° C , as indicated in Figure 4.4. It is believed that the plateaus were caused by non-uniform recrystallization in the structure which will be further discussed in the next section. 4.1.3 Isothermal Annealing - Microstructural Analysis Besides following the softening kinetics, it is also important to characterize the progress of recrystallization in terms of microstructural evolution because microstructures provide direct information on the recrystallization kinetics. Strong change in the microstructures can be observed since the recrystallization process involves nucleation and growth of a new set of dislocation free grains. This process is illustrated in Figures 4.5 to 4.8 where a series of microstructures of the samples annealed at 3 5 0 ° C is presented. The recovered microstructure (Figure 4.5) consists of bands of grains elongated in the rolling directions and is essentially the same structure as the one shown in Figure 4.2. That means recovery process did not introduce any observable microstructural changes. Small recrystallized nuclei can be detected after 15 seconds (Figure 4.6). These nuclei continued to grow and eventually consumed the entire structure after 490 seconds (Figure 4.8). The shape of the recrystallized grains is fairly equiaxed as compared to the elongated grains in the initial structure. 67 Figure 4.5. Recovered microstructure after isothermally annealed at 350°C for 5 seconds. Note that the structure resembles the cold rolled structure seen in Figure 4.2. Figure 4.7. Partially recrystallized structure after isothermally annealed at 350°Cfor 65 seconds. Figure 4.8. Fully recrystallized structure after isothermally annealed at 350°C for 490 seconds. 69 The measured average recrystallized grain sizes in the fully recrystallized structure are given in Figure 4.9 as a function of recrystallization temperature. No significant variation is observed with an averaged grain size between 30-35 pirn. 250 275 300 325 350 375 400 425 Recrystallization Temperature (°C) Figure 4.9. Averaged recrystallized grain sizes as a function of recrystallization temperatures for AA5754. Table 4.2 summarizes the recrystallization start and finish times for all the temperatures as well as the corresponding yield stress of the samples. The start time was determined from the first appearance of recrystallized nuclei (Figure 4.6). The recrystallization finish time was the time taken to completely transform the elongated 70 cold rolled structure to an equiaxed structure (Figure 4.8). At 2 7 5 ° C , annealing time longer than 17 hours is required to complete recrystallization. Table 4.2. Summary of isothermal recrystallization start and finish times determined by optical microscopy. Annealing Temperature (°C) Recrystallization Start time (s) Y.S. (MPa) Finish time (s) Y.S. (MPa) 275 7200 164 >60000 -300 500 169 10800 93 325 90 168 2500 91 350 15 162 490 90 It has been briefly mentioned before that the recrystallization process proceeds in a non-uniform manner. The through thickness variation in degree of recrystallization can be clearly seen in a partially recrystallized sample shown in Figure 4.10. This non-uniform structure indicates that the recrystallization nucleation rate was extremely inhomogeneous with most of the grains near the surface recrystallizing first. Recrystallization of the cold rolled grains in the centre layer of the structure will only begin after the grains near the surface have been fully recrystallized. The slower recrystallization in the centre layer is believed to be responsible for the plateaus seen in the softening curves in Figure 4.4. AA3104 alloy has also been found to exhibit this type of non-uniform recrystallization behaviour [Hirsch, 2000]. 71 Figure 4.10. Through thickness variation of fraction recrystallized for a partially recrystallized sample annealed at 300°Cfor 2490 seconds. Two factors have been proposed to explain this microstructural inhomogeneity: (1) Grain size variation in the hot rolled structure. Prior grain boundaries are preferred nucleation sites for recrystallization nuclei. Hence, finer grains near the surface in the hot rolled structure can provide more nucleation sites after cold rolling for subsequent recrystallization process. It has been found that the grain size difference between the grains near the surface and the centre can be as large as 38% in an industrial hot rolled AA5082 alloy [Wells, 1995]. 72 (2) Particle stimulated nucleation (PSN). If the density of coarse constituent particles such as dispersoids is higher near the surface, more effective recrystallization nuclei can be found in this region due to PSN. Evidence of the operation of this mechanism has been found in AA5083 alloy [Lloyd, 1985] and AA5182 alloy [Rabet et al., 1996]. The latter case is considered most likely to occur in the present work because AA5754 is an industrial processed alloy and thus will inevitably contain a significant amount of secondary particles. Quantification of the volume fraction recrystallized grains was carried out on samples annealed at 325 and 3 5 0 ° C . A l l the micrographs used for analysis were taken at approximately 1/4 section of thickness to give a representative account for the inhomogeneous recrystallization behaviour between the surface and the centre. The plot of the volume fraction recrystallized as a function of time assumes the characteristic sigmoidal form as shown in Figure 4.11. 73 10° 101 102 1 0 3 1 0 4 Time (s) Figure 4.11. Isothermal recrystallization kinetics of AA5754 at 325 and 350°C determined by quantitative metallography. 4.2 IF-Boron Steel 4.2.1 Characterization of As-received Materials Similar to AA5754, the mechanical properties of the as-received cold rolled sheets were measured. The results are summarized in Table 4.3. A typical engineering stress-strain curve is presented in Figure 4.12. The absence of yield point phenomena confirms that the amount of interstitial elements in solution such as carbon and nitrogen in this type of steel is insignificant. 74 Table 4.3. Mechanical properties of as-received cold rolled IF-boron steel. Gy,o°(MPa) UTS 0° (MPa) Vickers Hardness (1kg load, dwell time = 10s) 554 618 190 700 0.000 0.005 0.010 0.015 0.020 0.025 0.030 Strain Figure 4.12. Engineering stress-strain curve for cold rolled IF-boron steel. Unfortunately, the as-received cold rolled samples were very difficult to etch despite many attempts using different combinations of etchants. But it was found that a short heat treatment improved the etching response of the material dramatically. The poorly etched as-received microstructure is shown in Figure 4.13 where the grain boundaries can be hardly seen. Figure 4.14 shows the microstructure of a sample which has been annealed for only 5 minutes at 600°C in a vacuum furnace. The microstructure is not 75 expected to differ very much from the as-received structures because no recrystallization is expected to take place within such a short period of time at 6 0 0 ° C . However, it is more appropriate to consider this structure as a recovered structure. The significant improvements seen in the etching response can be attributed to the diffusion of boron to the grain boundaries during the heat treatment thereby enhancing the reactions between the etchant and grain boundaries [Yasuhara et al., 1994]. It can be clearly observed in Figure 4.14 that the slightly recovered structure consists of a ferrite matrix with two distinct morphologies: (1) elongated grains that are highly decorated with well defined but dense internal substructure and (2) clean elongated grains with no internal substructure. Most recently, the former has been termed as "fragmented" or "mosaic" grains due to their strongly contrasted nature when observed using electron channelling contrast [Regel, 2001]. The second type of grains which are highly elongated along the rolling direction are often referred to as "smooth" grains due to the absence of internal substructure. The distributions of fragmented and smooth grains do not seem to be affected by annealing temperature, i.e., all recovered structures possess similar features as the one shown in Figure 4.14. 76 Figure 4.13. Poorly etched as-received microstructure. 4.2.2 Isothermal Annealing - Hardness Measurements The first series of isothermal annealing experiments were performed in salt baths at temperatures ranging from 550 to 7 0 0 ° C for holding times up to 600 minutes. The results of these tests are presented in Figure 4.15. At 5 5 0 ° C , very slight change in the hardness was measured even after annealing for 400 minutes. As the annealing temperature was increased to 7 0 0 ° C , recrystallization was initiated and proceeded to completion within 5 minutes. 260 240 220 200 -180 -160 -140 -120 100 80 10" 10° 101 Time (min) 10 2 10 3 Figure 4.15. Isothermal softening curves obtained from salt bath annealing experiments. 78 The most notable results in Figure 4.15 are probably the dramatic increase in hardness after holding for 600 minutes at 6 0 0 ° C and 400 minutes at 6 5 0 ° C . The hardness is increased by nearly two-fold to values higher than those of the cold rolled material. These results are very much unexpected because IF steel is well known for its non-aging properties. A l l of the precipitates should have formed in the hot band prior to cold rolling. However, detailed examination of the through thickness microstructures of the hardened samples revealed that the regions near the top and bottom surface of the samples were severely carburised during the annealing process. The carburised layer is evidently shown in Figure 4.16 where the microstructure of the top half of a carburised sample is shown. It can be seen that the carburised layer was hardly recrystallized although the centre layer was almost completely recrystallized. The softening measurements shown in Figure 4.15 were therefore considered highly unreliable due to the effect of carburisation. It is interesting to note that the structure shown in Figure 4.16 is in fact very similar to the microstructures obtained in IF steel that has been intentionally carburised to improve the surface properties [Willem et al., 1998]. Diffusion of carbon atoms into the structure is believed to have occurred during annealing in the salt bath. To avoid this artifact, a second series of isothermal annealing tests was performed using the Gleeble 1500 thermomechanical simulator. The results are shown in Figure 4.17. Carburisation or even oxidation of the samples were no longer issues in this case because all the tests were conducted in vacuum as described in the previous chapter. The annealing temperatures were raised in order to shorten the holding time needed for 79 \ complete recrystallization. A l l holding times do not include the time spent on heating the samples to soaking temperature. The initiation of recrystallization on the softening curves corresponds to a hardness value of approximately 170 Hv for all the three temperatures. Fully recrystallized samples yield an average hardness value of 85 Hv. As compared to AA5754, the contribution of recovery to the overall softening is relatively small, only about 20%. Figure 4.16. Microstructure of a sample annealed at 650°Cfor 200 min. Note that the severely carburised layer near the surface is highly resistant to recrystallization. 80 200 T 180 -160 -(A (0 2 140 -T3 CO X 120 -to 5 100 -o > 80 -60 -40 -10-1 1 0 o 1 0 i 1 0 2 1 0 3 Time (s) Figure 4.17. Isothermal softening curves obtained from Gleeble annealing experiments. Arrows indicate start of recrystallization determined by optical microscopy. 4.2.3 Isothermal Annealing - Microstructural Analysis By following the evolution of microstructures in partially recrystallized specimens obtained at different stages of annealing, the process of recrystallization can be broken down into several sequential steps. For the purpose of this analysis, a series of micrographs obtained from samples annealed at 7 1 7 ° C for various lengths of time is presented in Figures 4.18 to 4.20. The fully recrystallized structure shown in Figure 21 was obtained by annealing at 7 4 2 ° C for 40 seconds. A l l micrographs were taken at 1/2 section of thickness on the transverse plane. 81 Step 1 (Figure 4.18): Clusters of recrystallized grains nucleate within the core of the fragmented grains. Preferred nucleation sites were both grain boundaries and grain interiors. No nuclei were found in the region of smooth grains. Step 2 (Figure 4.19): Coarsening of the recrystallized grains in the parent grains to consume neighbouring grains leaving behind the smooth recovered grains. At this stage, there is still little sign of nucleation associates with the smooth grains indicating that the driving force is extremely low in these grains. Step 3 (Figure 4.20): Recrystallization of smooth recovered grains was mostly accomplished by the growth of already recrystallized grains into the smooth grains. There are also some evidences of bulging of the grain boundaries of the smooth grains indicating grain boundaries nucleation. However, as will be shown later, the rate of recrystallization of these smooth grains was very slow causing the kinetics of recrystallization near the end of recrystallization to become extremely sluggish. Step 4 (Figure 4.21): Recrystallization was completed when recrystallized grains came into contact with each other. 82 Figure 4.18. Formation of clusters of recrystallized grains within fragmented recovered grains. Heat-treatment conditions: 717°C for 1 second. Figure 4.19. Coarsening of recrystallized grains within parent grains. Heat-treatment conditions: 717°C for 6 seconds. 83 Figure 4.20. Microstructure of a 60% recrystallized sample. Arrows 1, 2, and 3 indicate the growth of recrystallized grains into recovered smooth grains; arrow 4 indicates bulging of grain boundaries of the smooth grains. Heat-treatment conditions: 717°C for 10 seconds. Figure 4.21. Fully recrystallized structure. Heat-treatment conditions: 742°Cfor40 seconds. 84 In the early stage of recrystallization (step 1), Figure 4.18 clearly shows that the nucleation of recrystallization was a strongly heterogeneous event. Preferential nucleation sites for recrystallization were the grain boundaries and interior of the fragmented grains. In order to provide a rational explanation of this process, it is necessary to start by examining the deformed microstructure which is the precursor for the nucleation and growth of recrystallization. From Figure 4.14, it can be clearly observed that a strong internal substructure was developed in the fragmented grains after recovery. Based on the studies by Barnett and Jonas (1997) on the cold deformed microstructure of JJF steel, these substructure can be seen to originate from the so called "in-grain-shear bands" which are high in stored energy. Therefore, the driving force for nucleation of new grains in the regions of fragmented grains is high as compared to the smooth grains. Besides stored energy, the difference in texture of the two types of grains (fragmented and smooth) can also provide a clue on why recrystallized grains nucleate predominantly in the fragmented grains [Regel, 2001]. Statistically, the smooth grains are found to belong to the a-fibre whereas the fragmented grains belong to the y-fibre. By studying the Electron Back-Scattered Pattern (EBSP) of a 50% warm rolled IF steel, Regel (2001) showed that the intragranular misorientations in a-fibre grains are very low as compared to the local misorientations measured inside y-fibre grains. The high local misorientations ( > 1 0 ° ) inside the y-fibre grains provide the necessary driving 85 force for the abnormal coarsening of the subgrain structure which ultimately leads to the nucleation of recrystallization. Hashimoto et al. (1998) further provided evidence that the degree of scattering in local orientations after deformation also plays a decisive role in the nucleation of recrystallized grains. They were able to show that the development of the internal substructure was intensified if the scattering of local orientations inside a deformed grain is higher. In other words, deformed grains that contain a wide range of orientations will recrystallize first in the early stage of annealing. Figure 4.22 plots the volume fraction of recrystallized grains as a function of annealing time at 7 1 7 ° C . It is worth noting that after annealing for 15 seconds, approximately 75% of the structure was recrystallized. However, increasing the annealing time to 25 seconds only slightly increased the volume fraction of recrystallized grains to 80%. Near complete recrystallization (99%) was obtained after 60 seconds of annealing. The recrystallization kinetics becomes extremely sluggish after about 70% recrystallization. This gives an indication that the smooth grains in the partially recrystallized structure are quite reluctant to recrystallize. The sluggish recrystallization behaviour after 70% recrystallization is also reflected in the softening curves. For example, at 6 6 7 ° C , increasing the annealing time from 7 minutes to 12 minutes did not further soften the materials (Figure 4.17). In fact, fully softened structures were never obtained at 6 6 7 ° C . 86 1.0 0.9 A X 0.8 A Annealing Temperature = 717°C 0.2 A 0.1 A 0.0 0 10 20 30 40 50 60 70 Time (s) Figure 4.22. Volume fraction of recrystallized grains after annealing at 717°Cfor various lengths of times. Note the sluggish recrystallization kinetics after 70% recrystallization. The sluggish recrystallization kinetics towards the end of recrystallization has also been reported by Samajdar et al. (1997) in a 90% cold rolled Ti-stabilized IF steel. They found that the isothermal recrystallization kinetics at 6 5 0 ° C stagnates at about 60 to 70%. The J M A K exponent n which is an indicator of the rate of recrystallization was very low if the entire range of recrystallization was taken into account (n = 1.58 for 0-99% recrystallization). In comparison, the n-value obtained by only considering the intermediate stage of recrystallization was much higher (n = 3.1 for 7-70% recrystallization). Their D S C analysis of a 70% partially recrystallized structure reveals a near complete recovery in the non-recrystallized region causing a premature 87 reduction in stored energy before recrystallization can begin. By means of E B S P , they also confirmed that most of the grains that are highly resistant to recrystallization belong to a-fibre (smooth grains) which reinforces the observations by Regel (2001) discussed earlier. Hashimoto et al. (1998) have also convincingly shown that the migration of recrystallized grains into the smooth grains is difficult to proceed if the misorientation angles are less than 15° . In summary, the recrystallization process in IF steels proceeds by first consuming high stored energy grains. This process was mostly accomplished by growth of recrystallized grains within parent grains. Low energy grains (smooth grains) with low local misorientation were left intact in the initial stage of recrystallization (step 1 and 2). The recrystallization of low energy grains in later stage of annealing was mostly accomplished by growth of neighbouring recrystallized grains (step 3) although bulging of grain boundaries may suggest nucleation at grain boundaries. The fact that the grain boundaries of recrystallized grains do not readily migrate into neighbouring non-recrystallized region leads to a sluggish kinetics after about 70% recrystallization. These observations strongly suggest that the overall softening that occurred during annealing, as shown in Figure 4.17 is in fact the consequence of grain growth including abnormal grain growth. This issue is further discussed in the next chapter when the modelling results are compared to metallographic data. 88 It becomes apparent at this point that current experimental approaches (hardness measurements and optical metallography) are insufficient to provide a conclusive description on the recrystallization behaviour in IF-boron steel. Many questions remain unanswered. For example, the underlying mechanism that retards migration of grain boundaries into the smooth unrecrystallized grains is still unclear. Solute drag by excess solute atoms has been proposed as one of the possible mechanisms [Hashimoto et al., 1998]. Advanced experimental techniques such as E B S D and T E M need to be carried out to characterize the deformed structure which provides the driving force for subsequent changes in the structure. Further, the role of abnormal grain growth in the softening behaviour of the material needs to be clarified before a realistic physical model for the recrystallization process can be developed. The recrystallization start and finish time at different annealing temperatures along with the corresponding hardness values are listed in Table 4.4. The start time was determined from the first appearance of recrystallized nuclei (Figure 4.18). The recrystallization finish time is the time taken to completely transform the elongated cold rolled structure to an equiaxed structure (Figure 4.21). Average grain sizes of the final recrystallized structure are given in Figure 4.23 as a function of recrystallization temperature. A n average recrystallized grain size of approximately 9 p:m was obtained at all temperatures. 89 Table 4.4. Summary of isothermal recrystallization start and finish time as determined by optical microscopy. Annealing Temperature (°C) Recrystallization Start time (s) Hv Finish time (s) H v 667 30 172 >720 -691 10 176 300 87 7 1 7 3 171 60 88 12 -j 10 -Recrystallization Temperature (°C) Figure 4.23. Averaged recrystallized grain sizes as a function recrystallization temperatures for IF-boron steel. 90 C H A P T E R 5 M O D E L D E V E L O P M E N T 5.1 The Internal State Variable Approach The concept of microstructural modelling based on internal state variables was originally proposed by Richmond (1986) and applied to deformation processes. Since then, this idea has been expanded and applied to other industrially relevant processing of commercial alloys. A detail review of this subject has been recently provided by Grong and Shercliff (2000). Examples include casting, cooling after hot forming, heat-treatment and welding thereby illustrating the usefulness of the internal state variable approach in modelling non-isothermal process histories. This approach offers a robust modelling framework in which a non-isothermal kinetics model can be readily derived from fundamental isothermal theories by using an appropriate numerical procedure. This is extremely important because most classical theories tend to describe only isothermal heat-treatment while the complexity of industrial processes necessitates the incorporation of non-isothermal treatment paths. Generally, a microstructural evolution phenomenon can be well described by one state variable. It is unusual to consider more than three variables for a given microstructural phenomenon [Grong and Shercliff, 2000]. Each internal state variable, 5, may evolve with time and is a function of other state variables as well as processing parameters such as temperature and amount of cold reduction. These internal state variables are, in principle, measurable physical quantities although some of them are measured 91 indirectly in practise; for example, dislocation density is often quantified based on yield stress measurements. The mathematical formulation of this approach can be described by a system of coupled, in general non-linear first-order differential equations: ^ = g,(r ,5 1 ,5 2 ,5,) (5.1) where T is the instantaneous temperature, and Sj, S2, 5, are the instantaneous values of the internal state variables. Equation 5.1 is only applicable to a thermally controlled process where the evolution of each internal state variable in the next time increment is uniquely defined by these instantaneous values and the current temperature. Hence, introduction of some initial conditions, i.e., the condition at time t = 0 is required. These evolution laws can be integrated over the time-temperature history of the heat-treatment thereby determining the internal state variables of the resulting microstructure. The final results can then be fed into a microstructure-property equation to predict the material response, X,: X^MS^St, S{) (5.2) The critical step is to identify the internal state variables that should be incorporated in the formulation of the model. The number of state variables required depends on the complexity of the microstructural features of interest. However, in order to preserve 92 simplicity, the single internal state variable theory is assumed to be valid for both the recovery and recrystallization process in the present modelling approach. 5.1.1 Single State Variable Formulation for Recovery and Recrystallization In Chapter 2, a vast amount of experimental observations has been presented to show that the process of recovery is controlled by a single internal state variable, i.e., the dislocation density p. For recrystallization, the fraction recrystallized X is conveniently chosen as the single state variable. The mathematical expressions of the evolution law for these two state variables are derived in the following. For recovery, the evolution equation for dislocation density is obtained by combining the Kuhlman and Cottrell/Aytekin model (Equation 2.3) with the forest work hardening equation (Equation 2.1): ^ = _ 2 C ^ dt oMGb P Qv-C^ + aMGbp"2) RT (5.3) The term Ob in Equation 5.3 is equal to the yield stress in a fully recrystallized material, <7RX. For recrystallization, the evolution equation is simply the J M A K equation (Equation 2.11) in its differential form: ^ = bl/"n[- ln(l - X)~jr(l - X) (5.4) 93 The next step is to formulate the materials response equation. The experimental data presented in Chapter 4 have shown that both recovery and recrystallization contributes significantly to the overall softening during annealing. Hence, the biggest challenge is to formulate a material response equation that is able to take into consideration both recovery and recrystallization kinetics simultaneously. 5.1.2 Material Response Equation for Recovery and Recrystallization As a first approximation, it is assumed that recovery and recrystallization proceed independently during annealing. The microstructure at any given time t is treated as consisting of recovered and recrystallized regions as shown in Figure 5.1. Recovered cold rolled Dislocation free recrystallized grains grains Figure 5.L Schematic representations of the composite model of the structure in a partially recrystallized sample. 94 According to the composite model, if the fraction of recrystallized material is X, then the fraction of recovered material is (1-X). Hence, the overall yield stress, oys(t), at a given time t during annealing is obtained by a simple rule of mixture: crys(t) = (1 - X(t)X<y0 + cMGbfpDh X(t)aRx (5.5) Equation 5.5 is essentially the material response equation for the two internal state variables. It should be pointed out that the parameter p, is indirectly measured by yield stress. Hence, Equation 5.5 can also be rewritten as follows: oys{t) = (1 - X(t)XoRc(t))+ (5.6) where <jRc(t) is the recovered yield stress after annealing for a given time t. 5.2 Isothermal Annealing Model for AA5754 The Kuhlman and Cottrell/Aytekin recovery model is adopted to predict the recovery kinetics since it has been applied successfully to other A l - M g alloys (Chapter 2). Figure 5.2 shows the least square fit of Equation 2.4 to the isothermal recovery data using the parameters for the recovery model given in Table 5.1. In order to avoid the effects of heat up times, only measurements obtained from annealing tests with holding time longer than 60 seconds are taken into consideration. It can be seen that the model describes the softening in terms of yield stress very well within the range of 95 temperatures investigated. Discrepancies between the model fits and experimental data are within ± 5 MPa. Table 5.1. Fitting parameters for the isothermal recovery and recrystallization models for AA5754. Recovery Model Recrystallization Model Qo (kJ/mol) Cl (MPa/s) c 2 (J/mol/MPa) QR (kJ/mol) A (s'n) n 273 3.3xl0 9 827 245 9.2X10 1 8 1 240 230 -\ £ 220 ^ 210 (A 2> w 200 ^ 1 190 ™ 180 o 1 7 0 ^ 160 A 175°C • 200°C • 225°C A 250°C D 275°C - model 101 10 2 10 3 Time (s) Figure 5.2. Isothermal recovery model for AAS?'54. 10 4 96 The activation energy for recovery is in good agreement with the values proposed by Barioz et al. (1992) for an Al-3wt% M g alloy. In both cases, the values for Qo are larger than that for self-diffusion of aluminum (142 kJ/mol) indicating a strong retardation effect by solute drag due to M g in solution. By using the predictions from the recovery model, the volume fraction of recrystallized grains X(t) for samples annealed at higher temperatures can then be calculated by a simple rearrangement of Equation 5.6: The J M A K equation can be rearranged such that id = \nb + nlnt (5.8) to obtain the parameter b (y-intercepts) and n (slopes). The J M A K plot based on the fraction recrystallized calculated from Equation 5.7 is shown in Figure 5.3 for the four annealing temperatures. The correlation coefficient R2 for the four straight lines varied from 0.85 to 0.99. The four slopes yield an average value of n = 1, much less than the ideal J M A K exponents shown in Table 2.3. This 97 indicates that recrystallization kinetics follow the J M A K behaviour more in an empirical manner. Figure 5.3. JMAK plot of the isothermal recrystallization kinetics of AA5754. Further, the temperature dependence of the recrystallization rate can be represented by an Arrhenius type relationship. Then, the activation energy, QR, for the recrystallization can be derived according to the following equation: l50% ( O \ (5.9) 98 where t50% represents the time for 50% recrystallization and A is the pre-exponential factor. Using the J M A K exponent n and the b values obtained from Figure 5.3, the time for 50% recrystallization was back calculated for each of the temperature. The plot of ln(tso%) vs. 1/T is shown in Figure 5.4 with a linear slope corresponding to an activation energy of 245 kJ/mol. This value is close to the QR reported by Koizumi et al. (2000) for a 95% cold rolled Al-3wt%Mg alloy for up to 20% recrystallization. However, according to their results, the activation energy for recrystallization decreased as the fraction of recrystallized materials increased. Following the above analysis, the temperature dependency of the rate constant b in the J M A K equation can be expressed by: Table 5.1 summarizes the values of the J M A K exponent n, the pre-exponential factor A and the activation energy QR for the recrystallization model. Using these parameters, the volume fraction recrystallized grains are calculated and compared to the values obtained from the rule of mixture (Equation 5.7). Good agreements between the two set of values, as shown in Figure 5.5, confirms the suitability of the J M A K approach to describe the volume fraction of recrystallized grains in the present case, at least in an empirical fashion. (5.10) 99 100 In addition to softening measurements, the progress of recrystallization was also followed by quantitative metallography for some of the samples annealed at 325 and 3 5 0 ° C . The results are shown in Figure 5.6. The volume fraction of recrystallized grains calculated from the rule of mixture using yield stress measurements are shown for comparison. It can be seen that the fraction recrystallized obtained from softening using the rule of mixture is in good agreement with the metallographic data. This further confirms the suitability of the current modelling approach. Time (s) Figure 5.6. Comparison of volume fraction recrystallized calculated from quantitative metallography, rule of mixture and the JMAK model. 101 The overall yield stress evolution is modelled by combining the Kuhlman and Cottrell/Aytekin recovery model with the J M A K recrystallization model employing the rule of mixture (Equation 5.6). The modelling results along with the experimental data are shown in Figure 5.7. Excellent agreement is obtained between the model fits and the experimental data for all temperatures. This strongly indicates that the assumption of a composite model, as a first approximation, is a valid approach to model the recovery and recrystallization kinetics and that the interactions between recovery and recrystallization do not seem to influence the yield stress evolution during isothermal annealing in AA5754. 102 A more practical method to present the modelling results of the overall yield stress evolution is illustrated in Figure 5.8. This type of contour diagram has been referred to as an iso-yield diagram [Shercliff and Ashby, 1991] where given a combination of time and temperature for an isothermal annealing profile, the final yield stress of the material can be readily estimated. The most attractive feature of Figure 5.8 is the incorporation of the thermal cycle with the empirically determined microstructure-property relationships. This allows the user to optimize the heat-treatment conditions to achieve the desired properties. 260 250 200 Cold rolled yield stress = 245 MPa n 1 1 1 1 1 1 i 1 0 100 200 300 400 500 600 700 800 900 1000 Time (s) Figure 5.8. Empirically derived iso-yield diagram for isothermal recovery and recrystallization of cold rolled AA5754. 103 5.3 Isothermal Annealing Model for IF-Boron Steel Following the same procedure described in the previous section, an isothermal annealing model has been developed for IF-boron steel. Except in this case, Vickers hardness (Hv) was used to characterize the kinetics of recovery and recrystallization instead of yield stress. Figure 5.9 shows the fitting of the model to the isothermal annealing experimental results using the parameters given in Table 5.2. It can be seen that good agreement is obtained between model fits and experimental data despite the softening mechanism are significantly associated with grain growth which is not considered in the present modelling approach. Consequently, the model is considered as purely empirical in nature. 104 Table 5.2. Fitting parameters for the isothermal recovery and recrystallization models for IF-boron steel. Recovery Model Recrystallization Model Qo (kj/mol) Cx (Hv/s) c 2 (J/mol/Hv) Q R (kj/mol) A (s'n) n 664 l x l O 3 0 673 469 2 .9xl0 2 3 1.7 The recovery activation energy (664 kJ/mol) obtained for this material is very large as compared to the values reported by Mukuthan and Hawbolt for a 80% cold rolled IF steel without boron (173-312 kJ/mol). However, it must be noted that the merit of activation energies obtained in the present study is highly speculative as the model did not take into account the effect of grain growth which has been shown as an important mechanism that controls the softening kinetics.. On the other hand, the activation energy for recovery in IF-boron steel is expected to be higher than other grades of steels because fast segregation of boron to the grain boundaries can severely retard the recovery kinetics [Haga et al., 1998]. Seto et al. (1999) were able to show that after light recrystallization, the concentration of boron at the grain boundaries can be enhanced by factors of 250-400 with respect to the bulk concentration of boron. They also found evidence of carbon segregation to the boundaries although most of the carbon atoms should be stabilized as precipitates. Some dissolution of carbides may also occur and can systematically affect recovery and recrystallization kinetics as reported by DeMeo et al. (1991) and Satoh et al. (1992). The activation energy for recrystallization (469 kJ/mol) is comparable to the values provided by Bleck et al. (1990) for a Ti+Nb stabilized IF steel (Figure 2.19). 105 However, it must be pointed out that the values shown in Figure 2.19 were also obtained by employing the J M A K approach based on softening measurements. A n activation energy as high as 502 kJ/mol has been reported by Mukunthan and Hawbolt (1996) in a plain Ti+Nb stabilized IF steel without boron addition. This activation energy was derived based on quantitative metallography data using the J M A K equation. Figure 5.10 compares the fraction recrystallized calculated from the J M A K model with values obtained by quantitative metallography for a series of samples isothermally annealed at 7 1 7 ° C . The fraction recrystallized calculated based on the rule of mixture is also included for comparison. It can be seen that the J M A K model and the rule of mixture agree well with each other but both severely underestimate the fraction recrystallized obtained from microstructural analysis particularly at the beginning of recrystallization. This behaviour can be seen as a result of the abnormal growth of recrystallized grains which occurred in the early stage of recrystallization, as discussed in the previous chapter. The discrepancies between the fraction of recrystallized grains obtained based on softening measurements ( J M A K and the rule of mixture) and quantitative metallography indicates that a single internal state variable is not adequate to describe the recrystallization process. In addition to fraction recrystallized, grain size should be included as an additional state variable in the formulation of microstructure model to predict softening kinetics. 106 Time (s) Figure 5.10. Comparison of volume fraction recrystallized calculated from quantitative metallography, rule of mixture and the JMAK model. The relationship between yield strength and grain size is expressed by the well-known Hall-Petch equation: ay=<j0 + kyd-U2 (5.11) where d is the grain size, Ob the intrinsic stress of the material and ky is a constant. The total amount of softening in terms of yield stress (A<7y) can be estimated according to Acry=ky(di-l/2-df-U2) (5.12) 107 By assuming the initial grain size J , = 1 Jim, final grain size df= 10 u.m, ky = 21.4 M P a mm for body centred cubic iron [Gladman, 1997], Equation 5.12 gives a total softening of 463 M P a which is in the order of the value obtained experimentally, 404 M P a (the as-received and fully recrystallized yield stress for the IF-boron steel are 554 and 150 MPa, respectively). This simple calculation shows that grain size is a valid internal state variable and that the Hall-Petch equation can be taken as an alternative response equation. A more comprehensive approach, however, would be to develop a response equation which reflects both internal state variables; i.e., fraction recrystallized and grain size. This, however, would result in a more complex model which is beyond the scope of the present work. Simple models even if not physically precise, can be a better and more robust approach for application to industrial processes. 108 C H A P T E R 6 M O D E L VALIDATION In the previous chapter, the internal state variable approach has been shown to be a valid tool to quantitatively capture the evolution of mechanical properties during isothermal annealing for both AA5754 and IF-boron steel. The model for IF-boron steel is purely empirical because it does not take into account the effect of grain growth. Nevertheless, in order to expand the applicability of the model, continuous heating tests were carried out to validate the model predictions. Mathematically, the non-isothermal yield stress evolution is modelled by integrating the rule of mixture in its differential form over the time-temperature history of the heat-treatment. Hence, Equation 5.6 is differentiated to give The term dX/dt is simply the J M A K equation in its differential form which is given by Equation 5.4. The differential equation for the evolution of yield stress due to recovery is given by Equation 2.3 which is rewritten as follows: ^ f = -C,exp | (Qo-c2oRc) RT (6.2) A l l the required kinetic parameters are summarized in Tables 5.1 and 5.2. 109 Validation tests were preformed for two heating rates, 1 and 2 6 ° C / s with the latter being typical of continuous annealing lines. It must be pointed out that although all the continuous heating tests were designed to study the non-isothermal annealing behaviour without the effect of holding time, there was a slight delay observed at peak temperatures before quenching. On average, the holding time was determined to be 0.6 seconds. The effect of this very short holding time is large for samples heated very fast to peak temperatures. This is schematically shown in Figure 6.1 where the softening curve predicted by the model is superimposed on the thermal history obtained from the Gleeble experiments for a AA5754 sample. The test was interrupted at 4 0 0 ° C by rapid quenching. It is clearly shown that a very short holding time of less than 1 second at peak temperature resulting in an additional 20 M P a softening. 110 Taking into account the effect of holding time, Figures 6.2 and 6.3 show the modelling results for AA5754 and IF-boron steel, respectively. A l l the temperatures indicated in the graph for the experimental data are readings taken from the control thermocouple T C (Figure 4.3). It can be seen that the model predicts the non-isothermal softening kinetics in AA5754 materials quite satisfactorily. The effect of recovery and recrystallization in terms of softening can be easily separated for AA5754. At high heating rate, the model predictions for IF-boron steel deviate significantly from the experimental data towards the end of recrystallization. However, as pointed out earlier, it is possible that the recovery and recrystallization kinetics were altered by the dissolution of carbides at high temperatures resulting in an increase in the hardness of the samples. This behaviour has been reported by DeMeo et al. (1991) in a 80% cold rolled boron-containing IF steel. It must be emphasized that the model derived for IF-boron steel does not agree with the underlying physics of the softening process. It has been shown that grain growth is one of the primary softening mechanisms and hence the use of fraction recrystallized as the only internal state variable in the current modelling approach is inadequate. Table 6.1 summarizes the recrystallization start and finish temperatures determined by optical microscopy along with the corresponding mechanical properties for both materials. I l l 275 250 A 0 50 100 150 200 250 300 350 400 450 500 550 600 Temperature (°C) Figure 6.2. Comparison between the model predictions and continuous heating experimental data for AA5754. 220 200 180 A 160 A g 140 120 100 550 600 800 850 650 700 750 Temperature (°C) Figure 6.3. Comparison between the model predictions and continuous heating experimental data for IF-boron steel. 112 Table 6.1. Recrystallization start and finish temperatures during continuous heating. Materials Heating Rates (°C/s) Recrystallization Start T. (°C) Properties Finish T. (°C) Properties AA5754 1 297 191 M P a 375 92 M P a 26 326 194 M P a 433 88 M P a IF-boron steel 1 643 172 Hv 753 103 Hv 26 691 178 Hv >785 -The effect of heating rates can be seen by comparing the recrystallization start temperatures. At high heating rate ( 2 6 ° C / s ) , the initiation of recrystallization was delayed up to about 3 0 ° C and 5 0 ° C for AA5754 and IF-boron steel, respectively. This behaviour is expected because less time is available for the recrystallization to initiate when the specimens were heated very fast to temperatures. It is also worth noting that at high heating rate, IF-boron steel did not fully recrystallize even up to temperature close to 8 0 0 ° C . It is interesting to compare the non-isothermal recrystallization kinetics for the two materials. Figure 6.4 plots the continuous recrystallization kinetics (HR = l ° C / s ) predicted by the model as a function of homologous temperature for AA5754 and IF-boron steel. It can be seen that the homologous temperature for recrystallization for AA5754 is in fact higher than for IF-boron steel. Figure 6.4 also shows that the kinetics of recrystallization in IF-boron steel is slightly faster than in AA5754. This behaviour can, at least in part, be explained by the higher amount of cold reduction in IF-boron steel (80%) as compared to AA5754 (40%). 113 0.50 0.55 0.60 0.65 0.70 0.75 Homologous Temperature (°K) Figure 6.4. Non-isothermal recrystallization kinetics as a function of homologous temperatures for AA5754 and IF-boron steel. The final recrystallized grain sizes obtained at different heating rates are shown in Figure 6.5. At 2 6 ° C / s , IF-boron steel was not fully recrystallized under current experimental conditions therefore no grain size measurement was taken. The final structure after heating at l ° C / s consists of grains with average grain size of approximately 11 p:m in IF-boron steel. The averaged grain size for AA5754 is 35 p:m for both heating rates. For both materials, the recrystallized grain sizes are close to the values obtained in isothermal annealing (Figures 4.3 and 4.29) indicating that grain size is independent of thermal path. 114 40 26 1 1 Heating rate (°C/s) Figure 6.5. Measured recrystallized grain sizes after annealing with different heating rates for AA5754 and IF-boron steel. 115 C H A P T E R 7 S U M M A R Y AND CONCLUSIONS 7.1 Summary Continuous annealing is a versatile and cost effective process to produce advanced sheet metals for the automotive industry. However, there is still a lack of a process model that has the capability to provide a quantitative link between processing conditions and product properties. As part of a strategic project to address this deficiency, the present work has examined the kinetics of recovery and recrystallization behaviour of two important classifications of automotive alloys. Recovery and recrystallization are the two principal metallurgical phenomena that control the degradation of mechanical properties during annealing. As a result of the present research, a microstructure model was successfully developed to accurately predict the mechanical properties of A l - M g alloy AA5754 and under isothermal and non-isothermal heating conditions and under isothermal condition for boron-containing interstitial free steel. The model which draws on the concept of internal state variables adopts a rule of mixture to separate recovery from recrystallization based on the assumption that these two processes proceed independently. The Kuhlman and Cottrell/Aytekin recovery model and the J M A K recrystallization model were adapted to capture the time evolution of dislocation density and fraction recrystallized, respectively. 116 Experimentally, softening measurements were carried out in conjunction with optical microscopy to follow the evolution of the two internal state variables. It was found that the model satisfactory captures the evolution of microstructure and yield stress in AA5754. However, for IF-boron steel, the fraction recrystallized predicted by the model do not agree with the data obtained from quantitative metallography. This strongly indicates that the current modelling approach is too simple to adequately address the complexity involved in the recrystallization process of IF-boron steel. Nevertheless, the model can still be applied in an empirical fashion to predict the hardness of the steel under isothermal heating condition. Based on the experimental data and modelling results, the following conclusions are drawn: (1) Experimental results show that the recovery kinetics of AA5754 obeys a logarithmic type of relationship. A single internal variable description using dislocation density seems to be sufficient for the purpose of modelling the recovery kinetics. The contribution of recovery to overall softening is 50% for AA5754 and 20% for IF-boron steel. (2) The J M A K model can only be taken as a semi-empirical tool to model the kinetics of the recrystallization process as the underlying mechanisms for recrystallization do not conform to the assumptions 117 made in the ideal J M A K model. The J M A K exponent for AA5754 and JP-boron steel was found to be equal to 1 and 1.7, respectively. (3) Microstructural analysis shows that the nucleation of recrystallization is highly heterogeneous in both materials. In AA5754, the structures near the top and bottom surface recrystallized before the centre layer leading to a through thickness gradient in the degree of recrystallization. In IF-boron steel, recrystallization grains nucleate predominantly in cold rolled grains with dense in-grain-shear-bands. Low energy grains are highly resistant to recrystallization leading to sluggish recrystallization kinetics after approximately 70% recrystallization. (4) Optical microscopy reveals that the softening in IF-boron steel is in part caused by grain growth including abnormal grain growth. Hence, the use of fraction recrystallized as a single internal state variable is not adequate. As a result, the model for IF-boron steel is considered purely empirical. (5) The final average recrystallized grain size was 35 p:m and 10 p:m for AA5754 and IF-boron steel, respectively. The recrystallized grain size was found to be independent of the thermal path of the annealing process for the two materials. 118 7.2 Future Work In depth microstructural analysis needs to be carried out in order to clarify the softening mechanism of the IF-boron steel during annealing. Current microstructural analysis based on optical microscopy indicates that the recrystallization process in IF-boron steel is far more complex than in AA5754. Advanced characterization techniques such as E B S D are required to clarify the role of misorientation in the nucleation and growth of recrystallized grains in IF-boron steel. As for AA5754, further studies should be carried out to confirm the occurrence of particle simulated nucleation in the early stage of recrystallization. In terms of modelling, it has been shown that the softening mechanism in IF-boron steel is largely associated with grain growth. 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