8 Recrystallization Grain Growth in Polycrystals II,Kitabyushu Japan,(1995). Weiland,H.,Adams,B.L.and Rollett,A.D.(eds.).(1998).Grain Growth in Polycrystals III.TMS. International Conferences on Recrystallization and Grain Growth A combination of the former Recrystallization and Grain Growth series of International conferences,which will be held every three years. Gottstein,G.and Molodov,D.A.(eds.),(2001).First International Conference on Recrystallization and Grain Growth-Rex&GG.Springer-Verlag,Berlin. Second International Conference on Recrystallization and Grain Growth-Rex&GGII. (2004),Annecy,France. International Texture Conference (ICOTOM)Series Conferences are held every 3 years. The 13th Conference was held in Seoul,Korea in 2002. The 14th Conference will be held in Levven,Belgium in 2005. International Riso Symposia Held annually in Riso,Denmark,the proceedings in 1980,1983,1986.1991,1995 and 2000 are of particular relevance. International Thermomechanical Processing Conferences (Thermec) General coverage of all aspects of thermomechanical processing.Proceedings published by TMS. Thermec'97,Wollongong,Australia. Thermec'2000,Las Vegas,USA. Thermec'2003,Madrid,Spain. Other International Conferences Recrystallization in the Control of Microstructure.Institute of Metals,London.Keynote papers published in Metal Science J.,8.(1974). Recrystallization in the Development of Microstructure.Leeds.Institute of Metals, London.Published in Metal Science,13.(1979). Microstructure and Mechanical Processing.Cambridge.Institute of Materials,London. Keynote papers published in Materials Science and Tech.,6.(1990). Fundamental of Recrystallization.Zeltingen,Germany.A number of short papers from this meeting are published in Scripta Metall.Mater.,27,(1992). Thermomechanical Processing-TMP2,Stockholm,ASM,(1996)
Grain Growth in Polycrystals II, Kitabyushu Japan, (1995). Weiland, H., Adams, B.L. and Rollett, A.D. (eds.), (1998), Grain Growth in Polycrystals III. TMS. International Conferences on Recrystallization and Grain Growth A combination of the former Recrystallization and Grain Growth series of International conferences, which will be held every three years. Gottstein, G. and Molodov, D.A. (eds.), (2001). First International Conference on Recrystallization and Grain Growth - Rex&GG. Springer-Verlag, Berlin. Second International Conference on Recrystallization and Grain Growth - Rex&GGII. (2004), Annecy, France. International Texture Conference (ICOTOM) Series Conferences are held every 3 years. The 13th Conference was held in Seoul, Korea in 2002. The 14th Conference will be held in Levven, Belgium in 2005. International Risø Symposia Held annually in Risø, Denmark, the proceedings in 1980, 1983, 1986, 1991, 1995 and 2000 are of particular relevance. International Thermomechanical Processing Conferences (Thermec) General coverage of all aspects of thermomechanical processing. Proceedings published by TMS. Thermec’97, Wollongong, Australia. Thermec’2000, Las Vegas, USA. Thermec’2003, Madrid, Spain. Other International Conferences Recrystallization in the Control of Microstructure. Institute of Metals, London. Keynote papers published in Metal Science J., 8. (1974). Recrystallization in the Development of Microstructure. Leeds. Institute of Metals, London. Published in Metal Science, 13. (1979). Microstructure and Mechanical Processing. Cambridge. Institute of Materials, London. Keynote papers published in Materials Science and Tech., 6. (1990). Fundamental of Recrystallization. Zeltingen, Germany. A number of short papers from this meeting are published in Scripta Metall. Mater., 27, (1992). Thermomechanical Processing - TMP2 , Stockholm, ASM, (1996). 8 Recrystallization
Introduction 9 Deformation Processing of Metals,London.Published in Phil.Trans.Royal Soc., 1441-1729,(1999). Thermomechanical Processing:Mechanics,Microstructure and Control,University of Sheffield.Palmiere.Mahfouf and Pinna (eds.)BBR Solutions,(2003). 1.3 FORCES.PRESSURES AND UNITS The annealing processes discussed in this book mainly involve the migration of internal boundaries within the material.These boundaries move in response to thermodynamic driving forces,and specific quantitative relationships will be discussed in the appro- priate chapter.It is however useful at this stage to set out some of the terminology used and also to compare the energy changes which occur during the various annealing processes with those which drive phase transformations. 1.3.1 Pressure on a boundary The processes of recovery,recrystallization and grain growth are all driven by the defect content of the material.Consider a small part of the microstructure of a single-phase crystalline material as shown in figure 1.2,which consists of two regions A and B separated by a boundary at position x.Let us assume that the two regions contain different defect concentrations and that the free energies of these regions per unit volume are G and G respectively. The boundary will move if the Gibbs free energy of the system is thereby lowered,and if an area a of the boundary moves a distance dx,then the change in free energy of the system is dG dx(GA -GB)a (1.) The force,F,on the boundary is given by dG/dx,and the pressure,P,on the boundary. is given by F/a,and thus P---G-G-4G (1.2) P B X Fig.1.2.The pressure on a boundary
Deformation Processing of Metals, London. Published in Phil. Trans. Royal Soc., 1441–1729, (1999). Thermomechanical Processing: Mechanics, Microstructure and Control, University of Sheffield, Palmiere, Mahfouf and Pinna (eds.) BBR Solutions, (2003). 1.3 FORCES, PRESSURES AND UNITS The annealing processes discussed in this book mainly involve the migration of internal boundaries within the material. These boundaries move in response to thermodynamic driving forces, and specific quantitative relationships will be discussed in the appropriate chapter. It is however useful at this stage to set out some of the terminology used and also to compare the energy changes which occur during the various annealing processes with those which drive phase transformations. 1.3.1 Pressure on a boundary The processes of recovery, recrystallization and grain growth are all driven by the defect content of the material. Consider a small part of the microstructure of a single-phase crystalline material as shown in figure 1.2, which consists of two regions A and B separated by a boundary at position x. Let us assume that the two regions contain different defect concentrations and that the free energies of these regions per unit volume are GA and GB respectively. The boundary will move if the Gibbs free energy of the system is thereby lowered, and if an area a of the boundary moves a distance dx, then the change in free energy of the system is dG ¼ dxðGA GBÞa ð1:1Þ The force, F, on the boundary is given by dG/dx, and the pressure, P, on the boundary, is given by F/a, and thus P ¼ 1 a dG dx ¼ GA GB ¼ G ð1:2Þ Fig. 1.2. The pressure on a boundary. Introduction 9
10 Recrystallization If AG in equation 1.2 is given in units of Jm,then the pressure on the boundary(P)is in Nm-2.There is some confusion in the literature regarding terminology,and the terms force on a boundary and pressure on a boundary are both used for the parameter which we have defined above by P.As P has units of Nm-2 which are those of pressure,there is some logic in using the term pressure,and we will adopt this terminology. 1.3.2 Units and the magnitude of the driving pressure Although we will be discussing the forces and pressures acting on boundaries in some detail in later chapters,it is useful at this stage to examine,with examples,some of the forces involved in annealing.This will serve to demonstrate the units used in the book and also to give some idea of the relative magnitudes of the forces involved in annealing.A good discussion of forces arising from a variety of sources is given by Stuiwe (1978). Recrystallization-driving pressure due to stored dislocations The driving force for recrystallization arises from the elimination of the dislocations introduced during deformation.The stored energy due to a dislocation density p is ~0.5 pGb2,where G is the shear modulus and b the Burgers vector of the dislocations. A dislocation density of 10'5-1016 m-2,which is typical of the cold worked state in copper (G=4.2 x 1010 Nm-2,b=0.26 nm)therefore represents a stored energy of x10-2x 107 Jm-3 (10-100 J/mol)and gives rise to a driving pressure for recrystallization of ~2-20 MPa. Recovery and grain growth-driving pressure due to boundary energy Recovery by subgrain coarsening and grain growth following recrystallization are both driven by the elimination of boundary area.If the boundary energy is y per unit area and the boundaries form a three-dimensional network of spacing D,then the driving pressure for growth is given approximately as 3y/D.If the energy of a low angle grain boundary (ys)is 0.2 Jm2,and that for a high angle boundary (p)is 0.5 Jm-,we find that P~0.6 MPa for the growth of I um subgrains during recovery,and that P~10-2 MPa for the growth of 100 um grains. Comparison with the driving forces for phase transformations It is of interest to compare the energy changes which occur during annealing,as dis- cussed above,with those which occur during phase transformations.For example a typical value of the latent heat of fusion for a metal is ~10 kJ/mol and that for a solid state transformation is ~1 kJ/mol.We therefore see that the energies involved in annealing of a cold worked metal are very much smaller than those for phase transformations
If G in equation 1.2 is given in units of Jm3 , then the pressure on the boundary (P) is in Nm2 . There is some confusion in the literature regarding terminology, and the terms force on a boundary and pressure on a boundary are both used for the parameter which we have defined above by P. As P has units of Nm2 which are those of pressure, there is some logic in using the term pressure, and we will adopt this terminology. 1.3.2 Units and the magnitude of the driving pressure Although we will be discussing the forces and pressures acting on boundaries in some detail in later chapters, it is useful at this stage to examine, with examples, some of the forces involved in annealing. This will serve to demonstrate the units used in the book and also to give some idea of the relative magnitudes of the forces involved in annealing. A good discussion of forces arising from a variety of sources is given by Stu¨we (1978). Recrystallization – driving pressure due to stored dislocations The driving force for recrystallization arises from the elimination of the dislocations introduced during deformation. The stored energy due to a dislocation density is 0.5 Gb2 , where G is the shear modulus and b the Burgers vector of the dislocations. A dislocation density of 1015–1016 m2 , which is typical of the cold worked state in copper (G ¼ 4.2 1010 Nm2 , b ¼ 0.26 nm) therefore represents a stored energy of 2 106 –2 107 Jm3 (10–100 J/mol) and gives rise to a driving pressure for recrystallization of 2–20 MPa. Recovery and grain growth – driving pressure due to boundary energy Recovery by subgrain coarsening and grain growth following recrystallization are both driven by the elimination of boundary area. If the boundary energy is c per unit area and the boundaries form a three-dimensional network of spacing D, then the driving pressure for growth is given approximately as 3/D. If the energy of a low angle grain boundary (s) is 0.2 Jm2 , and that for a high angle boundary (b) is 0.5 Jm2 , we find that P 0.6 MPa for the growth of 1 mm subgrains during recovery, and that P 102 MPa for the growth of 100 mm grains. Comparison with the driving forces for phase transformations It is of interest to compare the energy changes which occur during annealing, as discussed above, with those which occur during phase transformations. For example a typical value of the latent heat of fusion for a metal is 10 kJ/mol and that for a solid state transformation is 1 kJ/mol. We therefore see that the energies involved in annealing of a cold worked metal are very much smaller than those for phase transformations. 10 Recrystallization
Chapter 2 THE DEFORMED STATE 2.1 INTRODUCTION The emphasis in this and the following chapter is quite different to that of the remaining chapters of the book.The most significant of the many changes associated with recrystallization and other annealing phenomena is the decrease in the density of dislocations.In this chapter we are concerned with dislocation accumulation rather than dislocation loss and with the increases in stored energy that are a result of deformation. The dislocations provide the driving force for the annealing phenomena dealt with in the remaining chapters. A comparison of the present chapter with those dealing with annealing will reveal discrepancies between our current knowledge of the deformed state and our requirements for the understanding of annealing.For example,we currently have an incomplete understanding of the rates of dislocation accumulation during deformation and of the large-scale deformation heterogeneities which are important in nucleating recrystallization,and this impedes the formulation of quantitative models of recrystallization.On the other hand,we now have a great deal of information about the formation of boundaries during deformation,but have not yet formulated annealing theories which adequately take these into account.Such discrepancies provide useful pointers to areas which require further research. During deformation the microstructure of a metal changes in several ways.First,and most obvious,the grains change their shape and there is a surprisingly large increase in the total grain boundary area.The new grain boundary area has to be created during 11
Chapter 2 THE DEFORMED STATE 2.1 INTRODUCTION The emphasis in this and the following chapter is quite different to that of the remaining chapters of the book. The most significant of the many changes associated with recrystallization and other annealing phenomena is the decrease in the density of dislocations. In this chapter we are concerned with dislocation accumulation rather than dislocation loss and with the increases in stored energy that are a result of deformation. The dislocations provide the driving force for the annealing phenomena dealt with in the remaining chapters. A comparison of the present chapter with those dealing with annealing will reveal discrepancies between our current knowledge of the deformed state and our requirements for the understanding of annealing. For example, we currently have an incomplete understanding of the rates of dislocation accumulation during deformation and of the large-scale deformation heterogeneities which are important in nucleating recrystallization, and this impedes the formulation of quantitative models of recrystallization. On the other hand, we now have a great deal of information about the formation of boundaries during deformation, but have not yet formulated annealing theories which adequately take these into account. Such discrepancies provide useful pointers to areas which require further research. During deformation the microstructure of a metal changes in several ways. First, and most obvious, the grains change their shape and there is a surprisingly large increase in the total grain boundary area. The new grain boundary area has to be created during 11
12 Recrystallization deformation and this is done by the incorporation of some of the dislocations that are continuously created during the deformation process.A second obvious feature, particularly at the electron microscope level,is the appearance of an internal structure within the grains.This too,results from the accumulation of dislocations.Except for the small contribution of any vacancies and interstitials that may have survived,the sum of the energy of all of the dislocations and new interfaces represents the stored energy of deformation.There is one other consequence of deformation that is relevant to the study of annealing processes.During deformation the orientations of single crystals and of the individual grains of a polycrystalline metal change relative to the direction(s)of the applied stress(es).These changes are not random and involve rotations which are directly related to the crystallography of the deformation.As a consequence the grains acquire a preferred orientation,or texture,which becomes stronger as deformation proceeds,and this is considered in chapter 3. Every stage of the annealing process involves loss of some of the stored energy and a corresponding change in microstructure.The release of stored energy provides the driving force for recovery and recrystallization,but it is the nature of the microstructure that controls the development and growth of the nuclei that will become recrystallized grains and also their orientation.If these changes are to be understood it is essential that we begin by examining the nature of the deformed state,the generation of microstructure and particularly the development of inhomogeneities in that micro- structure.Unfortunately our knowledge of these matters is still imperfect and Cottrell's assessment of the situation some 50 years ago is still valid. Few problems of crystal plasticity have proved more challenging than work hardening.It is a spectacular effect,for example enabling the yield strength of pure copper and aluminium crystals to be raised a hundredfold.Also,it occupies a central place in the subject,being related both to the nature of the slip process and to processes such as recrystallization and creep.It was the first problem to be attempted by the dislocation theory of slip and may well prove the last to be solved. A.H.Cottrell (1953) 2.2 THE STORED ENERGY OF COLD WORK 2.2.1 Origin of the stored energy Most of the work expended in deforming a metal is given out as heat and only a very small amount (~1%)remains as energy stored in the material.This stored energy,which provides the source for all the property changes that are typical of deformed metals, is derived from the point defects and dislocations that are generated during deformation. However,the mobility of vacancies and interstitials is so high that except in the special case of deformation at very low temperatures,point defects do not contribute significantly to the stored energy of deformation.In the common case of deformation at ambient temperatures almost all of the stored energy is derived from the accumulation of dislocations and the essential difference between the deformed and the annealed states lies in the dislocation content and arrangement.Because of this,discussion of the
deformation and this is done by the incorporation of some of the dislocations that are continuously created during the deformation process. A second obvious feature, particularly at the electron microscope level, is the appearance of an internal structure within the grains. This too, results from the accumulation of dislocations. Except for the small contribution of any vacancies and interstitials that may have survived, the sum of the energy of all of the dislocations and new interfaces represents the stored energy of deformation. There is one other consequence of deformation that is relevant to the study of annealing processes. During deformation the orientations of single crystals and of the individual grains of a polycrystalline metal change relative to the direction(s) of the applied stress(es). These changes are not random and involve rotations which are directly related to the crystallography of the deformation. As a consequence the grains acquire a preferred orientation, or texture, which becomes stronger as deformation proceeds, and this is considered in chapter 3. Every stage of the annealing process involves loss of some of the stored energy and a corresponding change in microstructure. The release of stored energy provides the driving force for recovery and recrystallization, but it is the nature of the microstructure that controls the development and growth of the nuclei that will become recrystallized grains and also their orientation. If these changes are to be understood it is essential that we begin by examining the nature of the deformed state, the generation of microstructure and particularly the development of inhomogeneities in that microstructure. Unfortunately our knowledge of these matters is still imperfect and Cottrell’s assessment of the situation some 50 years ago is still valid. Few problems of crystal plasticity have proved more challenging than work hardening. It is a spectacular effect, for example enabling the yield strength of pure copper and aluminium crystals to be raised a hundredfold. Also, it occupies a central place in the subject, being related both to the nature of the slip process and to processes such as recrystallization and creep. It was the first problem to be attempted by the dislocation theory of slip and may well prove the last to be solved. A.H. Cottrell (1953) 2.2 THE STORED ENERGY OF COLD WORK 2.2.1 Origin of the stored energy Most of the work expended in deforming a metal is given out as heat and only a very small amount (1%) remains as energy stored in the material. This stored energy, which provides the source for all the property changes that are typical of deformed metals, is derived from the point defects and dislocations that are generated during deformation. However, the mobility of vacancies and interstitials is so high that except in the special case of deformation at very low temperatures, point defects do not contribute significantly to the stored energy of deformation. In the common case of deformation at ambient temperatures almost all of the stored energy is derived from the accumulation of dislocations and the essential difference between the deformed and the annealed states lies in the dislocation content and arrangement. Because of this, discussion of the 12 Recrystallization