Y.Estrin,A.Vinogradov/Acta Materialia 61 (2013)782-817 787 Imparting large plastic strains to a work-piece is a chal- first requirement stimulated development of dies with lenging and technically formidable task.It requires a con- reduced friction by implementing surface hardening of siderable investment in tool design,which on one hand the channel walls,mobile walls [37,43],etc.,as well as the should be durable enough to sustain repetitive high loads introduction of new effective lubricants [441.The third during material forming,and on the other hand be suitable requirement led to the understanding of the significance for materials processing without causing damage to the of back-pressure for processing of billets with uniform work-piece.A distinctive feature of SPD processing,which microstructure and improved mechanical properties meets these requirements,is that the high strain is imposed [43,45,46].Segal showed that the performance of a die without any significant change in the overall dimensions of may be compromised by perceived simplicity of the die the work-piece.This is achieved due to special tool geom- design [38].In particular,he warned against the use of dies etries that prevent free flow of the material and thereby with a corner arc which leads to the occurrence of a widely produce a significant hydrostatic pressure.The presence spread fan-shaped plastic zone.This is equivalent to artifi- of this hydrostatic pressure is a clue for achieving the high cially increased friction that spreads shear and gives rise to strains required for exceptional grain refinement.Many significant heterogeneity of strain.Unfortunately,this crystalline materials,including those which are brittle important warning was disregarded in many later studies, under normal conditions(e.g.tungsten oxide,B2O3 glasses which utilized a"simplified"die design with a rounded and amorphous materials),gain substantial ductility under outer corner and had to pay a high price in form of sub- high hydrostatic pressure and can be deformed to large stantial heterogeneity of the deformed structure.By con- strains without failure.Nowadays many variants of SPD trast,by following Segal's philosophy,samples with techniques,which expressly or tacitly employ this generic uniform microstructure throughout the billet could be fab- feature of high hydrostatic pressure,are readily available ricated [47,48].While standard laboratory-scale ECAP rigs for fabrication of a great variety of UFG materials. can handle billets with cross-sectional dimensions in the range of 10-20 mm,Segal's ideas enabled development of 2.1.Principal processing schemes industry-scale ECAP facilities for processing of billets as large as 50 x 50 mm-in cross-section and 500 mm in length Equal-channel angular pressing (ECAP),less appropri- 「431 ately referred to as equal-channel angular extrusion High pressure torsion (HPT)refers to processing that (ECAE)in some publications,is at present the most highly evolved from Bridgman's anvils [6],cf.Table 1b,and developed SPD processing technique(Table la).A simple involves a combination of high(GPa range)pressure with shear strain is introduced when the billet passes through torsional straining.Today this technique is appreciated the plane where the two channels meet.The cross-sectional by many researchers as the one that allows the most effi- dimensions of the billet remain unchanged,thereby permit- cient grain refinement.A handicap of the method is that ting repetitive pressing,leading to accumulation of very only small coin-shaped samples,typically 10-15 mm in large strains.For example,the equivalent (von Mises) diameter and I mm in thickness,can be processed.The strain,Eeg,introduced per pass in ECAP with a 90 angle readers are referred to a comprehensive review on the sub- between the channels amounts to 1.15 [37,38].Different ject [30]for details.Because of size restrictions,the samples ECAP variants involving rotations of the billet about the manufactured by HPT are used primarily for research pur- pressing axis between the passes are possible,and they gen- poses.An important issue for many SPD processing erally lead to different results in terms of the microstructure schemes,including HPT,is the non-uniformity of deforma- and texture produced.The definitions of these ECAP tion.For instance,during HPT straining,Table Ib,the routes to which we refer below can be found in Refs. shear strain at the rotation axis should be zero,increasing [14.151. linearly in the radial direction if the geometry of the work- Against the backdrop of a flood of publications on piece does not change.This means that the material near ECAP processing,it is easy to forget where it all started. the rotation axis of the sample should stay undeformed. It is therefore timely to recall that the key advantages This is not supported by numerous microstructural obser- and fundamentals of ECAP.including the mechanics of vations and microhardness measurements showing a rea- extrusion,the derivation of the optimal process conditions sonably uniform distribution of grain dimensions and involving a balance between friction,tool geometry,strain microhardness,provided the compressive pressure and path and its efficiency for grain refinement,were formu- the number of revolutions of the anvil are sufficiently large lated by V.Segal in a series of early publications [12,38- (as in Fig.1)[49-51].Vorhauer and Pippan [52]explained 42].He defined ECAP as "a deformation technique to this discrepancy by the fact that it is virtually impossible to impart intensive,uniform and oriented simple shear for realize an ideal HPT deformation due to the misalignment materials processing".He also demonstrated that ECAP of the axes of the anvils.Alternatively,the development of is effective if(i)friction between the billet and the die walls a reasonably uniform strain (Fig.2)and homogeneous is kept at a minimum;(ii)the angle between the channels is microstructure was explained in terms of gradient plasticity close to 90:and (iii)the sharp outer corner is fully filled theory coupled with the microstructurally based constitu- ensuring that the shear zone is as narrow as possible.The tive modelling [53].This model will be addressed in theImparting large plastic strains to a work-piece is a chal￾lenging and technically formidable task. It requires a con￾siderable investment in tool design, which on one hand should be durable enough to sustain repetitive high loads during material forming, and on the other hand be suitable for materials processing without causing damage to the work-piece. A distinctive feature of SPD processing, which meets these requirements, is that the high strain is imposed without any significant change in the overall dimensions of the work-piece. This is achieved due to special tool geom￾etries that prevent free flow of the material and thereby produce a significant hydrostatic pressure. The presence of this hydrostatic pressure is a clue for achieving the high strains required for exceptional grain refinement. Many crystalline materials, including those which are brittle under normal conditions (e.g. tungsten oxide, B2O3 glasses and amorphous materials), gain substantial ductility under high hydrostatic pressure and can be deformed to large strains without failure. Nowadays many variants of SPD techniques, which expressly or tacitly employ this generic feature of high hydrostatic pressure, are readily available for fabrication of a great variety of UFG materials. 2.1. Principal processing schemes Equal-channel angular pressing (ECAP), less appropri￾ately referred to as equal-channel angular extrusion (ECAE) in some publications, is at present the most highly developed SPD processing technique (Table 1a). A simple shear strain is introduced when the billet passes through the plane where the two channels meet. The cross-sectional dimensions of the billet remain unchanged, thereby permit￾ting repetitive pressing, leading to accumulation of very large strains. For example, the equivalent (von Mises) strain, eeq, introduced per pass in ECAP with a 90 angle between the channels amounts to 1.15 [37,38]. Different ECAP variants involving rotations of the billet about the pressing axis between the passes are possible, and they gen￾erally lead to different results in terms of the microstructure and texture produced. The definitions of these ECAP routes to which we refer below can be found in Refs. [14,15]. Against the backdrop of a flood of publications on ECAP processing, it is easy to forget where it all started. It is therefore timely to recall that the key advantages and fundamentals of ECAP, including the mechanics of extrusion, the derivation of the optimal process conditions involving a balance between friction, tool geometry, strain path and its efficiency for grain refinement, were formu￾lated by V. Segal in a series of early publications [12,38– 42]. He defined ECAP as “a deformation technique to impart intensive, uniform and oriented simple shear for materials processing”. He also demonstrated that ECAP is effective if (i) friction between the billet and the die walls is kept at a minimum; (ii) the angle between the channels is close to 90; and (iii) the sharp outer corner is fully filled ensuring that the shear zone is as narrow as possible. The first requirement stimulated development of dies with reduced friction by implementing surface hardening of the channel walls, mobile walls [37,43], etc., as well as the introduction of new effective lubricants [44]. The third requirement led to the understanding of the significance of back-pressure for processing of billets with uniform microstructure and improved mechanical properties [43,45,46]. Segal showed that the performance of a die may be compromised by perceived simplicity of the die design [38]. In particular, he warned against the use of dies with a corner arc which leads to the occurrence of a widely spread fan-shaped plastic zone. This is equivalent to artifi- cially increased friction that spreads shear and gives rise to significant heterogeneity of strain. Unfortunately, this important warning was disregarded in many later studies, which utilized a “simplified” die design with a rounded outer corner and had to pay a high price in form of sub￾stantial heterogeneity of the deformed structure. By con￾trast, by following Segal’s philosophy, samples with uniform microstructure throughout the billet could be fab￾ricated [47,48]. While standard laboratory-scale ECAP rigs can handle billets with cross-sectional dimensions in the range of 10–20 mm, Segal’s ideas enabled development of industry-scale ECAP facilities for processing of billets as large as 50 50 mm2 in cross-section and 500 mm in length [43]. High pressure torsion (HPT) refers to processing that evolved from Bridgman’s anvils [6], cf. Table 1b, and involves a combination of high (GPa range) pressure with torsional straining. Today this technique is appreciated by many researchers as the one that allows the most effi- cient grain refinement. A handicap of the method is that only small coin-shaped samples, typically 10–15 mm in diameter and 1 mm in thickness, can be processed. The readers are referred to a comprehensive review on the sub￾ject [30] for details. Because of size restrictions, the samples manufactured by HPT are used primarily for research pur￾poses. An important issue for many SPD processing schemes, including HPT, is the non-uniformity of deforma￾tion. For instance, during HPT straining, Table 1b, the shear strain at the rotation axis should be zero, increasing linearly in the radial direction if the geometry of the work￾piece does not change. This means that the material near the rotation axis of the sample should stay undeformed. This is not supported by numerous microstructural obser￾vations and microhardness measurements showing a rea￾sonably uniform distribution of grain dimensions and microhardness, provided the compressive pressure and the number of revolutions of the anvil are sufficiently large (as in Fig. 1) [49–51]. Vorhauer and Pippan [52] explained this discrepancy by the fact that it is virtually impossible to realize an ideal HPT deformation due to the misalignment of the axes of the anvils. Alternatively, the development of a reasonably uniform strain (Fig. 2) and homogeneous microstructure was explained in terms of gradient plasticity theory coupled with the microstructurally based constitu￾tive modelling [53]. This model will be addressed in the Y. Estrin, A. Vinogradov / Acta Materialia 61 (2013) 782–817 787