On the shear band formation in F.C.C. metals

On the shear band formation in F.C.C. metals

Scripta METALLURGICA et MATERIALIA Vol. 25, pp. 1081-1085, 1991 Printed in the U.S.A. Pergamon Press plc All rights reserved ON THE SHEAR BAND FOR...

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Scripta METALLURGICA et MATERIALIA

Vol.

25, pp. 1081-1085, 1991 Printed in the U.S.A.

Pergamon Press plc All rights reserved

ON THE SHEAR BAND FORMATION IN F.C.C. METALS Yu-Lin Shen Division of Engineering Brown University Providence, Rhode Island 02912, U.S.A. (Received J a n u a r y 11, 1991) (Revised February 28, 1991) Shear banding in metallic materials during deformation processing has long been studied. One of the most interesting phenomenons is the orientation of shear bands in plane strain deformation, e.g. rolling. In rolled f.c.c, metals, though different shear band angles have been reported, they are prominently running at approximately 35 ° to the longitudinal direction while viewed from the transverse direction (1-3), as shown in Fig.1. Many works have been devoted to explaining the shear band orientations for a variety of materials under different processing conditions (4-9). However, most of the studies were based on the continuum analysis. The real crystallographic nature of shear band formation still needs to be investigated. In the present work, a crystallographic model is proposed to explain the 35 ° shear bands in rolled f.c.c, metals from a macro-constraint consideration. When polycrystalline materials are deformed plastically, texture gradually develops. For f.c.c, metals the predominant rolling textures are {I12} copper-type and {110}<112> brass-type (I0,II). At the beginning of the rolling process, the randomly oriented crystals deform homogeneously. In each grain several slip systems have to be activated to accommodate the deformation of neighboring grains. After an extensive amount of rolling, however, texture develops which prevents homogeneous deformation from occuring. The distinct texture makes the material somewhat like a

L

\

Fig.1. Typical 35 ° shear bands observed in rolled f.c.c, metals. transverse, S : short transverse. )

1081 0036-9748/91 $3.00 + .00 Copyright (c) 1991 Pergamon Press plc

( L : longitudinal, T :

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single crysatal. We can use a Thompson tetrahedron (12) to describe the crystallographic orientations of textures. The four faces of the tetrahedron are {111 } slip planes and the six edges are <110> slip directions of f.c.c, crystal. Fig.2(a) is the representation of the {112}<111> copper-type texture. The (112) plane normal coincides with the short transverse direction and [ i l l ] points to the longitudinal direction. It can be seen that the tetrahedron is symmetric about the L-S plane. For the {110}<112> brass-type texture, the representation is shown in Fig.2(b). The (01"i) plane normal coincides with the short transverse direction and [211] points to the longitudinal direction. The tetrahedron is symmetric about the L-T plane. Now consider the lattice rotation of a single crystal during plastic deformation. When a single crystal is deformed in tension and/or compression, the crystal lattice usually suffers a rotation (13). For rolling it tends to align the active slip planes and active slip directions parallel to the rolling plane and longitudinal axis, respectively. If slip is the dominant process of plastic deformation, which is essentially true for high stacking fault energy f.c.c, metals, lattice rotation can thus be determined for the two types of texture. For {112}<111> texture, no rotation about the S-axis happens because of the symmetry. But the slip planes will adjust themselves to cause the rotation about the T-axis, as shown in Fig.3. In the beginning ABC, ABD, BCD and ACD are the four possible slip planes, making the angles of 61.87 ° , 61.87 °. 19.47 ° and 90 ° to the rolling plane, respectively. However, ACD plane cannot be activated because it is perpendicular to the tensile axis and parallel to the compression axis. From the plane strain condition ( £11 = -css , Get = ~tl = c t s = 0 ), it can also be seen that ABC and ABD planes are unlikely to be activated. Thus, without going into the detailed calculation of Taylor factor, we know that the two symmetric slip directions on the BCD plane are the

[ii2]~I

L / ~

T

/ [iii3

[gii] (a)

Fig.2. Crystallographic orientations of (a) {112}<111> and represented by Thompson tetrahedrons.

[01[)

/ (b) Co) {110}<112>

textures

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s

B (a)

(b)

Fig.3. Crystallographic orientations of 1112}<111> texture represented by tetrahedron (a) before and (b) after lattice rotation.

a Thompson

major slip systems for (112}<111> texture. The BCD plane then tends to lie more parallel to the rolling plane, which will make the tetrahedron rotate about the T-axis in the sense shown in the figure. Once it rotates, slip systems of the ACD plane can take part in the deformation process, making the tetrahedron rotate continuously. At the time when the BCD plane becomes horizontal, the ACD plane is the only slip plane responsible for the rotation. After this moment, it seems that the ACD and BCD planes tend to rotate in opposite directions because they both try to lie more parallel to the rolling plane. However, it is not difficult to see that the rotation of the ACD plane will prevail provided that the angle between the BCD and rolling planes is less than the angle between the ACD and rolling planes. Thus the original lattice rotation proceeds. Finally the orientation comes to {110}<001> Goss-type texture as shown in Fig.3(b). Slip systems of BCD and ACD slip planes then take charge of the deformation while keeping the plane strain condition satisfied. The lattice cannot be rotated further because of its symmetry about the principal planes. The most important thing is that these two slip planes both incline at 35.26 ° to the rolling plane, in accordance with the orientation of shear bands. Chang, Hou and Chang (14) have calculated the Taylor factor of several orientation combinations for plane strain deformation and found that {110}<001> Goss texture is more easily deformed than 1112}<111> copper texture. For a {112}<111> textured material, the rotation toward [110}<001> texture certainly cannot happen everywhere homogeneously because of the shape constraint of deformation. But if the transition to Goss texture starts at some regions, the easily deformed nature of that texture makes strain concentrate along the 350 directions. Lattice rotation then takes place along the 35 ° bands and shear localization occurs. If the rolling texture of the material is (110}<112>, crystal lattice rotation can be represented as Fig.4. No rotation about the T-axis occurs because of the symmetry. At first the ABC, ACD, ABD and BCD planes make the angles of 90°, 90°, 35.2to and 35.26 °

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to the rolling plane. The activated slip planes are ABD and BCD. But the plane strain restriction will force them to rotate to make the slip systems symmetric about the longitudinal direction. The more the rotation proceeds, the more the plane strain condition is satisfied. Finally the crystallographic orientation becomes {110}<001> as in

!

L

D

c

B (a)

(b)

Fig.4. Crystallographic orientations of {110}<112> texture represented by tetrahedron (a) before and (b) after lattice rotation.

a Thompson

the case of the {112}<111> textured material. {110}<001> texture is also more easily deformed than (110}<112> texture (14). Hence the argument of shear band formation in the previous paragraph can be applied to the {110}<112> textured material. For rolled £c.c. metals in which slip is the major process of deformation, the formation of 35 ° shear bands can be summarized as follows. F.c.c. metals usually exhibit {112}<111> copper-type or {110}<112> brass-type textures after being rolled to some extent. These crystallographic orientations tend to become the stable {110}<001> Goss-type textures for further deformation. However, this cannot happen homogeneously throughout the material. Once the transition starts at some points, deformation then must extend along the confined bands while keeping the orientation of the outside lattice unchanged. The angle between these bands and the rolling plane is 35 °, which is essentially the angle of the active slip planes in [!10}<001> orientation. In fact, {110}<001> texture was found in rolled £c.c. metals as a minor component (3,14,15,16). This has been regarded that the Goss oriented grains cause the formation of 35 ° shear bands because of the easily deformed nature and the orientation consistency (14). But it is not convincing to say that few Goss oriented grains can

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produce the excessive transgranular 35 ° shear bands usually observed in the materials. The present study concludes that the {110}<001> Goss texture component might be the contribution of the localized lattice rotation within the copper and brass oriented grains. In these transition regions shear banding takes place. References 1. W. Kerth, E. Amann, X. Raber and H. Weber, Int. MetaU. Rev. 20, 185 (1975). 2. I. L. Dillamore, J. G. Roberts and A. C. Bush, Metal Sci. 13, 73 (1979). 3. S. C. Chang and J. H. Huang, Acta Metall. 34, 1657 (1986). 4. P. Van Houtte, J. Gil Sevillano and E. Aernoudt, Z. Metallk. 70, 426. 503 (1979). 5. G. R. Canova, U. F. Kocks and M. G. Smut, Scripta Metall. 18, 437 (1984). 6. R. Hill and J. W. Hutchinson, J. Mech. Phys. Solids 23, 239 (1975). 7. R. J. Asaro, Acta Metall. 27, 445 (1979). 8. L. Anand and W. A. Spitzig, Acta Metall. 30, 553 (1982). 9. W. Y. Yeung and B. J. Duggan, Acta Metall. 35, 541 (1987). 10. R. E. Smallman, J. Inst. Met. 84, 10 (1955). 11. I. L. Dillamore and W. T. Roberts, Acta MetaU. 12, 281 (1964). 12. N. Thompson, Proc. Phys. Soc. B66, 481 (1953). 13. R. E. Reed-Hill, Physical Metallurgy Principles, 2'nd ed. p.195, D. Van Nostrand Company Inc., New York (1973). 14. Shih-Chin Chang, Duen-Huei Hou and Yun-Kie Chang, Acta Metall. 37, 2031 (1989). 15. N. Hansen and D. J. Jensen, Metall. Trans. 17A, 253 (1986). 16. V. W. C. Kuo and E. A. Starke Jr., Metall. Trans. 16A, 1089 (1985).