- Email: [email protected]
Reduced value of stress active in the shear bands
Scripta METALLURGICA et MATERIALIA
Vol.
25, pp. 1513-1518, 1991 Printed in the U.S.A.
R2~UCED V A L U E OF STRESS A C T I V E IN T H E S ~ m R
Aleksander
Pergamon Press plc All rights reserved
BANDS
J a n Ku~nierz P o l i s h A c a d e m y of Sciences Krupkowski Institute for Metal R e s e a r c h Krak6w, Poland (Received December 18, 1990) (Revised April 15, 1991)
Introduction Shearing in the form of shear bands SB, registered during cold rolling as strain markings at ~=~Sxa~/180 tad to the rollin~ d i r e c t i o n RD (I), are still lacking a commonly accepted scientific explanation. Apart f r o m their role in fracture initiation they m a y be considered as a control m e c h a n i s m at large strains and regarded as the result of local instability w i t h an u n u s u a l l y high degree of non-dilatational s~rain (2). The appearance of shear bands is favoured by the plane-strain state conditions of d e f o r m a t i o n /e.g., rolling/ and low stackin~ fault energy SFE value /e.g., alloys: the SFE of CuZn30 is equal to 12 mJ/m 2 and the S F E of CuAI8 is equal to 5 mJ/m 2 (3)/. S h e a r Bands
Following the period of d e f o r m a t i o n due to cr~stallographic slIp~ w i t h possible participation of mechanical twinning, a n e w mode of deformation in the f o r m of shear bands becomes visible (~-16). The shear bands are a form of localized plastic instability with a n u n u s u a l l y h i g h de,Tee of nondilatational strain. I n the course of rollingp they appear after a deformation ~=I°2 /reduction z=70%/ in the case of Cu or, after z=~0~ /~=0.5/ in the case of CuZn~0 and assume the form of lamellae lying in the planes parallel to the transverse d i r e c t i o n T D and inclined to the sheet surface at an angle of ~5x~/180 rad. An increase in the deformation causes an increase of their volume f r a c t i o n /reaohin 6 90% after the r e d u c t i o n z=90~/ as well as their s i z e - s t a r t i n ~ w i t h bands of a grain size through bands covering a group of grains up to shear bands crossing the whole thickness of the rolled metal.
M a c r o s c o p i c Appearance o~f t h e ~
Formed SBs
Figure I presents the s t r e s s - s t r a l n curve of Cu~18 bron~o illustratlr~g the range of strains investigated durin~ the cold r o l l l n ~ experiment (18). The n e w l y formed macroscopic shear bands MSBs were identified on pro-polished longitudinal cross-sections of the polyor~stalline CuAI8 and AIMs2 samples after a small rerollin~ /compare SB formation i n c l u d i n ~ texttLve and m i o r o s t r u o t u r e exam~-,tion under rollin~ of CuAI8 (|9) and in deep drawing (20,21)/. At a small r o l l l n g r e d u c t i o n /less than 40~ for CuAI8/ only a w a v y surface f o r m e d by the surface of the particular 6Tains covered w i t h slip m a r k / n ~ w a s visible /Fig.2a/. New MSBa were recox~led after the rollin~ r e d u c t i o n z=40% / ~ = - I n (I-z)=0.5/. These markings /Fig.2b/, at first not so distinctly shaped on a w a v y baok6Tound of the particular &Tains, become more refined as the rollin~ r e d u c t i o n increases; the i n c l ~ - - t i o n an~le 8=35x~/|80 tad to RD m e a s u r e d in a longitudinal c r o s s - s e c t i o n is still maintained. T h e structure of MSBs at ~5x~/180 tad to RD is clearly seen at a
1513 0036-9748/91 $3.00 + .00 Copyright (c) 1991 Pergamon Press plc
1514
SHEAR BANDS
Vol.
25, No.
7
reduction of z=80~. Traces o f MSBs f o r m a characteristic p a r a l l e l o 6 T a m net /[email protected] and 2d/; at the end of rollin~, brittle failure is noted along the
HSBs (I 9 ) .
The salient feature o f f r e s h l y created MSBs is the constant value o f the inclination angle to RD, equal to ~5xJ~/180 red i n d e p e n d e n t l y of the FCC material tested (5,6,12,1~,18,19,22,2~). It is independent also of a rollin~ strain hiF,her than ~ 0 o 5 /case of metals with low SFE v a l u e / stressing the essential role of oonstraints induced by the rolllng conditions and the required level of cold w o r k i n g and/or the deformation texture. Tf we suppose the shearin~ stress in a plane-stress state is the only factor to b r i ~ about the s h e a r i n g inetability~ we expect to be able to observe the MSB onset at ~/~ red to RDo To overcome this discrepancy w i t h the experiment hypotheses based on: texture so£tenin6 (16, 17) /supported r e c e n t l y b y theoretical calculation (2~)/, the theory of bifurcation (25,26) , dynamical instability (27-29), layered structure (~K)) or orystallo6Tephioal initiation ( 2 1 , ~ 1 , ~ ) have been admitted but still some questions r e m a i n open /e.g° the principal question o o n c e r n i n ~ their origin/o For an isotropic body, which yields aooordin~ to a Huber-voMises-Henok-y yield function, this experimentally measured value, ~5x~/|80 red, corresponds to the onset of a local n e c k under compression in a plane-stress state, suggestin~ this state to be an ultimate one u n d e r cold rollln~ conditions. W h e n the anisotrol~y is introduced by its coefficient of a~Lsotropy /r-value/ we a r r i v e at the conclusion that it produces the ehiftin~ in the @ values which fall in the range of e~perimental error ( 2 ~ ) . T h e n , a ~ m ~ t t ~ n ~ t h e f o r m a t i o n o f SBs a t ~ 5 x ~ / | 8 0 r e d t o RD u n d e r p l a n e - s t r e s s state conditions, we o ~ p o s t u l a t e the only one p~rameter, i.e. the level of sold work.t~ that governs the a p p e a r a n c e of SBs. Reduced V a l u e The fixes1 statement
where
~k ~5B
o~f Shear Stress Active
in S.~B
of the last pex~a6Taph o~n be expressed
mathematically:
i s the reduced value of shear stress active in the SB, is the shearing stress at the tempez~ture T, is the shear modulus /nearly linear on T except in the temperature range (32)/,
is
the temperat~e
low
of £usion.
The r a t i o o f t e m p e r a t u r e s T/~ relates t h e m e a m a r e d v a l u e s t o t h e seine l e v e l of thermal energy determJ~aed by the ~ value, where k is Boltz'm'm's oonstsmt. Tak~a6 into account 0 = 3 5 x Y ~ 1 8 0 r i d we o b t a i n
where ~ is the compression i n (1) we h l y e
In
the
ease
o f CuA18 ~
is
stress
active
w h e n HSBe a p p e a r .
e q w a l t o 8 5 0 MPa ( 1 9 ) a n d i t
~ e r t ~
(2)
was e p p r o x i m t t e l 7
Vol.
25, No. 7
SHEAR BANDS
1515
o o n s t a n t d u r i n 8 SBs f o x ~ m t i o n /Fi~.l/; s i ~ L l a r behavlour w a s o b s e r v e d i n t h e e a s e o f A l ~ 2 w i t h ~ = - 3 4 0 NPa (3-3). F o l l o w i n g (3) t h e o a l o u l a t e d reduced 4 shear stress value T ~ f o r the alloys C u~18 and AIMg2 was equal to 17.Sx10/Table 1/. In Table I we l~esent also ~ f o r some metals ( ~ ) , a s s u m i n ~ that the SBs are formed at the level R of ultimate tensile strength, related
to~
by
and supposin~
the shear
modulus
~A i s
equal
to
E
P = where
2 (',+ ~')'
(5)
• is the u~J~'orm e l o n g a t i o n E is the elastio modulus and is Poisson's coefflolent. TA~ Shearin~
1
Chemaoteristio ,
|
R£
Metal
• =29 K
of Rolled Metals
s
rzJ l'opa] [ Pa] ,
,
[."Pal
,
,,
,,,
1100 Ou ETP Ag
0.33 0.33 0..37
93.3 1356 1234
69 117 76
26 4tt 28
90-166
.35- 5
310-.3q5 126
Au
O.t~2
1336
79
28
Ni
0.3 0.3.3
1726 1309
207 1 17
76
CuA18 A.1.1~2
0.3.3
916
69
A1
,
[10-".]
I'"Pa.]
,
6..3-9.o
12-20 48-54
121-174 3/~7-/414 186-19t4
221
/4
2.~
7.4
379-552 -
50-35
561-745
4/4.
-
850
5.2-6.8 17 • 8
232-.303 347
26
-
-
3/40
17.2
1.39
7.2-8.6 6.6-6.8
5 3 - 71 142-169 7 6 - 79 9/'1'
Pure metals, in spite of lar~g diffe~enoes i n SFE v a l u e s (3)j 6ire the reduoed shear s~ress value ~.=7x10on the avemge and with dispe~sion between 5.2x10 -q a n d 9 . ~ x 1 0 - ~ / T a b l e 1 / . As we h a v e J u s t s e e n t h e ~. v a l u e @ of alloys are ~eater / T K = - 1 7 . S x 1 0 " q / i n c o m p a r i s o n t o p u r e m e t a l s /~K=--TX10--4/ w h i o h may b e d u e t o t h e i n o e r t i t u d e of E and ~ values reported a n d may a s well be due to additional strengthenin~ e£fects pcoduoed by the alloying itself. I n o o n c l u s i o n we s u p p o s e t h a t t h e s h e a r i n 6 e £ f s o t i n t h e f o m o f S B s , observed under rollin~ conditions, is independent o f t h e de£ox~aed m e t a l a n d in this ease only the extex~al oonditions are responsible for their eppeamnoe. 0 n e e t h e ~K i s k n o w n o n e o a n o a l o u l a t e ~oD admittin~ the elastio properties of material are known, and =
(6)
This enables us to prediot t h e moment o f SB f o r m a t i o n ~ n ~ t h u s t h e r a n s ~ the heterogeneous mode o f d e £ o z , a a t i o n , w h i o h i s i m p o r t a n t i n i n d u s t r i a l praotioo. To h a v e t h e p r o p e r d a t a a p r e o i s e m e a s u r e m e n t o f s h e a r s t r e s s
of
1516
SHEAR BANDS
Vol. 25, No. 7
actin6 in the shear band plane at the onset of SB is necessary and this is expected to be dons in the next step. Cone lusions Newly formed MSBs are: /i/ inclined at a constant angle ~ equal to 3 5 x ~ 1 8 0 rod to the RD inoludin~ the anisotropy effect induced by crystallographic texture, /ii/ produced under rolling at approximately constant compression stress aotin~ in the plane-stress state. F o l l o w i n ~ / i / and /li/ it is demonstrated that the reduced shear stress value ~ necessary for the onset of SB, when related to elastic constant of material and thermal energy level, is independent of the material tested; then during cold rollln~ only the external constraints seem to be ~esponsible for the SB formation. The reduced ~k value is equal to (7+I .8)xi0 -q in the case of pure metals /AI, Cu, Ni, £~, Au/, whe~e the calculated one for alloys /CuAI8 and AIMg2/ is equal to 17.5x10 -~ which may be explained by the incertitude of elastic constants as well ae some strengthen1_n~.~ induced by the alloying addition itself. Ref ereno e s
1. F.Adcook, J . I n s t . M e t a l s , 27, 73 (1922) Viewpoint Set No. 6, Soripta Metall., 18, ~21 (198~) P.C.J.Gallagher, Met. Trans., I, 2429 (1970) , M.Cook, T.Li Riohar~s, Met. Sci., 78, 463 (1951) B.Farsette, O.Whitham, M&m. Soi. Roy. M&t., 73, 179 (1976~ B.J.Du~san, M.HatherIy, W.B.Hutohinson, P.T.Wekefield, Met. Sol., 12, ~43 (1978) 7. A . S . M e l i n , M . H a t h e r l y , Met. S o l o , 1~, 463 (1979) . 8. P.T.¥ake£ield, M.Hatherly, Met. Sol., 15, 109 (1981) 9. M.HatherI7, ICSM& 6, Melbourne 1982, V. 3, P. 1181 10. P.S.Mathtur, W.A.Baokofen, Met. Trans., 4, ~63 (1973) 11. K.Morii, M.Mera, Y.Nakayana, Trans. J. I. M., 18, 7 (1977) 12. T.Noda, B.Plege, J.Grewen, ICOTOM 5, Aachen BRG 1978, V. I, p. ~43 13. M.Hatherly, A.S.Malin, Met. Teohn., 6, ~08 (1979) 1~° J . G . S e v i l l a n o , P. Van H o u t t e , E . A e r n o u d t , S e r i p t a M e t a l l . , 11, 581 (1977) 15. M.Bllcharski, S.Gorcwyca, Met. Sci., 12, ~0~ (1978) 16. I.L.Dillamore, J.G.Roberts, A.C.Bush, Met. Sol., 13, 7 3 (1979) 17. P. Van Houtte, J.G.Sevillano, E.Aernoudt, Z. Mkde, 70, ~26, 503 (1979) 18. J.Kulnier ~., Sci. Bull. £MM, Metallurgy and Foundry Pz~aotioe, No. 1269 /123/, 63 (1989) 19. J . K u ~ n i e r z , A r c h i v e s o f M e t a l l u r g y , 35, 269 (1990) 20. J.Ku~nierffi, M.Gasperini, A.Mokhtari, M.Pernot, RoPenelle, ICOTOM 7, Noordwi~kerhout, Holland 1984, p. 509 21. J.Kulniex-z, £~chives of Metallur~y, 3~, 179 (1988) 22. W.Y.Yeun~, B.J.~_~an, Acta Met., 35, 541 (1987) 23. J.Ku~nierz, Bull. Aoad. Sole. Polon., S&r. Sole. Teohn., in press 24. T . O s t ~ k , G.J.Davies, Aota Met., 35, 2307 (1987) 25. R.HilI, J.¥.Hutchinson, J. Mech. Phys. Solids, 23, 239 (1975) 26. R.J.Asaro, Aota Met., 27, ~ 5 (1979) 27. E.Nes, W.B.Hutohlnson, A.A.Rldha, ICSM~ 7, Oxford 1985 /Ed. Me ~usen/, Pergamon Press, p. 57 28. A.Ko~bel, J.D.~-bux-y, M.Hatherly, P.L.Ma~tini, E.W.E~blosh, Aota Met., 1~, 1999 (1986) 29. K . M o r i i , H . T e r s ~ a , Y.Nakay~ma, T r a n s . J° X. M., 27, 769 (1986) 30. K . M o r i i , H.Mecb~-~, Y.Nakayama, Acta M e t . , 33, 379 (1985) 31. Z . J a s i e ~ s k / , XCSMA 7, Oxford 1985 / E d . Mc Queen/, Pergamon P r e s s , p. 583 32. H.Meokin~, B . N i o k l a s , N.Zarubowa, Aota M e t . , 3~, 527 (1986) 3~- Z.Jasie~ski, J.Kudnlerz, R.Penelle~ Internat. Coll. CNRS, Aussois, France 1-I0.0~. 1987 3~. Metal Fuandbook, V. 1, Properties and Selection o[ Metals, ~SM, Ohio 1961 2. 3. 5~. . 6.
Vol.
25, No.
7
SHEAR BANDS
1
1
1517
1
1
I
[MPo]
1000
-/,
O
in
(0
•
' BA8r
tension
O
BABz
....
13
8r
compression
gl
r7
---
10
r8
-,,-
g
rlO
-,,-
O
z4
-.-
500
I
Z6
I
1
- ',-
I
I
2
C=-In(1-z)
FIG. 1.
Strees-stz~in
ourve
o f Cu~18 b r o r ~ e
(18,19)
1518
FIG.2.
SHEAR BANDS
Vol.
25, No.
S t r a i n ma~k£n~s on l o n ~ i t u d ~ l oross-seotion d ~ ~o11~ o f 0u~18 /~D 4 - A i o a t e s m a g n i f i c a t i o n m a r k / : a / Wavy s ~ a o s o f CuAI8 r o l l e d t o ~ = 0 . 2 b / O n s e t o f MSB a t ~ 5 x ~ 1 8 0 m d t o RD i n s a m p l e s t r a i n e d t o 6 = 0 . 7 o / MiSB 4 . s a m p l e . t r a 4 - e d /;o ~=1.8 d / ~SB o a ~ i n ~ r o t a t i o n o f b l o o k ~ ~ = 2 . 2
7
Vol.
25, pp. 1513-1518, 1991 Printed in the U.S.A.
R2~UCED V A L U E OF STRESS A C T I V E IN T H E S ~ m R
Aleksander
Pergamon Press plc All rights reserved
BANDS
J a n Ku~nierz P o l i s h A c a d e m y of Sciences Krupkowski Institute for Metal R e s e a r c h Krak6w, Poland (Received December 18, 1990) (Revised April 15, 1991)
Introduction Shearing in the form of shear bands SB, registered during cold rolling as strain markings at ~=~Sxa~/180 tad to the rollin~ d i r e c t i o n RD (I), are still lacking a commonly accepted scientific explanation. Apart f r o m their role in fracture initiation they m a y be considered as a control m e c h a n i s m at large strains and regarded as the result of local instability w i t h an u n u s u a l l y high degree of non-dilatational s~rain (2). The appearance of shear bands is favoured by the plane-strain state conditions of d e f o r m a t i o n /e.g., rolling/ and low stackin~ fault energy SFE value /e.g., alloys: the SFE of CuZn30 is equal to 12 mJ/m 2 and the S F E of CuAI8 is equal to 5 mJ/m 2 (3)/. S h e a r Bands
Following the period of d e f o r m a t i o n due to cr~stallographic slIp~ w i t h possible participation of mechanical twinning, a n e w mode of deformation in the f o r m of shear bands becomes visible (~-16). The shear bands are a form of localized plastic instability with a n u n u s u a l l y h i g h de,Tee of nondilatational strain. I n the course of rollingp they appear after a deformation ~=I°2 /reduction z=70%/ in the case of Cu or, after z=~0~ /~=0.5/ in the case of CuZn~0 and assume the form of lamellae lying in the planes parallel to the transverse d i r e c t i o n T D and inclined to the sheet surface at an angle of ~5x~/180 rad. An increase in the deformation causes an increase of their volume f r a c t i o n /reaohin 6 90% after the r e d u c t i o n z=90~/ as well as their s i z e - s t a r t i n ~ w i t h bands of a grain size through bands covering a group of grains up to shear bands crossing the whole thickness of the rolled metal.
M a c r o s c o p i c Appearance o~f t h e ~
Formed SBs
Figure I presents the s t r e s s - s t r a l n curve of Cu~18 bron~o illustratlr~g the range of strains investigated durin~ the cold r o l l l n ~ experiment (18). The n e w l y formed macroscopic shear bands MSBs were identified on pro-polished longitudinal cross-sections of the polyor~stalline CuAI8 and AIMs2 samples after a small rerollin~ /compare SB formation i n c l u d i n ~ texttLve and m i o r o s t r u o t u r e exam~-,tion under rollin~ of CuAI8 (|9) and in deep drawing (20,21)/. At a small r o l l l n g r e d u c t i o n /less than 40~ for CuAI8/ only a w a v y surface f o r m e d by the surface of the particular 6Tains covered w i t h slip m a r k / n ~ w a s visible /Fig.2a/. New MSBa were recox~led after the rollin~ r e d u c t i o n z=40% / ~ = - I n (I-z)=0.5/. These markings /Fig.2b/, at first not so distinctly shaped on a w a v y baok6Tound of the particular &Tains, become more refined as the rollin~ r e d u c t i o n increases; the i n c l ~ - - t i o n an~le 8=35x~/|80 tad to RD m e a s u r e d in a longitudinal c r o s s - s e c t i o n is still maintained. T h e structure of MSBs at ~5x~/180 tad to RD is clearly seen at a
1513 0036-9748/91 $3.00 + .00 Copyright (c) 1991 Pergamon Press plc
1514
SHEAR BANDS
Vol.
25, No.
7
reduction of z=80~. Traces o f MSBs f o r m a characteristic p a r a l l e l o 6 T a m net /[email protected] and 2d/; at the end of rollin~, brittle failure is noted along the
HSBs (I 9 ) .
The salient feature o f f r e s h l y created MSBs is the constant value o f the inclination angle to RD, equal to ~5xJ~/180 red i n d e p e n d e n t l y of the FCC material tested (5,6,12,1~,18,19,22,2~). It is independent also of a rollin~ strain hiF,her than ~ 0 o 5 /case of metals with low SFE v a l u e / stressing the essential role of oonstraints induced by the rolllng conditions and the required level of cold w o r k i n g and/or the deformation texture. Tf we suppose the shearin~ stress in a plane-stress state is the only factor to b r i ~ about the s h e a r i n g inetability~ we expect to be able to observe the MSB onset at ~/~ red to RDo To overcome this discrepancy w i t h the experiment hypotheses based on: texture so£tenin6 (16, 17) /supported r e c e n t l y b y theoretical calculation (2~)/, the theory of bifurcation (25,26) , dynamical instability (27-29), layered structure (~K)) or orystallo6Tephioal initiation ( 2 1 , ~ 1 , ~ ) have been admitted but still some questions r e m a i n open /e.g° the principal question o o n c e r n i n ~ their origin/o For an isotropic body, which yields aooordin~ to a Huber-voMises-Henok-y yield function, this experimentally measured value, ~5x~/|80 red, corresponds to the onset of a local n e c k under compression in a plane-stress state, suggestin~ this state to be an ultimate one u n d e r cold rollln~ conditions. W h e n the anisotrol~y is introduced by its coefficient of a~Lsotropy /r-value/ we a r r i v e at the conclusion that it produces the ehiftin~ in the @ values which fall in the range of e~perimental error ( 2 ~ ) . T h e n , a ~ m ~ t t ~ n ~ t h e f o r m a t i o n o f SBs a t ~ 5 x ~ / | 8 0 r e d t o RD u n d e r p l a n e - s t r e s s state conditions, we o ~ p o s t u l a t e the only one p~rameter, i.e. the level of sold work.t~ that governs the a p p e a r a n c e of SBs. Reduced V a l u e The fixes1 statement
where
~k ~5B
o~f Shear Stress Active
in S.~B
of the last pex~a6Taph o~n be expressed
mathematically:
i s the reduced value of shear stress active in the SB, is the shearing stress at the tempez~ture T, is the shear modulus /nearly linear on T except in the temperature range (32)/,
is
the temperat~e
low
of £usion.
The r a t i o o f t e m p e r a t u r e s T/~ relates t h e m e a m a r e d v a l u e s t o t h e seine l e v e l of thermal energy determJ~aed by the ~ value, where k is Boltz'm'm's oonstsmt. Tak~a6 into account 0 = 3 5 x Y ~ 1 8 0 r i d we o b t a i n
where ~ is the compression i n (1) we h l y e
In
the
ease
o f CuA18 ~
is
stress
active
w h e n HSBe a p p e a r .
e q w a l t o 8 5 0 MPa ( 1 9 ) a n d i t
~ e r t ~
(2)
was e p p r o x i m t t e l 7
Vol.
25, No. 7
SHEAR BANDS
1515
o o n s t a n t d u r i n 8 SBs f o x ~ m t i o n /Fi~.l/; s i ~ L l a r behavlour w a s o b s e r v e d i n t h e e a s e o f A l ~ 2 w i t h ~ = - 3 4 0 NPa (3-3). F o l l o w i n g (3) t h e o a l o u l a t e d reduced 4 shear stress value T ~ f o r the alloys C u~18 and AIMg2 was equal to 17.Sx10/Table 1/. In Table I we l~esent also ~ f o r some metals ( ~ ) , a s s u m i n ~ that the SBs are formed at the level R of ultimate tensile strength, related
to~
by
and supposin~
the shear
modulus
~A i s
equal
to
E
P = where
2 (',+ ~')'
(5)
• is the u~J~'orm e l o n g a t i o n E is the elastio modulus and is Poisson's coefflolent. TA~ Shearin~
1
Chemaoteristio ,
|
R£
Metal
• =29 K
of Rolled Metals
s
rzJ l'opa] [ Pa] ,
,
[."Pal
,
,,
,,,
1100 Ou ETP Ag
0.33 0.33 0..37
93.3 1356 1234
69 117 76
26 4tt 28
90-166
.35- 5
310-.3q5 126
Au
O.t~2
1336
79
28
Ni
0.3 0.3.3
1726 1309
207 1 17
76
CuA18 A.1.1~2
0.3.3
916
69
A1
,
[10-".]
I'"Pa.]
,
6..3-9.o
12-20 48-54
121-174 3/~7-/414 186-19t4
221
/4
2.~
7.4
379-552 -
50-35
561-745
4/4.
-
850
5.2-6.8 17 • 8
232-.303 347
26
-
-
3/40
17.2
1.39
7.2-8.6 6.6-6.8
5 3 - 71 142-169 7 6 - 79 9/'1'
Pure metals, in spite of lar~g diffe~enoes i n SFE v a l u e s (3)j 6ire the reduoed shear s~ress value ~.=7x10on the avemge and with dispe~sion between 5.2x10 -q a n d 9 . ~ x 1 0 - ~ / T a b l e 1 / . As we h a v e J u s t s e e n t h e ~. v a l u e @ of alloys are ~eater / T K = - 1 7 . S x 1 0 " q / i n c o m p a r i s o n t o p u r e m e t a l s /~K=--TX10--4/ w h i o h may b e d u e t o t h e i n o e r t i t u d e of E and ~ values reported a n d may a s well be due to additional strengthenin~ e£fects pcoduoed by the alloying itself. I n o o n c l u s i o n we s u p p o s e t h a t t h e s h e a r i n 6 e £ f s o t i n t h e f o m o f S B s , observed under rollin~ conditions, is independent o f t h e de£ox~aed m e t a l a n d in this ease only the extex~al oonditions are responsible for their eppeamnoe. 0 n e e t h e ~K i s k n o w n o n e o a n o a l o u l a t e ~oD admittin~ the elastio properties of material are known, and =
(6)
This enables us to prediot t h e moment o f SB f o r m a t i o n ~ n ~ t h u s t h e r a n s ~ the heterogeneous mode o f d e £ o z , a a t i o n , w h i o h i s i m p o r t a n t i n i n d u s t r i a l praotioo. To h a v e t h e p r o p e r d a t a a p r e o i s e m e a s u r e m e n t o f s h e a r s t r e s s
of
1516
SHEAR BANDS
Vol. 25, No. 7
actin6 in the shear band plane at the onset of SB is necessary and this is expected to be dons in the next step. Cone lusions Newly formed MSBs are: /i/ inclined at a constant angle ~ equal to 3 5 x ~ 1 8 0 rod to the RD inoludin~ the anisotropy effect induced by crystallographic texture, /ii/ produced under rolling at approximately constant compression stress aotin~ in the plane-stress state. F o l l o w i n ~ / i / and /li/ it is demonstrated that the reduced shear stress value ~ necessary for the onset of SB, when related to elastic constant of material and thermal energy level, is independent of the material tested; then during cold rollln~ only the external constraints seem to be ~esponsible for the SB formation. The reduced ~k value is equal to (7+I .8)xi0 -q in the case of pure metals /AI, Cu, Ni, £~, Au/, whe~e the calculated one for alloys /CuAI8 and AIMg2/ is equal to 17.5x10 -~ which may be explained by the incertitude of elastic constants as well ae some strengthen1_n~.~ induced by the alloying addition itself. Ref ereno e s
1. F.Adcook, J . I n s t . M e t a l s , 27, 73 (1922) Viewpoint Set No. 6, Soripta Metall., 18, ~21 (198~) P.C.J.Gallagher, Met. Trans., I, 2429 (1970) , M.Cook, T.Li Riohar~s, Met. Sci., 78, 463 (1951) B.Farsette, O.Whitham, M&m. Soi. Roy. M&t., 73, 179 (1976~ B.J.Du~san, M.HatherIy, W.B.Hutohinson, P.T.Wekefield, Met. Sol., 12, ~43 (1978) 7. A . S . M e l i n , M . H a t h e r l y , Met. S o l o , 1~, 463 (1979) . 8. P.T.¥ake£ield, M.Hatherly, Met. Sol., 15, 109 (1981) 9. M.HatherI7, ICSM& 6, Melbourne 1982, V. 3, P. 1181 10. P.S.Mathtur, W.A.Baokofen, Met. Trans., 4, ~63 (1973) 11. K.Morii, M.Mera, Y.Nakayana, Trans. J. I. M., 18, 7 (1977) 12. T.Noda, B.Plege, J.Grewen, ICOTOM 5, Aachen BRG 1978, V. I, p. ~43 13. M.Hatherly, A.S.Malin, Met. Teohn., 6, ~08 (1979) 1~° J . G . S e v i l l a n o , P. Van H o u t t e , E . A e r n o u d t , S e r i p t a M e t a l l . , 11, 581 (1977) 15. M.Bllcharski, S.Gorcwyca, Met. Sci., 12, ~0~ (1978) 16. I.L.Dillamore, J.G.Roberts, A.C.Bush, Met. Sol., 13, 7 3 (1979) 17. P. Van Houtte, J.G.Sevillano, E.Aernoudt, Z. Mkde, 70, ~26, 503 (1979) 18. J.Kulnier ~., Sci. Bull. £MM, Metallurgy and Foundry Pz~aotioe, No. 1269 /123/, 63 (1989) 19. J . K u ~ n i e r z , A r c h i v e s o f M e t a l l u r g y , 35, 269 (1990) 20. J.Ku~nierffi, M.Gasperini, A.Mokhtari, M.Pernot, RoPenelle, ICOTOM 7, Noordwi~kerhout, Holland 1984, p. 509 21. J.Kulniex-z, £~chives of Metallur~y, 3~, 179 (1988) 22. W.Y.Yeun~, B.J.~_~an, Acta Met., 35, 541 (1987) 23. J.Ku~nierz, Bull. Aoad. Sole. Polon., S&r. Sole. Teohn., in press 24. T . O s t ~ k , G.J.Davies, Aota Met., 35, 2307 (1987) 25. R.HilI, J.¥.Hutchinson, J. Mech. Phys. Solids, 23, 239 (1975) 26. R.J.Asaro, Aota Met., 27, ~ 5 (1979) 27. E.Nes, W.B.Hutohlnson, A.A.Rldha, ICSM~ 7, Oxford 1985 /Ed. Me ~usen/, Pergamon Press, p. 57 28. A.Ko~bel, J.D.~-bux-y, M.Hatherly, P.L.Ma~tini, E.W.E~blosh, Aota Met., 1~, 1999 (1986) 29. K . M o r i i , H . T e r s ~ a , Y.Nakay~ma, T r a n s . J° X. M., 27, 769 (1986) 30. K . M o r i i , H.Mecb~-~, Y.Nakayama, Acta M e t . , 33, 379 (1985) 31. Z . J a s i e ~ s k / , XCSMA 7, Oxford 1985 / E d . Mc Queen/, Pergamon P r e s s , p. 583 32. H.Meokin~, B . N i o k l a s , N.Zarubowa, Aota M e t . , 3~, 527 (1986) 3~- Z.Jasie~ski, J.Kudnlerz, R.Penelle~ Internat. Coll. CNRS, Aussois, France 1-I0.0~. 1987 3~. Metal Fuandbook, V. 1, Properties and Selection o[ Metals, ~SM, Ohio 1961 2. 3. 5~. . 6.
Vol.
25, No.
7
SHEAR BANDS
1
1
1517
1
1
I
[MPo]
1000
-/,
O
in
(0
•
' BA8r
tension
O
BABz
....
13
8r
compression
gl
r7
---
10
r8
-,,-
g
rlO
-,,-
O
z4
-.-
500
I
Z6
I
1
- ',-
I
I
2
C=-In(1-z)
FIG. 1.
Strees-stz~in
ourve
o f Cu~18 b r o r ~ e
(18,19)
1518
FIG.2.
SHEAR BANDS
Vol.
25, No.
S t r a i n ma~k£n~s on l o n ~ i t u d ~ l oross-seotion d ~ ~o11~ o f 0u~18 /~D 4 - A i o a t e s m a g n i f i c a t i o n m a r k / : a / Wavy s ~ a o s o f CuAI8 r o l l e d t o ~ = 0 . 2 b / O n s e t o f MSB a t ~ 5 x ~ 1 8 0 m d t o RD i n s a m p l e s t r a i n e d t o 6 = 0 . 7 o / MiSB 4 . s a m p l e . t r a 4 - e d /;o ~=1.8 d / ~SB o a ~ i n ~ r o t a t i o n o f b l o o k ~ ~ = 2 . 2
7