Conditions for periodic serrations in tensile curves

Scripta METALLURGICA

Vol. 18, pp. 505-508, 1984 Printed in the U.S.A.

Pergamon Press Ltd. All rights reserved

CONDITIONS FOR PERIODIC SERRATIONS IN TENSILE CURVES

M.Teresa Nogueira* and M.A.Fortes** *Departamento de FTsica e Ciencia dos Materiais Universidade Nova de Lisboa, Quinta da Torre 2825 Monte da Caparica, Portugal **Departamento de Metalurgia, I n s t i t u t o Superior T~cnico Av. Rovisco Pais, lOg6 Lisboa Codex, Portugal (Received December 12, 1983) Tensile curves with periodic serrations separated by smooth curve segments (Portevin-LeChatelier e f f e c t , type A) are caused by LUders bands that nucleate at one specimen grip and propagate smoothly in succession, one at a time, to the other grip l l - 3 J - Periodic serrations appear only a f t e r an i n i t i a l s t r a i n characterized by i r r e g u l a r serrations ( F i g . l , curve a) corresponding to a jerky propagation of the bands. During this stage a more or less uniform s t r a i n gradient develops in the specimen 14-6J. When the uniform s t r a i n gradient is achieved, smooth band propagation occurs, with successive bands moving in the d i r e c t i o n of increasing s t r a i n . Each band increases the s t r a i n gradient, e s s e n t i a l l y because of the accumulated s t r a i n ahead of the band (deformation behind the band in n e g l i g i b l e ) and because the band s t r a i n i t s e l f increases as the band t r a v e l s along the specimen 16 I. Since the s t r a i n is a poor phenomenological v a r i a b l e 17J i t is preferable to think that the mechanical state of the specimen is defined by one structure variable which takes into account the d i s t r i b u t i o n of d i s l o c a t i o n s , d i s l o c a t i o n sources and obstacles, including the e f f e c t of solute atoms. I t is u n l i k e l y that under dynamic s t r a i n ageing conditions leading to serrated curves, a single variable defines the mechanical state, but for a simple semi- q u a n t i t a t i v e analysis we shall consider such an approach. We choose t h i s v a r i a b l e , oi , with the character of an internal stress that increases with s t r a i n and such that the s t r a i n rate is some increasing function of o-o i , where o is the applied stress. In the i n i t i a l state the d i s t r i b u t i o n oJ: ( x ) is i r r e g u l a r (Fig.2, • curve a) and the bands move I r r e g u l a r l y ; the stress has to r i s e when the band reaches regions with high o i . As deformation proceeds, t h i s i r r e g u l a r d i s t r i b u t i o n is replaced by a smooth d i s t r i b u t i o n o i ( x ), equivalent to a smooth s t r a i n gradient (Fig.2, curve b). This is achieved by deformation, provided the i r r e g u l a r i t i e s are not too large J8 I. Once the smooth gradient of o i is i n s t a l l e d , the following bands j u s t increase i t without destroying its smoothness (Fig.2, curve c). When large heterogeneities are present i n i t i a l l y ( e . g . , f a i r l y severe notches 191) or are introduced during deformation (e.g.,bya long load suppression or load relaxation during band propagation l l O | ) the conditions for smooth propagation may not be achieved or can be destroyed and i r r e g u l a r serrations are observed u n t i l p l a s t i c i n s t a b i l i t y (necking) occurs ( F i g . l , curve f ) . I f the heterogeneity is l o c a l i z e d , i t may happen that the uniform s t r a i n gradient can be formed on each side of the heterogeneity. In t h i s case, a t r a v e l l i n g band stops at the heterogeneity and then a new band is nucleated

505 0036-9748/84 $3.00 + .00 Copyright (c) 1984 Pergamon Press Ltd.

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ahead of i t , leading to a l t e r n a t i n g type A serrations ( F i g . l , curve b). This is occasionally observed in normal, unnotched specimens I g l . probably due to a "natural" localized heterogeneity. Alternating serrations are systematically observed for specimens containing a small notch 191. The o i ( x ) curve corresponding to one extra, type A, serration is of the type shown in Fig.2, curve d. A f u r t h e r condition for the occurrence of type A serrations is related to the test temperature and strain rate. Only intermediate values of these parameters lead to periodic s e r r a t i o n s l l l , 1 2 I. A delicate balance between the kinetics of solute d i f f u s i o n and the kinetics of dislocation overcoming of obstacles is required. I f solutes diffuse too quickly (high temperatures or low strain r a t e s ) , the bands move j e r k i l y , and non-periodic serrations of type B 13[ are observed ( F i g . l , curve c). The type B serrations are morphologically d i f f e r e n t from the i r r e g u l a r serrations due to heterogeneities ( F i g . l , curves d and f ) . I f solutes diffuse too slowly (low temperatures or high s t r a i n rates) the tendency is for uniform deformation I I l l , with no load serrations ( F i g . l , c u r v e e). F i n a l l y , since serrations are associated with dynamic strain ageing, a minimum concentration of solutes is required l l 3 [ . This concentration should increase as the total density of dislocations increases; for example, i f the i n i t i a l dislocation density is increased by cold working, i t is expected that uniform deformation can take the place of deformation by LUders bands. In this note we report experiments which confirm the arguments and predictions made above. The material is a commercial aluminium alloy (main alloy elements, wt.%: Fe:O.25; Mg:O.l]; Cu:O.lO; Si:O.08; Zn:O.02). Two heat treatments were used: HTl Homogenization at 480°C for I hour, quenching in water at 20°C and ageing for times ranging from 6min to 20 days at room temperature or for l hour at temperatures up to 320°C; uniform grain size of 25~m was obtained. HT2 -:Homogenization at 540°C for 1 hour, quenching in water at 20°C and ageing f o r 6 min to 6 hours at room temperature. Abnormal grain growth was observed following this treatment with some grains reaching l-2mm while the others had diameters of about 25-30~m. Specimen wires (Lo=6.8c ~, Ao=O.lOcm2) w e r e t e n s i l e tested at temperatures ranging from 20°C to 160°C and at crosshead speeds, ~, in the i n t e r v a l 5"10 -~ to 2"lO'Zcm mn"I Following HTl and for X=5-10-3-2.10-Zcm mn-Zat room temperature, type A serrations ( F i g . l , curve a) were observed for a l l ageing temperatures and times ( c f . r e f . 1 4 ) . In a few cases a l t e r n a t i n g type A serrations were observed 191. Type B serrations ( F i g . l , curve d) were observed in tests at 90°C and 5.10-3cm mn-z. A t r a n s i t i o n between type A and type B serrations ( F i g . l , curve c) was found for testing conditions intermediate between those leading to type A and to type B ( e . g . : a t 20°C with X=5.10-~-2"lO'3cm mn'Z; at 50-80°C with X=2"lO-2cm mn-Z). F i n a l l y , when solutes move too rapidl~ to d i s l o c a t i o n s , a smooth curve was obtained ( F i g . l , curve e), e.g.:T=135uc-160°C, R=2"lO-3cm mn- ) . All these results on the e f f e c t of test temperature and strain rate on the type of t e n s i l e curves are comparable with those found for other alloys l l l , 1 2 [ . I r r e g u l a r serrations ( F i g . l , curve f ) were observed following treatment HT2 and the same testing conditions as those leading to type A serrations in HTl specimens. The serrations are very similar to those r e s u l t i n g from sharp notches or long test i n t e r r u p t i o n s . I t was previously reported that coarse-grained specimens can give rise to i r r e g u l a r serrations )15,16J, but no explanation was Qiven for the e f f e c t and i t was not clear i f i t was associated with uniform large grains or with abnormal grain growth. I r r e g u l a r serrations following a high temperature s o l u b i l i z a t i o n have also been a t t r i b u t e d [171 to a high concentration of retained vacancies. This explanation does not seem to be compatible with the persistence of i r r e g u l a r serrations following long ageing times, as observed in this work.

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Experiments were made in which a specimen that had been submited to heat treatment HTl was heated with a small torch in a narrow central region, inducing abnormal grain growth in this region. Alternating serrations ( F i g . l , curve b) were observed following this treatment, indicating that the bands stop at the affected region, but propagate smoothly on both sides of i t . In some cases, the extra serration was found to fade with increasing strain. I t seems therefore that the irregular spacing of grain boundaries, characteristic of specimens which suffered abnormal grain growth, gives rise to an irregular d i s t r i b u t i o n ~i(x) which cannot be smoothed by deformation. When abnormal grain growth is localized, deformation generates a smooth gradient on both sides of the affected zone, while a peak in ~i is produced in this zone, as in Fig.2, curve d. Fairly large macroscopic heterogeneities may then lead to irregular serrations or to alternating serrations, depending on the " i n t e n s i t y " and degree of localization of the heterogeneity. Small heterogeneities are smoothed by deformation and normal type A serrations w i l l result. A quantitative approach to the e f f e c t of heterogeneities is of course impossible without adequate constitutive equations for inhomogeneous deformation; an attempt at developing such equations was recently made by one of us I181. The effect of solute concentration in relation to dislocation density has been investigated in experiments in which specimens that had been solution treated at 480°C and had a uniform grain size (treatment HTI) were swaged at room temperature (58% diameter reduction) prior to testing under conditions that would give rise to periodic serrations in the absence of swaging. Tensile curves with no serrations were observed in all cases. In conclusion, periodic load serrations (type A) in tensile curves can only occur i f a number of conditions are met. F i r s t , a minimum value of the ratio between solute concentration and dislocation density is required to enable the formation of strong atmospheres at the dislocations waiting at obstacles. A proper combination of testing temperature and strain rate is also required for type A serrations; otherwise uniform tensile curves or type B serrations w i l l be obtained. Finally, the i n i t i a l state of the specimen has to be f a i r l y homogeneous in order that a smooth strain gradient in the specimen can be produced by deformation. A localized heterogeneity allows the formation of the smooth gradient on both sides of the heterogeneity, and type A alternating serrations w i l l result. But i f the heterogeneity remains spread in the specimen, irregular serrations, d i s t i n c t from the type B serrations, w i l l appear in the entire tensile curve. Acknowledgements The authors are indebted to Laborat6rio Nacional de Engenharia e Tecnologia Industrial and to Laborat6rio Nacional de Engenharia Civil for the provision of research f a c i l i t i e s . References: I.B Russel, Phil. Mag., 8, 615 (1963). 2.A J.Thomas, Acta Met.,-14, 1363 (1963). 3.P R.Cetlin, A.S.GUIe~ a ~ R.E.Reed-Hill, Met.Trans.,4, 513 (1973). 4.M Teresa Correia and M.A.Fortes, Scripta Met.,15, 36~ (1981). 5.R E.Reed-Hill and S.Guleg, Met.Trans.,6A, 461 -(~F975). 6.A Wijler and S.J.van Westrum, Scripta ~ t . 5 , 821 (1971). 7.E W.Hart, Acta Met.,18, 599 (1970). 8 . j D.Campbell,R.H.Coo~r and T.J.Fischhof, Dislocation Dynamics, Materials Science and Engineering Series, McGraw-Hill, New York, 1968,p.723. 9.M Teresa Correia and M.A.Fortes, Mat.Sci.Eng.,54, 95 (1982). lO.M A.Fortes and M.Teresa Nogueira, submitted fo~--publication. l l . L J.Cuddy and W.C.Leslie, Acta Met., 20, I157 (1972). 12.R A.Mulford and U.F.Kocks, Acta M e t . , ~ , I125 (197g). 13.R Onodera, T.Ishibashi, M.Koga and M.~'llimizu, Acta Met.,4, 536 (1983). 14.D M.Riley and P.G.McCormick, Acta Met., 25, 181 (1977).

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15.P.G.McCormick, Phil.Mag., 23, 949 (1971). 16.G.Thomas and N.K.Srinivasan-~, Scripta Met., 7, 205 (1973). 17.G.Thomas and N.K.Srinivasan, Scripta Met., ~, 1163 (1974). 18.M.A.Fortes, J.Mat.Sci., in press.

{o)

FIG.I Types of tensile curves found under d i f f e r e n t conditions:(a) normal type A serrations; (b) alternating type A serrations; (c) t r a n s i t i o n to type B serrations; (d) type B serrations; (e) non-serrated curve; ( f ) irregular serrations due to heterogeneities.

(b)

T

(o3 Position in speclmenlx)

FIG.2 Variation of internal variable oi along the specimen: a) irregular p r o f i l e leading to irregular serrations; (b) smooth gradient leading to type A serrations; (c) as for (b) but after the passage of a number of bands; ( d ) p r o f i l e leading to alternating serrations.