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Directional strain softening in ferritic steel
Acra merall. Vol. 35, No. 5, pp. 10291036, 1987 Printed in Great Britain. All rights reserved
OOOl-6160/87 $3.00 + 0.00 Copyright 0 1987 Pergamon Journals Ltd
DIRECTIONAL STRAIN SOFTENING FERRITIC STEEL Y. STRAUVEN? Department
of Metallurgy
and Materials
and E. AERNOUDT
Engineering,
(Received
IN
22 August
Katholieke
University
Leuven,
Belgium
1986)
Abstract-Unidirectional cold working induces directionality of structure and properties. This directionality affects yielding and flow when the material comes into another deformation mode. In particular, when the strain is reversed a transient region of strain softening occurs. This special case of directional strain softening was studied for a wiredrawn ferritic steel which was compressed along the previous drawing direction. The transient strain softening was measured and the underlying structural changes investigated. Both change of texture and dissolution of an inherited substructure can induce directional softening. At least for the considered material under the considered strain reversal conditions, the substructure softening largely prevails over the texture softening effect. R&sum-haque deformation unidirectionelle induit une anisotropie de structure et de proprietes. Cette anisotropie influence la tension d’tcoulement ainsi que la courbe d’ecrouissage du materiel quand on change la mode de deformation. En particulier, si le sens de la deformation est inverse, on apercoit un adoucissement. Cet adoucissement par deformation etait ttudie pour un til d’acier ferritique t&l& qui ttait cornprime le long de son axe. L’adoucissement mecanique etait mesurt et mis en rapport avec les changements structuraux. En principe un adoucissement mecanique peut &tre induit par des changements de texture ou par des changements de sous-structure. I1 est dimontre que pour le cas ttudit le changement de la sous-structure de dislocations est l’influence clairement prtpondtrante determinant l’adoucissement. Zusammenfassung-Jede Kaltumformung erzeugt eine Struktur- und Eigenschaftsanisotropie. Durch diese Anisotropie werden Fliessgrenze und Fliesskurve, bei Anderung der Verformungsweise, beeinflusst. Insbesondere, wenn der Sinn der Verformung umgekehrt wird, findet Verformungsentfestigung statt. Diese besondere Art von Richtungsabhangige Entfestigung wurde studiert beim Stauchen eines vorgezogenen Drahtes aus Ferritischem Stahl. Die Entfestigung wurde gemessen und mit der dabei ablaufenden Strukturanderung korreliert. Wo im Princip sowohl Texturlnderungen als der Zusammenbruch der iibergeerbten Substruktur die Entfestigung erzeugen kann, wird gezeigt wie in dem betrachteten Fall die Versetzungs-Strukturlnderung die weitaus wichtigste Einflussgriisse ist.
INTRODUCTION The dislocation substructure, the residual stress pattern and the orientation distribution are the main characteristics of the cold worked state of metallic materials. They are directional characteristics with a symmetry reflecting the symmetry of the applied deformation mode. When reversing the applied stress tensor, relaxation of the residual macrostress pattern and Bauschinger effects influence subsequent yielding behaviour: the small-offset yield stresses are lowered and a steep strain hardening characterises the first percents of subsequent strain [l]. When the change in stress or strain mode is less drastic-only some components of the stress tensor change sign--cross effects due to new slip system interactions may lead to an increase in the subsequent yield stress [2,3]. Thus macrostress relaxation, Bauschinger and cross effects are typical for the small subsequent strain region. At larger subsequent strains directional strain softening can be observed which was defined
by Lowe and Miller [4] as, “a decrease in the flow stress or even just an inversion of the curvature of the stress-strain curve following a change in straining direction”. This softening behaviour has been observed in iron [5,6], medium and high carbon steels [7], copper [8,9] and aluminium [lo, 111 after various changes in the direction of straining. The amount of softening increases with the amount of primary strain [5,7,8]. It is larger for a strain reversal than for other changes in strain mode, such as wire drawing followed by torsion [12]. The present paper describes the directional strain softening that occurs when compressing severely predrawn low-carbon steel wire along the previous drawing direction. It is concentrated on the geometrical and physical processes determining the course of the subsequent flow curve.
MATERIALS
AND EXPERIMENTAL
A hot rolled wire rod of the following tPresent address: Belgium.
Metallurgie
Hoboken-Overpelt,
C 0.07
Overpelt-
1029
Mn 0.32
Si 0.03
Al 0.06
P 0.006
PROCEDURE
composition: S 0.021
wt%
STRAUVEN and AERNOUDT:
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DIRECTIONAL STRAIN SOFTENING
was used as material for investigation. The rod was drawn on a laboratory drawing bench from a starting diameter of 10.52 mm down to a diameter of 2.50mm. This corresponds to a true strain of ct = 3.32. The average drawing speed was 0.5 m/s. The drawing dies had an aperture angle of 2cr = 8”. Further, an industrially proven stearate lubricant film was used and the reduction per pass r was limited to 27% in the first and 17% in subsequent passes. Under those last conditions, the A-factor, as defined by Backofen [25] A=:[1
+-I2
(1)
had a value of about 1.5, meaning that the redundant deformation was negligeably small. The material was allowed to cool down after each pass so that accumulation of deformation heat was avoided. For all these reasons, the envelope of tensile stressstrain curves recorded at different intermediate stages in the drawing process can be considered to represent the room temperature large strain tensile flow curve at the applied (initial) strain rate of i, = 2.1. 10e4 s-i. At regular intervals of wire drawing prestrain, compression tests were performed on specimens with a height-to-diameter-ratio of 1.8 and at nearly the same initial strain rate as that used for the tensile strain mode, namely i, = 27. 10m4 s-‘. A molycote lubricant film was used and the recorded compression curves were corrected for the elastic deflections of the main- and the subpress-frame used on the 250-kN Instron testing machine. In this way, the calculated flow curves can be considered to represent isothermal compressive true stress-true strain curves. More details about the drawing and subsequent tensile and compressive testing are given in [7] and P31. STRAIN HARDENING, STRAIN SOFTENING AND UNDERLYING
SUBSTRUCTURES
Unidirectional straining
The tensile axisymmetric strain mode of iron and low-carbon steels is characterised by a parabolic hardening up to an intermediate strain of about ct = 0.5, followed by a continuous linear hardening
1000.
until exhaustion of wire drawing ductility [14]. The tensile flow-curve of the material of investigation given in Fig. 1 and determined until a wire drawing prestrain of et = 3.32 confirms this behaviour. As long as the low-carbon steel is essentially (e.g. more than 8Ovol.%) single-phase, the slope of the linear part of the flow curve is unaffected by the nature or concentration of carbon or other alloying elements [15, 161. In Fig. 1 this slope amounts to 150 N/mm2 per unit strain which is almost exactly the value found by other authors for Fe-O.O03%C [14] and for Titanium-gettered interstitial-free iron [ 151. It should be remembered however that an increased solute content increases the yield stress and the first parabolic part of the flow curve and by doing so, shifts the whole flow curve upwards. The development of substructure in wire drawn steel has been extensively studied by Langford [ 171on Fe-O.O07%C and by Zou Hua Minh [18] on the present material. They showed how an almost equiaxed thick-walled cell structure is developing in the grains from the initial stages of drawing until true strains of 20-50%; in that stage, the cell dimensions decrease faster than the wire diameter which proves a preponderance of cell wall multiplication. In the material under investigation, at strains beyond 6, = 0.3, the thick walled cell structure is gradually replaced by an elongated subgrain structure with two-dimensional walls parallel to the wire axis. From that strain on concommittant processes of cell and subgrain wall multiplication and annihilation result in a further decrease of the mean transverse linear intercept size of the substructure but at a mean rate smaller than the rate of decrease of the wire diameter. At strains beyond ct = 0.7, a majority of sheet- and needle-like subgrains characterise the substructure. Those still become thinner with further drawing but at a continuously decreasing rate compared to that of the wire diameter. At irregular intervals the long subgrains are crossed by single dislocations or by cell or subgrain walls. It is especially in a transverse section of the severely drawn wire that both sheet- and needle-like subgrains can be distinguished. The sheet-shaped subgrains are known to reflect the local plane strain deformation mode imposed by the (1 lO)-fibre texture. On a
_---___-----_______-----___----
______-----.
___----
2
____---500
-0-e
b
,/*-
t’ 0
0.5
1.0
2.0
1.5
2.5
3.0
3.5
c
Fig. 1. Tensile flow curve of the investigated low-carbon steel, obtained as an envelope of tensile stress-strain curves after successive drawing passes. Test conditions are described in the text.
DIRECTIONAL
P ;j
1031
STRAIN SOFTENING
(-7,)
I
600
I
5
I I
b 400
’ I I ,
200
Fig. 2. Substructure of the drawn wire. True strain t, = 2.59. Longitudinal section showing an elongated subgrain structure.
LM
, enl 0.25
0
0.75
0 50 c
1.00
Fig. 5. Compressive flow curve after a drawing prestrain of c,= 2.59. At point A (q,,, cM) the reverse strain curve reaches a course parallel to the forward curve. Point B (e,, em) marks the end of the strain softening region.
oft, = 2.59, Fig. 5, we see a dramatic drop in yield stress, compared to the forward flow stress, followed by a steep strain hardening; the curve soon levels off on further straining and reaches a course nearly parallel-but below-the forward curve at point A (a,, cM). For prestrains larger than 6, E 0.30, the curve reaches a maximum followed by a strain softening until a minimum flow stress is reached at B (Q,,,,cm). At still larger strains a new strain hardening phase is started. However, the flow curve after large compressive strains cannot be trusted because friction effects are too large to be properly accounted. Nevertheless the results indicate that the new hardening part of the true stress-true strain curves can approximately be brought to coincidence with the forward flow curve by a displacement over a strain distance Ae,. Reversing the strain mode hence wipes out a great part of the hardening built up during forward straining before a new but similar hardening history “on a partially cleaned slate” is started. Table 1 summarises the influence of the prestrain level on the different marking points of the subsequent compressive flow curve. These results are similar to those found by other authors when compressing predrawn copper wire [9] or when changing the sense of twisting after a large torsional prestrain [8]: strain softening extends over prestrain
Fig. 3. Substructure in a transverse section of the same drawn wire revealing needle- and sheet-like subgrains. A
small degree of curling character& subgrains.
the region of sheet-
larger scale, families of those subgrain sheets are bent in order to match the macroscopically required axisymmetric deformation [ 193. The structure as described above, though further decreasing in size, remains qualitatively unchanged at least until a drawing strain of c, = 2.59, the starting state for the compression tests discussed below. Figures 2 and 3 show this substructure in a longitudinal and in a transverse section respectively. Reverse straining
The compressive flow curves recorded at different predrawing levels are shown in Fig. 4. Looking in more detail to such a curve e.g. after the largest
1000
_______------
NE $
,,,y-e
500.
_--.
____.___-------__._ ____~y__
I’ 1
0
0.5
1.0
1.5
2.0
2.5
3.0
I 3.5
c
Fig. 4. Compressive flow curves, recorded after predrawing strains of 6, = 0.17, 0.37, 0.71, 1.20, 1.71 and 2.59 respectively. Test conditions are described in the test.
STRAUVEN and AERNOUDT:
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DIRECTIONAL STRAIN SOFTENING
Table 1. Influence of drawing prestrain on some characteristic features of the subseauent comuression flow curve 61
a,
0.17 0.37 0.71 1.20 1.71 2.59
407 460 528 613 691 731
CM
om
0.03 0.05 0.06 0.08 0.09 0.06
484 546 617 663 762
6,
0.12 0.24 0.31 0.32 0.42
a,
(6, - a,)o,. 100
423 495 571 653 734 863
2 4 6 IO 12
IJ,,, and cM represent stress and strain at which the subsequent flow curse reaches a course parallel to the forward curve; CT,,, and L, are the coordinates of the minimum in the Row curve marking the end of the strain softening region; 6, is the forward flow stress before compression and (u,~m)/u,.lOO represents the relative amount of softening obtained in the subsequent compression test.
a larger subsequent strain interval and the amount of increases with increasing prestrain. Substructural observations throw some light on the underlying events. The evolution of that substructure was followed for material belonging to the midlongitudinal and transverse sections of the subsequently compressed wires. By a pure geometrical reasoning one expects the elongated subgrains to be transformed by the compression first into equiaxed and at still larger strains into pancake-like shapes. The observations show that there is a transition first towards equiaxed and then towards a pancakestructure indeed. However the mode of transition is not the geometrical one as represented in Fig. 6(a). softening
This is proven by the electron micrographs of Fig. 7(a) and (b) showing the substructure of the material in longitudinal sections, at compressive strains of t, = 0.20 and 0.40, respectively. The substructural changes are best described as a succession of local collapses of the elongated subgrains into equiaxed cells. Such collapsed regions are indicated by arrows in Fig. 7(a), after a compressive strain of tc = 0.20. The transverse dimensions of the remaining fibered structure only change slowly, but the number of transverse walls clearly increases. Reverse straining hence seems to gradually wipe out the aligned subgrain walls and to braid new non oriented walls, as schematically illustrated in Fig. 6(b). At a reverse strain of d = 0.40 the structure is completely equiaxed with predominantly subgrain walls as can be deduced from the fringe patterns in tilted specimens,
(0)
(b)
Fig. 7. Substructure of a wire drawn to 6, = 2.59 after a subsequent compressive strain of (a) eC= 0.20, (b) cc = 0.40. The arrows in Fig. 7(a) indicate “collapsed” regions where an equiaxed structure has replaced the original elongated subgrain structure.
E.=
t
LOCALLY “COLLAPSEO” ZONE
rug. 6. Schematic representation of substructure evolution during compression. (a) Purely geometrical (b) Real behaviour as observed in TEM-micrographs such as those of Fig. 7.
Fig. 8. Fringe patterns indicating the subgrain character of the walls after a compressive strain of cc = 0.40 (6, = 2.59).
STRAUVEN and AERNOUDT:
DIRECTIONAL
STRAIN SOFTENING
1033
After a compression strain of t, = 0.40, the mean subgrain size in the equiaxed structure amounts to d = 0.31 pm.
Fig. 9. The completely equiaxed substructure obtained after a compressive strain of cc = 0.80 (c, = 2.59)
t %l
t=o
I
20
h-i L,=
0.4
1
10
0
i
0.2
0.4
0.6
0.8
1.0
Q
(pm1 I
Fig. 10. Distribution of subgrain sizes after a drawing strain of et = 2.59 (a) and after a subsequent compression of t, = 0.40 (b). see Fig. 8. In a transverse section some walls seem to be thicker than the subgrain walls in the wire drawn specimen but further observations, discussed below, showed that this is because the walls are no longer perpendicular to the foil surface and contain a more complex dislocation configuration. Beyond a compressive strain of c, = 0.40 the structure is gradually transformed into a pancake structure with subgrain walls parallel to the compression platens. At a reverse strain oft, = 0.80, this newly oriented substructure is clearly developed as shown by Fig. 9 in a transverse section of the compressed specimen. Quantitative observations
Figure 10 represents the distribution of (mean linear intercept) subgrain sizes in transverse sections of the drawn wire and of the subsequently compressed specimen respectively. The distribution in the drawn material is characterised by a mean transverse subgrain size of d=O.l8pm. tThe misorientation measurement technique is described in [71.
The last size is distinctly larger than the sizes predicted for a homologous axisymmetric (d = 0.23 pm) or (1 IO)-texture induced plane strain deformation (d < 0.27 pm) respectively. Thus during compression of the predrawn material, the substructural size changes at a faster rate than the macroscopic dimensions. This is contrary to what happens during forward straining when the decrease of substructural dimensions goes slower than the decrease of the wire diameter. But it is not in contradiction with it. Indeed, in both cases a general feature of large strain deformation substructures in metals is reflected: dynamic recovery always tries to rearrange the dislocations in configurations with a minimum surface-to-volume ratio of the subgrains: the substructure tends to equiaxiality. Thus during drawing dynamic recovery retards the geometrically induced shape change of cells and subgrains, during subsequent compression it accelerates it. At the same compressive strain of c, = 0.40, the reverse flow stress of Fig. 5 has reached a minimum of 762 N/mm2, about 100 N/mm2 below the forward flow stress, which means a relative softening of 12%. In order to understand this softening, a closer look at the substructure was desirable. Crystallographic as well as morphological aspects were investigated. The drawn wire has a sharp (llO)-fibre texture as shown in Fig. 11. This texture explains why the majority of subgrains in the transverse section showed up a (110) diffraction pattern. Though deviations from the (110) orientation certainly exist, even in heavily drawn wire- as was also demonstrated by Langford [17]--this so-called 6 -component of the misorientation (= deviation from (110)) is small compared to the @-component which gives the angular misorientation of neighbouring subgrains around the common (llO)-axis. The subgrain walls in the drawn material hence are tilt walls. The 8-misorientations were found to be cumulative when traversing several subsequent subgrains. The mean misorientation for a number of 60 subgrains was 4.6O.t After 40% compression, three transmitting zones were investigated. In one of them (situation A) 10 of the 12 subgrains still showed up a (110) pattern, the 2 others a (111) pattern. The second transmitting zone (situation B) contained mainly (012), but also (OOl), (115>, (013) and (135) diffraction patterns. The third one (situation C) contained more than 30 subgrains
with a (111)
zone axis.
In those compression substructures the B-component of the misorientation was determined as the angle between crystal directions with the same indices in two neighbouring subgrains and both being perpendicular to the wire axis e.g. between the (100)
1034
STRAUVEN and AERNOUDT:
DIRECTIONAL
STRAIN SOFTENING
Fig. 11. (llO)-pole figure of the transverse section of the drawn wire. (110) fibre texture.
directions in the subgrains with (001) and (012) orientation respectively. The mean o-value found was 4.1, 5.1 and 6.0” for the three transmitting zones respectively, not much different from the mean e-value found in the predrawn wire. However the existence of important 6 -misorientations makes any statement about changes in mean misorientation values rather prohibitive. All what can be said is that the dislocation configuration in the walls will be no more a pure tilt but a more complex configuration and that the neat fibre texture of the drawn wire is destroyed. DISCUSSION
The orientation changes measured lead us to look first if the change in the orientation distribution might be the reason for the work softening. This was checked by calculating the evolution of the mean Taylor-factor along the strain path followed using the existing software for deformation texture predictions [20]. After a drawing strain oft, = 2 the M-factor has reached a saturation value of M = 3.040 under triaxially constrained deformation conditions. With relaxed constraints-allowing the experimentally observed curling to occur the M-factor reaches a value of M = 2.150. Assuming that the nature of the constraint does not change during the subsequent 40% compressive strain, the M-factor decreases by 1.5% for the full constrained case (Fig. 12 path 1) and increases by 0.5% for a compression with relaxed constraints (Fig. 12 path 2) [21]. The influence of texture on flow stress is thus negligible in both cases. However it could be argued that the (1 IO)-textured material, deforming by plane strain and curling during wire drawing, goes into an axisymmetric strain
mode during subsequent compression: this would involve an abrupt increase of the M-factor from 2.150 to 3.040 followed by a small decrease to about 3.000 after 40% compressive strain as shown in Fig. 12 path 3. The material hence should show a texture induced strengthening of 40%. The argument of minimum internal work, used by Hosford [19] to explain the plane strain deformation mode in drawing, also predicts that local plain strain in drawing is preferentially followed by local plane strain in compression at least in the transition stage from the (1 lO)-drawing texture to the combined (100) and (111) compression texture, a stage which covers at least 40% compressive strain. Figure 13(a) and (b) show how the transition to (100) occurs by
I
2.1601 1
2.150
@
I 2
I,
I
.
:
:
1
0
0.1
0.2
0.3
0.4
:
:
:
0.5
0.6
0.7
OB-
lc Fig. 12. Calculated evolution of the mean M-factor during compression after a drawing strain of et = 2 [21]. (1) Under fully constrained conditions, (2) with relaxed constraints (curling allowed), (3) assuming relaxed constraints in drawing followed by full constraints in compression.
STRAUVEN and AERNOUDT:
DIRECTIONAL
1035
STRAIN SOFTENING
Texture changes will thus not soften the material. They will rather harden it when the compressive strains are large and a great number of grains has taken the strong highly symmetrical (11 l)-orientation. It can be concluded that the change in substructure size and morphology and in subgrain wall configuration represent the major contributions to softening. In a first attempt to relate the measured amount of strain softening to the change of the substructural dimensions we estimate the relative flow stress difference from the change in dislocation density, using the relation 0 = CJ,,+ czGb&
(2)
Thus
if the friction stress u,, is neglected. If we assume that the dislocation density per unit subboundary surface is the same in the two considered substructures, an assumption supported by the similar misorientation across their walls, the volumetric density of dislocations is directly proportional to the subgrain surface to volume ratio S/V. Relations from quantitative metallography [22] allow to calculate that ratio for different cell morphologies: for the drawn elongated substructure: S/V = n/2d and for the subsequently structure:
compressed equiaxed sub-
S/V = 2/d.
Fig. 13. Orientation paths followed by originally (llO)oriented subgrains during subsequent compressive deformation, (a) for a grain rotating towards (IOO), (b) for a grain rotating towards (111). In both eases plane strain deformation occurs with the [I IO] direction as direction zero strain.
the activity
of the two systems (lOl)(llT) and (1OT) (111) and the transition towards (111) by the joint and equal activity of the systems (lOl)(llT) and (011) (1 IT), assuming slip to occur only on { 110) planes; in both cases plane strain deformation
prevails on the microscopic scale and the macroscopically required axisymmetric deformation has to be fulfilled by some kind of curling-or uncurling of the previous structure. The three transmitting zones discussed in the previous paragraph represent the three situations indicated in the same Fig. 13 by A, B and C. Once a material volume approaches (001) or (111) orientations like some of the subgrains of B and C did, a gradual transition towards axisymmetric compressive flow can be expected.
Substituting find:
the two measured
Aa -_= c7
K7-*__120/ J8T
subgrain
sizes, we
O
which corresponds to the experimentally measured amount of relative softening. There is also plenty of experimental evidence [23] that, at least for materials which are strained along linear strain paths, the flow stress 0 is related to the substructural size d by a relation Q =q+kd-’
(41
where d represents the average “minimum” substructural size, given as the mean linear intercept size in the appropriate direction. This is the transverse direction in the case of drawn wire. We assume that the strength k of the walls is the same in the two conditions. This assumption is reasonable because at cc = 0.40 the original substructure is completely replaced by a new subgrain
1036
STRAUVEN and AERNOUDT:
DIRECTIONAL STRAIN SOFTENING
structure which at first sight should behave like any other large strain substructure.? When the d-values mentioned above are substituted in equation (4) and taking for k the value of 140 MPa found by Zou Hua Minh [18] (on the same material), the calculated softening amounts to Aa = 326 MPa and the relative softening to 38%, substantially larger than the observed values. In other words, the flow stress of the drawn and subsequently compressed material is much higher than the flow stress of the drawn material at equal subgrain size. The same holds when the wire is fatigue cycled after cold drawing [24]: also there an elongated substructure is gradually transformed into a more equiaxed subgrain structure which is stronger than the drawn structure at equal subgrain size. Zou Hua Minh et al. [24] explained this finding in Hall-Petch terms saying that the “strength” of the subgrain walls is probably larger in the fatigued condition than in the drawn condition, which could be explained by the somewhat larger misorientations-or better: a more complex dislocation configuration in the walls-in the first case. However to the authors opinion, a physically more acceptable argument is that the mean slip distance should be substituted in the equation (4), as was suggested by other authors [I 7,231, instead of the smallest intercept subgrain size. In that case we find for the drawn structure (with (110) texture). d, 6 d/cos 54” = 0.3 1 pm
where the “less than” sign represents the fact that d in the transverse section was measured in random directions and not in the projected slip direction which represents the smallest subgrain dimension. For the equiaxed compressed structure ds = d = 0.31 pm.
It follows that the mean slip distance in the compressed material equals the upper bound of the mean slip distance for the drawn material. According to equation (3) the 12% softening could be accounted for if ds = 0.27 pm which is a realistic value. We conclude that at least in the considered case both the c-& and the o-d-’ relationships can account for the observed differences in flow stress linked to substructures obtained along different strain paths. SUMMARY When compressing a heavily drawn low carbon steel wire along the previous drawing direction, strain softening occurs. This softening region extends over a strain range of lO-50%, depending on the amount of prestrain. On the substructural level the softening tThe same assumption can not be made in the “collapse” region of the compressional flow curve.
is characterised by a succession of local collapses of the elongated subgrain structure of the drawn wire into an equiaxed one. There is a concommitant change of the orientation distribution from a sharp (110) texture towards the ideal orientations of the b.c.c. compression texture. The effect of the change of texture on the course of the subsequent flow curve is negligibly small, at least up to the end of the softening region. Hence it can be concluded that the strain softening finds its explanation solely in the rearrangements in the subgrain structure. The maximum relative softening-at the end of the collapse strain-can be accounted for by the established relationships between flow stress and dislocation density or subgrain size. Acknowledgements-The present work was financially supported by the Belgian Instituut voor Wetenschappelijk Onderzoek in Nijverheid en Landbouw and by Nedschroef (Helmond-Holland). Also the support of Bekaert Steel Wire Corporation (Zwevegem-Belgium) which delivered the wire rod material is gratefully acknowledged. The authors thank Dr P. Van Houtte for the M-factor calculations and ir. W. De Bleser for the flow curve data obtained in his engineering thesis. REFERENCES 1. 0. B. Pederson, L. M. Brown and W. M. Stobbs, Acta metall. 29, 1843 (1981). 2. S. S. Hecker, M&all. Trans. 4, 985 (1973). 3. J. H. Schmitt. E. Aemoudt. B. Baudelet. Mater. Sci. Engng 75, 13 (1985). 4. T. C. Lowe and A. K. Miller, J. Engng. Mater. Tech. To be published. 5. F. W. Hecker, Arch. Eisenhiittenwer. 42, 819 (1971). 6. N. H. Polakowski, J. Iron. Steel Inst., 337 (1951). I. Y. Strauven, Ph. D. thesis, K. U. Leuven (1982). 8. H. G. Grewe and E. Kappler, Physica status solidi 6,339 (1964). 9. A. Thuvander and A. Melander, Swedish Inst. for Metals Research-Internal Reuort IM-1484 (1980). 10. T. Hasegawa and T. Yakou; Scripta metail. 96, 951 (1974). 11. R. Grimes and J. C. Wright, J. Inst. Mefals %, 182 (1968). 12. J. Gil-Sevillano, Ph.D. thesis, K. U. Leuven (1973). 13. W. De Bleser, Engng thesis, K. U. Leuven (1979). 14. G. Langford Ph.D. thesis, M.I.T. (1966). 15. H. J. Rack and M. Cohen, Mater. Sci. Engng 6, 320 (1970). 16. E. Aernoudt and J. Gil-Sevillano, J. Iron Steel Inst., p. 718 (1973). 17. G. Langford and M. Cohen, Trans. Am. Sot. Metals 62, 623 (1969). 18. Zou Hua Minh, Ph.D. thesis, K. U. Leuven (1982). 19. W. F. Hosford, Trans. Am. Inst. Min. Engrs 230,- 12 (1964). 20. P. Van Houtte, Proc. 7th Znt. Conf on Textures in Materials, Holland (edited by C. M. Brakman and P. Jonaenburaer). uu. _ __ 7-23 (1984). 21. P. Van Houtte, unpublished results. 22. C. S. Smith and L. Guttman. J. Metals 5, 81 (1953). 23. J. Gil-Sevillano, P. Van Ho&e and E. Aemoudt, in Progress in Materials Science 24, Chap. 4. Pergamon Press, Oxford (1980). 24. Zou Hua Minh, L. Delaey and A. Deruyttere, Acta metall. 33, 563 (1985). 25. W. Backofen, in Deformation Processing, Chap. 4. Addison Wesley, Reading, Mass. (1972).
OOOl-6160/87 $3.00 + 0.00 Copyright 0 1987 Pergamon Journals Ltd
DIRECTIONAL STRAIN SOFTENING FERRITIC STEEL Y. STRAUVEN? Department
of Metallurgy
and Materials
and E. AERNOUDT
Engineering,
(Received
IN
22 August
Katholieke
University
Leuven,
Belgium
1986)
Abstract-Unidirectional cold working induces directionality of structure and properties. This directionality affects yielding and flow when the material comes into another deformation mode. In particular, when the strain is reversed a transient region of strain softening occurs. This special case of directional strain softening was studied for a wiredrawn ferritic steel which was compressed along the previous drawing direction. The transient strain softening was measured and the underlying structural changes investigated. Both change of texture and dissolution of an inherited substructure can induce directional softening. At least for the considered material under the considered strain reversal conditions, the substructure softening largely prevails over the texture softening effect. R&sum-haque deformation unidirectionelle induit une anisotropie de structure et de proprietes. Cette anisotropie influence la tension d’tcoulement ainsi que la courbe d’ecrouissage du materiel quand on change la mode de deformation. En particulier, si le sens de la deformation est inverse, on apercoit un adoucissement. Cet adoucissement par deformation etait ttudie pour un til d’acier ferritique t&l& qui ttait cornprime le long de son axe. L’adoucissement mecanique etait mesurt et mis en rapport avec les changements structuraux. En principe un adoucissement mecanique peut &tre induit par des changements de texture ou par des changements de sous-structure. I1 est dimontre que pour le cas ttudit le changement de la sous-structure de dislocations est l’influence clairement prtpondtrante determinant l’adoucissement. Zusammenfassung-Jede Kaltumformung erzeugt eine Struktur- und Eigenschaftsanisotropie. Durch diese Anisotropie werden Fliessgrenze und Fliesskurve, bei Anderung der Verformungsweise, beeinflusst. Insbesondere, wenn der Sinn der Verformung umgekehrt wird, findet Verformungsentfestigung statt. Diese besondere Art von Richtungsabhangige Entfestigung wurde studiert beim Stauchen eines vorgezogenen Drahtes aus Ferritischem Stahl. Die Entfestigung wurde gemessen und mit der dabei ablaufenden Strukturanderung korreliert. Wo im Princip sowohl Texturlnderungen als der Zusammenbruch der iibergeerbten Substruktur die Entfestigung erzeugen kann, wird gezeigt wie in dem betrachteten Fall die Versetzungs-Strukturlnderung die weitaus wichtigste Einflussgriisse ist.
INTRODUCTION The dislocation substructure, the residual stress pattern and the orientation distribution are the main characteristics of the cold worked state of metallic materials. They are directional characteristics with a symmetry reflecting the symmetry of the applied deformation mode. When reversing the applied stress tensor, relaxation of the residual macrostress pattern and Bauschinger effects influence subsequent yielding behaviour: the small-offset yield stresses are lowered and a steep strain hardening characterises the first percents of subsequent strain [l]. When the change in stress or strain mode is less drastic-only some components of the stress tensor change sign--cross effects due to new slip system interactions may lead to an increase in the subsequent yield stress [2,3]. Thus macrostress relaxation, Bauschinger and cross effects are typical for the small subsequent strain region. At larger subsequent strains directional strain softening can be observed which was defined
by Lowe and Miller [4] as, “a decrease in the flow stress or even just an inversion of the curvature of the stress-strain curve following a change in straining direction”. This softening behaviour has been observed in iron [5,6], medium and high carbon steels [7], copper [8,9] and aluminium [lo, 111 after various changes in the direction of straining. The amount of softening increases with the amount of primary strain [5,7,8]. It is larger for a strain reversal than for other changes in strain mode, such as wire drawing followed by torsion [12]. The present paper describes the directional strain softening that occurs when compressing severely predrawn low-carbon steel wire along the previous drawing direction. It is concentrated on the geometrical and physical processes determining the course of the subsequent flow curve.
MATERIALS
AND EXPERIMENTAL
A hot rolled wire rod of the following tPresent address: Belgium.
Metallurgie
Hoboken-Overpelt,
C 0.07
Overpelt-
1029
Mn 0.32
Si 0.03
Al 0.06
P 0.006
PROCEDURE
composition: S 0.021
wt%
STRAUVEN and AERNOUDT:
1030
DIRECTIONAL STRAIN SOFTENING
was used as material for investigation. The rod was drawn on a laboratory drawing bench from a starting diameter of 10.52 mm down to a diameter of 2.50mm. This corresponds to a true strain of ct = 3.32. The average drawing speed was 0.5 m/s. The drawing dies had an aperture angle of 2cr = 8”. Further, an industrially proven stearate lubricant film was used and the reduction per pass r was limited to 27% in the first and 17% in subsequent passes. Under those last conditions, the A-factor, as defined by Backofen [25] A=:[1
+-I2
(1)
had a value of about 1.5, meaning that the redundant deformation was negligeably small. The material was allowed to cool down after each pass so that accumulation of deformation heat was avoided. For all these reasons, the envelope of tensile stressstrain curves recorded at different intermediate stages in the drawing process can be considered to represent the room temperature large strain tensile flow curve at the applied (initial) strain rate of i, = 2.1. 10e4 s-i. At regular intervals of wire drawing prestrain, compression tests were performed on specimens with a height-to-diameter-ratio of 1.8 and at nearly the same initial strain rate as that used for the tensile strain mode, namely i, = 27. 10m4 s-‘. A molycote lubricant film was used and the recorded compression curves were corrected for the elastic deflections of the main- and the subpress-frame used on the 250-kN Instron testing machine. In this way, the calculated flow curves can be considered to represent isothermal compressive true stress-true strain curves. More details about the drawing and subsequent tensile and compressive testing are given in [7] and P31. STRAIN HARDENING, STRAIN SOFTENING AND UNDERLYING
SUBSTRUCTURES
Unidirectional straining
The tensile axisymmetric strain mode of iron and low-carbon steels is characterised by a parabolic hardening up to an intermediate strain of about ct = 0.5, followed by a continuous linear hardening
1000.
until exhaustion of wire drawing ductility [14]. The tensile flow-curve of the material of investigation given in Fig. 1 and determined until a wire drawing prestrain of et = 3.32 confirms this behaviour. As long as the low-carbon steel is essentially (e.g. more than 8Ovol.%) single-phase, the slope of the linear part of the flow curve is unaffected by the nature or concentration of carbon or other alloying elements [15, 161. In Fig. 1 this slope amounts to 150 N/mm2 per unit strain which is almost exactly the value found by other authors for Fe-O.O03%C [14] and for Titanium-gettered interstitial-free iron [ 151. It should be remembered however that an increased solute content increases the yield stress and the first parabolic part of the flow curve and by doing so, shifts the whole flow curve upwards. The development of substructure in wire drawn steel has been extensively studied by Langford [ 171on Fe-O.O07%C and by Zou Hua Minh [18] on the present material. They showed how an almost equiaxed thick-walled cell structure is developing in the grains from the initial stages of drawing until true strains of 20-50%; in that stage, the cell dimensions decrease faster than the wire diameter which proves a preponderance of cell wall multiplication. In the material under investigation, at strains beyond 6, = 0.3, the thick walled cell structure is gradually replaced by an elongated subgrain structure with two-dimensional walls parallel to the wire axis. From that strain on concommittant processes of cell and subgrain wall multiplication and annihilation result in a further decrease of the mean transverse linear intercept size of the substructure but at a mean rate smaller than the rate of decrease of the wire diameter. At strains beyond ct = 0.7, a majority of sheet- and needle-like subgrains characterise the substructure. Those still become thinner with further drawing but at a continuously decreasing rate compared to that of the wire diameter. At irregular intervals the long subgrains are crossed by single dislocations or by cell or subgrain walls. It is especially in a transverse section of the severely drawn wire that both sheet- and needle-like subgrains can be distinguished. The sheet-shaped subgrains are known to reflect the local plane strain deformation mode imposed by the (1 lO)-fibre texture. On a
_---___-----_______-----___----
______-----.
___----
2
____---500
-0-e
b
,/*-
t’ 0
0.5
1.0
2.0
1.5
2.5
3.0
3.5
c
Fig. 1. Tensile flow curve of the investigated low-carbon steel, obtained as an envelope of tensile stress-strain curves after successive drawing passes. Test conditions are described in the text.
DIRECTIONAL
P ;j
1031
STRAIN SOFTENING
(-7,)
I
600
I
5
I I
b 400
’ I I ,
200
Fig. 2. Substructure of the drawn wire. True strain t, = 2.59. Longitudinal section showing an elongated subgrain structure.
LM
, enl 0.25
0
0.75
0 50 c
1.00
Fig. 5. Compressive flow curve after a drawing prestrain of c,= 2.59. At point A (q,,, cM) the reverse strain curve reaches a course parallel to the forward curve. Point B (e,, em) marks the end of the strain softening region.
oft, = 2.59, Fig. 5, we see a dramatic drop in yield stress, compared to the forward flow stress, followed by a steep strain hardening; the curve soon levels off on further straining and reaches a course nearly parallel-but below-the forward curve at point A (a,, cM). For prestrains larger than 6, E 0.30, the curve reaches a maximum followed by a strain softening until a minimum flow stress is reached at B (Q,,,,cm). At still larger strains a new strain hardening phase is started. However, the flow curve after large compressive strains cannot be trusted because friction effects are too large to be properly accounted. Nevertheless the results indicate that the new hardening part of the true stress-true strain curves can approximately be brought to coincidence with the forward flow curve by a displacement over a strain distance Ae,. Reversing the strain mode hence wipes out a great part of the hardening built up during forward straining before a new but similar hardening history “on a partially cleaned slate” is started. Table 1 summarises the influence of the prestrain level on the different marking points of the subsequent compressive flow curve. These results are similar to those found by other authors when compressing predrawn copper wire [9] or when changing the sense of twisting after a large torsional prestrain [8]: strain softening extends over prestrain
Fig. 3. Substructure in a transverse section of the same drawn wire revealing needle- and sheet-like subgrains. A
small degree of curling character& subgrains.
the region of sheet-
larger scale, families of those subgrain sheets are bent in order to match the macroscopically required axisymmetric deformation [ 193. The structure as described above, though further decreasing in size, remains qualitatively unchanged at least until a drawing strain of c, = 2.59, the starting state for the compression tests discussed below. Figures 2 and 3 show this substructure in a longitudinal and in a transverse section respectively. Reverse straining
The compressive flow curves recorded at different predrawing levels are shown in Fig. 4. Looking in more detail to such a curve e.g. after the largest
1000
_______------
NE $
,,,y-e
500.
_--.
____.___-------__._ ____~y__
I’ 1
0
0.5
1.0
1.5
2.0
2.5
3.0
I 3.5
c
Fig. 4. Compressive flow curves, recorded after predrawing strains of 6, = 0.17, 0.37, 0.71, 1.20, 1.71 and 2.59 respectively. Test conditions are described in the test.
STRAUVEN and AERNOUDT:
1032
DIRECTIONAL STRAIN SOFTENING
Table 1. Influence of drawing prestrain on some characteristic features of the subseauent comuression flow curve 61
a,
0.17 0.37 0.71 1.20 1.71 2.59
407 460 528 613 691 731
CM
om
0.03 0.05 0.06 0.08 0.09 0.06
484 546 617 663 762
6,
0.12 0.24 0.31 0.32 0.42
a,
(6, - a,)o,. 100
423 495 571 653 734 863
2 4 6 IO 12
IJ,,, and cM represent stress and strain at which the subsequent flow curse reaches a course parallel to the forward curve; CT,,, and L, are the coordinates of the minimum in the Row curve marking the end of the strain softening region; 6, is the forward flow stress before compression and (u,~m)/u,.lOO represents the relative amount of softening obtained in the subsequent compression test.
a larger subsequent strain interval and the amount of increases with increasing prestrain. Substructural observations throw some light on the underlying events. The evolution of that substructure was followed for material belonging to the midlongitudinal and transverse sections of the subsequently compressed wires. By a pure geometrical reasoning one expects the elongated subgrains to be transformed by the compression first into equiaxed and at still larger strains into pancake-like shapes. The observations show that there is a transition first towards equiaxed and then towards a pancakestructure indeed. However the mode of transition is not the geometrical one as represented in Fig. 6(a). softening
This is proven by the electron micrographs of Fig. 7(a) and (b) showing the substructure of the material in longitudinal sections, at compressive strains of t, = 0.20 and 0.40, respectively. The substructural changes are best described as a succession of local collapses of the elongated subgrains into equiaxed cells. Such collapsed regions are indicated by arrows in Fig. 7(a), after a compressive strain of tc = 0.20. The transverse dimensions of the remaining fibered structure only change slowly, but the number of transverse walls clearly increases. Reverse straining hence seems to gradually wipe out the aligned subgrain walls and to braid new non oriented walls, as schematically illustrated in Fig. 6(b). At a reverse strain of d = 0.40 the structure is completely equiaxed with predominantly subgrain walls as can be deduced from the fringe patterns in tilted specimens,
(0)
(b)
Fig. 7. Substructure of a wire drawn to 6, = 2.59 after a subsequent compressive strain of (a) eC= 0.20, (b) cc = 0.40. The arrows in Fig. 7(a) indicate “collapsed” regions where an equiaxed structure has replaced the original elongated subgrain structure.
E.=
t
LOCALLY “COLLAPSEO” ZONE
rug. 6. Schematic representation of substructure evolution during compression. (a) Purely geometrical (b) Real behaviour as observed in TEM-micrographs such as those of Fig. 7.
Fig. 8. Fringe patterns indicating the subgrain character of the walls after a compressive strain of cc = 0.40 (6, = 2.59).
STRAUVEN and AERNOUDT:
DIRECTIONAL
STRAIN SOFTENING
1033
After a compression strain of t, = 0.40, the mean subgrain size in the equiaxed structure amounts to d = 0.31 pm.
Fig. 9. The completely equiaxed substructure obtained after a compressive strain of cc = 0.80 (c, = 2.59)
t %l
t=o
I
20
h-i L,=
0.4
1
10
0
i
0.2
0.4
0.6
0.8
1.0
Q
(pm1 I
Fig. 10. Distribution of subgrain sizes after a drawing strain of et = 2.59 (a) and after a subsequent compression of t, = 0.40 (b). see Fig. 8. In a transverse section some walls seem to be thicker than the subgrain walls in the wire drawn specimen but further observations, discussed below, showed that this is because the walls are no longer perpendicular to the foil surface and contain a more complex dislocation configuration. Beyond a compressive strain of c, = 0.40 the structure is gradually transformed into a pancake structure with subgrain walls parallel to the compression platens. At a reverse strain oft, = 0.80, this newly oriented substructure is clearly developed as shown by Fig. 9 in a transverse section of the compressed specimen. Quantitative observations
Figure 10 represents the distribution of (mean linear intercept) subgrain sizes in transverse sections of the drawn wire and of the subsequently compressed specimen respectively. The distribution in the drawn material is characterised by a mean transverse subgrain size of d=O.l8pm. tThe misorientation measurement technique is described in [71.
The last size is distinctly larger than the sizes predicted for a homologous axisymmetric (d = 0.23 pm) or (1 IO)-texture induced plane strain deformation (d < 0.27 pm) respectively. Thus during compression of the predrawn material, the substructural size changes at a faster rate than the macroscopic dimensions. This is contrary to what happens during forward straining when the decrease of substructural dimensions goes slower than the decrease of the wire diameter. But it is not in contradiction with it. Indeed, in both cases a general feature of large strain deformation substructures in metals is reflected: dynamic recovery always tries to rearrange the dislocations in configurations with a minimum surface-to-volume ratio of the subgrains: the substructure tends to equiaxiality. Thus during drawing dynamic recovery retards the geometrically induced shape change of cells and subgrains, during subsequent compression it accelerates it. At the same compressive strain of c, = 0.40, the reverse flow stress of Fig. 5 has reached a minimum of 762 N/mm2, about 100 N/mm2 below the forward flow stress, which means a relative softening of 12%. In order to understand this softening, a closer look at the substructure was desirable. Crystallographic as well as morphological aspects were investigated. The drawn wire has a sharp (llO)-fibre texture as shown in Fig. 11. This texture explains why the majority of subgrains in the transverse section showed up a (110) diffraction pattern. Though deviations from the (110) orientation certainly exist, even in heavily drawn wire- as was also demonstrated by Langford [17]--this so-called 6 -component of the misorientation (= deviation from (110)) is small compared to the @-component which gives the angular misorientation of neighbouring subgrains around the common (llO)-axis. The subgrain walls in the drawn material hence are tilt walls. The 8-misorientations were found to be cumulative when traversing several subsequent subgrains. The mean misorientation for a number of 60 subgrains was 4.6O.t After 40% compression, three transmitting zones were investigated. In one of them (situation A) 10 of the 12 subgrains still showed up a (110) pattern, the 2 others a (111) pattern. The second transmitting zone (situation B) contained mainly (012), but also (OOl), (115>, (013) and (135) diffraction patterns. The third one (situation C) contained more than 30 subgrains
with a (111)
zone axis.
In those compression substructures the B-component of the misorientation was determined as the angle between crystal directions with the same indices in two neighbouring subgrains and both being perpendicular to the wire axis e.g. between the (100)
1034
STRAUVEN and AERNOUDT:
DIRECTIONAL
STRAIN SOFTENING
Fig. 11. (llO)-pole figure of the transverse section of the drawn wire. (110) fibre texture.
directions in the subgrains with (001) and (012) orientation respectively. The mean o-value found was 4.1, 5.1 and 6.0” for the three transmitting zones respectively, not much different from the mean e-value found in the predrawn wire. However the existence of important 6 -misorientations makes any statement about changes in mean misorientation values rather prohibitive. All what can be said is that the dislocation configuration in the walls will be no more a pure tilt but a more complex configuration and that the neat fibre texture of the drawn wire is destroyed. DISCUSSION
The orientation changes measured lead us to look first if the change in the orientation distribution might be the reason for the work softening. This was checked by calculating the evolution of the mean Taylor-factor along the strain path followed using the existing software for deformation texture predictions [20]. After a drawing strain oft, = 2 the M-factor has reached a saturation value of M = 3.040 under triaxially constrained deformation conditions. With relaxed constraints-allowing the experimentally observed curling to occur the M-factor reaches a value of M = 2.150. Assuming that the nature of the constraint does not change during the subsequent 40% compressive strain, the M-factor decreases by 1.5% for the full constrained case (Fig. 12 path 1) and increases by 0.5% for a compression with relaxed constraints (Fig. 12 path 2) [21]. The influence of texture on flow stress is thus negligible in both cases. However it could be argued that the (1 IO)-textured material, deforming by plane strain and curling during wire drawing, goes into an axisymmetric strain
mode during subsequent compression: this would involve an abrupt increase of the M-factor from 2.150 to 3.040 followed by a small decrease to about 3.000 after 40% compressive strain as shown in Fig. 12 path 3. The material hence should show a texture induced strengthening of 40%. The argument of minimum internal work, used by Hosford [19] to explain the plane strain deformation mode in drawing, also predicts that local plain strain in drawing is preferentially followed by local plane strain in compression at least in the transition stage from the (1 lO)-drawing texture to the combined (100) and (111) compression texture, a stage which covers at least 40% compressive strain. Figure 13(a) and (b) show how the transition to (100) occurs by
I
2.1601 1
2.150
@
I 2
I,
I
.
:
:
1
0
0.1
0.2
0.3
0.4
:
:
:
0.5
0.6
0.7
OB-
lc Fig. 12. Calculated evolution of the mean M-factor during compression after a drawing strain of et = 2 [21]. (1) Under fully constrained conditions, (2) with relaxed constraints (curling allowed), (3) assuming relaxed constraints in drawing followed by full constraints in compression.
STRAUVEN and AERNOUDT:
DIRECTIONAL
1035
STRAIN SOFTENING
Texture changes will thus not soften the material. They will rather harden it when the compressive strains are large and a great number of grains has taken the strong highly symmetrical (11 l)-orientation. It can be concluded that the change in substructure size and morphology and in subgrain wall configuration represent the major contributions to softening. In a first attempt to relate the measured amount of strain softening to the change of the substructural dimensions we estimate the relative flow stress difference from the change in dislocation density, using the relation 0 = CJ,,+ czGb&
(2)
Thus
if the friction stress u,, is neglected. If we assume that the dislocation density per unit subboundary surface is the same in the two considered substructures, an assumption supported by the similar misorientation across their walls, the volumetric density of dislocations is directly proportional to the subgrain surface to volume ratio S/V. Relations from quantitative metallography [22] allow to calculate that ratio for different cell morphologies: for the drawn elongated substructure: S/V = n/2d and for the subsequently structure:
compressed equiaxed sub-
S/V = 2/d.
Fig. 13. Orientation paths followed by originally (llO)oriented subgrains during subsequent compressive deformation, (a) for a grain rotating towards (IOO), (b) for a grain rotating towards (111). In both eases plane strain deformation occurs with the [I IO] direction as direction zero strain.
the activity
of the two systems (lOl)(llT) and (1OT) (111) and the transition towards (111) by the joint and equal activity of the systems (lOl)(llT) and (011) (1 IT), assuming slip to occur only on { 110) planes; in both cases plane strain deformation
prevails on the microscopic scale and the macroscopically required axisymmetric deformation has to be fulfilled by some kind of curling-or uncurling of the previous structure. The three transmitting zones discussed in the previous paragraph represent the three situations indicated in the same Fig. 13 by A, B and C. Once a material volume approaches (001) or (111) orientations like some of the subgrains of B and C did, a gradual transition towards axisymmetric compressive flow can be expected.
Substituting find:
the two measured
Aa -_= c7
K7-*__120/ J8T
subgrain
sizes, we
O
which corresponds to the experimentally measured amount of relative softening. There is also plenty of experimental evidence [23] that, at least for materials which are strained along linear strain paths, the flow stress 0 is related to the substructural size d by a relation Q =q+kd-’
(41
where d represents the average “minimum” substructural size, given as the mean linear intercept size in the appropriate direction. This is the transverse direction in the case of drawn wire. We assume that the strength k of the walls is the same in the two conditions. This assumption is reasonable because at cc = 0.40 the original substructure is completely replaced by a new subgrain
1036
STRAUVEN and AERNOUDT:
DIRECTIONAL STRAIN SOFTENING
structure which at first sight should behave like any other large strain substructure.? When the d-values mentioned above are substituted in equation (4) and taking for k the value of 140 MPa found by Zou Hua Minh [18] (on the same material), the calculated softening amounts to Aa = 326 MPa and the relative softening to 38%, substantially larger than the observed values. In other words, the flow stress of the drawn and subsequently compressed material is much higher than the flow stress of the drawn material at equal subgrain size. The same holds when the wire is fatigue cycled after cold drawing [24]: also there an elongated substructure is gradually transformed into a more equiaxed subgrain structure which is stronger than the drawn structure at equal subgrain size. Zou Hua Minh et al. [24] explained this finding in Hall-Petch terms saying that the “strength” of the subgrain walls is probably larger in the fatigued condition than in the drawn condition, which could be explained by the somewhat larger misorientations-or better: a more complex dislocation configuration in the walls-in the first case. However to the authors opinion, a physically more acceptable argument is that the mean slip distance should be substituted in the equation (4), as was suggested by other authors [I 7,231, instead of the smallest intercept subgrain size. In that case we find for the drawn structure (with (110) texture). d, 6 d/cos 54” = 0.3 1 pm
where the “less than” sign represents the fact that d in the transverse section was measured in random directions and not in the projected slip direction which represents the smallest subgrain dimension. For the equiaxed compressed structure ds = d = 0.31 pm.
It follows that the mean slip distance in the compressed material equals the upper bound of the mean slip distance for the drawn material. According to equation (3) the 12% softening could be accounted for if ds = 0.27 pm which is a realistic value. We conclude that at least in the considered case both the c-& and the o-d-’ relationships can account for the observed differences in flow stress linked to substructures obtained along different strain paths. SUMMARY When compressing a heavily drawn low carbon steel wire along the previous drawing direction, strain softening occurs. This softening region extends over a strain range of lO-50%, depending on the amount of prestrain. On the substructural level the softening tThe same assumption can not be made in the “collapse” region of the compressional flow curve.
is characterised by a succession of local collapses of the elongated subgrain structure of the drawn wire into an equiaxed one. There is a concommitant change of the orientation distribution from a sharp (110) texture towards the ideal orientations of the b.c.c. compression texture. The effect of the change of texture on the course of the subsequent flow curve is negligibly small, at least up to the end of the softening region. Hence it can be concluded that the strain softening finds its explanation solely in the rearrangements in the subgrain structure. The maximum relative softening-at the end of the collapse strain-can be accounted for by the established relationships between flow stress and dislocation density or subgrain size. Acknowledgements-The present work was financially supported by the Belgian Instituut voor Wetenschappelijk Onderzoek in Nijverheid en Landbouw and by Nedschroef (Helmond-Holland). Also the support of Bekaert Steel Wire Corporation (Zwevegem-Belgium) which delivered the wire rod material is gratefully acknowledged. The authors thank Dr P. Van Houtte for the M-factor calculations and ir. W. De Bleser for the flow curve data obtained in his engineering thesis. REFERENCES 1. 0. B. Pederson, L. M. Brown and W. M. Stobbs, Acta metall. 29, 1843 (1981). 2. S. S. Hecker, M&all. Trans. 4, 985 (1973). 3. J. H. Schmitt. E. Aemoudt. B. Baudelet. Mater. Sci. Engng 75, 13 (1985). 4. T. C. Lowe and A. K. Miller, J. Engng. Mater. Tech. To be published. 5. F. W. Hecker, Arch. Eisenhiittenwer. 42, 819 (1971). 6. N. H. Polakowski, J. Iron. Steel Inst., 337 (1951). I. Y. Strauven, Ph. D. thesis, K. U. Leuven (1982). 8. H. G. Grewe and E. Kappler, Physica status solidi 6,339 (1964). 9. A. Thuvander and A. Melander, Swedish Inst. for Metals Research-Internal Reuort IM-1484 (1980). 10. T. Hasegawa and T. Yakou; Scripta metail. 96, 951 (1974). 11. R. Grimes and J. C. Wright, J. Inst. Mefals %, 182 (1968). 12. J. Gil-Sevillano, Ph.D. thesis, K. U. Leuven (1973). 13. W. De Bleser, Engng thesis, K. U. Leuven (1979). 14. G. Langford Ph.D. thesis, M.I.T. (1966). 15. H. J. Rack and M. Cohen, Mater. Sci. Engng 6, 320 (1970). 16. E. Aernoudt and J. Gil-Sevillano, J. Iron Steel Inst., p. 718 (1973). 17. G. Langford and M. Cohen, Trans. Am. Sot. Metals 62, 623 (1969). 18. Zou Hua Minh, Ph.D. thesis, K. U. Leuven (1982). 19. W. F. Hosford, Trans. Am. Inst. Min. Engrs 230,- 12 (1964). 20. P. Van Houtte, Proc. 7th Znt. Conf on Textures in Materials, Holland (edited by C. M. Brakman and P. Jonaenburaer). uu. _ __ 7-23 (1984). 21. P. Van Houtte, unpublished results. 22. C. S. Smith and L. Guttman. J. Metals 5, 81 (1953). 23. J. Gil-Sevillano, P. Van Ho&e and E. Aemoudt, in Progress in Materials Science 24, Chap. 4. Pergamon Press, Oxford (1980). 24. Zou Hua Minh, L. Delaey and A. Deruyttere, Acta metall. 33, 563 (1985). 25. W. Backofen, in Deformation Processing, Chap. 4. Addison Wesley, Reading, Mass. (1972).