Army Materials and Mechanics Research Center, Watertown, MA 02172. (Received April 4, 1984). (Revised April 23, 1984). Introduction. The analysis (1,2) of ...
Scripta
METALLURGICA
V o l . 18, pp. 7 3 5 - 7 3 8 , 1984 Printed in t h e [I,S.A.
Pergamon P r e s s Ltd. All r i g h t s r e s e r v e d
THE INFLUENCE OF DYNAMIC STRAIN AGING ON THE TEMPERATURE DEPENDENCE OF FLOW STRESS AND THE IMPACT OF THIS ON ADIABATIC SHEAR ANALYSIS
M. R. Staker Army Materials and Mechanics Research Center, Watertown, ( R e c e i v e d A p r i l 4, ( R e v i s e d A p r i l 23,
MA
02172
1984) 1984)
Introduction The analysis (1,2) of adiabatic shear bands in metals, which predicts shear bands to form in a catastrophic manner at the shear stress maximum, depends on the evaluation of the temperature dependence of flow stress ~T/DT, the strain-hardening exponent n, and the specific heat C. According to Staker (2) the temperature dependence of flow stress produces about the same variation in the shear stress maximum point as the strain hardening exponent for 4340 steel. The purpose of this investigation is to study the temperature dependence of flow stress for various low alloy martensitic steels and examine its variation with strain caused by dynamic strain aging (DSA) phenomena. The implications of the results uncovered here with regard to the instability analysis are discussed in light of a localization analysis (3) treating shear band formation as a process rather than a catastrophic event. Materials and Experimental
Procedure
Tensile tests at a strain rate of 0.02/min, but otherwise according to ASTM E 21-79, were conducted at temperatures of 21, 93, 149 and 204oc. The specimen was a flat sheet specimen according to ASTM E 8 with a gage section of 50.8 mm long by 12.7 mm wide by 3.2 mm thick. These were prepared from as-received heat treated steel plates of approximately 6 mm thick by grinding with coolant. All of the heats of steel tested were low alloy steel with 30 points carbon. The exact compositions are given in Table I. As can be seen from Table I, there are two sets of heats (the A-serles and the B-series) having essentially common compositions. In general each heat was supplied by a different manufacturer with two exceptions: heats A-I and A-2 were from one manufacturer and heats B-I and B-3 were from another manufacturer. Each manufacturer processed the steel a little differently, having a varied melt practice, amount of cross rolling and/or heat treatment. In general the heat treatment consisted of austenitizing at a temperature between 815 and 927°C, water quenching and tempering at a temperature between 177 and 288°C, with most heats at or near 204°C. Five tensile specimens were tested at each of the four test temperatures. The average yield values for five specimens are reported in Table II at various percents offset. The proportional limit is reported as zero percent offset yield stress. These tensile values were converted to shear stress by dividing bye/-3 . A least squares line was put through the plot of TABLE I.
Chemical Analysis in Weight Percent
v
Element
A-I A-2 B-I B-2 B-3 C D E
0.30 0.29 0.31 0.29 0.31 0.29 0.30 0.30
Mn
Si
0.61 0.49 0.86 0.80 O. 89 0.82 0.68 1.57
0.35 0.28 0.43 0.37 0.49 0.27 0.50 0.28
S 0.014 0.015 0.010 0.023 0.011 0.025 0.013 0.019
0.006 0.004 0.015 0.015 0.017 0.011 0.016 0.012
Ni
Cr
Mo
0.12 0.17 0.82 1.01 1.21 0.53 0.03 0.03
1.06 0.97 0.49 0.51 0.63 0.53 0.52 0.06
0.21 0.20 0.43 0.43 0.46 0.20 0.18 0.23
0036-9748/84 Copyright (c) 1 9 8 4
735 $3.00 + Pergamon
B
O.010 0.006 0.007 0.015 0.012 0.010 0.009 0.012
0.002 0.002 0.001 0.001 0.002
.00 Press
Ltd.
AI 0.02 0.04 0.03 0.09 0.05 0.07 0.04 0.03
Ti 0.070 0.064 0.001 0.001 0.001 0.067 0.039 0.040
Cu 0.14 0.21 0.05 0.36 0.04 0.35 0.06 0.24
Zr
0.005 0.005 O.lOC 0.005 0.16C 0.005 0.12C 0.097
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shear stress versus temperature. The slope so calculated is referred to here as the temperature dependence of flow stress at constant strain and c o n s t a n t strain rate, ~T/~T)y ~,. where T is shear flow stress, T is temperature, y is shear strain and ~ is shear strain rate. TABLE II.
Y~eld Strength in MPa at Various Percent Offset for Four Temperatures*
21oc
ffeat** 0.I
0.2
0.3
1350 1331 1429 1331 1360 1316 1223 1320
1459 1440 1529 1409 1452 1376 1354 1390
1531 1507 1587 1453 1502 1419 1430 1440
0 A-1 989 A-2 958 B-1 1027 B-2 873
B-3 870 C 1027 D 803 E 979
93°C
149oc 0.i
0.2
204Oc
0
0.i
0.2
0.3
0
902 866 1031 i000 1004 971 748 858
1276 1266 1407 1296 1373 1230 1207 1247
1397 1390 1521 1364 1449 1295 1342 1317
1477 1471 1602 1416 1514 1345 1430 1372
706 1196 1361 1466 586 1120 1324_1445^ 8742126521376z1486z 701 1098 1255 1356. 731 1205 1367 1441 ~ 635 1038 1196 1296 651 1131 1307.1412.
0.3
5741104111207113141
0
0.i
0.2
0.3
476 1037 1218312891 429 976 1171 1294 522110271120711331~ 512 1045 1229.1322~ 636 1180 135341453 j 361 896 1088 1202 505 976 1151 1256 5171102011158112691
*
Superscripts indicate the number of specimens used in the average if it was other than 5. The average standard deviation for 0, 0.i, 0.2, and 0.3 are 62, 14, 14, and 14 respectively. ** The UTS of Heats A-I thru E are 1830, 1806, 1900, 1689, 1732, 1609, 1815, 1684 respectively. Results and Discussion The temperature dependence of flow stress ~T/~T)~ @ has been determined by the above is procedure for four values of offset yield strain and is plotted in Figure i. As can be seen the absolute value of ~T/~T is decreasing wlth increasing value of the offset yield strain used In its determination. All eight heats show this trend of decreasing J~T/~T I with increasing strain. The same trend continues to higher values of strain, so that ~T/~T is either zero or positive at a value of strain between one percent and the strain at the ultimate tensile strength. This phenomenon has been observed qualitatively before and has been linked to dynamic strain aging (4-8). For all cases in Figure i the change of I~T/~TI is about a factor of two between the proportional limit and the offset value of 0.2 percent. It can be seen from Figure 1 that alloys in the A-series which have the same composition and same manufacturer lie close to each other. However, for the B-series, which also have a common composition, the three curves are the lowest, middle and approximately the highest, respectively. In this latter case there does not seem to be a direct correlation between the level of the ~T/~T curve and the composition. Heats B-I and B-3 (highest and lowest curves) were also from the same manufacturer. It is therefore likely that processing differences (not composition) between heats accounts for the spread in the band in Figure i. In spite of the spread from one heat to the next, similar behavior is observed: a drop in I~T/$T[ wlth strain, used in its determination, of approximately a factor of two between the proportional limlt and 0.2 percent offset.
I
I
I
~A-II • A-2
. B-3
1862
-d't'/dT 124i (k Pal°C)
-.......~?.~.
150
-
IO0
~__.. - - - ~ . . ~
620
50
1
0
I
0.I
I
02
% plastic stroln
I
0.3
FIG. i. The temperature dependence of shear flow stress between room temperature and 204oc as a function of the percent plastic strain (percent offset) used in its determination. The offset values are those from the tensile tests, and the shear stress has been converted by dividing tensile stress by ~ The strain rate is O.02/min.
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This continual decrease in the absolute value of $~/~T with strain is an impediment for the determination of the appropriate ~T/~T for these types of alloys by quasl-static tests. For example, the values of $%/~T from the literature used by Staker (2) in his original analysis of adiabatic shear bands were 0.2% yield values under quasi-static conditions because dynamic values were unavailable and because yield values were thought to minimize the influence of strain-aging. Strain aging is not expected to be present in high strain rate deformation, and therefore, values determined at yield conditions were thought to be more realistic than higher strain values of ST/~T, which contain strain aging phenomenon. The present results show that even reducing the strain to the 0.2 percent offset will not ensure the exclusion of strain aging phenomenon. It also points out that the absolute values of ST/~T based on 0.2 percent offset yield from the literature used by Staker (2) are undoubtedly too low, probably by a factor of around two. This would cause the predicted critical strains (according to -Cn/($T/$T)) to be lower than the actual measured strains for shear band formation. In other words localization does not take place until strains which are higher than those predicted by the parameter -Cn/(~T/~T). This can be explained by an analysis by Semiatin, 8taker and Jonas (3) where shear bands are considered as a process which develops from the onset of deformation rather than a catastrophic event. The instability analysis of Staker (1,2) predicting that the strain must be equal to at least -Cn/($%/~T), should still be considered a necessary condition for shear band formation but would not be sufficient to ensure that shear bands would form. The localization analysis (3) predicts shear band formation to be a function of C, n, St/ST, m (strain-rate hardening exponent), f(strength or geometric defect ratio), and ~ (the flow localization parameter) but not as Yc = -Cn/(~T/~T). Based on the present results, this parameter - C n / ( ~ / ~ T ) characterizing the maximum in dynamic ~/y curves, is more accurately determined directly from such flow curves than by the determination of n, ~T/~T and C individually unless DSA is known to be absent as in the case of pure materials (9). The localization analysis (3) is based on the idea that the shear stress in the shear band, as it develops, must be equal to the shear stress in the remaining bulk of material undergoing uniform shear. This explains why the shear stress can be supported or carried across a developing shear band so that a second shear band may be nucleated even after the first one has developed extensively. Figure 2 shows examples of multiple shear bands in explosively expanded 4340 steel cylinders (1,2), suggesting that some may be incipient after preceding adjacent bands have developed. Conclusions i. For low alloy 0.3 percent carbon steels (quenched and tempered) investigated, the values of the temperature dependence of flow stress vary by about a factor of two between the proportional limit and 0.2 percent yield strain when determined under quasi-static conditions. This rapid drop in the absolute value of the temperature dependence of flow stress is attributed to dynamic strain aging. 2. This large variation in the temperature dependence of flow stress (as determined quasi-statically) is an impediment to its use for adiabatic shear band predictions of certain alloys. As an alternative, it is suggested that determination of ST/ST, n and C in the combined form Ymax = -Cn/(~T/~T) as the maximum in dynamic flow curves avoids this vexation. Acknowledgements The author wishes to thank Mr. E. H. Harvey for performing the tensile tests and Mr. R. E. Pasternak of AMMRC for help with various stages of this work. References i. 2. 3. 4. 5. 6. 7. 8. 9.
M. R. Staker, Scripta Met. 14, 677 (1980). M. R. Staker, Acta Met, 29, 683 (1981). S. L. Semiatin, M. R. Staker, and J. J. Jonas, Acta Met. 32 (1984) in press. A. van der Beukel, Phys. Stat. vol. A 30, 197 (1975). J. G. Morris, Mat. Sci. Eng. 34, 79 (1978). R. A. Mulford and U. F. Kocks, Acta Met, 27, 1125 (1979). J. D. Baird and C. R. MacKenzie, J. Iron Steel Institute 202, 427 (1964). A. van der Beukel, Scripta Met. 17, 659 (1983). U. S. Lindholm, A. Nagy, G. R. Johnson and J. M. Hoegfeldt, J. Eng. Mat. Tech., Trans. ASME 102, 376 (1980).
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(b)
(C)
FIG. 2 Adabatic shear bands in 4340 steel cylinders explosively expanded, from the work of Staker (i, 2). The micrographs are from transverse sections near the inside diameter of the cylinders. In (a), of the two shear bands shown, the left one is partially fractured, while the right one shows no sign of fracture. In (b), the right one is fractured while the left one (arrows) is at an early stage of development. In (c), of the three shear bands shown, the left two are at an early stage of development while the right one is beginning to fracture. In (c), shearing along the right shear band has displaced part of the middle shear band (at arrow). The micrographs (a), (b) and (c) are from cylinders 2, 22 and ii respectively of reference 2.
