Deformation, temperature and strain rate sequence experiments on OFHC Cu

International Journal of Plasticity 15 (1999) 375±399

Deformation, temperature and strain rate sequence experiments on OFHC Cu Albert B. Tanner*, David L. McDowell George W. Woodru€ School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0405, USA Received in revised form 24 July 1998

Abstract In this paper, we report a series of large strain deformation experiments on initially annealed oxygen-free high conductivity (OFHC) Cu involving sequences of deformation path, temperature, and strain rate (quasi-static to dynamic). Experiments were conducted to obtain a comprehensive data set for the development and evaluation of internal state variable (ISV) models and for the investigation of di€erent functional forms for internal state variable evolution. These included: (a) constant true strain rate tests at various temperatures, (b) load± unload±hold±reload tests at several nominal temperatures, and (c) sequence tests, including strain rate changes, temperature changes and deformation path changes. OFHC Cu demonstrates sensitivity to strain rate and temperature, and exhibits signi®cant history e€ects. Implications of these data are discussed for the evaluation and development of models which account for deformation path, temperature, and strain rate history e€ects. # 1999 Published by Elsevier Science Ltd. All rights reserved.

1. Introduction Accounting for complex paths of deformation, temperature, and strain rate is an important requirement of constitutive laws for large strain problems such as high speed machining, impact, and various primary metal forming operations. In general, sequence experiments reveal more sophisticated phenomena of path history dependence than do constant strain rate, monotonic deformation experiments such as compression tests. The development of new dynamic mechanical property tests and an improved ability to detect microstructural changes have resulted in an improved capability of examining material response. An understanding of deformation behavior *Corresponding author. Tel.:+1-410-306-0662; fax:+1-410-306-0661; e-mail: [email protected] 0749-6419/99/$ - see front matter # 1999 Published by Elsevier Science Ltd. All rights reserved. PII: S074 9-6419(98)0006 1-8

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over a wide range of temperatures and strain rates is necessary for many engineering applications. This experimental program is intended to support the development of improved internal state variable (ISV) constitutive laws for history dependent behavior of polycrystalline metals, principles for determining optimized ISV evolution equations and associated parameters, and to facilitate assessment of the capability to model strain rate history and temperature history e€ects in current constitutive models. Strain rate and temperature history e€ects were ®rst demonstrated by Dorn _ T† (Ludet al., (1949). Consequently, the mechanical equation of state,  ˆ …"; "; wick, 1909), is invalid since it assumes that the material ¯ow stress is dependent upon instantaneous values of strain, strain rate, and temperature. This necessitates the consideration of internal state variable models to supersede mechanical equation of state models (cf. McDowell and Voorhees, 1995). Strain rate and temperature history e€ects are shown schematically in Fig. 1 (Klepaczko, 1975 and Du€y, 1979). Stress±strain curves are plotted for two strain rates and temperatures. The lowest curve represents the stress±strain relation for an f.c.c. metal measured during loading at a relatively low constant strain rate, "_i . The upper curve pertains to a high constant strain rate, "_r . During a strain rate jump test, the stress±strain curve follows the path ABCD, where B is the strain, "i , at which the strain rate is changed abruptly from "_i to "_r . If the mechanical equation of state were valid, there would be no strain rate history e€ect; the response to the strain rate jump would be along path ABFG. The abrupt change in ¯ow stress is identi®ed as
s . At points C and F, the strain and strain rate are identical, while the stress di€ers. Therefore, material behavior depends on the strain rate history.
h is viewed as

Fig. 1. Strain rate and temperature history e€ects (Klepaczko, 1975; Du€y, 1979).

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re¯ective of the history dependence on strain rate, while
s is related to the instantaneous strain rate sensitivity. Beyond "i , the di€erence in stress levels, especially for f.c.c. metals, diminishes as the deformation continues. This is referred to as fading memory. In some instances, the di€erence reduces to zero. Analogous results are obtained whether a sharp decrease in temperature or increase in strain rate is imposed. The dependence of ¯ow stress on temperature history was investigated much earlier than strain rate or deformation path history e€ects. The range of temperatures required for the observation of temperature history e€ects was well within the capability of standard laboratory techniques, whereas the range of strain rates required specialized apparatuses. The ®rst sequence experiments involved temperature changes on aluminum loaded in tension at a low constant strain rate (Dorn et al., 1949). Additional temperature sequence experiments were conducted on f.c.c. metals: Al and Cu (Sylwestrowicz, 1958), Ni±30%wt Co (Hughes, 1986) and Al (Hartley and Du€y, 1984). The transient ¯ow stress, for these temperature sequence experiments, remains between the constant temperature curves. The sequence ¯ow stress does not exhibit a fading memory over the limited subsequent straining of approximately 25%. Temperature sequence experiments were also conducted on these b.c.c. alloys: low carbon steel (Lindley, 1965), 1020 HRS (Hartley and Du€y, 1984) and 4340 steel (Tanimura and Du€y, 1986). The b.c.c. alloy transient ¯ow stress reaches a level above the lower constant temperature curve, for a temperature decrease sequence, and remains above. A greater number of experiments have been conducted involving sequences of strain rate. An advantage of strain rate sequence experiments is the capability of imposing a rate change within a short period of time. Temperature sequence experiments necessitate a ®nite time to achieve changes in temperature. The ®rst experiments involving dynamic strain rates were conducted in compression on aluminum (Lindholm, 1964, 1968). The transient ¯ow stress remains between the two constant strain rate curves and approaches the higher rate curve during low to high strain rate sequences. Numerous investigations have been conducted using the torsional split Hopkinson pressure bar apparatus on Al and Cu (Campbell and Dowling, 1970), Al-1100 and 1199 (Nicholas and Whitmire, 1970), Al-1100 (Frantz and Du€y, 1972), Ni (Gulec and Baldwin, 1973), OFHC Cu (Eleiche and Campbell, 1974, 1976), Pb and Cu (Klepaczko and Du€y, 1974), OFHC Cu and Al-1100 (Senseny, 1977), Cu (Stelly and Dormeval, 1977), AISI 316 (Albertini et al., 1985) and OFHC Cu (Follansbee and Gray, 1991; Gourdin and Lassila, 1992). The transient ¯ow stress typically exhibits an initial sharp increase and then gradually approaches the higher rate constant curve. The actual approach to the upper curve is based on extrapolation due to limited straining after the sequence. Experiments which have been conducted on OFHC Cu include strain rate increases from "_ ˆ 0:0017 to 520 sÿ1, at 25, 200 and 400 C in torsion with polycrystalline material with an initial grain size of 53 mm (Eleiche and Campbell, 1974) and single crystal (Eleiche and Campbell, 1976). Additional torsional experiments have been completed with strain rate increases from "_ ˆ 0:0001 to 520 sÿ1, at ÿ196, ÿ125, 25 and 250 C using material with an initial grain size of 35 mm (Senseny, 1977) and

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strain rate decreases from "_ ˆ 460 to 115 sÿ1 and 690 to 175 sÿ1 at 25 C using material with an initial grain size of 80 mm (Lipkin et al., 1978). The most extensive experimental program investigating strain rate sequences was conducted using OFHC Cu at room temperature and represented about 600 compression experiments (Follansbee and Kocks, 1988). It was found that the transient ¯ow stress during strain rate changes exhibits an instantaneous jump, less than half of the difference between the two constant rate curves, and then gradually approaches the constant rate curve. During the past decade, there have been numerous investigations at strain rates above 104 sÿ1. These high strain rates are achieved through shock loading and pressureshear experiments (Clifton, 1990; Tong, 1991; Follansbee and Gray, 1991; Sakino and Shioiri, 1991; Gourdin and Lassila, 1992; Tong and Clifton, 1992; Klepaczko et al., 1993; Shioiri et al., 1994; Sakino and Shioiri, 1996). The experimental program reported here is believed to be among the most comprehensive involving sequences of temperature, strain rate and deformation path, using the same material and initial microstructure. This same material was used for sequences of deformation path (Graham, 1995; Horstemeyer, 1995). The paper is organized as follows. The experimental procedures are ®rst described, including techniques for sequencing path, strain rate and temperature. Next, experimental results are presented for a wide range of conditions. Finally, key experimental results are summarized and implications are discussed for necessary elements of an ISV constitutive model necessary to capture history e€ects. 2. Experimental procedures Compression and free-end torsion experiments were conducted on initially annealed OFHC Cu across a range of temperatures (25 to 541 C) and constant true strain rates (quasi-static ÿ0.0004 sÿ1 to dynamic ÿ6000 sÿ1), along with sequences involving di€erent temperatures, strain rates and paths. Tests were conducted using closed-loop servo-hydraulic test machines for strain rates at or below 1.0 sÿ1 at Sandia National Laboratories (SNL) and the Georgia Institute of Technology and a split Hopkinson pressure bar at SNL for the higher rates. True stress and strain measures are reported here. 2.1. Material OFHC f.c.c. copper (99.99% pure) was selected for this investigation. It has been rather widely studied under constant strain rate deformation, nominally isothermal. Copper has a moderate to high stacking fault energy which serves to accentuate the rate of dynamic recovery and to inhibit dynamic recrystallization (McQueen and Jonas, 1975; Sellars, 1979). The melting point of copper is Tm ˆ 1356 K. The material was furnished in 51 and 76 mm diameter extruded bar stock. The large specimens, 50.8 mm Lindholm specimens and 70.8 mm diameter compression specimens were machined from the larger stock. The remaining specimens were machined from

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the small stock. All specimens were machined such that their axis of symmetry was parallel to the axis of the bar. Initial specimen con®gurations are given in Table 1. All references herein to specimen ``type'' will refer to this table. After initial machining, the copper was annealed at 600 C for 4 h in vacuo and then quick cooled at room temperature. This is the same annealing schedule as the copper used in experiments reported by Graham (1995) and Horstemeyer (1995). This heat treatment resulted in an average grain diameter of 62 mm using the average grain intercept method (Underwood, 1970). The initial material texture is shown in Fig. 2 for a surface normal to the specimen axis. The texture is essentially random, with the maximum intensity of 4.74 (times random, normalized to a random intensity of 1.0). Ideally, the intensity of an initially untextured, random sample would be 1.0 and uniform, but small intensity peaks with a maximum intensity of 5.25 are common (e.g. Bronkhorst et al., 1992). 2.2. Experimental apparatuses Experiments were performed at both the Georgia Institute of Technology Mechanical Properties Research Laboratory (MPRL) and Sandia National Laboratories (SNL) in Livermore, CA. All compression specimen design, fabrication, and experiments were performed at SNL and all torsional tests were conducted in the MPRL. Two di€erent compression apparatuses were used at SNL. Low strain rate experiments for "_ ranging from 0.0004 to 1.0 sÿ1 were performed using a high capacity MTS closed-loop servohydraulic test machine. High strain rate experiments were obtained using a modi®ed split Hopkinson pressure bar apparatus.

Table 1 Specimen con®guration Type 1

Test

Size mm (inches)

End ®nish

Remachine

Size mm (inches)

Hopkinson

8.894.45 (0.3500.175)

Polished

Compression

7.627.62 (0.3000.300) 2.547.62 (0.1000.300)

Double shear

2

Compression

10.1615.24 (0.4000.600)

Grooved

3

Compression

30.4845.72 (1.21.8)

Grooved

71.12106.7 (2.84.2)

Grooved

4

5

Compression

Lindholm

50.882032 (2.08.0)

Compression Lindholm Compression Lindholm

10.1615.24 (0.4000.600) 25.427.9 (1.01.1) 10.1615.24 (0.4000.600) 50.863.5 (2.02.5)

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2.3. Compression experiments The advantages and diculties of the compression test are well established (ASTM Standard E209-65, 1983; Miller, 1993). As compared to tension tests, larger strains can be achieved due to the absence of necking. Another advantage is the simplicity of ®xtures and specimens for compression tests. Uniform deformation is achieved by reducing the e€ects of friction between the specimen and the compression platens. At low strain rates a 110 kip servohydraulic test machine was used. The actuator was controlled using displacement feedback, resulting in a constant true strain rate compression test. Load, stroke, temperature, and extensometer data were collected using a digital oscilloscope. Load and displacement data were converted into engineering stress …a † and axial engineering strain …"a †. True axial strain …"t † and true axial stress …t † were then calculated by "t ˆ ln…1 ‡ "a † and t ˆ a …1 ‡ "a †

…1†

Strain was determined using the stroke data from the MTS machine. These stroke data were corrected for test machine compliance. A correction factor was determined for each of the test temperatures. An MTS extensometer, modi®ed for use within the three-zone furnace during elevated temperature tests, was used to verify the accuracy of this correction. The corrected strain data compared precisely with the data obtained using the extensometer.

Fig. 2. Initial texture of annealed OFHC Cu material. Pole ®gure for (111) orientation.

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Uniform material deformation was obtained by reducing the friction between the specimen and the compression platens. Hastelloy was used as compression platen material since it could be easily polished to maintain a smooth compression surface and to distribute the specimen contact load evenly over the cross section of the push rods. Concentric grooves were machined into the ends of the specimens to hold special lubricants, depending upon the strain rate and temperature as shown in Fig. 3. At low strain rates, an oil-based molybdenum disul®de lubricant was used from 25 to 134 C, an oil-based silver lubricant was e€ective from 200 to 300 C, and a powered glass with boron nitrate was used above 300 C. Lubricant was placed in the grooves on the specimen ends. The center three grooves were not lubricated on the larger specimens, types 3 and 4. The specimen sides were coated to prevent oxidation. The grooves retain lubricant during compression and release it as the hydrostatic pressure in the grooves increases. This con®guration of specimens works well in achieving homogenous compression. Figure 3 shows a typical copper compression specimen before and after quasistatic constant strain rate compression to a true strain of 1.0. The deformed specimen is still cylindrical, with no barreling resulting from side roll-over. Homogenous deformation is obtained using this method. High strain rate compression experiments were conducted using a split Hopkinson pressure bar apparatus. The specimen was placed between the two, 76.2 cm long, elastic pressure bars which were instrumented with strain gages. The incident wave was generated by propelling the striker bar using compressed gas. The strain rate within the specimen is directly proportional to the amplitude of the re¯ected wave in the incident bar which is measured by a strain gage. Stress in the specimen is directly proportional to the amplitude of the transmitted wave, measured by another strain gage mounted on the output bar. Strain rates of magnitude 103 sÿ1 were obtained. Friction between the specimen and bars was reduced by using polished specimens and lubrication. At low temperatures, an oil-based molybdenum disul®de lubricant was used. At temperatures between 200 and 350 C, an oil-based silver lubricant was used. 2.4. Torsion experiments The torsional tests were all conducted in the MPRL. Tests were performed using an MTS closed loop axial±torsional servohydraulic test machine with simultaneous axial and torsional control. Specimens were gripped with a hydraulic grip system

Fig. 3. Typical compression specimens: (left) no strain, (middle) 0.5 strain, and (right) 1.0 strain.

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using either 25.4 or 50.8 mm collets. All torsional tests were conducted free-end, i.e. the axial load was maintained at zero. The rotation angle, , and the torque, T, were measured using the servohydraulic ram's RVDT and a torsional load cell. The tests were controlled and the data collected using a digital control system. The design of the thin walled torsion specimens, shown in Fig. 4, was adapted from a design developed by Lindholm et al. (1980). These specimens limit the deformation to the gage section even at large strain. A high degree of uniformity of shear strain is maintained within the gage section. The ends of the specimens were plugged with stainless steel inserts to resist signi®cant inelastic deformation during gripping. The inserts extended from the specimen ends but ended before the beginning of the beveled region so as not to signi®cantly a€ect the stress or strain distributions in the gage section. The gage section wall thickness encompassed an average of 30 grains. The assumption of homogenous deformation in the gage section permits de®nition of the engineering shear strain , according to 1 …ro ‡ ri †g

ˆ2 go

…2†

where g is the angle of rotation of the top of the gage section relative to the bottom, go is the initial gage length of the specimen, ri is the inner radius of the gage section, and ro is the outer radius. The shear stress, assumed uniform, is given by ˆ

3T 2…r3o ÿ r3i †

…3†

where T is the torque. Machine compliance corrections were made for the shear strain measurements since the angle of twist between the grips, not within the actual gage section, was measured by the RVDT. The beveled region of the specimen was assumed to remain

Fig. 4. Drawing of a 50.8 mm diameter Lindholm specimen. All dimensions are in mm.

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elastic and to be the main contributor to the additional strain outside of the gage section. The compliance correction, as determined by Graham (1995), was applied to all torsional experiments. 2.5. Temperature response of specimens Many experiments were conducted above room temperature. A three-zone furnace and an induction heater were used. At lower strain rate (0.0004 to 1.0 sÿ1) compression, elevated temperature experiments were achieved with a three-zone furnace capable of heating to 1100 C. Additionally, heaters were installed in the 50.8 mm diameter Inconel push-rods and controlled using a digital temperature controller. Temperature was controlled to ‹1 C using three thermocouples mounted in the furnace and two in each push rod. Specimen temperature was monitored and recorded during compression using a spring-loaded contact thermocouple. Elevated temperature experiments were conducted using the split Hopkinson pressure bar with a 5.0 kW induction heater. Specimen temperature was controlled using a thermocouple placed between the specimen and the pressure bar. The pressure bars are maintained at low temperature by using a water cooling system. Torsion elevated temperature experiments were conducted using either a 2.5 kW induction heater or a three-zone furnace. Due to the high conductance of OFHC copper, steel susceptors were used along with the induction heater to heat the specimens. Temperature was controlled using thermocouples attached to the specimen gage section. Specimen gage section temperature was maintained to ‹3 C during constant temperature tests. During elevated temperature testing, specimens were heated until they reached the desired uniform temperature. The amount of time spent at elevated temperature resulted in static thermal recovery and recrystallization, depending on temperature; therefore the time was minimized, and was just long enough to reach uniform temperature. Figure 5 shows the average specimen temperature increase from the time it was inserted into the furnace and the temperature decrease from 269 C after removal from the furnace. The initial temperature increase is primarily radiative heat transfer, while the steep slope at 30 s includes e€ects of conduction resulting from the specimen contact with both push rods. Specimen temperature was recorded during all tests for purposes of thermomechanical modeling. 2.6. Strain rate (high) sequence experiments A series of strain rate change experiments were conducted. These included sequences of high rate deformation followed by low rate at various temperatures, and from quasi-static strain rate to higher rates also at various temperatures. The initial deformation at high strain rate was applied using a split Hopkinson pressure bar apparatus at SNL. The results for the constant high strain rate case re¯ect an average of approximately ®fteen di€erent experiments. Subsequent sequence experiments involving quasi-static strain rates and both 25 and 269 C were conducted using an MTS servohydraulic machine. These second sequence specimens

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were obtained using three split Hopkinson pressure bar specimens (Type 1). Each split Hopkinson pressure bar specimen surface was machined ¯at with grooves added to the outside ends. The three specimens were then bonded together using a ceramic glue (Fig. 6). The glued specimen was pressed while drying such that the glue thickness was 25.4 mm. The bonded specimen was then machined such that the ®nal diameter was equal to the ®nal height. Machining was accomplished such that material removal during the last three passes was no more than 76.2 mm per turn to prevent additional work hardening. 2.7. Strain rate (low) and temperature sequence experiments A series of experiments were conducted with changes in temperature (25 and 269 C) and strain rate (0.0004 and 0.1 sÿ1). The initial deformation was conducted

Fig. 5. Specimen temperature response after insertion into three-zone furnace at 269 C and after removal from three-zone furnace at 269 C.

Fig. 6. Diagram of the second phase sequence specimens (quasi-static following high strain rate).

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with larger compression specimens (Types 3 and 4). Type 2 compression specimens (10.1615.24 mm) were then obtained from the pre-strained material. The material was removed using electro-discharge machining (EDM) and then machined to the ®nal con®guration, removing material at the rate of 76.2 mm per turn, to prevent alteration of the internal structure. 2.8. Path sequence experiments Path change experiments were conducted from compression pre-strain to subsequent torsion. These included high rate (103 sÿ1) compression at 25 and 269 C followed by quasi-static (0.0004 sÿ1) shear at 25 and 269 C. Additionally, quasi-static experiments compression were followed by quasi-static shear at combinations of 25 and 269 C. The high rate compression specimen was approximately 3.61 mm in length and 10.16 mm in diameter after deformation of 0.3 true strain. A novel double shear specimen was designed to conduct the subsequent shear experiments on the small volume of material available (Fig. 7) following high rate pre-straining. Quasi-static path sequence experiments were conducted by ®rst compressing material to 0.5 true strain and then machining a Lindholm specimen from the pre-strained material. The Lindholm specimen was electro-discharge machined to maintain the material's internal structure. 2.9. Experimental consistency Several experiments were conducted at the same temperature and strain rate conditions to verify repeatability. Figure 8 shows ®ve results for 0.0004 sÿ1 and 25 C.

Fig. 7. Double shear specimen design for path and strain rate sequence experiments.

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The results are very repeatable and indicate that the testing procedure and material response were consistent. Figure 9 shows the sequence of loading at either 25 C at 0.0004 sÿ1 or 269 C at 0.0004 sÿ1, unloading and remachining the specimen, and then reloading at the same strain rate and temperature. The results show that the reload response is the same as the constant strain rate and temperature response. This demonstrates that the test procedure is consistent and the remachining process has not altered the subsequent material behavior. At 269 C, the reload curve (after remachining) shows that the mechanical behavior is not signi®cantly a€ected by the cool down and subsequent heat up, nor the remachining events.

Fig. 8. Repeatability of compression tests. Five experimental tests are shown.

Fig. 9. Load, unload and remachine, and reload at same temperature and strain rate.

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3. Experimental results All of the data presented for compression experiments corresponded to low barreling (less than 2.0%), con®rming uniform deformation. All stress±strain curves are plotted using true strain and true stress (in MPa). Shear results are plotted using the uniaxial normalized von Mises equivalent strain and stress, i.e. p

" ˆ p  ˆ 3 3

…4†

3.1. Results of experiments with hold times Load±unload±hold±reload experiments were performed under constant true strain rate and nominally isothermal conditions to evaluate the recovery/recrystallization behavior. In these experiments, the stress was reduced to zero during hold periods applied after initial straining. The di€erence between the stress just before unloading and the yield stress upon reloading represents the change in state due only to di€usionallygoverned static recovery and/or recrystallization processes. In this work we will refer to all such processes as ``restoration'' (cf. McQueen and Jonas, 1975). Increasing the hold time increases the cumulative e€ect of these processes. At 269  C, the stress upon reloading at 0.3 strain is not signi®cantly di€erent from that measured just before unloading at 0.3 strain, even for relatively long hold periods (Fig. 10). There are signi®cant di€erences in reload stress after holding at 0.5 strain for increasing amounts of time (Fig. 11). Although static thermal recovery may play some role in the observed behavior, determination of grain sizes before the hold period and subsequent to the hold period established that recrystallization occurred during the hold periods at 269 C and indeed was essential to consider in

Fig. 10. Static restoration results at 269 C, 0.0004 sÿ1 and di€erent hold times at 0.3 strain.

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modeling this behavior. Grain size measurements are shown in the boxes in Fig. 10 and show the tendency for re®nement for constant strain rate deformation (single peak dynamic recrystallization) with grain growth during hold periods. These results show that the recrystallization is pre-strain dependent, being much more strongly activated at 0.5 pre-strain than 0.3. In related modeling work (Tanner, 1998) we have found that the recrystallization dominately accounts for the behavior observed in Fig. 11, with static thermal recovery playing only a minor role. At 541 and 676 C (T=Tm ˆ 0:6 and 0.7, respectively), the amount of restoration after a pre-strain of 0.5, as evidenced by the change in ¯ow stress before and after unloading, is very similar for the various hold times (Fig. 11). Oscillations of the ¯ow stress are highly repeatable from test to test. When polycrystalline materials are deformed at elevated temperatures, the accumulated dislocations are continuously annihilated by two separate processes, dynamic recovery and dynamic recrystallization, which both result in the release of the internal energy stored during deformation. At temperatures above about 0.3 Tm and at low strain rates, oscillations in OFHC Cu ¯ow stress have been observed (Blaz et al., 1983; Chen and Kocks, 1992), similar to those reported in Fig. 11. During deformation, the dislocation density and the stored energy increase. When the stored energy becomes high enough, dynamic recrystallization is observed to nucleate at prior grain boundaries (Derby and Ashby, 1987; McQueen and Jonas, 1975). The nucleation and growth of new grains eliminates dislocations and reduces the stored energy, resulting in a reduction in ¯ow stress. These new grains continue to deform, the local dislocation density increases until nucleation occurs, resulting in local recrystallization. The resulting behavior causes the cyclical variation of the ¯ow stress. These oscillations tend to die out with the ¯ow stress reaching a steady state value. At lower temperatures or higher strain rates, the ¯ow stress passes through a single peak before decreasing to a steady state value, similar to the ¯ow stress at 269 C in Fig. 10. This steady state stress is associated with

Fig. 11. Static restoration results for OFHC Copper at 0.0004 sÿ1, 269, 541 and 676 C for di€erent hold times at 0.5 strain.

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a new, constant mean grain size within the material, and re¯ects a dynamic balance between nucleation and growth (Blaz et al., 1983; Sakai and Jonas, 1984). Single peak behavior is associated with grain re®nement while multiple peaks occur with discrete cycles of grain coarsening (Saki and Jonas, 1984). It is interesting to note that the in¯uence of hold time is indiscernible at 541 and 676 C, likely because the kinetics of restoration processes are so rapid that hardening and restoration are nearly equilibrated. Moreover, the frequency and amplitude of oscillations of the ¯ow stress are very repeatable, and are largely una€ected by the hold time. 3.2. Constant true strain rate experimental results Compression experiments were conducted at true strain rates of 6000, 1.0, 0.1, 0.01 and 0.0004 sÿ1 and at various temperatures ranging from room temperature (25 C) to 0.7 Tm (676 C). Both strain rate and temperature dependence of ¯ow stress are clearly shown in Figs. 12±15, respectively. At strain levels on the order of 0.02, the ¯ow stress at all temperatures nearly coincide, indicating a range of a thermal hardening (Mecking, 1980). At medium to high strains, the curves exhibit a temperature dependence. The transition between single and multiple peak oscillations associated with dynamic recrystallization occurred between 303 and 337 C for a strain rate of 0.0004 sÿ1; the measured average grain size for the specimens at the various temperatures are shown in boxes in Fig. 15 at the strain level where the measurements were taken. Clearly, there is a marked decrease of the grain size at 236 C, even though no softening of the ¯ow stress was observed. Single peak recrystallization for temperatures up to 303 C corresponded to a decreasing measured grain size, down to 26.6 mm at true strain on the order of unity from the initial grain size of 62 mm. Multiple peak recrystallization occurred at 337 C and above, corresponding to grain coarsening due to episodic cycles of re®nement and growth. Blaz

Fig. 12. Strain rate dependence of OFHC Cu in compression at 25 C.

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Fig. 13. Strain rate dependence of OFHC Cu in compression at 269 C.

Fig. 14. Strain rate dependence of OFHC Cu in compression at 541 C.

et al. (1983) determined the transition, for OFHC copper with an initial grain size of 78 mm and strain rate 0.002 sÿ1, to be about 825 K. Chen and Kocks (1992) determined that the transition for Cu occurred at 400 C for a strain rate of 0.01 sÿ1. Torsion experiments were conducted at a constant von Mises equivalent strain rate of 0.0004 sÿ1 (0.00069 sÿ1 shear strain rate) and at various temperatures ranging from room temperature (25 C) to 0.5 Tm (405 C). Torsional data exhibit softening relative to compression at 25, 269 and 405 C as shown in Fig. 16. The von Mises equivalent torsional ¯ow stress is considerably below that of compression at 25 C. Reduction of slip constraint due to both texture development and formation of different dislocation substructures have been identi®ed as the main contributors to the

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Fig. 15. Temperature dependence of OFHC Cu in compression at 0.0004 sÿ1. Average grain sizes for OFHC Cu from compression at constant strain rate, 0.0004 sÿ1, isothermal experiments. The sizes (mm) are shown at the corresponding strain and temperature at completion of strain. Two values are shown at 0.5 strain, 25 and 269 C, which were determined from separate experiments. The standard deviation on the measurements was 4 (mm).

torsional softening e€ect (cf. Miller, 1993; Miller and McDowell, 1996). The di€erence in the magnitude of compression and von Mises equivalent torsional ¯ow stress decreases with increasing temperature, and vanishes at 405 C. We are unaware of comparable experimental data reported previously in the literature. This suggests that the kinetics of dislocation motion and/or the role of dislocation substructure development overwhelms textural anisotropy in compression and shear for T=Tm 50:5. 3.3. Sequence experiments Figure 17 shows the results for a material which is initially deformed in compression at a high strain rate (6000 sÿ1) and at room temperature (25 C). A pre-strain of 0.34 is achieved at the high strain rate. After remachining, the specimen is deformed quasi-statically (0.0004 sÿ1) in compression to a strain of 0.84. During temperature sequence experiments at 269 C, the specimen is rapidly heated, remaining in the furnace for 45 s before imposing the quasi-static deformation. This time was necessary to achieve uniform temperature throughout the specimen. Upon reloading, the ¯ow stress rapidly rises somewhat above the constant strain rate curve, and then displays accentuated softening. Figure 18 shows the results for a material initially deformed at high strain rate (5200 sÿ1) and at 269 C. A pre-strain of 0.28 is achieved at the high rate. After remachining, the specimen is deformed quasi-statically (0.0004 sÿ1). The ¯ow stress rises somewhat above the constant strain rate curve, but then eventually coincides.

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Fig. 16. Comparison of compression and torsion OFHC Cu data sets based on von Mises equivalent stress and strain at a strain rate of 0.0004 sÿ1.

Fig. 17. Strain rate and temperature history e€ects for OFHC Cu in compression: sequence from high strain rate to quasi-static deformation.

Figure 19 shows results for a strain rate change from 0.0004 to 0.1 sÿ1 after a prestrain of 0.5. After remachining, the ¯ow stress is initially between the two conditions, then moves toward the constant strain rate curve for the new conditions. Figures 19 and 20 also show the copper response to temperature sequences. Figure 19 shows the stress±strain behavior of material initially deformed at 269 C and then reloaded at 25 C. Figure 20 shows the response for copper initially deformed at 25 C and then reloaded at 269 C. The material is strained to 0.5, unloaded and remachined and then reloaded at 269 C to a total strain of 1.0. Initial material response after

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393

Fig. 18. Strain rate and temperature history e€ects for OFHC Cu in compression: sequence from high strain rate to quasi-static deformation.

Fig. 19. Strain rate history e€ects of OFHC Cu in compression (0.0004 sÿ1, 269 C then 0.1 sÿ1, 269 C) and temperature history e€ects of OFHC Cu in compression (269 C, 0.0004 sÿ1 then 25 C, 0.0004 sÿ1).

reloading is clearly dependent upon the amount of time spent in the furnace before the start of the experiment; the longer the time, the greater the amount of restoration that occurs. The initial reload response for material held at zero stress for 20 min in the furnace at 269 C is similar to that of an annealed material subjected to a strain of about 0.3. Deformation path change experiments were conducted involving compression followed by torsion. These included high rate (103 sÿ1) compression at 25 and 269 C followed by quasi-static (0.0004 sÿ1) shear at 25 and 269 C. Additionally, experiments at quasi-static compression were followed by quasi-static shear at temperatures of 25 and 100 C. The high strain rate compression specimen was approximately 3.61 mm

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Fig. 20. Temperature history e€ects of OFHC Cu in compression (25 C, 0.0004 sÿ1 then 269 C, 0.0004 sÿ1) for increasing times held in furnace prior to compression.

in length and 10.16 mm in diameter after deformation. Figure 21 shows the results of the high rate compression at 25 C followed by quasi-static shear at 25 and 269 C, respectively. The subsequent equivalent ¯ow stress in shear persists well above the level for pure torsion experiments at the same e€ective strain level due to prior formation of a di€erent texture and dislocation substructure in compression. 4. Discussion These experiments reinforce that a mechanical equation of state (Ludwick, 1909) does not exist for OFHC Cu. The sequence experiments clearly show that the ¯ow stress is not only a function of instantaneous values of strain, strain rate and temperature, but contain transients and in some cases di€erent asymptotic ¯ow stress levels, representing history e€ects resulting from sequences of temperature, strain rate and/or deformation path. There are multiple values of ¯ow stress for the same strain, strain rate and temperature and di€erent preceding histories. OFHC Cu demonstrates softening due to static thermal recovery and recrystallization. Recrystallization at 269 C during hold periods (Figs. 10 and 11) is strain level dependent. Little recrystallization occurs at 269 C at strains of 0.3 or less, but is signi®cant at strains of 0.5 at this temperature. The rate of static thermal recovery is strongly temperature dependent, increasing with temperature. Dynamic recrystallization is evident during deformation (Figs. 13±15) at temperatures above 236 C. At 202 C and below, the ¯ow stress continues to increase at quasi-static strain rate and at a strain of unity. As temperature increases above 236 C, the ¯ow stress attains a peak stress and then decreases towards a steady state value. The strain to the peak stress decreases with increasing temperature: from 0.75 for 236 C to 0.38

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Fig. 21. Path sequence experiments on OHFC Cu: von Mises equivalent responses for high rate compression followed by quasi-static shear.

for 286 C and 0.12 for 541 C. Additionally, as the strain rate increases, the strain corresponding to the peak stress also decreases. Oscillations in ¯ow stress occur at temperatures above 337 C. The steady state stress level decreases with increasing temperature. Average grain size measurements shown in Fig. 15 con®rm that recrystallization coincides with the observed single and multiple peak softening behaviors. During ®nite deformation, the internal structure changes, strain hardening occurs due to an increasing dislocation density and softening occurs due to recovery and recrystallization processes. These experiments indicate the requirement for constitutive models to have an evolutionary relation which results in a balance between hardening and recovery of various forms, and the capability of compensatory softening at increasing temperature to account for the peak stress behavior and recrystallization e€ects. Strain rate, temperature, and deformation path history e€ects are evident from the sequence experiments (Figs. 17 and 19). Strain rate sequences, both high to low and low to high, result in a transient ¯ow stress that stays between the constant rate curves and gradually approaches the constant strain rate curve, indicating that the e€ect of the pre-strain is eliminated with additional strain on the order of the pre-strain. The initial response upon reloading is intermediate to the two curves which correspond to each of the strain rate and temperature conditions. The work hardening rate is higher for the transient curve for lower to higher strain rate sequences than for the constant strain rate and temperature curve. This greater slope results in the transient curve approaching the constant curve with additional strain on the order of the pre-strain. For sequences from higher strain rates to lower, the reverse phenomenon occurs. Temperature sequence experiments also result in transients in ¯ow stress (Figs. 19 and 20). The ¯ow stress remains between the two constant temperature curves during temperature sequences from 269 to 25 C, but does not ultimately reach

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the lower temperature curve; a permanent o€set is evident which is not erased by further strain. The transient ¯ow stress is strongly dependent on recrystallization processes for pre-straining at 25 C, at both high and low strain rates, and then straining quasistatically at 269 C. The internal structure resulting from the 25 C pre-strain recovers with time but, while this recovery is signi®cant, it is not complete; a small o€set below the constant temperature curve remains. All deformation path changes (e.g. compression to torsion) result in a signi®cant permanent o€set of the ¯ow stress; the stress following the path change remains between the two constant stress levels. The subsequent equivalent ¯ow stress in shear persists well above the level for pure torsion experiments at the same " level due to prior formation of texture and dislocation substructure in compression. The experimental results presented are consistent with other sequence experimental results. The ¯ow stress after a temperature sequence remains between the constant temperature curves and does not completely achieve the constant temperature curve corresponding to the new temperature (Sylwestrowicz, 1958), Ni± 30%wt Co (Hughes, 1986) and Al (Hartley and Du€y, 1984). The transient ¯ow stress after a strain rate sequence remains between the two constant strain rate curves and approaches the higher rate curve during low to high strain rate sequences (Lindholm, 1964, 1968; Campbell and Dowling, 1970; Nicholas and Whitmire, 1970; Frantz and Du€y, 1972; Gulec and Baldwin, 1973; Eleiche and Campbell, 1974, 1976; Klepaczko and Du€y, 1974; Senseny, 1977; Stelly and Dormeval, 1977; Follansbee and Gray, 1991; Gourdin and Lassila, 1992). The transient ¯ow stress typically exhibits an initial sharp increase and then gradually approaches the higher rate constant curve.

Fig. 22. Path sequence experiments for OFHC Cu: von Mises equivalent responses for quasi-static compression followed by quasi-static torsion.

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5. Conclusions This paper presents results of constant true strain rate experiments, hold time experiments, and experiments involving combined sequences of strain rate, temperature and deformation path. These OFHC Cu experiments form a comprehensive set of data for assessing model features necessary for describing thermomechanical ®nite strain material behavior, including strain rate, temperature, and path history e€ects. Including these history e€ects in predictive models is necessary to accurately describe the response to arbitrary strain and temperature events. This is especially evident during multiple changes in loading conditions and when there are continuously varying conditions. The e€ects of high strain rate deformation persist upon unloading and reloading at quasi-static strain rates, suggesting signi®cant di€erences of dislocation substructure evolution with strain rate. The rate of microstructural evolution at a given level of plastic strain and a given temperature also depends on strain rate. The strain rate and temperature history e€ects are due to the fact that the existing microstructure at the current temperature depends on strain rate, strain level and the history of formation of that microstructure. The strain rate sensitivity of the ¯ow stress is comprised of two components, the rate sensitivity at ®xed structure and the sensitivity of the evolution of the structure. Strain rate hardening within the structure of the evolution equations of internal structure variables is therefore an important aspect (cf. Klepaczko and Chiem, 1986; Estrin and Mecking, 1986, 1991; Moosbrugger and McDowell, 1990, etc.). These experiments point to the need to consider various elements within the ISV constitutive model to model material behavior over a wide range of temperatures and strain rates that might be typical of forming operations, elastic±viscoplastic impact, and machining or metal removal. For OFHC Cu over the range of temperatures and strain rates investigated, these elements must address instantaneous viscosity, viscosity of material work hardening, dynamic recovery, dynamic and static recrystallization, static thermal recovery or di€usion-driven recovery of internal structure with time at relatively higher homologous temperatures, and the in¯uence of texture and dislocation substructure on ¯ow anisotropy at large strains. Acknowledgements Support for this work was provided by the US Army Research Oce (Dr K. Iyer, monitor). Compression experiments were conducted at Sandia National Laboratories in Livermore, CA, with the support of Drs. D.A. Mosher and W.A. Kawahara. References Albertini, C., Eleiche, A.M., Montagani, M., 1985. Strain-rate history e€ects on the mechanical properties of AISI 316 stainless steel. In: Murr, L.E., Staudhammer, K.P., Meyers, M.A. (Eds.), Metallurgical Applications of Shock-Wave and High-Strain-Rate Phenomena. Marcel Dekker, New York, p. 583. ASTM Standard E209-65, 1983. Standard Practice for Compression Tests of Metallic Materials at Elevated Temperatures with Conventional or Rapid Heating Rates and Strain Rates. ASTM, Philadelphia, PA., p. 383.

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