doi:10.1016/j.msea.2007.01.147 A c d s u e S © K 1 u f o s s g b p E r t a d o i 1 t 0 d Materials Science and Engineering A 464 (2007) 202–209 Instrumented anvil-on-rod tests for constitutive model validation and determination of strain-rate sensitivity of ultrafine-grained copper M. Martin a, A. Mishra b, M.A. Meyers b, N.N. Thadhani a,∗ a School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, GA 30332, United States b Department of Mechanical and Aerospace Engineering, University of California, San Diego, CA 92093, United States Received 8 December 2006; received in revised form 28 January 2007; accepted 31 January 2007 bstract Anvil-on-rod impact tests were performed on as-received (cold-rolled) OFHC copper rods and copper processed by 2- or 8-passes of equal hannel angular pressing (ECAP). The average grain size ranged from ∼30 �m for the as-received sample to ∼440 nm for the 8-pass sample. The ynamic deformation states of the samples were captured by high-speed digital photography and velocity interferometry was used to record the ample back (free) surface velocity. Computer simulations utilizing AUTODYN-2D hydrocode with the Johnson–Cook constitutive model were sed to generate free surface velocity traces and transient deformation profiles for comparison with the experimental data. The comparison of xperimental results with AUTODYN simulations provided a means for extracting the strain-rate sensitivity of copper as a function of grain size. train-rate sensitivity was found to increase as grain size decreased. 2007 Elsevier B.V. All rights reserved. trafine l t T a t a fl i i c s i n J ( eywords: Strain rate sensitivity; Grain size effects; Dynamic deformation; Ul . Introduction Nanocrystalline and ultrafine-grained (UFG) metals have nique mechanical properties (e.g., strength, hardness, and atigue resistance) that render them good candidates for vari- us structural applications [1–6]. Recent results indicate that train-rate sensitivity in UFG metals is enhanced in compari- on with conventional polycrystalline metals having micro-scale rains [7–12]. The strain-rate sensitivity of UFG copper has een studied by Gray et al. [13] by performing quasistatic com- ression tests and split Hopkinson pressure bar experiments on CAP-processed specimens. This study revealed that the strain- ate sensitivity of UFG Cu is significantly higher than that of ypical annealed, polycrystalline Cu, and its yield strength is bove that extrapolated from the Hall-Petch relation. The work escribed in this paper is an extension of what has been previ- usly done to determine the strain-rate sensitivity enhancement n UFG, ECAP-processed Cu at strain rates on the order of 103 to 05 s−1 using dynamic reverse Taylor [14] anvil-on-rod impact ests. ∗ Corresponding author. Tel.: +1 404 894 2651. E-mail address: naresh.thadhani@mse.gatech.edu (N.N. Thadhani). p o b t i a 921-5093/$ – see front matter © 2007 Elsevier B.V. All rights reserved. oi:10.1016/j.msea.2007.01.147 -grained (UFG) copper The rod-on-rigid-anvil impact experiment developed by Tay- or [14] in 1948 has become a standard method for investigating he high strain rate (∼103 to 105 s−1) response of materials. In aylor’s impact experiment, a cylindrical specimen is acceler- ted to impact a rigid anvil and deformation propagates through he cylinder as a wave. After impact, the specimen is recovered nd the changes in its dimensions are used to infer its dynamic ow strength [14,15]. This test has become a common tool for nvestigating the constitutive response of materials by attempt- ng to reproduce the final deformed shape of the specimen with a onstitutive model [15–19]. However, simply matching the final hape of the specimen does not necessarily provide a robust val- dation of the constitutive model since the deformation path is ot considered [20]. Constitutive models based on empirical relationships (i.e., ohnson–Cook [16]) as well as physically based relationships i.e., Zerilli–Armstrong [17]) have been commonly used in the ast for comparison with experimental results. It is not the intent f this paper to choose one model or type of model over another, ut simply to explain the validation method which was used in his study. In recent years, the Taylor impact test has been performed n its reverse configuration, with the rigid anvil impacting stationary rod-shaped sample, allowing for simultaneous mailto:naresh.thadhani@mse.gatech.edu dx.doi.org/10.1016/j.msea.2007.01.147 and E v [ d m t t b i [ d g i t m m v a f t w i u 2 2 u o F 8 T s M. Martin et al. / Materials Science elocity interferometry of the free (back) surface velocity 21,22] and high-speed photography of the impact and specimen eformation throughout the entire deformation event. The imple- entation of multiple time-resolved diagnostics which monitor he entire deformation event allows for development of consti- utive models and more robust validation, as described in detail y Eakins and Thadhani [20]. In the present work, a reverse Taylor anvil-on-rod impact test nstrumented with high-speed digital photography and VISAR 23] velocity interferometry was used to investigate the dynamic eformation response of copper of nano- to micro-meter scale rain size. This method has also been applied to other materials ncluding bulk metallic glass matrix composites [24]. Although it is useful to validate the extent to which a consti- utive equation predicts the dynamic deformation response of a aterial by comparing simulations and experimental data, the ethod also enables determination of the constants which pro- ide the best fit to the experimental data. In this study on Cu, u s m p ig. 1. (a) Optical micrograph of initial Cu with a grain size of 30 �m, and TEM micro -pass ECAP-processed Cu with a grain size of ∼440 nm. The grain size distribution he initial as-received Cu illustrates an extensive deformation cell substructure typic ize. ngineering A 464 (2007) 202–209 203 well-characterized material, the Johnson–Cook equation [16], or which all relevant constants except for the strain-rate sensi- ivity were previously known [16] or determined experimentally, as used to extract the effect of grain size on strain rate sensitiv- ty by examining three Cu specimens which had been processed sing 0, 2, or 8 ECAP passes. . Experimental procedure .1. Materials Commercially obtained OFHC, cold-rolled Cu was processed sing a horizontal split ECAP die with an interior channel angle f 102◦ and exterior angle of 20◦ [25]. The processing route tilized was BC, in which the sample is rotated by 90 ◦ in the ame direction between consecutive passes [26,27]. Fig. 1 shows icrographs and grain size distributions of the as-received, 2- ass and 8-pass ECAP Cu. These figures show the reduction in graphs of (b) 2-pass ECAP-processed Cu with a grain size of ∼890 nm, and (c) s of the 2- and 8-pass ECAP samples are below the corresponding micrograph. al of cold-rolled rods, and the ECAP Cu shows clear evidence of refined grain 2 e and Engineering A 464 (2007) 202–209 g r i E o E o 9 r t 2 r a t o r v [ 2 [ d d a e c s s r A i g s [ F E a r l Table 1 Experiment details including the number of ECAP passes the specimen had undergone during processing and the impact velocity Material (no. of ECAP passes) Impact velocity (m/s) Average strain rate (s−1) As-received (cold-rolled) 88 1093 2 123 1528 8 125 1557 T l 3 e t 2 m t e σ a d t p l w s a m l s T by Johnson and Cook. The strain rate constant, C, the only remaining variable, was then empirically obtained by fitting the simulated free surface velocity trace with that obtained experi- 04 M. Martin et al. / Materials Scienc rain size that occurred with increasing ECAP passes. The as- eceived Cu had an average grain size, measured using the line ntercept method on optical micrographs, of ∼30 �m. After two CAP passes the grain size had been reduced to an average size f ∼890 nm, with even further reduction to ∼440 nm after eight CAP passes. The Cu samples were machined into cylindrical specimens f 4 mm diameter and 4 mm length for static testing and rods of .4 mm diameter and 40.13 mm length for dynamic testing. The ods were lapped on both ends with 45 �m diamond suspension o insure parallel surfaces. .2. Static compression testing Compression tests were performed on the as-received (cold- olled), 2-pass and 8-pass Cu samples. The tests were performed t strain rates of 5 × 10−3 and 1 s−1 using a Satec compression esting machine. These data were used to compare the strengths f the three differently processed specimens at various strain ates. The data collected at 1 s−1 were also used to determine the alues of constants needed for modeling with the Johnson–Cook 16] equation, as described later. .3. Reverse Taylor impact tests Instrumented reverse Taylor anvil-on-rod impact tests 20,24,28], were conducted to permit correlation of simulated eformation profiles with transient deformation states recorded uring the experiment. A schematic of the reverse Taylor nvil-on-rod impact test setup is shown in Fig. 2. Complete xperimental details are described in Ref. [20]. The projectile onsisted of an 80 mm diameter 2024 Al sabot with a maraging teel rigid anvil plate (∼6.2 mm thickness) secured to the front urface. The rod-shaped samples were mounted onto a target ing and aligned with a laser beam to ensure parallel impact. n IMACON-200 high-speed digital camera, used to capture mages of the deformation of the rods during impact, was trig- ered using crush pins. The free surface velocity of the back urface of the rod was captured in each experiment by a VISAR 23] probe, which was positioned behind the sample, as seen in ig. 2. The details of each experiment, including the number of CAP passes the specimen had undergone, the impact velocity, nd average strain rate are given in Table 1. The average strain ate was defined based on the impact velocity and change in ength of the specimen [29]. Higher strain rates (on the order of Fig. 2. Schematic of the reverse Taylor anvil-on-rod impact test setup. m F p o he average strain rate was estimated using the impact velocity and change in ength of the specimen according to the method described by Meyers [29]. 600 s−1 for 125 m/s impact of the 8-pass sample) were experi- nced by the specimens during the early stages of impact, and he strain rate subsequently decreased as deformation continued. .4. Autodyn-2D modeling AUTODYN simulations of the anvil-on-rod impact experi- ents were performed to validate the constitutive response of he ECAP Cu specimens using the Johnson–Cook constitutive quation [16]. = [A + Bεn][1 + C ln ε̇∗][1 − T ∗m] (1) The unknown strain rate sensitivity constant, C, was gener- ted by fitting the simulated free surface velocity trace to that etermined experimentally using VISAR. The models were fur- her validated by comparing simulated transient deformation rofiles with the images captured during deformation. Simu- ations were run in 2D as an axisymmetric problem, and gauges ere placed on the specimen’s rear surface to track the free urface velocity; the model setup can be seen in Fig. 3. For the Johnson–Cook equation, the hardening constant, B, nd hardening exponent, n, were obtained from stress–strain data easured at ε̇ = 1 s−1. The yield strength coefficient, A, was eft at 90 MPa, the value determined by Johnson and Cook [16] ince this value represents yield stress in undeformed copper. he thermal softening exponent, m, was also left as determined entally, as described by Eakins and Thadhani [20]. ig. 3. Axisymmetric problem setup and mesh in AUTODYN-2D showing the rojectile (partial), flyer plate and specimen. The gauge on the back (free) surface f the specimen tracks the free surface velocity. M. Martin et al. / Materials Science and Engineering A 464 (2007) 202–209 205 Fig. 4. True stress–strain plots for Cu samples in as-received state and after two and eight ECAP passes (ε̇ = 5 × 10−3 and 1 s−1). F i 3 3 2 s r Table 2 Quasistatic 0.2% offset flow stress values for ECAP specimens tested in com- pression at two different (quasi-static) strain rates No. of ECAP passes Flow stress at ε̇ = 5 × 10−3 s−1 (MPa) Flow stress at ε̇ = 1 s−1 (MPa) 0 301 316 2 371 388 8 374 421 Table 3 Final axial and areal strain values measured from recovered specimens No. of ECAP passes Impact velocity (m/s) Axial strain, ε̇ = ln (Lf/L0 ) Areal strain, ε̇ = 1 − (A0/A) 0 88 0.137 0.377 2 8 t i e t t z i f r p 3 f E F T o s ig. 5. Eight-pass Cu specimen recovered after reverse Taylor anvil-on-rod mpact tests at 125 m/s. . Results and discussion .1. Static compression testing Static stress–strain curves were obtained for the as-received, - and 8-pass ECAP Cu specimens. Fig. 4 shows the true stress- train response for as-received, 2- and 8-pass ECAP Cu at strain ates of 5 × 10−3 and 1 s−1. The effects of significant deforma- m s t a ig. 6. Four of 16 high-speed digital images from (a) impact of a 2-pass ECAP Cu sp hese images show the projectile + flyer plate assembly accelerating from the left to f the impact face and decrease in specimen length. Comparison of the 2- and 8-pass pecimen. 123 0.177 0.549 125 0.169 0.518 ion during ECAP processing and the accompanying reduction n grain size on the strength of these copper specimens were vident in the static test data. It is important to note that even he as-received (0-pass) Cu sample had an extensive deforma- ion substructure due to cold-rolling consistent with the almost ero work hardening observed in the stress-strain curves shown n Fig. 4. Table 2 lists the values of the flow strengths obtained rom quasistatic experiments. For both static strain rates, these esults show an increase in flow strength with increasing ECAP asses. .2. Dynamic testing Reverse Taylor anvil-on-rod impact experiments were per- ormed on the as-received Cu specimen at 88 m/s, the 2-pass CAP Cu specimen at 123 m/s, and the 8-pass ECAP Cu speci- en at 125 m/s. A representative image of the recovered 8-pass pecimen (impacted at 125 m/s) is shown in Fig. 5, with indica- ions of its initial and final dimensions. Table 3 lists the final axial nd areal strains measured from the recovered samples. Compar- ecimen at 123 m/s and (b) impact of an 8-pass ECAP Cu specimen at 125 m/s. impact the stationary rod-shaped specimen, which deforms by mushrooming specimens shows that the 2-pass specimen is deforming more than the 8-pass 2 e and Engineering A 464 (2007) 202–209 i s d s a i a s t i o i t s 3 C f e m m s f D s t c t m o t t w e w t e a t p r w o t fi u e p w d a a Fig. 7. Simulated vs. experimental free surface velocity trace for each ECAP Cu specimen. Simulation is based on modified Johnson–Cook parameters from s ( c s 06 M. Martin et al. / Materials Scienc son of the recovered ECAP specimens showed that the 8-pass pecimen exhibited less deformation than the 2-pass specimen uring dynamic testing at a similar impact velocity, due to greater train hardening achieved during additional ECAP passes. Fig. 6 shows 4 of 16 images captured during reverse Taylor nvil-on-rod testing of the (a) 2- and (b) 8-pass ECAP Cu spec- mens. These images show the projectile + flyer plate assembly ccelerating from the left to impact the stationary rod-shaped pecimen, which is in the center of the image. It can be seen in hese images that the impact face of the specimens are expand- ng, or mushrooming, and the length is decreasing. Comparison f the 2- and 8-pass specimens shows that the 2-pass specimen s deforming more than the 8-pass specimen due to the addi- ional strain hardening endured by the 8-pass specimen during ix more ECAP passes. .3. AUTODYN-2D modeling AUTODYN simulations were performed using the Johnson– ook constitutive model with hardening constants obtained rom stress-strain data measured at strain rate of 1 s−1 and an mpirically determined strain-rate sensitivity parameter that was odified such that the simulated free surface velocity trace atched the experimentally measured velocity trace. Fig. 7 hows the comparisons between the experimentally measured ree surface velocity traces and those obtained from the AUTO- YN simulation using the Johnson–Cook model for each pecimen. It can be seen that the simulations capture details of he slope and peak of the free surface velocity and result in a very lose to fit to the experimental data. The differences between he simulation and experiment in the first step size appear to be ore obvious in the case of the 8-pass ECAP sample than the thers. We attribute this to the effects of the ultrafine grains and heir associated boundaries, the details of which are not cap- ured in the simulations. The increase in the number of grains ith increasing grain size can result in more dispersion of the lastic waves, and consequently lower amplitude reverberation, hich was observed in the experimental traces, as compared to he simulated traces. The final values of the Johnson–Cook constants used for ach case resulting in the best match to the experimental data re summarized in Table 4. The Johnson–Cook equation with he modified constants was then used to generate deformation rofiles for comparison with deformation profiles of the final ecovered samples, as well as the transient profiles recorded ith the high-speed digital camera. The dimensions of each f the recovered specimens and those from the final state of he simulation are reported in Table 5. The simulations show nal deformation geometries that differ from experimental val- es by < 7.38% in length and < 2.01% in impact face radius for ach sample. The larger error in the final length is due to the hysical measurements performed on the recovered specimens, hich had slightly non-parallel ends and non-round impact face ue to secondary impact in catch tank. The experimental and simulated length and impact face radius t transient times are compared in Tables 6 and 7 for the 2-pass nd 8-pass samples, respectively. These results demonstrate a t p b p tress-strain data and empirical fit to the experimental free surface velocity trace. a) Initial Cu, 88 m/s, (b) 2-pass Cu, 123 m/s, and (c) 8-pass Cu, 125 m/s. lose match (<2.7% difference for each time) of these dimen- ions between simulations and experiments for each of the ransient times, indicating that the model provides an accurate rediction of the deformation, and the constants obtained can e used to further investigate the deformation response. Com- arisons of the simulated and experimental transient profiles of M. Martin et al. / Materials Science and Engineering A 464 (2007) 202–209 207 Table 4 Modified Johnson–Cook parameters used in AUTODYN simulations No. of ECAP passes Yield stress, A (MPa) Hardening constant, B (MPa) Hardening exponent, n Strain rate constant, C Thermal softening exponent, m 0 90 340 0.0334 0.009 1.09 2 90 390 0 0.011 1.09 8 90 423 0 0.017 1.09 A and m were left as determined by Johnson and Cook [16], B and n were determined using σ = Bεn in the plastic range of the stress–strain data obtained at ε̇ = 1 s−1, and C was then determined by empirically fitting the simulations to the experimental data. Table 5 Comparison of final dimensions from simulations and experiments No. of ECAP passes Lf (mm) %Difference Rf at impact face (mm) %Difference 0 Expt: 35.00 7.23 Expt: 5.97 2.01 Sim: 37.53 Sim: 6.09 2 Expt: 33.63 7.03 Expt: 6.96 1.01 Sim: 36.17 Sim: 7.03 8 Expt: 33.88 7.38 Expt: 6.73 1.93 Sim: 36.38 Sim: 6.86 Experimental values were measured from recovered specimens, which had undergone secondary impact in the catch tank, resulting in non-parallel ends or imperfectly round cross sections, and subsequently a small amount of error associated with measurement of these values, so average values are reported. Table 6 Transient dimensions of the 2-pass ECAP specimen during deformation obtained from high-speed digital images during the experiment and from simulations at corresponding times Time (�s) L (Expt) (mm) L (Sim) (mm) %Difference in length R (Expt) (mm) R (Sim) (mm) %Difference in radius 12.49 38.67 ± 0.09 38.69 0.06 5.93 ± 0.08 5.75 1.55 21.93 37.80 ± 0.11 37.82 0.04 6.28 ± 0.18 6.29 0.06 31.37 36.94 ± 0.17 37.10 0.43 6.59 ± 0.14 6.65 0.43 40.81 36.37 ± 0.10 36.53 0.43 6.91 ± 0.23 6.91 0.00 50.26 36.16 ± 0.10 36.19 0.07 6.83 ± 0.43 7.02 1.41 Table 7 Transient dimensions of the 8-pass ECAP specimen during deformation obtained from high-speed digital images during the experiment and from simulations at corresponding times Time (�s) L (Expt) (mm) L (Sim) (mm) %Difference in length R (Expt) (mm) R (Sim) (mm) %Difference in radius 14.15 38.28 ± 0.06 38.53 0.66 6.06 ± 0.14 5.81 2.03 24.14 37.51 ± 0.20 37.63 0.31 6.40 ± 0.17 6.33 0.52 33.82 36.43 ± 0.06 36.99 1.55 6.72 ± 0.27 6.64 0.57 4 5 t i u s c m ( c J o i E received Cu samples. The plot of flow strengths also indicates the effect of strain rate on the flow strength, with a ∼42% increase in strength of the as-received Cu versus a ∼53% increase for the 8-pass ECAP Cu over strain rates of seven orders of magnitude. Table 8 Dynamic flow stress values calculated using the Johnson–Cook equation No. of ECAP passes Dynamic flow stress, Johnson–Cook 3.65 36.44 ± 0.28 36.50 0.15 3.49 36.44 ± 0.03 36.31 0.37 he 2- and 8-pass ECAP Cu specimens at selected times during mpact are shown in Fig. 8. A close correlation, within the pixel ncertainty associated with the image resolution, between the imulated and experimental deformation states is observed. The orrelation provides further validation that the Johnson–Cook odel is accurately describing deformation of the as-received cold-rolled) and ECAP Cu, so the significance of each constant an be further evaluated. Values of the dynamic flow stress were calculated using the ohnson–Cook equation, and are listed in Table 8. The variation f flow strength as a function of strain rate for each specimen s plotted in Fig. 9. It can be seen from this plot that the 8-pass CAP sample is consistently stronger than the 2-pass and as- 0 2 8 6.66 ± 0.22 6.82 1.19 6.52 ± 0.19 6.87 2.70 (Eq. (1)) (MPa) 427 513 571 208 M. Martin et al. / Materials Science and Engineering A 464 (2007) 202–209 Fig. 8. Radius as a function of distance from impact end plots comparing Johnson–Cook simulations with the experimental transient deformation pro- fi i m C C t t s u [ p a t i p c F s e r e s v i o 4 s a d u c e s o s t b 0 s p A n a s F References les at various times after impact of the (a) 2- and (b) 8-pass ECAP Cu samples mpacted at 123 and 125 m/s, respectively. (a) shows a marker indicating the aximum pixel uncertainty corresponding to the image resolution. Table 4 lists a strain rate constant of 0.009 for the as-received u, 0.011 for 2-pass ECAP Cu, and 0.017 for the 8-pass ECAP u, which are the strain rate constants that provided the best fit of he simulation to the experimental free surface velocity trace and ransient profiles. These values show an increase in strain-rate ensitivity of the ECAP samples, which is due to the effect of ltrafine grain size, consistent with that observed in other studies 9,13]. The strain rate sensitivity of the as-received Cu is com- arable with that for microcrystalline fcc materials including Cu s determined by Conrad [30] (Conrad found a strain rate sensi- ivity of 0.004.). The 2-pass ECAP specimen shows only a slight ncrease in strain rate sensitivity compared to the initial sample, ossibly due to incomplete formation of sub-grain structure. In ontrast, the 8-pass ECAP sample, with a ∼440 nm grain size, ig. 9. Flow strengths of the ECAP Cu specimens at different strain rates ranging even orders of magnitude. xhibited nearly twice as much strain-rate sensitivity as the as- eceived Cu. These results are consistent with the mechanism xplained by Goeken et al. [8], who have observed an enhanced train rate sensitivity corresponding to a decrease in activation olume V = ( √ 3kT/σm), which has been attributed to a change n the rate-controlling mechanism from forest dislocations to ther behaviors in the ultrafine grain size domain. . Conclusions The dynamic deformation of as-received (cold-rolled) and ubsequently ECAP-processed Cu tested using reverse Taylor nvil-on-rod impact experiments was captured by high speed igital photography and compared with AUTODYN-2D sim- lations using the Johnson–Cook constitutive equation with onstants obtained from stress–strain data and by fitting to an xperimentally measured free surface velocity trace. 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