We investigate the temperature and rate dependence of slip, twinning, and secondary twinning in high-purity hexagonal close packed a-Zr over a wide range of temperatures and strain rates (from 76 K to 673 K and 0.001 s À1 to 4500 s À1 ). To reliably identify the dominant deformation mechanisms for each condition, we employ electron-backscattered diffraction (EBSD), dislocation theory, multi-scale polycrystal constitutive modeling, and a thermally activated dislocation density evolution based hardening law. We demonstrate with direct comparison with measurement that the constitutive model, with a single set of intrinsic material parameters, can predict the underlying texture evolution, primary and secondary slip and twin activity, and twin volume fraction associated with the different loading orientations and applied temperatures and strain rates. We find that the f1 0 1 2gh1 0 1 1i twin is the preferred tension twin, either as a primary or secondary twin depending on the sample orientation, over the broad temperature and strain rate range tested. In contrast, we show that the preferred contraction twin, whether f1 1 2 2gh1 1 2 3i or f1 0 1 1gh1 0 1 2i, is sensitive to temperature but insensitive to strain rate and whether it is a primary or secondary twin. Based on the concomitant changes in the dominant slip mode predicted by the model and revealed by the texture development, we rationalize that the temperature-induced transition in contraction twinning is due to the increased predominance of basal hai slip at high temperatures (>673 K). Last, our analysis implies that all twin modes studied are rate insensitive and so the strong influence of strain rate and temperature on twinning is due to the rate-sensitivity of slip.

We develop a polycrystal plasticity constitutive law based on the elasto-plastic self-consistent (EPSC) theory for the prediction of cyclic tension-compression deformation. The crystallography based model integrates a dislocation based hardening model and accounts for inter-granular stresses and slip system level backstresses, which make it capable of capturing non-linear unloading and the Bauschinger effect (BE). Furthermore, the model features dissolution of dislocation population upon the load reversal, which enables it to predict the change in hardening rate during reverse loading from that during forward loading. To demonstrate these capabilities of the model, we investigate elasto-plastic behavior of AA6022-T4 sheets under in-plane cyclic tension-compression. From a set of carefully performed cyclic tests to several strain levels, we observe that the material exhibits (1) a typical decreasing hardening rate during forward loading, (2) a linear followed by non-linear unloading upon the load reversal, (3) a transient softening followed by rapid work hardening (the BE), and (4) a decrease in subsequent hardening rate during reverse loading (the permanent softening phenomenon). To predict these effects, we calibrate the model to establish a set of material parameters using a portion of the measured data. The remaining measured data is used for verification of the model. We show that using the single set of material parameters, the developed model is capable of predicting all the particularities pertaining to the cyclic deformation of the material with great accuracy. From the favorable comparison of the predictions and experimental data, we infer first that the non-linearity of unloading increases with the amount of pre-strain, next that the backstresses have a dominant effect in capturing non-linear unloading while both the backstresses and inter-granular stresses govern the BE, and finally that the inclusion of reversible dislocation motion is the key for capturing hardening rates during reverse loading.

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a b s t r a c tIn this work, we develop a polycrystal mean-field constitutive model based on an elastic-plastic selfconsistent (EPSC) framework. In this model, we incorporate recently developed subgrain models for dislocation density evolution with thermally activated slip, twin activation via statistical stress fluctuations, reoriented twin domains within the grain and associated stress relaxation, twin boundary hardening, and de-twinning. The model is applied to a systematic set of strain path change tests on pure beryllium (Be). Under the applied deformation conditions, Be deforms by multiple slip modes and deformation twinning and thereby provides a challenging test for model validation. With a single set of material parameters, determined using the flow-stress vs. strain responses during monotonic testing, the model predicts well the evolution of texture, lattice strains, and twinning. With further analysis, we demonstrate the significant influence of internal residual stresses on (1) the flow stress drop when reloading from one path to another, (2) deformation twin activation, (3) de-twinning during a reversal strain path change, and (4) the formation of additional twin variants during a cross-loading sequence. The model presented here can, in principle, be applied to other metals, deforming by multiple slip and twinning modes under a wide range of temperature, strain rate, and strain path conditions.

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