In this work, we present a multiscale physically based constitutive law for predicting the mechanical response and texture evolution of body-centered cubic (BCC) metals as a function of strain-rate and temperature. In the model, deformation of individual single crystals results not only from the resolved shear stress along the direction of slip (Schmid law) but also from shear stresses resolved along directions orthogonal to the slip direction as well as the three normal stress components (non-Schmid effects). We account for coupled Schmid and non-Schmid effects through the modification of the resolved shear stress for both 1/2〈11 ത 1〉ሼ110ሽ and 1/2〈111 ത 〉ሼ112ሽ slip systems and the modification of the slip resistance for 1/2〈111 ത 〉ሼ112ሽ slip systems. The single crystal model is implemented into a self-consistent homogenization scheme containing a hardening law for crystallographic slip. The hardening law is based on the evolution of dislocation densities that incorporates strain-rate and temperature effects through the Peierls stress, thermally activated recovery, dislocation substructure formation and dislocation interactions. The polycrystal model is calibrated and validated using a set of mechanical and texture data collected on a tantalum-tungsten alloy, Ta-10W, at temperatures ranging from 298 K to 673 K and strain-rates from 10-3 to 2400 s-1. We show the model effectively captures the anisotropic hardening rate and texture evolution for all data using a single set of single-crystal hardening parameters. Comparisons between predictions and measured data allow us to discuss the role of slip on ሼ110ሽ and ሼ112ሽ in determining plasticity and texture evolution in Ta-10W.

we propose a modelling framework to explore the interplay between martensitic phase transformations and plastic slip in polycrystalline materials, with an eye towards computational efficiency. The resulting framework uses a convexified potential for the internal energy density to capture the stored energy associated with transformation at the meso-scale, and introduces kinetic potentials to govern the evolution of transformation and plastic slip.The framework is novel in the way it treats plasticity on par with transformation.We implement the framework in the setting of anti-plane shear, using a staggered implicit/explict update: we first use a Fast-Fourier Transform (FFT) solver based on an Augmented Lagrangian formulation to implicitly solve for the full-field displacements of a simulated polycrystal, then explicitly update the volume fraction of martensite and plastic slip using their respective stick-slip type kinetic laws. We observe that, even in this simple setting with an idealized material comprising four martensitic variants and four slip systems, the model recovers a rich variety of SMA type behaviors. We use this model to gain insight into the isothermal behavior of stress-stabilized martensite, looking at the viii effects of the relative plastic yield strength, the memory of deformation history under non-proportional loading, and several others.We extend the framework to the generalized 3-D setting, for which the convexified potential is a lower bound on the actual internal energy, and show that the fully implicit discrete time formulation of the framework is governed by a variational principle for mechanical equilibrium. We further propose an extension of the method to finite deformations via an exponential mapping. We implement the generalized framework using an existing Optimal Transport Mesh-free (OTM) solver. We then model the α-γ and α-ε transformations in pure iron, with an initial attempt in the latter to account for twinning in the parent phase. We demonstrate the scalability of the framework to large scale computing by simulating Taylor impact experiments, observing nearly linear (ideal) speed-up through 256 MPI tasks. Finally, we present preliminary results of a simulated Split-Hopkinson Pressure Bar (SHPB) experiment using the α-ε model. ix

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The use of constitutive equations to describe the electromechanical behavior of electrostrictive materials began over 100 years ago. While these equations have been used to model a host of ceramic-based and polymer-based electroactive materials, a fully characterized model has not yet been developed to predict the response of transversely isotropic polymer electrostrictives. A constitutive model is developed within a thermodynamic and hyperelastic framework that incorporates the transversely isotropic material symmetry that is present in many polymer-based electrostrictives. The resulting constitutive model is characterized for three electrostrictive polymer systems using empirical data that are available in the literature. The model has a relatively simple functional form that is easily adaptable to other polymer electrostrictive material systems.

We employ electron backscatter diffraction (EBSD) to investigate microstructural evolution of uranium during recrystallization. To understand the relationship between microstructure and recrystallization, we use measures of intra-granular misorientation within grains and near grain boundaries in both deformed (non-recrystallized) uranium and recrystallizing uranium. The data show that the level of intra-granular misorientation depends on crystallographic orientation. However, contrary to expectation, this relationship does not significantly affect the recrystallization texture. Rather, the analysis suggests that recrystallization nucleation occurs along high angle grain boundaries in the deformed microstructure. Specifically, we show that the nucleation of recrystallized grains correlates well with the spatially heterogeneous distribution of high angle boundaries. Due to the inhomogeneous distribution of high angle boundaries, the recrystallized microstructure after long times exhibits clustered distributions of