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Rapid solidification in Additively Manufactured (AM) metallic materials results in the development of significant microscale internal stresses, which are attributed to the printing induced dislocation substructures. The resulting backstress due to the Geometrically Necessary Dislocations (GNDs) is responsible for the observed Tension-Compression (TC) asymmetry. We propose a combined Phase Field (PF)-Strain Gradient $J_2$ Plasticity (SGP) framework to investigate the TC asymmetry in such microstructures. The proposed PF model is an extension of Kobayashi's dendritic growth framework, modified to account for the orientation-based anisotropy and multi-grain interaction effects. The SGP model has consideration for anisotropic temperature-dependent elasticity, dislocation strengthening, solid solution strengthening, along with GND-induced directional backstress. This model is employed to predict the solute segregation, dislocation substructure and backstress development during solidification and the post-solidification anisotropic mechanical properties in terms of the TC asymmetry of rapidly solidified Fe-Cr alloys. It is observed that higher thermal gradients (and hence, cooling rates) lead to higher magnitudes of solute segregation, GND density, and backstress. This also correlates with a corresponding increase in the predicted TC asymmetry. The results presented in this study point to the microstructural factors, such as dislocation substructure and solute segregation, and mechanistic factors, such as backstress, which may contribute to the development of TC asymmetry in rapidly solidified microstructures., Comment: 30 pages, 12 figures

This work presents an open source, dislocation density based crystal plasticity modeling framework, $\rho$-CP. A Kocks-type thermally activated flow is used for accounting for the temperature and strain rate effects on the crystallographic shearing rate. Slip system-level mobile and immobile dislocation densities, as well slip system-level backstress, are used as internal state variables for representing the substructure evolution during plastic deformation. A fully implicit numerical integration scheme is presented for the time integration of the finite deformation plasticity model. The framework is implemented and integrated with the open source finite element solver, Multiphysics Object-Oriented Simulation Environment (MOOSE). Example applications of the model are demonstrated for predicting the anisotropic mechanical response of single and polycrystalline hcp magnesium, strain rate effects and cyclic deformation of polycrystalline fcc OFHC copper, and temperature and strain rate effects on the thermo-mechanical deformation of polycrystalline bcc tantanlum. Simulations of realistic Voronoi-tessellated microstructures as well as Electron Back Scatter Diffraction (EBSD) microstructures are demonstrated to highlight the model's ability to predict large deformation and misorientation development during plastic deformation., Comment: 30 pages, 19 figures, 5 tables, v2

This work proposes a dislocation density-based strain gradient $J_2$ plasticity framework that models the strength contribution due to Geometrically Necessary Dislocations (GNDs) using a lower order, Taylor hardening backstress model. An anisotropy factor is introduced to phenomenologically represent the differential hardening between grains in this $J_2$ plasticity framework. An implicit numerical algorithm is implemented for the time integration of the finite deformation plasticity model. The framework is first used to predict directional hardening due to the GND-induced backstress during cyclic loading. Deformation contours are studied to understand the substructure attributes contributing to directional hardening. The framework is then used to predict the intrinsic, grain size-dependent strengthening of polygrain ensembles. Model predictions of simulations with different grain sizes are shown to agree with the Hall-Petch effect and also with Ashby's model of hardening due to GNDs in polygrain ensembles., Comment: 21 pages, 11 figures