A crystal plasticity model for slip in hexagonal close packed metals based on discrete dislocation simulations

Abstract

This work develops a method for calibrating a crystal plasticity model to the results of discrete dislocation (DD) simulations. The crystal model explicitly represents junction formation and annihilation mechanisms and applies these mechanisms to describe hardening in hexagonal close packed metals. The model treats these dislocation mechanisms separately from elastic interactions among populations of dislocations, which the model represents through a conventional strength-interaction matrix. This split between elastic interactions and junction formation mechanisms more accurately reproduces the DD data and results in a multi-scale model that better represents the lower scale physics. The fitting procedure employs concepts of machine learning—feature selection by regularized regression and cross-validation—to develop a robust, physically accurate crystal model. The work also presents a method for ensuring the final, calibrated crystal model respects the physical symmetries of the crystal system. Calibrating the crystal model requires fitting two linear operators: one describing elastic dislocation interactions and another describing junction formation and annihilation dislocation reactions. The structure of these operators in the final, calibrated model reflect the crystal symmetry and slip system geometry of the DD simulations.

Flow Stress of beryllium: Attempt for a Bayesian Crossed-data Analysis from Hopkinson Bars to Rayleigh-Taylor Instabilities

“…Another possible deformation mechanism for beryllium is the onset and migration of twins [18] of the {1012} 1011 system, a mechanism strongly dependent on the direction of loading with respect to the crystal orientation [19]. Since the twinning boundaries are strong barrier for dislocations (Hall-Petch type mechanism), the density of twins play a role is the hardening mechanisms, but with its own threshold and kinetics [20]. A model aiming at modeling plasticity and twinning should have dedicated parameters, which was not in the scope of the PTW model.…”

Combined Effects of Texture and Grain Size Distribution on the Tensile Behavior of α-Titanium

“…Although in elasto-viscoplasticity all non-zero shear stress levels produce some slip, can be described as the critical resolved shear stress (CRSS) given the values considered for (see further Table 2 ). It writes as the sum of the lattice friction stress and a generalized dislocation strengthening relation that accounts for dislocation interactions between systems [ 35 , 36 ]. Moreover, following references [ 2 , 4 , 10 , 11 , 12 , 13 ], is also assumed to depend on the individual grain size in a Hall–Petch type relationship: denotes the interaction coefficient which is related to the strength of the interaction between system and .…”

From mechanism-based to data-driven approaches in materials science

“…A clever way to parametrize the constitutive model for CP from DDD has been shown in Messner et al (2017). The CP model was developed to describe the slip resistance on a slip system taking into account interaction with all other slip systems by an interaction matrix H. The evolution of the dislocation density was described by another matrix K. Technically H and K have 1521 and 59319 free parameters, but the authors reduce these numbers by taking into account crystal and physical symmetries in the system and applying LASSO regression.…”

“…So the search for a way to enable machine crafted features is in our opinion the main issue for ML approaches to DDD. In CP, the route is more straightforward and the two publications discussed above (Messner et al 2017;Pandey and Pokharel 2020) have already shone light on what can be done. Crystallographic information can be incorporated into the underlying constitutive model via LASSO or other regularization methods.…”