Stochastic modeling of discontinuous dynamic recrystallization at finite strains in hcp metals

Abstract

We present a model that aims to describe the effective, macroscale material response as well as the underlying mesoscale processes during discontinuous dynamic recrystallization under severe plastic deformation. Broadly, the model brings together two well-established but distinct approaches -first, a continuum crystal plasticity and twinning approach to describe complex deformation in the various grains, and second, a discrete Monte-Carlo-Potts approach to describe grain boundary migration and nucleation. The model is implemented within a finite-strain Fast Fourier Transform-based framework that allows for efficient simulations of recrystallization at high spatial resolution, while the grid-based Fourier treatment lends itself naturally to the Monte-Carlo approach. The model is applied to pure magnesium as a representative hexagonal closed packed metal, but is sufficiently general to admit extension to other material systems. Results demonstrate the evolution of the grain architecture in representative volume elements and the associated stress-strain history during the severe simple shear deformation typical of equal channel angular extrusion. We confirm that the recrystallization kinetics converge with increasing grid resolution and that the resulting model captures the experimentally observed transition from single-to multi-peak stress-strain behavior as a function of temperature and rate.

A review of nonlinear FFT-based computational homogenization methods

“…FFT-based computational techniques proved useful for studying the viscoelasticity of cement paste [310], mortar samples [311], cement [312] and concrete [313]. Furthermore, FFT-based techniques were used for studying explosive materials [314], secondary creep in a porous nuclear fuel [315], the thermal expansion of an energetic material [316], optical properties of deposit models for paint [317], dynamic recrystallization [318], to compute geodesics in two-dimensional media [182], fitting microstructure-property relationships [319], topology optimization [320] and for finding emerging microstructures associated to non-convex potentials [93,321].…”

An efficient temperature-dependent crystal plasticity framework for pure magnesium with emphasis on the competition between slip and twinning

“…Our SCP model is an extension of the original formulations by Chang and Kochmann (2015), Vidyasagar et al (2018), andTutcuoglu et al (2019b), which we summarize in the following to the extent necessary for subsequent discussions. As a novelty, we render the model temperature-dependent, and we modify the representation of the individual deformation modes.…”

“…Following Chang and Kochmann (2015), we introduce the Helmholtz free energy density, here dependent on temperature 𝑇 , as The twin and slip contributions to the energy density account for self-and latent hardening. We base our description of the twin hardening on Chang and Kochmann (2015), Tutcuoglu et al (2019b), while incorporating the CT effect similar to Zhang and Joshi (2012), assuming they follow the same Schmid-type behavior as TTs. 1 The hardening of TTs and CTs is assumed to follow a linear law, which leads to…”

Quantification of 3D spatial correlations between state variables and distances to the grain boundary network in full-field crystal plasticity spectral method simulations

“…Therefore, considerable experimental effort [8,18] has been devoted to the characterization of these deformation microstructure heterogeneities, both in 2D [19][20][21][22][23][24] and recently also 3D [25,26]. Nowadays, it is common practice to investigate the evolution of the deforming microstructure with full-field 3D crystal plasticity representative volume element (RVE) computer modeling [27][28][29] and compare explicitly such results to experiments [18,[30][31][32][33][34][35][36][37][38].…”