Joint crystal plasticity and phase field models

Introduction to the crystal plasticity method

Crystal plasticity modeling methods (CP) are continuum field approaches for the simulation of elastic-plastic material deformation where the underlying elementary shear carriers such as dislocations or twins follow tensorial kinematics.

Deformation resistance on each of these discrete shear systems is often described in terms of material- and defect specific self-hardening and latent hardening laws.

The resulting differential equations can be solsved using homogenization models, the finite element method or FFT based spectral solvers.

Results of such simulations are stresses, strain, crystallographic textures as well as detailed insights on the activated deformation systems and collective effects at a grain and subgrain scale.

 

Introduction to the phase field method

The phase field method applies diffusion-type kinetic evolution equations to Landau-type energy landscapes. It is derived from the time dependent Ginzburg-Landau equation and can be applied to conserved as well as to not conserved field variables which may either represent atomic species or microstructural phases or crystals. 

 

 

Projects where we combine crystal plasticity with phase field simulations to simulate coupled chemo-structural-mechanical problems

Elasto-viscoplastic phase field modelling of anisotropic cleavage fracture

Elasto-viscoplastic phase field modelling of anisotropic cleavage fracture
J. Mech. Phys. Solids 99 (2017) 19–34
JMPS 2017 Elasto-viscoplastic phase fiel[...]
PDF-Dokument [1.4 MB]

A finite-strain anisotropic phase field method is developed to model the localisation of damage on a defined family of crystallographic planes, characteristic of cleavage fracture in metals. The approach is based on the introduction of an undamaged configuration, and the inelastic deformation gradient mapping this configuration to a damaged configuration is microstructurally represented by the opening of a set of cleavage planes in the three fracture modes. Crack opening is modelled as a dissipative process, and its evolution is thermodynamically derived. To couple this approach with a physically-based phase field method for brittle fracture, a scalar measure of the overall local damage is introduced, whose evolution is determined by the crack
opening rates, and weakly coupled with the non-local phase field energy representing the crack opening resistance in the classical sense of Griffith. A finite-element implementation of the proposed model is employed to simulate the crack propagation path in a laminate and a polycrystalline microstructure. As shown in this work, it is able to predict the localisation of damage on the set of pre-defined cleavage planes, as well as the kinking and branching of the
crack resulting from the crystallographic misorientation across the laminate boundary and the grain boundaries respectively.

 

A phase-field model for incoherent martensitic transformations including plastic accommodation processes in the austenite

A phase-field model for incoherent martensitic transformations including plastic accommodation processes in the austenite
Journal of the Mechanics and Physics of Solids 59 (2011) 2082–2102
phase-field-model-martensitic-transforma[...]
PDF-Dokument [1.4 MB]

A phase field model for damage in elasto-viscoplastic materials

A phase field model for damage in elasto-viscoplastic materials
Comput. Methods Appl. Mech. Engrg. 312 (2016) 167–185
phase field damage elasto-viscoplastic m[...]
PDF-Dokument [2.3 MB]

A phase field method for brittle fracture is formulated for a finite strain elasto-viscoplastic material using a novel obstacle phase field energy model. The obstacle energy model results in a crack profile with compact support, and thus gives a physically realistic description of the material behaviour at the vicinity of the crack tip. The resulting variational inequality is discretised by a finite element method, and is efficiently solved using a reduced space NEWTON method. The solution accuracy and numerical performance of this method is compared with a conventional phase field energy model for brittle fracture through representative
examples, and a significant reduction in the numerical solution cost is demonstrated.

 

Coupled Crystal Plasticity–Phase Field Fracture Simulation Study on Damage Evolution Around a Void: Pore Shape Versus Crystallographic Orientation

Coupled Crystal Plasticity–Phase Field Fracture Simulation on Damage Evolution
JOM, Vol. 69, No. 5, 2017
Crystal Plasticity Phase Field Fracture [...]
PDF-Dokument [987.3 KB]

Various mechanisms such as anisotropic plastic flow, damage nucleation, and
crack propagation govern the overall mechanical response of structural materials. Understanding how these mechanisms interact, i.e. if they amplify mutually or compete with each other, is an essential prerequisite for the design of improved alloys. This study shows—by using the free and open source software DAMASK (the Dusseldorf Advanced Material Simulation Kit)—how the coupling of crystal plasticity and phase field fracture methods can increase the understanding of the complex interplay between crystallographic orientation and the geometry of a void. To this end, crack initiation and propagation around an experimentally obtained pore with complex shape is investigated and compared to the situation of a simplified spherical void. Three different crystallographic orientations of the aluminum matrix hosting the defects are considered. It is shown that crack initiation and propagation depend in a non-trivial way on crystallographic orientation and its associated plastic behavior as well as on the shape of the pore.

 

Constitutive modeling of strain induced grain boundary migration via coupling crystal plasticity and phase-field methods

Strain induced grain boundary migration
International Journal of Plasticity 99 (2017) 19
IJP 2017 crystal plasticity and phase-fi[...]
PDF-Dokument [1.8 MB]

In this project we used a thermodynamically consistent finite-deformation-based constitutive theory to describe strain induced grain boundary migration due to the heterogeneity of stored deformation energy in a plastically deformed polycrystalline cubic metal. Considering a representative volume element, a mesoscale continuum theory is developed based on the coupling between dislocation density-based crystal plasticity and phase field methods. Using the Taylor model-based homogenization method, a multiscale coupled finite-element and phase-field staggered time integration procedure is developed and implemented into the Abaqus/Standard finite element package via a user-defined material subroutine. The developed constitutive model is then used to perform numerical simulations of strain induced grain boundary migration in polycrystalline tantalum. The simulation results are shown to qualitatively and quantitatively agree with experimental results.

 

 

Acta Mat. 2011, 59, p. 364