Computational Homogenization of Polycrystals

Abstract

This paper reviews the current state-of-the-art in the simulation of the mechanical behavior of polycrystalline materials by means of computational homogenization. The key ingredients of this modelling strategy are presented in detail starting with the parameters needed to describe polycrystalline microstructures and the digital representation of such microstructures in a suitable format to perform computational homogenization. The different crystal plasticity frameworks that can describe the physical mechanisms of deformation in single crystals (dislocation slip and twinning) at the microscopic level are presented next. This is followed by the description of computational homogenization methods based on mean-field approximations by means of the viscoplastic self-consistent approach, or on the full-field simulation of the mechanical response of a representative polycrystalline volume element by means of the finite element method or the fast Fourier transform-based method. Multiscale frameworks based on the combination of mean-field homogenization and the finite element method are presented next to model the plastic deformation of polycrystalline specimens of arbitrary geometry under complex mechanical loading. Examples of application to predict the strength, fatigue life, damage, and texture evolution under different conditions are presented to illustrate the capabilities of the different models. Finally, current challenges and future research directions in this field are summarized.

References in corpus (15)

• A numerical method for computing the overall response of nonlinear composites with complex microstructure
• Structural composites for multifunctional applications: current challenges and future trends
• Fourier-based schemes for computing the mechanical response of composites with accurate local fields
• Accelerating a FFT-based solver for numerical homogenization of periodic media by conjugate gradients
• Review on Slip Transmission Criteria in Experiments and Crystal Plasticity Models
• Cu/Ag EAM Potential Optimized for Heteroepitaxial Diffusion from ab initio Data
• An FFT-based Galerkin Method for Homogenization of Periodic Media
• Finite strain FFT-based non-linear solvers made simple
• A finite element perspective on non-linear FFT-based micromechanical simulations
• Microstructure-based fatigue life model of metallic alloys with bilinear Coffin-Manson behavior
• An analysis of the influence of grain size on the strength of FCC polycrystals by means of computational homogenization
• Crystal plasticity simulation of the effect of grain size on the fatigue behavior of polycrystalline Inconel 718
• Kinematic description of crystal plasticity in the finite kinematic framework: a micromechanical understanding of F=FeFp
• Derivation of $\mathbf{F}={\mathbf{F}}^e{\mathbf{F}}^p$ as the continuum limit of crystalline slip
• Aperiodic compression and reconstruction of real world material systems based on Wang tiles

Cited by in corpus (22)

• Simulation of the Hall-Petch effect in FCC polycrystals by means of strain gradient crystal plasticity and FFT homogenization
• On the accuracy of spectral solvers for micromechanics based fatigue modeling
• Development of a thermo-mechanically coupled crystal plasticity modeling framework: application to polycrystalline homogenization
• DBFFT: A displacement based FFT approach for non-linear homogenization of the mechanical behavior
• Materials knowledge system for nonlinear composites
• Accelerated computational micromechanics
• Grain boundary strengthening of FCC polycrystals
• A Statistical Perspective for Predicting the Strength of Metals: Revisiting the Hall-Petch Relationship using Machine Learning
• Towards Quantum Computational Mechanics
• Multiscale dendritic needle network model of alloy solidification with fluid flow
• FFT-based homogenisation accelerated by low-rank tensor approximations
• Numerical analysis of several FFT-based schemes for computational homogenization
• Phase-field modeling of microstructure evolution: Recent applications, perspectives and challenges
• Effect of slip transmission at grain boundaries in Al bicrystals
• Learning from 2D: machine learning of 3D effective properties of heterogeneous materials based on 2D microstructure sections
• Universal Fourier Neural Operators for periodic homogenization problems in linear elasticity
• On the effect of slip transfer at grain boundaries on the strength of FCC polycrystals
• Experimental and numerical analysis of cyclic deformation and fatigue behavior of a Mg-RE alloy
• An analysis of (the lack of) slip transfer between near-cube oriented grains in pure Al
• Effect of ZrH2 particles on the microstructure and mechanical properties of IN718 manufactured by selective laser melting
• An analysis of the influence of the precipitate type on the mechanical behavior of Al-Cu alloys by means of micropillar compression tests
• Non-local optical response of a multi-phased quantum material