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Boundary value problems; Fast Fourier transforms; Finite element method; Iron; Numerical methods; Polycrystals; Strain; Textures, Application-oriented; Constitutive behaviors; Convergence analysis; Coupled boundary-value problems; Elasto-viscoplastic; Mechanical behavior; Microstructural deformation; Polycrystalline aggregates, Polycrystalline materials
Abstract:
The purpose of this work is the development of an efficient two-scale numerical scheme for the prediction of the local and overall mechanical behavior of polycrystalline materials with elasto-viscoplastic constitutive behavior at finite strains. Assuming scale separation, the microstructural deformations are prescribed by the kinematics of the macroscopic continuum body. The macroscopic constitutive behavior is in turn determined by the mean response of the point-wise linked microstructure which is represented by a periodic unit cell. The algorithmic formulation and numerical solution of the two locally coupled boundary value problems is based on the FE-FFT method. In particular, the presented work is concerned with the development of a CPU- and memory-efficient solution strategy for two-scale finite strain crystal plasticity simulations of polycrystalline aggregates which is based on a microstructural convergence analysis. This efficient solution strategy allows a two-scale simulation of complex macroscopic boundary value problems in a reasonable time period. In order to demonstrate the versatile use of the proposed method, three polycrystalline materials namely copper, aluminum and iron are studied with different textures for three distinct macroscopic loading conditions. On this basis, the micromechanical fields and the overall material response of an iron-based polycrystal are predicted for a deep rolling process, which serves as a testing example for a representative and application oriented simulation. © 2020 Elsevier B.V.
