Accounting for local interactions in the prediction of roping of ferritic stainless steel sheets

Abstract

The effect of the spatial distribution of crystallographic orientations on roping amplitude and wavelength in ferritic stainless steel has been evaluated. The through-thickness mechanical behaviour of a sheet deformed in tension has been tested experimentally and simulated using a full-field viscoplastic fast Fourier transform formulation. These crystal plasticity simulations use orientation imaging microscopy data as input, allowing for large-scale simulation domains to be investigated while accounting for the clustering of orientations with similar deformation behaviour. The simulations predict both the local deformation response as well as the macroscopic surface roughness. The latter is compared quantitatively with experimental measurements and is shown to predict both the wavelength and amplitude of the observed roping. The results of these simulations have also been compared with previously proposed mean-field crystal plasticity simulations of roping, performed using the viscoplastic selfconsistent code, in which each crystal orientation is, at most, influenced by the behaviour of a homogenized matrix, but not by its local neighbourhood. Comparison between these two kinds of approaches thus allows us to assess the significance of the local neighbourhood on the macroscopic prediction of roping.

Use of composite voxels in FFT-based homogenization

“…An extension of the basic scheme to viscoplastic behavior of polycrystals has been studied in [18][19][20][21][22][23][24][25][26][27]. The benefits of mixing rules discussed here are expected to carry over to these situations.…”

“…The third extended the range of applicability of the Moulinec-Suquet method, originally developed for elasticity at small strains. Applications include hyperelasticity [12][13][14], heat conductivity [15,Section 12.1], thermoelasticity [16], piezoelectricity [17] and elastoviscoplasticity in polycrystals [18][19][20][21][22][23][24][25][26][27], just to name a few.…”

Computational homogenization of elasticity on a staggered grid

“…The method can also be adapted to treat problems concerning heat conductivity , thermoelasticity , large deformations , piezoelectricity , transient creeping of ice , and elasto‐viscoplasticity in polycrystals , among others. Still, the performance of all introduced numerical schemes deteriorates for media with sufficiently high contrast, in particular, for porous three‐dimensional elasticity problems.…”

“…Thus, in contrast to the CFE, IFE, and X-FEM, emphasis was put on performing solvers instead of an analysis of the local approximation capabilities. Convergence of the effective elastic moduli computed by Moulinec-Suquet's method was considered much later and proved under minimal hypotheses on the microstructural elastic tensor field [22][23][24].The method can also be adapted to treat problems concerning heat conductivity [17], thermoelasticity [25], large deformations [26][27][28], piezoelectricity [29], transient creeping of ice [30], and elasto-viscoplasticity in polycrystals [31][32][33][34][35][36][37][38][39][40][41], among others. Still, the performance of all introduced numerical schemes deteriorates for media with sufficiently high contrast, in particular, for porous three-dimensional elasticity problems.…”

FFT‐based homogenization for microstructures discretized by linear hexahedral elements

“…The FFT-based homogenization technique of Moulinec and Suquet [1,2], based upon a Lippmann-Schwinger formulation [3,4], enables the computation of effective material properties of complex microstructures discretized on a regular grid. Applications include heat conductivity [5], thermoelasticity [6], large deformations [7][8][9], piezoelectricity [10], transient creeping of ice [11], and elasto-viscoplasticity in polycrystals at small and finite strains [12][13][14][15][16][17][18][19][20][21][22]. However, there are three important limitations of the original FFT-based homogenization scheme of Moulinec-Suquet. Firstly, there are difficulties with infinitely contrasted media.…”