Computationally efficient predictions of crystal plasticity based forming limit diagrams using a spectral database

Abstract

is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible.This is an author-deposited version published in: https://sam.ensam.eu Handle ID: .http://hdl.handle.net/10985/13136 To cite this version :Akash GUPTA, Mohamed BEN BETTAIEB, Farid ABED-MERAIM, Surya KALIDINDIComputationally efficient predictions of crystal plasticity based forming limit diagrams using a spectral database -International Journal of Plasticity -Vol. 103, p.168-187 -2018 Any correspondence concerning this service should be sent to the repository A B S T R A C TThe present investigation focuses on the development of a fast and robust numerical tool for the prediction of the forming limit diagrams (FLDs) for thin polycrystalline metal sheets using a Taylor-type (full constraints) crystal plasticity model. The incipience of localized necking is numerically determined by the well-known Marciniak-Kuczynski model. The crystal plasticity constitutive equations, on which these computations are based, are known to be highly nonlinear, thus involving computationally very expensive solutions. This presents a major impediment to the wider adoption of crystal plasticity theories in the computation of FLDs. In this work, this limitation is addressed by using a recently developed spectral database approach based on discrete Fourier transforms (DFTs). Significant improvements were made to the prior approach and a new database was created to address this challenge successfully. These extensions are detailed in the present paper. It is shown that the use of the database allows a significant reduction in the computational cost involved in crystal plasticity based FLD predictions (a reduction of about 96% in terms of CPU time).

A multiscale constitutive model for metal forming of dual phase titanium alloys by incorporating inherent deformation and failure mechanisms

“…Most of these models are at the macroscale and they are unable to provide insight into micromechanical aspects of the forming process. There has been a limited effort in the past to get insight into the micromechanics of ductile failure (for details see references [58], [59] and references therein). Viatkina et al [58] used strain localisation as the criterion for failure in the polycrystalline aggregate and the response of each of the single crystals in the aggregate was solved using the CPFEM method.…”

“…Viatkina et al [58] used strain localisation as the criterion for failure in the polycrystalline aggregate and the response of each of the single crystals in the aggregate was solved using the CPFEM method. Gupta et al [59] used the Marciniak-Kuczynski (M-K) model at the macroscopic scale of the polycrystalline aggregate to simulate sheet-necking along with the CPFEM formulation for the nonporous single crystals. The constitutive model presented here tries to overcome this shortcoming by extending the current crystal plasticity finite element method to incorporate the effects of crystal anisotropy and the phase boundary orientation in the context of porous crystal plasticity.…”

Assessment of full field crystal plasticity finite element method for forming limit diagram prediction

“…In the group of mean field models, the classical Taylor model [40,41,42,43,44,45,46,47,48,39] and the viscoplastic self-consistent model [49,33,50,51,52,53,54,55,56,57,58,59,60] are often applied. Essentially, a crystal plasticity formulation together with a numerical homogenization scheme provides the stress-strain relation of a polycrystalline material, i.e.…”

“…As mentioned above, both the MK-model and BT are very flexible in terms of the constitutive law. Hence, these mean field polycrystal models are usually coupled with the MKmodel [40,41,42,43,44,45,46,47,48,39,49,33,50,52,51,53,54,57,55,56,58,59,60] or BT [39,57,59].…”

Development of a thermo-mechanically coupled crystal plasticity modeling framework: Application to polycrystalline homogenization

“…The use of CP models within homogenization frameworks allows to simulate the response of a full polycrystal including texture evolution by explicitly considering grain orientation and shape changes in the micro-scale (see [8] for a review). Such type of models, due to their verified predictive capacity, have been used in the prediction of the mechanical response under monotonic loading [9,10,11,12,13,14,15] , cyclic loading [16,17,18] and fatigue response [19,20,21,22,23] or to simulate forming processes such as rolling [24,25,26,27].…”