Prediction of Plastic Instability in Sheet Metals During Forming Processes Using the Loss of Ellipticity Approach

Abstract

The prediction of plastic instability in sheet metals during forming processes represents nowadays an ambitious challenge. To reach this goal, a new numerical approach, based on the loss of ellipticity criterion, is proposed in the present contribution. A polycrystalline model is implemented as a user-material subroutine into the ABAQUS/Implicit finite element (FE) code. The polycrystalline constitutive model is assigned to each integration point of the FE mesh. To derive the mechanical behavior of this polycrystalline aggregate from the behavior of its microscopic constituents, the multiscale self-consistent scheme is used. The mechanical behavior of the single crystals is described by a finite strain rateindependent constitutive framework, where the Schmid law is used to model the plastic flow. The condition of loss of ellipticity at the macroscale is used as plastic instability criterion in the FE modeling. This numerical approach, which couples the FE method with the self-consistent scheme, is used to simulate a deep drawing process, and the above criterion is used to predict the formability limit of the studied sheets during this operation.

An advanced elastoplastic framework accounting for induced plastic anisotropy fully coupled with ductile damage

“…Then, the use of the error function (50) does not provide a significant improvement of the identification strategy. Hence, for the sake of simplicity and in order to reduce the computational effort required by the application of the identification procedures, one chooses to use the error function (49).…”

“…Therefore, the macroscopic tangent modulus , which is the main unknown variable in the self-consistent approach, is computed by using the iterative fixed-point method. Further details about the application of this method to solve the self-consistent equations can be found in [45,49].…”

“…Moreover, the equilibrium condition across the grain boundaries is satisfied within the self-consistent approach. This scheme has been coupled in several recent contributions with the FE method [45,[48][49][50]. The fullfield homogenization approaches are generally based on solving the multiscale equations by means of -5-the FE method, after spatial discretization of the studied polycrystalline aggregate [51][52][53].…”