Strain localization analysis using a large deformation anisotropic elastic–plastic model coupled with damage

Abstract

Sheet metal forming processes generally involve large deformations together with complex loading sequences. In order to improve numerical simulation predictions of sheet parts forming, physically-based constitutive models are often required. The main objective of this paper is to analyze the strain localization phenomenon during the plastic deformation of sheet metals in the context of such advanced constitutive models. Most often, an accurate prediction of localization requires damage to be considered in the finite element simulation. For this purpose, an advanced, anisotropic elastic-plastic model, formulated within the large strain framework and taking strain-path changes into account, has been coupled with an isotropic damage model. This coupling is carried out within the framework of continuum damage mechanics. In order to detect the strain localization during sheet metal forming, Rice's localization criterion has been considered, thus predicting the limit strains at the occurrence of shear bands as well as their orientation. The coupled elastic-plastic-damage model has been implemented in Abaqus/Implicit. The application of the model to the prediction of Forming Limit Diagrams (FLDs) provided results that are consistent with the literature and emphasized the impact of the hardening model on the strain-path dependency of the FLD. The fully threedimensional formulation adopted in the numerical development allowed for some new results -e.g. the out-of-plane orientation of the normal to the localization band, as well as more realistic values for its in-plane orientation.

Determination of Forming Limit Diagrams Based on Ductile Damage Models and Necking Criteria

“…The expression of the latter is given by the following relationship (see, e.g., Haddag et al, 2009;Mansouri et al, 2014): (17) and (28), respectively). The fourth-order tensors 1 L , 2 L and 3 L , which only depend on Cauchy stress components, result from the large strain framework.…”

Bifurcation Analysis Versus Maximum Force Criteria in Formability Limit Assessment of Stretched Metal Sheets

“…Indeed, while the M-K analysis and Maximum Force Criteria (MFC) have been widely used in the literature, few applications of Rice's strain localization theory to sheet metal formability have been published, and they are mostly restricted to plane-stress assumptions and simple constitutive models [see, e.g., Doghri and Billardon, 1995]. Recently, Rice's bifurcation criterion has been used to investigate formability limits of metallic materials (see, Haddag et al [2009] and Mansouri et al [2014] using phenomenological constitutive modeling and Franz et al [2009] using micromechanical approaches). Besides its sound theoretical basis, this bifurcation criterion has also been shown to provide a useful tool to investigate the impact of microstructural mechanisms on the formability limit of multiphase polycrystalline materials [Franz et al, 2011;.…”

Laser heating induced plastic deformation in a pre-elastic-stretched titanium alloy strip

“…The plastic deformation concentration of the materials under pure mechanical loading was extensively discussed by many literatures. For instance, Doghri and Billardon [10] investigated the localized plastic deformation for rate-independent plasticity, Haddag et al [11] set up a large deformation anisotropic elastic-plastic model to describe the plastic strain concentration, Kobayashi [12] analyzed this phenomenon via a proposed theory of ultrasonic wave velocity, Bychkov and Karpinskii [13] studied the localized plastic behavior in a thermoviscoplastic rod in dynamic tension by the methods of linear perturbation analysis. Considering that fact that temperature elevation is also a kind of disturbance, the plastic strain concentration of the structure subjected to both thermal and mechanical loadings also attracted many interests.…”