Formability prediction using bifurcation criteria and GTN damage model

Abstract

In this paper, four plastic instability criteria, which are based on the bifurcation theory, are coupled with the GTN damage model for the prediction of diffuse and localized necking. General bifurcation (GB) criterion and limit-point bifurcation (LPB) criterion are used to predict diffuse necking, while loss of ellipticity (LOE) criterion and loss of strong ellipticity (LOSE) criterion are used to predict localized necking. The resulting constitutive equations and instability criteria are implemented into the finite element code ABAQUS/Standard. The constitutive equations are formulated within the framework of large deformations and fully three-dimensional approach. Since the developed numerical tools have intended applications mainly for thin sheet metals; therefore, the plane-stress conditions are considered within the instability criteria. The present contribution focuses on the effect of destabilizing mechanisms, due to non-associative plasticity and non-normal plastic flow rule, on the prediction of forming limit diagrams (FLDs). Theoretical classification of the bifurcation criteria, in terms of their order of prediction of critical necking strains, is first presented. Then, several variants of the GTN model are combined with the bifurcation criteria for the prediction of FLDs for fictitious materials. It is shown that the hierarchical prediction order of the different instability criteria is consistent with the theoretical classification, for all the considered variants of the GTN model. More specifically, it is shown that the GB criterion provides a lower bound to all bifurcation criteria, in terms of necking prediction, while the LOE criterion represents an upper bound.

Damage and fracture analyses of wire with V‐shaped microcrack on multi‐pass drawing under back tensions

“…Therefore, this model can better reflect the microstructure of material than the other damage models. Meanwhile, the GTN model has an advantage of being simple for implementation in standard FE codes and has been widely used in ductile damage community 29–31 . The following is a detailed introduction about the model.…”

“…Meanwhile, the GTN model has an advantage of being simple for implementation in standard FE codes and has been widely used in ductile damage community. [29][30][31] The following is a detailed introduction about the model. The plastic potential of ductile failure predicted is expressed as follows 32 :…”

Numerical analyses of damage behavior of wire with inclusion in multipass drawing process

“…Meanwhile, its void volume has clearer geometric and physical meaning than other meso‐damage variables (such as microcrack density). In addition, the GTN model is one of the most widely used damage models in the study of plastic damage of porous metals 37,38 . Considering comprehensively, it will be a meaningful decision to choose the GTN model as the wire material model other than inclusions.…”

“…In addition, the GTN model is one of the most widely used damage models in the study of plastic damage of porous metals. 37,38 Considering comprehensively, it will be a meaningful decision to choose the GTN model as the wire material model other than inclusions. The model will be introduced in detail in the following part.…”

Numerical Analysis of the Damage Evolution of DP600 Steel Using Gurson–Tvergaard–Needleman Model

“…After the modifications to Gurson's constitutive equations, the model is called as "GTN model" and enabled to predict ductile damage in metals. Researchers have carried out numerous studies to model ductile fracture for different applications, including tensile testing, [10][11][12][13][14][15] formability limit diagrams, [16][17][18][19][20] small punch tests, [21][22][23] electromagnetic impaction, [24] Charpy V-notch test, [25,26] bending, [27][28][29] tube hydroforming, [30,31] roll forming. [32] The constitutive equations of the GTN damage model require nine different parameters.…”