Anisotropic Damage-coupled Sheet Metal Forming Limit Analysis

Abstract

This article presents a review of the sheet metal formability analysis based on the theory of damage mechanics. Specifically, the damage anisotropy is considered. Forming limit analyses based on the anisotropic damage are summarized, including the accumulative critical damage method, the damage-coupled vertex theory and the damage-coupled acoustic tensor method. The accumulative critical damage method postulates that the critical damage at the localized necking is strain-path or loading history independent. It can be applied to predict the forming limit diagrams under either proportional or nonproportional loading. The vertex theory considers that localized necking is associated with the vertex developed on yield surface. The theory is applicable to engineering materials exhibiting the strain-hardening and/or strain-rate dependent behaviors. The acoustic tensor method, on the other hand, can only be applied to the strain-softening materials, which are often observed in warm/hot sheet metal forming or hydroforming.

Influence of surface roughness on cold formability in bending processes: a multiscale modelling approach with the hybrid damage mechanics model

“…In the coupled models, the effect of damage on plastic flow is taken into consideration. The Gurson family models [34,36,[38][39][40][41][42][43][44][45][46][47][48] and the continuum damage mechanics (CDM) models [27,[49][50][51][52][53][54] are the two famous types of coupled models that are widely applied. Based on the fundamental work of Gurson, Tvergaard, and Needleman [36,[43][44][45], the void volume fraction variable as a measure of damage effect has been integrated into the yield potential and the void nucleation, evolution and coalescence effect has been considered in the GTN model.…”

“…In the CDM models, an integral damage variable is introduced to quantify the degree of material degradation [27]. Further developments of the CDM models have been conducted by many researchers to consider kinematic hardening, anisotropy, and crack closure effects due to its relatively easy implementation [51][52][53][54]. The macroscopic consideration of damage in coupled models restricts their capability in the description of microscopic damage mechanisms.…”

Decomposition of healing tensor: In continuum damage and healing mechanics

“…Several constitutive material models have been proposed by various researchers such as elasto-plastic models (Chaboche, 1991; Kattan and Voyiadjis, 1990, 1993; Ladeveze et al., 1982; Ladeveze and Lemaitre, 1984; Lee et al., 1985; Voyiadjis, 1988; Voyiadjis and Kattan, 1990, 1992, 2012c), elasto-viscoplastic models (Chaboche, 1997; Lemaitre and Chaboche, 1990), continuum damage models (Kachanov, 1958; Voyiadjis and Kattan, 2009), and coupled elasto-plastic damage models (Chow and Jie, 2009; Lemaitre, 1985) during the past decades. In the case of damage mechanics, the damage variable (or tensor) represents the average material degradation.…”

Continuum damage mechanics for sintered powder metals

“…In the continuum damage mechanics (CDM) model a macroscopic damage indicator as an internal variable is used to represent the microdefects in the material. The kinetic evolution law of damage is derived with specified potential function within the thermodynamics framework based on the effective stress concept and the strain equivalence hypothesis or the strain energy equivalence hypothesis [16][17][18]. With the development of CDM, the damage variable is extended from scalar variable to tensor variable to describe the damage of material more generally due to the anisotropy of micro-defects [19][20][21].…”