Damage accumulation and fracture initiation in uncracked ductile solids subject to triaxial loading

Abstract

A damage plasticity model for ductile fracture is proposed. This model is established on the cylindrical coordinate system of principal stress space. Experimental results show that fracture initiation in uncracked ductile solids is sensitive to the hydrostatic pressure and dependent on the Lode angle. The joint effects of pressure and Lode angle define a fracture envelope in principal stress space. Plastic deformation induced damage is calculated by an integral of the damage rate measured at current loading and deformation status with respect to the fracture envelope. A power law damage rule is proposed to characterize the nonlinearity in damage accumulation. A damage-related weakening factor is adopted to describe the material deterioration. The material parameters are calibrated from standard laboratory tests. The proposed model is numerically implemented. Four simulations with emphasis on crack path prediction are presented.

Damage prediction in single point incremental forming using an extended Gurson model

“…Moreover, the GTN model uncouples this damage parameter with hardening. Other models like the one proposed by Xue (2007) or the Lemaitre model used by Ben Hmida (2014), which predicts failure in the SPIF process, couple the damage evolution and failure with the plastic strain. This research indicates that the developed failure mode cannot be predicted by the classical assumptions of the GTN model.…”

“…Malhotra et al (2012) used the Xue (2007) damage model to predict the mechanics of fracture on a SPIF cone and funnel through FE simulations. The Xue (2007) model is a coupled damage model which combines plastic strain, hydrostatic pressure and shear on fracture. One of the main features of this model is that not only damage accumulation and fracture can be predicted, but also the occurrence of diffused and localized necking (Xue and Belytschko, 2010).…”

“…The Lemaitre model is based on the strain equivalence principle, which establishes a coupling between hardening and the damage variable. Malhotra et al (2012) used a fracture model developed by Xue (2007). This model leads to good results when predicting the force and the depth at which fracture happens.…”

“…This model leads to good results when predicting the force and the depth at which fracture happens. In the Xue (2007) model, the damage evolution is function of the ratio of plastic strain and the fracture strain (the self-similarity hypothesis). In both cases, the main difference with the GTN model is that the damage models present a coupling between damage and the plastic strain.…”

“…Originally, the Gurson (1977) model was developed to represent the deterioration of a porous material, based on unit-cells calculations. On the contrary, the Xue (2007) model is based on a theory where the plastic damage incorporates all the three stress invariants.…”