The Mohr–Coulomb (M–C) fracture criterion is revisited with an objective of describing ductile fracture of isotropic crack-free solids. This criterion has been extensively used in rock and soil mechanics as it correctly accounts for the effects of hydrostatic pressure as well as the Lode angle parameter. It turns out that these two parameters, which are critical for characterizing fracture of geo-materials, also control fracture of ductile metals (Bai and Wierzbicki 2008; Xue 2007; Barsoum 2006; Wilkins et al. 1980). The local form of the M–C criterion is transformed/extended to the spherical coordinate system, where the axes are the equivalent strain to fracture $${\bar \varepsilon_f}$$
 , the stress triaxiality η, and the normalized Lode angle parameter $${\bar \theta}$$
 . For a proportional loading, the fracture surface is shown to be an asymmetric function of $${\bar \theta}$$
 . A detailed parametric study is performed to demonstrate the effect of model parameters on the fracture locus. It was found that the M–C fracture locus predicts almost exactly the exponential decay of the material ductility with stress triaxiality, which is in accord with theoretical analysis of Rice and Tracey (1969) and the empirical equation of Hancock and Mackenzie (1976), Johnson and Cook (1985). The M–C criterion also predicts a form of Lode angle dependence which is close to parabolic. Test results of two materials, 2024-T351 aluminum alloy and TRIP RA-K40/70 (TRIP690) high strength steel sheets, are used to calibrate and validate the proposed M–C fracture model. Another advantage of the M–C fracture model is that it predicts uniquely the orientation of the fracture surface. It is shown that the direction cosines of the unit normal vector to the fracture surface are functions of the “friction” coefficient in the M–C criterion. The phenomenological and physical sound M–C criterion has a great potential to be used as an engineering tool for predicting ductile fracture.

Application of extended Mohr–Coulomb criterion to ductile fracture

Failure of metals I : brittle and ductile fracture

A model for the axisymmetric growth and coalescence of small internal voids in elastoplastic solids is proposed and assessed using void cell computations. Two contributions existing in the literature have been integrated into the enhanced model. The first is the model of Gologanu-Leblond-Devaux, extending the Gurson model to void shape effects. The second is the approach of Thomason for the onset of void coalescence. Each of these has been extended heuristically to account for strain hardening. In addition, a micromechanically-based simple constitutive model for the void coalescence stage is proposed to supplement the criterion for the onset of coalescence. The fully enhanced Gurson model depends on the flow properties of the material and the dimensional ratios of the void-cell representative volume element. Phenomenological parameters such as critical porosities are not employed in the enhanced model. It incorporates the effect of void shape, relative void spacing, strain hardening, and porosity. The effect of the relative void spacing on void coalescence, which has not yet been carefully addressed in the literature. has received special attention. Using cell model computations, accurate predictions through final fracture have been obtained for a wide range of porosity, void spacing, initial void shape, strain hardening, and stress triaxiality. These predictions have been used to assess the enhanced model. (C) 2000 Elsevier Science Ltd. All rights reserved.

An extended model for void growth and coalescence - application to anisotropic ductile fracture

Ductile fracture: Experiments and computations

Ductile fracture experiments with locally proportional loading histories

Effects of the stress state on plasticity and ductile failure of an aluminum 5083 alloy

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On stress-state dependent plasticity modeling: Significance of the hydrostatic stress, the third invariant of stress deviator and the non-associated flow rule

The main purpose of this paper is to demonstrate that besides the stress triaxiality parameter, the Lode angle, which can be related to the third invariant of the deviatoric stress tensor, also has an important effect on ductile fracture. This is achieved by conducting a series of micromechanics analyses of void-containing unit cells and experimental-numerical studies of carefully designed specimens experiencing a wide range of stress states. As a result, a fracture criterion is expressed in terms of the equivalent failure strain as a function of the stress triaxiality and the Lode angle (or the third invariant of the stress deviator) and this function is calibrated for a DH36 steel plate.

Charles Roe

Papers

Effects of the stress state on plasticity and ductile failure of an aluminum 5083 alloy

On stress-state dependent plasticity modeling: Significance of the hydrostatic stress, the third invariant of stress deviator and the non-associated flow rule

A Study on the Effect of the Stress State on Ductile Fracture

An investigation of the loading rate dependence of the Weibull stress parameters

An experimental investigation of the effect of biaxial loading on the master curve transition temperature in RPV steels