Application of extended Mohr–Coulomb criterion to ductile fracture

  • Yuanli BaiEmail author
  • Tomasz Wierzbicki
Original Paper


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.


Mohr–Coulomb criterion Ductile fracture 3D Fracture locus Crack direction 


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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Impact and Crashworthiness LaboratoryMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.General Electric Global Research CenterNiskayunaUSA

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