Topic
Mohr–Coulomb theory
About: Mohr–Coulomb theory is a research topic. Over the lifetime, 553 publications have been published within this topic receiving 9541 citations. The topic is also known as: Mohr-Coulomb yield criterion.
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TL;DR: In this article, the Mohr-Coulomb (M-C) fracture criterion is revisited with an objective of describing ductile fracture of isotropic crack-free solids.
Abstract: 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.
937 citations
TL;DR: Inherent shear strength (cohesion) is defined in terms of the angle of internal friction as discussed by the authors, with no regard to order of principal stresses, with or without regard to the order of the principal stresses.
Abstract: List of Symbols a (m 1)/(m ? 1) b 1/(m ? 1) c Cohesion C0 Uniaxial compressive strength m (1 ? sin /)/(1 sin /) S0 Inherent shear strength (cohesion) T Uniaxial tensile strength T0 Theoretical MC uniaxial tensile strength / Angle of internal friction l = tan / Coefficient of internal friction r Normal stress on plane s Shear stress on plane r1, r2, r3 Principal stresses, with no regard to order rI, rII, rIII Major, intermediate, minor principal stresses rm (rI ? rIII)/2 sm (rI rIII)/2 rI * C0 mT rIII * -T 1 Description
453 citations
TL;DR: In this paper, a phenomenological fracture initiation model for metals is developed for predicting ductile fracture in industrial practice based on the assumption that the onset of fracture is imminent with the formation of a primary or secondary band of localization.
369 citations
296 citations
TL;DR: In this paper, the vertical bearing capacity of circular and strip footings on soil which satisfies a linear Mohr-Coulomb strength criterion was established. But the method of characteristics was used to establish consistent factors for the verticalbearing capacity of vertical footings.
Abstract: The method of characteristics is used to establish consistent factors for the vertical bearing capacity of circular and strip footings on soil which satisfies a linear Mohr–Coulomb strength criteri...
270 citations