Mohr-Coulomb criterion with circular failure envelope, extended to materials with strength-differential effect

Bârsănescu, P D; Sandovici, Adrian; Şerban, Alexandru

doi:10.1016/j.matdes.2018.03.043

Cited by 32 publications

(15 citation statements)

References 49 publications

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“…The tensile normal stress is expected to open these flaws and cause them to grow, whereas under the normal compressive stress the flaws tend to have their opposite sides pressed together [6]. The shear stress drives the dislocation movement of a large number of planes of atoms [19], leading to macroscopic material distortion. Hence it can be concluded that the normal tensile stress and the shear stress promote material failure, while the normal compressive stress inhibits failure.…”

Section: Discussion Of the Linear Mohr-coulomb Criterionmentioning

confidence: 99%

“…Although Coulomb's linear failure envelope is able to distinguish the different effects of the normal tensile and compressive stresses on material failure, the experimentally-determined envelopes often exhibit non-linear behavior [21]. Thus, the linear strength response is regarded as a major limitation of the classic Mohr-Coulomb criterion [19], and a non-linear form of the envelope is supposed to fit the experimental data better. Nevertheless, besides the common uniaxial tension and compression tests, additional experiments are usually required in order to determine the unknown parameters of the non-linear failure function.…”

Section: Discussion Of the Linear Mohr-coulomb Criterionmentioning

confidence: 99%

“…Experiments have shown that isotropic materials can be loaded to very high values of hydrostatic pressure without failure [19], i.e., C tri →∞. Hence β C can be approximated by…”

Section: Failure Function For σ N ≤mentioning

confidence: 99%

“…The failure envelope is commonly expected to be as smooth as possible considering the implementation of numerical methods [19]. The left derivative of the failure envelope at σ n = 0 can be derived from Equation 6:…”

Section: Of 14mentioning

confidence: 99%

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A Macroscopic Strength Criterion for Isotropic Metals Based on the Concept of Fracture Plane

Chen

et al. 2019

Metals

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Although the linear Mohr–Coulomb criterion is frequently applied to predict the failure of brittle materials such as cast iron, it can be used for ductile metals too. However, the criterion has some significant deficiencies which limit its predictive ability. In the present study, the underlying failure hypotheses of the linear Mohr–Coulomb criterion were thoroughly discussed. Based on Mohr’s physically meaningful concept of fracture plane, a macroscopic strength criterion was developed to explain the failure mechanism of isotropic metals. The failure function was expressed as a polynomial expansion in terms of the stresses acting on the fracture plane, and the quadratic approximation was employed to describe the non-linear behavior of the failure envelope. With an in-depth understanding of Mohr’s fracture plane concept, the failure angle was regarded as a generalized strength parameter in addition to the failure stress (i.e., the conventional basic strength). The undetermined coefficients of the non-linear failure function were calibrated by the strength parameters obtained from the common uniaxial tension and compression tests. Theoretical and experimental assessment for different types of isotropic metals validated the effectiveness of the proposed criterion in predicting material failure.

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Section: Discussion Of the Linear Mohr-coulomb Criterionmentioning

confidence: 99%

Section: Discussion Of the Linear Mohr-coulomb Criterionmentioning

confidence: 99%

“…Experiments have shown that isotropic materials can be loaded to very high values of hydrostatic pressure without failure [19], i.e., C tri →∞. Hence β C can be approximated by…”

Section: Failure Function For σ N ≤mentioning

confidence: 99%

Section: Of 14mentioning

confidence: 99%

See 2 more Smart Citations

A Macroscopic Strength Criterion for Isotropic Metals Based on the Concept of Fracture Plane

Chen

et al. 2019

Metals

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“…This choice of the yield criterion leads to two simple separable differential equations shown in (12). Moreover, the Mohr-Coulomb yield criterion, which is a particular case of the yield criterion considered in the present paper, is widely used for various materials (please see [26] and the list of references in this paper). Nevertheless, this criterion has been criticized in many works, for example [26,27].…”

Section: Other Yield Criteriamentioning

confidence: 99%

Geometry of principal stress trajectories for piece‐wise linear yield criteria under axial symmetry

Alexandrov

Jeng

2020

Z Angew Math Mech

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Rigid-and elastic-plastic solids obeying quite a general yield criterion represented by linear functions of the principal stresses are considered. A general axisymmetric state of stress satisfying the hypothesis of Haar and von Karman is analyzed in quasi-static flow. The circumferential velocity vanishes. A superimposed restriction on the yield criterion is that the system of stress equations is hyperbolic. The primary objective of this study is to select optimal coordinates and unknowns for deriving the integrable differential relations in their most convenient form for numerical treatments.It is shown that there exists a simple relation between the scale factors of the principal lines coordinate system (the coordinate curves of this coordinate system coincide with the trajectories of the principal stresses). Another simple relation exists between the scale factors and the principal This article is protected by copyright. All rights reserved.stresses. The mapping between the principal lines and cylindrical coordinates is determined by a system of hyperbolic differential equations.

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An Extension Strain Type Mohr–Coulomb Criterion

Staat

2021

Rock Mech Rock Eng

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Extension fractures are typical for the deformation under low or no confining pressure. They can be explained by a phenomenological extension strain failure criterion. In the past, a simple empirical criterion for fracture initiation in brittle rock has been developed. In this article, it is shown that the simple extension strain criterion makes unrealistic strength predictions in biaxial compression and tension. To overcome this major limitation, a new extension strain criterion is proposed by adding a weighted principal shear component to the simple criterion. The shear weight is chosen, such that the enriched extension strain criterion represents the same failure surface as the Mohr–Coulomb (MC) criterion. Thus, the MC criterion has been derived as an extension strain criterion predicting extension failure modes, which are unexpected in the classical understanding of the failure of cohesive-frictional materials. In progressive damage of rock, the most likely fracture direction is orthogonal to the maximum extension strain leading to dilatancy. The enriched extension strain criterion is proposed as a threshold surface for crack initiation CI and crack damage CD and as a failure surface at peak stress CP. Different from compressive loading, tensile loading requires only a limited number of critical cracks to cause failure. Therefore, for tensile stresses, the failure criteria must be modified somehow, possibly by a cut-off corresponding to the CI stress. Examples show that the enriched extension strain criterion predicts much lower volumes of damaged rock mass compared to the simple extension strain criterion.

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Mohr-Coulomb criterion with circular failure envelope, extended to materials with strength-differential effect

Cited by 32 publications

References 49 publications

A Macroscopic Strength Criterion for Isotropic Metals Based on the Concept of Fracture Plane

A Macroscopic Strength Criterion for Isotropic Metals Based on the Concept of Fracture Plane

Geometry of principal stress trajectories for piece‐wise linear yield criteria under axial symmetry

An Extension Strain Type Mohr–Coulomb Criterion

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