A model of the fracture of a slightly porous material under compression or tension

Gol'Dshtein, R. V.; Ladygin, V. M.; Осипенко, Н. М.

doi:10.1007/bf02501596

Cited by 13 publications

(9 citation statements)

References 7 publications

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“…Practical accuracy of the approximation with some discrepancies of numerical results obtained by different authors 13,14,16 is in the range of about 5%. Practical accuracy of the approximation with some discrepancies of numerical results obtained by different authors 13,14,16 is in the range of about 5%.…”

Section: B R I T T L E F R a C T U R E A T C O M P R E S S I O N A mentioning

confidence: 82%

“…14 Here, following, Refs [3] and [13], we will consider a model of brittle fracture initiation in a porous medium. This follows from the solutions of the fracture mechanics problems for bodies with cracks.…”

Section: B R I T T L E F R a C T U R E A T C O M P R E S S I O N A mentioning

confidence: 99%

“…Refs [11] and [13][14][15] are inconvenient for the visual parametric analysis. Numerical solutions of this problem at the plane loading by uniform stresses σ 1 and σ 2 (see, e.g.…”

Section: B R I T T L E F R a C T U R E A T C O M P R E S S I O N A mentioning

confidence: 99%

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Development of multiple ordered fracture in an elastic homogeneous, structured and layered medium

Goldstein

Осипенко

2014

Fatigue Fract Eng Mat Struct

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Mechanical models of a series of fracture processes accompanied by formation of structures of fracture (ordered systems of cracks (violations)) are presented. The models are based on the fracture mechanics concepts and account for an influence of an initial structure and texture of material (medium) and loading conditions. Attention is paid to the model of linear structures of fracture formation in a porous material (medium) under the combined action of compression and tension. An influence of various mechanisms of local brittle fracture in the vicinities of pores and microcracks on the material bearing capacity at complex stress state is considered. Possibilities of a hierarchy of echelon‐like crack systems formation near a macroconcentrator of stresses are illustrated by experiments on fracture near a macrocut (notch) of longitudinal shear. A model of the process is also discussed.

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Section: B R I T T L E F R a C T U R E A T C O M P R E S S I O N A mentioning

confidence: 82%

Section: B R I T T L E F R a C T U R E A T C O M P R E S S I O N A mentioning

confidence: 99%

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Development of multiple ordered fracture in an elastic homogeneous, structured and layered medium

Goldstein

Осипенко

2014

Fatigue Fract Eng Mat Struct

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“…It was developed by Atkinson and Thiercelin [5], Galybin [9] and Gol'dshtein et al [24], who considered the particular cases of one or two cracks represented by a continuous distribution of dislocations. The problem of interaction of the circular hole and an edge dislocation has been solved by Dundurs and Mura [25].…”

Section: Introductionmentioning

confidence: 99%

Interaction between a circular opening and fractures originating from its boundary in a piecewise homogeneous plane

Mogilevskaya

Rothenburg

Dusseault

2000

Int. J. Numer. Anal. Meth. Geomech.

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SUMMARYThe complex variables boundary element method (CVBEM) is used to study interaction between a circular opening and fractures originating from its boundary in a piecewise homogeneous plane. A new complex hypersingular equation for piecewise homogeneous media with a circular opening is obtained. The equation is solved using the CVBEM technique with circular and straight boundary elements and polynomial approximations (with square root asymptotics for crack tip elements) for the unknown functions. The algorithm is veri"ed through comparison with known semi-analytical and numerical solutions that involve interaction between a circular opening and speci"c systems of cracks or other openings. New numerical results concerning the interaction of the circular opening with the cracks and circular inclusions are presented. The method is applied to an important problem in the petroleum industry: modelling propagation of hydraulic fractures in the vicinity of a borehole.

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“…These cracks are oriented along the compression direction. This kind of fracture was addressed both in some theoretical models (Martin [37], Sammis and Ashby [38], Nikitin and Odintsev [39], Dyskin et al [40]) and experimentally (Martin [37], Sammis and Ashby [38], Hoek and Bieniawski [41], Gol'dshtein et al [42]). Let us consider the problem that serves as basis for some models of fracture in a porous material under biaxial loading ( [38], [42] and [43]).…”

Section: Biaxial Compression-extension Of a Perforated And Cracked Mamentioning

confidence: 99%

On some general properties of strength criteria

Germanovich

Черепанов

1995

Int J Fract

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In this paper the concept of strength criteria is analyzed from a fracture mechanics point of view. A potential function is introduced to examine strength criteria using the results of catastrophe (singularity) theory. Although the diversity of failure behavior is enormous, there exist a few generic elements, so that only some standard modes occur in most cases. Four example problems in fracture mechanics with two and three independent loading parameters are studied in detail. These examples are shown to be representative and the set of failure states in the space of loading parameters generally appears to form a certain sub-space (manifold) which has the same dimension and is called failure domain, so that depending on the loading path, a failure can either occur or not occur at the given point of the failure domain. The brittle strength criteria are shown to depend on the loading history in the general case. The classical concept of a failure criterion and the postulate of convexity of the limiting fracture surface in the space of loading parameters are discussed. It is shown that importation of the convexity postulate from the plasticity theory to the theory of strength is not necessarily legitimate. Finally, two failure criteria are suggested; one characterizing a lower bound for some possibilities of a total failure, and the other guaranteeing the total failure. In the intermediate domain between both criteria, total failure can either occur or not, depending on the loading path.

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A model of the fracture of a slightly porous material under compression or tension

Cited by 13 publications

References 7 publications

Development of multiple ordered fracture in an elastic homogeneous, structured and layered medium

Development of multiple ordered fracture in an elastic homogeneous, structured and layered medium

Interaction between a circular opening and fractures originating from its boundary in a piecewise homogeneous plane

On some general properties of strength criteria

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