An asymptotic analysis of crack initiation from an interfacial zone surrounding the circular inclusion

Profant, Tomáš; Hrstka, Miroslav; Klusák, Jan

doi:10.1016/j.compstruct.2018.10.020

Cited by 5 publications

(7 citation statements)

References 20 publications

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“…The basis for the expression of the fundamental solution is the complex analysis in the plane elasticity represented by Muskhelishvili's complex potentials, e.g. [10], which for the matrix 1 W can be written in the form (the series of complex potential for domains 2 W and 3 W can be found in [3], [4])…”

Section: Fundamental Solutionmentioning

confidence: 99%

“…The composite expansion, i.e. an asymptotic expansion with respect to the small parameter e , is introduced under the assumption that the crack e g is small with respect to the dimensions of the inclusion 3 W and can be written as follows, see [3],…”

Section: Asymptotic Analysis and Stress Intensity Factor Evaluationmentioning

confidence: 99%

“…The inner problem is due to the scaled coordinate / X x e = independent of the parameter e . Similarly to [9], the crack in (7), (8) and (9) is modelled using the continuously distributed dislocation technique [3], [5]. If the dislocation with Burgers vector i…”

Section: Asymptotic Analysis and Stress Intensity Factor Evaluationmentioning

confidence: 99%

“…The shape optimization methods tender an interesting way to eliminate the problem of the complexity of the geometry of the presented problem. The shape functional ( ) U e W plays an important role in the following method, because represents the potential energy of the fracture problem (3). The change of the shape functional with respect to the small perturbation de of the crack e g at its tip x e = can be expressed by its asymptotic expansion, see [3], [8] and [9],…”

Section: Energy Release Rate Evaluationmentioning

confidence: 99%

“…icrocracking is a phenomenon appearing in the vicinity of some stress rising features, where relatively short cracks rise and grow. An inclusion whose material properties differ from the ones of the surrounding matrix can be taken into account as a potential generator of such stresses [1], [2], [3]. The stress distribution generated by the presence of the inclusion can be influenced by its interfacial zone between the inclusion and the matrix.…”

Section: Introductionmentioning

confidence: 99%

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Microcrack interaction with circular inclusion and interfacial zone

Hrstka

Klusák²,

Profant

2019

Frattura Ed Integrità Strutturale

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A geometrically simplified plane elasticity problem of a finite small crack emanating from a thin interfacial zone surrounding the circular inclusion situated in the finite bounded domain is investigated. The crack is arbitrarily oriented and modelled using the distribution dislocation technique. This model represents the inner solution of the studied problem. The corresponding fundamental solution is based on the application of Muskhelishvili complex potentials in the form of the Laurent series. The coefficients of the series are evaluated from the compatibility conditions along the interfaces of the inclusion, the interfacial zone and the enclosing matrix. The fundamental solution is also used in the solution of the boundary integral method approximating the stress and strain relations of the so-called outer solution. The asymptotic analysis at the point of the crack initiation combines the inner and the outer solution and results in the evaluation of the stress intensity factors of the crack tip, which lies in the matrix. The topological derivative is subsequently used to approximate the energy release rate field associated with the perturbing crack in the matrix. The extreme values of the energy release rate allow one to assess the crack path direction of the initiated microcrack.

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