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386648

Closed form solution for a semi‑infinite crack moving in an infinite orthotropic material with a circular crack breaker under antiplane strain

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Last updated: 05 Jan 2025

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Abstract

This study investigates the influence of a circular crack breaker on mode-III deformation behavior of a semi-infinite crack in a homogeneous, elastic orthotropic material subjected to longitudinal shear loads. The Galilean transformation is employed to convert the governing wave equation to Laplace's equation which is time independent, rendering the problem amenable to analysis within the realm of the classical theory of twodimensional elasticity. Considering the geometrical configuration of the problem, the analytical solution of the problem is possible if the problem is transformed using the appropriate mapping function. Our construction of a holomorphic function that mapsthe circular hole into a straight line with the edge terminating at the origin is a novelty which enables the use of integral transform method to obtain an analytic solution of the displacement, leading to closed-form expression for mode-III stress intensity factor, K111 . The asymptotic values of the fields are obtained and shown to depend on the radius of the crack breaker. A parametric study shows that, for a fixed loading interval, a crack breaker of larger radius leads to increased stress intensity factor.

DOI

10.1186/s42787-022-00150-1

Keywords

Closed form solution, Semi-infinite crack, Infinite orthotropic material, Circular crack breaker, Antiplane strain, Stress Intensity Factor

Volume

30

Article Issue

1

Related Issue

51015

Issue Date

2022-01-01

Receive Date

2024-10-16

Publish Date

2022-01-01

Page Start

1

Page End

11

Print ISSN

1110-256X

Online ISSN

2090-9128

Link

https://joems.journals.ekb.eg/article_386648.html

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https://joems.journals.ekb.eg/service?article_code=386648

Order

386,648

Type

Original Article

Type Code

3,248

Publication Type

Journal

Publication Title

Journal of the Egyptian Mathematical Society

Publication Link

https://joems.journals.ekb.eg/

MainTitle

Closed form solution for a semi‑infinite crack moving in an infinite orthotropic material with a circular crack breaker under antiplane strain

Details

Type

Article

Created At

21 Dec 2024