An Effective Numerical Approach for Multiple Void-Crack Interaction

This paper presents a numerical approach to modeling a general system containing multiple interacting cracks and voids in an infinite elastic plate under remote uniform stresses. By extending Bueckner’s principle suited for a crack to a general system containing multiple interacting cracks and voids, the original problem is divided into a homogeneous problem (the one without cracks and voids) subjected to remote loads and a multiple void-crack problem in an unloaded body with applied tractions on the surfaces of cracks and voids. Thus the results in terms of the stress intensity factors (SIFs) can be obtained by considering the latter problem, which is analyzed easily by means of the displacement discontinuity method with crack-tip elements (a boundary element method) proposed recently by the author. Test examples are included to illustrate that the numerical approach is very simple and effective for analyzing multiple crack/void problems in an infinite elastic plate. Specifically, the numerical approach is used to study the microdefect-finite main crack linear elastic interaction. In addition, complex crack problems in infinite/finite plate are examined to test further the accuracy and robustness of the boundary element method.

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Hole Crack Problems in Infinite Elastic Plate in Tension

Journal of Pressure Vessel Technology ◽

10.1115/1.4002261 ◽

2011 ◽

Vol 133 (4) ◽

Author(s):

Xiangqiao Yan ◽

Baoliang Liu

Keyword(s):

Elastic Plate ◽

Homogeneous Problem ◽

Crack Problem ◽

Infinite Plate ◽

Elliptical Hole ◽

Numerical Approach ◽

Displacement Discontinuity ◽

Center Crack ◽

Crack Problems ◽

Hole Geometry

This paper deals with crack(s) emanating from a hole in infinite elastic plate in tension. Such a crack problem is called a hole crack problem for short. By extending Buckner’s principle suited for a crack to a hole crack problem in infinite plate in tension, here, the original problem (the hole crack problem in infinite plate in tension) is divided into a homogeneous problem (the one without hole crack) subjected to remote loads and a hole crack problem in an unloaded body with applied tractions on the surfaces of the hole and crack. Thus, the results in terms of the stress intensity factors (SIFs) can be obtained by considering the latter problem, which is analyzed easily by means of a hybrid displacement discontinuity (a boundary element method) proposed recently by Yan. Numerical examples are included to illustrate that the numerical approach is very simple and effective for analyzing the hole crack problem in infinite plate in tension. By using the proposed approach, three hole crack problems (i.e., a pair of cracks emanating from an elliptical hole, a pair of cracks emanating from a rhombus hole, and a crack emanating from a triangular hole in infinite plate in tension) are analyzed in detail. By changing the hole geometry form and the hole geometry parameters and by comparing the SIFs of the hole crack problem with those of the center crack problem, the effect of the hole geometry form and the hole geometry parameters on the SIFs is revealed. It is found that a hole has a shielding and an amplifying effect on the SIFs of crack(s) emanating from the hole. The shielding and amplifying effects varied with the hole geometry form and the hole geometry parameters.

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