AIMS Materials Science

2016, Issue 4: 1796-1810. doi: 10.3934/matersci.2016.4.1796
Research article Special Issues

Interacting cracks 3D analysis using boundary integral equation method

• Received: 02 October 2016 Accepted: 05 December 2016 Published: 12 December 2016
• This paper presents a modification of the method of boundary integral equations suitable for the efficient solution of 3D problems on the arbitrarily oriented plane cracks interaction with the influence of body surface. The hypersingular boundary integral equations on the crack-surface are transformed into new form, where the solution behavior near the crack front is accounted implicitly. This modification allows the direct determination of the stress intensity factors (SIF) in the crack vicinity after solution of equations by the collocation technique. We also propose the approach based on the determination of the effective stress field formed in the vicinity of a fixed crack by neighboring cracks interacting with this crack and with boundary surface. Numerical examples concern an asymmetric problem for interacting penny-shaped plane cracks in the unlimited and limited bodies. The reliability of the results obtained by the method of effective stress field is checked by comparing with the exact solution of the problem of interaction of two penny-shaped cracks.

Citation: Bohdan Stasyuk. Interacting cracks 3D analysis using boundary integral equation method[J]. AIMS Materials Science, 2016, 3(4): 1796-1810. doi: 10.3934/matersci.2016.4.1796

Related Papers:

• This paper presents a modification of the method of boundary integral equations suitable for the efficient solution of 3D problems on the arbitrarily oriented plane cracks interaction with the influence of body surface. The hypersingular boundary integral equations on the crack-surface are transformed into new form, where the solution behavior near the crack front is accounted implicitly. This modification allows the direct determination of the stress intensity factors (SIF) in the crack vicinity after solution of equations by the collocation technique. We also propose the approach based on the determination of the effective stress field formed in the vicinity of a fixed crack by neighboring cracks interacting with this crack and with boundary surface. Numerical examples concern an asymmetric problem for interacting penny-shaped plane cracks in the unlimited and limited bodies. The reliability of the results obtained by the method of effective stress field is checked by comparing with the exact solution of the problem of interaction of two penny-shaped cracks.

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