Interacting cracks 3D analysis using boundary integral equation method

Bohdan Stasyuk; Bohdan Stasyuk

doi:10.3934/matersci.2016.4.1796

AIMS Materials Science

2016, Volume 3, Issue 4: 1796-1810. doi: 10.3934/matersci.2016.4.1796

Previous Article Next Article

Research article Special Issues

Interacting cracks 3D analysis using boundary integral equation method

Bohdan Stasyuk ^,

Lviv Polytechnic National University, 12 Bandera Str., 79013 Lviv, Ukraine

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.
- cracks interaction,
- boundary integral equation method,
- penny-shaper crack,
- stress intensity factor,
- boundary surface
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:

Abstract

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.

References

[1]	Berezhnytskyi LT, Panasiuk VV, Stashchuk NH (1983) Interaction of rigid linear inclusions and cracks in the deformable body, Kiev: Naukova Dumka, 288 [in Russian].
[2]	Savruk MP (1981) Two-dimensional elasticity problem for bodies with cracks, Kiev: Naukova Dumka, 323 [in Russian].
[3]	Guz AN, Dyshel MS, Nazarenko VM (2004) Fracture and stability of materials and structural members with cracks: Approaches and results. Int Appl Mech 40: 1323–1359. doi: 10.1007/s10778-005-0040-5
[4]	Kassir MK, Sih GC (1975) Mechanics of fracture. Three dimensional crack problems, Leyden: Netherlands Noordhoff International Publishing, 452.
[5]	Kit GS, Khai MV, Laushnyk IA (1978) The first main problem of the elasticity theory for bodies with penny-shaped cracks. Math Method Phys-Mech 7: 26–32 [in Russian].
[6]	Kit GS, Khai MV (1989) Potential Method in Three-Dimensional Thermoelastic Problems of Cracked Bodies, Kiev: Naukova Dumka, 284 [in Russian].
[7]	Saha TK, Chatterjee M, Roy A (1999) Interaction between coplanar elliptic cracks-II Shear Loading. Int J Solids Struct 36: 619–637. doi: 10.1016/S0020-7683(98)00038-9
[8]	Saha TK, Ganguly S (2005) Interaction of a penny-shaped crack with an elliptic crack under shear loading. Int J Fracture 131: 267–287. doi: 10.1007/s10704-004-5104-8
[9]	Balas J, Sladek J, Sladek V (1989) Stress Analysis by Boundary Element Methods, Amsterdam: Elsevier, 686.
[10]	Gaul L, Kögl M, Wagner M (2003) Boundary Element Methods for Engineers and Scientists, Berlin-Heidelberg: Springer, 489.
[11]	Kachanov M (1987) Elastic solids with many cracks: a simple method of analysis. Int J Solids Struct 23: 23–45. doi: 10.1016/0020-7683(87)90030-8
[12]	Stasyuk BM (2009) Method of effective stress field in three-dimensional problems of interaction of plane cracks. Mater Sci 45: 28–40. doi: 10.1007/s11003-009-9157-8
[13]	Andreykiv OY (1982) Three-Dimensional Problems of Crack Theory, Kiev: Naukova Dumka, 345 [in Russian].
[14]	Stankevich VZ, Khai MV (2002) Study into the Interaction of Cracks in an Elastic Half-Space under a Shock Load by Means of Boundary Integral Equations. Int Appl Mech 38: 440–446. doi: 10.1023/A:1016220628759

Reader Comments

Your name:*

Email:*
© 2016 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)