Numerical Solutions of Singular Integral Equations for Planar Rectangular Interfacial Crack in Three Dimensional Bimaterials

XU Chun-hui; QIN Tai-yan; NODA Nao-Aki

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2007 > 28(6): 668-674

XU Chun-hui, QIN Tai-yan, NODA Nao-Aki. Numerical Solutions of Singular Integral Equations for Planar Rectangular Interfacial Crack in Three Dimensional Bimaterials[J]. Applied Mathematics and Mechanics, 2007, 28(6): 668-674.

Citation:

PDF( 445 KB)

Numerical Solutions of Singular Integral Equations for Planar Rectangular Interfacial Crack in Three Dimensional Bimaterials

1.
College of Science, China Agricultural University, Beijing 100083, P. R. China;

Received Date: 2006-10-20
Rev Recd Date: 2007-03-12
Publish Date: 2007-06-15

Abstract

Abstract

Stress intensity factors for a three dimensional rectangular interfacial crack are considered on the idea of the body force method.In the numerical calculations,unknown body force densities were approximated by the products of the fundamental densities and power series.Here the fundamental densities were chosen to express singular stress fields due to an interface crack exactly.The calculation shows that the present method gives rapidly converging numerical solutions and highly satisfied boundary conditions.The stress intensity factors for a rectangular interface crack are indicated accurately with varying the aspect ratio and bimaterial parameter.
- stress intensity factor,
- body force method,
- interface crack,
- composite material,
- fracture mechanics,
- singular integral equation

FullText(HTML)

References(19)

References

[1]	Salganik R L.The brittle fracture of cemented bodies[J].Prikl Mat Mekh,1963,27：957-962.
[2]	Erdogan F.Stresses distribution in a non-homogeneous elastic plane with crack[J].J Appl Mech,1963,3(2)：232-236.
[3]	England F.A crack between dissimilar media[J].J Appl Mech,1965,32(3)：400-402. doi: 10.1115/1.3625813
[4]	Rice J R,Sih G C.Plane problems of cracks in dissimilar media[J].J Appl Mech,1965,32(3)：418-423. doi: 10.1115/1.3625816
[5]	Comninou M.The interface crack[J].J Appl Mech,1977,44(4)：631-636. doi: 10.1115/1.3424148
[6]	Noda N A,Oda K.Interaction effect of stress intensity factors for any number of collinear interface cracks[J].Internat J Fracture,1997,84(2)：117-128. doi: 10.1023/A:1007313200779
[7]	Willis J R.Fracture mechanics of interfacial crack[J].J Mech Phys Solids,1971,19(6)：353-368. doi: 10.1016/0022-5096(71)90004-4
[8]	Tucker M O.In two-phase solids under longitudinal shear loading[J].Internat J Fracture,1974,10(3)：323-336. doi: 10.1007/BF00035494
[9]	England F,Gupta G D.Bonded wedges with an interface crack under anti-plane shear loading[J].Internat J Fracture,1975,11(4)：593-593.
[10]	Willis J R.The penny-shaped crack on an interface[J].J Mech Appl Math,1972,25(2)：367-385. doi: 10.1093/qjmam/25.3.367
[11]	Mossakovski V I,Rybka M T.Generalization of the griffith-senddon criterion for the case of a non-homogeneous body[J].Prikl Mat Mekh,1964,28：1061-1069.
[12]	England F.Stress distribution in bonded dissimilar materials containing circular or ring-shaped cavities[J].Trans ASME, Ser E, J Appl Mech,1965,32(4)：829-836. doi: 10.1115/1.3627323
[13]	Kassir M K,Bregman A M.The stress intensity factor for a penny-shaped crack between two dissimilar materials[J].Trans ASME, Ser E, J Appl Mech,1972,39(1)：308-310. doi: 10.1115/1.3422648
[14]	Lowengrub M,Senddon I N.The effect of internal pressure on a penny-shaped crack at the interface of two bonded dissimilar elastic half-spaces[J].Internat J Engng Sci,1974,12(5)：387-396. doi: 10.1016/0020-7225(74)90049-4
[15]	Shibuya T,Koizumi T,Iwamoto T.Stress analysis of the vicinity　of　an　elliptical crack at the interface of two bonded half-spaces[J].JSME Internat J,1989,32：485-491.
[16]	Noda N A,Kakita M,Chen M C.Analysis of stress intensity factors of a ring-shaped interface crack[J].Internat J Solids and Structures,2003,40(24)：6577-6592. doi: 10.1016/S0020-7683(03)00245-2
[17]	WANG Qing，Noda N A.Variation of stress intensity factors along the front of 3d rectangular crack by using a singular integral equation method[J].Internat J Fracture,2001,108(2)：119-131. doi: 10.1023/A:1007669725341
[18]	Chen M C,Noda N A,Tang R J.Application of finite-part integrals to planar interfacial fracture problems in three dimensional bimaterials[J].J Appl Mech,1999,66(6)：885-890. doi: 10.1115/1.2791793
[19]	Qin T Y,Noda N A.Stress intensity factors of rectangular crack meeting a bimateral interface[J].Internat J Solids and Structures,2003,40(10)：2473-2486. doi: 10.1016/S0020-7683(03)00015-5