In this article, the behaviour of three parallel non-symmetric finite-length cracks in an infinite functionally graded material plane subjected to anti-plane shear stress loading was studied by the Schmidt method. The problem was formulated through Fourier transform into three pairs of dual integral equations, in which unknown variables are the jumps of displacements across the crack surfaces. To solve the dual integral equations, the jumps of displacements across the crack surfaces were directly expanded as a series of Jacobi polynomials. The results show that the stress intensity factors depend on the crack lengths, spacing of cracks, and the material parameters. It was also revealed that the crack shielding effect is present in functionally graded materials.
KoizumiM.The concept of FGM. In Ceramic transactions: functionally graded materials (Eds. HoltJ. B.KoizumiM.MunirZ. A.)1993vol. 34, pp. 3–10 (American Ceramic SocietyOhio).
2.
LeeY. D.ErdoganF.Residual/thermal stress in FGM and laminated thermal barrier coating. Int. J. Fract.199469145–165.
3.
SureshS.MortensenA.Functionally graded metals and metal-ceramic composites: Part 2 thermomechanical behaviour. Int. Mater. Rev.197729306–312.
4.
DelaleF.ErdoganF.On the mechanical modeling of the interfacial region in bonded half-planes. Trans. ASME J. Appl. Mech.199855317–324.
5.
ChenY. F.Interface crack in nonhomogeneous bonded materials of finite thickness PhD Dissertation, Lehigh University1990.
6.
OzturkM.ErdoganF.Axisymmetric crack problem in bonded materials with a graded interfacial region. Int. J. Solids Struct.199633193–219.
7.
WangB. L.HanJ. C.DuS. Y.Crack problem for non-homogeneous composite materials subjected to dynamic loading. Int. J. Solids Struct.2000371251–1274.
8.
ButcherR. J.RousseauC. E.TippurH. V.A functionally graded particulate composite: Preparation, measurements and failure analysis. Acta Mater.199947259–268.
9.
RousseauC. E.TippurH. V.Compositionally graded materials with cracks normal to the elastic gradient. Acta Mater.2000484021–4033.
10.
GuP.DaoM.AsaroR. J.A simplified method for calculating the crack tip field of functionally graded materials using the domain integral. J. Appl. Mech.199966101–108.
11.
AnlasG.SantareM. H.LambrosJ.Numerical calculation of stress intensity factors in functionally graded materials. Int. J. Fract.2000104131–143.
12.
ErdoganF.WuH. B.Crack problems in FGM layer under thermal stress. J. Therm. Stresses199619237–265.
13.
ChenJ.LiuZ. X.On the dynamic behavior of a functionally graded piezoelectric strip with periodic cracks vertical to the boundary. Int. J. Solids Struct.2005423133–3146.
14.
WangB. L.MaiY. W.A periodic array of cracks in functional graded materials subjected to thermo-mechanical loading. Int. J. Eng. Sci.200543432–446.
15.
ZhangP. W.ZhouZ. G.WuL. Z.Basic solutions of two parallel mode-I permeable cracks or four parallel mode-I permeable cracks in magnetoelectroelastic composite materials. Philos. Mag.2007871–34.
16.
ZhouZ. G.ZhangP. W.WuL. Z.Two parallel limited-permeable mode-I cracks or four parallel limited-permeable mode-I cracks in the piezoelectric materials. Int. J. Solids Struct.2007444184–4205.
17.
ZhouZ. G.WangB.Two parallel symmetry permeable cracks in functionally graded piezoelectric/piezomagnetic materials under anti-plane shear loading. Int. J. Solids Struct.2004414407–4422.
18.
MorseP. M.FeshbachH.Methods of theoretical physics1958, p. 926 (McGraw-HillNew York).
19.
ItouS.Three dimensional waves propagation in a cracked elastic solid. Trans. ASME J. Appl. Mech.197845807–811.
20.
GuoL. C.NodaN.Modeling method for a crack problem of functionally graded materials with arbitrary properties-piecewise-exponential model. Int. J. Solids Struct.2007446768–6790.
21.
GradshteynI. S.RyzhikI. M.Table of integrals, series and products1980, p. 480 (Academic PressNew York).
22.
ErdelyiA.Tables of integral transformsvol. 11954 (McGraw-HillNew York).
23.
RatwaniM.GuptaG. D.Interaction between parallel cracks in layered composites. Int. J. Solids Struct.197410(7)701–708.
