两种材料角区尖端裂纹异性分析

A Crack Emanating from the Tip of Bonded Dissimilar Materials

摘要: 本文分析两种材料角区尖端产生的裂纹现象。设裂纹位于两种材料角区的分角线上,利用问题的几何和材料对称性,可将原问题分解为对称和反对称两种状态。通过特征展开法,分别导出两种状态下裂纹的特征方程,进而计算出不同材料比值和角区张角下的特征值序列,其中最小正特征值可用来反映裂纹的奇异性程度,最后推导出裂纹尖端附近位移应力表达式。
- 双材料 /
- 奇异性 /
- 位移应力场
Abstract: A crack is assumed to emanate from the tip of bonded dissimilar materials with the crack on the bisector of one of the bonded wedges.The problem is firstly divided into symmetric and anti-symmetric modes according to the characteristics of the local geometry.By eigenexpansion method,the eigenequations for the two modes are derived,respectively,and the corresponding eigenvalues are obtained with different ratios of dissimilar material constants and angles of the wedges.The singularity of the crack is then analyzed by the eigenvalues that are less then one.The fields of displacement and stress in the vicinity of the tip of the crack are finally derived in an explicit form.
- Dissimilar material /
- singularity /
- fields of displacement and stress

[1]	D.B.Bogy and K.C.Wang,Stress singularities at interface corners in bonded dissimilar isotropic elastic materials,Int J.Solids Structures,7(1971),993-1005.
[2]	W.C.Carpenter and C.Byers,Apath independent integral for computing stress intensities for V-notched cracks in a bi-material,Int.J.Fract.,35(1987),245-268.
[3]	D.H.Chen and H.Nisitani,Singular stress field near the corner of jointed dissimilar materials, Journal of Applied Mechanics,60(1993),607-613.
[4]	D.H.Chen,Acrack normal to and terminating at a bimaterial interface,Engineering Fracture Mechanics,49(1994),517-532.
[5]	D.H.Chen,Analysis of singular stress field around the inclined cornertip,Engineering Fracture Mechanics,49(4)(1994),533-546.
[6]	J.P.Dempsey and G.H.Sinclair,On the stress singularities in the plane elasticity of the composite wedge,J.Elasticity,9(1979),373-391.
[7]	D.N.Fenner,Stress singularities in composite materials with an arbitrarity oriented crack meeting an interface,Int.J.of Fracture,12(1976),705-721.
[8]	N.I.Muskhelishvili,Some Basic Problems of Mathematical Theory of Elasticity,4th Ed.,Noordhoff,The Netherlands,(1963).
[9]	W.C.Wang and J.T.Chen,Singularities of an arbitrarily inclined semi-infinite crack meeting a bimaterial interface,Engineering Fracture Mechanics,49(5)(1994),671-680.
[10]	M.L.Wiliams,Stress singularities resulting from various boundary conditions in angular corners of plates in extension,Journal of Applied Mechanics,19(1952),526-528.