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Dynamic stress intensity factors of two collinear mode-III cracks perpendicular to and on the two sides of a bi-FGM weak-discontinuous interface
Authors:Yong-Dong Li  Kang Yong Lee  Yao Dai
Institution:aDepartment of Mechanical Engineering, Academy of Armored Force Engineering, No. 21, Du Jia Kan, Chang Xin Dian, Beijing 100072, PR China;bSchool of Mechanical Engineering, Yonsei University, Seoul 120-749, South Korea
Abstract:The mechanical model was established for the anti-plane dynamic fracture problem for two collinear cracks on the two sides of and perpendicular to a weak-discontinuous interface between two materials with smoothly graded elastic properties, as opposed to a sharp interface with discontinuously changing elastic properties. The problem was reduced as a system of Cauchy singular integral equations of the first kind by Laplace and Fourier integral transforms. The integral equations were solved by Erdogan's collocation method and the dynamic stress intensity factors in the time domain were obtained through Laplace numerical inversion proposed by Miller and Guy. The influences of geometrical and physical parameters on the dynamic stress intensity factors were illustrated and discussed, based on which some conclusions were drawn: (a) to increase the thickness of the FGM strip on either side of the interface will be beneficial to reducing the DSIF of a crack perpendicular to a bi-FGM interface and embedded at the center of one of the FGM strips; (b) To increase the rigidity of the FGM strip where the crack is located will increase the DSIF. However, when the material in one side of the interface is more rigid, the DSIF of the interface-perpendicular embedded crack in the other side will be reduced; (c) To decrease the weak-discontinuity of a bi-FGM interface will not necessarily reduce the stress intensity factor of a crack perpendicular to it, which is different from the case of interfacial crack; (d) For two collinear cracks with equal half-length, when the distance between the two inner tips is less than about three times of the half-length, the interaction of them is intensified, however, when the distance is greater than this the interaction becomes weak.
Keywords:Bi-FGM interface  Weak-discontinuity  Collinear cracks  Singular integral equation  Dynamic stress intensity factor
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