Mechanical modeling and transient anti-plane fracture analysis for the graded inter-diffusion regions in a bonded structure. (English) Zbl 1198.74074
The paper investigates the transient anti-plane fracture problem of inter-diffusion interface model (IDIM) for a bounded layered structure by using the method of integral transforms and singular integral equations. The physical background for IDIM is that when the two base materials are easy to permeate, the graded interlayer may be negligible thin, and only two graded regions in the base materials are formed. Due to various diffusibilities of nearest materials, two non-homogeneous regions with dissimilar variations of properties might be formed on both sides of the center interface. Therefore, material properties of the two graded regions are assumed to vary exponentially and linearly, respectively. So, the structure considered consists of homogeneous layer-I, interface-I, graded layer-I with central crack, interface-II, graded layer-II, interface-III, and homogeneous layer-II. An initially-boundary value problem governs the loading of crack surfaces by dynamic anti-plane shear tractions.
First, the constitutive equations are reduced to singular integral equations by using Laplace and Fourier integral transforms. As a result, the problem is reduced to solution of Cauchy singular integral equation of the first kind. By this, infinite integral is evaluated by Gauss-Laguerre method, and numerical results are obtained by using Lobatto-Chebyshev collocation method. The effects of geometrical and physical parameters on the peak and limiting static values of transient stress intensity factors are studied. In particular, the authors discuss the influence of weak/micro-discontinuity of interfaces based on the concept of weak discontinuity. In this concept, if across interface-I the material properties are continuous, but their derivatives are discontinuous, then interface-I is a kind of weakly discontinuous boundary. Comparison between IDIM and the graded interlayer model shows that the interlayer model is not enough to treat all possible cases of fracture of bonded layered structures, and when inter-diffusion is prominent, IDIM should be applied instead.
First, the constitutive equations are reduced to singular integral equations by using Laplace and Fourier integral transforms. As a result, the problem is reduced to solution of Cauchy singular integral equation of the first kind. By this, infinite integral is evaluated by Gauss-Laguerre method, and numerical results are obtained by using Lobatto-Chebyshev collocation method. The effects of geometrical and physical parameters on the peak and limiting static values of transient stress intensity factors are studied. In particular, the authors discuss the influence of weak/micro-discontinuity of interfaces based on the concept of weak discontinuity. In this concept, if across interface-I the material properties are continuous, but their derivatives are discontinuous, then interface-I is a kind of weakly discontinuous boundary. Comparison between IDIM and the graded interlayer model shows that the interlayer model is not enough to treat all possible cases of fracture of bonded layered structures, and when inter-diffusion is prominent, IDIM should be applied instead.
Reviewer: I. A. Parinov (Rostov-na-Donu)
Keywords:
functionally-graded materials; integral transforms; Cauchy singular integral equation; Lobatto-Chebyshev collocation method; stress intensity factors; weak discontinuityReferences:
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