Automated numerical simulation of the propagation of multiple cracks in a finite plane using the distributed dislocation method

Abstract

In this paper, an automated numerical simulation of the propagation of multiple cracks in a finite elastic plane by the distributed dislocation method is developed. Firstly, a solution to the problem of a two-dimensional finite elastic plane containing multiple straight cracks and kinked cracks is presented. A serial of distributed dislocations in an infinite plane are used to model all the cracks and the boundary of the finite plane. The mixed-mode stress intensity factors of all the cracks can be calculated by solving a system of singular integral equations with the Gauss-Chebyshev quadrature method. Based on the solution, the propagation of multiple cracks is modeled according to the maximum circumferential stress criterion and Paris' law. Several numerical examples are presented to show the accuracy and efficiency of this method for the simulation of multiple cracks in a 2D finite plane.

Simplified numerical algorithms for generalized strip saturated two equal collinear cracks in piezoelectric media using distributed dislocation technique

“…Considering the principle of superposition, a crack problem in a finite domain is equivalent to a multiple cracks problem in an infinite solid with prescribed loads on the actual cracks faces and traction/induction free conditions on the boundary of the specimen [21][22][23]26]. This is because for analysis under DDT, the boundary of the domain is also considered as a crack with traction/induction free conditions on the crack faces.…”

“…Zhang et al [22] derived a numerical solution based on DDT and Gauss-Chebyshev quadratures for the studies of interaction between cracks and a circular inclusion in a finite plate. Zhang et al [23] presented an automated numerical simulation for the propagation of multiple cracks in a finite elastic plane by DDT. Further, Chen [24] presented a numerical solution of a Dugdale-type crack problem for two cracks lying in a series using DDT.…”

“…However, no studies have been found in literature related to numerical solution of the SS two equal collinear cracks in finite piezoelectric media. Further, the numerical studies of non-linear fracture models like Dugdale's model in elastoplastic materials and SS models in piezoelectric or magneto-electro-elastic materials based on FEM, Mesh Free Methods and X-FEM involve a high computational cost than DDT [22,23,25,26]. The other advantage of applying DDT is that the mathematical modeling of these kinds of problems is easier than the other existing numerical techniques.…”

Numerical Solution for Crack Phenomenon in Dissimilar Materials under Various Mechanical Loadings

“…Complex potential function (CPF) method introduced by Muskhelishvili [1] is the simplest and most rigorous method to investigate the behavior of SIFs, measured at the tip of cracks to determine the stability behavior of bodies or materials containing cracks or flaws. Many researchers used CPF methods to investigate the crack problems in an infinite plane [2][3][4], finite plane [5,6] and half plane [7][8][9]. Gray et al [2] and Nik Long et al [3] established the relevant hypersingular integral equations (HSIEs) using CPF method in calculating the SIFs with Green's function, and crack opening displacement (COD) function as the unknown, respectively.…”

“…Lai and Schijve [5] analyzed a single hole-edge crack in a finite plane using CPF methods with the treatment of boundary condition with the minimum potential energy principle. Moreover, Zhang et al [6] analyzed multiple cracks in a finite plane by numerically solved a system of singular integral equations with the Gauss-Chebyshev quadrature, and evaluating the SIFs. Legros et al [7] performed the analysis of multiple circular inclusions in an elastic half plane based on complex singular integral equation with the unknown tractions at each circular boundary approximated by a truncated complex Fourier series.…”