Crack-particle interaction in a two-phase composite Part II: crack deflection

Abstract

A numerical analysis has been performed on a system involving a crack near a single particle with the objective of finding a general relation for the size and shape of the elastic, crack-particle interaction zone which necessarily exists near particles in two-phase composites. In order to quantify the zone boundaries, various crack-particle geometries were modelled and a single characterization parameter was developed. Results show that a zone in which the energy release rate and direction of crack propagation are significantly affected can be simply defined near a particle as a function of the crack-particle geometry and elastic mismatch. A wide range of elastic combinations was examined with the result that for any significant crack deflection to occur away from the particle the magnitude of the first Dundurs parameter, I~1, must be greater than ,,~ 0.2. Numerical results show good agreement with experimental fatigue crack path data.

Modeling of crack growth through particulate clusters in brittle matrix by symmetric-Galerkin boundary element method

“…Analytical approaches have been developed for problems concerning cracks along the interface of various types of inclusions (e.g., Tamate 1968;Sendeckyj 1974;Hwu et al 1995). Numerical techniques, including finite element method (e.g., Chudnovsky 1993a,b Ferber et al 1993;Lipetzky and Schmauder 1994;Lipetzky and Knesl 1995;Haddi and Weichert 1998]) and boundary element method (BEM) (e.g., [Bush 1997;Knight et al 2002;Wang et al 1998]), have been employed to investigate this type of fracture behavior under static loading conditions. Recently, the dynamic response of the interaction between a crack and an inclusion using the time-domain BEM has been studied by Lei et al (2005).…”

The stress intensity factors for a short crack partially penetrating an inclusion of arbitrary shape

“…Due to the complexity of the interaction between crack and inclusion, the analytical solutions were obtained only for a few limited cases, e.g., a semi-infinite crack halfway penetrating a circular inclusion (Steif 1987); a short crack with one crack tip lodged in a circular stiff particle (Erdogan and Gaupta 1975), and a long crack partially penetrating a circular inhomogeneity (Wang and Ballarini 2003). Most of the studies were performed by numerical approaches, such as finite element (FE) method (Li and Chudnovsky 1993;Lipetzky and Knest 1995), boundary element method (Bush 1997), and singular integral equation method (Tamate 1968;Helsing 1999). Although these numerical analyses provide some insights into understanding the interaction between crack and inclusion, these numerical results are limited to fixed calculation parameters.…”

Crack-particle interaction in two-phase composites Part I: Particle shape effects

“…The remaining variable, aspect ratio, is included in the closed form solutions of (18)(19)(20)(21) in the range 0.08 < w / h <_ 3.2. For model geometries corresponding to an abscissa value between 1 and 5, (22) provides a good estimate of A K / K H .…”

“…All calculations are based on tensile loading and it is assumed that stresses remain within the elastic range of both the matrix and the inclusion. The specimen was not simplified to one-half its full size because in the course of related calculations some asymmetric features existed in the model [19]. The finite element model described above is used with the modified crack closure integral method to calculate the energy release rate and stress intensity factor at the crack tip [20,21].…”