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

Abstract

The interaction of a crack with perfectly bonded rigid isolated inclusions and clusters of inclusions in a brittle matrix is investigated using numerical simulations. Of particular interest is the role inclusions play on crack paths, stress intensity factors (SIFs) and the energy release rates with potential implications to the fracture behavior of particulate composites. The effects of particle size and eccentricity relative to the initial crack orientation are examined first as a precursor to the study of particle clusters. Simulations are accomplished using a new quasi-static crack-growth prediction tool based on the symmetric-Galerkin boundary element method, a modified quarter-point crack-tip element, the displacement correlation technique for evaluating SIFs, and the maximum principal stress criterion for crack-growth direction prediction. The numerical simulations demonstrate a complex interplay of crack-tip shielding and amplification mechanisms leading to significant toughening of the material.

Dynamic effects of inclusions and microcracks on a main crack

“…Here the superscript "max" represents the maximum value of K * I and K max Figure 9b presents the variation of the amplification ratio K max I /K max 0 of the right cracktip A with the distance d, which is very similar to Fig. 5 given in Kitey et al (2006) for the static case. It should be pointed out that the solid curve in Fig.…”

“…Knight et al (2002) examined the crack deflection/attraction mechanisms in a crack-particle interaction study by performing a series of parametrical studies for different Young's modulus and Poisson's ratio mismatches and the results showed that Poisson's ratio may significantly affect the crack trajectory. In two consecutive papers, Kitey et al (2006) and Williams et al (2007) used a symmetric-Galerkin BEM to model the crack growth through particulate clusters and demonstrated a complex interplay of the cracktip shielding and amplification mechanisms leading to significant toughening of the material. In contrast to the static case, still relatively limited studies are yet concerning this type of crack-inclusion or crack-crack interaction problems under dynamic loading conditions.…”

Predicting crack propagation with peridynamics: a comparative study

“…Therefore, a total of six test cases were examined. The material properties (Kitey et al 2006) for the epoxy are: elastic modulus of E = 3.2 GPa and mass density of ρ = 1,000 kg/m 3 while those for the glass are elastic modulus of E = 70 GPa and mass density of ρ = 2,450 kg/m 3 .…”

SGBEM modeling of fatigue crack growth in particulate composites

“…Here, the central particle of the cluster is located at a distance c = 16 mm from the initial crack tip, and is surrounded by five identical particles at the vertices of a pentagon. As suggested in [1], this pentagonal arrangement of particles better represents the random distribution of fillers in a matrix than other arrangements using polygons of even number of sides. The particle diameter under investigation in this section is d = 4 mm for every particle.…”

“…The cluster density (CD) is defined as the ratio of the area inside the pentagon occupied by the particles to the area of the pentagon itself. This parameter is considered instead of the volume fraction since, as discussed in [1], it is not straightforward to define a control volume which is needed for determining the volume fraction for the chosen pentagonal arrangement of inclusions. To avoid the particle size effects, different CDs, namely CD = 10, 15, 20, 25%, are created by changing the cluster radius R while keeping the particle diameter constant (d = 3 mm in this investigation).…”