In many composites consisting of hard and brittle inclusions embedded in a ductile matrix failure can be attributed to particle cleavage followed by ductile crack growth in the matrix. Both mechanisms are significantly sensitive towards the presence of residual stresses.
On the one hand particle failure depends on the stress distribution inside the inclusion, which, in turn, is a function of various geometrical parameters such as the aspect ratio and the position relative to adjacent particles as well as the external load. On the other hand it has been observed that the absolute size of each particle plays a role as well and will, therefore, be taken into account in this work by means of the Weibull theory. Unit cells containing a number of quasi-randomly oriented elliptical inclusions serve as the basis for the finite element calculations. The numerical results are then correlated to the geometrical parameters defining the inclusions. The probability of fracture has been evaluated for a large number of inclusions and plotted versus the particle size. The parameters of the fitting curves to the resulting data points depend on the choice of the Weibull parameters.
A crack tip opening angle criterion (CTOA) is used to describe crack growth in the matrix emanating from a broken particle. It turns out that the crack resistance of the matrix largely depends on the distance from an adjacent particle. Residual stresses due to quenching of the material tend to reduce the risk of particle cleavage but promote crack propagation in the matrix.