The Susceptibility to Failure of the Constituents of Particulate Two-Phase Composites

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 to 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 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 inclusion 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. Similarly, the distribution of matrix stresses has been recorded depending on the particle content and the external loading conditions. A method to determine the Weibull parameters based on the numerical results will be pointed out. Residual stresses due to quenching of the material tend to reduce the risk of particle cleavage but promote fracture of the matrix.