Fracture mechanisms in particle composites: statistical aspects in lattice type analysis

Abstract

The effect of material microstructure on crack growth and force–deformation behaviour under uniaxial tension has been investigated in an extensive numerical study. A simple beam lattice model has been used to estimate the effect of strength and stiffness contrast, and particle density in a three-phase particle composite as found in concrete. The results from these explicit three-phase analyses have been compared to the outcome of simulations where the effects of microstructure were mimicked by assigning random strength values drawn from a Weibull or Gauss distribution to a regular triangular lattice. The results indicate that strength contrast is more important than stiffness contrast, and that global behaviour is largely governed by percolation of the weakest material phase. This behaviour was obvious from the three-phase analyses. The results from the different Weibull simulations resemble the mode of failure observed in the more realistic three-phase particle overlay. Bridging is a salient phenomenon observed in these analyses. In contrast the (symmetric) Gauss distribution is not appropriate. Although a large variety in force–deformation diagrams can be simulated, depending on the two parameters in the Gauss distribution and the lattice geometry, the failure mode along a single straight crack does not resemble the real fracture behaviour of three-phase composites like concrete. It is not recommended to use statistical strength distributions for simulating the behaviour of three-phase particle composites. Furthermore, the results clearly indicate that the force–deformation diagram cannot be used as a single indicator for judging the accuracy of a model for the fracture behaviour of materials. The crack mechanisms and the ensuing crack patterns are considered a salient element in such judgements. The model simulations can be applied as a guideline to design real three-phase composites. In particular optimization of tensile strength of the composite by selecting the correct amount of particles seems possible.