Effective Toughness of Heterogeneous Materials

Composite materials are widely used because of their extraordinary performance. It is understood that the heterogeneity / microstructure can dramatically affect the effective behavior of materials. Although there is a well-developed theory for this relation in elasticity, there is no similar theory in fracture mechanics. Therefore, we use theoretical, numerical, and experimental approaches to study the relationship between heterogeneity / microstructure and the effective fracture behavior in this thesis. We use the surfing boundary condition, a boundary condition that ensures the macroscopic steady crack growth, and then define the effective toughness of heterogeneous materials as the peak energy release rate during crack propagation. We also use the homogenization theory to prove that the effective J-integral in heterogeneous materials is well defined, and that it can be calculated by the homogenized stress and strain field. In order to study the relationship between heterogeneities and effective toughness, we first use the semi-analytical method under the assumption of small elastic contrast to study selected examples. For strong heterogeneities, we use the phase field fracture method to study the crack propagation numerically. We then optimize the microstructure with respect to effective stiffness and effective toughness in a certain class of microgeometries. We show that it is possible to significantly enhance toughness without significant loss of stiffness. We also design materials with asymmetric toughness. We develop a new experimental configuration that can measure the effective toughness of specimens with arbitrary heterogeneities. We confirm through preliminary tests that the heterogeneities can enhance the effective toughness. Besides study the effective toughness of heterogeneous materials, we also study a model problem of peeling a thin sheet from a heterogeneous substrate. We develop a methodology to systematically optimize microstructure.