Brittle to Quasi-Brittle Transitions in the Soft Clamp Fiber Bundle Model

Abstract

In this thesis I describe a soft clamped quasi static fiber bundle model for two dimensional interfacial fracture. The soft clamps distribute the stress amongst the fibers through elastic forces. The model display three distinct modes of damage development depending on the elasticity of the clamps and the distribution of fiber strength.

1) The stiff clamp regime: The elastic forces of the clamps are in effect turned off. The model behaves like equal load sharing and damage is developing through random dilution of the system.

2) The soft clamp - quasi brittle regime: The elastic forces are turned on. The strength distribution of the fibers are large enough to affect the damage development. The elastic forces and the heterogeneities of the system are competing.

3) The soft clamp - brittle regime: The distribution of fiber strength is no longer strong enough to compete with the elastic redistribution of stress from the soft clamps. The damage development is determined by the elastic forces.

The model is then expanded with a gradient in the distribution of fiber strength to induce a clear fracture front. By this we can show that the model reproduces not only both the different roughness exponents ζ+ = 0.39 and ζ÷ = 1/2, but also the dynamic development of the fracture seen in laboratory experiments.