Effect of interaction between collinear cracks on the strength distribution of brittle materials

Weibull theory neglects interaction between the defects and between defects and stress field, and accordingly obtains that the strength of a material follows a Weibull distribution whose modulus is a material constant, and whose mean value only is affected by the geometry and loading condition. For the limit case of a cracked structure, this corresponds to a paradoxical zero mean strenght. A full account of interaction requires direct Montecarlo simulations (each elasticity problem being solved by an efficient dual boundary element formulation) and shows that mean value and scatter deviate from the theoretical ones. A simple geometry has been considered where an infinite plate uniform remote tension σ∞, containing N collinear cracks with statistical distribution of sizes and spacings