Fracture mechanics of a randomly heterogeneous double cantilever beam

A Heterogeneous Double Cantilever Beam, commonly used for fracture energy measurements, is analyzed by the Functional Perturbation Method (FPM). External force and displacement are considered as functionals of materials morphology. Both stiffness and fracture energies are random fields, from which the average and variance of the external loading and displacement at the onset of crack growth are found explicitly. The inverse problem, in which the stochastic properties of the fracture energy (average and variance) are found from the load-displacement-crack length data, is also solved. The solution is given in terms of intrinsic correlation length, which is equivalent to `grain size' in polycrystals. It is shown that a different characteristic length for the fracture energy and for moduli may exist. Special attention is given to very small or very large `grains', for which an analytical approximation is permitted. It is shown that the `classical' design loads for a common, fracture related reliability level, may be non-conservative and deviate significantly from the accurate value.