The initiation J-integral for linear viscoelastic solids with constant Poisson's ratio

Abstract

The present work examines the fracture response of homogeneous and linear isotropic visco-elastic solids with constant Poisson's ratio. For this type of materials it is shown that the J-integral at fixed crack size is proportional to the area under the load-vs-load point displacement record of a fracture test, and that, for given boundary conditions, the factor of proportionality depends on crack and specimen geometry – and also, perhaps, on Poisson's ratio – but is independent of material heredity. As a consequence, the factor of proportionality – or crack configuration factor – can be established by analysis of the test article, subjected to the same displacement and traction boundary conditions as the test, but using – if desired – an arbitrary linear elastic material with the constant Poisson's ratio of the viscoelastic solid. The same approach is shown valid for a class of nonlinear viscoelastic materials whose constitution involves single hereditary integrals, and whose property functions do not depend on stress. The methodology is used with the results of constant displacement-rate tests of centrally cracked specimens to construct a portion of the master initiation J-integral function for a solid propellant.