An inverse problem of the crack-tip cohesive zone model and applications to fracture processes in glassy polymers

A framework for an inverse analysis of the crack-tip cohesive zone model has been developed to measure the cohesive zone laws by analytical, experimental and numerical approaches. An analytical solution method of the inverse problem is developed to extract cohesive-zone laws from elastic far-fields surrounding a crack-tip cohesive zone. A general form of cohesive-crack-tip fields is obtained and used for eigenfunction expansions of the plane elastic field in a complex variable representation. The closing tractions and the separation-gradients at the cohesive zone are expressed in terms of orthogonal polynomial series expansions of the general-form complex functions. The coefficients of the eigenfunctions in J-orthogonal representation are extracted directly, using interaction J-integrals at far field between the physical field and auxiliary fields. The results from numerical experiments suggest that the proposed algorithms are well suited for extracting cohesive-zone laws from the far-field data. An experimental measurement technique called the Electronic Speckle Pattern Interferometry has been applied to measure whole-field crack-tip displacement near fracture process zones. A 4-beam laser speckle interferometer has been constructed to measure 2-dimensional displacement field around a crack tip in glassy polymers. The experimentally measured deformation fields around a crack-tip are used later as input data for the inverse analysis of the crack-tip cohesive zone problem. A numerical noise reduction algorithm, called Equilibrium Smoothing Method, is developed to extract smooth equilibrium fields from the experimentally measured displacement fields. The obtained smooth displacement field is used in inverse analysis of the crack problem. Two nonlinear fracture processes in glassy polymers have been investigated by the framework for the inverse problem. The environmental crazing in PMMA under methanol environment and the nonlinear fracture process in the rubber-toughened HIPS have been investigated. The results from the inverse analyses of fracture processes in glassy polymers have shown that the proposed framework of the field projection scheme could provide a unique way of finding the shape of the cohesive zone laws governed by the different micro-mechanisms in the fracture processes.