Inverse estimation of cohesive zone laws from experimentally measured displacements for the quasi-static mode I fracture of PMMA

In this paper, an efficient hybrid procedure combining experimental measurements and an inverse algorithm called the field projection method (FPM) is presented to estimate cohesive zone laws for the quasi-static mode I fracture of PMMA. The procedure is made up of the measurement of displacements in a region far away from the crack tip using the digital image correlation technique, its transfer to finite element (FE) nodes from measurement locations using the moving least square approximation, and inverse analyses using numerical auxiliary fields and the conservation nature of the interaction J- and M-integrals. Since it is very difficult to measure the tractions and separations ahead of the crack tip where a highly nonlinear behavior of materials emerges at very small scales, the present method can be a very successful approach to extract the cohesive zone laws from experimentally measured displacements in a far-field region. In particular, the FPM using numerical auxiliary fields facilitates its use for determining the mesh-dependent cohesive zone laws in FE computations.