In Plane Displacement Formulation for Finite Cracked Plates Under Mode I Using Grid Method and Finite Element Analysis

A grid method is used to experimentally determine the in-plane displacement fields around a crack tip in a Single-Edge-Notch (SEN) tensile polyurethane specimen. Horizontal displacement u _x-exp and vertical displacement u _y-exp are expressed as functions of circular coordinates centred on the crack tip. These are compared with the approximate solutions of linear elastic fracture mechanics with a view to studying the applicability to polymers. The results show that this solution is not in agreement with the experiments at the focused on the vicinity of a crack tip. Taking this into account, an FEA program is developed with CAST3M for the purpose of comparing the experimental displacements and the numerical data. New formulations of displacements u _x and u _y are then developed. These formulations are derived from the principle of superposition and based on Arakawa’s formulation. With the displacement gradients obtained from the FEA and the new formulations, the determination of J-integrals is found to be in very good agreement with those derived from numerical calculation. Consequently, the proposed formulations can give displacement fields compatible with the J-integral calculation for the region near the crack tip. An application based on an experimental test is proposed to evaluate the performances of the proposed formulations.