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

Abstract

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 Jintegral 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.

Experimental and numerical in-plane displacement fields for determine the J-integral on a PMMA cracked specimen

“…Nevertheless, it is possible to derivate the displacement fields near the crack tip. An optical method has been adapted to extract the large fields in fracture mechanics [8]. The grid method has the advantage of giving an accurate measurement with a high spatial resolution.…”

“…The used approach consists to minimize the displacement gaps by 2 adapted formulations (eq.5 and eq.6) representing correctly the displacement fields and the displacement gradients. These expressions are based on the Arakawa's formulations [15] and are modified by Hedan [8].…”

“…The SEN specimen is loaded in mode I (crack opening mode) and the used brittle material (PMMA) presents the mechanical characteristics listed in the table 1. The 3D character, the boundary conditions and behaviour law (linear elastic) are validated by comparisons of experimental displacement fields on the free surface [8] and by comparisons displacement fields on the bulk of 3D real cracked specimen [16].…”

“…For the numerical simulation, finite element software is used (CASTEM). The calculation of experimental J-integral requires experimental in-plane fields on the free surface and 2 theoretical formulations [8]. Experimental displacement fields u x-exp and u y-exp are measured in a SEN tensile specimen loaded in mode I (crack opening) using the grid method and are drifted.…”

X-ray computed tomography coupled to Digital Volume Correlation applied to a stationary crack case

“…This extension to a 3D case with a finite plate has been developed in order to validate boundary conditions and the behaviour law from surface measurement data [15]. It was developed under the finite element software CASTEM.…”