J-integral of a penny-shaped crack on the end of stiff cylindrical cord embedded in rubbery materials

Abstract

The general purpose of this study is the determination of J-integral when dealing with fracture of a penny-shaped crack on the end of the stiff cylindrical cord embedded in rubber matrix. The dimensional analysis is applied to derive a general equation of J-integral, and then it is assumed that the equation of J-integral can be separated into the deformation and geometry functions, the validity of which is proved by using separation parameter. The J-integral is expressed in a multiplicative form in which the geometry calibration function (or factor) is introduced in order to take into account the finite dimensions. The values of the J-integral for the rubber-cord composites with various crack and specimen radius are obtained by using finite element analysis (FEA), and these results are used for concretely determining the geometry calibration function, which, in this work, is expressed in a polynomial form of fourth order. The deformation calibration function, which is a constant for a linear elastic materials, characterizing the large deformable nonlinear effect in rubbery materials is obtained by comparing the equation of J-integral with the ones for the linear elastic deformation. As we approach the infinitesimal strain, the value of the deformation calibration function comes close to the result of linear elastic fracture mechanics (LEFM).