Single-point measuring method for J-integral based on the integrating isopleth

Abstract

Stem from the path-independence of the J-integral, the computational notion of integrating isopleth is conceived, along which the integral term preserves constant, and the correlated parameters are abstracted to describe the characteristic of the isopleth. Considering the finite plate with a central crack subject to uniform tensile stress, the expression for the token parameter of the J-integral isopleth is deduced based on the general form of the crack field. Accordingly, a single-point method is first proposed exploiting the characteristics of the isopleth. Through the isopleth exploration algorithm and the numerical results, the relations between token parameters and the proposed method are scrupulously verified. Concerning the applicability of the proposed method, numerical tests are performed towards the central cracked thin plate under various loading conditions, while the J-integrals calculated by the single-point method yield high consistency with the real value. Moreover, the optimal locations of the computation point are derived from the relative error distribution, at which guarantees a computational precision within ± 2 %. Overall, the J-integral of the cracked finite plate under symmetric loading can be swiftly acquired utilizing the single-point method, free of the complicated contour integrating.