Experimental Evaluation of the M Integral in an Elastic Plastic Material Containing Multiple Defects

Abstract

An experimental technique for evaluation of the Mintegral in an elasticplastic material containing multiple defects is proposed by using digital image correlation (DIC). This technique makes direct use of the definition of M by experimentally evaluating the integrand of M at various points along a square contour and determining the integral by numerical integration. The nonlinear Ramberg–Osgood model is used to capture the elasticplastic behavior such as the elasticplastic stress and the total strain energy density in terms of the measured displacements by DIC used in an ARAMIS 4M instrument. Compared with the previous experimental method proposed by King and Herrmann (King and Herrmann, 1981, “Nondestructive Evaluation of the J and M Integrals,â€‌ ASME J. Appl. Mech., 48, pp. 83–87), the present technique could be suitable to measure the Mintegral for the various complicated damages, specimen geometries, loading conditions, and material behaviors. The pathindependence or pathdependence of the Mintegral is investigated under smallscale and largescale yielding conditions, respectively. It is found that the values of M are path independent when the contours entirely enclose the nonlinear plastic region near the multiple defects. In contrast, the pathdependence is concluded for an elasticplastic solid under largescale yielding condition when the contours have to pass through the plastic zone. This interesting pathdependence of the Mintegral is consistent with numerical prediction via the finite element method and theoretical analysis developed in this paper.