Stress intensity factor calculations based on a conservation integral

It is observed that one of the integral conservation laws of elastostatics, the so-called M-integral conservation law, has certain special features which make it possible to apply this conservation law for a class of plane elastic crack problems in order to calculate the elastic stress intensity factor in each case without solving the corresponding boundary value problem. The main characteristics which a problem must have in order for the approach to be useful are (1) for points very near to the origin of coordinates, the known elastic stresses are 0(r^?r) where r is the radial coordinate and γ ? 1, (2) for points very far from the origin, the known elastic stresses are 0(r^?r) where γ ? 1, and (3) the boundary of the body is made up of radial lines on which certain traction and/or displacement conditions are satisfied. The approach is demonstrated by determining the stress intensity factors for four familiar elastic crack problems directly from the conservation law, and then four similar additional applications of the M-integral conservation law are discussed.