Combined Stresses in an Orthotropic Plate Having a Finite Crack

Abstract

Using a formulation in integral equations, a solution for the combined extension-classical bending stress and displacement solution is presented for the case of an infinite orthotropic flat plate containing a finite crack. While the solution can be expressed in closed form for the entire field, primary emphasis is placed upon the stresses near the crack point. Qualitatively, no major difference in behavior due to orthotropy was found although certain quantitative features are noted, mainly as a function of the characteristic rigidity ratio (Ex /Ey )1/2 . The inverse square-root character of the isotropic stress bending and extension is not changed by orthotropy, although amplitudes and distribution are affected. Account is taken of recent important work by Knowles and Wang dealing with Reissner bending of the plate which shows that the extensional and surface bending stresses are identical in singular character and circumferential distribution. A bending-extension interaction curve for fracture initiation is derived and shown to be linear when based upon the more exact bending theory.