Elastic stress singularities and corresponding generalized stress intensity factors for angular corners under various boundary conditions

The present paper deals with an analytical description of the stress and displacement fields around a sharp angular corner subjected to various loading and displacement boundary conditions, in plane problems of elasticity. The goal has been gained using a general solution of differential equations of equilibrium in terms of displacements and asymptotic stress function near the notch tip, expressed in polar coordinates. All possible combinations of the boundary conditions applied to the notch faces, such as: free, clamped and for a roller support, have been analyzed as well as symmetric and anti-symmetric loading modes being distinguished. Each case is accompanied by the corresponding characteristic equation of the complex eigenvalues lambda and by its numerical solution presented in graphical form, showing the leading and the higher order terms of the series. Next, the solution to the similar problem for anti-plane shear has been given. Finally, the possibility of application of the generalized stress intensity factors to practical problems of fracture mechanics in all the cases mentioned above is discussed. A numerical method developed to solve the characteristic equations is also described. Copyright (C) 1996 Elsevier Science Ltd.