~~t-The inffueuce of geometric non-linea~ty on the s~ess-intensity factor for D centraIty cracked plate subjected to u~forml~ distributed ioad is studied. The bending and stretching stress-intensity factors have been derived by strain energy release rate technique. It is found that the bending stress-~nteos~~ factor varies in a nor&ear fashion as load increases for large deffections of the plate and the resulting in-plane stretching of the plate introduces a stretching stress-intensity factor. NOTATIONS s~ess-intensity factor in bending stress-intensjty factor in s~tching Young's modulus plate thickness Poisson's ratio Cartesian co-ordinates polar co-ordinates displacements in X, y, z directions stress resultants in bending stress resultants in stretching transverse shear KirchhofYs shear semi-crack length plate dimensions rt.d.l. on the pfate E/2(1 f V) moduius of rigidity strain energy due to bending strain energy due to stretching strain energy release rate in bending strain energy release rate in stretcbjng mass densities in L y, z directions damping factors in x, y, z directions residues of equations of equilibrium in X, y, z directions respectively time increment dynamic relaxation THE INVESTIGATION regarding the strength of plate or a she11 with through crack of finite length is of great practicai interest in areas like nuclear and aerospace engineering. Knowledge regarding the nature of the elastic stresses near the crack tip is essential for the study of the strength of structures with flaws, since these are the stresses which are respansibie for possible crack propagation. The characteristics of stresses at the crack tip can be determined using the concept of stress intensity factors which are dependent upon load, geometry and in the case of plates and shells, on Poisson's ratio. Regarding plate and shell type of structures. it was Williamsfl] who applied linear fracture mechanics for a cracked plate in bending and showed that the stresses possess singularity of the order of Ily'r. Duncan-Mama, Sandar, Erdogan and Ratwani using linear thin shell theory have shown that the stresses in shells also have a singularity of the order of I/d/r. All these investigations are based upon the classical theory of bending derived using Kirchhoff assumptions, Recentfy, in view of the three dimensional character of crack tip stresses, higher order plate theories have been applied to bending of cracked plates by Sih et GE.@, 31.
AlI the above investigations are confined to the application of linear fracture mechanics in the sense that no non-linearities come into piay either in the constitutive equations or in the tprofessor & Head, Elasticity Laboratory.