A Finite Deformation Analysis of the Near Field Surrounding the Tip of Crack Like Ellipses
VIRGINIA POLYTECHNIC INST AND STATE UNIV BLACKSBURG DEPT OF ENGINEERING SCIENCE AND MECHANICS
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A finite deformation analysis of the region surrounding the tip of small crack like ellipses in an infinite plate under all around tension is presented. The study is carried out in the deformed geometry and includes the effects of finite strains and rotations. A stress function is first introduced to the complete compatibility equations through linear constitutive relations the resulting governing equation is solved through finite differences. The range of root radii investigated varies from one to nine times that of a deformed crack. Normal stresses and strains, maximum in-plane shear stress, displacements and stress intensity factors are presented. The results of the analysis are compared to the linear analysis of Inglis. The effects of finite strains and rotations are shown to be large but are concentrated within a few root radii of the tip. It has been found that two types of behavior exist at the tip of notches, depending on the size of the root radius small root radii produce maximum stresses away from the tip, whereas larger root radii produce maximum stresses at the tip itself.