Analytical/numerical solutions for a single hole-edge crack in a wide plate under pure bending

✍ Scribed by H. Gong; K.P. Jen; J.N. Majerus; S. Santhanam

• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 600 KB
• Volume: 46
• Category: Article
• ISSN: 0013-7944
• DOI: 10.1016/0013-7944(93)90124-b

✦ Synopsis

Abatraet-Several solutions to the bending problem of an edge crack on a hole on the neutral axis in a wide plate are presented. Linear elastic fracture mechanics is used to generate analytical solutions for pure bending assuming no width or length effects. The finite element method is also used to analyze certain #nfi~tions.

Obviously, the trade-off between the analytical and numerical analyses involves the required level of accuracy in the solution. Therefore, some sensitivity and convergence studies using both anaIytica1 and numerical FE solutions are presented. The analytical solution is found to be within a few percent of the numerical predictions. NOMENCLATURE crack length dislocation-density function displacement due to a fictitious dislocation located at the center of the hole coefficient of variation = standard deviation/average diameter of hole Young's modulus of elasticity kernel of an integral moment per unit plate thickness radius of hole radius of a circular array of finite elements width of the plate distance from the crack tip along the imaginary crack-line nondimensional stress intensity factor = geometry factor geometry factors using different normalizing stresses function associated with the dislocation-density function stress intensity factor elastic constant location of a dislocation of unit strength shear modulus Poisson's ratio axiai stress in a plate under pure bending tensile stress in a plate with a central hole under pure bending tensile stress associated with a ~st~bution of climb disioeations tensile stress due to a fictitious dislocation located at the center of the hole