Stress Fields and Concentrations around Circular Discontinuity: A Methodological Review with Principles of Elasticity
Sunil Bhat *
Department of Mechanical Engineering, MVJ College of Engineering, Bangalore-560067, Karnataka, India
Vijay G. Ukadgaonker
Department of Mechanical Engineering, Indian Institute of Technology, Bombay-400076, Mumbai, India
*Author to whom correspondence should be addressed.
Abstract
A comprehensive review on the methodology to obtain two dimensional stress field around a discontinuity in the form of a circular hole in the plate subjected to various types of, uniform, axisymmetric and non-axisymmetric monotonic loads at infinity viz. uni-axial tensile, equal bi-axial (tensile-tensile and tensile-compressive) and pure shear is presented with the help of the basic principles of elasticity. The material of the plate is considered to be homogenous, isotropic and linear elastic. Effect of the difference in the type of far field load over the nature and the magnitude of stress fields is examined. Fundamental bi-harmonic equation involving Airy’s stress function is used. The stress function, determined by assuming it in the form of trigonometric series and by employing suitable mathematical substitutions, is made to satisfy the bi-harmonic equation. Constants of the stress function are found from the boundary conditions. Stress concentrations at the surface of the hole and at locations away from the hole are obtained for all the investigated load cases. Criteria of failure and fatigue life estimations of the plate made of linear elastic or elastic plastic material are touched upon. Stress solutions in cases of bi-axial loads of unidentical magnitudes are also presented.
Keywords: Airy’s stress function, bi-harmonic equation, circular hole, discontinuity, stress concentration