Three-Dimensional Stress Concentration Factor in Finite Width Plates with a Circular Hole

Abstract

The three-dimensional stress concentration factor (SCF) at the edge of elliptical and circular holes in infinite plates un der remote tension has been extensively investigated considering the variations of plate thickness, hole dimensions and material properties, such as the Poisson’s coefficient. This study employs three dimensional finite element modeling to numerically investigate the effect of plate width on the behavior of the SCF across the thickness of linear elastic iso tropic plates with a through-the-thickness circular hole under remote tension. The problem is governed by two geomet ric non-dimensional parameters, i.e. , the plate half-width to hole radius (<i>W</i>/<i>r</i>) and the plate thickness to hole radius (<i>B</i>/<i>r</i>) ratios. It is shown that for thin plates the value of the SCF is nearly constant throughout the thickness for any plate width. As the plate thickness increases, the point of maximum SCF shifts from the plate middle plane and ap proaches the free surface. When the ratio of plate half-width to hole radius (<i>W</i>/<i>r</i>) is greater than four, the maximum SCF was observed to approximate the theoretical value determined for infinite plates. When the plate width is reduced, the maximum SCF values significantly increase. A polynomial curve fitting was employed on the numerical results to generate empirical formulas for the maximum and surface SCFs as a function of <i>W</i>/<i>r</i> and <i>B</i>/<i>r</i> . These equations can be applied, with reasonable accuracy, to practical problems of structural strength and fatigue, for instance.