The influence of Poisson’s ratio on thickness-dependent stress concentration at elliptic holes in elastic plates

Abstract The influence of Poisson’s ratio (ν) on the thickness-dependent stress concentration factor (SCF) along the root of elliptic holes in elastic plates subjected to tension is systematically investigated by use of three-dimensional finite element method. It is found that the thickness-dependent maximum of SCF, (Kt)max, increases significantly with increasing ν. As the thickness to root radius ratio B/ρ grows from 0.1 to 1000, the (Kt)max undergo a peak value, which can be increased 9% for a circular hole and 23% for an elliptic hole with length of short to long axial aspect ratio t = 0.1 when ν increases from 0.1 to 0.49. It is also found that the peak value occurs in a narrow range of the thickness to elliptic short axis ratio B/b (2–3) with different t and ν. When B/ρ is high enough, an increase of ν from 0.1 to 0.49 leads to decreasing in the SCFs on the free surface (Kt)surf about 24% and 61% and increasing in the ratio of (Kt)max/(Kt)surf about 38% and 195% for circular hole and elliptic hole with t = 0.1. The ν-dependent empirical formulae of the relationships among (Kt)max, (Kt)surf and the corresponding planar solution (Kt)p−σ have been obtained by fitting the numerical results with satisfied accuracy, which will be useful for strength and fatigue designs of engineering structures with notches and holes.