A High-Accuracy Empirical Formula for the Strain Concentration Factor in Countersunk Holes

Abstract

This paper presents a modified high-accuracy empirical formula for the strain concentration factor in a centrally-placed countersunk holes in isotropic plate under uniaxial tension. Finite Element Method (FEM) was used to investigate the effect of the problem geometric parameters including, plate width and thickness, as well as the hole radius, countersinking depth and angle on the strain concentration factor. The important influence of Poisson’s ratio was also thoroughly discussed. Based on the FEM-generated data and nonlinear regression, a general and high-precision equation for the strain concentration factor was developed. The formulation process was based on producing a general formula for computing the strain concentration factor with unknown coefficients. Such coefficients are determined by minimizing the relative error between the fitted equation and the FE data using nonlinear least squares method. The results of this newly-developed equation were validated with FEA. The comparison showed high accuracy of the present equation in evaluating strain concentration factor in countersunk holes with a relative approximate error of less than 7%. Besides, this equation was efficiently employed to test the various geometric and material parameters on the strain concentration value of countersunk holes. The results of the present equation were compared to the results of older equation available in literature. The comparison proved much higher accuracy of the present equation in evaluating strain concentration factor especially for deeper and larger countersunk holes than the previously published formula.