A hybrid stress measurement using only x-displacements by phase shifting method with fourier transform (PSM/FT) in laser speckle interferometry and least squares method

Abstract

Stress measurement around the edge of a circular hole at the center of a tensile-loaded plate was performed using an improved hybrid method. Phase-shifting method by Fourier transformation (PSM/FT) in laser speckle interferometry was utilized to measure micro-scale displacement of points away from the edge of the hole. Using few x-displacement and location data only, least-squares method integrated with a Laurent series representation of the stress function and local collocation was used to do reliable stress evaluation on the hole boundary. Traction-free conditions are satisfied at the geometric discontinuity using conformal mapping and analytic continuation. The results of the present improved hybrid method agree well with that of finite element method using commercial software, ABAQUS. Different values of number of term (m) in the complex stress functions were tested to see its effect. In the comparison between input x-displacement data and calculated the hybrid method is effective with an error below 1% in all values of m. On the other hand, it came out that at point of high stress concentration (θ =90°), well-comparable results was attained at decreasing value of m. The best value of m is consistently known to be equal to 1 which results are accurate by less than one percent. Results showed that the method is accurate and reliable as compared with the widely-used ABAQUS.