Newton-Raphson Algorithm for Determination of SIFs and Crack-tip from Photoelastic Images

The combination of multi-parameter stress field equations and photoelastic images, a nonlinear least-squares method was deduced and applied to determine the parameters in the stress field equations of crack tip by fitting the isochromatic phase field obtained by the ten-step phase-shifting in digital photoelasticity. Not only the parameters in the stress field equations but also the coordinates of crack tip were determined simultaneously and automatically by using the proposed method. A set of over-determined nonlinear equations were established to estimate the unknown parameters by an iterative procedure based on Newton-Raphson method. Simulation and experimental results validated the correctness of the proposed method.