Hybrid full-field stress analysis around holes in tensile-loaded plates by phase-shifting photoelasticity

A hybrid stress determination around circular and elliptical holes utilizing photoelastic phase-shifting and nonlinear least-squares methods is presented. The method was demonstrated by calculating fringe orders of distant points along straight lines using 8-step phase-shifting method. The data was used to evaluate the coefficients in the complex stress functions for hybrid analysis. Tangential stresses around the boundary of the holes were obtained using conformal mapping technique. Different number of terms in a power-series representation of the complex type stress function was tested to qualitatively observe the effects of varying stress field. Actual fringes were related with the reconstructed and sharpened fringes along with the change in the number of terms, m. Good agreement was obtained when m in stress functions was equal to nine. At high stress concentration, the result obtained from the hybrid method agrees with FEM by two and five percent for circular and elliptical hole, respectively. The results show that the established numerical-experimental method for stress analysis is considerably reliable.