Photoelastic Determination of Mixed-Mode Stress Intensity Factors K I and K II

Consider a crack in a mixed-mode stress field governed by the values of the opening-mode KI and sliding-mode KII stress intensity factors. Obtain the singular stress components and subtract the constant term σ0x from the stress σx to account for distant field stresses. Determine the isochromatic fringe order N from equation [1] $$ 2{\tau _m} = \frac{{Nf}}{t} $$ (1) where τm is the maximum in-plane shear stress, f is the stress-optical constant and t is the plate thickness. Obtain an expression for N. Consider the opening-mode. If rm and θm are the polar coordinates of the point on an isochromatic loop, furthest from the crack tip (Figure 1), show that [2]