A three-parameter method for determining stress intensity factors from isochromatic fringe loops

Abstract

Methods for determining the stress intensity factor, K, from isochromatic fringe loops obtained from photoelastic models with sharp cracks are briefly reviewed. A new three-parameter method is introduced which follows the two-parameter approach developed previously by Irwin. In the three-parameter method, three different terms in an analytical solution are adjusted to obtain a suitable match between the theoretical and experimental isochromatic loops. The three parameters are: K/√2πz, which describes the crack-tip singularity, (b) βK/√z, to account for variations in the stress field removed from the crack tip and (c) σ_oa = α¹K/√2πa, which is added to the σ _x component of the stres field to account for the biaxiality of the far-field stresses.

A relationship is derived for the maximum shear stress, τ_m, in terms of the three fitting parameters (K, α, and β) and the two geometric parameters (r_m and θ_m) associated with the isochromatic fringe loops. A method of solution based on measurements of r_m and θ_m from any two independent fringe loops is given.

The accuracy of the three-parameter method was determined by using exact results from the central crack problem for a standard. It was found that the error was within ± 1 per cent for 69° < θ_m < 145°. Comparison with the two-parameter method shows that the three-parameter method is more accurate and is applicable over a wider range of θ_m.