A general method is presented for determining mixed-mode stress intensity factors Kr and Kn from isochromatic fringes near the crack tip. The method accounts for the effects of the far-field, non.singular stress, Β’o,. A non-linear equation is developed which relates the stress field in terms of Kt, Ku, and Β’o~ to the co-ordinates, r and 0, defining the location of a point on an isochromatic fringe of order N.
Four different al~roaches for the solution of the non-linear equation are given. These include: a selected line approach in which data analysis is limited to the line 0 = ~r and the K-N relation can be linearized and simplified, the classical approach in which two data points at (r,,, 0,) are selected where Or, DO=O; a deterministic method where three arbitrarily located data points are used; and an over-deterministic approach where m ( > 3) arbitrarily located points are selected from the fringe field.
Except for the selected fine approach, the method of solution involves an iterative numerical procedure based on the Newton-Raphson technique. For the over-deterministic approach, the method of least squares was employed to fit the K-N relation to the field data.
All four methods provide solutions to 0.1% providing that the input parameters r, 0, and N describing the isochromatic field are exact. Convergence of the iterative methods is rapid (3-5 iterations) and computer costs are nominal. When experimental errors in the measurements of r and 0 are taken into consideration, the over-deterministic approach which utilizes the method of least squares has a significant advantage. The method is global in nature and the use of multiple-point data available from the full-field fringe patterns permits a significant improvement in accuracy of Kr, Kn, and ~ox determinations.