A general method for determining mixed-mode stress intensity factors from isochromatic fringe patterns

A general method is presented for determining mixed-mode stress intensity factors KI and KII from isochromatic fringes near the crack tip. The method accounts for the effects of the far-field, non-singular stress, ?ox. A non-linear equation is developed which relates the stress field in terms of KI, KII, and ?ox to the co-ordinates, r and ?, defining the location of a point on an isochromatic fringe of order N. Four different approaches 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 ? = ? and the K?N relation can be linearized and simplified, the classical approach in which two data points at (rm, ?m)are selected where ?rm/?? = 0; 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 line approach, the method of solution involves an iteractive 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 percent providing that the input parameters r, ?, 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 ? 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 KI, KII, and ?ox determinations.