LEAST SQUARE ANALYSIS FOR DETERMINATION OF SIF-K, FROM WHOLE FIELD DATA OF AN ISOCHROMATIC FRINGE

Abstract

Failure of cracked components is governed by the stresses in the vicinity of the crack tip. The experimental determination of stresses surrounding a crack tip is a challenging target to those involved in experimental stress analysis. In LEFM single parameter characterization of the crack tip stress field is through the stress intensity factor (SIF)-K, representing a quantity, which gives the magnitude of the elastic stress field surrounding a crack tip. In the present dissertation work, the photoelastic methods to extract stress intensity factor, K from isochromatic fringe loop/loops are critically reviewed. Recent developments using single parameter, two-parameter, three parameter and multi-parameter stress field formulations to determine SIF-K1 are presented. In this dissertation work, a photoelastic method to extract stress intensity factor from single isochromatic fringe loop is described. The proposed method requires measured coordinates of three points located on an isochromatic fringe namely apogee point radius (rm ), its tilt angle (0.) and two end points of maximum width(r2,r3) and their corresponding angles 02,03) respectively, which highlights the characteristic shape of the loop present ahead of the crack tip. In application of the method, theoretically generated fringe loops are required. Therefore, crack tip formulation provided by Etheridge et al. [30] sirtg four parameters a, k, 03 and ? has been adopted in this work. Two computer programs: "fringe_loop" and "Least square" were developed. Through "Least square" program refined R and parameter values were obtained, which are then used in "fringe loop" program to compare the characteristic dimensions of three location points of experimental fringe loop in a refined manner. To validate the "Least square" program, a loading frame was fabricated through which any biaxial load can be applied and biaxial load ratio can be varied on photoelastic plate type of specimen having through thickness crack. Manual data collection for 16 points located on an isochromatic fringe for a single cracked specimen using TELEMICROSCOPE available in the laboratory is a very tedious and time consuming process. So, a new photoelastic data collection method has been evolved. In this method image of isochromatic fringe was grabbed through digital camera (1600 x 1200 pixels) image size and later used with AutoCAD software. Further, SIF results obtained using single loop method proposed in this dissertation are compared with the results obtained using Irwin and Theocaris methods. Experimental values are found to be in good agreement with theoretical results.