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

Abstract

Professor of Mechanical Engineering, University of MarylandMethods 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 twoparameter 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 / G , which describes the crack-tip singularity, (b) P K J , z to account for variations in the stress field removed from the crack tip and (c) uox = d K / G a , which is added to the u, component of the stress field to account for the biaxiality of the far-field stresses.A relationship is derived for the maximum shear stress, r,,,, in terms of the three fitting parameters ( K , m, and P, and the two geometric parameters (r, and 0,) associated with the isochromatic fringe loops. A method of solution based on measurements of rm and 0, 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 k 1 per cent for 6 9 O < 0, < 1 4 5 O . Comparison with the twoparameter method shows that the three-parameter method is more accurate and is applicable over a wider range of

The Investigation of Crack's Parameters on the V-Notch Using Photoelasticity Method

“…There are many efforts to increase results accuracy including K I and T. All of them use the information of one, two, or three points (fringe order N and position r, θ), and therefore, particular determination of stress intensity coefficients faces many difficulties [9][10][11]. Dally and Sanford presented a general method to determine K I and T based on overdeterministic analysis using information of many points near crack tip [12].…”

Why K? High order singularities and small scale yielding

“…Some researchers have attempted to compute the amplitude of these higher order terms, i.e., al, ..., am... for m > 0 so as to improve on, or to confirm the SSY description of the near tip stress field (e.g. [4][5][6][7]). In fact, however, if the entire series (1) is valid outside the inelastic zone f~, any attempt to estimate or calculate a m ' s in (2) is not only futile but incorrect as infinitely many terms with rn < -1 are thus neglected.…”

“…Recently, higher order weight functions have been developed to evaluate the coefficients of the non-singular terms of the series expansion with the implicit assumption that terms in the series expansion of the stresses in actual crack bodies that are more singular than r -1/2 do not exist near the crack tip [10]. For example, it is commonly believed that the inclusion of the non-singular terms permits a more accurate interpretation of stress data obtained at finite distances from the crack tip [5,6,7,10]. However, the analysis we have presented indicates that the sole inclusion of the non-singular terms does not necessarily improve the accuracy of the stress field near the crack tip in real materials.…”

Photoelastic Analysis of Cracked Thick Walled Cylinders

“…Schroedel and Smith [4] proposed the calculation of the stress intensity factor using the values of the fringe order on a line normal to the crack tip, method which was subsequently developed by Smith [5]. A methodology similar to that proposed in [3] was developed by Etheridge and Dally [6], which introduced a correction factor for the boundary effects in the expressions of the stress intensity factor. Chona et al [7] used the Westergaard stress field expressions, written as series expansion and obtained the coefficients of the expansion using photoelastic data.…”