An integral is developed for calculating opening mode stress intensity factor at any point on the front of an irregular planar crack embedded in an infinite solid and subjected to an arbitrary normal stress field. No other solutions are available for irregular cracks, therefore the integral is first used to analyze three-dimensional regular cracks for which there are solutions. An embedded square crack is used to illustrate the integral procedure for an irregular shape. The integral is also used to explain qualitatively how irregular fatigue cracks will grow.

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A root mean square (RMS) type stress intensity factor, K, which is defined and used in [1] and [2] for crack growth and fracture calculations, is investigated in this study. Whereas the common K studies use approximate numerical integration of the influence function to analyze various configurations, in the present study the K definition is used analytically to derive accurate K values for various ellipticaljiracks subjected to uniform tensile stress and also to pure bending. The significance of these K results are explored via comparison with the exact classical maximum and minimum stress intensity factors along the front of the corresponding elliptical cracks.

Analytical method has been developed to minimize and quantify the effect of crack length measurement interval Δa on the error due to the K gradient in the interpretation of da dN derived from crack growth test data using the secant method. The associated error has been quantified in a general form and used to demonstrate the specific errors due to the selection of average crack length a per ASTM E 647-91. Test Method for Measurements of Fatigue Crack Growth Rates. It is shown that the selection of the geometric mean (a¯=a1a2) in the data analysis will reduce the associated error in the crack growth rate interpretation. It is recommended that ASTM E 647-91 be revised accordingly.