applied fracture mechanics

286Applied Fracture Mechanicsbody. In order to account for the finite thickness of a body and the plastic zone at the cracktip, correction factors were introduced for the “front” surface and the “rear” surface of thebody and for the plastic region at the crack tip (Shah & Kobayashi, 1973). However, solutionsby different authors often showed rather considerable disagreement. Scott andThorpe (Scott & Thorpe, 1981) therefore tested the accuracy of the solutions presented byvarious authors by measuring changes in the shape of a crack throughout its fatigue growth.They concluded that the best engineering estimation of the stress intensity factor for a partthroughcrack in a plate was provided by Newman’s solution (Newman, 1973). An adjustedform of this solution for a thin-walled shell is given by: sa aK M Ekc a M Mt E kI F F TM(5)whereMF is the function depending on the crack geometry (on the ratio a/c) 22 2E 1 k sin dk is an elliptical integral of the second kind, k being02a1 cs is the function depending on the crack geometry (the ratio a/c) and the relative crack depth(the ratio a/t)MTM at1 M T is the correction factor for the curvature of a cylindrical shell and for an1 atincrease in stress owing to radial strains in the vicinity of the crack rootIn the last relationship, MT is the Folias correction factor, determined by any of the relations(1) – (3). The functions MF and s differ in form for the lowest point of the crack tip (point Ain Fig. 2) and for the crack mouth on the surface of the cylindrical shell (point B in Fig. 2).Figure 2. External longitudinal semi-elliptical crack in the wall of a cylindrical shell