Process zone size effects on naturally curving cracks

Abstract

In a fuselage crack turning application, a crack may grow under stable tearing conditions for some length, achieving a somewhat steady-state condition, then encounter a region of high tensile T-stress as it nears a stiffener, causing the crack to turn. While a T-stress related crack path instability has been described by Cotterell and Rice [Int J Fract 16 (1980) 155], recent experimental evidence indicates that crack turning is also influenced by the size of the process zone. In order to study this problem, the perturbed crack path solution of Cotterell and Rice is extended to include the effects of a process zone represented by cohesive tractions on the crack flanks trailing the crack tip. The characteristic length, r c, over which the tractions are prescribed, represents a strain-localization zone which precedes the physical crack tip, and through which the crack presumably must pass. The strain-localization zone is assumed to be smaller than common measures of plastic zone size, and other than the strain-localization zone, plasticity is not explicitly modeled. The solution, which uses cohesive tractions analogous to the Dugdale–Barenblatt crack tip model [J Mech Phys Solids 8 (1960) 100; Advances in Applied Mechanics, vol. VII, Academic Press, 1962. p. 55], is accurate to first-order deviations from a straight crack path in an infinite medium for small strain-localization zones. A correction factor is provided to the process zone parameter to approximate the solution for larger process zones, but loses accuracy as the strain-localization zone approaches the plastic zone size. Increased process zone size is shown to result in an increase in the perturbation sensitivity of a crack in a positive T-stress environment, causing more rapid turning of the crack, as has also been experimentally observed.