Growth rate models for short surface cracks in AI 2219-T851
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loading conditions, for which slip associated with the propagation of short cracks is localized near the surface and is confined by the grain boundaries. MICROCRACK PROPAGATION MODEL A model of early crack growth in A1 2219-T851 alloy is proposed. It is rationalized by using literature data and new experimental results described in more detail later. Two processes are assumed to affect the propagation of short surface cracks in A1 2219-T851: 1) an incubation period for propagation of a crack beyond a grain boundary; 2) crack closure stress. Both mechanisms are influenced by crack length and grain size, as the result of a noncontinuum deformation behavior at the crack front at the surface. Unless otherwise specified, this paper deals with transgranular, noncrystallographic, Mode I surface cracks, which abound in A1 2219-T851 subjected to fatigue. Also the modeling is limited to fully reversed constant stress amplitude loading with the peak applied stress less than the alloy yield strength. Incubation: Chang et al 1~have proposed a dislocation based model of incubation which considers the development of banded slip at the tip of a crack in an initially undeformed medium. They demonstrate that crack propagation cannot occur unless a critical strain energy density is exceeded at a microcrack tip. An incubation period is calculated from the applied cyclic stress amplitude, the microcrack length and the distance of a surface crack tip to the next grain boundary (i.e., the maximum slip length). It represents the number of fatigue cycles necessary to accumulate the critical strain energy required for propagation at that crack tip. Assumptions include: 1) The slip important to propagation occurs in a thin layer at the free surface and at approximately _+45 deg to the applied stress axis; 2) Slip does not occur in substantial amounts beyond the next grain boundary in the direction of crack propagation. A recent study of the crack tip deformation behavior of short cracks in A1 2219-T851 supports the suitability of these assumptions for this alloy? l Previously, the Chang model has been applied by Morris and James 12to predict the statistical distribution
ISSN 0360-2133/81/0112-0057500.75/0 ~3 1981 AMERICAN SOCIETY FOR METALS AND THE METALLURGICALSOCIETY OF AIME
VOLUME12A, JANUARY 1981--57
of fractured intermetallic particle sizes and the encompassing grain sizes which produce crack propagation into the matrix during fatigue of A1 2219-T851. To improve agreement to observations, a modification was proposed to account for the influence of the grain's crystallographic orientation on the propensity for slip parallel to the surface. In its initial form the Chang model assumed that the crack length is constant during incubation. The modification proposed below removes this constraint. This situation is encountered in the growth of short cracks when only one of the two surface crack tips reaches a grain boundary. The number of fatigue cycles comprising incubation, N d, is given by N~+Na
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