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Experiments [i] and analyses [2] on metallic materials have shown that fatigue cracks, under constant and variable amplitude loading, remain closed during part of the load cycle. The crack closure concept has been used to correlate crack growth rates under constant amplitude loading at various stress ratios (R = S . /S ) [i]. It has mln. max , .also been shown to be a significant factor in causlng ±oaa interaction effects on crack growth rates (retardation and acceleration). There have been several attempts to develop simple analytical models of crack closure (see [3], for example) to calculate crack opening stresses (S).Most of these models were based on a concept like the Dugdale mo~el [4] or strip-yield model, but were modified to leave plasticallydeformed material in the wake of the advancing crack.These two-dimensional models have shown that S is a function of stress ratio and stress level (S ) o. • Crack opening stresses are also a function of • . max speclmen thickness (or three dimensional constraint)•The purpose of this note is to present a general crack opening stress equation for constant amplitude loading.The equation is a function of stress ratio R, stress level S , and three dimensional constraint.The effects of three dimensio~ constraint have been simulated in a two dimensional closure model [3] by using a "constraint" factor ~ on tensile yielding; that is, the material yields when the stress is ao . The material is assumed to yield in compression when .O the stress is -~ . Plane stress or plane strain conditions are simulated in the mod~l with ~ = i or 3, respectively.The crack opening stresses were calculated from the closure model [3] for a center crack tension specimen as a function of constraint, stress ratio, and stress level.Equations were then fitted to these numerical results.These equations were So/Smax=A0 + AIR + A2R2 + A3R3 for R>__0 (i) and So/Smax = A0 + AIR for -i~ R < 0 (2) when S > S . The coefficients were o--min A 0 = (0.825 -0.34a + 0.05~2)[cos (~Smax/2Oo)]i/a(3) Int Journ of Fracture 24 (1984)

Experiments on metallic materials have shown that fatigue cracks remain closed during part of the load cycle under constant- and variable-amplitude loading. These experiments have shown that crack closure is a significant factor in causing load-interaction effects (retardation and acceleration) on crack growth rates under variable-amplitude loading. The present paper is concerned with the development and application of an analytical model of cyclic crack growth that includes the effects of crack closure. The model was based on a concept like the Dugdale model, but was modified to leave plastically deformed material in the wake of the advancing crack tip. The model was used to correlate crack growth rates under constant-amplitude loading and to predict crack growth under aircraft spectrum loading on 2219-T851 aluminum alloy plate material. The predicted crack growth lives agreed well with experimental data. The ratio of predicted-to-experimental lives ranged from 0.66 to 1.48. These predictions were made using data from an ASTM Task Group E24.06.01 round-robin analysis.

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The purpose of this paper is to present stress-intensity factor influence coefficients for a wide range of semi-elliptical surface cracks on the inside or outside of a cylinder. The crack surfaces were subjected to four stress distributions: uniform, linear, quadratic, and cubic. These four solutions can be superimposed to obtain stress-intensity factor solutions for other stress distributions, such as those caused by internal pressure and by thermal shock. The results for internal pressure are given herein. The ratio of crack depth to crack length from 0.2 to 1; the ratio of crack depth to wall thickness ranged from 0.2 to 0.8; and the ratio of wall thickness to vessel radius was 0.1 or 0.25. The stress-intensity factors were calculated by a three-dimensional finite-element method. The finite-element models employ singularity elements along the crack front and linear-strain elements elsewhere. The models had about 6500 degrees of freedom. The stress-intensity factors were evaluated from a nodal-force method. The present results were also compared to other analyses of surface cracks in cylinders. The results from a boundary-integral equation method agreed well (±2 percent), and those from other finite-element methods agreed fairly well (±10 percent) with the present results.

This paper reviews the capabilities of a plasticity-induced crack-closure model to predict fatigue lives of metallic materials using "small-crack theory" for various materials and loading

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