Estimating the Effects of Residual Stress on the Fatigue Life of Notched Components
by
F. V. Lawrence, Jr.
J.-Y. Yung
Abstract
1. INTRODUCTION
There are four important attributes of notched components which together with the magnitude of the fluctuating stresses applied, determine their resistance to metallic fatigue: the ratio of the axial and the applied or self-induced bending stresses; the severity of the notch or discontinuity; the notch-root residual stresses which result from fabrication, post-fabrication treatment or subsequent use; and the mechanical properties of the notch-root material in which the fatigue crack initiation and growth takes place. In this review, the application of an analytical model for predicting the fatigue behavior of notched components will be discussed with emphasis given to estimating the effects of residual stresses.
The authors and their coworkers have developed a model for the fatigue life of weldments which can be applied quite generally to estimate the fatigue resistance of notched components [1]. This model considers the total fatigue life (NT) to be comprised of a period devoted to crack initiation and early growth (NI) and a period devoted to the growth of a dominant crack (NP). While the total life is the sum of these two periods, at long lives, NI dominates [1,2] and the fatigue life or fatigue strength of a notched member can be estimated by considering only crack initiation and early growth through the Basquin equation with the Morrow mean stress correction:
σa = (σ′f – σm)(2NI)b(Fig. 1)
where σa is the stress amplitude, σ′f is the fatigue strength coefficient, σm is the mean stress which includes the residual and local mean stress after the first cycle of load (set-up cycle), 2NI is the reversals devoted to crack initiation and early growth (one cycle equals two reversals) and b is the fatigue strength coefficient.
The general scheme for estimating NI is diagrammed in Fig. 1. Estimates of the total fatigue life (NT) can be obtained by adding the crack propagation life (NP) to these estimates of NI. A method of estimating the effects of residual stresses on the crack propagation life (NP) is summarized in the Appendix. The intent of the remainder of this review is to give a step-by-step summary of the authors’ method of estimating the fatigue crack initiation life NI using the schematic diagram of Fig. 1 as a guide.
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