Abstract
A non-linear modification to Miner’s rule for damage accumulation is proposed to reduce the scatter between experimental fatigue life and fatigue life predicted according to the original Miner’s sum. Based on P-s-n probability distribution and design s-n curves, the modification satisfies the assumption of equality between the mean damage degree (at the critical level) and fatigue life random variables, which is not covered in the original formulation. The adopted formulation shows the discrepancies between the fatigue lives predicted according to the design s-n curves and the estimated probability distribution. It also proves that it is inappropriate to apply a normal distribution to fatigue life analysis and that the model becomes non-linear only for non-normal distributions. The predictions according to the established model were compared to the predictions obtained with Miner’s rule.
Highlights
The estimation of the degree of accumulated fatigue damage is necessary for the most common deterministic approach for the fatigue life analysis of structural materials under variable amplitude loading [1,2]
Estimates of the accumulated damage are obtained mostly on the basis of the widely available stress–life (s-n) curves. The fact that these curves have been identified by the least squares method [3] leads to the inappropriate assumptions that 50% of the experimental lives are on the left side of the reference s-n curve, and 50% of the experimental lives are on the right side and that the normal distribution is appropriate for modeling fatigue damage
Karolczuk and Palin-Luc investigated the fatigue lives of 1.0570 steel, which allowed them to estimate the probability–stress–number of load cycles (P-s-n) Weibull distribution for log fatigue lives (i.e., log( N ) ∼ W); Gao and Yuan re-published the data for the P-n Weibull distribution for the fatigue lives of aluminium alloy LY12-CZ (i.e., N ∼ W (h, g)), which was originally published by Ji and
Summary
The estimation of the degree of accumulated fatigue damage (damage degree) is necessary for the most common deterministic approach for the fatigue life analysis of structural materials under variable amplitude loading [1,2]. Estimates of the accumulated damage are obtained mostly on the basis of the widely available stress–life (s-n) curves The fact that these curves have been identified by the least squares method [3] leads to the inappropriate assumptions that 50% of the experimental lives are on the left side of the reference s-n curve, and 50% of the experimental lives are on the right side and that the normal distribution is appropriate for modeling fatigue damage. In order to maintain the simplicity of the widely used ASTM standard [3], the modified approach should correspond to the existing s-n curves
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