Abstract
A probabilistic methodology is proposed to evaluate fatigue damage accumulation and fatigue lives of specimens under variable amplitude loading. With probabilistic modifications in the present model, the calculative consistency is achieved between fatigue damage and fatigue life. The load sequence effects on fatigue damage accumulation are properly accounted for variable amplitude loading. The developed damage model overcomes the inherent deficiencies in the linear damage accumulation rule, but still preserves its simplicity for engineering application. Based on the Monte Carlo sampling method, numerical verification of this model is conducted under two kinds of spectrum loading. The predicted probabilistic distributions of fatigue lives are validated by fatigue tests on Al-alloy straight lugs. KEYWORDS. Fatigue damage; Fatigue life; Probabilistic statistical model; Load sequence effect; Statistical self-consistency.
Highlights
Fatigue damage is one of the most common failure modes encountered in engineering structures
M n j 1 j where DB is the damage introduced by one loading block with m stress levels; m is the number of stress levels in a spectrum loading; nj is the cycle number under the jth stress level; aj is the self-consistent exponent dependent on the fatigue life distribution under jth load level, which makes the mean value of nf (Eq(2 )) approximate to the original N; Nj is a random number obeying the distribution of fatigue life under jth stress level; E(Nj) is the mean value of fatigue life under the jth load level and Nf is the random fatigue life under spectrum loading
It can be found that the test data all fall into the 95% interval of life distributions based on the modified fatigue damage accumulation model under the spectrum loading
Summary
Fatigue damage is one of the most common failure modes encountered in engineering structures. The statistically self-consistency between the probabilistic distributions of fatigue damage and failure cycles is achieved by introducing a consistent index b (greater than one) and a random disturbance Δ. In order to enlarge the mean value and the standard deviation of nf, a consistent index b (greater than one) and a random disturbance Δ with mean value equal to zero are introduced to the left and right sides of Eq (1) respectively, which makes the linear fatigue damage prediction model statistically consistent, given by n f i 1. The self-consistent index b is related to statistical parameters α and β of fatigue life distribution It can be solved by comparing the mean values of nf with N through numerical simulation. Eq (5) can be extended to the case of spectrum loading naturally, written as m nj j
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