Abstract
Models proposed to study the multiaxial fatigue damage phenomenon generally lack probabilistic interpretation due to their deterministic form. This implies failure compulsory happening at the plane exhibiting the maximum damage value, whereas the remaining planes are disregarded. Nevertheless, the random orientation of the predominant defect evidences the possibility of failure being initiated as a function of the predominant defect presence without requiring, necessarily, maximum values of the damage parameter, which emphasizes the need of introducing probabilistic concepts into the failure prediction analysis. In this paper, a probabilistic model is presented that enables the failure probability to be found for any selected plane orientation by considering the damage gradient as a parameter for both proportional and non-proportional loading. The applicability of the model is elucidated by means of an example. Assuming the cdf for the local failure of the material to be known, the probability of failure is calculated for a cross shaped specimen in which shift between the principal stresses sigma xx and sigma yy ranges from 0º to 180º.
Highlights
U sually, models proposed to study the multiaxial fatigue damage phenomenon are applied in their deterministic form
The random orientation of the predominant defect evidences the possibility of failure being initiated as a function of the predominant defect presence without requiring maximum values of the damage parameter, which emphasizes the need of introducing probabilistic concepts in the failure prediction analysis
Once this relation is established, the probability of failure for any of the orientation planes can be calculated as a function of the local multiaxial damage value and, by extension, the global probability of failure for the component can be determined from the survival probabilities for all the planes assuming the weakest link principle
Summary
U sually, models proposed to study the multiaxial fatigue damage phenomenon are applied in their deterministic form This implies failure always happening compulsory at the plane exhibiting the maximum damage, whereas the remaining planes are disregarded. The generalization of the probabilistic fatigue model of Castillo-Canteli [1] proposed by Muniz-Calvente et al [2] allows the primary Weibull cdf of failure to be derived for any failure parameter, regardless of its distribution. In this way, any multiaxial damage value can be related to a number of cycles for a certain probability of failure. The GLM stablishes that the probability of failure for a plane exhibiting a certain value of the generalized parameter (GP) can be obtained by using the primary failure cumulative distribution function (PFCDF): P exp log(GP)
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