THE USE OF MARKOV CHAINS THEORY FOR APPROXIMATION OF ATIGUE CURVE OF COMPOSITE MATERIAL
Some simple mathematical model for fatigue life of composite m aterial consisting mainly of parallel rigidd components (strands) is offered.. The model,, whi chh is foundedd onn the use of Markov chainn theory,, allows too get S-type curve of internal stress growthh and, finally,, too s ee the connectionn betweenn static strengthh distributionn parameters andd S-N fatigue curve (Wholer curve).. The model is tooo simple andd does not provide numerica l coincidence with experimental fatigue test data but by the use of some additional parameters we cann fit the model too actual fatigue datasets,, we can use it for nonlinear regressionn model of S-N fatigue curveandd predict consequence of static strengthh parameter changes.
Estimating Fatigue Curves With the Random Fatigue-Limit Model
In a fatigue-limit model, units tested below the fatigue limit (also known as the threshold stress) theoretically will never fail. This article uses a random fatigue-limit model to describe (a) the dependence of fatigue life on the stress level, (b) the variation in fatigue life, and (c) the unit-tounit variation in the fatigue limit.We fit the model to actual fatigue datasets by maximum likelihood methods and study the fits under different distributional assumptions. Small quantiles of the life distribution are often of interest to designers. Lower confidence bounds based on likelihood ratio methods are obtained for such quantiles. To assess the fits of the model, we construct diagnostic plots and perform goodness-of-fit tests and residual analyses.
Estimation of threshold stress in accelerated life-testing
The author presents a method that uses accelerated life-test data to estimate the mean life at the service stress and the threshold stress below which a failure is unlikely to occur. The relation between stress and mean-life at that stress is assumed to follow an inverse power law that includes a threshold stress. The failure times at a given stress are assumed to follow a Weibull distribution in which the shape parameter varies with the stress. This model extends the well-known Weibull inverse power law model. If only the mean life but not a specific percentile point at a service stress is sought, the maximum likelihood method is useful for parameter estimation. This is a tradeoff in the parametric approach. For adoption of an appropriate probability model, the likelihood ratio test as well as the Akaike Information Criterion are used. Type I right censored data are considered. Extensions of the method are discussed. >