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This study presents a probabilistic life (failure) and damage assessment approach for components under general fatigue loadings, including constant amplitude loading, step-stress loading, and variable amplitude loading. The approach consists of two parts: (1) an empirical probabilistic distribution obtained by fitting the fatigue failure data at various stress range levels, and (2) an inverse technique, which transforms the probabilistic life distribution to the probabilistic damage distribution at any applied cycle. With this approach, closed-form solutions of damage as function of the applied cycle can be obtained for constant amplitude loading. Under step-stress and variable amplitude loadings, the damage distribution at any cycle can be calculated based on the accumulative damage model in a cycle-by-cycle manner. For Gaussian-type random loading, a cycle-by-cycle equivalent, but a much simpler closed-form solution can be derived.

A newly developed approach, Virtual Rig Simulation for exhaust, is introduced in this paper. An OEM exhaust system durability performance is simulated and simulation results are correlated to test results. The correlation results prove that the Virtual Rig Simulation predicates critical locations very well. The modal transient analysis is applied and input loading is from full event RLDA data. The advantage of the approach is that it can be applied in upfront design stage to predict exhaust system durability performance so that test cost and time are reduced significantly. Also, the presented approach is not only useful for exhaust system development but also useful for other product development.

Weibull analysis is widely used in many industries to predict the fatigue life of different components. Three typical Weibull distributions are introduced in this paper. The application of two parameter Weibull distribution in exhaust component fatigue life prediction is presented. Potential issues in component testing are addressed. Criteria are provided to define normal test data, and when replacement of a tested sample is required. The studies demonstrate that Weibull method is effective to predict component R90C90 life. However, data investigation and processing are critical to predict component life properly. The predicted fatigue life may differ by more than an order of magnitude if the sample life data is unrepresentative of the testing and manufacturing conditions.

A statistic fatigue life assessment procedure is presented in this paper for estimating fatigue damage under stationary Gaussian multi-axial loadings with narrow-band frequency. The fatigue damage is determined by using the Miner-Palmgren rule in connection with a recently developed path-length based multi-axial cycle counting and fatigue life assessment method. In this procedure, the path length is determined by averaging sinusoidal waves with uniformly distributed phase angles while the cycles are estimated from the observation of peak counting results of stress components. Numerically simulated random loading paths with different degrees of non-proportionality are used here to compare the proposed statistical method with its time domain counterpart. Possible further improvement in this research direction is also indicated.

The equilibrium mechanism, which can be considered as the basis of least squares method for linear curve fitting, is investigated in this paper. Both conventional methods, such as vertical offsets method, and total least squares methods, such as perpendicular offsets method, are examined. It is found that both methods have the equilibrium bases. However, the conventional methods may give inaccurate prediction if using vertical offsets method to fit data with variation in horizontal direction or using horizontal offsets method to fit data with variation in vertical direction while the perpendicular method can give best fit solution to data with variation in both vertical and horizontal directions. The application of these methods is also presented in fatigue S-N curve data analysis and two-parameter Weibull distribution in exhaust component fatigue life prediction.

In this paper, the uncertainty of the estimated parameters of lognormal and Weibull distributions for test data with small sample size is investigated. The confidence intervals of the estimated parameters are determined by solving available analytical equations, and the scatters of the estimated parameters with respect to the true values are estimated by using Monte Carlo simulation approaches. Important parameters such as mean, standard deviation, and design curve are considered. The emphasis is on the interpretation and the implication of the obtained shape parameter β of the Weibull distribution function and the design curve obtained from a lognormal distribution function. Finally, the possible impact of this study on the current engineering practice is discussed.

Great efforts have been made to develop the ability to accurately and quickly predict the durability and reliability of vehicles in the early development stage, especially for welded joints, which are usually the weakest locations in a vehicle system. A reliable and validated life assessment method is needed to accurately predict how and where a welded part fails, while iterative testing is expensive and time consuming. Recently, structural stress methods based on nodal force/moment are becoming widely accepted in fatigue life assessment of welded structures. There are several variants of structural stress approaches available and two of the most popular methods being used in automotive industry are the Volvo method and the Verity method. Both methods are available in commercial software and some concepts and procedures related the nodal force/moment have already been included in several engineering codes.