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Road vibrations cause fatigue failures in vehicle components and systems. Therefore, reliable and accurate damage and life assessment is crucial to the durability and reliability performances of vehicles, especially at early design stages. However, durability and reliability assessment is difficult not only because of the unknown underlying damage mechanisms, such as crack initiation and crack growth, but also due to the large uncertainties introduced by many factors during operation. How to effectively and accurately assess the damage status and quantitatively measure the uncertainties in a damage evolution process is an important but still unsolved task in engineering probabilistic analysis. In this paper, a new procedure is developed to assess the durability and reliability performance, and characterize the uncertainties of damage evolution of components under constant amplitude loadings.

Active regeneration systems for cleaning diesel exhaust can operate at extremely high temperatures up to 1000°C. The extremely high temperatures create a unique challenge for the design of regeneration structural components near their melting temperatures. In this paper, the preparation of the sheet specimens and the test set-up based on induction heating for sheet specimens are first presented. Tensile test data at room temperature, 500, 700, 900 and 1100°C are then presented. The yield strength and tensile strength were observed to decrease with decreasing strain rate in tests conducted at 900 and 1100°C but no strain rate dependence was observed in the elastic properties for tests conducted below 900°C. The stress-life relations for under cyclic loading at 700 and 1100°C with and without hold time are then investigated. The fatigue test data show that the hold time at the maximum stress strongly affects the stress-life relation at high temperatures.

Numerous test data have been generated in many testing institutions over the years and the historical information from previous similar designs and operating conditions can shed light on the current and future designs since they would share some common features when the changes are not drastic. To effectively utilize the historical information for current and future designs, two steps are necessary: (1) finding an approach to consistently correlate the test data; (2) utilizing Bayesian statistics, which can provide a rigorous mathematical tool for extracting useful information from the historical data. In this paper, a procedure for test sample size reduction is proposed based on historical fatigue S-N test data and Bayesian statistics. First, the statistical information is extracted from a large amount of fatigue test data collected over the years.

This paper reviews the correlation concepts and tools available, with the emphasis on their historical origins, mathematical properties and applications. Two of the most commonly used statistical correlation indicators, i.e., modal assurance criterion (MAC) for structural deformation pattern identification/correlation and the coefficient of determination (R2) for data correlation are investigated. The mathematical structure of R2 is critically examined, and the physical meanings and their implications are discussed. Based on the insights gained from these analyses, a data scatter measure and a dependency measure are proposed. The applications of the measures for both linear and nonlinear data are also discussed. Finally, several worked examples in vehicle dynamics analysis and statistical data analyses are provided to demonstrate the effectiveness of these concepts.

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.

Vehicle exhaust components and systems under fatigue loading often show multiple failure modes, which should be treated, at least theoretically, with rigorous advanced bi-modal and multi-modal statistical theories and approaches. These advanced methods are usually applied to mission-critical engineering applications such as nuclear and aerospace, in which large amounts of test data are often available. In the automotive industry, however, the sample size adopted in the product validation is usually small, thus the bi-modal and multi-modal phenomena cannot be distinguished with certainty.

In the Big Data era, the capability in statistical and probabilistic data characterization, data pattern identification, data modeling and analysis is critical to understand the data, to find the trends in the data, and to make better use of the data. In this paper the fundamental probability concepts and several commonly used probabilistic distribution functions, such as the Weibull for spectrum events and the Pareto for extreme/rare events, are described first. An event quadrant is subsequently established based on the commonality/rarity and impact/effect of the probabilistic events. Level of measurement, which is the key for quantitative measurement of the data, is also discussed based on the framework of probability. The damage density function, which is a measure of the relative damage contribution of each constituent is proposed. The new measure demonstrates its capability in distinguishing between the extreme/rare events and the spectrum events.

Structural stress methods are now widely used in fatigue life assessment of welded structures and structures with stress concentrations. The structural stress concept is based on the assumption of a global stress distribution at critical locations such as weld toes or weld throats, and there are several variants of structural stress approaches available. In this paper, the linear traction stress approach, a nodal force based structural stress approach, is reviewed first. The linear traction stress approach offers a robust procedure for extracting linear traction stress components by post-processing the finite element analysis results at any given hypothetical crack location of interest. Pertinent concepts such as mesh-insensitivity, master S-N curve, fatigue crack initiation and growth mechanisms are also discussed.

Durability and reliability performance is one of the most important concerns of a recently developed Thermal Regeneration Unit for Exhaust (T.R.U.E-Clean®) for exhaust emission control. Like other ground vehicle systems, the T.R.U.E-Clean® system experiences cyclic loadings due to road vibrations leading to fatigue failure over time. Creep and oxidation cause damage at high temperature conditions which further shortens the life of the system and makes fatigue life assessment even more complex. Great efforts have been made to develop the ability to accurately and quickly assess the durability/reliability of the system in the early development stage. However, reliable and validated simplified engineering methods with rigorous mathematical and physical bases are still urgently needed to accurately manage the margin of safety and decrease the cost, whereas iterative testing is expensive and time consuming.

Fatigue, creep, oxidation, or their combinations have long been recognized as the principal failure mechanisms in many high-temperature applications such as exhaust manifolds and thermal regeneration units used in commercial vehicle aftertreatment systems. Depending on the specific materials, loading, and temperature levels, the role of each damage mechanism may change significantly, ranging from independent development to competing and combined creep-fatigue, fatigue-oxidation, creep-fatigue-oxidation. Several multiple failure mechanisms based material damage models have been developed, and products to resist these failure mechanisms have been designed and produced. However, one of the key challenges posed to design engineers is to find a way to accelerate the durability and reliability tests of auto exhaust in component and system levels and to validate the product design within development cycle to satisfy customer and market's requirements.

A probabilistic distribution function roughly consists of two parts: the middle part and the tails. The fatigue life distribution at a stress/load level is often described with two-parameter lognormal or Weibull distribution functions, which are more suitable for modeling the mean (middle) behaviors. The domains of the conventional probabilistic distribution functions are often unbounded, either infinite small (0 for the two-parameter Weibull) or infinite large or both. For most materials in low- and medium-cycle fatigue regimes, the domains of fatigue lives are usually bounded, and the inclusion of the bounds in a probabilistic model is often critical in some applications, such as product validation and life management. In this paper, four- and five-parameter Weibull distribution functions for the probabilistic distributions with bounds are developed. Finally, the applications of these new models in fatigue data analysis and damage assessment are provided and discussed.

Durability and reliability assessment of stress raisers is difficult in testing because the true deformation at a stress raiser often cannot be directly measured. Many approximate engineering approaches have been developed over the last decades, but further fundamental understanding of the problems and the development of more effective engineering methods are still strongly demanded. In this paper, several new concepts and engineering testing approaches are developed and introduced with the emphasis on thermal-fatigue assessment of welded structures.

Over the decades, several attempts have been made to develop new fatigue analysis methods for welded joints since most of the incidents in automotive structures are joints related. Therefore, a reliable and effective fatigue damage parameter is needed to properly predict the failure location and fatigue life of these welded structures to reduce the hardware testing, time, and the associated cost. The nodal force-based structural stress approach is becoming widely used in fatigue life assessment of welded structures. In this paper, a new nodal force-based structural stress recovery procedure is proposed that uses the least squares method to linearly smooth the stresses in elements along the weld line. Weight function is introduced to give flexibility in choosing different weighting schemes between elements. Two typical weighting schemes are discussed and compared.

Life testing or test-to-failure method and binomial testing method are the two most commonly used methods in product validation and reliability demonstration. The two-parameter Weibull distribution function is often used in the life testing and almost exclusively used in the extended time testing, which can be considered as an accelerated testing method by appropriately extending the testing time but with significantly reduced testing samples. However, the fatigue data from a wide variety of sources indicate that the three-parameter Weibull distribution function with a threshold parameter at the left tail is more appropriate for fatigue life data with large sample sizes. The uncertainties introduced from the assumptions about the underlying probabilistic distribution would significantly affect the interpretation of the test data and the assessment of the performance of the accelerated binomial testing methods, therefore, the selection of a probabilistic model is critically important.

Recent stringent government regulations on emission control and fuel economy drive the vehicles and their associated components and systems to the direction of lighter weight. However, the achieved lightweight must not be obtained by sacrificing other important performance requirements such as manufacturability, strength, durability, reliability, safety, noise, vibration and harshness (NVH). Additionally, cost is always a dominating factor in the lightweight design of automotive products. Therefore, a successful lightweight design can only be accomplished by better understanding the performance requirements, the potentials and limitations of the designed products, and by balancing many conflicting design parameters. The combined knowledge-based design optimization procedures and, inevitably, some trial-and-error design iterations are the practical approaches that should be adopted in the lightweight design for the automotive applications.

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.

The approaches of obtaining both fatigue strength distribution and fatigue life distribution for a given set of fatigue S-N data are reviewed in this paper. A new fatigue S-N curve transformation technique, which is based on the fundamental statistics definition and some reasonable assumptions, is specifically developed in this paper to transform a fatigue life distribution to a fatigue strength distribution. The procedures of applying the technique to multiple-stress level, two-stress level, and one-stress level fatigue S-N data are presented.

A design curve, such as a fatigue design S-N curve, is required in engineering design processes. The design curve is usually constructed by analyzing test data, which often exhibit relatively large scatter. For assumed linear test data, two-stress level test plan is commonly used for accelerated life testing (ALT) and subsequent design curve construction. In this paper, based on the two-stress level test plan, a tolerance limit approach is adopted to develop a simple design curve construction procedure. The predicted results from the new method are compared with that of other methods. The advantage of the new method is demonstrated by analyzing the fatigue S-N test data of exhaust components. The determination of minimum sample size is also discussed with a worked table and a graph.

Driven by diesel engine emission regulation, more emission aftertretment products have been under development by Tenneco to address the Particular Matter (PM) and NOx reduction needs. The T.R.U.E. (Thermal Regeneration Unit for Exhaust) Clean active thermal management system is one of the examples to reduce PM. The system is designed to increase exhaust temperatures for DPF (Diesel Particulate Filter) regeneration. This product is exposed to high temperature and high oxidation. Therefore, thermal fatigue, creep, oxidation and the interaction become critical mechanism to be considered for its durability. One of the key challenges to validate this product is to find a way of accelerated testing for thermal, creep, and oxidation as well as for vibration. In this paper, accelerated durability test strategy for high temperature device like T.R.U.E Clean is addressed.