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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.

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.

High-temperature thermal-mechanical systems are considered as an indispensable solution to modern vehicle emission control. Such systems include advanced engines, manifolds, thermal regeneration systems, and many other systems. Creep, fatigue, oxidation, or their combinations are the fundamental underlying material degradation and failure mechanisms in these systems subjected to combined thermal and mechanical loadings. Therefore, the basic understanding and modeling of these mechanisms are crucial in engineering designs. In this paper, the state-of-the-art methods of damage/failure modeling and life assessment for components under thermal-fatigue loading, are reviewed first. Subsequently, a new general life assessment procedure is developed for components subjected to variable amplitude thermal- and mechanical- loadings, with an emphasis on hold-time effect and cycle counting.

Engineering components and systems are usually subjected to mixed-mode and multiaxial fatigue loadings, and these conditions should be considered in product durability and reliability design and the maintenance of aging equipment, especially mission-critical components and systems. However, modeling the damage and degradation processes under these complex loading conditions is difficult and challenging task because not only the concepts, such as range, mean, peak, valley etc., developed for uniaxial loading usually cannot be directly transferred to mixed-mode and multiaxial loadings, but also some very unique phenomena related to these complex loading conditions. One such a phenomenon is the loading path effect that can be simply described as: out-of-phase loading is more damaging than in-phase loading for some ductile materials.

Durability and reliability performance is one of the most important concerns for vehicle components and systems, which experience cyclic fatigue loadings and may eventually fail over time. Durability and reliability assessment and associated product validation require effective and robust testing methods. Several testing methods are available and among them, three basic testing methods are widely used: life testing, binomial testing (bogey testing), and degradation testing. In fact, their commonalities, differences, and relationships have not been clearly defined and fully understood. Therefore, the maximum potential of these testing methods to generate efficient, optimized, and cost-effective testing plans, consistent results, and meaningful results interpretation have been significantly limited. In this paper, a unified framework for representing these testing methods and conducting reliability analysis in a single damage-cycle (D-N) diagram is provided.

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.

There is a broad range of material choices for on-road and off-road exhaust systems. The final selection of the materials depends on the balance of engineering performance of the materials and the cost. Thermal-cycling resistance of exhaust materials is an extremely important criterion for the long-term durability and reliability performance of very high temperature exhaust components and systems. To optimize the thermal-cycling resistance and cost of those materials, a selection matrix must be established. Several material evaluation and selection matrices are already available, however, these are not sufficient to meet the industry needs. The current procedure of material selection is essentially based on the trial-and-error approach, which is not efficient in the current market environment. In this paper, a general rational approach for thermal-cycling resistance characterization and ranking is demonstrated.

Corrosion resistance is an extremely important technical issue for long-term durability and reliability performance of exhaust components and systems. Failure mechanisms, such as corrosion, fatigue, corrosion-fatigue and stress corrosion cracking, have long been recognized as the principal degradation and failure mechanisms of vehicle components and systems under combined mechanical and corrosive environmental conditions. The combination of fluid flow, introduced by components such as advanced injectors, and corrosive environment leads to corrosion-erosion failure mechanism. These failure mechanisms are strongly material, environment, and loading dependent. How to characterize, screen, rank and select the materials in corrosion resistance is a big challenge posed to materials scientists and engineers. In this paper, the common corrosion related failure mechanisms appearing in auto exhaust systems are reviewed first.

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.

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.

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.

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.

Corrosion-fatigue (CF) and stress corrosion cracking (SCC) have long been recognized as the major degradation and failure mechanisms of engineering materials under combined mechanical loading and corrosive environments. How to model and characterize these failure phenomena and how to screen, rank, and select materials in corrosion-fatigue and stress corrosion cracking resistance is a significant challenge in the automotive industry and many engineering applications. In this paper, the mathematical structure of a superposition-theory based corrosion-fatigue model is investigated and possible closed-form and approximate solutions are sought. Based on the model and the associated solutions and test results, screening and ranking of the materials in fatigue, corrosion-fatigue are discussed.

It is important to quantitatively characterize the automotive events in order to not only accurately interpret their past but also to reliably predict and forecast their short-term, medium-term, and even long-term future. In this paper, several automotive industry related events, i.e. vehicle safety, vehicle weight/HP ratio, the emissions of CO2, HC, CO, and NOx, are analyzed to find their general trends. Exponential and power law functions are used to empirically fit and quantitatively characterize these data with an emphasis on the two functions’ effectiveness in predictability. Finally, three empirical emission laws based on the historical HC, CO, and NOx data are proposed and the impact of these laws on emission control is discussed.

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.

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 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 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.

Time-domain and frequency domain methods are two common methods for fatigue damage and life assessment. The frequency domain fatigue assessment methods are becoming increasingly popular recently because of their unique advantages over the traditional time-domain methods. Recently, a series of moment of load path based multiaxial fatigue life assessment approaches have been developed. Among them, the most recently developed effective second moment of load path (ESMLP) approach demonstrates its potentials of conducting fatigue damage and life assessment accurately and efficiently. ESMLP can be used for fatigue analysis even without resorting to cycle counting because of its unique mathematical and physical properties, such as quadratic form in the kernel of the moment integral, rotationally invariant, and being proportional to damage. Developing a better parameter for frequency-domain analysis is the driving force behind the development of ESMLP as a new fatigue damage parameter.

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.