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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.

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.

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.

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.

Product validation and reliability demonstration require testing of limited samples and probabilistic analyses of the test data. The uncertainties introduced from the tests with limited sample sizes and the assumptions made about the underlying probabilistic distribution will significantly impact the results and the results interpretation. Therefore, understanding the nature of these uncertainties is critical to test method development, uncertainty reduction, data interpretation, and the effectiveness of the validation and reliability demonstration procedures. In this paper, these uncertainties are investigated with the focuses on the following two aspects: (1) fundamentals of the RxxCyy criterion used in both the life testing and the binomial testing methods, (2) issues and benefits of using the two-parameter Weibull probabilistic distribution function.

Fatigue life assessment is an integral part of the durability and reliability evaluation process of vehicle exhaust components and systems. The probabilistic life assessment approaches, including analytical, experimental, and simulation, CAE implementation in particular, are attracting significant attentions in recent years. In this paper, the state-of-the-art probabilistic life assessment methods for vehicle exhausts under combined thermal and mechanical loadings are reviewed and investigated. The loading cases as experienced by the vehicle exhausts are first categorized into isothermal fatigue, anisothermal fatigue, and high-temperature thermomechanical fatigue (TMF) based on the failure mechanisms. Subsequently, the probabilistic life assessment procedures for each category are delineated, with emphasis on product validation.

Fatigue testing and related fatigue life assessment are essential parts of the design and validation processes of vehicle components and systems. Fatigue bench test is one of the most important testing methods for durability and reliability assessment, and its primary function is to construct design curves based on a certain amount of repeated tests, with which recommendations on product design can be advised. How to increase the accuracy of predictions from test results, the associated life assessment, and to reduce the cost through reducing test sample size is an active and continuous effort. In this paper the current engineering practices on constructing design curves for fatigue test data are reviewed first.

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.

In product design and development stage, validation assessment methods that can provide very high reliability and confidence levels are becoming highly demanded. High reliability and confidence can generally be achieved and demonstrated by conducting a large number of tests with the traditional approaches. However, budget constraints, test timing, and many other factors significantly limit test sample sizes. How to achieve high reliability and confidence levels with limited sample sizes is of significant importance in engineering applications. In this paper, such approaches are developed for two fundamental and widely used methods, i.e. the test-to-failure method and the Binomial test method. The concept of RxxCyy (e.g. R90C90 indicates 90% in reliability and 90% in confidence) is used as a criterion to measure the reliability and confidence in both the test-to-failure and the Binomial test methods.

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.