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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 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.

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.

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.

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.

Tensile and fatigue properties of continuous braided carbon fiber reinforced polymer (CFRP) composite to AA6111 self-piercing riveted (SPR) lap shear joints are presented. Rivets were inserted at two target head heights separated by 0.3 mm. Even within the narrow range of head heights considered, the flushness of the rivet head was found to have a dominant effect on both the monotonic and fatigue properties of the lap shear SPR joints. Joints created with a flush head resulted in a greater degree of fiber breakage in the top ply of the CFRP laminate, which resulted in lower lap shear failure load as compared to SPR joints produced with a proud rivet head. Irrespective of the lap shear failure load, rivet pullout was the most common failure mode observed for both rivet head heights. In fatigue tests, the SPR joints produced with a proud head exhibited higher fatigue life compared to SPR joints produced with a flush head.

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.

The introduction of carbon fiber reinforced polymer (CFRP) composites to structural components in lightweight automotive structures necessitates an assessment to evaluate that their crashworthiness dynamic response provides similar or higher levels of safety compared to conventional metallic structures. In order to develop, integrate and implement predictive computational models for CFRP composites that link the materials design, molding process and final performance requirements to enable optimal design and manufacturing vehicle systems for this study, the dynamic mechanical response of unidirectional (UD) and 2x2 twill weave CRFP composites was characterized at deformation rates applicable to crashworthiness performance. Non-standardized specimen geometries were tested on a standard uniaxial frame and an intermediate-to-high speed dynamic testing frame, equipped with high speed cameras for 3D digital image correlation (DIC).

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.

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.

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.

Failure modes of friction stir spot welds in lap-shear specimens of dissimilar high strength dual phase steel (DP780GA) and hot stamped boron steel (HSBS) sheets are investigated under quasi-static and cyclic loading conditions based on experimental observations. Optical micrographs of dissimilar DP780GA/HSBS friction stir spot welds made by a concave tool before and after failure are examined. The micrographs indicate that the failure modes of the welds under quasi-static and cyclic loading conditions are quite similar. The micrographs show that the DP780GA/HSBS welds mainly fail from cracks growing through the upper DP780GA sheets where the concave tool was plunged into during the welding process. Based on the observed failure modes, a kinked fatigue crack growth model is adopted to estimate fatigue lives.

Failure mode and fatigue behavior of friction stir spot welds made with convex and concave tools in lap-shear specimens of dissimilar high strength dual phase steel (DP780GA) and hot stamped boron steel (HSBS) sheets are investigated based on experiments and a kinked fatigue crack growth model. Lap-shear specimens with the welds were tested under both quasistatic and cyclic loading conditions. Optical micrographs indicate that under both quasi-static and cyclic loading conditions, the welds mainly fail from cracks growing through the upper DP780GA sheets where the tools were plunged in during the welding processes. Based on the observed failure mode, a kinked fatigue crack growth model is adopted to estimate fatigue lives of the welds. In the kinked crack fatigue crack growth model, the stress intensity factor solutions for fatigue life estimations are based on the closed-form solutions for idealized spot welds in lap-shear specimens.

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.

Fatigue crack growth tests have been carried out to investigate the mixed mode fatigue crack propagation behavior of an automotive structural adhesive BM4601. The tests were conducted on a compound CMM (Compact Mixed Mode) specimen under load control with 0.1 R ratio and 3Hz frequency. A long distance moving microscope was employed during testing to monitor and record the real time length of the fatigue crack in the adhesive layer. The strain energy release rates of the crack under different loading angles, crack lengths and loads were calculated by using finite element method. The pure mode I and mode II tests show that an equal value of mode I strain energy release rate results in over ten times higher FCGR (Fatigue Crack Growth Rate) than the mode II stain energy release rate does. The mixed mode tests results show that under a certain loading angle, the mixed mode FCGR is changed by changing the load, which is contrary to the find in pure mode I and mode II tests.

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.

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.

High silicon molybdenum (HiSiMo) ductile cast iron (DCI) is commonly used for high temperature engine components, such as exhaust manifolds, which are also subjected to severe thermal cycles during vehicle operation. It is imperative to understand the thermomechanical fatigue (TMF) behavior of HiSiMo DCI to accurately predict the durability of high temperature engine components. In this paper, the effect of the minimum temperature of a TMF cycle on TMF life and failure behavior is investigated. Tensile and low cycle fatigue data are first presented for temperatures up to 800°C. Next, TMF data are presented for maximum temperatures of 800°C and minimum cycle temperatures ranging from 300 to 600°C. The data show that decreasing the minimum temperature has a detrimental effect on TMF life. The Smith-Watson-Topper parameter applied at the maximum temperature of the TMF cycle is found to correlate well with out-of-phase (OP) TMF life for all tested minimum temperatures.

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.

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.