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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.

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.

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.

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.

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.