Study of Local Fatigue Methods (TCD, N-SIF, and ESED) on Notches and Defects Related to Numerical Efficiency

Abstract

The fatigue strength of structural components is strongly affected by notches and imperfections. Both can be treated similarly, as local notch fatigue strength methods can also be applied to interior defects. Even though Murakami’s √area approach is commonly used in the threshold-based fatigue design of single imperfections, advanced concepts such as the Theory of Critical Distances (TCD), Notch Stress Intensity Factors (N-SIF), or Elastic Strain Energy Density (ESED) methods provide additional insight into the local fatigue strength distribution of irregularly shaped defects under varying uniaxial load vectors. The latter methods are based on the evaluation of the elastic stress field in the vicinity of the notch for each single load vector. Thus, this work provides numerically efficient methods to assess the local fatigue strength by means of TCD, N-SIF, and ESED, targeting the minimization of the required load case count, optimization of stress field evaluation data points, and utilization of multi-processing. Furthermore, the Peak Stress Method (PSM) is adapted for large opening angles, as in the case of globular defects. In detail, two numerical strategies are devised and comprehensively evaluated, either using a sub-case-based stress evaluation of the defect vicinity with an unchanged mesh pattern and varying load vector on the exterior model region with optimized load angle stepping or by the invocation of stress and strain tensor transformation equations to derive load angle-dependent result superposition while leaving the initial mesh unaltered. Both methods provide numerically efficient fatigue post-processing, as the mesh in the evaluated defect region is retained for varying load vectors. The key functions of the fatigue strength assessment, such as the evaluation of appropriate planar notch radius and determination of notch opening angle for the discretized imperfections, are presented. Although the presented numerical methods apply to planar simulation studies, the basic methodology can be easily expanded toward spatial fatigue assessment.

A Numerically Efficient Method to Assess the Elastic–Plastic Strain Energy Density of Notched and Imperfective Cast Steel Components

“…Three different stress ratios R have been observed, where R c is defined as the arithmetic mean value. In order to ensure appropriate element sizing within the control volume Ω, the results of a mesh sensitivity study conducted in a preceding study [104] are considered. The SED within Ω is rather insensitive to the element size.…”

“…A stress range of ∆σ = 1 MPa acting in the cross-section with a diameter of 30 mm is utilised in order to evaluate the elastic SED ∆W (e) DEF,97.5% according to [10]. The evaluation of ∆W (e) DEF,97.5% includes the partitioning of individual control volumes along the respective defect contour which corresponds to Method 1 reported in a preceding study [104].…”

“…As associated numerical efforts are substantially reduced compared to non-linear finite element analyses, the elastic-plastic approximation method represents a promising tool to assess arbitrarily shaped defect geometries. In order to minimize computational efforts for complex defect geometries or imperfection networks even further, the implementation of a free-mesh approach as reported in [104] is encouraged for future work. Moreover, the presented elastic-plastic approximation framework can be expanded from planar case studies towards spatial fatigue assessment as well.…”