An analytical relation between the Weibull and Basquin laws for smooth and notched specimens and application to constant amplitude fatigue

Abstract

Starting from the classical definition of stress‐life Wöhler curve in the form of the Basquin law, an analytical procedure for the calibration of the four parameters' Wöhler curve (the Weibull law) for a plain specimen is proposed. The obtained parameters are then adjusted by means of an additional slope factor preserving the inflection point of the curve while changing its slope in order to model the experimental observations in which an increase of the scatter in life prediction is observed when reducing the stress amplitude. The same approach has then been adopted to calibrate the Weibull law parameters for a notched specimen, and the fitting slope factor has been found to be a value that changes with the material but remains constant with the stress concentration factor. The findings have been validated with existing experimental data on 2024‐T3 aluminum alloy and normalized SAE 4130 steel.

Quantifying the Contributing Factors toward Signal Fatigue in Nanocomposite Strain Sensors

“…When examining the fatigue experienced by a material brought about by the Mullins effect, decay in mechanical stress amplitude in relation to repeated, constant low strain cycling can be plotted as a log–log graph, known as Wöhler’s plot . This scaling in stress amplitude can then be universally modeled using Basquin’s law, − rewritten below in terms of stress range ( i.e. , height of the stress signal) …”

“…Essentially, this expression describes a power-law decay in the measured stress range (σ R ) with cycle number ( C ) up until a saturation point, known as the endurance limit ( C E ), at which the stress decay slope becomes infinitesimally small and the failure limit is said to be infinite. , Here, σ 0 is a material constant related to the stress range after one cycle, and B is the Basquin exponent, which is a universal constant equal to ∼0.1 , but has been reported to vary between ∼0.05 and ∼0.2 depending on material properties . It is important to note that Basquin’s law can only be applied to cycling conditions below the yield point .…”

Generalization of the Weibull probabilistic compatible model to assess fatigue data into three domains: LCF, HCF and VHCF

“…In this way, two boundary conditions have to be fulfilled consisting in the upper left branch with the condition Δσ up = Δσ u , supposedly starting at 0 or 1 cycle (according to the model), and the lower right branch fulfilling the condition of asymptotic matching to the fatigue limit Δσ lim . Two different categories of regression functions are distinguished: those representing non-scaled regression curves, such as the Stüssi [36], and Kohout-Věchet [37] models, and those normalized to the interval [1] which are identified as biparametric Weibull cdfs, such as those of Ravi-Chandran [38,39] and D'Antuono [40] models whereas the Kurek model [41] represents a special case as discussed below. In both cases, the improved version includes a limit number of cycles N 0 as the minimum required to cause LCF failures and an upper bound of the stress range identified with Δσ u .…”

“…4. In this section, the model proposed by Stüssi [36], Kohout-Věchet [37], Ravi-Chandran [38,39], D'Antuono [40] and Kurek et al [41] are analyzed as a preliminary proposal for modeling the entire S-N field by a single equation encompassing the LCF, the HCF and the VHCF domains, see Fig. 5.…”

A modified fatigue damage model considering loading sequence effect

“…In engineering practices, the loading conditions are usually categorized to constant amplitude loading (CAL) and variable amplitude loading (VAL). Tremendous efforts have been made by researchers to predict fatigue failure and fatigue lifetime under CAL(Alexopoulos et al., 2013; D’Antuono, 2020; Pandey and Chand, 2004) and VAL (Huffman and Beckman, 2013; Kwofie and Rahbar, 2013; Li et al., 2021).…”