A computational framework for predicting the effect of surface roughness in fatigue

TL;DR

The paper addresses the challenge of predicting how surface roughness influences high-cycle fatigue through the surface factor $K_s$. It introduces a unified framework that couples a phase-field fatigue fracture model with a stochastic roughness generator, enabling direct computation of $K_s$ as a function of $R_a$, $\ell_{cor}$, and material strength using a fatigue degradation function $f(\bar{\alpha})$ and a no-tension energy split. Validation against literature data shows strong quantitative agreement, particularly when the correlation length is known and the ACF-based criterion $\mathrm{ACF}=0.2$ is used; the tool also yields robust maps of $K_s$ over roughness parameters and reveals the substantial fatigue-life reduction possible for rough surfaces. The framework thus provides a physics-based, stochastic design tool that can inform material selection, manufacturing processes, and future data-driven approaches for predicting surface roughness effects on fatigue.

Abstract

Surface roughness is a critical factor influencing the fatigue life of structural components. Its effect is commonly quantified using a correction coefficient known as the surface factor. In this paper, a phase field based numerical framework is proposed to estimate the surface factor while accounting for the stochastic nature of surface roughness. The model is validated against existing experimental data. Furthermore, we investigate the influence of key parameters on the fatigue life of rough surfaces, such as surface topology and failure strength. An important effect of surface roughness is observed when the average surface roughness increases and the correlation length of the surface profile decreases. This effect becomes more pronounced with higher failure strengths.

Figures (14)

• Figure 1: Analysis of the rough surface topology in a 1D profile. In (a) two examples are represented in blue colours. The green points represent the smooth surface. In (b) the autocorrelation function (ACF) is represented, highlighting the three criteria proposed for determining the correlation length.
• Figure 2: Computational framework flowchart for determining the number of cycles to failure ($N_f$) of a specific rough specimen under a given stress amplitude $\sigma_a$, with characteristic roughness parameters $R_a$ and $\ell_\mathrm{cor}$.
• Figure 3: Geometry of the problem. Dimensions, in mm, taken from Ref. Singh2019. The applied distributed force is denoted as $q$.
• Figure 4: S-N curve of the polished surface. Comparison with experiments Singh2019.
• Figure 5: Comparison of the calculated surface factor to empirical results found in the literature Singh2019Johnson1973.