Stress concentration of 3-D surfaces with small undulations: Analytical solution

Cheng, Zhengkun; Zhang, Yi; Wang, Tao; Li, Shengquan

doi:10.1016/j.ijsolstr.2020.09.027

Cited by 8 publications

(3 citation statements)

References 37 publications

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“…Medina (2015) derived the first-order perturbation equations for stress concentration formula suitable for multiple shallow irregularities and extended them to the high-order analysis for the surface under the plane stress condition by using the Hilbert transform. Cheng et al (2017Cheng et al ( , 2020 derived analytical solutions for the stress concentration of slightly undulating twodimensional (2D) and 3D surfaces using the first-order perturbation method. Cheng et al (2022) derived an analytical approach to calculate the stress distribution in machined round bars with a slightly axisymmetric surface topography.…”

Section: Introductionmentioning

confidence: 99%

Finite-element method for the analysis of surface stress concentration factor and relative stress gradient for machined surfaces

Xu,

Qiao,

et al. 2023

Mech. Sci.

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Abstract. Surface topography is an important parameter for evaluating the quality of surface machining, and the stress concentrations produced at notches can have a profound effect on the fatigue life of notched components. The stress concentration factor (SCF, Kt) and relative stress gradient (RSG, χ) are important parameters used to quantitatively characterize stress concentration. In this study, a finite-element (FE) method was used to evaluate the surface SCF and RSG and determine the effect of microscopic surface topography on machined surfaces. An FE simulation of the static tension test of V-notched round-bar specimens was performed, and the stress due to the local surface topography was investigated. The FE method was used to analyze the stress concentration of round-bar specimens with Kt=1, and the reliability of the results was verified using a perturbation method. The FE method was used to calculate the surface SCF and RSG with high accuracy. The surface SCF and RSG values increased with the surface roughness, and the local maximum values of the surface SCF and RSG were at the bottom of the local topography. Therefore, the SCF and RSG could be estimated based on a linear relationship involving average roughness.

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Section: Introductionmentioning

confidence: 99%

Finite-element method for the analysis of surface stress concentration factor and relative stress gradient for machined surfaces

Xu,

Qiao,

et al. 2023

Mech. Sci.

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“…The finite element descriptions of surface topography to calculate the SCF were then put forward [7][8][9][10][11]. Recently, the theoretical formulas to obtain the SCF imposed by surface morphology based on Fourier representations were built as well [12][13][14][15]. Nevertheless, the SCF introduced by surface roughness is not enough to estimate the fatigue strength of rough specimens due to notch effects [16].…”

Section: Introductionmentioning

confidence: 99%

Fatigue Life Prediction of Machined Specimens with the Consideration of Surface Roughness

Zhu

Zhang

et al. 2021

Materials

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The fatigue strength and fatigue life of high-strength steels are greatly affected by their surface roughness. This study investigates the underlying mechanisms responsible for fatigue failure of the high-strength steel 42CrMo. Bending fatigue tests of stepped shafts with different levels of surface roughness were conducted to observe the fatigue live reduction affected by surface topography. Besides, the mechanical properties of 42CrMo and its strain–life relationship were established. Moreover, the analytical formulas to describe the stress concentration factor (SCF) and fatigue notch factor (FNF) induced by surface topography were introduced. To estimate the fatigue life of machined specimens with the consideration of surface roughness, the elastic portion of the total strain–life curve of the material was revised with the proposed analytical FNF imposed by surface topography. Comparisons between the estimated fatigue lives and experimentally obtained fatigue lives show that the effect of surface roughness on fatigue lives could be estimated effectively and conveniently by the proposed procedure.

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“…From a technical perspective, having a theoretical approach to consider the resolution definition of the surface roughness in fatigue limit predictions is very appealing. Recently, the stress concentration for 2D and 3D machined surfaces have been comprehensively investigated, and analytical solutions via Fourier representation were derived as well 31–35 . However, the analytical derivation about the stress concentration for predicting the fatigue limit of machined round bars is still lacking.…”

Section: Introductionmentioning

confidence: 99%

Analytical prediction of the fatigue limit for axisymmetric round bars with rough surface morphology

Cheng

Zhu

Zhang

et al. 2021

Fatigue Fract Eng Mat Struct

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Analytical approaches to calculating stress distribution in machined round bars with slightly axisymmetric surface topography were derived. Surface morphologies of machined round bars were simplified as axisymmetric geometries and simulated in the form of Fourier representation. According to the point method of the theory of critical distance (TCD), an analytical expression for predicting the fatigue notch factor (FNF) of rough round specimens was proposed as well. The effectiveness of the proposed analytical expression was well verified by finite element method (FEM), with relative errors of less than 15%. Besides, the definition of the upper cut‐off frequency for estimating the fatigue limit of rough round bars was discussed comprehensively. Results showed that stress concentration factor (SCF) was sensitive to the upper cut‐off frequency and unable to be convergent, while FNF tended to be convergent and was mainly determined by low frequencies of surface topography. It explained why the height parameters of surface morphologies are the most significant characteristic parameters in determining fatigue behaviors.

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Stress concentration of 3-D surfaces with small undulations: Analytical solution

Cited by 8 publications

References 37 publications

Finite-element method for the analysis of surface stress concentration factor and relative stress gradient for machined surfaces

Finite-element method for the analysis of surface stress concentration factor and relative stress gradient for machined surfaces

Fatigue Life Prediction of Machined Specimens with the Consideration of Surface Roughness

Analytical prediction of the fatigue limit for axisymmetric round bars with rough surface morphology

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