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We present numerical computation of stresses under fretting fatigue conditions derived from closed form expressions. The Navier-Cauchy equations, that govern the problem, are solved with strong and weak form meshless numerical methods. The results are compared to the solution obtained from well-established commercial package ABAQUS, which is based on finite element method (FEM). The results show that the weak form meshless solution exhibits similar behavior as the FEM solution, while, in this particular case, strong form meshless solution performs better in capturing the peak in the surface stress. This is of particular interest in fretting fatigue, since it directly influences crack initiation. The results are presented in terms of von Mises stress contour plots, surface stress profiles, and the convergence plots for all three methods involved in the study.

We present numerical computation of stresses under fretting fatigue conditions derived from closed form expressions. The Navier-Cauchy equations, that govern the problem, are solved with strong and weak form meshless numerical methods. The results are compared to the solution obtained from well-established commercial package ABAQUS, which is based on finite element method (FEM). The results show that the weak form meshless solution exhibits similar behavior as the FEM solution, while, in this particular case, strong form meshless solution performs better in capturing the peak in the surface stress. This is of particular interest in fretting fatigue, since it directly influences crack initiation. The results are presented in terms of von Mises stress contour plots, surface stress profiles, and the convergence plots for all three methods involved in the study.

Fretting is a phenomenon that occurs at the contacts of surfaces that are subjected to oscillatory relative movement of small amplitudes. Depending on service conditions, fretting may significantly reduce the service life of a component due to fretting fatigue. In this regard, the analysis of stresses at contact is of great importance for predicting the lifetime of components. However, due to the complexity of the fretting phenomenon, analytical solutions are available for very selective situations and finite element (FE) analysis has become an attractive tool to evaluate stresses and to study fretting problems. Recent laboratory studies in fretting fatigue suggested the presence of stress singularities in the stick-slip zone. In this paper, we constructed finite element models, with different element sizes, in order to verify the existence of stress singularity under fretting conditions. Based on our results, we did not find any singularity for the considered loading conditions and coefficients of friction. Since no singularity was found, the present paper also provides some comments regarding the convergence rate. Our analyses showed that the convergence rate in stress components depends on coefficient of friction, implying that this rate also depends on the loading condition. It was also observed that errors can be relatively high for cases with a high coefficient of friction, suggesting the importance of mesh refinement in these situations. Although the accuracy of the FE analysis is very important for satisfactory predictions, most of the studies in the literature rarely provide information regarding the level of error in simulations. Thus, some recommendations of mesh sizes for those who wish to perform FE analysis of fretting problems are provided for different levels of accuracy.

Fretting is a phenomenon that occurs at the contacts of surfaces that are subjected to oscillatory relative movement of small amplitudes. Depending on service conditions, fretting may significantly reduce the service life of a component due to fretting fatigue. In this regard, the analysis of stresses at contact is of great importance for predicting the lifetime of components. However, due to the complexity of the fretting phenomenon, analytical solutions are available for very selective situations and finite element (FE) analysis has become an attractive tool to evaluate stresses and to study fretting problems. Recent laboratory studies in fretting fatigue suggested the presence of stress singularities in the stick-slip zone. In this paper, we constructed finite element models, with different element sizes, in order to verify the existence of stress singularity under fretting conditions. Based on our results, we did not find any singularity for the considered loading conditions and coefficients of friction. Since no singularity was found, the present paper also provides some comments regarding the convergence rate. Our analyses showed that the convergence rate in stress components depends on coefficient of friction, implying that this rate also depends on the loading condition. It was also observed that errors can be relatively high for cases with a high coefficient of friction, suggesting the importance of mesh refinement in these situations. Although the accuracy of the FE analysis is very important for satisfactory predictions, most of the studies in the literature rarely provide information regarding the level of error in simulations. Thus, some recommendations of mesh sizes for those who wish to perform FE analysis of fretting problems are provided for different levels of accuracy.