# Fretting Fatigue Experiment and Finite Element Analysis for Dovetail Specim at High Temperature
## 3 Numerical Simulation Method
### Finite Element Analysis Method  
Traditional fretting fatigue tests employ a basic contact configuration in which fretting is produced by the contact of a flat specimen and cylindrical pads [16]. This line contact form enables an analytical stress estimation through a traditional Hertz contact. However, in the dovetail configuration, a theoretical solution of the stress distribution is perhaps more challenging and finite element analysis would be helpful. The contact pressure and stress distribution were calculated using the commercial program ANSYS in this analysis. What is more, the finite element model developed in the ANSYS program can be used to analyze the fretting fatigue damage and verify the test results. In the ANSYS finite element modeling, the fretting contact can be characterized either by surface or contact element. To describe the interaction between the dovetail specimen and fretting pads, we used the surface-to-surface contact with Coulomb friction. Detailed analyses were performed on the accurate three-dimensional model of dovetail specimen and fretting pads to achieve a more credible result, though a 2D model [14] may improve the efficiency. The temperature will affect the elastic modulus and Poisson's ratio of DD10 and FGH99. Through the measured values of elastic modulus \(E\) and Poisson's ratio \(v\) at specific temperatures shown in Tables 4 and 5, the accurate material parameters under the test temperature 630 \({}^{\circ}\)C can be calculated. To simplify the scale of the finite element model, only the dovetail specimen and two fretting pads are meshed in the ANSYS program. Besides, only the local elements near the contact surfaces are refined to ensure the accuracy of contact calculation. Figure 5 depicts the boundary conditions and the load application in the finite element model in the global coordinate system, as well as the exact mesh at the contact surfaces. The local coordinate system of \(x\)'-\(y\)'-\(z\)' is established based on the contact surface. The fatigue load is applied on the top of the dovetail specimen in a type of sine wave. Fixed supports are applied on the three side surfaces except for the contact surface of each fretting pad. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline
**T(\({}^{\circ}\)C)** & **25** & **300** & **600** & **700** & **760** & **850** & **980** & **1070** & **1100** & **1120** & **1140** \\ \hline \(E\) (GPa) & 128.149 & 121.668 & 113.044 & 108.178 & 104.466 & 98.835 & 90.129 & 81.411 & 77.069 & 74.101 & 71.238 \\ \(v\) & 0.369 & 0.382 & 0.399 & 0.407 & 0.414 & 0.420 & 0.432 & 0.442 & 0.451 & 0.457 & 0.464 \\ \hline \end{tabular}
\end{table} 
Table 4: Material parameters for DD10. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline
**T(\({}^{\circ}\)C)** & **20** & **200** & **350** & **400** & **500** & **600** & **700** & **750** & **800** \\ \hline \(E\) (GPa) & 221 & 216 & 210 & 205 & 198 & 180 & 161 & 193 & 178 \\ \(v\) & & & & & 0.3 & & & & & \\ \hline \end{tabular}
\end{table} 
Table 5: Material parameters for FGH99. Solid 186 of quadratic hexahedral elements is used for the solid structure in the finite element model, which is defined by 20 nodes for each element. The contact surfaces between the dovetail specimen and fretting pads are defined as contact pairs. Conta174 and Targe170 of contact elements overlay the contact and target surfaces of the finite element model, respectively, thus small sliding between the contact surfaces is permitted during the numerical computation due to the unique characteristics of the contact elements. The meshing method of \"Contact sizing\" was used to create same size meshes where the surfaces of the two pads and dovetail specimen are coming in contact. To enhance the convergence and the quality of results for structural contact analysis, the mesh is refined at the contact surfaces to capture the accurate stress distribution and the minimum size of the mesh is 0.008 mm.