# Comparison of Tensile and Fatigue Properties of Copper Thin Film Depending on Process Method
## 3 Tensile and Fatigue Test
### Fatigue Test and Fatigue Properties  
In this study, in order to obtain the fatigue properties for each of the rolled copper and the electrodeposited copper through the stress-life curve, the target of fatigue life is set to four levels (10,000/50,000/100,000/500,000 cycles). At least three tests were performed for each target level to obtain stress and life data. To analyze the fatigue properties, the stress and life data from the fatigue test were used to plot the stress-life curve. When the fatigue test, the stress ratio between the maximum stress value and the minimum stress value was set to R = 0.1, and a cyclic load of 3 Hz was applied. The relationship between the number of cycles to failure (\(N_{f}\)) and the amplitude stress (\(S_{a}\)), which are frequently used to evaluate fatigue properties, is obtained. In the stress-life (\(S_{a}-N_{f}\)) curve of the log-log scale, the linear equation is generally expressed as Equation (1) [16], as in the form of the Basquin's equation. Where \(o_{f}^{\prime}\) and \(b\) are the fatigue strength coefficients and the exponents, respectively. \[S=o_{f}^{\prime}(2N_{f})^{b} \tag{1}\]  
Figure 10 is a stress-life curve which is shown the relationship between amplitude stress and life for the fatigue test results of rolled and electrodeposited copper depending on the process. In addition, stress-life curves were obtained for amplitude stress and alternating stress. Alternating stress was calculated by applying [PERSON]'s fatigue equation as shown in Equation (2) [17]. It was obtained using experimental data repeated three times for each target life level, and the error of experimental data was small. Since copper is a nonferrous metal material, the fatigue limit cannot be obtained. However, the fatigue test was performed up to 500,000 cycles with a high cycle [18]. \[\text{Goodman method}:\ \frac{S_{a}}{S_{alt}}+\frac{S_{m}}{S_{u}}=1 \tag{2}\]  
Figure 9: Stress-Strain curves: Mechanical properties for Cu thin films depending on process method. where \(S_{a}\) is amplitude stress, \(S_{m}\) is mean stress, \(S_{u}\) is ultimate tensile strength, and \(S_{alt}\) is alternating stress. In this study, the mean stress is not 0 when the fatigue test performed. The fatigue test is not considered the mean stress, but fixed the stress ratio R = 0.1 and set the maximum stress for life. We performed the fatigue test without considering the average stress. Fatigue experiments were performed by fixing the stress ratio R = 0.1 and finding the maximum stress for the target life. It is difficult to compare the fatigue properties at R \(\
eq-1\) with the bulk material or with other experimental results. Goodman method had originally been proposed to consider mean stress when predicting the fatigue life. Therefore, we obtained the alternating stress using the Goodman method that is best known for a reasonable comparison considering the mean stress. As a result, from the fatigue life equation obtained for amplitude stress, the fatigue strength coefficients were 513.28 MPa and 276.77 MPa, respectively, and the fatigue strength exponents are \(-0.1113\) and \(-0.0759\), respectively. The fatigue life equations for the alternating stresses of the rolled and the electrodeposited copper were 2054.64 MPa and 776.37 MPa, respectively, and the fatigue strength exponents were \(-0.1836\) and \(-0.1225\), respectively. The experimental results show that the rolled copper has higher fatigue strength and fatigue limit than the electrodeposited copper. In this study, fatigue life equations in the finite-life region are obtained and analyzed. In Table 2, the results of the fatigue life equations of the rolled and electrodeposited copper and the fatigue life equations according to the plating method of [12] are presented as amplitude stress and alternating stress. Types A, B, and C are the results of fatigue tests with constant 0.5 of tensile strength at mean stress.