# Fatigue of Friction Stir Welded Aluminum Alloy Joints: A Review
## 5 Fatigue Life of Friction Stir Welded Joints
### The Strain Cycle (EN) Analysis  
The strain cycle (EN) analysis can also be used to estimate the number of cycles to failure. For lower cycle fatigue, the weld is subject to higher stress ranges and local plasticity. The strain life analysis is suitable for the lower cycle fatigue since it has an additional term account for the  
Figure 14: S–N curve for some materials [23; 25; 55; 65; 23]. plastic fatigue properties. The equation used for the strain cycle method is derived from the Basquin-Coffin-Manson law:  
\[\frac{\Delta\varepsilon}{2}=\frac{\sigma_{f}}{E}\times\left(2N_{f}\right)^{b}+ \varepsilon_{f}\times\left(2N_{f}\right)^{c} \tag{5}\]  
where, \(\Delta\varepsilon\) is stain range, \(\sigma_{f}\) is fatigue strength coefficient, \(E\) is young's modulus, \(\varepsilon_{f}\) is fatigue ductility coefficient, and \(b\) and \(c\) are strength and ductility exponent, respectively. Compared to high cycle fatigue analysis, fewer studies on the low cycle fatigue properties of FSW joints were reported so far. [PERSON] (2007) carried out strain-controlled low-cycle fatigue experiments on a 6061 Al-T651 weld with different welding parameters. A summary of the fatigue parameters for [PERSON]'s equations is given in Table 2. Fatigue life was increased with greater welding speed, but was nearly not affected by the rotational rate ([PERSON], 1988; [PERSON], 1990). In [PERSON]'s work [PERSON] (1990) on fatigue behavior of the Al 7075 weld, the energy per cycle and fatigue life were determined, as shown in Table 3. With the increment of total strain amplitude, the energy per cycle increased and the number of cycles decreased. [PERSON] et al. [PERSON] et al. (2017) analyzed low-cycle fatigue performance for a friction stir welded 2219-T62 aluminum alloy with varying welding parameters and cooling conditions. Fatigue life slightly reduced with the increasing welding speed from 60 to 200 mm/min with air cooling. The friction stir welded joints with water cooling condition had greater stress amplitude and fatigue life. The Basquin-Coffin-Manson parameters of base metal and FSW welds with air and water cooling are tabulated in Table 2. [PERSON] et al. [PERSON] et al. (2017) performed a low cycle fatigue test on a semisolid processed (thixomodled) Mg-9 Al-1 Zn magnesium alloy (AZ91D) FSW joint. The plot of strain amplitude against the number of cycles to failure for the base metal and friction stir welded joint is shown in Figure 15. The FSW joint exhibited a shorter fatigue life than the base material at strain amplitudes less than 1.2, at strain amplitude of 0.1% no fatigue failure was found for all specimens. The estimated fatigue life parameters from Basquin-Coffin-Manson are provided in Table 2. [PERSON] (2018) investigated low-cycle fatigue behavior of dissimilar FSW of AA6061-to-AA7050. The fatigue life for various tool rotational speeds was given in Figure 16. The fatigue results showed a lower fatigue lives at high strain amplitudes (>0.3% strain) when compared to the results by [PERSON] et al. [PERSON] (2007) For low strain amplitudes (0.2% strain) the fatigue lives were all close to each other. A summary of the fatigue properties for the specimen is presented in Table 2.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Specimen** & \begin{tabular}{c} **Rotation-Welding** \\ **Speed (rpm-mm/min)** \\ \end{tabular}  & \begin{tabular}{c} **Fatigue Strength** \\ **Coefficient**, \(\varepsilon_{f}\) **(MPa)** \\ \end{tabular}  & \begin{tabular}{c} **Fatigue Strength** \\ **Exponent**, \(b\) \\ \end{tabular}  & \begin{tabular}{c} **Fatigue Ductility** \\ **Coefficient**, \(\varepsilon_{f}\) **(**\(\varepsilon\)**)** \\ \end{tabular}  & \ \begin{tabular}{c} **Fatigue Ductility** \\ **Exponent**, \(c\) \\ \end{tabular}  & \begin{tabular}{c} **Ref.** \\ \end{tabular}  \\ \hline \multirow{6}{*}{6061 AI-T651} & Base Metal & 760 & \(-\)0.12 & 0.22 & \(-\)0.72 & \\  & 1400–600 & 509 & \(-\)0.09 & 0.29 & \(-\)0.71 & \\  & 1400–400 & 476 & \(-\)0.09 & 0.34 & \(-\)0.73 & [PERSON] et al.