# Fatigue of Friction Stir Welded Aluminum Alloy Joints: A Review
## 4 Crack Growth Rate  
Linear elastic fracture mechanics has been applied to describe the fatigue crack growth behavior. The crack propagation is divided into three stages: initiation, crack growth, and crack failure. The crack does not expand when the crack tip stress intensity factor amplitude \(\Delta K\) is less than a certain threshold \(\Delta K_{th}\). When \(\Delta K\) is larger than the threshold \(\Delta K_{th}\), the cyclic crack gradually expands. The crack length gradually increases but the crack growth rate decreases to steady stage, before the fracture fails the crack expansion rate is accelerated. The Paris formula is used for calculating the crack growth rate:  
\[\frac{da}{dN}=\mathrm{C}(\Delta\mathrm{K})^{m} \tag{2}\]  
where, \(C\) and \(m\) are related to the material, environment, frequency, temperature, and stress ratios.  
The main factors affecting the crack propagation rate are the postveld treatment process, process parameters, and defects. [PERSON] et al. [83] studied the effects of shot peening and laser treatment on the fatigue properties of friction stir welded joints. At ambient and elevated temperature, shot peening treatment has similar fatigue crack growth resistance as the as-welded condition and crack growth rates were higher than the laser peened case. [PERSON] [84] found that single-layer laser peening had little effect on fatigue crack growth but multilayer laser peening greatly improved fatigue crack growth rate. Similar conclusion was also drawn by [PERSON]. [85] Shot peening did not result in a significant reduction to fatigue crack growth in FSW specimens. Samples treated with three layers of laser peening showed the highest improvement in fatigue life over the unpeened conditions and base unwelded material, as illustrated in Figure 12. At cryogenic temperature, Figure 13, the crack growth rate varied greatly, making it difficult to distinguish the trend between residual stress treatment and crack growth data [83; 85]. [PERSON] et al. [86] concluded that under the condition of lower stress intensity factor difference (\(\Delta K\leq 13\) MPa\(\cdot\)m\({}^{1/2}\)), the fatigue crack growth rate of all welded samples is slower than that of the base alloy; however, at higher \(\Delta K\) values, the fatigue crack growth rate of the welded sample is much faster than the fatigue crack growth rate of the base alloy. The compressive residual stress generated by laser peening decreased the average stress and closed the crack, which significantly reduced the crack growth rate, and the material fatigue life was improved. The influence of process parameters on the crack growth rate is mainly reflected in the unreasonable parameters which are prone to producing defects. The optimized process parameters can facilitate the material plastically movement, and break the hardened material precipitates and the surface oxide layer [7]. The existence  
Figure 11: Hook defect of the dissimilar joint (AA5754–AA6082) [82].  
of defects will reduce the crack initiation time and generate stress concentration to increase the crack growth rate. For material properties, fracture toughness can also affect the crack propagation, the higher material fracture toughness, the lower crack growth rate.  
Figure 12: Fatigue growth data for FSW 7075-T7351 [85].  
Figure 13: _da/dN_ versus applied stress intensity factor range, \(\Delta K\), for 2195 aluminum at \(-140\)\({}^{\circ}\)C [83].