*4.2. Microstructural Variations Affect Data Fluctuation and Failure Behaviors*

Referring to the aforementioned microstructural observations and tensile testing results, a fair amount of the data fluctuation for the FSWA1/C1, A6/C1, and A1/C2 dissimilar joints shown in Figure 7a should be significantly related to the joint inhomogeneity with a different metallurgical bonding area fractionin the WZ region. Since the Weibull model is commonly adopted to forecast the reliability and failure behaviors of engineering components, the hazard function (*λ*(*σi*)) listed in Equation (2) at each corresponding tensile strength is further defined as the ratio of the failure probability density function and reliability functionin the present study for the assessment of failure behaviors. Figure 8a shows the reliability function (*R*(*σi*)) curves of the Al–Cu joints. These curves start from the minimum strength (*σ*0), and the reliability of joints is decreased with increasing tensile loading. The failure rate curves calculated from the hazard function (*λ*(*σi*)) of Al–Cu joints are shown in Figure 8b.

$$\lambda(\sigma\_{\bar{i}}) = \frac{f(\sigma\_{\bar{i}})}{R(\sigma\_{\bar{i}})} = \frac{m}{\sigma\_{\bar{c}}^{\;\;\;\;m}} (\sigma\_{\bar{i}} - \sigma\_0)^{m-1} \tag{2}$$

The Weibull modulus (*m*) is a dimensionless value, and it is a main factor for the Weibull model to determine which Al–Cu joint displays better engineering reliability. It is noted that the Weibull modulus represents the variability of experimental data, which becomes larger as the degree of tensile strength fluctuation decreases and the reliability of the joints increases. As a result of Table 3 and Figure 8b, the Weibull statistical analysis demonstrates that all of the A1/C1, A6/C1, and A1/C2 welding conditions are reliable FSW dissimilar joints with a wear-out failure model (*m* > 1) of the increasing failure rate (IFR) behavior. However, the A1/C1 joint (*m* = 5.4) and the A6/C1 joint (*m* = 9.2) significantly show a larger Weibull modulus compared with the A1/C2 joint (*m* = 1.7). The A1/C2 joints with a lower Weibull modulus generally characterize an early failure behavior because of the much higher initial failure probability of the tensile specimens compared with the A1/C1 and A6/C1 joints, as shown in Figure 7a. Therefore, referring to the microstructural observations illustrated in Figures 2 and 3, it is demonstrated that the FSW Al-Cu dissimilar joints with a large amount of Al–Cu reacting mixtures of uniformly dispersed Al–Cu IMCs particles can resist a higher tensile failure load and also display better engineering reliability because of the larger Weibull modulus. The FSW A6/C1 dissimilar joint with a successful metallurgical bonded WZ region (see Figures 2a and 3a cf. Figure 6b) represent better tensile strength and reliability than a mainly mechanical kissing bonded A1/C2 joint interface (see Figure 2c cf. Figure 6c). Moreover, the reliability of FSW A1/C2 joints is rapidly decreased through just slightly increasing the tensile loading to be larger than the minimum strength, as shown in Figure 8a. Since the minimum strength can be recognized as the safety value of an engineering component, the existence of minimum strength *σ*<sup>0</sup> is needed in order to evaluate the critical reliable tensile strength of varied FSW Al–Cu dissimilar joints. Therefore, FSW Al–Cu dissimilar joints with a larger Weibull modulus can properly be selected for engineering application, as this may be an indicator of lower technique sensitivity and less reliability decrease (see Figure 8a) while the applied tensile loading exceeds the minimum strength.

**Figure 8.** (**a**) The reliability function curves *R*(*σi*) and (**b**) the failure rate curves from the hazard function *λ*(*σi*) of various FSW Al–Cu dissimilar joints. These curves start from the minimum strength (*σ*0), which is the safety tensile strength for FSW Al–Cu dissimilar joints.

Properly friction stir welded joints should have high tensile strength and display ductility, whereas the joints with low tensile strength will fail in a brittle fracture at the WZ region. In order to realize the fracture mechanism with the above-mentioned Weibull statistical analysis results, Figures 9–11 show the representative SEM fracture morphologies of the FSW A1/C1, A6/C1, and A1/C2 dissimilar joints, respectively. Figure 9a gives the BEI fracture sub-surface of A1/C1 joints to identify the Al and Cu base metals and Al–Cu IMCs more clearly. A fair amount of reacting mixtures (the light gray region indicated by the triangular mark) composed of Al2Cu and Al4Cu9 IMCs (identified by XRD analysis, see Figure 4a) are observed within the WZ region of the A1/C1 joint. In addition, cracks propagation is observed at the IMCs/Cu interface, and the internal cracks are perpendicular to the tensile direction, as those encircled in Figure 9a. Figure 9b shows the BEI tensile fracture surface of the A1/C1 joints. Figure 9 c,d represent the EDS mapping analysis region denoted by the triangular mark in Figure 9b, and the composition of this region is about 54.8 Al and 45.2 Cu (in atomic %) by semi-quantitative SEM/EDS analysis. It can be seen that a brittle fracture appears, and the fracture can

be recognized as a result of the interfacial cracks propagation along the Al–Cu IMCs within the WZ region (see Figure 9b cf. Figures 2a and 6a).

**Figure 9.** (**a**) Failure sub-surface, (**b**) fracture surface, (**c**) representative fracture morphology denoted by the arrow in (**b**), and (**d**) Al, Cu elements energy-dispersive X-ray spectroscopy (EDS) mapping of the A1/C1 joint.

Figure 10a shows the SEM tensile fracture surface of the A6/C1 joints for illustration. As seen from the fracture morphologies of the A6/C1 joint, a ductile failure behavior appears with necking and dimpled ruptures (see Figure 10a cf. Figure 6b) at the AA6061 Al base metal. Therefore, it is recognized that A6/C1 joints obviously display better elongation (as listed in Table 2) than A1/C1 and A1/C2 joints. Figure 10b displays the EDS mapping analysis results of Al and Cu elements (with chemical compositions of 31.2 Al and 68.8 Cu, in atomic %) obtained from the WZ region of tensile failed A6/C1 joints. Referring to the above-mentioned microstructural observations, significant reacting mixtures of dispersed Al–Cu IMCs particles represent that intense material plastic flow effectively induces a larger area fraction of the metallurgical bonded zone (see Figures 2b and 3b cf. Figure 4b) within the WZ region of the A6/C1 joint during the FSW process. As a result, Figure 10b illustrates a typical WZ region of good welding quality with a textureof elongated joining materials flow along the tensile direction without an apparent cracking effect after tensile tests. Since the Al–Cu IMCs can be used as reinforcing phases through the distribution of particles [27,45], as shown in the experimental results mentioned in Table 2, Figures 8a and 10b demonstrate that a large fraction of metallurgical bonding of obvious onion rings with dispersed Al–Cu IMCs particles provides a successful firm welding structure, higher tensile strength, better welding quality, and joint reliability of the FSW A6/C1 joint compared with the A1/C1 joint.

Figure 11a,b shows the BEI fracture sub-surface and fracture surface of the A1/C2 joints, respectively. Figure 11c,d represent the EDS mapping analysis result of the rectangular region denoted in Figure 11b, and the composition in this region is about 51.7 Al and 48.3 Cu (in atomic %) by SEM/EDS analysis. Referring to Figure 6c, the fracture of the A1/C2 joints is almost located at the A1050H-aluminum and C2600-brass joint interface. It is reported that FSW dissimilar joints with

an excessively generated thick interfacial IMCs layer generally display poor mechanical properties because of the brittleness of IMCs and quite easier crack propagation [27,32]. Therefore, comparing Figure 11a with Figure 6c, it can be found that many of the cracks that were significantly initiated at the AA1050H/C2600brass joint interface (cracks are also observed on the fracture surface of Figure 11c), and the failure of joints occurred while the cracks penetrated through Al–Cu IMCs (as denoted by the triangular marks in Figure 11a). This phenomenon demonstrates that a thick continuous interfacial IMC results in a significant deterioration of tensile strength and the presence of much lower Weibull modulus (*m* = 1.7) with a rapid increase in the failure probability (see Table 3 and Figure 7a) for the A1/C2 joint. Therefore, FSW A1/C2 joints obviously display the lowest tensile strength with a brittle fracture and an unfavorable welding reliability in this study (see Figure 11a,b cf. Figure 8a).

**Figure 10.** (**a**) Fracture surface and (**b**) EDS mapping of the Al and Cu elements at the WZ region of the tensile failed A6/C1 joint.

**Figure 11.** (**a**) Failure sub-surface, (**b**) fracture surface, (**c**) representative fracture morphology of the rectangular area in (**b**), and (**d**) EDS mapping of the Al and Cu elements of the A1/C2 joint.
