*4.2. Fracture Mechanisms*

Eutectic alloys often exhibit poor fracture strength, which hinders their structural applications [9]. Recent studies have revealed significant improvements in fracture strength due to refinements of the microstructure [10–12]. Laser surface processing is an effective way to refine the microstructure, and it leads to a reduction in interlamellar spacing; it is evidence that microstructure refinement improves the plastic or fracture strain. These findings can be explained by two kinds of theoretical methods: one is a dislocation pile-upbased approach, and the other is a fracture-based approach. According to the dislocationbased approach, the deformation of eutectics is controlled by dislocation pile-ups at the interphase boundaries [20–22]. The interface between the soft phase (Al) and hard phase (Al2Cu or Si) provides an obstacle for dislocation pile-ed up, which controlled the plasticity in this model. The interface hardening controls the yield strength. The stress arises irrespective of the detailed mechanism of the slip, since the plasticity is highly localized in such cases; here, the stress at the tip of the pile-up is given by [2].

$$
\pi\_P = \frac{K \cdot D \cdot \varepsilon\_P}{b \cdot \sqrt{2\lambda}} \tag{7}
$$

where *K* is the constant, *D* is the distance between the two dislocations, *b* is the Burger vector (*b* = 0.285 nm), *λ* is the lamellar spacing, and *ε*<sup>p</sup> is the strain. Equation (6) indicates that the shear stress increases at a given strain with the decrease of inter-lamellar spacing, resulting in improvements in the strength of the eutectic alloy. This agrees well with the experimental data in this work.

Fracture is thought to be controlled by dislocation and interface behavior [23]. Griffith relation was applied in the other model based on crack propagation [3]. The critical crack size for cleavage crack propagation can be calculated as follows:

$$
\sigma\_{\rm F} = \left[\frac{4 \cdot E \cdot \gamma}{\pi \cdot \mathbf{a} \cdot (1 - \nu^2)}\right]^{0.5} \tag{8}
$$

where σ<sup>F</sup> is the fracture stress, *E* is the Young's modulus, *γ* is the surface energy (219.5 mJ/m<sup>2</sup> [24], *a* is the critical crack length, and *v* is the Poisson's ratio (*v*Al = 0.35 and *ν*Al2Cu = 0.34). Here, the Al–Al2Cu eutectic is taken as an example for the analysis of the fracture mechanism. The Al2Cu has a higher modulus (103 GPa ) compared to Al (69 GPa). Substituting the above value, the fracture stress could be calculated: for Al lamellar, σAl <sup>F</sup> = 101.34*a*<sup>−</sup>1/2, while for Al2Cu, <sup>σ</sup>*A*l2Cu <sup>F</sup> = 180.415*a*<sup>−</sup>1/2. Thus, the fracture stress of Al2Cu lamellar is larger than Al lamellar. As the eutectic micropillars were compressed, both Al lamellar and Al2Cu lamellar were compressed, leading to plastic deformation. Since plastic deformation in Al lamella is easier than that in Al2Cu lamella, the load transfers to Al2Cu lamella; correspondingly, cracks were observed in Al2Cu lamella (Figure 4a2,a3). For bulk materials, the critical crack length is mostly around a few millimeters to tens of millimeters, while the eutectic microstructure had two kinds of different ductility phases, whose critical crack length was limited by the inter-lamellar spacing. Supporting that the critical crack length is equal to the inter-lamellar spacing, the fracture stress increased dramatically as the inter-lamellar spacing was reduced from microscale to nanoscale. Thus, the laser-treated Al–Al2Cu–Si and Al–Al2Cu eutectics exhibit higher fracture strength and higher total strain to failure.

In summary, laser surface processing was conducted on Al–Al2Cu–Si and Al–Al2Cu eutectics to refine and manipulate the microstructures. Both laser-remelted ternary Al– Al2Cu–Si and binary Al–Al2Cu eutectics showed high strengths with maximum compressive strength of 1586 MPa and 2075 MPa and improved compressive plasticity with a failure strain of around 26%. By comparison, the as-cast ternary and binary eutectics with coarse microstructures exhibited low strength (lower than 740 MPa) and poor compressive plasticity (failure strain less than 5%). The enhanced compressive strength and improved compressive plasticity were interpreted in terms of microstructural refinement and hierarchical eutectic morphology. Laser-processed nanoscale eutectics show a bright promise of achieving ultra-high strength without loss of plastic deformability.

**Author Contributions:** Writing—original draft, Q.L.; Writing—review & editing, J.W. and A.M. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by U.S. Department of Energy: DE-SC0016808.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** This research was sponsored by DOE, Office of Science, Office of Basic Energy Sciences, grant DE-SC0016808. The authors acknowledge the assistance of J. Mazumder, B.P. Prashanth, and Y.C. Wang at the University of Michigan in material synthesis and laser surface treatment. Nanomechanical testing and electron microscopy were performed at the Michigan Center for Materials Characterization at the University of Michigan.

**Conflicts of Interest:** The authors declare no conflict of interest.
