**2. Simulation Methods and Details**

Intermetallic compound Ni3Al has a face-centered cubic lattice structure and *Pm*-3*m* space group; its lattice constant is *a* = 3.572 Å [22], as shown in Figure 1a. In this study, the CASTEP program [23] was used to perform first-principles calculations based on DFT. In the lattice-structure optimization and elastic-constant calculation, the local density approximation proposed by Ceperley and Alder was applied to investigate the exchange-correlation potential [24]. In addition, Vanderbilt ultra-soft pseudo potentials [25] and the Broyden–Fletcher–Goldfarb–Shanno algorithm [26] were also used during the lattice-structure optimization. The energy cutoff was taken as 600 eV, the *k*-points were set to <sup>10</sup> <sup>×</sup> <sup>10</sup> <sup>×</sup> 10, and the convergence tolerance of energy was set as 5.0 <sup>×</sup> <sup>10</sup>−<sup>6</sup> eV/atom. The self-consistent field had a convergence accuracy of 5.0 <sup>×</sup> <sup>10</sup>−<sup>7</sup> eV/atom, and the maximum ionic Hellmann–Feynman force was 0.01 eV/Å. The stress deviation during the calculation was less than 0.02 GPa.

The length of the TLP bonding sample, the diameter of the joint, and the thickness of the intermediate layer were 66 mm, 5 mm, and 80 μm, respectively, as shown in Figure 1b,c.

A simple tension load of 50 MPa was applied to the ends of the sample at room temperature. Given the axisymmetry of the sample, a one-fourth (1/4) symmetric FE model was established for three-dimensional (3D) finite element analysis (FEA) (Figure 1d), which can drastically reduce calculations and save time. The FE model comprised the parent alloy (i.e., single-crystalline Ni3Al) and an intermediate-layer alloy (i.e., polycrystalline Ni3Al), and there were 50,688 elements and 221,201 nodes. Obviously, the mesh density of the TLP bonded joint in the model, as further shown in the magnification of the indicated zone in Figure 1d, was not sufficiently fine to accurately analyze the localized stress and strain distribution; thus, the submodel method was adopted in the FEA on the basis

of Saint-Venant's principle, as displayed in Figure 1e. The location of the submodel is the same as the indicated zone in Figure 1d, and the submodel comprises 186,850 elements and 775,736 nodes. All FE calculations were performed with the ABAQUS 2018 software, and quadratic complete integration (C3D20) and full Newton iteration were employed to accurately solve the stress–strain relationship.

**Figure 1.** TLP bonded joint sample: (**a**) crystal structure of cubic Ni3Al, (**b**) a sample prepared in experiments, (**c**) the geometry of the sample for FE modeling (mm), and (**d**) the one-fourth 3D FE model and (**e**) submodel.
