**4. Conclusions**

Elastic constants of single-crystalline Ni3Al as well as the elastic modulus, shear modulus, and the Poisson's ratio of polycrystalline Ni3Al were calculated via DFT, and the calculation results were subsequently verified against previously reported experimental data. Based on the calculated mechanical properties of both single-crystalline and polycrystalline Ni3Al, 3D FEA was used to characterize the mechanical behavior of the TLP bonded joint of single-crystalline Ni3Al under a simple tension load. The simulation results revealed obvious stress concentrations in the joint as a result of

different states of crystal orientation between the parent metals (single crystals) and intermediate layer (polycrystals), which will lead to failure in the polycrystalline Ni3Al and thereby weaken the mechanical strength of the TLP bonded joint. The maximum values of the first principal stress, maximum shear stress, equivalent stress, and the damages equivalent stress in the joint decrease linearly with decreasing elastic modulus of the intermediate layer; thus, reducing the elastic modulus of the intermediate layer can relieve the stress concentration and benefit the mechanical reliability of a TLP bonded joint, which can be verified by experiments.

**Supplementary Materials:** The following are available online at http://www.mdpi.com/1996-1944/12/17/2765/s1, Figure S1: The strain conditions for deriving nine elastic stiffness coefficients; Figure S2: Relationship between the average stress and elastic modulus of intermediate layer; Figure S3: The grain boundary and crystal orientation in the TLP bonded joint: (a) SEM-EBSD image of the joint, (b) grain boundary in the joint; (c) all Euler map; and (d) IPF-Y0 map. The instrument used is FEI Quanta 650F+HKL Channel 5; Figure S4: Nanoindentation test: (a) SEM image of a typical zone in TLP bonded joint; and (b) schematic of a location of nanoindentation array (Berkovich indenter, instrument: Agilent G200); Figure S5: The influence of the post weld heat treatment (PWHT) on the elastic modulus (a) and hardness (b) of parent alloy and intermediate-layer alloy; Figure S6: The tensile strengths of TLP bonded joints before and after PWHT (three samples were measured for each point; instrument: universal testing machine, GP-TS2000M); Table S1: The stress in the joint ignoring the crystal orientation of intermediate layer.

**Author Contributions:** H.Q. and Y.Y. conceived and designed the research; H.Q., T.K., and Q.L. performed the first principles calculation and analyzed the data; Q.L., X.Y., and H.G. carried out the experimental study; T.K. wrote the manuscript; X.Y. and F.L. reviewed and edited the manuscript. All authors read and approved the final manuscript.

**Funding:** This research was funded by Implementing Innovation-Driven Development Capacity Building Special Funds project of Guangdong Academy of Sciences (2018GDASCX-1005 & 2018GDASCX-0113), Key Program for International Cooperation of Science and Technology (China-Ukraine, 2015DFR50310).

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