*3.3. Temperature Effect on Tensile Properties of Polycrystalline Cu6Sn5*

The stress–strain curves of the polycrystalline Cu6Sn5 at strain rates ranging from 0.001 to 100 ps−<sup>1</sup> were recorded in the temperature range of 250 K to 500 K, as illustrated in Figure 4. The changing trends of all stress–strain curves are similar in the temperature range of 250–500 K, with the strain rate ranging from 0.001 to 100 ps<sup>−</sup>1. The stretching deformation shifted from the elastic stage to the plastic stage and then cracked. There is no yield phase and plastic deformation in this tensile process, which indicates that the elastic deformation is prominent, and the failure of the polycrystalline Cu6Sn5 at strain rates from 0.001 to 100 ps−<sup>1</sup> is due to brittle fracture. It was also observed that the stress– strain curve at the tensile strain rate of 100 ps−<sup>1</sup> was very close to that at the strain rate of 10 ps<sup>−</sup>1. This indicates that for a stain rate exceeding 10 ps<sup>−</sup>1, its effects on the stress– strain response are negligible. Research shows that the failure modes of materials can be affected by strain rate [4]. It was found that elastic deformation is dominant before UTS and exhibits a brittle failure when the polycrystal is stretched, with the strain rate ranging from 0.01 to 100 ps<sup>−</sup>1, as shown in Figure 4a–e. Plastic deformation occurs when the strain rate is less than 0.001 ps−<sup>1</sup> despite the dominance of elastic deformation, as shown in Figure 4f. More information about the ductile performance under a low strain can be found in Section 3.5. The polycrystal exhibits obvious ductile deformation with strain rates lower than 0.001 ps<sup>−</sup>1. Therefore, 0.001 ps<sup>−</sup><sup>1</sup> was chosen as a boundary. Therefore, in this study, strain rates ranging from 0.001 to 100 ps−<sup>1</sup> are defined as high strain rate stretching, and those less than 0.001 ps−<sup>1</sup> are considered as low strain rate stretching.

According to the generalized Hooke's Law, during linear elastic deformation, the stress (*σ*) and strain (*ε*) satisfy Equation (3), where *E* is Young's modulus. Therefore, the slope of the linear part of the stress–strain curve is recorded as Young's modulus.

$$E = \frac{\sigma}{\varepsilon} \tag{3}$$

The calculated results of Young's modulus according to Figure 4 are shown in Figure 5. It is observed that Young's modulus decreases approximately linearly with increasing temperature at different strain rates. Young's modulus decreases from 136.15 to 125.15 GPa, 137.29 to 126.90 GPa, 155.86 to 147.71 GPa, 180.26 to 174.33 GPa, 182.99 to 177.89 GPa, and 183.04 to 178.02 GPa when the temperature increases from 250 to 500 K at strain rates of 0.001, 0.01, 0.1, 1, 10, and 100 ps<sup>−</sup>1, respectively. The decreasing rates of Young's modulus are 44.03, 41.57, 32.61, 23.71, 20.37, and 20.07 MPa/K, respectively. Young's modulus is the tensile modulus, which represents the ability of a material to resist elastic tensile deformation. Thus, the ability of the polycrystalline Cu6Sn5 to resist tensile deformation at a lower temperature is greater than that at a higher temperature.

The UTSs at different temperatures are shown in Figure 6. It is observed that the UTS decreases with an increase in temperature when the strain rate is kept constant. It decreases from 8.91 to 8.53 GPa, 10.90 to 10.53 GPa, 12.96 to 12.22 GPa, 15.29 to 14.46 GPa, 16.58 to 16.00 GPa, and 16.65 to 16.13 GPa when temperature increasing from 250 to 500 K at strain rates of 0.001, 0.01, 0.1, 1, 10, and 100 ps<sup>−</sup>1, respectively. Moreover, it is observed that most strains at corresponding UTSs are nearly the same, while the strain rates are maintained constant, which indicates that temperature has little effect on the strain of the UTS during stretching at a strain rate ranging from 0.001 to 1 ps<sup>−</sup>1, as shown in Figure 4.

From what has been discussed above, the temperature can affect Young's modulus and UTS during stretching, and they both decrease with increasing temperature. This is because both the initial kinetic energy and potential energy of the relaxed system at a high temperature are higher than those at a low temperature, as shown in Figure 7. The potential energy represents the interaction between atoms; thus, the stability of a system increases with a decrease in the potential. On the other hand, kinetic energy represents the random thermal motion between atoms. With an increase in temperature, the atomic motion is more intense, thus leading to an increase in the kinetic energy and, consequently, a decrease in atomic interactions. As the total energy is the sum of the potential and kinetic energy, the initial total energy of the system also increases as the temperature increases. The total energy of the system at the UTS and the energy absorbed during the stretching process (the total energy at UTS minus the initial total energy) are shown in Figures 8 and 9, respectively. The total energy of the system at the UTS increases with the increase in temperature, while the absorbed energy is almost constant. The change in the total energy is due to the initial

energy differences, while the energy absorbed by the system is almost unaffected by the temperature at a constant strain rate stretching.

**Figure 4.** Stress-strain curves of polycrystalline Cu6Sn5 at temperatures of (**a**) 100 ps<sup>−</sup>1, (**b**) 10 ps<sup>−</sup>1, (**c**) 1 ps<sup>−</sup>1, (**d**) 0.1 ps<sup>−</sup>1, (**e**) 0.01 ps<sup>−</sup>1, and (**f**) 0.001 ps<sup>−</sup>1.

**Figure 5.** Young's modulus at different temperatures.

**Figure 6.** UTS at different temperatures.

**Figure 7.** Initial energy of the polycrystalline Cu6Sn5 of (**a**) potential energy and (**b**) kinetic energy.

**Figure 8.** Total energy at UTS with temperature increasing.

**Figure 9.** Energy absorbed at UTS with temperature increasing.

The above reasons account for the decrease in Young's modulus and UTS when the temperature increases. Both Young's modulus and UTS decrease approximately linearly with increasing temperature, but the linearity at higher strain rates (0.01 to 100 ps<sup>−</sup>1) is better than that at lower strain rates (0.001 ps<sup>−</sup>1), as shown in Figures 5 and 6. According to the previous description, 0.001 ps−<sup>1</sup> is the critical strain rate between low and high strain rates. We infer that it may be a ductile–brittle mixed failure when stretching at this strain rate. The energy values absorbed at UTS with different temperatures are shown in Figure 9. It can be found that the absorbed energy exhibits inconsistency according to the temperature variation when stretching with 0.001/ps. Therefore, it can be concluded that the above reasons lead to the inconsistency of UTS with temperature change. This means that as the strain rate decreases, the polycrystalline Cu6Sn5 is subjected to more complex stresses when stretching. The strain rate effects on tensile properties of polycrystalline will be discussed in the next section.
