*3.4. High Strain Rate Effects on Tensile Properties of Polycrystalline Cu6Sn5*

Figure 10 shows the stress–strain curves with strain rate changing from 0.001 to 100 ps−<sup>1</sup> at (a) 250 K, (b) 300 K, (c) 350 K, (d) 400 K, (e) 450 K, and (f) 500 K. The strain rates changing from 0.001 to 100 ps−<sup>1</sup> are denoted as high strain rates in this study. With an increase in the strain rate, the stress at the corresponding strain before the UTS is larger than that at a lower strain rate, and the plastic deformation is more significant at lower strain rates. Despite this, elastic deformation is predominant at high strain rate stretching. When elastic deformation is dominant in the stretching process (strain rate from 0.001 to 100 ps<sup>−</sup>1), the corresponding strain of the UTS increases with the increase in the strain rate, which indicates that the tensile strength of the IMC at a high strain rate is higher than that at a lower strain rate. However, the stress-train response at the strain rate of 100 ps−<sup>1</sup> is very close to that at the strain rate of 10 ps<sup>−</sup>1. This means that when the strain rate is sufficiently large, the effect of the stress–strain response is almost negligible in this study.

Young's modulus and UTS were also calculated based on the stress–strain curves in Figure 10. The results are shown in Figures 11 and 12. Logarithmic coordinates were chosen for abscissa in both figures and the curves reveal the existence of logarithmic relationships between both Young's modulus and UTS to the strain rate. Moreover, they both increase with increasing strain rates. The mechanical properties of Cu3Sn also exhibit a similar logarithmic trend [22].

We can presume that due to fast stretching at high strain rates, dislocations among grain boundaries occur later; thus, the effect of the dislocations is negligible. In this case, the forces at all positions of the polycrystalline Cu6Sn5 are almost the same. Therefore, the ability of the polycrystal to resist tensile deformation is enhanced, thus leading to an increase in Young's modulus and UTS.

To further evaluate the influence of the strain rate on the deformation of the polycrystalline Cu6Sn5, polycrystals with 0.25 and 0.5 strains at 300 K are shown in Figure 13. All the grains are uniformly deformed when stretched at the strain rate of 1 ps<sup>−</sup>1, and the defects between the grain boundaries, even the elongation up to 0.5, are negligible, as shown in Figure 13a,b. This is because the polycrystals are destroyed before the dislocations between the grain boundaries occur owing to the speed of the tensile velocity. However, the deformation characteristics change exponentially with decreasing strain rate. When the strain rate is reduced to 0.001 ps<sup>−</sup>1, there is adequate time for the grain boundaries to dislocate, which leads to defects in the polycrystal, as shown in Figure 13c,d. In addition, with a decrease in the strain rate, the dislocations are more significant among the grain boundaries at the same strain, which results in a decrease in the UTS of the material, as shown in Figure 12.

The radial distribution function (RDF) is the most common mathematical language used to describe the microstructure of liquid and amorphous materials. It denotes the ratio of the local density of a molecule to the bulk density at a distance of *r* around a central atom. In the binary intermetallic compounds system, the RDF for atoms *α* and *β* can be calculated as Equation (4) [16].

$$\lg(r) = \frac{V}{N\_a N\_\beta} \left\langle \sum\_{i=1}^{N\_a} \frac{n\_{i\beta}(r)}{4\pi r^2 \Delta r} \right\rangle \tag{4}$$

where *V* represents the volume of the system and *n*(*r*) the number of particles, which can be found in the shell from *r* to *r* + Δ*r* [16].

The calculated RDFs at different strain rates when the strain is 0.1 are shown in Figure 14. The peak value of the RDFs varies with the strain rates and then gradually approaches 1 with increasing r. It can be seen from the local enlargement that the RDF decreases with an increasing strain rate. This is because an increase in the strain rate causes more disorder in the atomic structure, which increases amorphization and hinders the formation of slip planes [34,35]. As there is no dislocation surface, the UTS improves [16]. The analysis results here are consistent with those shown in Figure 11. The energy absorbed

by the system with different strain rates at the UTS is shown in Figure 15. As the strain rate increases to a larger value, more energy is absorbed by the system when reaching the UTS. Figure 10 shows that the corresponding strain value at the UTS changes over a small range; thus, the increased stress causes more energy to be absorbed.

**Figure 10.** Stress–strain curves with strain rate changing from 0.001 to 100 ps−<sup>1</sup> at (**a**) 250 K, (**b**) 300 K, (**c**) 350 K, (**d**) 400 K, (**e**) 450 K, and (**f**) 500 K.

**Figure 12.** UTS at different strain rates.

**Figure 13.** Polycrystals at different strain rates of (**a**) *<sup>ε</sup>* = 0.25, . *<sup>ε</sup>* = 1 ps<sup>−</sup>1; (**b**) *<sup>ε</sup>* = 0.5, . *ε* =1 ps<sup>−</sup>1; (**c**) *<sup>ε</sup>* = 0.25, . *<sup>ε</sup>* = 0.01 ps<sup>−</sup>1; (**d**) *<sup>ε</sup>* = 0.5, . *ε* = 0.01 ps<sup>−</sup>1.

**Figure 14.** RDF of 10% strain at different strain rates.

**Figure 15.** Energy absorbed at UTS.

*3.5. Low Strain Rate Effects on Tensile Properties of Polycrystalline Cu6Sn5*

The stress-strain curves at 300 K with the strain rate from 0.00001 to 0.0005 ps−<sup>1</sup> are shown in Figure 16. When the strain rate is lower than 0.001 ps<sup>−</sup>1, the stress does not decrease rapidly after the UTS but shows an obvious stage of plastic deformation. Within this strain rate range, the UTS still decreases with a decrease in the strain rate. However, at high strain rates, the relationship between UTS and strain rate is approximately logarithmic, while at low strain rates, the relationship between UTS and strain rate is approximately quadratic, as shown in Figure 17. As the strain rate decreases, the UTS gradually approaches a constant. The polycrystals when the strain rate is 0.00001 and the strains are 0.2 and 0.4 are shown in Figure 18. It can be found that there are no obvious dislocations when stretching at this strain rate. This is because when the tensile velocity is too low, there is sufficient time for stress relaxation. As seen from the local magnification of Figure 14, with a decrease in the strain rate, the plastic deformation of the polycrystalline Cu6Sn5 becomes more significant.

**Figure 16.** Stress–strain curve at low strain rates.

**Figure 17.** UTS at different strain rates.

**Figure 18.** Polycrystals at strain of (**a**) 0.2; (**b**) 0.4.
