*3.2. Cavity Nucleation*

The superplastic tensile specimen was analyzed using a TEM at 500 ◦C and 1 × <sup>10</sup>−<sup>3</sup> <sup>s</sup>−<sup>1</sup> with the strain *ε* = 0.65, as shown in Figure 2. This illustrates that the increase of stress at the initial stage of the superplastic tensile stage due to the increase of the dislocation density under the grain boundary sliding (GBS), in addition, the density of the dislocation was ~3.65 × 1014 <sup>m</sup>2.

(**a**) (**b**)

**Figure 2.** The relationship between the dislocations, precipitate phases (**a**) and grain boundaries (**b**) found using the TEM tests at 500 ◦C and 1 <sup>×</sup> <sup>10</sup>−<sup>3</sup> <sup>s</sup>−<sup>1</sup> (*<sup>ε</sup>* = 0.65).

The diffusion activation energy ranged from 135 to 139 kJ/mol at temperatures ranged from 400 to 500 ◦C, which were close to the lattice diffusion activation energy, 143.4 kJ/mol, of pure aluminum [27]. Analysis of the superplastic behavior in terms of the diffusion activation energy and surface morphology illustrates that lattice diffusion dominates the GBS deformation mechanism of FG 5A70 alloy, and the GBS occurs through the dislocation sliding/climbing on grain boundaries. At 500 ◦<sup>C</sup> and 1 × <sup>10</sup>−<sup>3</sup> <sup>s</sup>−1, when the applied stress accumulation reached the maximum point in superplastic tensile stage, it was clearly found that under the shear stress the GBS caused dislocations to pile up near the precipitation phase, as shown in Figure 2a, and dislocations crossed the grain boundary by sliding and climbing to form a subgrain boundary, as shown in Figure 2b. The dislocation density was higher and the plugging/gathering occurred at the head of the precipitation phases, leading to the stress concentration. When the pile-up stress, *σp*, exceeded the theoretical decohesion strength of the (Al-matrix/Second phase particles) interphase boundary, a small cavity formed, and the cavity began to nucleate attached to the precipitation phase [28]. The stress at the head of the pile-up, *σp*, is given by [29]:

$$
\sigma\_p = \frac{2L\tau^2}{Gb},
\tag{1}
$$

where *L* is the length of the pile-up and equivalent to the linear intercept grain size. *G* is the shear modulus (MPa). The pure aluminum temperature control model was adopted. In this paper, *L* = *d*/1.74, *τ* = *σ*/ <sup>√</sup>3. *<sup>b</sup>* is the Burgers vector, *<sup>b</sup>* <sup>=</sup> *<sup>a</sup>*/ <sup>√</sup><sup>2</sup> = 2.863 <sup>×</sup> <sup>10</sup>−<sup>10</sup> m [30]. When the test temperature was 500 ◦C, the maximum applied stress (*σmax* = 3.75 MPa) solution was plugged into the type product stress *σ<sup>p</sup>* = 7.87 MPa. The plugging stress threshold was more than twice the applied stress in the superplastic tensile state. It is obvious that the Al matrix and the strengthening phase particles were easily separated, which promoted the cavity nucleation under the different stress levels. In addition, dislocations coalesced at the grain boundary to form a subgrain boundary, as showed in Figure 2b. It is

assumed that the shape of the cavity is circular and the equivalent radius of the cavity is *r*. The change of the Helmholtz free energy of the system was obtained as follows [27,31,32]:

$$
\Delta G = -2.53(\frac{2}{3} \times \frac{d}{1.74b} \times \frac{\sigma^2}{G})r^3 + (9.31\gamma - 0.5 \times 2.93\gamma) - 3.79 \times \frac{\left(\frac{2}{3} \times \frac{d}{1.74b} \times \frac{\sigma^2}{G}\right)^2}{2E} r^3,\tag{2}
$$

where *γ* is the surface energy of the cavity, *d* is the grain size and *E* is the Young's modulus of pure aluminum. Figure 3 shows the change of the Helmholtz free energy as a function of the cavity radius of the 5A70 alloy deformed at different tensile temperatures, with the strain *ε* = 0.3 and the strain rate was . *<sup>ε</sup>* = 1 × <sup>10</sup>−<sup>3</sup> <sup>s</sup>−1. By increasing the tensile temperature range from 400 to 550 ◦C, the maximum values of the Helmholtz free energy ranged from 8.32 × <sup>10</sup>−<sup>16</sup> to 8.41 × <sup>10</sup>−<sup>14</sup> J, and the corresponding critical radius of the cavity nucleation maximum values increased from 2.16 × <sup>10</sup>−<sup>8</sup> to 2.37 × <sup>10</sup>−<sup>7</sup> m, indicating that the cavity was very different and nucleated at a higher superplastic tensile temperature. That is, at 500–550 ◦C, it was more difficult for the cavity to cross the nucleation barrier than at 400–450 ◦C. According to Figure 1a, it is suggested that when the superplastic tensile temperatures were 500 and 550 ◦C, the strain hardening led to an increase of the true stress. Meanwhile, the cavity nucleation was beneficial to the superplastic flow.

**Figure 3.** The relationship between the nucleation free energy and cavity radius of 5A70 aluminum alloy in the superplastic tensile state (400–550 ◦C).
