1. Power dissipation efficiency and dynamic softening behavior

According to the principle of the dynamic material model,^{Reference Raj and Pharr30} the work-piece during hot deformation is treated as a power dissipator with the assumption that the deformed material is regarded as a closed adiabatic system.^{Reference Ning, Xie, Liang, Li, Yang and Guo21} The power dissipation (P) consists of two complementary functions, G content and J co-content. The first part G is dissipated by plastic deformation, leading to the temperature rising of the work-piece, while the other part J is absorbed by the deformation material, resulting in DRV, DRX, cavity formation, superplastic flow, phase transformation, etc.^{Reference Wen, Lin, Li, Chen, Deng and Li31} The power dissipation can be represented as a function of flow stress, strain, and strain rate:

(8)$$P = \sigma \dot{\varepsilon } = G + J = \int_0^{\dot{\varepsilon }} {\sigma {\rm{d}}\dot{\varepsilon }} + \int_0^{\sigma }} {\dot{\varepsilon }{\rm{d}}\sigma } \quad .$$

The flow stress can be expressed as follows:

(9)$$\sigma = K{\dot{\varepsilon }^m}\quad ,$$

where K is the material constant and m is the strain rate sensitivity coefficient.

(10)$$m = {{{\rm{d}}J} \over {{\rm{d}}G}} = {{{\rm{d}}\left( {\ln \sigma } \right)} \over {{\rm{d}}\left( {\ln \dot{\varepsilon }} \right)}}\quad .$$

The J co-content can be represented by

(11)$$J = \int_0^\sigma {\dot{\varepsilon }{\rm{d}}\sigma } = {m \over {m + 1}}\sigma \dot{\varepsilon }\quad .$$

Then the power dissipation efficiency η can be represented by

(12)$$\eta = {J \over {{J_{\max }}}} = {{2m} \over {m + 1}}\quad .$$

The plots of ln(σ) versus $\ln \left( {\dot{\varepsilon }} \right)$ of the Ti–6Al–4V alloy at different temperatures are shown in Fig. 5. Taking differential coefficient of every value of ln(σ) at different strain rates and deformation temperatures, m values at different strain rates and deformation temperatures are obtained. Finally, the power dissipation efficiency η is calculated according to Eq. (12). The power dissipation efficiency η is relevant to the material dynamic softening that operated in a given regime of temperature and strain rate.^{Reference Peng, Guo, Shi, Qin, Zhao and Yao23} DRV occurs when the value of η is within 0.1–0.3, whereas DRX takes place when the value of η is within 0.35–0.55.^{Reference Du, Jiang and Zhang15,Reference Ning, Xie, Liang, Li, Yang and Guo21,Reference Wen, Lin, Li, Chen, Deng and Li31,Reference Liu, Ning, Yao and Guo32}

FIG. 5.

Variation of ln (σ) versus $\ln \left( {\dot{\varepsilon }} \right)$ at different temperatures for the Ti–6Al–4V alloy.

The variations of power dissipation efficiency η as a function of true strain at different strain rates and temperatures are plotted in Fig. 6, in which the DRV and DRX regimes are also indicated. It can be found that η is sensitive to strain, strain rate, and deformation temperature. Generally, the values of η increase with increasing the strain and decreasing the strain rate at relatively low temperatures of 750 and 850 °C, except those under conditions of 10 s⁻¹ and 850 °C. It is attributed to the fact that the low strain rate and increasing strain provide sufficient time and energy for dynamic softening. At the deformation temperature of 950 °C, there exists a similar increasing trend of η with the decrease of strain rate, but the effects of strain on power dissipation efficiency are not significant, especially at the strain rates of 0.001 and 0.01 s⁻¹. The main reason for this phenomenon is due to the sufficient energy that has been absorbed for DRX at the early deformation stage at a temperature of 950 °C. In addition, it can be observed from Figs. 6(a)–6(c) that η increases with increasing the deformation temperature owing to that high temperature is beneficial to dynamic softening.

FIG. 6.

Variations of power dissipation efficiency and true strain at different strain rates: (a) 750 °C, (b) 850 °C, and (c) 950 °C.

At low strain rates of 0.001 and 0.01 s⁻¹, the dynamic softening mechanism is DRX with the strain over 0.4 at 750 °C. However, when the deformation temperature increases up to 850 °C, DRX occurs for all the strains at the strain rates of 0.001 and 0.01 s⁻¹. At 950 °C, as shown in Fig. 6(c), η maintains a high level distributing in the DRX region at the strain rates of 0.001, 0.01, and 0.1 s⁻¹. Even at a high strain rate of 1 s⁻¹, η is also located in the DRX region as the strain is elevated to 0.4. Thus, an increase in temperature and strain, or a decrease in strain rate facilitates the occurrence of DRX.

2. Processing maps

The flow instability can be identified by Prasad instability criterion as^{Reference Wen, Lin, Li, Chen, Deng and Li31,Reference Chen, Liu, Liu, Tang, Luo, Feng, Li and Fu33}

(13)$$\xi \left( {\dot{\varepsilon }} \right) = {{\partial \ln \left( {{m \over {m + 1}}} \right)} \over {\partial \ln \dot{\varepsilon }}} + m \le 0\quad .$$

The instability map is constituted by the variation of $\xi \left( {\dot{\varepsilon }} \right)$ at different temperatures and strain rates, and the flow instability is predicted to occur when the $\xi \left( {\dot{\varepsilon }} \right) \lt 0$. Afterward, superposing the instability map to the power efficiency distribution, the processing maps of the Ti–6Al–4V alloy with starting lamellar microstructure in the temperature range of 700–1000 °C and strain rate range of 0.001–10 s⁻¹ at the strains of 0.3, 0.5, and 0.69 and all the strain are displayed in Fig. 7. In Figs. 7(a)–7(c), the safe domain and unsafe domain (the red shadows) are indicated. The curves are the contours of the efficiency of power dissipation η.

FIG. 7.

Processing maps of the Ti–6Al–4V alloy at the strains of (a) 0.3, (b) 0.5, (c) 0.69, and (d) all the strains.

It can be found from the processing maps that high values of η appear at the bottom of the maps (safe domain) with relatively low strain rate at all the temperatures. It demonstrates that low strain rate and high temperature are in favor of occurrence of high value of η and further promote stable flow during hot deformation. Moreover, it is noticed that a distinct change in the curvature of the iso-efficiency curves appears in the temperature range of 925–950 °C for all the tested strain rates, indicating that phase transformation from α + β → β has occurred.^{Reference Peng, Guo, Shi, Qin, Zhao and Yao23} As the phase transformation temperatures of 925–950 °C during hot deformation are much lower than that of ∼1000 °C under static conditions, the strain-induced phase transformation should have happened during the hot deformation process.^{Reference Peng, Guo, Shi, Qin, Zhao and Yao23,Reference Koike, Shimoyama, Ohnuma, Okamura, Kainuma, Ishida and Maruyama34,Reference Zhang, Ding, Pereira, Huang and Langdon35}

From Figs. 7(a)–7(c), it can be found that the strain has a significant effect on the shapes of instability regimes. The instability domain in the processing map expands with the increase of strain and mainly appears in the region with low value of η, whereas the stable region becomes narrower as the strain is increased. It means that defects may not exist at a certain strain, but it may evolve into defects with the strain increasing.^{Reference Li, Lu, Wang, Fu and Cao36} Similar result has also been obtained in the research on the Ti–47.5Al–Cr–V alloy.^{Reference Du, Jiang and Zhang15} In practice, the strain distribution in the deformation specimen is not homogeneous. To ensure a stable and homogeneous material flow during hot deformation, a processing map being appropriate for all the strains are developed by superposing the processing maps with the strains of 0.3, 0.5, and 0.69, as shown in Fig. 7(d). It shows a large instability region for the entire testing temperatures. Moreover, the domain and shape of the instability are similar to that in Fig. 7(c) at the strain of 0.69. Therefore, the instability domain is mainly depended on high strain. Based on Fig. 7(d), the preferable processing regime should be located at high temperatures and low strain rates, which can avoid the occurrence of instability during the hot deformation of the Ti–6Al–4V alloy with initial lamellar microstructure.

3. Microstructural evolution

The predicted instability regime is validated by microstructural observations. A typical microstructure of the specimens deformed at the strain rates of 1–10 s⁻¹ and temperatures of 750–1000 °C is shown in Figs. 8(a)–8(k). All the deformed specimens exhibit flow localization shear bands, and the intensity of them decreases with the increase of temperature and the decrease of strain rate. The formation of shear bands is thought to be owing to the adiabatic conditions created during hot deformation and the low conductivity of the Ti–6Al–4V alloy.^{Reference Seshacharyulu, Medeiros, Frazier and Prasad10,Reference Seshacharyulu, Medeiros, Frazier and Prasad11} During hot deformation, local plastic deformation induces much heat but cannot be carried away due to insufficient time at high strain rates, which decrease local flow stress and cause flow localization.^{Reference Seshacharyulu, Medeiros, Frazier and Prasad11} These results are similar to that reported in the Ti–6Al–4V alloy with initial lamellar microstructure by Seshacharyulu et al.^{Reference Seshacharyulu, Medeiros, Frazier and Prasad11} Seshacharyulu et al.^{Reference Seshacharyulu, Medeiros, Frazier and Prasad11} observed cracks in the specimens deformed at temperatures below 800 °C and strain rates above 1 s⁻¹. Differently, no cracks are observed in the specimens deformed under the same processing conditions in the present study.

FIG. 8.

OM microstructure of the specimens deformed in the temperature range of 750–1000 °C at the strain rate of 0.1–10 s⁻¹: (a) 750 °C and 10 s⁻¹, (b) 850 °C and 10 s⁻¹, (c) 900 °C and 10 s⁻¹, (d) 950 °C and 10 s⁻¹, (e) 1000 °C and 10 s⁻¹, (f) 750 °C and 1 s⁻¹, (g) 850 °C and 1 s⁻¹, (h) 900 °C and 1 s⁻¹, (i) 950 °C and 1 s⁻¹, (j) 1000 °C and 1 s⁻¹, and (k) 750 °C and 0.1 s⁻¹.

The deformed specimens at the true strain of 0.69 are characterized using OM, SEM, and TEM to reveal the microstructural evolution and dynamic softening mechanism of the Ti–6A–4V alloy with initial lamellar structure, as shown in Fig. 9. Figure 9(a) shows the microstructure of the as-compressed Ti–6Al–4V alloy at the strain rate of 0.1 s⁻¹ and 750 °C. It can be seen that the microstructure exhibits mainly residual lamellar morphology, which may be attributed to that there was no sufficient time for DRX nucleation and growth. Based on Fig. 9(b), dislocation cells, which are an indicator of occurrence of DRV, exist in the specimen deformed. As the strain rate is decreased to 0.001 s⁻¹, more time is provided for facilitating the occurrence of DRX. The initial lamellar structure is nearly fully transformed to equiaxed grains, as shown in Figs. 9(c) and 9(d). Even so, DRV still exists which are evidenced by dislocation walls, as shown in Fig. 9(d). According to the microstructural characteristics of the deformed specimens at 750 °C, it can be concluded that the hot deformation undergoes dynamic softening of DRV at high strain rate and DRX at low strain rate, which is consistent with the results shown in Fig. 6(a).

FIG. 9.

OM, SEM, and TEM images for the deformed specimens with the strain of 0.69 at the temperature and strain rate of 0.1 s⁻¹ and 750 °C for (a) and (b), 0.001 s⁻¹ and 750 °C for (c) and (d), 0.1 s⁻¹ and 850 °C for (e) and (f), 0.001 s⁻¹ and 850 °C for (g) and (h), 0.1 s⁻¹ and 950 °C for (i) and (j), and 0.001 s⁻¹ and 950 °C for (k) and (l). Here, the TEM image corresponded to SEM or OM image on its left side.

Figure 9(e) shows the SEM image of the specimen deformed at 0.1 s⁻¹ and 850 °C. Compared with the specimen deformed at 750 °C with the same strain rate of 0.1 s⁻¹, the residual lamellar structure disappears and fully transforms to equiaxed grains. The newly formed uniform and equiaxed α grains with little dislocations are demonstrated in Fig. 9(f). The occurrence of equiaxed grains are a result of DRX, which is attributed to the sufficient activation energy generated as the deformation temperature is elevated to 850 °C. The microstructure of the specimen deformed at a strain rate of 0.001 s⁻¹ and a temperature of 850 °C is demonstrated in Figs. 9(g) and 9(h). It exhibits a duplex microstructure which consists of recrystallized α grains and β transformed microstructure (accounting for about 40%), as demonstrated by the light and dark color regions in Fig. 9(g), respectively. Figure 9(h) shows the TEM microstructure of the deformed specimen at 0.001 s⁻¹ and 850 °C, a fine lamellar structure can be observed. This lamellar microstructure is thought to be formed during cooling to room temperature in the prior β phase after deformation.^{Reference Koike, Shimoyama, Ohnuma, Okamura, Kainuma, Ishida and Maruyama34} Therefore, the β-transformed microstructure is considered as the β phase during hot deformation at testing temperature. Moreover, it can be noticed that the prior β phase is characterized as exquiaxed morphology during the deformation process at testing temperature. Thus, both α phase and β phase undergo dynamic softening of DRX during the hot compression process. In addition, the volume fraction of β transformed microstructure is about 40%, which is greater than that at room temperature (about 10%). Since the temperature of phase transformation from α to β is about 890 °C, which is higher than the deformation temperature of 850 °C, strain-induced phase transformation should have occurred. Meanwhile, strain has lowered the temperature of phase transformation from α to β 40 °C approximately.

When the deformation temperature is elevated to 950 °C, the microstructure is transformed to lamellar structure at the strain rates of both 0.1 and 0.001 s⁻¹, as shown in Figs. 9(i)–9(l). This indicates that the deformation takes place in the β phase field. Therefore, the deformation temperature of 950 °C was much lower than the β-transus temperature of ∼1000 °C in the present Ti–6Al–4V alloy, which further confirmed the presence of strain-induced phase transformation and β-transus temperature lowered about 50 °C by strain. In addition, equiaxed prior β grains are observed at 950 °C, as shown in Figs. 9(i) and 9(k), which confirms the occurrence of DRX in the β-phase field during hot deformation.