Figure 2 shows an example for the general view of a dilatometric curve (compression/dilation as a function of temperature) obtained during heating and cooling of a sample of TC21 Ti-alloy. Transformation temperatures are determined from the slope changes in the curve that denoted to the change in sample length.

By heating the sample above 720˚C (Point A in Figure 3), the curve started to be non-linear. In such case, the curve reaching a certain peak at 830˚C and then goes down till 950˚C. This could be attributed to the shrinking influence caused by crystal structure changing from duplex (α + β) structure into a single structure of β phase [11] [14] . As the α + β → β phase transformation continues, the sample continuously shrinks and then finally stops at 950˚C (Point B in Figure 3). As the temperature continues to increase, the length of the sample starts to increase and becomes linear due to stopping the α + β → β phase transformation with further increase in temperature.

At 720˚C (Point A in Figure 3), the amount of α phase achieved the maximum. This means that there will be an equilibrium state between α and β phases

at this temperature. When the temperature obtains higher than 720˚C, the equilibrium will be broken, and α phase will be transformed to β phase. Then, the ratio of β to α increases and the expansion of the phase dominates the overall expansion of the alloy. As a result, a relative increase in sample length will be observed on the dilatometric curve until the β transus (950˚C). With further increase in temperature more than β transus, T_β (950˚C), a complete β phase will be formed. Two characteristic reflection points can be observed in the above mentioned dilatometric curve with increasing the heating temperature. They are defined as (T_s) which referred to starting transformation temperature of α + β → β and (T_f) finishing transformation temperature of α + β → β. T_s for the investigated TC21 Ti-alloy was reported at 720˚C, whereas the corresponding T_f was obtained at 950˚C.

In addition, the first derivative for the studied dilatometric heating curve showed that starting and finishing temperatures of the α + β → β phase transformation were more accurately and objectivity, Figure 4. The started and finished transforming temperatures using the first derivative curve (Figure 4) were reported at 730˚C and 955˚C, respectively, which are close to the values obtained in the dilatometric heating curve (720˚C and 950˚C).

Studying phase transformation kinetics during continuous cooling from both α + β range and β range is essential if the material is to be properly processed [11] . Dilatometric cooling curve for TC21 Ti-alloy from β range (1100˚C) using cooling air is shown in Figure 5. The starting temperature of β → β + α phase transformation was 885˚C; however, the corresponding finishing temperature was 665˚C. These temperatures are smaller than the observed in heating, motivated by the transformation β → β + α. It is clear that during the heating process, the volume shrinks as the sample transform from the α + β phase to β phase, and the volume increases when cooled. These results were in agreement with previous results [11] [14] . Figure 6 describes the first derivative for dilatometric

cooling curve. The starting and finishing temperatures were obtained at 665˚C and 885˚C, respectively. It is found that the starting and finishing temperatures of β → β + α phase transformation were more accurately and objectivity.

The α + β → β phase transformation fraction is used to reflect the α + β → β phase kinetics during continuous heating. The dilatation characteristics of titanium alloy, which is a polycrystalline material, can be isotropic in the solid-state phase transformation [11] [14] . Thus, the relationship between variation in volume (ΔV/V_o) and relative length (ΔL/L_o) in the solid-state phase transformation process can be expressed as [11] :

( Δ V / V o ) = 3 ( Δ L / L o ) (1)

where L_o is the original sample length, V_o is the original sample volume, and ΔV and ΔL are the volume and length variations of the sample, respectively. Considering the dilatometric heating curve of the investigated TC21 sample, the degree of deviation degree of the dilatometric curve should be proportional to the α + β → β transformed volume fraction. Therefore, the level rule can be employed to analyze the dilatometric curve to explore the relationship between the α + β → β transformed volume fraction (ƒ) and heating temperature (Figure 3).

ƒ = L EO / L EF (2)

where L_EO and L_EF are the measuring lengths of EO and EF lines representing in Figure 3. Figure 7 shows the α + β → β transformation curve that exhibited a typical S-shaped pattern. This means that the α + β → β phase transformation for the TC21 Ti-alloy is a nucleation-growth-controlled process [7] [15] . This finding was in agreement with the results reported by Wan et al. [11] and Hui et al. [16] .

The α + β → β phase transformation in the TC21 Ti-alloy during continuous heating was identified by quenching the samples from different temperatures. Three samples were chosen based on the dilatometric curve measurements. The samples were heated continuously to 830˚C, 900˚C and 1000˚C and then immediately quenched in water. Figure 8 shows the microstructure feature of the three tested samples. When samples 1 and 2 were heated to 830˚C and 900˚C, respectively (Figure 8(a) & Figure 8(b)), the volume fraction of the primary α phase significantly reduces as the heating temperatures increases, but the β grain grows gradually. This indicated that the transformation from α to β has been obtained.

When the temperature was above the β transus at 1000˚C (Figure 8(c) & Figure 8(d)), the whole microstructure has transformed into β phase; the quenched microstructure of β is a complete martensitic structure. The β grain then became very coarse with a grain size of approximately 300 µm. This result was consistent with a previous study [7] [14] .