Numerical Analysis of Friction Effects on Temperature and Phases within Forged Ti-6Al-4V Alloy Aeroengine Drum

: Friction conditions signiﬁcantly impact the temperature and phases of titanium forged parts, further directly affecting the microstructures and mechanical properties of ﬁnal parts. In this paper, a 2D simpliﬁed ﬁnite element (FE) model combined with phase transition equations is developed to simulate a Ti-6Al-4V drum forging procedure. Then, friction effects on the temperature and phases of the forged drum are numerically analyzed and veriﬁed by experiments. The simulated results indicate that a reasonable range of friction factor is needed to obtain a relatively homogenous temperature distribution within the forged drum. Moreover, unlike its small inﬂuence on the α + β phase, improving friction obviously decreases the general levels of temperature and β phase and increases the homogeneities of α and β phases within the forged drum, which are associated with cooling rates and the heating effects of friction and deformation.


Introduction
Titanium drums are crucial aeroengine components which have a significant influence on the reliability of aircrafts [1]. According to previous works, the forging of titanium aeronautic components is a difficult operation [2][3][4], and friction conditions greatly affect the temperature and phases of forged parts [5,6], further impacting the corrosion resistance and fatigue life of final parts [7,8]. Hence, an investigation of friction effects on temperature and phases within titanium forged drums is of vital importance and urgent necessity to optimize their ultimate mechanical properties and service life.
Ti-6Al-4V, including α and β phases, is a representative dual phase titanium alloy [9]. Focusing on its phase transition behaviors, two predictive equations have been carried out. Hereinto, a simplified Avrami equation developed by Sha et al. [10] was used to identify the α→β phase transition characteristics in a heating operation. In contrast, a Johnson-Mehl-Avrami (JMA) equation established by Malinov et al. [11] was utilized to predict β→α + β phase transition behaviors in a cooling operation. Moreover, embedding the above equations into 2D FE approaches, Pan et al. [12] predicted machining-induced phase transition in Ti-6Al-4V cutting procedures. Quan et al. [13] studied the phase transition characteristics of a Ti-6Al-4V cylinder during the non-isothermal upsetting procedure. Ducato et al. [14] simulated phase transition of a U-shaped Ti-6Al-4V workpiece in the hot forging procedure. Bruschi et al. [15] revealed the phase transition behaviors of a Ti-6Al-4V blade section in the hot forging operation. Luo et al. [16] reported the phase transition characteristics of a Ti-6Al-4V drum during hot forging and subsequent cooling operations.
Furthermore, based on 3D FE approaches, Mi et al. [17] predicted the phase transition characteristics in a Ti-6Al-4V alloy welding operation. Ducato et al. [18] reflected the phase transition behaviors in a Ti-6Al-4V flange hot forging procedure. Buffa et al. [19] studied Ti-6Al-4V phase distributions during a welding process and verified the simulated results with experiments. Luo et al. [20] revealed the phase transition behaviors of a large Ti-6Al-4V turbine blade during the hot forging operation. Note that, although plenty of studies have been performed, none of them are tied to friction effects on the temperature and phase of Ti-6Al-4V drums, particularly on their general levels and distribution uniformities.
Consequently, the aim of this paper is to investigate the influences of friction conditions on the temperature and phases within a Ti-6Al-4V aeroengine drum in the forging procedure. For this purpose, a 2D simplified FE model combined with phase transition equations is established by DEFORM software. Then, based on two evaluation indexes, friction effects on the temperature and phase transition characteristics of the forged drum are analyzed quantitatively. Finally, experiments are conducted to demonstrate the validation of the simulated results. This work can provide guidance for the process optimization, further improving the mechanical properties and service life of Ti-6Al-4V drums.

FE Modeling
Owing to the axisymmetric structure of drums described in Figure 1a, a 2D simplified FE model is developed to simulate their forging procedure [13,16], as shown in Figure 1b. Hereinto, the deformation of the workpiece is restricted to the X-Z plane and the movements of the workpiece and forging dies at the rotatory central line in x negative direction are restricted. Moreover, for the workpiece, heat exchange with the environment is defined on all faces (pink lines) except the central line. Furthermore, there are about 8000 and 4000 quadrilateral elements used for the workpiece and forging dies, with mesh details described in Figure 1c. Moreover, the material of the workpiece is Ti-6Al-4V alloy, with stress-strain curves shown in [21]. Its heat capacity (C) and thermal conductivity (K) are described by Equations (1) and (2) [22]. The material of dies is AISI H13 tool steel with above two material parameters as shown in [23].
Then, the simplified Avrami and JMA equations are, respectively, used to predict the phase transition percentages of α → β and β → α + β, corresponding to the heating and cooling processes. The above two equations are given below [15]: where f v(α → β) and f v(β → α + β) , respectively, denote the transformed percentage of β and α + β phases, T means the instantaneous temperature, T e = 980 • C and T s = 600 • C are the ending and starting temperatures of phase transformation, A = −1.86 and D = 4.35 are material constants [20], t is the cooling time, n = 1.35 is the Avrami index [16], and b is the coefficient decided by the time-temperature-transformation (TTT) start curve [15]. Furthermore, to describe frictional stress (τ) in the drum forging procedure, a shear friction model is employed [24].
where m represents the friction factor and k denotes the shear stress. Finally, the critical parameters of materials and the hot forging procedure are listed in Table 1. Further, to better present the distributions of temperature and phases within the forged drum, the 2D simulated results are transformed into 3D ones by using the postprocessor of DEFORM-2D TM V10.2, which is developed by American scientific forming technologies corporation (Columbus, OH, USA) [16].

Evaluation Indexes
For temperature, its average (T avg ) and standard deviation (T sd ) values are selected to quantitatively reflect the variations of its general level and distribution uniformity, which are defined as [20]: where N represents the total quantity of elements, and T i means the temperature of element i. Moreover, for the α phase, its average volume fraction (f avg (α)) and standard deviation (f sd (α)) values are obtained by [6]: where f i (α) represents the α phase volume fraction of element i. Additionally, similar equations are employed for β and α + β phases. Figure 2a presents the variation range of temperature and friction effects on the maximal and minimal values (T max and T min ) of the forged drum. Hereinto, the T max increases from 997 • C to 1160 • C, and the T min decreases from 754 • C to 692 • C with the increment of m from 0.1 to 0.6. These can be owing to the heating effects of friction and deformation. Specifically, as friction is enhanced, the friction heating effect is strengthened, further leading to an obvious increment of heat generation within the internal wall area of the forged drum. In contrast, the intensive friction weakens the deformation heating effect within hard deformation areas, thereby resulting in a decrement of heat generation within the bottom area of the forged drum illustrated in Figure 3. This view can be indirectly sustained by our previous work [6]. Moreover, as shown in Figure 2b, unlike the slight increment of T avg , the value of T sd first dramatically drops, and then gradually increases from the level of 24 • C as the m exceeds 0.3. This finding indicates that a reasonable range of friction conditions exists, which leads to a homogeneous distribution of temperature within the forged drum, as described in Figure 3.   Figure 4a presents the variation range of equiaxed α phase volume fraction and friction effects on its maximal and minimal values (f max (α) and f min (α)) within the forged drum. It can be found that the f max (α) remains unchanged (about 36.5%) with the increment of m. This is because the phase transition behavior from β to equiaxed α phases only occurs when cooling rates are less than 0.03 • C/s. This explanation can be sustained by previous studies [29,30], which reported that a relatively low cooling rate can promote the nucleation of subgrains, resulting in the occurrence of static recrystallization and more homogenous microstructures. Moreover, the f min (α) decreases from 12% to 0.6% with the increment of m from 0.1 to 0.6. This phenomenon is ascribed to the α→β phase transition prompted by the strengthening of T max , as plotted in Figure 2a. Then, as shown in Figure 4b, the f avg (α) decreases from 24.5% to 21.5% with the increment of m from 0.1 to 0.6. This result is highly consistent with the evolutions of f max (α) and f min (α), which can be related to the increment of T avg presented in Figure 2b. Conversely, f sd (α) generally increases from 4.94% to 6.56% as the m is enhanced from 0.1 to 0.6. This result reveals that the α phase distribution becomes more homogenous as improving friction conditions, as described in Figure 5.   Figure 6a presents the variation range of equiaxed β phase volume fraction and friction effects on its maximal and minimal values (f max (β) and f min (β)) within the forged drum. Unlike f min (α), the f max (β) shows an opposite evolution, which increases from 88% to 99.5% as m is enhanced from 0.1 to 0.6. The above phenomenon is also owing to the α→β phase transition influenced by the heating effects of friction and deformation, as mentioned in Section 3.3.1. Moreover, it can be found that the f min (β) stays unchanged (about 63.5%) and presents good consistency with the evolution of f max (α) described in Figure 4a. Then, as shown in Figure 6b, the f avg (β) rises from 75.3% to 78.5% with the increment of m, which is related to the strengthening of T avg illustrated in Figure 2b. Besides, the f sd (β) increases from 4.94% to 6.56% as the m is increased from 0.1 to 0.6, showing the same evolution with f sd (α). This result indicates that the β phase distribution is more homogenous with a good lubricated condition, as described in Figure 7.   Figure 8a presents the variation range of lamellar α + β phase volume fraction and friction effects on its maximal and minimal values (f max (α + β) and f min (α + β)) within the forged drum. Distinct from α and β phases, the volume fraction of α + β phase is dozens of times smaller, and both values of f max (α + β) and f min (α + β) (about 0.06% and 0%) remain basically unchanged with the increment of m. This finding suggests that friction has little effect on the β → α + β phase transition within the forged drum. These phenomena are ascribed as the reason that the large forging velocity (300 mm/s) shortens the forging time (0.7 s), further limiting the phase transition time, and thereby causing a tiny volume fraction of the α + β phase. This view can be proved by the investigation of Pan et al. [12], which described in detail the time-temperature-transformation curves of titanium alloy. Moreover, as shown in Figure 8b, both values of f avg (α + β) and f sd (α + β) can also be considered to maintain invariability with the increment of m, corresponding to about 0.004% and 0.01%, respectively. This result suggests that the distribution of the α + β phase is more homogenous than the ones of α and β phases, as presented in Figure 9.   Figure 10a presents the glass lubricant-assisted hot drum forging experiments with the forging parameters described in Table 1. For Ti-6Al-4V alloy, the friction factor under the glass lubricant condition is about 0.3, according to the work of Zhu et al. [31]. Figure 10b shows the simulated result with the same forging parameters. It can be seen from Table 2 that the experimental and simulated geometries, including internal and external dimensions (h, d, H, and D), present good agreement with errors less than the allowed error margin (2%). Then, after a two-hour air cooling operation, the microstructures at the bottom (P 1 ) and flash (P 2 ) areas of the cooled drum are observed as displayed in Figure 10c, which mainly consist of α and α + β phases. Finally, due to the fact that the volume fraction of equiaxed α phase remains unchanged after air cooling process, the volume fraction of simulated equiaxed α phase within the forged drum is compared with the experimental one of the cooled drum. It can be found from Figure 10d that the simulated α phase volume fractions qualitatively agree with the experimental ones, showing errors less than 7.6%. Therefore, the 2D FE model and its simulation results are effective.

Conclusions
(1) Unlike the decrement of T min , the values of T max and T avg increase with the increment of m, which is related to the heating effects of friction and deformation. Moreover, the value of T sd first dramatically drops, and then gradually increases as the m exceeds 0.3. This finding indicates that a reasonable range of friction is exists to obtain a more homogenous temperature distribution in the forged drum.
(2) Different from the invariable f max (α), the values of f min (α) and f avg (α) decrease with the increment of m, which are ascribed to the α→β phase transition prompted by the increments of T max and T avg . Moreover, the value of f sd (α) presents an inverse evolution, which indicates that the α phase distribution of the forged drum becomes more inhomogeneous with a poor lubricated condition.
(3) In contrast to the α phase, the values of f max (β) and f min (β) reveal an opposite evolution as friction is enhanced, which is associated with the variations of temperature and cooling rates. Moreover, both values of f avg (β) and f sd (β) increase with the increment of m. This finding indicates that β phase distribution of the forged drum becomes more homogenous as friction conditions improve.
(4) Compared with α and β phases, the volume fraction of the α + β phase is much smaller, and the values of f max (α + β), f min (α + β), f avg (α + β), and f sd (α + β) can be regarded as constants with the increment of m. These findings indicate that the β→α + β phase transition hardly occurs in the drum forging operation, owing to the short phase transition time decided by high forging velocity.

Conflicts of Interest:
The authors declare no conflict of interest.