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# High Temperature Materials and Processes

Editor-in-Chief: Fukuyama, Hiroyuki

Editorial Board: Waseda, Yoshio / Fecht, Hans-Jörg / Reddy, Ramana G. / Manna, Indranil / Nakajima, Hideo / Nakamura, Takashi / Okabe, Toru / Ostrovski, Oleg / Pericleous, Koulis / Seetharaman, Seshadri / Straumal, Boris / Suzuki, Shigeru / Tanaka, Toshihiro / Terzieff, Peter / Uda, Satoshi / Urban, Knut / Baron, Michel / Besterci, Michael / Byakova, Alexandra V. / Gao, Wei / Glaeser, Andreas / Gzesik, Z. / Hosson, Jeff / Masanori, Iwase / Jacob, Kallarackel Thomas / Kipouros, Georges / Kuznezov, Fedor

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Volume 34, Issue 7

# Identification of Stable Processing Parameters in Ti–6Al–4V Alloy from a Wide Temperature Range Across β Transus and a Large Strain Rate Range

Guo-Zheng Quan
/ Hai-Rong Wen
/ Shi-Ao Pu
/ Zhen-Yu Zou
/ Dong-Sen Wu
Published Online: 2015-01-14 | DOI: https://doi.org/10.1515/htmp-2014-0129

## Abstract

The hot workability of Ti–6Al–4V alloy was investigated according to the measured stress–strain data and their derived forms from a series of hot compressions at the temperatures of 1,023–1,323 K and strain rates of 0.01–10 s−1 with a height reduction of 60%. As the true strain was 0.3, 0.5, 0.7 and 0.9, respectively, the response maps of strain rate sensitivity (m-value), power dissipation efficiency ($\mathrm{\eta }$-value) and instability parameter ($\mathrm{\xi }$-value) to temperature and strain rate were developed on the basis of dynamic material model (DMM). Then the processing map was obtained by superimposition of the power dissipation and the instability maps. According to the processing map, the stable regions ($\mathrm{\eta }>0$ and $\mathrm{\xi }>0$) and unstable regions ($\mathrm{\eta }<0$ or $\mathrm{\xi }<0$) were clarified clearly. Further, the stable regions (temperatures of 1,198–1,248 K and strain rates of 0.01–0.1 s−1) with higher $\mathrm{\eta }$ value ($>$0.3) corresponding to the ideal deformation mechanisms involving globularization and superplasticity were identified and recommended. The microstructures of the deformed samples were then observed by microscopy. And homogeneous microstructures with refined grains were found in the recommended parameter domains. The optimal working parameter domains identified by processing map and validated by microstructure observations contribute to the design in reasonable hot forming process of Ti–6Al–4V alloy without resorting to expensive and time-consuming trial-and-error methods.

## Introduction

Ti–6Al–4V alloy, a kind of $\mathrm{\alpha }+\mathrm{\beta }$-type titanium alloy, was firstly developed in the early 1950s, and now it becomes one of widely used alloys in aerospace industry due to its desirable properties, such as high specific strength (strength to density ratio), excellent mechanical properties and great corrosion resistance at high temperature [14]. It is common that the mechanical property of a material primarily depends on its microstructure which is strongly sensitive to processing parameters (deforming temperature, strain, strain rate, etc.) [5]. In order to achieve the ideal mechanical properties of the final products, it is necessary to understand the mechanisms of microstructure evolution of workpiece in forging process. Then, how to find a way to predict such mechanisms of Ti–6Al–4V alloy in a hot working process corresponding to different deformation conditions, including strains, strain rates, and temperatures, is a significant issue. Over the past few decades, considerable researches have been carried out on the microstructure evolution and hot deformation behavior of titanium alloys. Now, it has been widely accepted that processing map is a very useful way to identify the deformation mechanisms during hot working processes and determine the optimal processing parameters. Furthermore, processing map has been widely used to evaluate the formability, optimize the hot working process and control the microstructures of titanium alloys, magnesium alloys, aluminum alloys, zircaloy alloys, Ni-based superalloy, etc. [68].

Workability refers to the plastic deformation ability that a metal can be deformed easily without the formation of any defect during bulk deformation process such as forging, extrusion, rolling, etc. The workability consists of two independent parts: state of stress (SOS) workability and intrinsic workability [911]. SOS workability is governed by the geometry of deformation zone and the externally imposed stress state, both of which vary with different deformation processes. Intrinsic workability is determined by the microstructure evolution under certain deformation conditions (temperature, strain rate, strain, etc.) which is implicit in flow behavior [11]. As one of important performances, the intrinsic workability can be indicated by the means of processing map on the basis of dynamic material model (DMM) under which the workpiece is considered as a dissipator of power [12]. The DMM was firstly proposed on the fundamental principles of continuum mechanics of large plastic flow by Y.V.R.K. Prasad and H.L. Gegel in 1984, and then its variant was carried out by Murty [6, 1014]. Processing map has been widely used to predict unstable deformation behaviors in actual forging process and optimize process parameters.

Up until now, the hot deformation behaviors and the hot workability of Ti–6Al–4V alloy have been extensively studied. Park et al. [15] constructed the processing map of Ti–6Al–4V alloy at a true strain of 1.0 by using the stress–strain data in the temperature range of 1,123–1,273 K and strain rate range of 0.001–10 s−1, and then identified the stable deformation regions by Malas’ instable criterion which is different from the criterion adopted in this work. Seshacharyulu et al. [16] analyzed microstructural mechanisms during hot working of Ti–6Al–4V alloy with a lamellar starting microstructure by the processing map at a strain of 0.5 in the temperature range of 1,023–1,373 K across $\mathrm{\beta }$-transus and strain rate range of 0.0001–10 s−1. Luo et al. [17] constructed the processing map at a strain of 0.6 in the temperature range from 1,093 to 1,303 K and the strain rate range from 0.001 to 10 s−1. Bruschi et al. [2] studied the hot workability of Ti–6Al–4V alloy in the temperature range of 1,153–1,223 K corresponding with $\mathrm{\alpha }+\mathrm{\beta }$ coexisting two-phase, and strain rate range of 1–50 s−1. Generally speaking, the processing map of Ti–6Al–4V alloy corresponding with a single strain and even a narrow two-phase temperature range has been constructed. However, a deep understanding of the hot workability for this alloy needs a series of processing maps corresponding with a series of strains, a large strain rate range and a wide temperature range across $\mathrm{\beta }$-transus.

In the present study, the stress–strain data of Ti–6Al–4V alloy were collected from a series of hot compressions in a wide temperature range of 1,023–1,323 K across $\mathrm{\beta }$-transus and in a large strain rate range of 0.01–10 s−1 with a height reduction of 60%. The processing map was constructed by superimposition of the power dissipation and the instability maps, which involve the calculation of three key indicators in DMM such as strain rate sensitivity (m-value), power dissipation efficiency (η-value) and instability parameter ($\mathrm{\xi }$-value). According to the processing map, the stable and unstable regions were clarified clearly, and then the different mechanisms of microstructure evolution were identified and described. The grain refinement mechanism in the recommended parameter domains were validated by microstructure observations. The workability evaluation by processing map contributes to the design in reasonable hot forming process of Ti–6Al–4V alloy without resorting to expensive and time-consuming trial-and-error methods.

## Basis for processing map

In DMM theory, hot forming process is described as a system in which workpiece is a nonlinear dissipator of power [6, 1012]. The power-dissipation characteristics of the material are bound up with the constitutive flow behaviors of material, which follows a power-law equation: $\mathrm{\sigma }=K{\stackrel{˙}{\mathrm{\epsilon }}}^{m}$, where $\mathrm{\sigma }$ is flow stress, K stress coefficient, $\stackrel{˙}{\mathrm{\epsilon }}$ strain rate, m strain rate sensitivity of flow stress.

During a hot deformation process, the total power, P, absorbed by the workpiece is dissipated by the dissipator content, G, which is the power dissipated by plastic deformation, and the dissipator co-content, J, which is the work related to the metallurgical phenomena such as recovery, recrystallization, superplastic flow and phase transformation. Then, the total power, P, absorbed by workpiece can be determined by eq. (1): $P=\underset{0}{\overset{\stackrel{˙}{\epsilon }}{\int }}\sigma \text{d}\stackrel{˙}{\epsilon }+\underset{0}{\overset{\sigma }{\int }}\stackrel{˙}{\epsilon }\text{d}\sigma \text{\hspace{0.17em}}\text{=}\text{\hspace{0.17em}}G+J$(1)where $\mathrm{\sigma }$ is instantaneous flow stress and $\stackrel{˙}{\mathrm{\epsilon }}$ is applied strain rate. The partitioning of total power, P, between J and G is decided by strain rate sensitivity of flow stress (m) which is calculated using eq. (2): $m=\text{d}J/\text{d}G=\left(\stackrel{˙}{\epsilon }\text{d}\sigma \right)\text{\hspace{0.17em}}/\left(\stackrel{˙}{\epsilon }\text{d}\sigma \right)=\text{dlg}\sigma /\text{dlg}\stackrel{˙}{\epsilon }$(2)At a given temperature and strain, the J co-content is determined as eq. (3): $J=\frac{m}{m+1}\mathrm{\sigma }\stackrel{˙}{\mathrm{\epsilon }}$(3)where $\stackrel{˙}{\mathrm{\epsilon }}$ is strain rate and m is strain rate sensitivity. For an ideal linear dissipator, m= 1 and ${J}_{\mathrm{max}}=\sigma \stackrel{˙}{\epsilon }/2$. The value of J for a non-linear dissipator is normalized with that of an ideal liner dissipater, and thus a dimensionless parameter called efficiency of power dissipation ($\mathrm{\eta }$) is obtained as eq. (4). The values of parameter $\mathrm{\eta }$ correspond with various microstructural evolution mechanisms of workpiece. The variations of $\mathrm{\eta }$-values along with temperatures and strain rates constitute the power dissipation map, in which specific regions are correlated with specific microstructural evolution mechanisms: $\eta =J/{J}_{\mathrm{max}}=2m/m+1$(4)To identify the flow instability regimes during a hot deformation process, a continuum instability criterion as eq. (5) based on the extremum principles of irreversible thermodynamics applied to large plastic flow was proposed by Kumar and Prasad [18, 19]. Equation (5) defines the onset of flow instability during a hot deformation process. The variations of $\mathrm{\xi }$-values along with temperatures and strain rates constitute an instability map, in which instability regimes are indicated by contours with negative $\mathrm{\xi }$-values. $\xi \left(\stackrel{˙}{\epsilon }\right)=\partial \text{lg}\left(m/\left(m+1\right)\right)/\partial \text{lg}\stackrel{˙}{\epsilon }+m\text{<}0$(5)A superimposition of an instability map on a power dissipation map gives a processing map. Processing map not only provides optimum deformation conditions but also describes the regimes of flow instability. The approach of processing map has been applied for the process design of various materials [2023].

## Materials and experimental procedures

The studied Ti–6Al–4V alloy has the following chemical composition (wt%): 6.50 Al, 4.25 V, 0.16 O, 0.04 Fe, 0.015 N, 0.02 C, 0.0018 H and the balance of Ti. The $\mathrm{\beta }$-transus of this material is approximately 1,263 K. The typical duplex microstructures of as-received alloy are shown in Figure 1, from which it can be seen that the starting microstructures consist of an equiaxed primary $\mathrm{\alpha }$-phase with a hexagonal close-packed structure (hcp), and a small amount of inter-granular $\mathrm{\beta }$-phase with a body-centered cubic structure (bcc). The hcp unit cell of $\mathrm{\alpha }$-phase and the bcc unit cell of $\mathrm{\beta }$-phase are illustrated in Figure 2. In order to achieve the basic stress–strain data for the following calculations, 28 compression tests with a height reduction of 60% were scheduled in a temperature range from 1,023 to 1,323 K at intervals of 50 K under four strain rates of 0.01, 0.1, 1 and 10 s−1. Twenty-nine cylindrical specimens of 10 mm diameter and 12 mm height were machined from the as-received bar. Then 28 specimens were compressed on a computer-controlled thermo-mechanical simulator, Gleeble 3500, and other than the 28 specimens deformed, 1 specimen was considered as the as-received specimen for the observation of original microstructure, which was not heated and compressed. During a compression process, the specimen was resistance heated to deformation temperature at a heating rate of 30 K/s and held for 180 s by thermo-coupled feedback-controlled AC current, aiming to obtain a uniform temperature field and decrease the material anisotropy.

Figure 1

Figure 2

Unit cells of $\mathrm{\alpha }$- and $\mathrm{\beta }$-phases: (a) hcp $\mathrm{\alpha }$-phase, (b) bcc $\mathrm{\beta }$-phase

The stress–strain data were recorded automatically in an isothermal compression process. After compression, the deformed specimens were rapidly quenched in water to retain the deformed microstructure at high temperature. Finally, all specimens were sectioned in the center parallel to the compression axis direction, and the cut-surface was polished and corroded by the solution containing 10% HF, 30% HNO3 and 70% H2O for metallographic examination.

## Flow stress curves

The continuous stress–strain curves of Ti–6Al–4V alloy at investigated temperatures and strain rates are shown in Figure 3. It is obvious that strain rate and temperature affect flow stress significantly. The stress level decreases with the increasing temperature at a given strain rate and decreasing strain rate at a given temperature. In two-phase range, flow stress increases with deformation degree extending until a peak stress value, following which decreases gradually to a steady value. In $\mathrm{\beta }$-phase range, flow stress reaches rapidly a constant value with deformation degree extending. It is common that the characteristics of hot flow behaviors indicate the microstructural changes due to the interaction of work hardening and softening mechanisms. In fact, the main softening mechanisms include dynamic recovery (DRV), phase transformation, globularization and superplasticity which coexist with one being predominant. Although temperature is a main factor to determine softening mechanisms, the influence of strain rate is more and more recognized by researchers [2]. It is believed that different softening mechanisms correspond with different temperatures and strain rates. For example, the predominant softening mechanism in a two-phase temperature of 1,023 K and a strain rate of 0.01 s−1 must be significantly different with that in a single-phase temperature of 1,323 K and a strain rate of 10 s−1, and the previous may be globularization while the latter may be DRV. It is a severe issue how to identify the different softening mechanisms from a wide range of temperature and strain rate.

The processing map on the basis of DMM is a valuable approach. Three indicators such as strain rate sensitivity (m-value), power dissipation efficiency ($\mathrm{\eta }$-value) and instability parameter ($\mathrm{\xi }$-value) are introduced into DMM. According to the levels of these three indicators, the stable and instable parameter regions can be clarified clearly, meanwhile the intrinsic relationships between softening mechanisms, i.e. microstructure evolution mechanisms and deformation parameters can be uncovered.

Table 1

The m-values calculated at different forming temperatures, strains and strain rates

## Strain rate sensitivity

During a hot forming process, strain rate sensitivity of flow stress is a very important indicator, which contributes to the variations of another two indicators including efficiency of power dissipation $\mathrm{\eta }$ and instability criteria $\mathrm{\xi }$. In order to understand the response of strain rate sensitivity index, m, to deformation conditions for Ti–6Al–4V alloy, m-values at different strains, strain rates and temperatures were calculated according to the fitted cubic splines for $\mathrm{l}\mathrm{g}\phantom{\rule{thickmathspace}{0ex}}\mathrm{\sigma }$ versus $\mathrm{l}\mathrm{g}\phantom{\rule{thickmathspace}{0ex}}\stackrel{˙}{\mathrm{\epsilon }}$ (shown as Figure 4(a)–(d)). The detailed calculation results were presented in Table.1, and then the 3D smooth response surfaces of m to deformation conditions were plotted as Figure 5(a)–(d) by interpolation. From Figure 5, it can be seen that m-values vary irregularly with strain, strain rate and temperature. From Table 1, it can be noted that m-values are negative at true strain of 0.9 under temperatures of 1,023 and 1,073 K, and strain rates of 1 and 10 s−1. According to DMM theory, negative m-values usually correspond to these conditions that promote instabilities such as dynamic strain aging (DSA), adiabatic shear bands (ASB), flow localization bands or initiation and growth of microcracks [2325].

Figure 3

True stress–strain curves of Ti–6Al–4V alloy obtained by Gleeble 3500 under the different deformation temperatures with strain rates (a) 0.01 s−1, (b) 0.1 s−1, (c) 1 s−1, (d) 10 s−1

Figure 4

The relationships between stress and strain rate in lg scale at different deforming temperatures and true strains: (a)$\mathrm{\epsilon }=0.3$, 1,023–1,323 K, (b) $\mathrm{\epsilon }=0.5$, 1,023–1,323 K, (c) $\mathrm{\epsilon }=0.7$, 1,023–1,323 K, (d) $\mathrm{\epsilon }=0.9$, 1,023–1,323 K

Figure 5

The response 3D surface of m-value on temperature and strain rate as the true strain: (a) $\mathrm{\epsilon }=0.3$, (b) $\mathrm{\epsilon }=0.5$, (c) $\mathrm{\epsilon }=0.7$, (d) $\mathrm{\epsilon }=0.9$

The variations of m-values suggest a transition of different deformation mechanisms. Basal slip is athermal in the studied temperature range and makes m-value almost equal to zero. So it is not the reason for m-value change. A phase diagram of Ti–6Al–4V alloy is shown in Figure 6. Ti–6Al–4V alloy exhibits an allotropic phase transformation at about 1,263 K, changing from an hcp crystal structure ($\mathrm{\alpha }$-phase) to a bcc crystal structure ($\mathrm{\beta }$-phase), and corresponding slip planes and slip directions in the hcp and bcc unit cell are shown in Figure 2. When the temperature is lower than 1,263 K, $\mathrm{\alpha }$-phase is the primary microstructure type. Furthermore, as for such hcp crystals slip is permitted with a-type slip directions on basal, prismatic and pyramidal planes and c + a-type slip directions on pyramidal planes. However, the basal, prismatic and pyramidal planes with a-type burgers vector only possess four independent slip systems during a hot forming process. Therefore, in order to satisfy the von Mises criterion, which requires at least five independent slip systems for a homogeneous plastic deformation of polycrystals, the operation of one of the slip systems $\left\{10\stackrel{ˉ}{1}1\right\}$ with a c + a Burgers vector needs to be activated. When the temperature is above 1,263 K, phase transformation has been completed and only $\mathrm{\beta }$-phase with a bcc exists. The slip systems generally observed in $\mathrm{\beta }$-Ti are $\left\{1\phantom{\rule{thickmathspace}{0ex}}1\phantom{\rule{thickmathspace}{0ex}}0\right\}$, $\left\{1\phantom{\rule{thickmathspace}{0ex}}1\phantom{\rule{thickmathspace}{0ex}}2\right\}$ and $\left\{1\phantom{\rule{thickmathspace}{0ex}}2\phantom{\rule{thickmathspace}{0ex}}3\right\}$, all with the Burgers vector of $<1\phantom{\rule{thickmathspace}{0ex}}1\phantom{\rule{thickmathspace}{0ex}}1>$, and the choice of slip planes in the metal is often influenced by temperature, and non-basal slips increase with increasing temperature because they are strongly thermally activated. Therefore, m-value is controlled by non-basal slips because more such slip systems contribute to increasing m-value [22, 23]. However, another plastic deformation mechanisms coupling with basal slips and non-basal slips such as micro-cracks, DSA, ASB, etc. contribute to decreasing m-value. In general, several deformation mechanisms such as basal slip, non-basal slip, etc. coexist during the compression process of Ti–6Al–4V alloy, and their synergism results in the variation of m-value.

## Power dissipation efficiency map

It is a severe issue to describe the continuous response of η, to three variables such as temperature, strain and strain rate, and in following, this issue was simplified by scattering one variable, here true strain as 0.3, 0.5, 0.7 and 0.9. Based on the principle of power dissipation efficiency ($\mathrm{\eta }$-value) described in Section “Basis for Processing Map”, the distribution of power dissipation efficiency (i.e. power dissipation map) at each true strain and different seven temperatures and four strain rates was plotted as Figure 7(a)–(d). In a power dissipation map the value against each contour indicates $\mathrm{\eta }$-value, which characterizes the rate of microstructure evolution in a hot working process. Thus, it can be summarized that a power dissipation map containing iso-efficiency contours represents the dynamic microstructure state of the deformed material and may be viewed as microstructural “trajectories.” That is, the microstructure evolution of the hot deformation system may be tracked by following the changes in power dissipation maps. It is worth noting that the efficiency peaks in the domains of a power dissipation map represent the lowest dissipative energy state or the highest rate of entropy production. Therefore, it can be deduced that the domains appearing in a power dissipation map represent basins of attraction [22, 26].

Figure 6

Phase diagram of Ti–6Al–4V alloy

Figure 7

Power dissipation maps for Ti–6Al–4V alloy as the true strain: (a) $\mathrm{\epsilon }=0.3$, (b) $\mathrm{\epsilon }=0.5$, (c) $\mathrm{\epsilon }=0.7$, (d) $\mathrm{\epsilon }=0.9$

The black regions in Figure 7(a)–(d) with negative $\mathrm{\eta }$-values are considered as the regimes where flow is unstable. In fact, the negative m-values are directly responsible for the negative $\mathrm{\eta }$-values. By comparing these four power dissipation maps with one another, it is noted that in the temperature range of 1,023–1,323 K and strain rate range of 0.01–0.1 s−1, $\mathrm{\eta }$-values remain higher levels ($>$ 0.2) at all strains. In addition, the distribution of efficiency does not show any significant changes even with increasing true strain from 0.3 to 0.7, while as true strain changes from 0.7 to 0.9, it shows obvious changes in the temperature range of 1,023–1,098 K and strain rate range of 0.56–10 s−1. Near $\mathrm{\beta }$-transus, the iso-efficiency contours in the power dissipation maps at true strain of 0.3, 0.5, 0.7 and 0.9 exhibit sharp demarcations. This phenomenon is commonly observed in various materials that show phase transformation including precipitate dissolution [27]. In Figure 7(a) at a true strain of 0.3, the $\mathrm{\eta }$-value varies in the range of 0.10–0.58. In Figure 7(b) at a true strain of 0.5, the η-value varies in the range of 0.09–0.58. In Figure 7(c) at a true strain of 0.7, the $\mathrm{\eta }$-value varies in the range of 0.077–0.55. In Figure 7(d) at a true strain of 0.9, the $\mathrm{\eta }$-value varies in the range of –0.16–0.64. During a hot forming process, the deformed material dissipates the power in the forms of heat loss in tools and surrounding air, several metallurgical processes (DRV, globularization, phase transformation, superplasticity, etc.) and even material damage.

In general, DRV, globularization or dynamic recrystallization (DRX) and superplasticity are stable deformation mechanisms. As for titanium alloys, the efficiency value related to DRV is less than 0.25, the value associated with DRX or globularization is about 0.25–0.55, when the value is greater than 0.55, superplasticity or wedge cracking may occur [28, 29]. It can be concluded that higher power dissipation efficiency is purposed to achieve more uniform and more refined microstructures. However, higher power dissipation efficiency doesn’t mean the ensurement of stable deformation mechanisms and even stable microstructures, and in following, the unstable regimes need to be identified by the third indicator, instability parameter, $\mathrm{\xi }$.

## Instability map

The variations of instability parameter,$\mathrm{\xi }$, along with temperatures and strain rates construct an instability map in which instable (unsafe) regimes are indicated by negative $\mathrm{\xi }$-values, while stable (safe) domains by positive $\mathrm{\xi }$-values. Figure 8(a)–(d) shows the instability maps of Ti–6Al–4V alloy at strains of 0.3, 0.5, 0.7 and 0.9. In Figure 8(a) corresponding to $\mathrm{\epsilon }=0.3$, flow instability is limited to two regions, and the area of instability regions is about a quarter of the area of instability map window. In Figure 8(b) corresponding to $\mathrm{\epsilon }=0.5$, flow instability is limited to three regions, and the area of instability regions is about one-third of the area of instability map window. However, in Figure 8(c) corresponding to $\mathrm{\epsilon }=0.7$, flow instability does not occur at all temperatures (1,023–1,323 K) and strain rates (0.01–10 s−1). In Figure 8(d) corresponding to $\mathrm{\epsilon }=0.9$, flow instability is limited to one region, and the area of instability region is about one-twelfth of the area of instability map window. In the stable regions, the occurrence of globularization in $\mathrm{\alpha }$-phase in the two-phase temperature range of 1,023–1,263 K and the occurrence of DRV in $\mathrm{\beta }$-phase in the single-phase temperature range of 1,263–1,323 K inhibit the formation of instability features, meanwhile these microstructural modifications during a hot deformation process degrade the strain accumulation and therefore the formation of intercrystalline cavity, DSA, triple junction (wedge) cracking or ASBs [30].

After all, the general response of strain rate sensitivity (m-value) to strain, temperature and strain rate can be fundamentally responsible for the variation of power dissipation efficiency ($\mathrm{\eta }$-value) and instability criteria ($\mathrm{\xi }$-value). Generally, the regions with lower m-values, which mean fewer slip systems, mainly correspond with unstable regions. However, this doesn’t mean that higher m-values are safer due to the complexity in the dynamic transition or coexisting of different deformation mechanisms induced by the combined actions of strain, temperature and strain rate. The stable, unstable regions are identified based on the comprehensive comparisons of strain rate sensitivity, power dissipation efficiency and instability criterion.

## Processing map

A superimposition of an instability map on a power dissipation map gives a processing map, which reveals the deterministic domains where specific microstructure process occurs and the limiting conditions for the regimes of flow instability. By avoiding the regimes of flow instability and processing under conditions of higher efficiency in the “safe” domains, the intrinsic workability of the material may be optimized and microstructure control may be achieved. The “safe” domains in a processing map have the characteristics of dynamic restoration mechanisms, such as DRV, globularization or DRX and superplasticity. The processing maps of Ti–6Al–4V alloy at true strains of 0.3, 0.5, 0.7 and 0.9 are shown in Figure 9(a)–(d). In each processing map, the regimes of flow instability are distinguished from “safe” domains by using thick curves and different region marks including “Domain” and “INST.”

Figure 8

Instability maps as the true strain: (a) $\mathrm{\epsilon }=0.3$, (b) $\mathrm{\epsilon }=0.5$, (c) $\mathrm{\epsilon }=0.7$, (d) $\mathrm{\epsilon }=0.9$, representing different regions of stable and unstable flow in the frame of strain rate and temperature

Figure 9

Processing maps as the true strain: (a) $\mathrm{\epsilon }=0.3$, (b) $\mathrm{\epsilon }=0.5$, (c) $\mathrm{\epsilon }=0.7$, (d) $\mathrm{\epsilon }=0.9$

In Figure 9(a) the processing map at the true strain of 0.3 exhibits three domains with higher $\mathrm{\eta }$-value: Domain #1: 0.3 occurs in the temperature range from 1,073 to 1,323 K and strain rate range from 0.01 to 0.56 s−1, with a peak $\mathrm{\eta }$-value of about 0.58 occurring at about 1,223 K and 0.016 s−1. Domain #2: 0.3 occurs in the temperature range from 1,123 to 1,248 K and strain rate range from 0.56 to 10 s−1, with a peak $\mathrm{\eta }$-value of about 0.46 occurring at about 1,223 K and 5.62 s−1. Domain #3: 0.3 occurs in the temperature range from 1,023 to 1,048 K and strain rate range from 1 to 10 s−1, with a peak $\mathrm{\eta }$-value of about 0.16 occurring at about 1,036 K and 6.4 s−1. In Figure 9(b) the processing map at the true strain of 0.5 exhibits three domains with higher $\mathrm{\eta }$-value: Domain #1: 0.5 occurs in the temperature range from 1,198 to 1,323 K and strain rate range from 0.01 to 0.75 s−1, with a peak $\mathrm{\eta }$-value of about 0.58 occurring at about 1,210 K and 0.016 s−1. Domain #2: 0.5 occurs in the temperature range from 1,023 to 1,248 K and strain rate range from 1 to 10 s−1, with a peak $\mathrm{\eta }$-value of about 0.41 occurring at about 1,223 K and 5.6 s−1. Domain #3: 0.5 occurs in the temperature range from 1,086 to 1,148 K and strain rate range from 0.01 to 1 s−1, with a peak $\mathrm{\eta }$-value of about 0.26 occurring at about 1,123 K and 0.056 s−1. In Figure 9(c) the processing map at the true strain of 0.7 exhibits only one domain with higher $\mathrm{\eta }$-value: Domain #1: 0.7 occurs in the temperature range from 1,023 to 1,323 K and strain rate range from 0.01 to 10 s−1, with a peak $\mathrm{\eta }$-value of about 0.55 occurring at about 1,198 K and 0.017 s−1. In Figure 9(d) the processing map at the true strain of 0.9 exhibits two domains with higher $\mathrm{\eta }$-value: Domain #1: 0.9 occurs in the temperature range from 1,098 to 1,323 K and strain rate range from 0.01 to 10 s−1, with a peak $\mathrm{\eta }$-value of about 0.64 occurring at about 1,223 K and 0.017 s−1. Domain #2: 0.9 occurs in the temperature range from 1,023 to 1,098 K and strain rate range from 0.01 to 0.56 s−1, with a peak $\mathrm{\eta }$-value of about 0.49 occurring at about 1,060 K and 0.01 s−1.

According to processing maps, the stable and unstable regions were clarified clearly, and microstructure evolution mechanisms were identified by combining processing maps with m-values. It is worth noting that in the two-phase temperature range and the single-phase temperature range, $\mathrm{\eta }$-values maybe equal, while this doesn’t mean the same microstructure evolution mechanism, on the contrary, different mechanisms usually exist. For example, in Figure 9(d), in the domain within two-phase temperature range, the $\mathrm{\eta }$-values are higher than 0.55 and m-values are about 0.3–0.56, which indicates the existence of superplastic flow. Such characteristics are also well documented [27, 31]. In the domains with lower strain rates ($<0.1$ s−1), $\mathrm{\eta }$-values are about 0.25–0.55 and m-values are about 0.2–0.3, which represents globularization of $\mathrm{\alpha }$-phase, a type of DRX. And in the domain with higher strain rates ($\ge 0.1$ s−1), $\mathrm{\eta }$-values are lower than 0.25, DRV of $\mathrm{\alpha }$-phase is predominant mechanism. In the domain within single $\mathrm{\beta }$-phase temperature range with $\mathrm{\eta }$-values lower than 0.55, DRV of $\mathrm{\beta }$-phase is predominant. Furthermore, in more narrow temperature range of 1,313–1,323 K and strain rate range of 0.01–0.018 s−1, m-values are higher than 0.3, which indicated large-grained superplasticity of $\mathrm{\beta }$-phase. Such characteristic has been reported by Seshacharyulu et al. [27] and Prasad et al. [31].

## Microstructure observations

The frozen microstructures of the compressed specimen with a true strain of 0.9 were observed by optical microscopy in order to validate the stable and instable flow as well as to find the practical relationships between microstructures and processing parameters. Figure 10(a)–(f) shows the microstructures corresponding to a strain rate of 0.1 s−1 and different temperatures. From Figure 10(a)–(f), it is seen that with increasing temperature more and more $\mathrm{\alpha }$-phase was transformed to $\mathrm{\beta }$-phase till the completion at 1,273 K. On the other hand, with increasing temperature the percentage of globularization volume fraction in $\mathrm{\alpha }$-phase increases. However, from Figure 10(a)–(f) it is obviously seen that with increasing temperature the volume fraction of equiaxed grains in $\mathrm{\alpha }$-phase induced by globularization decreases. This is due to the fact that with increasing temperature the volume fraction of $\mathrm{\alpha }$-phase decreases, while the percentage of globularization volume fractions in $\mathrm{\alpha }$-phase increases. Figure 10(f) shows the single $\mathrm{\beta }$-phase covered by a large amount of martensite, i.e. ${\mathrm{\alpha }}^{\prime }$-phase. This is due to the fact that as the temperature of 1,273 K is above $\mathrm{\beta }$-transus, 1,263 K, all $\mathrm{\alpha }$-phase was transformed to $\mathrm{\beta }$-phase, and when the deformed specimen was quenched in water, a large amount of $\mathrm{\beta }$-phase transformed into ${\mathrm{\alpha }}^{\prime }$-phase. It can be observed from Figure 10(f) that the $\mathrm{\beta }$-phase grains are larger and elongated, which indicates that DRV occurs in $\mathrm{\beta }$-phase. Thus it can be summarized that the thermal softening due to DRV becomes predominant when the material is deformed in the temperature range of $\mathrm{\beta }$-phase for Ti–6Al–4V alloy. However, DRV would lead to coarse grains though it is a better deformation mechanism. And this kind of coarse grains is hazardous to workability and the mechanical properties of the materials.

Figure 10

Optical microstructures of Ti–6Al–4V at a fix true strain of 0.9, a fix strain rate of 0.1 s−1 and different temperatures: (a) 1,023 K, (b) 1,073 K, (c) 1,123 K, (d) 1,173 K, (e) 1,223 K, (f) 1,273 K

Micrographs of specimens deformed at 1,123 K and different strain rates are shown in Figure 11(a)–(d). These micrographs clearly reveal that with increasing strain rate the volume fraction of globularization decreases. From Figure 11(a)–(d), globularization process is predominant at lower strain rates ($\le$ 0.1 s−1) and the kinking of $\mathrm{\alpha }$-phase dominates at higher strain rates ($\ge$ 1 s−1). Liu et al. revealed that such globularization includes four typical steps, viz. lath shearing, dislocation generation, nucleation of dislocation interface and interface migration [29]. In the thermal compression process of Ti–6Al–4V alloy, phase transformation, globularization processes are considered as important steps to produce fine-grained microstructure, which obtains good workability.

Figure 11

Microstructures of Ti–6Al–4V specimens deformed at 1,123 K and different strain rates: (a) 0.01 s−1, (b) 0.1 s−1, (c) 1 s−1, (d) 10 s−1

The processing map at the true strain of 0.9 predicts a single regime of flow instability at lower temperatures ($\le$ 1,098 K) and higher strain rates ($\ge$ 0.56 s−1), which is shown as shaded area in Figure 9(d). Flow localization bands may occur in the regime of flow instability, and these predictions are validated with microstructural observation made on the deformed specimens. Figure 12 corresponding to 1,023 K and 10 s−1 shows the microstructure of flow instability regime. At this deformation condition η-value is about –0.16, m-value –0.11 and $\mathrm{\xi }$-value –0.17. From Figure 12, flow localization band is observed at an angle of about 45° to the compressive axis. Its formation may be bound up with the adiabatic condition generated during a hot deformation and low thermal conductivity of the alloy, namely the heat produced during deformation is not conducted away due to insufficient time, which reduces the local flow stress and causes flow localization, and intense flow localization possibly results in cracking when these specimens deformed at lower temperatures and higher strain rates. In stable regions, the occurrence of globularization inhibits the formation of instability features. Figure 13 shows the microstructure at temperature of 1,223 K and strain rate of 0.01 s−1. At this deformation condition η-value is about 0.64, m-value 0.56 and $\mathrm{\xi }$-value 1.0. According to the previous discussion, temperature 1,223 K is below $\mathrm{\alpha }\to \mathrm{\beta }$ phase transus, thus a part of $\mathrm{\alpha }$-phase with hcp-type crystals was transformed into $\mathrm{\beta }$-phase with bcc-type crystals and thus two phases coexist in the deformed material. From Figure 13, it can be seen that the $\mathrm{\alpha }$-phase grains are fined by globularization, and small equiaxed $\mathrm{\alpha }$-phase dispersed in the matrix of $\mathrm{\beta }$-phase. It is worth noting that the volume fraction of $\mathrm{\alpha }$-phase is small at this condition due to $\mathrm{\alpha }\to \mathrm{\beta }$ phase transformation. It is common that in original $\mathrm{\alpha }+\mathrm{\beta }$ phase, $\mathrm{\beta }$-phase grains are surrounded by lamellar $\mathrm{\alpha }$-phase grains forming $\mathrm{\beta }$-phase grain boundaries and $\mathrm{\beta }$-phase grains are covered by a large amount of lamellar $\mathrm{\alpha }$-phase grains. In fact, when the specimen is compressed, it is significantly difficult to identify the grain boundaries of $\mathrm{\beta }$-phase due to the fact that the lamellar $\mathrm{\alpha }$-phase grains surrounding and covering $\mathrm{\beta }$-phase grains have been crushed, globularized and then confused.

During hot deformation processes, the common deformation mechanisms include DRV, globularization, superplasticity and the flow instabilities. Generally, globularization and superplasticity are the stable, optimal and preferred deformation mechanisms, and DRV is a stable and alternative deformation mechanism due to occurrence of coarse grain [32]. And if the coarse grains due to DRV cannot be accepted, DRV will not be a recommended deformation mechanism. However, the instable deformation mechanism should be avoided. For the hot working of Ti–6Al–4V alloy, DRV leads to coarse grains and thus it is not a recommended deformation mechanism. Based on the analyses and observations of the microstructure evolution at different deformation conditions, it is found that the processing map is a feasible approach for the determination of process parameters. In the forging industry, Ti–6Al–4V alloy is commonly considered as a titanium alloy with $\mathrm{\alpha }+\mathrm{\beta }$ phase type, and the temperature range of near $\mathrm{\beta }$-transus is recommended.

Figure 12

Microstructure manifestation of instability in Ti–6Al–4V alloy at 1,023 K and 10 s−1

Figure 13

Microstructure of Ti–6Al–4V alloy at 1,223 K and 0.01 s−1

## Conclusions and remarks

Hot deformation behavior of Ti–6Al–4V alloy has been investigated in the temperature range of 1,023–1,323 K and the strain rate range of 0.01–10 s−1 by means of the processing map. The noticeable results are listed below:

• 1)

The stress–strain curves of Ti–6Al–4V alloy are sensitive to temperature and strain rate. Generally, the stress decreases with the increasing temperature at a given strain rate and decreasing strain rate at a given temperature. And the stress–strain curves can indicate the intrinsic relationships between the flow stress and mechanisms of microstructure evolution.

• 2)

The response 3D surfaces of m-value to forming conditions for Ti–6Al–4V alloy were plotted, and then the forming conditions corresponding to negative m-values were initially identified as unstable regions. The effect of deformation mechanisms involving basal slip and non-basal slip on the variations of m-values was interpreted.

• 3)

The power dissipation maps for Ti–6Al–4V alloy were constructed, and the regions corresponding to negative $\mathrm{\eta }$-values were secondly identified as unstable regions. In addition, the instability maps for Ti–6Al–4V alloy were developed, and the regions corresponding to negative $\mathrm{\xi }$-values were thirdly identified as unstable regions.

• 4)

The processing maps for Ti–6Al–4V alloy were plotted by superimposing instability maps on power dissipation maps. According to processing maps, the stable and unstable regions were clarified clearly. The safe regions as the true strains are different levels were obtained as follows:

$\mathrm{\epsilon }=0.3$, domain: 1,198–1,248 K and 0.01–0.1 s−1.

$\mathrm{\epsilon }=0.5$, domain: 1,198–1,248 K and 0.01–0.032 s−1.

$\mathrm{\epsilon }=0.7$, domain: 1,173–1,323 K and 0.01–1 s−1.

$\mathrm{\epsilon }=0.9$, domain: 1,198–1,323 K and 0.01–10 s−1

• 5)

By processing map and observation of microstructure at a strain of 0.9, the stable and unstable regions were clarified clearly. The flow instability regime occurs in the temperature range of 1,023–1,098 K and strain rate range of 0.56–10 s−1, and the optimal deformation parameter for hot deformation is the temperature of 1,223 K and strain rate of 0.01 s−1, with the peak $\mathrm{\eta }$ of 0.64.

## Acknowledgment

This work was supported by National Key Technologies R & D Program of China (2012ZX04010-081).

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Accepted: 2014-10-16

Published Online: 2015-01-14

Published in Print: 2015-11-01

Citation Information: High Temperature Materials and Processes, Volume 34, Issue 7, Pages 715–729, ISSN (Online) 2191-0324, ISSN (Print) 0334-6455,

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