An Investigation on the Deformation Heating in Billet and Die During Equal-Channel Angular Pressing and High-Pressure Torsion

Equal-channel angular pressing (ECAP) and High-pressure torsion are widely used to refine grain structure and improve the mechanical properties of various materials. ECAP and HPT are performed under high applied pressures and at low temperatures 1,2. In the ECAP process, a well-lubricated billet is pressed in a die comprising two channels intersecting at a constant angle. The material is then subjected to shear deformation 3,4. Since the cross section remains constant, repetitive pressing is possible to impose large cumulative strains. However, the imposed cumulative strain will depend on the material, temperature, speed and geometry of the die. Multiple ECAP processing makes it possible to rotate the billet around its central axis between the passes. Different routes are then created that has been classified into four routes: (I) Route A, no rotation around central axis (II) Route BA , rotating 90° in opposite directions, (II) Route Bc , rotating 90° in the same direction and (IV) Route C, rotating 180° 5. In HPT the billets are subjected to a compressive force and concurrent torsional straining in which the deformation is continuous 6. ECAP and HPT are considered useful to strengthen materials by inducing large plastic deformation in one deformation step. Various studies have been performed to show the importance of these methods in improving the properties of different materials. Significant improvement in tensile strength 7, fatigue resistance 8 , impact toughness 9 , wear resistance 10,11, corrosion behavior 12,13 superplasticity 14,15, formability 16, etc were observed using this method. ECAP processing is usually carried out at room temperature and homogeneous grain refinement is expected throughout the sample. Some brittle materials are processed at high temperature and the mechanism of grain refinement may lead to heterogeneous grain structure with multi-modal grain size distribution 17. However, new methods are proposed to develop homogeneous grain size distribution in the materials 18,19. In addition, the material processed by ECAP may present mechanical anisotropy, where the stress‐strain behavior may vary with respect to the orientation of processing by ECAP 20-23. To analyze the deformation behavior and predict the mechanical anisotropy in the samples, finite element method (FEM) has been widely used by some researchers 24-28. In these simulations, isothermal condition was assumed while in an experiment a temperature rise of 73° was recorded 29. This temperature rise in the sample may affect the grain size and homogeneous grain refinement 30,31. Some analytical models are developed to predict the average temperature rise in ECAP 32. However, FEM may predict the temperature rise in various points of the billet 33-35. Similarly, FEM could be successfully used to predict the induced strain, damage and temperature rise in HPT 36. This work aims to investigate the temperature rise due to deformation heating in ECAP and HPT processes using 3D‐FEM. The roles of various parameters are investigated and the heating of die due to the work-piece deformation is included in the simulations. An Investigation on the Deformation Heating in Billet and Die During Equal-Channel Angular Pressing and High-Pressure Torsion


Introduction:
Equal-channel angular pressing (ECAP) and High-pressure torsion are widely used to refine grain structure and improve the mechanical properties of various materials. ECAP and HPT are performed under high applied pressures and at low temperatures 1,2 . In the ECAP process, a well-lubricated billet is pressed in a die comprising two channels intersecting at a constant angle. The material is then subjected to shear deformation 3,4 . Since the cross section remains constant, repetitive pressing is possible to impose large cumulative strains. However, the imposed cumulative strain will depend on the material, temperature, speed and geometry of the die. Multiple ECAP processing makes it possible to rotate the billet around its central axis between the passes. Different routes are then created that has been classified into four routes: (I) Route A, no rotation around central axis (II) Route B A , rotating 90° in opposite directions, (II) Route B c , rotating 90° in the same direction and (IV) Route C, rotating 180° 5 .
In HPT the billets are subjected to a compressive force and concurrent torsional straining in which the deformation is continuous 6 .
ECAP and HPT are considered useful to strengthen materials by inducing large plastic deformation in one deformation step. Various studies have been performed to show the importance of these methods in improving the properties of different materials. Significant improvement in tensile strength 7 , fatigue resistance 8 , impact toughness 9 , wear resistance 10,11 , corrosion behavior 12,13 superplasticity 14,15 , formability 16 , etc were observed using this method.
ECAP processing is usually carried out at room temperature and homogeneous grain refinement is expected throughout the sample. Some brittle materials are processed at high temperature and the mechanism of grain refinement may lead to heterogeneous grain structure with multi-modal grain size distribution 17 . However, new methods are proposed to develop homogeneous grain size distribution in the materials 18,19 . In addition, the material processed by ECAP may present mechanical anisotropy, where the stress-strain behavior may vary with respect to the orientation of processing by ECAP [20][21][22][23] . To analyze the deformation behavior and predict the mechanical anisotropy in the samples, finite element method (FEM) has been widely used by some researchers [24][25][26][27][28] . In these simulations, isothermal condition was assumed while in an experiment a temperature rise of 73° was recorded 29 . This temperature rise in the sample may affect the grain size and homogeneous grain refinement 30,31 . Some analytical models are developed to predict the average temperature rise in ECAP 32 . However, FEM may predict the temperature rise in various points of the billet [33][34][35] . Similarly, FEM could be successfully used to predict the induced strain, damage and temperature rise in HPT 36 .
This work aims to investigate the temperature rise due to deformation heating in ECAP and HPT processes using 3D-FEM. The roles of various parameters are investigated and the heating of die due to the work-piece deformation is included in the simulations.

Finite element model
Three-dimensional simulations of ECAP and HPT were performed using the DEFORM 3D 10.2 software. General simulation conditions for ECAP and HPT are summarised in Table 1. Material properties are mostly selected from library of the software while the friction data are available elsewhere 37 . 30000 and 8000 three-dimensional four node tetrahedron (linear tetrahedron) elements were used in the simulations of ECAP and HPT, respectively.
In this transient thermal equation, ρC p is volumetric heat capacity, u is displacement vector, k is thermal conductivity, Q is external heating sources, and W is heating due to deformation which in turn is a function of stress variations inside the billet and contact friction. In rate form one can obtain: In these equations, η is the thermal efficiency (between 0.8-0.9), σ and ε ⋅ are effective stress and strain rate, respectively. In addition, F is friction force and V is relative velocity between sample and die. For F: . .
Where m is shear factor, t is shear strength, v is relative velocity between billet and die, and α is the value of relative sliding velocity below which sticking occurs.
The simulations of HPT assumed sticking conditions between the work-piece and the anvils on top and bottom surfaces and no slippage was allowed. Simulations considered rigid die and punch while thermal analysis was coupled with the deformation analysis. The mesh independency of the results was checked and finally a reasonable number of elements were selected in the simulations to attain relatively accurate and computationally efficient results.

Temperature contours in work-piece and die
For validation purpose, the temperature rise during ECAP for AA-1100 using a plunger speed of 18mm/s was modeled. The results showed reasonable agreement with the measured and calculated data for temperature rise in pure Al. In this work, a temperature rise of 39°C was observed while about 17.8°C temperature rise was calculated 38 and about 29°C temperature rise was measured 29 using V=18mm/s. The difference between the simulated values with calculated and measured values can be related to difference in die parameters, experimental/numerical errors, simplifications, and estimating material properties. Fig.1 shows the isosurfaces of temperature in the work-piece after ECAP. As shown in this figure the highest temperature is attained in the vicinity of shear line and deformation zone of the work-piece. This work shows the temperature change not only in the work-piece, but also for the ECAP die. The temperature isosurfaces in the die show temperature rise where the channel is bent. It can be seen in Fig.1 and Fig.2 that temperature contours are extended towards the exit channel that originates from the work-piece displacement within the die. While the work-piece moves in the exit channel, the generated heat is transferred to die via conduction and therefore the temperature isosurfaces in die are extended in the direction of inlet and exit channels. The difference in the temperature rise in different parts of the work-piece has several reasons. First, during the deformation, heat transfers from the deformed part to the un-deformed part of the work-piece that makes the later to be deformed at higher temperature and causes more temperature rise in those parts 33 . Second, die temperature increases by the deformed part, and then the undeformed part is deformed in a pre-heated die that causes less heat loss and more temperature rise 33 .  Fig.3 shows the maximum work-piece temperature after ECAP. The maximum work-piece temperature is shown as a function of velocity and friction. It is shown that the dependency of maximum work-piece temperature to velocity is more than its dependency to friction. While increasing the friction factor from 0 to 0.3 increases the maximum work-piece temperature only 8°C, increasing the plunger velocity from 0.5 to 2 increases the maximum work-piece temperature 49° C in average. Fig.4 shows the maximum die temperature after ECAP. The maximum die temperature is shown as a function of velocity and friction. The dependency of maximum die temperature to velocity is more than its dependency to friction alike maximum work-piece temperature. Nonetheless, the rate of variations are lower in die, e.g. increasing the friction factor from 0 to 0.3 increases the maximum die temperature 7°C and increasing the plunger velocity from 0.5 to 2 increases the maximum die temperature 18° C in average. This shows that the maximum work-piece temperature is more dependent to velocity variation than the maximum die temperature.  shows the temperature distribution in the centre line of the work-piece (points P1 to P20 shown in Fig.1) for frictionless condition. As mentioned in the previous section, the dependency of maximum work-piece temperature to velocity is more than its dependency to friction. Fig.5 shows that not only the maximum work-piece temperature, but also the temperature distribution is dependent to velocity. Increasing the plunger velocity increases the difference between maximum and minimum temperatures. Additionally, the maximum work-piece temperature is attained at the deformation zone. Fig.6 shows the temperature distribution in the centre line of the work-piece as a function of friction. Increasing the plunger velocity increases the maximum work-piece temperature and the difference between maximum and minimum temperatures in all conditions. It is also interesting to note to the temperature history in different points as shown elsewhere 39 . In figure 7, one can see that temperature varies sharply in the beginning of the deformation while it is directly dependent to the punch speed.    Fig.8 shows the work-piece temperature after two HPT turns. As shown in this figure the variation of temperature is narrow due to the small size of the work-piece. Not only the work-piece size, but also the good heat conduction of aluminium makes the temperature distribution uniform.

Temperature distribution in HPT
The temperature rise during HPT in the earlier report of Pereira et al. 40 was reported about 15°C with a normal pressure of 940Mpa, a rotation speed of 0.1 rad/s for a titanium sample after two turns. However, in this work the temperature rise was about 7°C. Although the main simulation conditions are identical, variation in billet size, friction and processed material are the major reasons for this difference.
The temperature distribution in the centreline of the work-piece is shown in fig. 9. Two friction factors are considered in the simulations. As shown in this figure the temperature rise in HPT is less than ECAP due to the small size of the HPT work-piece compared to ECAP. Nonetheless, increasing the friction factor increases the generated heat during this process. Although the temperature distribution appears uniform, the maximum temperature is attained around r=4mm.

Conclusions:
This work investigates the temperature rise due to the deformation heating in ECAP and HPT using finite element method. The results show that while the work-piece moves in the exit channel in ECAP, the generated heat is transferred to die via conduction and therefore the temperature isosurfaces in die are extended in the direction of inlet and exit channels.
It is shown that the dependency of maximum ECAP work-piece temperature to velocity is more than its dependency to friction. Increasing the plunger velocity increases the difference between maximum and minimum temperatures. Additionally, the maximum work-piece temperature is attained at the deformation zone.
The temperature rise in HPT is less than ECAP due to the small size of the HPT work-piece compared to ECAP. Not only the work-piece size, but also the good heat conduction of aluminium makes the temperature distribution roughly uniform in HPT.