Using finite element modeling to examine the temperature distribution in quasi-constrained high-pressure torsion
Introduction
High-pressure torsion (HPT) [1] is now an established procedure that is used to process metallic materials through the application of severe plastic deformation (SPD) [2]. To date, processing by HPT has proven to be the most effective of all the SPD methods in producing bulk nanostructured materials with exceptionally small grain sizes. The principle of HPT is that a sample, generally in the form of a thin disk, is subjected to a high pressure between massive anvils and then processed through the application of torsional straining. The high imposed compressive hydrostatic pressure prevents any cracking of the disk and the low thickness to diameter ratio leads to the production of a high strain during anvil rotation. In practice, the effective strain, ε, imposed on the sample is given by the relationship:where N is the number of turns in HPT, R is the distance to the center of the disk, h is the disk thickness, ω is the rotation rate and t is the time of processing.
The precise characteristics of HPT processing may be divided into three separate categories, depending upon the geometry of the anvil and consequent restrictions on the lateral flow of the material [1], [3]. In unconstrained HPT, the anvils are flat so that the sample flows laterally, and there is a monotonic thinning of the disk during processing. In fully constrained HPT, the disk is placed within a cavity in the lower anvil so that any lateral flow is prevented. In practice, however, HPT is generally conducted using a quasi-constrained condition in which the disk is placed between depressions in the upper and lower anvils and these partial lateral walls constrain the sample but permit some outward flow of material between the two anvils. The present analysis is concerned specifically with processing using quasi-constrained conditions.
Most of the reports on HPT processing are concerned with experimental measurements of the hardness distributions, the evolution of microstructure and/or the strength properties after processing; by contrast, there are only a limited number of reports describing the flow properties during HPT. Three early reports described the flow process in HPT using finite element modeling (FEM) [4], [5], [6], but all of these analyses relate specifically to unconstrained HPT. A more recent analysis applied FEM to quasi-constrained HPT and demonstrated that in HPT processing a thin ribbon of material flows outwards around the periphery of the disk between the upper and lower anvils [7]. This flow has been widely documented in experiments using quasi-constrained HPT [3], [8]. The FEM analyses used disks with an initial thickness of 0.8 mm, and confirmed that the effective strains imposed on the samples after one turn varied from very low values near the disk centers to high values near the edges [7].
An important parameter in HPT processing is the thermal characteristics of the disks, and especially the rise in disk temperature, because this will determine the potential for achieving a high degree of grain refinement. To date, only very limited information is available on the temperature effects that occur during HPT. In HPT processing of pure Ti at room temperature, a temperature rise to ∼45 °C was recorded in the upper anvil at a distance of 10 mm from the disk when processing at 0.5 rpm for 10 turns using a pressure of 2.0 GPa [9]. A similar temperature rise was recorded in pure Al, measured in the upper anvil at 1 mm from the disk surface, when processing at room temperature for 10 turns at 5.0 GPa using the faster rate of 5 rpm [10]. However, a higher temperature rise of almost 40 °C was recorded when testing at the same pressure and rate with the disk immersed in liquid nitrogen [10]. By contrast, a negligible temperature rise of <10 K was reported in the processing of disks of Ag–Ni and Nb–Zr at a pressure of 5.0 GPa for up to 100 turns at a rate of 0.2 rpm [11]. Some analytical treatments have estimated temperature rises of more than 100 K in HPT [12], [13], but very recent experiments have demonstrated that the temperature rise within the anvil is dependent upon both the disk material and the rate of anvil rotation such that the temperature rise is higher when processing hard materials at faster processing rates [14].
These disparities highlight the importance of providing a clear analytical treatment of the thermal characteristics in HPT processing. Accordingly, the present work was initiated to provide a comprehensive analysis of the temperature evolution in samples processed by HPT, including the effects of experimental variables such as the strength of the material, the rate of anvil rotation, the magnitude of the applied pressure, the influence of the material outflow between the anvils and the effect of the size of the anvils. The principles of the analytical treatment are outlined in Section 2, the FEM results are presented in Section 3 and the calculations are compared with experimental data in Section 4.
Section snippets
Principles of the analytical approach
The fundamental thermal characteristics of HPT processing can be simplified into three distinct parts: the heat source, the heat conductivity resistance and the heat sinks. In this approach, the heat source is the plastic deformation of the workpiece. The heat conductivity resistance derives from the conductivity of the material used for processing, the interface between the workpiece and the anvil, the conductivity of the anvil, the external conductivity to the HPT processing facility, the
The predictions from finite element modeling
Simulations were performed using the FEM DEFORM software, version 10.0 (Scientific Forming Technologies Corporation, Columbus, OH), and incorporated both the plastic deformation and the thermal evolution during HPT processing. Since there is axial symmetry around the central axis in HPT processing, the calculations were simplified by considering a two-dimensional model using only the axial and radial directions.
The geometries of the anvils and the workpiece used in this study are depicted in
General characteristics of the predictions
The general temperature distributions after various numbers of turns of HPT is shown in Fig. 3 for a simulation where the disk is pure Fe, the pressure is 2.0 GPa and the rotation speed is 1.0 rpm. Initially, the workpiece and the upper and lower anvils are at room temperature (20 °C), but, as shown in Fig. 3, there is a rapid temperature rise in the workpiece, and after only one turn there are regions with temperatures between 40 and 44 °C. Thereafter, the temperature rises more slowly in the
Discussion
When materials are processed by HPT, an important question arises concerning the magnitude of any rise in temperature within the HPT disks. Estimates of the temperature rise have ranged from calculated values up to >100 K [12], [13] to direct experimental measurements suggesting rises from <10 K [11] to >60 K [14]. The present model was designed to provide the first comprehensive predictions of the temperature rises that are incurred in HPT for a range of materials processed under different
Summary and conclusions
- 1.
Finite element modeling was used to evaluate the thermal characteristics and temperature rises occurring in quasi-constrained HPT processing. The effects of various parameters were evaluated, including the material strength, the rate of rotation, the applied pressure and the volume of the anvils.
- 2.
The calculations show that the heat generated by plastic deformation of the workpiece and by friction of the material that flows outwards between the upper and lower anvils leads to a rapid initial
Acknowledgements
This work was supported by the Brazilian Research Council (CNPq), the Research Agency of the State of Minas Gerais (FAPEMIG), the National Science Foundation of the United States under Grant No. DMR-0855009 and the European Research Council under ERC Grant Agreement No. 267464-SPDMETALS.
References (18)
- et al.
Prog. Mater. Sci.
(2008) - et al.
Prog. Mater. Sci.
(2000) J. Mater. Proc. Technol.
(2001)- et al.
J. Mater. Proc. Technol.
(2003) - et al.
J. Mater. Proc. Technol.
(2008) - et al.
Mater. Sci. Eng.
(2011) - et al.
Scripta Mater.
(2004) - et al.
Scripta Mater.
(2007) - et al.
J. Alloys Compd.
(2010)
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