A simple model for material's strengthening under high pressure torsion
Graphical abstract
Introduction
Severe plastic deformation (SPD) refers to the processing of metals under a combination of extensive hydrostatic pressure and large strains [1]. This produces ultra-fine grained material with a very high dislocation density and modifies properties of the original material. Several new SPD techniques have been developed recently including accumulative roll bonding (ARB) [2], equal channel angular extrusion (ECAE) [3], high pressure torsion (HPT) [4], twist extrusion [5] and axisymmetric forward spiral extrusion [6].
Un-constrained and (semi)constrained modes of high pressure torsion, (semi)CHPT, are widely used by several researchers. A CHPT, allows establishing an effective back-pressure, reduces bulging effect and decreases surface defect. The constrained mode, in its ideal sense, is not practical due to the brittle nature of the punches and the manufacturing errors. A semi-constrained version of HPT has been commonly employed in the existing literature to minimize the implementation problems. Analytically, the constrained mode is reasonably close to the semi-constraint mode. Both semi-constrained and constrained modes are considered in this article. CHPT has been viewed [7] as the realisation of an ideal torsion test in which the fracture of the sample is being postponed indefinitely due to the presence of high hydrostatic pressure. Such a process permits a defined continuous variation of strain and is applicable to relatively brittle materials. Compared to many other SPD processes, CHPT can develop a higher hydrostatic pressure in its sample allowing a more efficient grain refinement even in high strength materials.
CHPT was recently utilized for physical simulation of contact problems [8], [9]. Conventional simulation of the problems is typically expensive, in many cases impractical and therefore should be simulated physically (e.g. rolling contact fatigue [10], [11], [12]). A real contact problem usually closely relates to “friction induced non-linear deformation”. Thus conventional simulators (such as tensile or torsion tests) cannot adequately represent the problem. Advantages of using CHPT as a physical simulator include development of a friction induced deformation mechanism in the test sample in a “zero shape change” and non-linear fashion. CHPT was also proposed recently as a mechanical test [13] to identify stress strain curves of material under very large strains. Both of these new applications are interesting paradigm shifts but they have to develop well analytically before they can be seriously used at the experimental stage.
A key challenge to utilize CHPT as a mechanical test or a physical simulator is to reduce the uncertainties surrounding slippage between the sample and its upper/lower anvils. Very little is known about the boundary conditions in the CHPT including the distribution of loads, velocity fields and possible local slippage at the tool-sample interface. Slippage during CHPT was studied by [14]. In-process observations of the test sample are extremely difficult due to the transient nature of the conditions and inaccessibility of the sample during the process. For a better understanding of the slippage, the boundary conditions could be indirectly monitored by studying the measured overall torque-twist-pressure response. Embossing CHPT's die-sample interface, as suggested by Yogo et al. [13], suppresses sliding between the specimen and the upper\lower die. However the significantly modified geometry requires a proper (complex) post processing of the test measurements. In an ideal CHPT, the main deformation mechanism is pure shear under a high hydrostatic pressure while the modified interface produces a multi-axial and complex deformation route. Given the small size of the sample (~ 1 mm in thickness), the embossing and material flash-out through the die-sample gaps are significant and result in multi-axial deformation. Use of FEM to describe the complex deformation (Yogo et al. [13]) is questionable. A mechanical test (CHPT in this case) is to identify material's constitutive behaviour but the constitutive description is a pre-requisite for a sound and reliable FE analysis. The numerical simulations of the test also require critical assumptions on boundary conditions and constitutive parameters of the test material as priori known information. Experimental observations [15] and numerical studies [16] showed that the plastic deformation is highly heterogeneous along the thickness direction due to the die geometry and high friction, as well as along the radial direction due to the characteristics of torsion. They showed that plastic deformation increased from the centre to the edge in the middle zone in the thickness direction of the disk processed by the CHPT. Also, they found that the deformation vanished in the “dead metal zone” due to the vertical wall constraint under high pressure. More realistic boundary conditions could be defined based on experimental observations. Due to such doubts, typically CHPT's induced strain is simply reported in terms of the numbers of revolutions.
There are several advantages in developing a closed form relationship between the torque-twist-pressure and the flow parameters of CHPT under sticking friction condition. The relationship is useful to quickly design the test, to predict its requirements and to optimize the die geometry. This analytical tool allows a better understanding of microstructure evolution during CHPT processing. To optimize the final properties, through microstructure control, detailed understanding of grain refinement mechanisms is essential. This involves proper simulation of driving forces for grain refinement using crystal plasticity models (e.g. [17], [18]) at a sub grain scale. To calibrate such models by inverse method (e.g. [19]), the sample's load-displacement response can be used. The closed form solution is also useful as a guide to constitutive specification, driving forces for dislocation velocity, nucleation rates and the boundary conditions needed for a crystal plasticity formulation.
This work aims to estimate the minimum pressure to initiate a sticking friction between a CHTP's anvil and its sample. It also estimates a “threshold torque” required to start the friction induced plastic deformation. A bi-linear kinematically admissible velocity field is employed to estimate effective strain rate and strain in the sample and to derive an upper bound solution of the problem. This correlates the torque twist response during CHPT to its constitutive and test parameters. Finally to assess the accuracy of the derivations, a comparison is made between the predicted torque-twist-pressure response and the experimental measurements for three cases of Armco iron samples deformed under pressures of 1.9, 3.8 and 7.5 GPa, respectively.
Section snippets
Constrained HPT formulation
In CHPT, the sample fits into a cavity on the lower anvil and it deforms in a “zero shape change” fashion. Given the brittle nature of the tools, proper clearances are necessary and a perfectly constrained condition is impractical. Therefore experiments are often conducted under a semi-constrained condition [4] where there is at least some limited outward flow near the tool-material interfaces. High pressure torsion is practically easier to perform than its (semi)constrained version, CHPT.
Experimental examples and verification
In order to compare the results from the presented upper bound solution with the experimental data, case studies were carried out using Armco iron samples and deformation behaviour of the samples under CHPT were analysed and investigated.
The material has a homogeneous structure of pure ferrite containing exceptionally low contents of carbon, oxygen and nitrogen, together with a low incidence of non-metallic inclusions. The material's work hardening is typically described by the yield and
Conclusion
The minimum pressure to start a sticking friction condition for (semi)CHPT was evaluated. Using a bi-linear kinematically admissible velocity field, an upper bound solution of the process was formulated to estimate the external torque as a function of the process parameters and material properties. The formulations accounted for the friction induced deformation and hydrostatic pressure in CHPT. To assess the accuracy of the upper bound derivations, three case studies were presented for Armco
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High-pressure torsion of iron with various purity levels and validation of Hall-Petch strengthening mechanism
2019, Materials Science and Engineering: ACitation Excerpt :Following this publication, the focus of majority of works on SPD processing of Fe has been on the microstructural evolutions and enhanced mechanical properties [23–67], although the magnetic properties [56] and phase transformations [31] of UFG Fe are still of interest. Close examination of publications on HPT processing of Fe indicates that the deviations of reported mechanical properties and grain sizes are in a wide range mainly because of the difference in the purity levels and partly because of the processing routes [15–69]. For example, the reported hardness values for HPT-processed Fe are in a wide range from 300 HV [34] to 1200 HV [60] with the grain sizes ranging from 20 nm [60] to 600 nm [35].
Analytical and numerical approaches to modelling severe plastic deformation
2018, Progress in Materials ScienceCitation Excerpt :Indeed, if one were to limit oneself to just the most important factors and to aim at characterising the effect of, say, two channel shapes, two different cross-section sizes, five different friction conditions (corresponding, for example, to different lubricants, the quality of the die wall machining, or the die design), five different materials, four most common strain paths (A, B, C and Bc, see [2] for the definition of the ECAP routes), three different pressing velocities, three levels of back pressure, and three different temperatures, one would need to perform over 10,000 pressings followed by microstructure characterisation and mechanical testing. Therefore, the use of modelling tools in either mechanistic analytical formulations, cf. [129–133], or finite element analysis [84–86,134] is indispensable for optimisation of the processing schemes and conditions for a given material in a cost- and time-effective way. Of course, the mathematical models discussed in the previous section, particularly the analytical models, provide useful insights in the deformation behaviour.
A detailed model of high pressure torsion
2017, Materials Science and Engineering: ACitation Excerpt :However, an analysis at the “crystal plasticity level”, requires several key inputs such as the flow data. The inputs are typically obtained by other mechanical tests such as compression and torsion test in an average sense which do not accurately represent the SPD process [14]. Recently, HPT was proposed as a mechanical test [15] to provide a more representative flow data but given the uncertainties surrounding the friction during HPT, such data may be inaccurate.
In situ observation of the “crystalline⇒amorphous state” phase transformation in Ti<inf>2</inf>NiCu upon high-pressure torsion
2017, Materials Science and Engineering: ACitation Excerpt :The samples were deformed at a constant quasi-hydrostatic pressure of 6 GPa at room temperature, the rotation rate of the movable anvil was 0.67 rpm, and the degree of deformation n =6–8, where n is the number of revolutions of the movable anvil. Note: interval of hydrostatic pressure eliminating slippage of samples for Ti2NiCu material amounts 4–8 GPa, which follows from the works [16,17]. The structure was examined by transmission electron microscopy (TEM) with a JEOL JEM 1400 microscope at an accelerating voltage of 160 and 200 kV.
New Mathematical Stress Analysis in the Compressive Stage of the High-Pressure Torsion Process
2021, Metals and Materials InternationalFinite element analysis of plasticity behaviour of aluminium alloys in high-pressure torsion compressive loading stage
2019, International Journal of Structural Integrity