Equivalent Strain At Large Shear Deformation: Theoretical, Numerical ...

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ISSN: 1665-6423 e-ISSN: 2448-6736

The Journal of Applied Research and Technology (JART) is a bimonthly open access journal that publishes papers on innovative applications, development of new technologies and efficient solutions in engineering, computing and scientific research. JART publishes manuscripts describing original research, with significant results based on experimental, theoretical and numerical work. The journal does not charge for submission, processing, publication of manuscripts or for color reproduction of photographs. JART classifies research into the following main fields: Material Science Biomaterials, carbon, ceramics, composite, metals, polymers, thin films, functional materials and semiconductors. Computer Science Computer graphics and visualization, programming, human-computer interaction, neural networks, image processing and software engineering. Industrial Engineering Operations research, systems engineering, management science, complex systems and cybernetics applications and information technologies Electronic Engineering Solid-state physics, radio engineering, telecommunications, control systems, signal processing, power electronics, electronic devices and circuits and automation. Instrumentation engineering and science Measurement devices (pressure, temperature, flow, voltage, frequency etc.), precision engineering, medical devices, instrumentation for education (devices and software), sensor technology, mechatronics and robotics.

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See more Follow us: RSS Alerta email View more metrics Discontinued publication Hide Journal Information Previous article | Next article Vol. 15. Issue 5. Pages 413-512 (October 2017) Export reference Share Share Twitter Facebook Bluesky Linkedin whatsapp E-mail Print Download PDF More article options Statistics Outline

• Abstract
• Keywords
• Introduction
• Effective strain at large shear strains
• Numerical calculations
• Abstract
• Keywords
• Introduction
• Effective strain at large shear strains
• Simple shear
• Pure shear
• Numerical calculations
• Finite element analysis procedure
• Simple shear deformation
• Pure shear deformation
• Results and discussion
• Summary and conclusions
• Conflict of interest
• Acknowledgments
• Bibliography

Visits 13769 Vol. 15. Issue 5. Pages 413-512 (October 2017) Original DOI: 10.1016/j.jart.2017.05.002 Open Access Equivalent strain at large shear deformation: Theoretical, numerical and finite element analysis Visits 13769 Download PDF Nima Pardisa, Ramin Ebrahimia, Corresponding author Ebrahimy@shirazu.ac.irCorresponding author. , Hyoung Seop Kimba Department of Materials Science and Engineering, School of Engineering, Shiraz University, Shiraz, Iranb Department of Materials Science and Engineering, Pohang University of Science and Technology (POSTECH), Pohang 790-784, South Korea This item has received 13769 Visits Under a Creative Commons license Article information Abstract Full Text Bibliography Download PDF Statistics Figures (10) Abstract

In this study, effective strain is evaluated for large simple/pure shear deformations and new expressions are derived. The validity of these relations was checked by numerical calculations. In addition, finite element analysis of simple shear and pure shear modes of deformation was conducted using ABAQUS software. Additionally, two other major expressions for evaluating effective strain at large simple shear deformation were investigated and compared with finite element results. Based on FEM results, the linear relation between shear strain and effective strain large strains shall be replaced with the logarithmic one. It is also found that for the same amount of shear strain, a higher value of effective strain is accumulated in the material when it is deformed through simple shear rather than pure shear.

Keywords:Simple shearPure shearEquivalent strainFinite element analysisShear strainSevere plastic deformation Full Text 1Introduction

Simple shear and pure shear are considered as the most important modes in deformation of materials. While pure shear is an ideal deformation mode in metal forming operations (Segal, 1995), simple shear is considered as an optimal mode of deformation for grain refinement via severe plastic deformation (SPD) (Segal, 2002, 2006). Generally, most SPD techniques benefit from shear deformation of materials. In some techniques like equal channel angular pressing (ECAP) (Valiev & Langdon, 2006), high pressure torsion (HPT) (Zhilyaev & Langdon, 2008), twist extrusion (TE) (Beygelzimer, Varyukhin, Synkov, & Orlov, 2009) and simple shear extrusion (SSE) (Pardis & Ebrahimi, 2009), simple shear is a dominant mode of deformation while some other methods like pure shear extrusion (PSE) (Eivani, 2015) and accumulative channel-die compression bonding (ACCB) (Kamikawa & Furuhara, 2013) are based on pure shear deformation. In addition, in some other techniques such as cyclic extrusion-compression (CEC) (Richert & Richert, 1986) and cyclic expansion-extrusion (CEE) (Pardis, Chen, Ebrahimi, Toth, Gu, Beausir, & Kommel, 2015; Pardis, Chen, Shahbaz, Ebrahimi, & Toth, 2014; Pardis, Talebanpour, Ebrahimi, & Zomorodian, 2011) the two deformation modes (simple and pure shear) are both active. Since all of these SPD methods deal with giant straining of materials, the amount of accumulated equivalent strain can be considered as a suitable factor for comparing the degree of SPD imposed by these different techniques. Therefore, relations which convert shear strain to its equivalent effective strain are of great importance. This fact becomes even more important when considering the increasing interests on SPD processing of materials as well as development and modifications of various SPD techniques. However, fewer studies have been devoted to the basic relations between shear and equivalent strain values. In this study, these relations are reconsidered and investigated by finite element method (FEM). In addition, new expressions are presented for evaluation of effective strain at large shear deformation and their validity is examined by FEM. The results can be applied to estimate the accumulated strain after processing the samples by any specific forming/SPD technique. Before that, however, it is needed to determine the dominant deformation mode. In this regard, the kinematically admissible velocity field proposition for a given deformation process can make it much easier for considering simple shear/pure shear deformation modes in some techniques like Axi-symmetric forward spiral extrusion (Khoddam, Farhoumand, & Hodgson, 2011) and Vortex Extrusion (Shahbaz, Pardis, Ebrahimi, & Talebanpour, 2011; Shahbaz, Pardis, Kim, Ebrahimi, & Kim, 2016) where such classification might not be easily possible.

2Effective strain at large shear strains2.1Simple shear

Generally, there are two main expressions for evaluating the equivalent strain at large simple shear deformation. Shrivastava, Jonas, and Canova (1982) suggested the following common equation for evaluating nominal equivalent strain at large simple shear deformation.

However, Polakowski and Ripling (1966) stated Eq. (1) would not be valid at large shear strains as the directions of the maximum normal stress and strain are not coincident in simple shear deformation and derived the following Eq. (2):

This equation had been previously proposed by Eichinger (1955). Furthermore, there are records on a similar expression presented by Nadai (1937) for evaluating octahedral shear strain in simple shear deformation. However, the resulting values of these two major expressions would be significantly different at high shear strain values as illustrated in Figure 1.

Fig. 1.

Illustration of the equivalent strain as a function of shear strain calculated by Eqs. (1) and (2).

According to Figure 1, these two equations are nearly coincident at relatively low shear strains (γ