IJMF, Iranian Journal of Materials Forming, Vol.1, No.1, pp. 56-63
Printed in The Islamic Republic of Iran, 2014
©Shiraz University
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Received by the editors January 19, 2014; Revised February 23, 2014 and Accepted February 26, 2014
* Corresponding author (E mail: maghaei@kntu.ac.ir)
A Comparison Between Numerical and Analytical Modeling of ECAP
M. Rejaeian and M. Aghaie-Khafri
*
Faculty of Mechanical Engineering, K.N. Toosi University of Technology, Tehran, Iran.
Abstract: Recent developments in nanostructured products draw considerable attention to
ultrafine grained materials. These materials are normally manufactured by different severe plastic
deformation (SPD) methods. In the present study, analytical models and finite element method
(FEM) are used to calculate strain imposed to a specimen that was deformed by equal channel
angular pressing (ECAP). In addition, strain inhomogeneity in term of coefficient of deviation
(CV) for an aluminum alloy (AA6101) which was processed under ECAP was calculated. Dies
with 90º, 105º and 120º intersecting angles were modeled based on FEM. Furthermore, the effect
of friction on force-displacement curves was investigated using analytical and numerical
approaches. Moreover, the energy loss that is due to friction was computed. Strains calculated by
FEM for different die angles were identical to those evaluated by analytical models. Based on the
numerical and analytical models, it has been shown that strain inhomogeneity increases when the
angle between two channels decreases.
Keywords: ECAP, simulation, strain inhomogeneity, friction
1. Introduction
Since nanotechnology is regarded as an essential element for advanced industry fields, various methods
such as powder metallurgy, thermo mechanical processing and severe plastic deformation (SPD) have
been proposed in order to manufacture ultra-fine grained materials. SPD can be used to manufacture a full
dense product whose strength is noticeably high. Equal channel angular pressing (ECAP) which was
invented by Segal is known as a technique for imposing severe deformation on materials. It is possible to
repeat this process for a number of passes to refine grain structure [1].
Many studies and experiments have been carried out for understanding this technique. Segal, who is
known as pioneer of this process studied ECAP using slip-line method. Full solutions were considered as
a function of contact friction, back pressure and tool design. He showed that various boundary conditions
had a moderate effect on the equivalent strain [2]. An upper bound model based on linear and rotational
velocity field was extended by Reihanian et al [3]. The load prediction of square cross sectioned ECAP
was successfully attained by the new velocity field [3]. Deformation of the material during a 90º ECAP
process was studied via upper bound theorem by Altan et al. This model considers the effect of friction
between the sample and die walls, radius of inner corner of the die and the dead metal zone [4]. Paydar et
al. analyzed equal channel angular extrusion with circular cross-sections by upper bound approach [5].
They concluded that the size of the plastic deformation zone and the relative extrusion pressure increase
with increasing the constant friction factor [5]. Narooie et al. developed a three dimensional (3D)
kinematically admissible velocity field based on Bezier formulation in order to predict the strain
distribution and extrusion load in ECAP process of a circular cross section billet [1]. A study of the
required force for performing the ECAP process was done by Perez et al [6]. Nagasekhar et al. considered
the strain hardening of pure copper and the friction between the sample and the die channel using finite