Stress and strain histories in equal channel angular extrusion/pressing
Introduction
Equal channel angular extrusion/pressing (ECAE/ECAP) is the most promising among the developed severe plastic deformation (SPD) techniques to fabricate bulk ultrafine (nano and submicron) grain materials. It has been widely used to enhance microstructural, mechanical and physical properties of different materials [1], [2]. It can also be used to consolidate ultrafine powders nearer to theoretical density [3], and to enhance the properties of tubular materials [4]. The severe plastic strains generate equiaxed grains and high angle grain boundaries for multiple passes of ECAE. This technique is quite simple and different from conventional metal forming techniques, and the load/pressure requirements are also much lower. The ECAE die shown in Fig. 1 consists of two channels of equal cross-section intersecting with a channel angle of ‘ϕ’, and with an outer corner angle of ‘ψ’. A well lubricated billet is placed in the first channel and is extruded into the intersecting channel by a punch, without varying its original cross-section. Strain induced in the material during the deformation is given by constitutive equations of ECAE [2], [5]. According to the constitutive equations, the strains induced depend on the tool angles. In addition, the strain induced is influenced also by strain hardening of material and friction between the die and the sample [6], [7]. Different channel angles, 60–160°, have been used to produce ultrafine grain structures in different materials [8], [9], based on the material strength and ductility. The channel angle dominates the strain induced in the material, and influences the deformation behavior, stress state and load requirements for the deformation. In order to design a sound ECAE die, and to produce sound ultrafine grain billets from different materials, a good knowledge on stress–strain histories and load requirements is required. The analytical equations can give stress–strain histories and load requirements but neglect the influence of important parameters like strain hardening of material [2], [5], [10], [11] and friction [2], [5]. In order to consider the influence of all these realistic factors, and to find out the deformation behavior, stress–strain histories, and load requirements during ECAE, finite element analysis is a proven choice. Most of the earlier finite element studies were limited to specific channel angles [6], [7], [12], [13], [14], [15], [16], [17], [18], ideal conditions [15], [17] and multiple ECAE passes [16], [17], [18]. But in the current study deformation behavior, stress–strain histories, and load requirements were calculated for a range of channel angles by incorporating the influence of realistic parameters.
Section snippets
Finite element analysis
Finite element code Abaqus/Explicit was used for the current study. Simulations were carried for a range of channel angles, ϕ = 60–150° with an increment of 15°, while keeping the outer corner angle, ψ, constant at 10°. The outer corner angle was chosen based on our earlier studies [13], [14]. AA1100 alloy with elastic–plastic properties: σf = 173.79 ɛ0.304, and a friction coefficient of 0.05 were adopted for the studies. Die and punch were modeled with analytical rigid elements. A Billet of 60 mm × 10
Results and discussion
To observe the stress–strain histories during the ECAE, three locations of interests: P1, P2 and P3 (Fig. 1) were chosen across the sample width at the middle of the sample. When the sample is in the deformation zone, P1 will be nearer to the outer corner of the die, P3 will be nearer to inner corner of the die, and P2 will be at the centre of the sample width.
Deformation behavior during the ECAE can be extracted from the equivalent plastic strain/effective strain (PEEQ) variations during the
Conclusions
Deformation behavior, stress–strain histories, and punch force requirements during ECAE were studied for a range of channel angles by using finite element code Abaqus/Explicit along with the consideration of realistic parameters. Deformation took place in three steps with ϕ < 90°, and in two steps with ϕ ≥ 90°. The differences between the effective strain values at different points are high with ϕ both above and below 90° and low with ϕ = 90°. The maximum principle stress values at different points
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