Non-uniform microstructure and texture evolution during equal channel angular extrusion

Abstract

Intense plastic deformation during equal–channel angular extrusion (ECAE) can occur in a broad region at the channel die intersection called the plastic deformation zone (PDZ). When the outer corner of the ECAE die is rounded, PDZs deviate from the model of single–plane simple shear, causing flow to be inhomogeneous. In this work, we explore the validity of using an analytical description of the PDZ by comparing model predictions against finite element (FE) simulations using various material and friction conditions and orientation imaging microscopy (OIM) measurements on ECAE one–pass copper. Inhomogeneous deformation divided the sample into two distinct regions across the sample thickness, wherein the accumulated strain, velocity gradient, texture evolution, and microstructural features are distinct. We demonstrate that intense deformation in the upper part is described well by sequences of simple shearing in a central fan and deformation in the lower part by a combination of low–intensity shear and rigid body rotation. Texture predictions by FE provided the same result as the PDZ model and OIM for the upper part, regardless of the friction and strain hardening variables considered. However, texture results for the lower part were sensitive to choices of friction and strain hardening. Though an idealization, this analytical two–region PDZ model, once characterized, can lend insight and be computationally efficient for multi-pass predictions.

Acknowledgements

This study was supported by a Los Alamos National Laboratory-Directed Research and Development Project (no. 20030216).

Notes

† The corresponding outer corner angle Ψ centred about inner corner O in figure 2 is 36.9°.

† The velocity gradient L is the time rate of change of the displacement gradient and is related to the deformation gradient F by

.

† This component is the only non-zero component of the velocity gradient expressed in the 1^′–2^′ system.

† Since D ₂₂ = − D ₁₁, D ₂₂ could be used just as well as D ₁₁.

† Cases 2 and 3 are similar and thus case 3 is not shown.

† Note that this description is a simplification of the actual deformation. The D ₁₂ component is not exactly zero, so the deformation is not ‘purely’ tensile or ‘purely’ compressive when entering and exiting the lower part.

† For the first pass, starting with an initially random texture, this association between the shear plane and texture could be made. However, for subsequent passes it cannot as the texture and shear plane direction are altered and hence, texture evolution becomes sensitive to route and pass number [23]. Only for route A does the alignment between the B fibre maxima and the shear plane persist [7].

† The FE Case 1 is selected due to its good agreement with OIM texture measurements for the upper part and its symmetric and less intense shearing deformation in the bottom layer (see ahead to section 6.4.1).

‡ We list the medians rather than the mean values as these histograms are generally not Gaussian in nature.

§ As these distributions are rather “flat”, median values for the lower part are not very meaningful.

† These data are internal grain misorientations and not misorientations between neighbouring grains and therefore the Mackenzie distribution [30] for a random distribution of cubics is not expected.

† More detailed substructure evaluations are possible with OIM, but for investigating the impact of inhomogeneous deformation, examining changes in Δθ is sufficient.