Elsevier

Scripta Materialia

Volume 49, Issue 5, September 2003, Pages 411-415
Scripta Materialia

Strain gradients and geometrically necessary dislocations in deformed ice single crystals

https://doi.org/10.1016/S1359-6462(03)00303-8Get rights and content

Abstract

Hard X-ray diffraction experiments were performed on ice single crystals deformed in torsion. This work shows the relationship between the density of geometrically necessary dislocations and strain gradients. The torsion strain appears to be totally accommodated by geometrically necessary basal screw dislocations.

Introduction

There has recently been great interest in developing mechanism-based theories of strain-gradient plasticity including an internal length scale, to describe the deformation of crystalline materials on the micron scale [1], [2], [3], [4]. Strain gradients can be caused by the loading geometry. Strengthening effects arising from strain gradients are observed in indentation and torsion experiments on the micron scale [1], [3]. In torsion, strength increases with decreasing wire diameter. These results are interpreted in terms of geometrically necessary dislocations associated with strain gradients. Strain gradients can also be induced in polycrystals by the mismatch of slip at boundaries [1], [5]. Large spread of orientations was found in grains of aluminium alloys after deformation in plane strain compression by using the back scattering diffraction technique (EBSD) [6], [7]. The concept of geometrically necessary dislocations was used as the central tool in the description of such deformation inhomogeneities [8].

Geometrically necessary dislocations play a key role in the modelling of size-dependent plasticity. The hardening associated with these dislocations becomes significant when plastic deformation takes place on small scales [9], [10], [11]. The relevant size scale to consider in strain-gradient plasticity theory is the scale associated with the dislocation structure that evolves during deformation. There is hence a great need for experimental characterisation of geometrically necessary dislocations associated with non-uniform plastic deformation [12], [13].

The density of geometrically necessary dislocations has already been estimated for a few ice samples from polar ice sheets [14]. In ice polycrystals, strain gradients can be induced by the mismatch of slip at the boundaries, greatly enhanced by the strong plastic anisotropy of ice crystals. Ice essentially deforms by the activity of the basal slip systems 〈1 1 2̄ 0〉 (0 0 0 1) [15]. With such behaviour, the length scale at which strain gradients significantly influence flow-stress increments is expected to be very large in ice.

The purpose of this work is to estimate the nature and density of geometrically necessary dislocations associated with strain gradients resulting from torsion tests on ice single crystals on a scale of several millimeters. Hard X-ray diffraction experiments were carried out to characterise the geometrically necessary dislocations required to accommodate the lattice distortion and to evaluate their density. Emphasis is placed on the relationship between geometrically necessary dislocations and hardening.

Section snippets

Experimental method

Torsion experiments were performed on single crystals artificially grown in the laboratory. The initial dislocation density of the sample was estimated to be less than 108 m−2 [16]. Samples were cylindrical, and grips consisted in refrozen water at the interface with the torsion device. Three different samples were tested (see characteristics in Table 1). A constant torsion torque was applied to each sample in order to obtain a shear stress of 0.2 ± 0.05 MPa on the surface. The temperature was

Results

Fig. 2b shows the diffraction pattern obtained for sample XR2. Distortion of the lattice as seen on the (1 0 1̄ 0) diffraction line was too large to be observed in a single pattern. Reconstruction of the global (1 0 1̄ 0) diffraction line was made possible by the rotation of the sample around the vertical axis (see Fig. 2c). Results concerning lattice distortion Δθ observed on prismatic (1 0 1̄ 0) and basal (0 0 0 2) diffraction lines are given in Table 2. A close estimate of the corresponding density of

Discussion

As observed in semiconductors with diamond structures, a continuous increase in the creep rate is observed with no apparent strain hardening (Fig. 1). The multiplication of mobile dislocations during deformation is the reason for the shape of the creep curves [19]. The plastic properties of ice single crystals determined by uniaxial tension and compression are similar to those found in this study [20], [21]. Strain rates calculated here for a strain of about 5% are of the same order of

Acknowledgements

This work was supported by CNRS, Département des Sciences Pour l’Ingénieur (SPI) (Programme Matériaux). We are very grateful to P. Sassin and F. Dominé for providing samples. We thank O. Brissaud for the design of the cooling device and the help during the experiments, as well as ILL staff and particularly C. Menthonnex and A. Elaazzouzi for technical and computing assistance. Helpful comments of J. Gil Sevillano were appreciated.

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