Experimental characterization of the intragranular strain field in columnar ice during transient creep

Abstract

A digital image correlation (DIC) technique has been adapted to polycrystalline ice specimens in order to characterize the development of strain heterogeneities at an intragranular scale during transient creep deformation (compression tests). Specimens exhibit a columnar microstructure so that plastic deformation is essentially two-dimensional, with few in-depth gradients, and therefore surface DIC analyses are representative of the whole specimen volume. Local misorientations at the intragranular scale were also extracted from microstructure analyses carried out with an automatic texture analyzer before and after deformation. Highly localized strain patterns are evidenced by the DIC technique. Local equivalent strain can reach values as much as an order of magnitude larger than the macroscopic average. The structure of the strain pattern does not evolve with strain in the transient creep regime. Almost no correlation between the measured local strain and the Schmid factor of the slip plane of the underlying grain is observed, highlighting the importance of the mechanical interactions between neighboring grains resulting from the very large viscoplastic anisotropy of ice crystals. Finally, the experimental microstructure was introduced in a full-field fast Fourier transform polycrystal model; simulated strain fields are a good match with experimental ones.

Introduction

The deformation of polycrystalline materials gives rise to the build-up of heterogeneous stress and strain fields inside individual grains (intragranular scale), but also between adjacent grains (intergranular scale). These field heterogeneities originate from the anisotropic mechanical behavior of individual grains, which is responsible for complex mechanical interactions between adjacent grains upon macroscopic specimen loading. They have a large influence on the overall material response, as illustrated, for example, by Brenner et al. [1] for the yield stress of elastoplastic polycrystals.

The development of stress and strain heterogeneities has been studied in a number of papers by making use of full-field numerical approaches [2], [3], [4], [5], [6], [7]. It has been observed that field heterogeneities increase quickly with the anisotropy of the local constitutive relation. A similar dependence to the non-linearity is expected, i.e. heterogeneities blow up when the local behavior becomes strongly non-linear [8]. It should also be mentioned that these trends are recovered by mean-field models based on homogenization theories [9].

On the experimental side, local strain can be characterized by means of digital image correlation (DIC) techniques. The method is based on the acquisition of successive images of the specimen surfaces at different strain increments. The comparison of these images allows the identification of the displacement field at the specimen surface, which can be then derived to obtain the strain field of interest. This has been the subject of several studies on different metallic alloys exhibiting equiaxed and small (i.e. micrometer range) grains [10], [11], [12], in which the systematic development of localization bands at about 45° from the tensile angle and extending along several grain sizes has been observed. In these studies, the interpretation of strain localization is limited by the unknown microstructure of grains underneath the specimen free surface [11], [13]. The application of DIC to geomaterials has so far been carried out on argillaceous rock [14], soft rock [15] and marble [16].

In this work, the DIC technique is applied to polycrystalline ice. This material exhibits a number of specific characteristics that can be used advantageously to gain an understanding of polycrystal behavior:

• Large specimens exhibiting columnar microstructures with centimetric grain size can be elaborated. Due to the absence of through-thickness microstructure gradients, fields measured at the specimen surface are representative of the whole specimen volume.

• Ice single crystals exhibit a single easy slip plane for dislocations; the viscoplastic anisotropy is therefore huge at the grain scale. Unlike in most hexagonal materials, twinning is not an active deformation mode, leading to a relatively simple behavior. The grain response can thus be characterized by a single Schmid factor, compared to many more for cubic or hexagonal metals.

Consequently, since the complete specimen microstructure and main active slip systems are known, one can also anticipate an easier interpretation of results.

This work is focused on the evolution of strain localization during the transient creep regime, corresponding to an overall strain of less than 10⁻². In that regime, the progressive development of an internal stress field is at the origin of the severe decrease in strain rate [17], [18]. Concerning geophysical applications, the transient creep of polycrystalline ice is of interest with regard to, for example, the behavior of ice shelves submitted to ocean tides [19], [20] and the production of heat within icy satellites [21], [22].

This paper is organized as follows. Section 2 is devoted to the description of the specimen elaboration technique and obtained columnar microstructures. In Section 3, adaptation of the DIC technique to our sample configuration is described. The experimental resolution is estimated for the displacement and strain fields. The main results in terms of macroscopic strain and strain field evolution are given in Section 4. Specific results that can be inferred from these columnar microstructure are discussed in Section 5. The relation between local strain and local grain orientation is also analyzed. Results are also compared to predictions obtained by full-field modeling, based on the fast Fourier transform (FFT) approach of Moulinec and Suquet [23].