Measurements and full-field predictions of deformation heterogeneities in ice
Research highlights
► Resulting from very high local strain heterogeneities, local lattice misorientations can be characterised by EBSD in polycrystalline ice deformed under compression creep. ► A full-field viscoplastic approach well predict the stress and strain heterogeneities responsible for the measured local misorientation at the intragranular scale. ► The nature of the dislocations responsible for the kink-band structures observed in laboratory deformed ice was revealed by EBSD analyses.
Introduction
To improve climatic signal interpretation, and thus predictions, accurate modelling of ice dynamics is essential. In particular, an understanding of the deformation and recrystallization processes is necessary to correctly represent the ice flow in ice sheet modelling (Castelnau et al., 1996b, Durand et al., 2007). Indeed, to interpret the climatic signal correctly, dating of the ice core strongly relies on ice flow models, available ice-age markers, and ice texture characterization as a marker of ice flow discontinuities (Greenland Ice core Project (GRIP) Members, 1993, Parrenin et al., 2001, Buiron et al., 2011).
Ice is an hexagonal material in which deformation mainly occurs by dislocation glide along the basal plane conferring a strong viscoplastic anisotropy to the crystal (Duval et al., 1983). Such anisotropy at the crystal scale induces the development of strong internal stresses during deformation of the polycrystal, associated with the mismatch of dislocation slip between neighbouring grains. This internal state of stress strongly influences the deformation behaviour and recovery mechanisms such as dynamic recrystallization. Dynamic recrystallization mechanisms are very efficient in ice (Duval, 1979, Jacka and Li, 1994, Kipfstuhl et al., 2006, Montagnat et al., 2009). They are known to accommodate deformation processes as observed along ice cores taken from ice sheets (Alley et al., 1986a, Alley et al., 1986b, de la Chapelle et al., 1998, Duval and Castelnau, 1995, Montagnat and Duval, 2000) and to influence the texture evolution and thus the flow of ice.
Metals, rocks and ice, all polycrystalline aggregates, show remarkable similarities in their deformation and recrystallization behaviour (see for instance Goodman et al., 1981, Frost and Ashby, 1982, Humphreys and Hatherly, 1996, Kocks et al., 1998, Schulson and Duval, 2009). In this respect, both ice core data and ice deformation laboratory experiments provide very good systems to study the deformation heterogeneity development and dynamic recrystallization mechanisms for highly anisotropic materials. As such they constitute a valuable data set to validate modelling approaches for polycrystal mechanical behaviour (Castelnau et al., 1996b, Castelnau et al., 1997, Gilormini et al., 2001, Lebensohn et al., 2007).
We present a detailed study of the characterization of deformation heterogeneities and link these with the internal stress development during the creep of ice. We place particular emphasis on frequently observed kink bands in relation to the nature of the dislocations involved, and strain accommodated.
Laboratory experiments with columnar grained ice were used to quantify the intragranular misorientations that appear at the end of transient creep, and are considered as precursors to recrystallization mechanisms. An Automatic Ice Texture Analyser (AITA) (Russell-Head and Wilson, 2001) provides c-axis rotation measurements at the full sample scale (up to 120 × 120 mm2), and electron backscatter diffraction (EBSD) measures the full crystal orientation data at the grain scale following Piazolo et al. (2008).
Although common in metallic materials, such detailed local characterization of misorientations is at present not commonly performed in ice. For ice, most observations of local misorientations have been qualitative (Hamman et al., 2007, Mansuy et al., 2000, Mansuy et al., 2002, Wilson and Zhang, 1994), or obtained with X-ray diffraction techniques which do not allow mapping of a full area within the sample (Montagnat et al., 2003, Weikusat et al., 2011). Previous EBSD measurements were performed mainly to provide fabric data on the samples extracted along ice cores, with little consideration of local misorientations (Obbard and Baker, 2007, Obbard et al., 2006).
In order to predict quantitatively the internal state of stress and strain rate responsible for the observed intragranular misorientations we use the FFT full-field viscoplastic modelling approach (Lebensohn, 2001). Although this has already been validated for ice (Lebensohn et al., 2009), here, for the first time, we extend the methodology by using direct input from experimental measurements.
Section snippets
Experimental procedure and analyses
Experiments were carried out on laboratory grown ice samples with columnar grains in the direction perpendicular to the compression axis. Laboratory grown columnar ice is an excellent model material as its starting grain structure is well defined, near “2D” and without heterogeneities such as bubbles or impurities.
The sample dimensions were 50 × 50 × 10 mm3, with an average grain diameter of about 10 mm. The specimens were deformed in a cold room at − 11 °C +/ −1 °C using a mechanical press with a level
Substructure characterization: subgrain boundaries, local misorientations and type of dislocations
Fig. 2 shows the c-axis orientation image from the sample after the compression test, along with two azimuth profiles from selected representative areas (profiles along the two thick black lines).
The observations performed with the AITA at the sample scale reveal that a strong localisation of misorientations develops close to triple junctions and grain boundaries. In addition, at grain boundary asperities, misorientations including discontinuous subgrain boundaries and occasionally small
Prediction of the local state of stress responsible for deformation heterogeneities
We used the full-field FFT-based formulation, originally proposed by Moulinec and Suquet (1998) and adapted to compute the local response of viscoplastic anisotropic 3D polycrystals by Lebensohn (2001), to investigate the intragranular state of stress and strain rate responsible for the formation of the local misorientations and kink bands observed in our experiments.
The viscoplastic FFT-based formulation consists in finding a strain-rate field, associated with a kinematically-admissible
Concluding remarks
Experimental observations from the c-axis orientation measurements at the sample scale (from AITA), and the full lattice misorientation analyses in selected areas (from EBSD) clearly show a high level of local misorientations close to grain boundaries, and particularly at triple junctions. A specific focus was on some straight subgrain boundaries crossing grains from triple junctions that occurred frequently. The characterization performed at these two different scales demonstrates that these
Acknowledgements
We acknowledge Albert Griera for the help in providing the initial model microstructure input, Gaël Durand for helping with the output toolbox, Paul Duval, Chris Hall and Michael Zaiser for the fruitful discussions and perceptive comments. Financial support by the Swedish Research Council (VR 621-2004-5330), the Knut and AliceWallenberg Foundation (financing of equipment), department INSIS of CNRS, France, and the Royal Society (joint project grant University of Edinburgh and LGGE Grenoble) are
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2019, Acta MaterialiaCitation Excerpt :Kink bands are reported in strongly anisotropic hexagonal crystals such as ice or Zinc [3–7], as a crack-tip localization mode [8–10] or for titanium alloys under high strain rate deformation [11]. Asaro and Rice bifurcation analysis [12] showed that in presence of strain softening the constitutive equations of crystal plasticity can predict both slip and kink localization modes, and a few authors have studied the formation of kink bands in crystal plasticity simulations [4,13–15]. In ductile metals, slip localization can be observed after large plastic deformation, in the form of instabilities induced by exhaustion of hardening and inhomogeneous lattice rotations.