SESolid EarthSESolid Earth1869-9529Copernicus PublicationsGöttingen, Germany10.5194/se-8-943-2017Strain field evolution at the ductile-to-brittle transition: a case study on iceChauveThomasMontagnatMaurineLachaudCedricGeorgesDavidVacherPierreUniversité Grenoble Alpes, CNRS, IRD, G-INP, IGE, 38041 Grenoble, FranceLaboratoire SYMME, Université de Savoie Mont Blanc, BP 80439, 74944 Annecy le Vieux CEDEX, FranceM. Montagnat (maurine.montagnat@univ-grenoble-alpes.fr)18September20178594395327February201717March201720June20177August2017This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/3.0/This article is available from https://se.copernicus.org/articles/8/943/2017/se-8-943-2017.htmlThe full text article is available as a PDF file from https://se.copernicus.org/articles/8/943/2017/se-8-943-2017.pdf
This paper presents, for the first time, the evolution of the local
heterogeneous strain field around intra-granular cracking in polycrystalline
ice, at the onset of tertiary creep. Owing to the high homologous temperature
conditions and relatively low compressive stress applied, stress
concentration at the crack tips is relaxed by plastic mechanisms associated with
dynamic recrystallization. Strain field evolution followed by digital image correlation (DIC) directly shows the redistribution of strain during crack opening,
but also the redistribution driven by crack tip plasticity mechanisms and recrystallization.
Associated local changes in microstructure induce modifications of the
local stress field evidenced by crack closure during deformation. At the ductile-to-brittle transition in ice, micro-cracking and dynamic recrystallization
mechanisms can co-exist and interact, the later being efficient to relax
stress concentration at the crack tips.
Introduction
The evaluation and the characterization of strain heterogeneities
is of primary importance in material sciences at various scales of
observation. Plastic strain localization in metals plays a crucial role on the
propagation of fracture and on the response to fatigue conditions, and
Portevin-Le-Chatelier is a strong example of plastic strain heterogeneities
development during mechanical tests in some metal alloys (see
, for a review). Similarly, strain heterogeneities and
localization are known to strongly influence the rheological behavior of the
Earth lithosphere, in particular to explain post-seismic deformation
.
In the context of ice sheet flow, successive
layers of ice with slightly different viscosity can experience different
strain history as a result of strain localization initiated by bedrock
topography . Strain localization
can induce flow disturbances that can mix the climatic signal and counteract
the search for the oldest ice . These flow
disturbances can form as folding that is observed at large scale from
ice-penetrating radar surveys now able to highlight deep stratigraphy
, but also at smaller scales from
microstructure observations .
During ductile deformation of ice in natural or laboratory conditions (at high homologous temperature of ∼ 0.97 Tm,
low strain rate of ∼10-7s-1 and low stress of 0.5–1 MPa), plastic deformation is mainly accommodated by the
glide of basal dislocations .
The resulting strongly anisotropic viscoplastic behavior of the single crystal leads to
the development of strong strain heterogeneities during deformation of polycrystalline ice .
Strain heterogeneities evaluated during transient creep of ice were shown to
reach local values higher than 10 times the macroscopic strain, and to settle
into bands whose dimensions are higher than the grain size. Strain
localization bands may follow grain boundaries, but they also cross entire grains,
and there is no statistical link between the crystallographic orientation and
the amount of local strain . These first measurements of
strain localization during laboratory experiments were restricted to
transient (or primary) creep conditions, in ductile conditions (σ<
0.5 MPa and T> 0.97 Tm) and prior to any microstructure modification
due to dynamic recrystallization.
More generally, creep of isotropic polycrystalline ice is characterized by a three-stage behavior, with a
strong decrease in strain rate during primary creep, down to a minimum reached at about 1 % strain, also
called secondary creep, immediately followed by a increase in strain rate to reach tertiary creep at about
10 % strain (see , for instance).
At the onset of tertiary creep, for experiment performed at low strain rate
(<10-7 s-1) or low stress (< 0.5 MPa), dynamic recrystallization
mechanisms occur increasingly to relax the kinematic hardening and enable for
further ductile deformation to occur . Dynamic
recrystallization leads to strong modification in microstructure and texture
through various mechanisms such
as nucleation of new grains or polygonization associated with sub-grain
boundaries and bulging, recently characterized by cryo-EBSD (electron backscatter
diffraction; ). While showed that sub-grain boundary
formation such as kink bands could be correlated with heterogeneities of
local stress (simulated with a full-field crystal plasticity code, CraFT),
were able to directly associate nucleation mechanisms
(polygonization, bulging) with local modification of the strain field estimated
in situ from digital image correlation (DIC) measurements.
During experiments performed at higher imposed stress (typically above 0.9 MPa), the increase in strain rate after secondary creep can also be
associated with the occurrence of micro-cracking without a total collapse of
the sample . The local stress
field is therefore relaxed by cracks opening at or close to grain boundaries,
and depending on the boundary conditions, crack propagation can occur at
various rates. This mechanical response is typical of a ductile-to-brittle
transition .
In this domain, most of the
studies performed so far, some of which are mentioned here, have focused on
macroscopic parameters (deformation and creep curves, evaluation of the
effect of temperature and grain size on strength) and optical observations of
the full sample to characterize the nature of the cracks . From these observations, a theoretical framework was elaborated
based on the assumption of the formation of wing cracks at the tip of initial
cracks to relax the local stress field . In particular,
the conditions required to form these secondary cracks were shown to control
the ductile-to-brittle transition under compression. More recently,
showed that this model was able to take into account the
effect of a pre-strain, including recrystallization mechanisms, on the
increase in ductile-to-brittle transition strain rate for ice.
At the ductile-to-brittle transition, mixture of creep by dislocations and
cracking will occur, and it is related to the ability of the material to
relax the stress accumulated at the tip of the initial cracks. For instance,
showed that a small amount of creep relaxation at the crack
tip could be enough to postponed the transition to brittle behavior (in time
or in strain-rate level). The mechanism of relaxation of the stress produced
by a crack opening in mode I through rapid multiplication of dislocations at
the crack tip was pioneered by and has been reviewed by
for metallic materials. More recently,
were able to simulate the complexity of the
effect of strain gradient plasticity on the level of stress at the crack tip and
on crack-tip blunting. Crack-tip-initiated plasticity is a crucial mechanism
to explain a ductile-like behavior at the ductile-to-brittle transition.
In the present work we use the DIC technique, already
well proven on ice, to evaluate the strain field evolution during a creep
experiment on ice polycrystal performed at the ductile-to-brittle transition.
After a brief presentation of the experimental setup (Sect. ), Sect. will explore stress conditions during which strain-rate
increase with tertiary creep results from local cracking. We will see that
plasticity is strongly active at the crack tips as evidenced by the occurrence of
dynamic recrystallization mechanisms. These mechanisms, by modifying the
microstructure, indeed play a crucial role to reduce and redistribute the
local stress concentration that appears at the crack tips during the ductile-to-brittle transition.
Experimental setup
Unconfined uniaxial creep tests have been carried out on polycrystalline
columnar ice samples of type S2 . Parallelepipedic samples
(∼ 90 × 90 × 15 mm) were built and the column
axes were positioned perpendicularly to the larger surface, and to the
compression axis (Fig. ). By doing so, the samples
provide a “2-D–1/2” microstructure, from which surface characterization
satisfactorily reflects volume behavior. Sample microstructure and texture
were measured using an automatic ice texture analyzer (AITA;
), which is an optical technique measuring the
c axis (or optical axis) orientation (azimuth θ and
colatitude ϕ) with a spatial resolution from 50 to 5 µm, and an
angular resolution of about 3∘. Although large areas can be analyzed
(up to 120 × 120 mm), this technique requires the preparation of
thin sections of ice (∼ 0.3 mm thick), and is then destructive. By
taking advantage of the columnar microstructure, we were able to compare
pre- and post-deformation microstructures by carefully
extracting thin layers of ice before and after the test (Fig. ). Details of the procedure for sample preparation can
be found in and .
During the experiment, DIC analyses were performed over the full surface of
the samples by following the procedure adapted to ice by
. DIC provides in situ measurements of the displacement
and therefore strain field on the sample surface, from the correlation of
surface images of a grey-level speckle that follows the sample deformation.
By taking advantage of the 2-D–1/2 configuration, we assumed the surface
strain field to be as representative as possible of the volume deformation.
This configuration makes it possible to compare the microstructures measured
by AITA (before and after the test) to the strain field evaluated by DIC
(Fig. ).
The spatial resolution strongly depends on
the quality of the speckle, the illumination and the sensitivity of the
camera used. In the following experiments, we used a Phase One 80 Mpx camera,
the speckle was made of shoe polish that offers good cohesion with the ice
surface and good illumination was obtained thanks to two neon lamps. From
this, we ended up with a spatial resolution of 0.19 mm pix-1, and a
strain resolution between 3.10-3 and 4.10-3 for the different
strain components (see Table ).
Characteristics of the DIC measurements.
CameraDIC spatialDIC strain resolution resolutionσεxxσεyyσεxyPhase One 80 Mpx0.19 mm pix-14.10-33.10-34.10-3
Displacement and total strain data were extracted using the 7-D software
from . This DIC method provides a set of displacement
vectors over a given grid, defined for the DIC calculation as a function of
the speckle and picture qualities . From the displacement
field components, the total strain components are extracted by using
Green–Lagrange expression. Please note that the elastic and plastic
components can not be separated, and strain field refers to the total strain
field. In the case of ice, elasticity is very low and nearly isotropic, and
can be neglected . In-plane components of strain are
therefore provided (εxx, εyy and
εxy), from which an equivalent strain
(εeq=23εxx2+εyy2+2εxy2) and principal strain
components are calculated. The later will be plotted along their principal
directions in the following figures.
Discontinuities such as cracks produce
displacements whose translation in terms of strain is not direct but could be
estimated as shown by . In the present study, we simply use
the direction of the principal strain components calculated around a crack to
interpret the direction of the crack opening (or closing), since the
displacement produced is small enough to be followed by the speckle on each
side of the crack.
Since all surfaces except the loaded ones remained free
(unconfined tests), a limited amount of out-of-plane shear cannot be excluded.
The effect of a deformation going out of the plane xOy was estimated in
previous analyses performed by and shown to remain low,
within the limit of the small macroscopic deformations reached in the present
study (less than 5.5%). In order to reduce the noise and this out-of-plane strain effect on the evaluation of the strain evolution during the
experiment, we calculated the strain field during short increments of
macroscopic deformation of 0.1 to 0.5%. Additionally, observation
of the incremental strain field enables individualizing consecutive events
that would be hidden in a strain field calculation integrating the whole
experiment duration.
Scheme of the experimental setup showing the shape of the sample with the direction of imposed stress
(red arrow). Position 0 corresponds to the sample surface (during the test) on top of which the speckle
is marked. The microstructure analyzed by AITA prior to deformation is located at about -0.5 mm and
the one after deformation is at about 0.5 mm from the sample surface (0.5 mm corresponds to the ice
thickness needed to make the thin section). The strain-field image, measured at position 0, is added in the front plan for illustration.
Table summarizes the experimental conditions of the test used as an illustration in this paper, and Fig.
provides the creep curves.
The minimum strain rate is reached at about 0.5 % of compressive macro-strain, slightly before the standard 1 % value.
This can be attributed to a microstructure effect since our 2-D–1/2 samples contain only few grains and do not form good representative volume elements.
In the following, a negative sign will be given to the compressive strain, at the macroscopic and local scale.
Experimental conditions at the ductile-to-brittle transition for the illustrative test presented here.
The minimum creep rate is reached at about -0.5 % strain.
Evolution of the macroscopic strain and strain rate measured by DIC.
Values less than 10-3 macro-strain were not calculated.
Strain field evolution at the ductile-to-brittle transition
The macroscopic strain curve reveals an increase in strain rate after
-0.5 % of εyy (vertical) macro-strain (Fig. ). At -0.5 % of macro-strain the minimum strain
rate is 5.0×10-6 s-1 and at the end of the experiment the
strain rate reaches 8.1×10-5 s-1, evidencing an acceleration
at the onset of tertiary creep captured here.
The initial microstructure of the sample, the ending one and an optical
observation of the full sample at the end of the test are shown in Fig. . Thanks to the transparency of ice, cracks and
de-cohesion features can be observed with natural light. They appear as grey
and black areas in Fig. . Both features were clearly
distinguished and analyzed by . From the c axis orientation
color scale, one can see that the initial texture is not isotropic. On top of
the expected columnar grain-shape effect, we therefore expect, as observed
(Fig. ), a macroscopic mechanical response
different from the one of an isotropic granular sample.
The global strain field measured prior to any visible crack opening on the
speckle, at -0.5% of macro-strain (at the minimum creep rate), is
represented in Fig. via the equivalent strain
εeq at two different spatial resolutions in order to
illustrate the structure of strain heterogeneities. Similarly to what was
already observed by , the deformation is organized into
bands crossing most of the sample. The main orientation of the bands is about
20 to 30∘ E from the compression direction. Local equivalent strain
amplitude in the deformation bands can reach more than 10 %, for a
εyy macro-strain of about -0.5 %.
Microstructure (color-coded c axis orientation, from AITA analysis) before deformation (a) and
after -5.5 % of compressive creep at -7 ∘C under 1 MPa (b). (c) Raw picture of the sample taken
in natural light at the end of the compressive test. Black areas result from light diffusion by cracks and de-cohesion features.
The dashed black rectangle shows the area studied in detail in the paper.
Map of equivalent strain (εeq) after -0.47% of compressive deformation.
The blue rectangle shows the area studied in detail in the paper. (a) Spatial resolution
of 0.76 mm pix-1. (b) Spatial resolution of 0.19 mm pix-1.
In the following, focus will be given to a small area located within the dashed black rectangle of Fig. .
The initial microstructure and orientations of the grains in this area, the final microstructure where cracks, sub-grain boundaries
and small nucleated grains appear and a picture of the speckle from the surface of the sample where crack locations are visible
(arrows 1 to 4) are shown in Fig. .
Very small grains visible inside the cracks are artifacts from the thin sectioning process (shaving produces small chips that fill
the crack interior), but new grains from dynamic recrystallization mechanisms (DRX) can be distinguished away from the crack interior.
See for instance the new blue area in between the bottom of crack 2 and top of crack 3. Also the dark blue grain at the bottom of crack
3, and the pink–purple ones surrounding crack 4.
None of these new grains were pre-existing in the initial microstructure, therefore illustrating DRX nucleation.
Grain boundaries surrounding new small grains can appear more irregular than in reality because of intrinsic limitation of the AITA observation
based on thin sections (about 0.3 mm thick).
A lot of sub-grain boundaries similar to the tilt and kink bands characterized in are visible after deformation.
A tilt band is composed of basal edge dislocations and can accommodate a large misorientation, as observed here. A kink band is composed of
two nearby tilt bands that accommodate opposite misorientations.
For instance, a highly misoriented tilt band is visible as a sharp transition between orange and light brown close to cracks 2 and 3
(ellipse). Between cracks 2 and 1, the two close color transitions (from green to blue to green, and from brown to green to brown) illustrate misorientations resulting from kink bands.
Intra-granular cracks (cracks 1, 3 and 4) and cracks along grain
boundaries (crack 2) are observed. Observed intra-granular cracks do not
always cross the entire grain, such as crack 1, which seems interrupted in
the middle of the grain (Fig. ). This final
microstructure very likely results from strong strain heterogeneities at
grain boundaries and within grain interiors.
Studied area extracted from the sample of Fig. . (a) Initial microstructure
measured by AITA. The black lines show the superimposed and artificially enlarged grain boundaries. The irregular
white lines and small white areas are measurement artifacts. (b) Microstructure measured by AITA
after deformation. Crack locations are highlighted by black full lines and labeled. Areas where recrystallization
by sub-grain rotation took place are shown by black dashed ellipses. (c) Raw picture of the surface
speckle at the end of the test where cracks 1 to 4 can be seen by speckle discontinuities.
In the following, we track the history of formation of the four cracks
labeled in Fig. by analyzing the strain field
evolution through the principal strain components, such as in
. The principal strain component representation enables us to
distinguish among the components of the local strain.
Within this area of interest, the
deformation before the apparition of any crack is localized in two main
bands, one crossing the full area at about 10 to 20∘ E from the
vertical (compression) direction, and another one in the bottom part of the
area, nearly perpendicular to the first one (Fig. , left). Both bands are following
some boundaries and crossing some grains. The principal strain components
are typical of a local pure shear configuration.
The accumulated strain field just before (at εyy=-1.35 %),
and just after the opening of cracks 1, 2 and 3 (at εyy=-1.46 %) is shown in Fig. . As an
illustration, the location of cracks 2 and 3 is shown by a blue
ellipse, and the small dark dots within this ellipse highlight an apparent
high equivalent strain due the speckle modifications from cracking. Cracks
2 and 3 occurred at the side of the main deformation bands, but not on
these bands. Crack 2 appears to be the closest to the grain boundary,
although grain boundaries cannot be positioned precisely enough on top of the
image after deformation .
As mentioned in Sect. , maps of accumulated strain include some noise, and likely some
out-of-plane component of strain. In order to provide a more precise
description of the relationship between strain field and crack opening, the
following analyses will be performed based on strain-field increments
measured during adapted macro-strain increments. This procedure strongly
reduces the effect of accumulated noise and out-of-plane strain is negligible
during small strain increments.
As a departure point, the strain field during increment of macro-strain
between -1.34 and -1.35 %, just before any visible crack event, is shown in
Fig. , by both εeq (grey color scale)
and the projections of the principal strain components (arrows). During this
strain increment, strain field is very similar to the one accumulated during
the entire experiment before cracking events (Fig. , left). Blue ellipses were drawn on
the position of future opening of cracks 1, 2 and 3. Local strain within the
ellipses is low compared to the one accommodated by the two main bands.
Evaluation of the total accumulated strain field in the focused area from Fig.
represented by εeq and by the principal components. (a) Total strain accumulated after
-1.35 % of macro-strain. (b) Total strain accumulated after -1.46 % of macro-strain, just
after the crack formation. The blue ellipse shows the area of formation of crack 2.
The strain field measured during increments at later steps of the experiment
is presented on the different parts of Fig. . Cracks
1, 2 and 3 are first observed to open between -1.35 and -1.46%
of macro-strain (Fig. a). Cracks can be visualized on
the speckle as discontinuities, and the DIC calculation provides an apparent
strain characterized by a pure extension which provides the main direction of
the crack opening. Cracks 1 to 3 could have opened mainly in mode I since
no shear component was measured by DIC in the area of crack formation just
before the opening (Fig. ), within the limit of resolution
of our observations. During this strain increment, associated with the crack
opening, strain is still localized in the nearly horizontal band. The nearly
vertical deformation band, which was accommodating a lot of deformation
before the cracks start to open, is not active anymore (compare Figs. and ).
During the next increment (Fig. b), cracks continue
opening, as illustrated by the tension component evaluated by DIC around the
crack sides. From the final microstructure picture (Fig. ), we see that the top right part of crack 1
is connected to a grain boundary but the bottom part of this crack remains
inside the grain, while no clear strain localization can be observed at this
position (within our limit of accuracy).
About 30 min later, between macro-strain of -2.40 and -2.59%
(Fig. c), the strain field evaluation (together with
speckle observation) tends to show that cracks 1 and 2 are still
expanding when crack 3 remains stable, since DIC calculation shows no more
tensile strain components in the area of crack 3.
During this increment, crack 4 appears at the bottom left and two new
deformation bands appear at the lower tip of crack 2, and at the bottom tip
of crack 3, both being parallel to the main transverse deformation band
observed from the beginning of this sequence. These new lines of strain
localization end up joining each other and the initial transverse
deformation band during the macro-strain interval between -3.12 and
-3.37% (Fig. d). By looking at the final
microstructure (Fig. ), these new deformation
bands appear to be localized in an area where new grains recrystallized.
Since we follow the strain field evolution during the test, we are able to
verify that the new grains formed after the apparition of the cracks as
in .
At the same time, crack 3 closes, as evidenced by the thinning of the
corresponding white zone in the speckle image. Strain in the crack 3 area
turns into a pure compressive component (blue arrows, Fig. d), which is likely to be responsible for this crack
closure. Similarly, during the last increment of deformation (between
-5.05 and -5.50% of macro-strain), pure compressive principal
strain components are calculated in most of the observed crack
discontinuities (Fig. ). Together with the visual
observation of crack evolution on the speckle images, these observations
reveal a crack closure mechanism.
During this last increment, strain field is also characterized by several new
bands of strain localization in the area (Fig. ). By
observing the final microstructure, we can attribute this strain localization
to the formation of high-angle sub-grain boundaries and kink bands. Their
likely locations are shown by dashed black ellipses in Figs. and to facilitate the
observation. In particular, the two kink bands marked by the top black dashed
ellipses seem to be localized at the tips of cracks 2 and 1. Please note
that crack 1 bottom tip localized in the grain interior strongly coincides
with the edge of a high-angle sub-grain boundary.
Strain field increment during the 5 min before the apparition of cracks between -1.34
and -1.35% of macroscopic strain. (a) Pictures of the speckled surface used for the DIC.
(b) Principal component of the strain field superimposed on the equivalent strain field (εeq).
Four steps of 5 min strain field increment during crack opening.
(a, c) Pictures of the speckled surface used for the DIC. (b, d) Principal
component of the strain field superimposed on the equivalent strain field. (a) Increment
between -1.35 and -1.46%. (b) Increment between -1.46 and -1.60%.
(c) Increment between -2.40 and -2.59%. (d) Increment between -3.12 and -3.37%.
Increment of deformation during the last 5 min of the test (between -5.05 and -5.55%).
Kink band formation (within dashed black ellipses) at the crack tips and crack closure are observed. (a) Pictures of the speckled surface
used for DIC. (b) Principal components of the strain field superimposed on the equivalent strain field.
To summarize, by measuring the strain field evolution during the onset of tertiary creep, at the ductile-to-brittle transition, we were able to
follow crack formation close to grain boundaries and within grain interiors, as well as their consequences on the local strain field.
Some cracks appear at the side of high strain localization bands, where stress must have concentrated in “hard” zones for deformation.
Following the crack opening, we observe a strong redistribution of the local strain, with the disappearance of one of the major localization band.
Additionally, we show that stress concentration at the crack tips can be efficiently relaxed by dynamic recrystallization mechanisms (nucleation and sub-grain
boundary formation), and that the stress redistribution induced by crack opening and microstructure changes due to DRX mechanisms can lead to the
closure of cracks during the test.
The occurrence of dynamic recrystallization mechanisms is here strongly enhanced by the high homologous temperature conditions of the experiment.
Discussion – mechanisms to relax local stress concentration
During compressive tests on an isotropic material, the maximum shear stress
occurs at 45∘ E from the compression direction (Tresca criterion).
For material with plastic anisotropy such as ice, a redistribution of stress
is expected to occur which depends on the orientation relationship between grains.
Such a redistribution has been simulated by full-field crystal plasticity
approaches by and for instance.
Although the stress field is not experimentally accessible so far, these modeling
results were validated by a comparison between predicted and measured strain
field magnitudes and heterogeneities .
At the onset of
tertiary creep in laboratory deformed ice, strain rate increases thanks to
accommodating processes. As summarized by , depending on
the deformation conditions (temperature, imposed stress or imposed
strain rate), accommodation can take place through dynamic recrystallization
or micro-cracking. To our knowledge, no direct observations exist of
the effect of micro-cracking on the redistribution of strain and therefore on
local stress relaxation. The results presented here fill this gap by
exploring the ductile-to-brittle transition where micro-cracking and
plasticity can coexist. Common features with previous observations made by
and are the strong strain
heterogeneities, with local strains more than 10 to 20 times as great as the
macroscopic strain. Although influenced by the boundary conditions, grain
interactions tend to deviate the strain concentration from the main
45∘ E directions. While the work of remained in the
primary creep regime, and mostly concentrated on sample-scale field
characterizations, went a step further and found that DRX
mechanisms explained the interplay between local changes in microstructure
and strain-field evolution. In particular, strain was shown to re-localize
close to the newly formed grain boundaries and sub-grain boundaries. This has
also been observed in the present study.
Compared with previous works, conditions imposed during the experiment
presented here induced local cracking at the onset of tertiary creep (which
occurs before 1 % of macro-strain for the sample studied very likely
because of the influence of a non-isotropic texture and of a columnar
microstructure). Most of the local cracks observed were intra-granular. Cracks
appeared in areas near strain localization bands, but not within these
bands, as evidenced by Fig. and by
comparing Figs. and a (cracks 1
and 2). These observations highlight the fact that local stresses can be
concentrated at the side of high strained region. This can result from strain
incompatibilities between regions of different orientations, with regions
with locally low Schmid factors (relative to the local stress tensor)
behaving as solid inclusions in composite materials. The likely impact of low
local Schmid factors might be strengthened by the strong viscoplastic
anisotropy of ice that renders some orientations strongly unfavorable for
basal dislocation slip.
Crack formation relaxes these high local
stresses, and meanwhile, stress concentration is translated at the crack
tips. Previous studies on columnar ice performed at higher strain rate
(ε˙=4×10-3 s-1) but similar temperature
(T=-10 ∘C; ) evidenced the typical
mechanism of wing-crack formation at the crack tips. Wing cracks appear as the
result of tensile stress concentration at the crack tips and can lead to the
overall failure of the sample by propagating through it, or by connecting to
other cracks. Recently, a similar mechanism of wing cracks propagation has
been characterized by DIC in a soft rock by , and they were
able to quantify the different fracture modes (opening, closing and shearing)
thanks to local strain measurements.
As the experiment presented here is performed in conditions equivalent to a lower strain rate (although through
imposed load conditions) compared to , the stress
concentration at the crack tips is not relaxed by the formation of wing
cracks but by plasticity mechanisms in the creep zone at the tip.
Dislocations are therefore expected to nucleate and propagate at the crack tips
as shown by . Recently, showed that both
nucleation of dislocations at the crack tip, and the mobility of the nucleated
dislocations come into play to induce the stress relaxation responsible for a
crack arrest. Considering the high-temperature conditions of our experiments,
the dislocation multiplication leads to dynamic recrystallization mechanisms
to occur in the creep zone near crack tips. Indeed, nucleation of new
grains is observed very close to the crack tips of cracks 2, 3 and 4
(Fig. ) and dislocation substructures as
sub-grains are formed, for instance around crack tips of cracks 1 and
2 (Fig. ). These observations reveal that
plasticity-driven recrystallization mechanisms are efficient to relax the
local tensile stresses initiated at the crack tips.
Local stresses associated
with grain interactions during deformation of ice was indeed shown to be
strongly heterogeneous, and to be responsible for the initiation of sub-grain
boundaries at the end of primary creep . Observation of
crack initiation near grain boundaries and within grain interior is another
evidence of such local stress concentration.
By following the strain field
evolution all along the tests, we observe the closure of some parts of the
cracks, in areas where nucleation and sub-grain boundary formation were the
most active. Crack closure is evidenced by the representation of principal
strains which directions evolve from a tension component to a compressive
component that ensures the recovering of continuity (Fig. d). In order to obtain a local closure of cracks, the
stress field components should be drastically modified, and possibly turn to
a compressive component. The new microstructure formed by recrystallization
mechanisms must therefore drive a redistribution of the local stress field to
enable such a modification, still compatible with the macroscopic stress
conditions.
Ductile fracture occurring at elevated temperature in metals can
be related to void propagation, growth and coalescence. Recently,
showed that DRX mechanisms induced a softening that
reduces the local stress concentration, which serves as the driving force for
this void-induced ductile fracture. Similar observations of a ductile-to-brittle transition in Olivine driven by plasticity mechanisms was thoroughly
studied by . In samples deformed at 20,
300 and 600 ∘C they observed micro-cracking at grain
boundaries and in the grain interiors, but also arrays of dislocations
related to crystal plasticity. Similarly to our observations, at the highest
temperature, plasticity took place in the form of strongly misoriented
undulatory extinctions (associated with various types of dislocations),
deformation lamellae and 3-D dislocation cells inducing strong modifications
of the microstructure. Our results therefore present some interest beyond the
ice community. Similar procedures could very interestingly be applied to a
wide range of materials in order to estimate the role of the level of plastic
anisotropy on strain localization and on the efficiency of plasticity-driven
recrystallization mechanisms to relax the local stress field at the crack tips.
On top of the mechanical meaning of these observations, we highlight the fact
that, since we were able to follow local crack closure during the test, care
must be taken when performing experimental tests in conditions close to the
ductile-to-brittle transition (typically at strain rates above 10-6 s-1, or compressive stress above 0.9 MPa), and at high temperature.
Micro-cracking and DRX mechanisms can influence the local stress relaxation,
and therefore the mechanical response, without leaving any track in the final
microstructure.
Concluding remarks
The present work reveals, for the first time
in ice, the evolution of the heterogeneous strain field during the onset of
tertiary creep, in conditions where local cracking occurs to relax the local
stress field. This observation was made possible by taking advantage of
samples with 2-D–1/2 microstructures from which surface observations reflect
bulk behavior.
While strain field localizes into bands with a length larger than the grain
dimensions, cracks appear to relax stress concentration at the side of the
strain localization bands, where deformation by dislocation glide must have
been impeded by low local Schmid factor conditions.
Relaxation of the local
stress field by crack opening results in a local redistribution of the strain
field, as evidenced by the abrupt weakening of some deformation bands after
cracking. At the crack tips, where stress concentrates, plasticity-driven
dynamic recrystallization mechanisms are observed as new small grains and
high-angle sub-grain boundaries in the final microstructure. The new formed
boundaries also appear visible on strain field patterns during the test, as
new strain concentration areas. While induced by local stress concentration
at the crack tip, recrystallization mechanisms in turn generate a stress field
redistribution as a result of microstructure modifications. This
redistribution is indirectly evidenced by the modification of the measured
strain field in the area, but also by the original observation of local crack
closure, likely associated with a measured local compressive stress in place of the
initial tensile stress responsible for the observed mode I crack opening. To
conclude, the main results show that micro-cracking and dynamic
recrystallization mechanisms both resulting from a strongly heterogeneous
stress field can coexist locally and that these mechanisms are efficient to
relax local stresses at the ductile-to-brittle transition. Hence one should be
careful when working at the frontiers of this transition since
recrystallization can hide local cracking in the final microstructures.
Data are accessible by a simple request to the corresponding author.
TC, DG and CL performed the laboratory experiments. DG and
TC
provided the data treatment. MM and TC analyzed the data and wrote the paper. PV provided some support
for the DIC analyses and interpretation.
The authors declare that they have no conflict of interest.
This article is part of the special issue “Analysis of deformation microstructures and mechanisms on all scales”.
It is a result of the EGU General Assembly 2016, Vienna, Austria, 17–22 April 2016.
Acknowledgements
Financial support by the French “Agence Nationale de la Recherche” is acknowledged (project DREAM, ANR-13-BS09-0001-01).
This work benefited from support from the INSIS and INSU institutes of CNRS. It was supported by a grant from Labex OSUG@2020
(ANR10 LABEX56) and from INP-Grenoble and UJF within the “Grenoble Innovation Recherche AGIR” proposal.
Support from the imagery center IRIS of Grenoble-INP is acknowledged. Maurine Montagnat benefited from a visitor research fellowship from WSL
(Switzerland) in 2016–2017.
Edited by: Ilka Weikusat
Reviewed by: two anonymous referees
ReferencesAntolovich, S. D. and Armstrong, R. W.: Plastic strain localization in metals:
origins and consequences, Prog. Mater. Sci, 59, 1–160,
10.1016/j.pmatsci.2013.06.001,
2014.
Argon, A.: Mechanics and physics of brittle to ductile transitions in fracture,
J. Eng. Mater.-T. ASME, 123, 1–11, 2001.Batto, R. A. and Schulson, E. M.: On the ductile-to-brittle transition in ice
under compression, Acta Metall. Mater., 41, 2219–2225,
10.1016/0956-7151(93)90391-5,
1993.Bons, P. D., Jansen, D., Mundel, F., Bauer, C. C., Binder, T., Eisen, O.,
Jessell, M. W., Llorens, M.-G., Steinbach, F., Steinhage, D., and Weikusat,
I.: Converging flow and anisotropy cause large-scale folding in Greenland's
ice sheet, Nat. Commun., 7, 1–6,
10.1038/ncomms11427, 2016.Chauve, T., Montagnat, M., and Vacher, P.: Strain field evolution during
dynamic recrystallization nucleation; A case study on ice, Acta Mater.,
101, 116–124, 10.1016/j.actamat.2015.08.033,
2015.Chauve, T., Montagnat, M., Barou, F., Hidas, K., Tommasi, A., and Mainprice,
D.: Investigation of nucleation processes during dynamic recrystallization of
ice using cryo-EBSD, Philos. T. R. Soc. A, 375, 1–20, 10.1098/rsta.2015.0345, 2017.
Dahl-Jensen, D., Albert, M. R., Aldahan, A., et al.: Eemian interglacial reconstructed from a Greenland
folded ice core,
Nature, 493, 489–494, 2013.
Druiventak, A., Trepmann, C. A., Renner, J., and Hanke, K.: Low-temperature
plasticity of olivine during high stress deformation of peridotite at
lithospheric conditions – An experimental study, Earth Planet. Sc.
Lett., 311, 199–211, 2011.Durand, G., Graner, F., and Weiss, J.: Deformation of grain boundaries in polar
ice, Europhys. Lett., 67, 1038, 10.1209/epl/i2004-10139-0,
2004.Durand, G., Gillet-Chaulet, F., Svensson, A., Gagliardini, O., Kipfstuhl, S., Meyssonnier, J., Parrenin, F.,
Duval, P., and Dahl-Jensen, D.: Change in ice rheology during climate variations – implications for ice flow modelling and dating of the
EPICA Dome C core, Clim. Past, 3, 155–167, 10.5194/cp-3-155-2007, 2007.
Duval, P.: Creep and recrystallization of polycrystalline ice, Bull. Mineral,
102, 80–85, 1979.
Duval, P., Ashby, M., and Anderman, I.: Rate controlling processes in the creep
of polycrystalline ice, J. Phys. Chem., 87, 4066–4074, 1983.Fischer, H., Severinghaus, J., Brook, E., Wolff, E., Albert, M., Alemany, O., Arthern, R., Bentley, C., Blankenship, D.,
Chappellaz, J., Creyts, T., Dahl-Jensen, D., Dinn, M., Frezzotti, M., Fujita, S., Gallee, H., Hindmarsh, R., Hudspeth, D.,
Jugie, G., Kawamura, K., Lipenkov, V., Miller, H., Mulvaney, R., Parrenin, F., Pattyn, F., Ritz, C., Schwander, J.,
Steinhage, D., van Ommen, T., and Wilhelms, F.: Where to find 1.5 million yr old ice for the IPICS “Oldest-Ice” ice core,
Clim. Past, 9, 2489–2505, 10.5194/cp-9-2489-2013, 2013.
Grennerat, F., Montagnat, M., Castelnau, O., Vacher, P., Moulinec, H., Suquet,
P., and Duval, P.: Experimental characterization of the intragranular strain
field in columnar ice during transient creep, Acta Mater., 60,
3655–3666,
2012.Iliescu, D. and Schulson, E. M.: The brittle compressive failure of fresh-water
columnar ice loaded biaxially, Acta Mater., 52, 5723–5735,
10.1016/j.actamat.2004.07.027,
2004.
Jacka, T. H. and Maccagnan, M.: Ice crystallographic and strain rate changes
with strain in compression and extension, Cold Reg. Sci. Technol., 8,
269–286, 1984.Jansen, D., Llorens, M.-G., Westhoff, J., Steinbach, F., Kipfstuhl, S., Bons,
P. D., Griera, A., and Weikusat, I.: Small-scale disturbances in the
stratigraphy of the NEEM ice core: observations and numerical model
simulations, The Cryosphere, 10, 359–370, 10.5194/tc-10-359-2016,
2016.
Lebensohn, R. A., Liu, Y., and Ponte-Castañeda, P.: On the accuracy of the
self-consistent approximation for polycrystals: comparison with full-field
numerical simulations, Acta Mater., 52, 5347–5361, 2004.
MacGregor, J. A., Fahnestock, M. A., Catania, G. A., Paden, J. D.,
Prasad Gogineni, S., Young, S. K., Rybarski, S. C., Mabrey, A. N., Wagman,
B. M., and Morlighem, M.: Radiostratigraphy and age structure of the
Greenland Ice Sheet, J. Geophys. Res.-Earth, 120,
212–241, 2015.Martínez-Pañeda, E. and Niordson, C. F.: On fracture in finite strain
gradient plasticity, Int. J. Plasticity, 80, 154–167,
10.1016/j.ijplas.2015.09.009,
2016.Montagnat, M., Chauve, T., Barou, F., Tommasi, A., Beausir, B., and
Fressengeas, C.: Analysis of dynamic recrystallization of ice from EBSD
orientation mapping, Front. Earth Sci., 3, 1–13,
10.3389/feart.2015.00081,
2015.Nguyen, T. L., Hall, S. A., Vacher, P., and Viggiani, G.: Fracture mechanisms
in soft rock: Identification and quantification of evolving displacement
discontinuities by extended digital image correlation, Tectonophysics, 503,
117–128, 10.1016/j.tecto.2010.09.024,
2011.
Panton, C. and Karlsson, N. B.: Automated mapping of near bed radio-echo layer
disruptions in the Greenland Ice Sheet, Earth Planet. Sc. Lett.,
432, 323–331, 2015.
Paterson, W. S. B.: The physics of glaciers, Pergamon, Oxford, 1994.
Peternell, M., Russell-Head, D., and Wilson, C.: A technique for recording
polycrystalline structure and orientation during in situ deformation cycles
of rock analogues using an automated fabric analyser, J. Microsc.,
242, 181–188, 2011.Piazolo, S., Montagnat, M., Grennerat, F., Moulinec, H., and Wheeler, J.:
Effect of local stress heterogeneities on dislocation fields: Examples from
transient creep in polycrystalline ice, Acta Mater., 90, 303–309,
10.1016/j.actamat.2015.02.046,
2015.Ple, O. and Meyssonnier, J.: Preparation and Preliminary Study of
Structure-Controlled S2 Columnar Ice, J. Phys. Chem. B,
101, 6118–6122, 10.1021/jp963256t, 1997.Renshaw, C. E. and Schulson, E. M.: Universal behaviour in compressive failure
of brittle materials, Nature, 412, 897–900,
10.1038/35091045, 2001.
Rice, J. R. and Thomson, R.: Ductile versus brittle behaviour of crystals,
Philos. Mag., 29, 73–97, 1974.
Schulson, E. and Buck, S.: The ductile-to-brittle transition and ductile
failure envelopes of orthotropic ice under biaxial compression, Acta Metall. Mater., 43, 3661–3668, 1995.Schulson, E. M. and Duval, P.: Creep and Fracture of Ice, Cambridge
University Press, 10.1017/CBO9780511581397,
2009.Schulson, E. M., Lim, P. N., and Lee, R. W.: A brittle to ductile transition in
ice under tension, Philos. Mag. A, 49, 353–363,
10.1080/01418618408233279,
1984.Shang, X., Cui, Z., and Fu, M. W.: Dynamic recrystallization based ductile
fracture modeling in hot working of metallic materials, Int. J.
Plasticity, 95, 105–122,
10.1016/j.ijplas.2017.04.002,
2017.Snyder, S. A., Schulson, E. M., and Renshaw, C. E.: Effects of prestrain on the
ductile-to-brittle transition of ice, Acta Mater,, 108, 110–127,
10.1016/j.actamat.2016.01.062,
2016.Tommasi, A., Knoll, M., Vauchez, A., Signorelli, J., Thoraval, C., and
Logé, R.: Structural reactivation in plate tectonics controlled by
olivine crystal anisotropy, Nat. Geosci., 2, 423–427,
10.1038/ngeo528,
2009.
Vacher, P., Dumoulin, S., Morestin, F., and Mguil-Touchal, S.: Bidimensional
strain measurement using digital images, P. I.
Mech. Eng. C-J. Mec., 213,
811–817, 1999.
Vauchez, A., Tommasi, A., and Mainprice, D.: Faults (shear zones) in the
Earth's mantle, Tectonophysics, 558, 1–27, 2012.Weiss, J. and Schulson, E. M.: Grain-boundary sliding and crack nucleation in
ice, Philos. Mag. A, 80, 279–300, 10.1080/01418610008212053,
2000.
Wilson, C., Russell-Head, D., and Sim, H.: The application of an automated
fabric analyzer system to the textural evolution of folded ice layers in
shear zones, Ann. Glaciol., 37, 7–17, 2003.