General shear experiments on Black Hills Quartzite (BHQ) deformed in
the dislocation creep regimes 1 to 3 have been previously analyzed
using the CIP method
This contribution is dedicated to Jan Tullis, whose superb work on experimental rock deformation and microstructure analysis continues to be an inspiration to us all.
Mechanical data for general shear experiments of Black Hills Quartzite.
(1) Dislocation creep regimes: 1, 2, 3; a, b,
c
Black Hills Quartzite (BHQ) has been used extensively in experimental
rock deformation. Coaxial and general shear experiments have been
carried out, for example, to define the dislocation creep regimes of
quartz
General shear experiments on Black Hills Quartzite. Shear
stress (
The rock deformation experiments that produced the samples analyzed in this
study are described in
Orientation images. Details of four orientation images are
shown with pole figures calculated from total maps. Top row:
EBSD maps obtained from SEM using IPFZ (inverse pole figure
coloring) for the
Of each of the deformed samples, a polished thin section of approximately
20
Grain size measurements.
(1) Processed maps: prefixes 1, 2, 3 indicate regimes 1, 2, 3; a,
b, c
Azimuth and inclination images for the
To decide on the technique for segmentation, automatic and supervised
segmentations are performed on three EBSD maps using the method implemented
in the MTEX Toolbox
From segmented orientation images, grain size maps are derived
The 2-D diameter of each segment is calculated from the cross-sectional
area. The number-weighted distribution
Grain size maps. Color-coded grain size maps visualizing the
diameter of area equivalent circles. From left to right: for
undeformed Black Hills Quartzite and samples deformed in regimes 1, 2,
and 3. Scale, shear sense, and look-up table for grain size apply to
all. Red indicates the diameter of an area equivalent circle
To obtain a possible parent distribution of 3-D grains, the program
StripStar (Fortran source stripstarD.f and Matlab script stripstar.m; see
the
Supplement) is used
Here, the concept of a “texture component” is not based on the full
crystallographic information, i.e., not defined by all three Euler angles;
instead it refers to aspects of
To investigate the conspicuous grain size gradient of the regime 1, 2,
and 3 samples shown in Fig.
Recrystallized grain size for dislocation creep regimes 1, 2,
and 3. Volume-weighted histograms
To analyze the shape and size of the texture domains and subdomains,
the autocorrelation function (ACF) is used. To determine spatial
clustering, the internal grain boundaries and the subdomain boundaries
are subjected to a contact area analysis (Lazy Contacts macro). Both
of these methods are described in
For the three high-strain samples of regimes 1, 2, and 3 (w1092, w946, w935),
segmentations with increasing misorientation angles up to 15
Details of
The 2-D grain size distribution is visualized using grain size maps
(Fig.
Recrystallized grain size as a function of misorientation density.
Maps of grain kernel average misorientation (gKAM) are shown for
three dislocation creep regimes. Maps cover nearly the full width of the
shear zone. Gradients of gKAM are clearly visible. Modes of
Upon closer inspection, the pole figures reveal that the maxima of the
Y- and B-texture components are usually composed of two distinct
submaxima. Selecting these (“upper” and “lower”) submaxima in
a pole figure, two separate orientation images for the corresponding
texture component, i.e., two subdomains, can be created
(Fig.
Grain size as a function of segmentation angle. Mean grain
sizes calculated without grain completion from full texture data
(EBSD maps) using full misorientations (solid lines, bottom
To explore the relation between grain size and the state of
deformation (as indicated by misorientation density), the grain maps
are evaluated separately for high- and low-gKAM regions
(Fig.
The grain size analysis for the Y domain of sample w935 (regime 3) and
its subdomains is visualized in Fig.
Grain size in texture domain. Grain size maps of sample w935
(regime 3) are shown. From left to right: all grains, grains
in the upper and lower Y subdomains (as indicated by the inset pole
figures), in the whole Y domain, and for
The grain sizes of the (combined) B and Y domains have been
calculated for the high-strain samples in regimes 1, 2, and 3
(Fig.
The grain size data are plotted on the piezometer of
Processing and representing the EBSD mapping as
The
Recrystallized grain size as a function of texture. Grain size
distributions of recrystallized grains for four samples of regimes 1,
2, and 3 of dislocation creep, arranged in four rows with
For the LGB segmentation, eight misorientation images (MOIs) were used (see
Appendix A). On account of the histogram equalization carried out to enhance
the contrast in the MOIs, the effective
Recrystallized grain size as a function of flow stress. Two
measures of average grain size are plotted against differential
stress,
LGB and EBSD segmentations were tested on a number of samples. The
result was always the same regardless of the level of indexing: the
resulting grain size of the LGB method was smallest followed by the
EBSDnc, and the largest grain size was returned by the EBSDc. Comparative
histograms of 2-D diameters of LGB vs. EBSDc and EBSDnc and values
for the 2-D RMS and 3-D mode values are shown in Appendix
Fig.
In EBSD segmentation, a misorientation angle of 10
Recrystallized grain size piezometer relations are written as
To assess grain growth during annealing,
When
Where does this discrepancy come from? A number of explanations are
possible.
Comparing general shear experiments to axial shortening ones requires
a conversion of shear stress to differential stress. Lower
differential stresses could result if, instead of the Mohr circle
construction,
The piezometer experiments of
In their study on texture evolution in regime 3 dislocation creep,
In this study another interesting point emerges: the ratio between the
recrystallized grain sizes in the different domains depends on the
regime and may change depending on the stress level. For regimes 1 and
2, the size ratios of the recrystallized grains in the Y and B
domains with respect to the average can also be extracted from
Fig.
The misorientation density as measured by the gKAM can be interpreted
as an indicator of deformation intensity; in the case of continuous
subgrain rotation recrystallization, more highly deformed,
recrystallized grains have a higher density of low-angle boundaries
and/or low-angle boundaries with higher misorientation angles. Thus,
highly deformed grains have high gKAM values. Comparison of the grain
size maps (Fig.
Spatial distribution and cluster size of Y subdomains.
Results are shown for sample w935 of regime 3.
Regardless of the absolute stress levels of the experiments
discussed here, a relation of misorientation density and
recrystallized grain size can be documented. The stress–grain size
relation (Fig.
It is interesting to note that the Y domain and the B domain are
arranged as layers with clusters of grains belonging to one or the
other submaximum in the pole figure (see
Fig.
Relation of quartz domains and bulk sample strain.
In this contribution, however, we prefer not to pursue the approach by
Another interesting point to note is the ratio of the apparent shear
strain, usually reported as
To assess the size of the subdomains, we consider the ACF again. The long
diameters of the 30 % contours
A microstructure and texture analysis of seven samples of Black Hills Quartzite, deformed experimentally in the dislocation creep regimes 1, 2, and 3, was carried out with the aim of comparing previously published data obtained by the CIP method to a renewed analysis making use of the higher resolution (both spatially and in terms of crystallographic orientation) of EBSD.
In order to best reproduce the visual identification of grains,
segmentations have to be performed using a Comparison of CIP and EBSD method: For grain sizes The recrystallized grain size depends
on the level of the shear stress supported by the sample
during the experiment; locally, on the CPO of a given texture domain; and locally, on the deformation intensity as measured by the
misorientation density (gKAM). The Y domain (identified previously as the prism domain)
is composed of two subdomains, and the same is true of the
B domain (basal domain). The size of the Y subdomains corresponds to the original
grain size of BHQ. The shape and long axis trend suggest
that they deform equi-viscous to the bulk experiment but
potentially to a lower shear strain than the bulk experiment,
calling for an additional deformation mechanism other than
dislocation creep. The recrystallized grain sizes of the Y and B domains
appear to have different stress dependences; i.e., under the
assumption of iso-stress conditions, the grain size of Y and
B domains defines different piezometric relationships. The stress dependence of the recrystallized grain size of
the shear experiments analyzed here predicts higher stress for
a given grain size or larger grain size for a given flow
stress than the piezometer of
Thus, the averaged recrystallized grain size does not depend
on the total strain achieved by the sample or the volume
fraction of recrystallization, but in detail on the local
strain in the sample.
Future work is suggested to examine whether the discrepancy between the grain sizes obtained here and the published piezometer are only due to discrepancies between the stress calculations for solid-medium confining pressure as opposed to the molten salt assembly, as was used for the piezometer experiments. If so, this would suggest that the stresses reported in the literature for experiments carried out with solid-medium confining pressures are too high by a factor of 2 or more (a rather alarming situation). Discrepancies could also arise from the state of stress experienced by the recrystallized grains, which may deviate considerably from the stress supported by the bulk sample. Alternatively, it may indeed show that coaxial and non-coaxial progressive deformation produce different recrystallized grain sizes.
The data sets used in this paper are not yet publicly available. Please contact the lead author for access.
Segmentation is carried out using Image SXM and the Lazy Grain
Boundaries (LGB) macro
Segmentation of grains from EBSD data can be
accomplished based on a misorientation angle threshold assuming that grains
are objects enclosed by boundaries that fulfill the segmentation criterion
at every point along the boundary. Here, a minimum angle of misorientation of
10
EBSD data acquisition.
(1) Sample name, (2) acceleration voltage, (3) probe current, (4) chamber
pressure (variable pressure setting), (5) aperture of beam, (6) working
distance, (7) magnification, (8) speed of acquisition, (9) total recording
time, (10) number of reflectors and number of bands detected, (11) mean value
of MAD (mean angular deviation), (12) Hough resolution, (13) binning,
(14) step size, (15) map size; NA indicates that data are not available. Recording dates and
software:
Image processing and segmentation.
(1) Dislocation creep regimes: 1, 2, 3; a, b, c
Distribution fitting.
(1) Processed maps: prefixes 1, 2, 3 indicate regimes 1, 2, 3; a, b,
c
Segmentation based on texture. Comparison of segmentations
based on
Deriving modal grain size. Volume-weighted histograms
Renée Heilbronner is a member of the editorial board of the journal.
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.
We are indebted to Jan Tullis who not only provided the samples of this study but who continues to contribute, in the generous fashion typical for her, to the advancement of microstructure and rock deformation studies. We wish to thank Willy Tschudin of Basel University for the preparation of excellent thin sections and Tom Eilertsen and Kai Neufeld of the Arctic University of Tromsø for their dedicated technical support and the time and effort spent during the acquisition of the EBSD maps. Michael Bestmann is thanked for always sharing his immense experience. The paper has further profited from discussions with Michael Stipp, Greg Hirth, and Andreas Kronenberg. Support by the National Science Foundation of Switzerland (grant no. NF 200021-138216; Deformation mechanisms in naturally and experimentally deformed minerals and rocks) is gratefully acknowledged. Edited by: Bernhard Grasemann Reviewed by: two anonymous referees