Heterogeneity of inelastic strain during creep of Carrara marble: Microscale strain measurement technique

Abstract

We combined the split cylinder technique with microfabrication technology to observe strain heterogeneities that were produced during high‐pressure transient creep of Carrara marble. Samples were patterned with a custom‐designed grid of markers spaced 10 µm apart and containing an embedded coordinate system. The microscale strain measurement (MSSM) technique described here allowed us to analyze the local strain distribution with unprecedented detail over large regions. The description of the strain field is a function of the area over which strain is being computed. The scale at which the strain field can be considered homogeneous can provide insight into the deformation processes taking place. At 400–500°C, when twinning production is prolific, we observe highly strained bands that span several grains. One possible cause for the multigrain bands is the need to relieve strain incompatibilities that result when twins impinge on neighboring grains. At 600–700°C, the strain fields are still quite heterogeneous, and local strain varies substantially within grains and near grain boundaries, but the multigrain slip bands are not present. Deformation is concentrated in much smaller areas within grains and along some grain boundaries. The disappearance of the multigrain slip bands occurs when the deformation conditions allow additional slip systems to be activated. At 600°C, when the total strain is varied from 0.11 to 0.36, the spatial scale of the heterogeneity does not vary, but there are increases in the standard deviation of the distribution of local strains normalized by the total strain; thus, we conclude that the microstructure does not achieve a steady state in this strain interval.

Grain‐ to multiple‐grain‐scale deformation processes during diffusion creep of forsterite + diopside aggregate: 1. Direct observations

“…[] are difficult to interpret with simplistic classical models, requiring us to explore new methods, particularly those allowing us to detect a single‐grain to multiple‐grain‐scale deformation directly. In this study, we will show that observations of sample surfaces with etched fine‐scale markers are a powerful tool allowing us to detect microdeformation processes [ Quintanilla‐Terminel and Evans , ], especially GBS and grain rotation, which we consider key processes for CPO development during diffusion creep [ Miyazaki et al ., ]. Together with the mechanical data, we are able to interpret the mechanisms involved, which is essentially impossible using conventional experimental techniques.…”

Microscale and nanoscale strain mapping techniques applied to creep of rocks

“…Different image processing techniques can be used for locating the markers before and after deformation, such as a convolution (Biery et al, 2003) or a Hough transform algorithm (Quintanilla-Terminel and Evans, 2016). Depending on the application, the user could rely on the regularity of the grid and not identify the markers before deformation.…”

“…(a) The n-point configurations for n = 3, 5, 9, and 25. (b) Corresponding strain maps and strain distributions for strain along axis 1 in the sample reference (see insert for reference frame) for a Carrara marble cylinder isostatically annealed at T = 700 • C and P c = 300 MPa for 3 h. (c) Corresponding strain distribution for each strain map; it can be observed that the mean is always 0 but the spread of the distribution becomes smaller with increasing n. Modified after Quintanilla-Terminel and Evans (2016). ence between the modeled and the measured material lines, dx * i = F • dX and dx i , respectively.…”

“…However, when n is larger, the characteristic length scale of the strain heterogeneity is also larger. Thus, a compromise exists between the resolution of spatial variations in local strain and the errors involved in its calculation (Quintanilla-Terminel and Evans, 2016;Xu and Evans, 2010;Bourcier et al, 2013). Figure 6 illustrates the different n configurations and their corresponding strain map and strain distribution along the 1 axis (in the sample reference) for a "zero strain" experiment.…”

“…Figure 6 illustrates the different n configurations and their corresponding strain map and strain distribution along the 1 axis (in the sample reference) for a "zero strain" experiment. This experiment was performed on a half cylinder of Carrara marble at T = 700 • C and P c = 300 MPa in order to evaluate the resolution of the experimental series in Quintanilla-Terminel and Evans (2016). The mean strain is zero for all n point configurations, but the standard deviation is larger for smaller n. Both the "real" strain coming from experimental artifacts and the computational error coming from the marker locations are evaluated.…”