Forty, 10 inch long by 1 1/2 inch wide by 1/4 inch thick specimens were placed individually in an Instron Universal testing machine. Five specimens each identi fied .as "6", "8", and "cracked and unrepaired", were tested with the crack in tension (face-down) and five specimens of each sample were tested with the crack in compression (face-up).
Failures occurred as a result of one or both layers of glass fracturing. All failures occurred at or between the loading points, and ran across the width of the specimens. Any failures which occurred at the repaired crack occurred after the maximum load of the specimen was reached. In no case did the failure at
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This difference is of prime importance when studying brittle materials, where the number and severity of flaws exposed to the maximum stress is directly related to the flexural strength and crack initiation. Compared to the three-point bending flexural test, there are no shear forces in the four-point bending flexural test in the area between the two loading pins.[1] The four-point bending test is therefore particularly suitable for brittle materials that cannot withstand shear stresses very well.
Ceramics are usually very brittle, and their flexural strength depends on both their inherent toughness and the size and severity of flaws. Exposing a large volume of material to the maximum stress will reduce the measured flexural strength because it increases the likelihood of having cracks reaching critical length at a given applied load. Values for the flexural strength measured with four-point bending will be significantly lower than with three-point bending.,[7] Compared with three-point bending test, this method is more suitable for strength evaluation of butt joint specimens. The advantage of four-point bending test is that a larger portion of the specimen between two inner loading pins is subjected to a constant bending moment, and therefore, positioning the joint region is more repeatable.[8]
Rock, concrete, and other engineered materials are often composed of several minerals that change volumetrically in response to variations in the moisture content of the local environment. Such differential shrinkage is caused by varying shrinkage rates between mineral compositions during dehydration. Using both 3D X-ray imaging of geo-architected samples and peridynamic (PD) numerical simulations, we show that the spatial distribution of the clay affects the crack network geometry with distributed clay particles yielding the most complex crack networks and percent damage (99.56%), along with a 60% reduction in material strength. We also demonstrate that crack formation, growth, coalescence, and distribution during dehydration, are controlled by the differential shrinkage rates between a highly shrinkable clay and a homogeneous mortar matrix. Sensitivity tests performed with the PD models show a clay shrinkage parameter of 0.4 yields considerable damage, and reductions in the parameter can result in a significant reduction in fracturing and an increase in material strength. Additionally, isolated clay inclusions induced localized fracturing predominantly due to debonding between the clay and matrix. These insights indicate differential shrinkage is a source of potential failure in natural and engineered barriers used to sequester anthropogenic waste.
A challenge in using natural and engineered materials as barriers for subsurface sequestration of anthropogenic waste (e.g., nuclear waste) is that these materials evolve over time in response to physical and chemical processes. A critical component of this evolution is the initiation, propagation, and coalescence of cracks that causes mechanical instabilities and potentially introduces highly conductive flow paths. While methods exist to predict the formation and propagation of cracks in brittle materials1,2,3, models are needed that account for heterogeneous materials composed of minerals with varying strengths, interfacial bonding conditions, and responses to chemical stimuli. Differential shrinkage is of particular concern in polymineralic materials used as barriers. Volumetric mineral shrinkage can arise from changes in humidity when fluids are injected or withdrawn from a subsurface site, or from changes in temperature that occur during nuclear waste disposal. A drying front induced by changing conditions can cause localized differential shrinkage that results in induced deformation gradients and non-uniform stress fields. Failure of a polymineralic material from dehydration can occur if the induced tensile stresses are greater than the mineral strength, which causes the mineral to crack, or if a mineral shrinks at a rate faster than other components, which causes debonding at the interface between constituent materials. Cracking of a polymineralic material during dehydration will vary with the relative strengths of the interfaces and the constituent material. A key question is whether the induced cracks will exist in isolation or propagate and coalesce into a network that diminishes the hydraulic integrity of the material by forming connected flow paths.
The CB synthetic rocks are characterized by a mixture that is rich in CaCo3, SiO2, and clay, a composition that is analogous to that of argillaceous rocks such as marls that are also clay-bearing carbonate rich porous media. The CB rock samples are also comparable to cement stabilized Marl, clayey soils, or clays which are used in several applications (e.g., embankments, tunnels, mining, engineered barriers, etc.). Marls are rocks that are comprised of 35% to 65% carbonate with the remaining percentage consisting of various quantities of clay and silt-sized particles11. The strength of clay-bearing rocks like marl vary with moisture content and mineral composition12 including the type of clay that is contained within the microstructure. Samples were also fabricated with different clay types to investigate the relation between chemical composition and moisture loss and the effect on induced crack formation for materials with different shrinkage rates. The CB sample group also includes samples with (i) different Montmorillonite compositions CB-SWY (Fig. S7d) and CB-STX (Fig. S7c) , (ii) a lower percentage of Montmorillonite CB-SK10-5 (Fig. S7e) , and (iii) a non-swelling clay CB-SKAO (Fig. S4) for which no shrinkage was expected. The LICI, MSCS, and CB-SK10 samples were cured for 7 days via submerged curing, while the CB-SWY, CB-STX, CB-SKAO, and CB-SK10-5 samples were cured for 14 days to improve material strength. Additional details regarding sample fabrication can be found in Supplementary Note 1 and Supplementary Note 2.
Material property testing of the geo-architected samples determined that the amount, location, and type of clay affected both the unconfined compressive strength (UCS) and the rate of moisture loss from the sample. Embedding swelling clay into the cement matrix tended to reduce the strength of a sample. During desiccation the swelling clay will tend to shrink so that it no longer provides load-bearing capacity to the pore spaces of the matrix. The CB samples, CB-SWY (1.15 MPa) and CB-SK10 (4.6 MPa), exhibited the lowest average UCS values, while the UCS for CB-STX (6.36 MPa) and CB-SK10-5 (8.05 MPa) were lower than the mortar reference sample (11.4 MPa) and the MSCS samples (11.05 MPa). The LICI sample had an intermediate average UCS value of 6.1 MPa, and the average UCS for the sample fabricated with non-swelling clay (CB-SKAO) was 7.7 MPa. Though the unconnected porosity of the samples were similar, the moisture loss in the distributed CB-SWY (38%) and CB-SK10 sample (21%) was 2.92 and 1.6 times higher than the observed moisture loss for the reference mortar sample (13%). In the initial sample group (reference versus LICI, MSCS, and CB-SK10) the greatest moisture loss occurred in the sample CB-SK10 which was observed, experimentally, to contained the most complex crack network after drying (Fig. 1d). A representative CB-SWY sample experienced the most moisture loss (1.8 times higher than CB-SK10), and the crack network that developed was dissimilar to that of CB-SK10 sample (Fig. 9d). Additional details on material properties can be found in Supplementary Note 4.
2D images from the center of the sample along the vertical axis, and 3D visualizations of the interior for the geo-architected samples after 6 full days of dehydration. The pixel edge length resolution is \(\sim 40\; \upmu \textm\) and the average radius is 19.05 mm. All samples contain non-connected pores (displayed in blue) which are shown only for the reference sample (a) and the LICI sample (b). Clay inclusions are displayed in brown. All cracks are displayed in red, as shown for the MSCS sample (c) and the CB-SK10 sample (d). Cracks are only observed in samples containing localized or distributed clay which can result in a 40% reduction in material strength (a comparison between the reference and the CB-SK10 sample). Data are visualized with Dragonfly Pro software, Version 2020.2 for [Windows] from ORS13.
The nucleation and propagation of cracks in a polymineralic material that arise from differential shrinkage depends on the mineral strengths, the interfacial bonding strengths among the mineral constituents, and how the constituents are distributed throughout a sample. 3D X-ray microscopy (Zeiss Xradia 510 Versa) was used to image the samples immediately after removal from the curing tank and intermittently over a period of 6 days. The reference sample M, along with the CB samples (STX, SWY, SKAO, and SK10-5 ) were only scanned after removal from the curing environment, and then again after 6 full days of drying. The samples were dried inside the X-ray system at ambient relative humidity and a temperature of 28 C that was maintained by the X-ray system. 2ff7e9595c
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