A likelihood ratio test for shrinkage covariance estimators
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Highlights: • Inorganic polymer mortar has mainly macropores and a drying shrinkage of 5.1 mm/m. • 2-methyl-2,4-pentanediol acts as air entrainer in inorganic polymer mortars. • Optimal dosage 2 wt% 2-methyl-2,4-pentanediol reduced drying shrinkage to 1.8 mm/m. • Heat curing inorganic polymer mortars reduced drying shrinkage more than 50%. • Blast Furnace slag addition increased drying shrinkage and reduced strength. Inorganic polymer (IP) binder is formed upon alkali-activation of Fe-rich (41 wt%) metallurgical slag leading to materials with mechanical properties comparable to ordinary Portland cement binders. Crack formation is reported in IPs, which can be related to volumetric stability, which is to date not thoroughly understood in IPs. This study determined the autogenous and drying shrinkage of IP mortars. Shrinkage mitigation strategies, such as the addition of 2-methyl-2,4-pentanediol (2MPL), blast furnace slag (GGBFS), and applying heat curing, were used separately or in combination. IP mortars exhibited autogenous expansion and high drying shrinkage. The addition of 2MPL led to a porosity increase, as air was entrained, decreasing the drying shrinkage with 64%. Additional heat curing had no effect on samples with 2MPL. Introducing GGBFS resulted in smaller pores, increasing drying shrinkage. Shrinkage in IP mortars is driven by its pore size distribution and higher shrinkage resulted in lower flexural strength.
Cementitious materials shrink when exposed to decreasing relative humidities, which may result in cracking. Shrinkage reducing admixtures (SRAs) can be used to reduce this drying shrinkage. Although many studies have shown that SRAs reduce the surface tension of the pore solution, the effects of SRAs on other pore solution properties and their relationship to drying shrinkage have been poorly characterized. In this work, we investigate the impact of an SRA (hexylene glycol) on the drying and re-humidification of a cement paste over an extended relative humidity range. The reduction in the first drying shrinkage by the SRA depends on relative humidity. The SRA also significantly reduces the irreversible drying shrinkage. We concluded that the SRA impacts drying shrinkage by acting on the capillary forces, by acting on the specific range of relative humidity over which those forces occur, and potentially by acting on the surface stresses through pore wall adsorption.
Autogenous shrinkage of alkali-activated slag cement (AASC) paste prepared with different levels of alkali dosage and silicate modulus (M{sub s}) is investigated. The results show that autogenous shrinkage of AASC paste increases at a decreasing rate with alkali dosage, which is attributed to enhanced capillary pore pressure and syneresis of C-A-S-H gels. Autogenous shrinkage of AASC paste with a constant alkali dosage increases as M{sub s} increases from 0.5 to 1.0, followed with a reduction as M{sub s} further increases to 2.0. Increasing M{sub s} initially enhances the capillary pore pressure due to the enhanced reaction degree, and promotes the formation of saturated capillary pores and viscoelasticity, which facilitates the autogenous shrinkage of AASC paste. However, excessive silicate in the activator retards the internal moisture consumption, and subsequently decreases the autogenous shrinkage of AASC paste. Furthermore, increasing M{sub s} can also intensify syneresis of C-A-S-H gels, contributing to the early-age autogenous shrinkage of AASC paste.
Despite more than a century of research, drying shrinkage still causes unwanted stresses and cracks in our concrete infrastructures. This is partly due to the lack of understanding of the underlying mechanisms governing the drying shrinkage in cementitious materials. Inspired by the tremendous impact of atomistic simulations on materials science, we expect such innovative simulation techniques to hold a key to unlocking the enigmatic nature of drying shrinkage at the nanoscale. In this treatise, we first introduce basic physics concepts and atomistic simulation methods in detail. Afterward, we discuss the progress brought by atomistic simulations in understanding the drying shrinkage in cementitious materials and other nanoporous and nanolayered systems. This review also highlights important remaining fundamental questions and practical issues regarding drying shrinkage and delineates how atomistic simulations can help resolve them.
It is well-known that supplementary cementitious materials (SCMs) and low water-to-binder (w/b) ratio increase autogenous shrinkage, but the impact on microcracking and long-term transport properties is less understood. This paper examines the effect of microcracking induced by autogenous shrinkage on transport properties of concretes cured up to ~3.6 years. Variables include SCM type (9% SF, 70% GGBS), w/b ratio (0.20–0.45), maximum-aggregate-size (MSA: 5–20 mm) and shrinkage reducing admixture (SRA). Oxygen diffusivity, permeability and water sorptivity were correlated with microcracks characterised using laser scanning confocal microscopy and 3D X-ray microtomography. Results show greater microcracking in mixes containing SCMs, low w/b ratio and large MSA. At the same w/b ratio and binder type, strong positive correlations are observed between transport and microcracking with increasing MSA, confirming the negative impact of autogenous shrinkage. SRA was effective in reducing these effects. The significance is compared with drying shrinkage and implications for durability are discussed.
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.
The shrinkage cracking occurring in oil & gas well cement material is a major factor that reduces the cement sheath integrity and impairs the durability of an underground well. Shrinkage mainly takes place in the early hydration period of the cement, and the resulting restrained shrinkage cracking can form a leaking network for oil & gas or carbon dioxide stored in an underground reservoir. It is thus important to understand the early age behavior of well cement and the leaking pathway formation in the well. This study describes the application of the digital image correlation (DIC) method as a tool to measure the strain development and crack distributions of well cement in the lab during early phase changes. A theoretical model is presented to calculate the stress distribution built up in the cement sheath during early ages of well cement hydration, which helps to interpret the experimental observations and determine the major factors influencing the cracking sequences. This study presents the whole hydration – drying shrinkage – and cracking mechanism of early age well cement under restrained ring conditions experimentally and theoretically. Finally, the results offer useful insights on the key material and geometric parameters which control the fracture of a well cementing structure.
Devitrification and shrinkage of three batches of silica fibers were investigated in the temperature range of 1200 to 1350 C. Fibers with high water and impurity content devitrified rapidly to cristobalite and quartz and exhibited rapid, but the least amount of, shrinkage. A batch with low water and impurity content devitrified more slowly to cristobalite only and underwent severe shrinkage by the mechanism of viscous flow. A third batch of intermediate purity level and low water content devitrified at a moderate rate mainly to cristobalite but shrunk very rapidly. Completely devitrified silica fibers did not exhibit any further shrinkage.
We consider problem of nonlinear shrinkage of the metal part during bound metal deposition manufacturing on the ground and in zero-G. To analyze this problem we developed multi-scale physics-based approach that spans atomistic dynamics at the scale of nanoseconds and the full part shrinkage at the time scale of hours. Using this approach we estimated the key parameters of the problem including grain boundary width, coefficient of surface diffusion, initial redistribution of particles during debinding stage, micro-structure evolution from round particles to densely packed grains and corresponding change of the total and chemical free energy, and sintering stress. The introduced method was used to predict shrinkage at the level of two particles, filament cross-section, sub-model, and the whole green, brown, and metal parts. To further improve accuracy and reliability of the shrinkage predictions we propose concept of intelligent additive manufacturing of metal powders in space that combines the strengths of both physics-based and data-driven methods of analysis of AM.
Early-age drying (immediately after casting) of mortars and the corresponding plastic shrinkage were studied using bimodal neutron/X-ray computed tomography. This novel, correlative 3D imaging mode enabled studying simultaneously and without any source of spurious perturbation the water migration and loss processes together with the corresponding deformations due to plastic shrinkage. Bimodal imaging opens up new possibilities for studying dynamic processes of coupled water transport and deformations in porous solids. The measurements were carried out on model systems (cylindrical mortar specimens with height of 19 mm). The study focused on the effect of a paraffin-based curing compound. Our results confirm that when the curing compound was applied directly onto the drying surface in a sufficient amount, both the evaporation rate and the rate of vertical displacement (settlement) were substantially reduced. The results shed a new light on the mechanisms of plastic shrinkage and the action of curing compounds.
Highlights: • Extensive experimental study on drying shrinkage, creep and microcracking of concrete • All specimens prepared from a single batch of ordinary-strength structural concrete • 1st year of measurements of (not only) non-uniformly drying beams with span up to 3-m • The database is downloadable from free-to-use research data repository • Modified MPS model for concrete creep used in blind prediction of all experiments The material models for creep and shrinkage operating on the material point level in FEM are usually intended for challenging complex applications and structures, where the average cross-sectional approach does not suffice. The identification of the growing number of material parameters induced by increasing model capabilities relies on very specific and narrow-oriented yet interconnected experiments which are scarce. The presented comprehensive experiments aim to provide a clearer image of the complicated interaction among the basic phenomena: drying, shrinkage, creep, and microcracking. The cornerstone of this ongoing research is a unique set of 30 partially-sealed unreinforced concrete beams with span 1.75–3.0 m subjected to drying. To minimize material variation, all specimens in this study were cast from a single batch of ordinary strength structural concrete with slag-blended binder. The resulting experimental database will be suitable both for validation and development of the constitutive models.
A new image analysis procedure for quantifying microcracks from three-dimensional (3D) X-ray microCT images of concrete is presented. The method separates microcracks from air voids and aggregates by combining filtering and morphological operations. It was applied to study the effects of supplementary cementitious materials (SCMs) and curing age on autogenous shrinkage-induced microcracks in low w/b ratio concretes, and to determine the representative elementary volume (REV) for various properties of microcracks and air voids. Results showed that slag and silica fume significantly increased autogenous shrinkage and related microcracking. These SCMs increased volume fraction, width, length, dendritic density, anisotropy, and connectivity of microcracks, but decreased specific surface and tortuosity. Similar trends were observed with age. Comparison between 3D and 2D measurements was made. REV analysis showed that a sampling volume of ~20 × 20 × 25 mm{sup 3} is sufficient for characterising most parameters of autogenous shrinkage microcracks and air voids in concrete.
This study explored the reactive processes of atmospheric carbonation and the consequences with respect to cementitious materials. Two model pastes were used: hydrated C{sub 3}S (including C-S-H and portlandite) and a paste prepared by hydrating a blend of C{sub 3}S and nanosilica (including C-S-H only). The two pastes were carbonated under accelerated conditions in the laboratory. The resulting mineralogical assemblage was examined using X-ray diffraction, thermogravimetric analysis and nuclear magnetic resonance. The microstructural changes were studied by X-ray tomography and porosimetry, and their macroscopic impacts were evaluated through gas diffusion and shrinkage measurements. The use of model pastes allowed for the evaluation of the change in solid volume induced by the carbonation of C-S-H. C-S-H decalcification and subsequent silica chain polymerisation were found responsible for carbonation shrinkage (and potentially cracking). Finally, the results highlight the protective role of portlandite: portlandite helped in limiting C-S-H decalcification and then reducing carbonation shrinkage and cracking.
Austenitic 21Cr32Ni model alloy thin foils, previously irradiated with 5 MeV Fe ++ ions in bulk to create voids, were re-irradiated in-situ in the Intermediate Voltage Electron Microscope Facility (IVEM). The voids which had been formed under bulk-ion irradiation shrank and disappeared after in-situ Kr ion irradiation in the temperature range 50 K-713 K to an additional dose of 1 dpa. The voids were unaffected by eithersuccessive thermal annealing to 673 K and by prolonged exposure to the 200 keV electron beam at the irradiation temperature. The high void shrinkage rate observed did not change significantly for irradiation temperatures between 50 K and 713 K, suggesting that the void shrinkage process in thin foils during in-situ heavy-ion irradiation results from the interactions of displacement cascades with the voids. Finally, possible void shrinkage mechanisms under thin foil irradiation are discussed in this study.
Hydrogen release during pyrolysis of woody biomass is studied considering anisotropicity and inhomogeneity of wood structure. A new anisotropic shrinkage model is proposed based on the decomposition of main wood constituents, i.e., cellulose, hemicellulose, and lignin. The new shrinkage model can predict the temporal evolution of the wood structure, and the differences between axial and radial shrinkage during pyrolysis. The model agrees very well with several experimental data from the literature. Based on particle temperature during conversion, the pyrolysis is partitioned into four stages, and the hydrogen release and H 2 formation from each stage are investigated. Stage (IV) of pyrolysis, from 1000 to 1273 K, is found to be efficient for H 2 production owing to the production of considerable mass of H with a minimal amount of tar species. Furthermore, the char quality is found to be different at the end of stages (II), (III), and (IV), where around 67.7, 80.5, and 93.4% wt. of solid residue is made of carbon, respectively. The model is also used to explain how the heating rate affects the temperature distribution inside the particle and how it shifts the peak of hydrogen release. Finally, the pyrolysis of two inhomogeneous wood samples — a beech twig with bark and a beech dowel with growth rings — are investigated. The bark can affect the pyrolysis rate, products, and flow pattern inside the particle. The growth rings do not have a considerable effect on the pyrolysis rate and products, but they have a significant impact on the flow pattern. This has an important implication for char conversion studies where the internal surface area and porosity field distribution have a significant effect on the gasification and oxidation rates.
Thermal curing induces shrinkage in material extrusion based additive manufacturing silicone elastomer samples, resulting in discrepancies between as printed and final geometries. Knowing the extent to which the samples change in shape and size allows us to make appropriate modifications to the printing design to better control the geometry of the samples. We present an X-ray computed tomography (CT) based approach to determine filament-level shrinkage due to thermal curing of silicone elastomer samples printed with direct ink writing (DIW). The approach relies on custom-designed build plates that are resistant to the elevated curing temperatures and that have sufficiently distinct X-ray absorption characteristics from the silicone elastomer to ensure adequate segmentation of the latter in X-ray imaging data. We implement the approach to evaluate shrinkage in DIW ‘log pile’ samples with three distinct strand arrangements and demonstrate of how filament-level information can be extracted from the X-ray CT data.
The separator, an ionic permeable and electronic insulating membrane between cathode and anode, plays a crucial role in the electrochemical and safety performance of batteries. However, the commercial polyolefin separators not only suffer from inevitable thermal shrinkage at elevated temperature, but also fail to inhibit the hidden chemical crosstalk of reactive gases such as O 2 , leading to often reported thermal runaway (TR) and hence preventing large-scale implementation of high-energy-density lithium-ion batteries. Herein, a nanoporous non-shrinkage separator (GS-PI) was fabricated via a novel gel-stretching orientation approach to eliminate TR. In situ synchrotron small angle X-ray scattering during heating clearly showed that the as-prepared thin GS-PI separator exhibits superior mechanical tolerance at high temperature, thus effectively preventing internal short circuit. Meanwhile, the unique nanoporous structure design further blocks chemical crosstalk and the associated exothermic reactions. Accelerating Rate Calorimetry test revealed that the practical 1 Ah LiNi 0.6 Co 0.2 Mn 0.2 O 2 (NCM622)/graphite pouch cell using GS-PI nanoporous separator show a maximum temperature rise (dT/dt max ) of only 3.7 °C s -1 compared to 131.6 °C s -1 in the case of Al 2 O 3 @PE macroporous separator. Furthermore, despite the reduced pore size, the GS-PI separator demonstrates better cycling stability than conventional Al 2 O 3 @PE separator at high temperature without sacrificing specific capacity and rate capability.