Reversible planar gliding and microcracking in a single-crystalline Ni-rich cathode
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99 GENERAL AND MISCELLANEOUS↗
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A directional microcrack damage theory for brittle solids based on continuous hyperplasticity
We present a novel microcrack-damage theory for brittle solids under compression. Instead of using internal variables like zeroth, second or fourth rank damage tensors, the state of material damage is represented by an internal function that encapsulates the information of direction, density and size of microcracks. Just like other internal variables, the evolution of this state function must obey the second law of thermodynamics for arbitrary loading paths. This is done by casting the model in the framework of continuous hyperplasticity and enforcing a non-negative dissipation rate functional. The proposed framework offers predictions on the continuous evolution of microcrack density and the induced material anisotropy along with the macroscopic stress-strain curves. The use of continuous damage function grants the model significantly enhanced resolution in characterizing the direction-dependent response of cracked solids compared to classical models that are based on damage tensors. Two scenarios are considered in developing the theory, one assumes frictionless cracks and the other incorporates friction between crack surfaces. The results highlight that inelasticity, pressure dependence, and loading-unloading hysteresis exhibited by brittle solids are natural consequences of frictional microcracks. The proposed theory offers a generic and versatile framework to upscale micromechanical processes operating at individual crack scale to explain the macroscopic behavior of cracked solids.
Materials Science↗
Microcracking, microcrack-induced delamination, and longitudinal splitting of advanced composite structures
A combined analytical and experimental study was conducted to analyze microcracking, microcrack-induced delamination, and longitudinal splitting in polymer matrix composites. Strain energy release rates, calculated by a variational analysis, were used in a failure criterion to predict microcracking. Predictions and test results were compared for static, fatigue, and cyclic thermal loading. The longitudinal splitting analysis accounted for the effects of fiber bridging. Test data are analyzed and compared for longitudinal splitting and delamination under mixed-mode loading. This study emphasizes the importance of using fracture mechanics analyses to understand the complex failure processes that govern composite strength and life.
Nairn, John A.↗
Microcracking of Materials for Space
The effect of thermal-cycling-induced microcracking in fiber-reinforced polymer matrix composites is studied. Specific attention is focused on microcrack density as a function of the number of thermal cycles, and the effect of microcracking on the dimensional stability of composite materials. Changes in laminate coefficient of thermal expansion (CTE) and laminate stiffness are of primary concern. Included in the study are materials containing four different Thornel fiber types: a PAN-based T50 fiber and three pitch-based fibers, P55, P75, and P120. The fiber stiffnesses range from 55 Msi to 120 Msi. The fiber CTE's range from -0.50 x 1O(exp -6)/degrees F to -0.80 x 10(exp -6)/degrees F. Also included are three matrix types: Fiberite's 934 epoxy, Amoco's ERL1962 toughened epoxy, and YLA's RS3 cyanate ester. The lamination sequences of the materials considered include a cross-ply configuration, [0/90](sub 2s), and two quasi-isotropic configurations, [0/+45/-45/90](sub s), and [0/+45/90/-45](sub s). The layer thickness of the materials range from a nominal 0.001 in. to 0.005 in. In addition to the variety of materials considered, three different thermal cycling temperature ranges are considered. These temperature ranges are +/-250 degrees F, +/-l5O degrees F, and +/-50 degrees F. The combination of these material and geometric parameters and temperature ranges, combined with thermal cycling to thousands of cycles, makes this one of the most comprehensive studies of thermal-cycling-induced microcracking to date. Experimental comparisons are presented by examining the effect of layer thickness, fiber type, matrix type, and thermal cycling temperature range on microcracking and its influence on the laminates. Results regarding layer thickness effects indicate that thin-layer laminates microcrack more severely than identical laminates with thick layers. For some specimens in this study, the number of microcracks in thin-layer specimens exceeds that in thick-layer specimens by more than a factor of two. Despite the higher number of microcracks in the thin-layer specimens, small changes in CTE after thousands of cycles indicate that the thin-layer specimens are relatively unaffected by the presence of these cracks compared to the thick-layer specimens. Results regarding fiber type indicate that the number of microcracks and the change in CTE after thousands of cycles in the specimens containing PAN-based fibers are less than in the specimens containing comparable stiffness pitch-based fibers. Results for specimens containing the different pitch-based fibers indicate that after thousands of cycles, the number of microcracks in the specimens does not depend on the modulus or CTE of the fiber. The change in laminate CTE does, however, depend highly on the stiffness and CTE of the fiber. Fibers with higher stiffness and more negative CTE exhibit the lowest change in laminate CTE as a result of thermal cycling. The overall CTE of these specimens is, however, more negative as a result of the more negative CTE of the fiber. Results regarding matrix type based on the +/-250 degree F temperature range indicate that the RS3 cyanate ester resin system exhibits the greatest resistance to microcracking and the least change in CTE, particularly for cycles numbering 3000 and less. Extrapolations to higher numbers of cycles indicate, however, that the margin of increased performance is expected to decrease with additional thermal cycling. Results regarding thermal cycling temperature range depend on the matrix type considered and the layer thickness of the specimens. For the ERL1962 resin system, microcrack saturation is expected to occur in all specimens, regardless of the temperature range to which the specimens are exposed. By contrast, the RS3 resin system demonstrates a threshold effect such that cycled to less severe temperature ranges, microcracking does not occur. For the RS3 specimens with 0.005 in. layer thickness, no microcracking or changes in CTE are observed in specimens cycled between +/-150 degree F or +/- 50 degree F. For the RS3 specimens with 0.002 in. layer thickness, no microcracking or changes in CTE are observed in specimens cycled between +/-50 degree F. Results regarding laminate stiffness indicate negligible change in laminate stiffness due to thermal cycling for the materials and geometries considered in this investigation. The study includes X-ray examination of the specimens, showing that cracks observed at the edge of the specimens penetrate the entire width of the specimen. Glass transition temperatures of the specimens are measured, showing that resin chemistry is not altered as a result of thermal cycling. Results are also presented based on a one-dimensional shear lag analysis developed in the literature. The analysis requires material property information that is difficult to obtain experimentally. Using limited data from the present investigation, material properties associated with the analysis are modified to obtain reasonable agreement with measured microcrack densities. Based on these derived material properties, the analysis generally overpredicts the change in laminate CTE. Predicted changes in laminate stiffness show reasonable correlation with experimentally measured values.
Brown, Timothy L.↗
On the phenomenon of curved microcracks in /(S)/90n/s laminates - Their shapes, initiation angles and locations
A variational analysis of the stress state in microcracked cross-ply laminates has been used to investigate the phenomenon of curved microcracking in /(S)/90n/s laminates. Previous investigators proposed that the initiation and orientation of curved microcracks are controlled by local maxima and stress trajectories of the principal stresses. We have implemented a principal stress model using a variational mechanics stress analysis and we were able to make predictions about curved microcracks. The predictions agree well with experimental observations and therefore support the assertion that the variational analysis gives an accurate stress state that is useful for modeling the microcracking properties of cross-ply laminates. An important prediction about curved microcracks is that they are a late stage of microcracking damage. They occur only when the crack density of straight microcracks exceeds the critical crack density for curved microcracking. The predicted critical crack density for curved microcracking agrees well with experimental observations.
Hu, Shoufeng↗
Matrix Microcracking Effect on the Structural Response of a Thermal Protection System
The effect of microcracking in the phenolic matrix of a three-dimensional woven thermal protection system (TPS) and resulting material stiffness reduction was studied via a comparison of finite element results from linear and iterative linear analyses. A dual-layer continuous dry weave material with a low-density phenolic resin matrix has been developed for use in extreme environments. Due to high stresses in the through-the-thickness direction, microcracks may form in the matrix. The matrix does not have structural load transfer requirements, and testing has shown that microcracked phenolic resin satisfies thermal requirements. Microcracks in the matrix would result in a reduction of stiffness, which could alter the structural performance. A study was conducted to determine if reduction in material stiffness would change the load paths or structural margins. A linear finite element analysis that did not account for microcracking and an iterative linear finite element analysis that accounted for propagation microcracks were compared. Four subcases were analyzed with results indicating that the assumed propagation strength for the microcracking is the critical parameter for determining the extent of microcracking. Phenolic microcracking does not appear to have an adverse effect on the structural response and is not a critical failure for the modeled TPS.
Thermal Protection System↗
Microcracks in lunar rocks
Lunar samples contain abundant open microcracks that have closure characteristics completely unlike any shocked terrestrial rock; however, the microcracks present in the lunar rocks before the rocks reached the surface of the moon were likely similar to the microcracks in the shocked terrestrial rocks. Because the microcracks present in the lunar rocks in situ inside the moon were different, radically different, from the microcracks present today in returned lunar samples, any property that is sensitive to microcracks measured on the returned lunar samples is inappropriate for predicting that property as a function of depth in the moon. Therefore, many data that have been measured already on lunar samples simply do not apply to rocks in situ inside the moon. A plausible mechanism with which to account for the difference in microcrack characteristics of lunar samples on the surface of the moon and the microcrack characteristics of lunar rock in situ inside the moon is thermal cycling during residence on the moon's surface.
Simmons, G.↗
Microcrack Quantification in Composite Materials by a Neural Network Analysis of Ultrasound Spectral Data
Intra-ply microcracking in unlined composite pressure vessels can be very troublesome to detect and when linked through the thickness can provide leak paths that may hinder mission success. The leaks may lead to loss of pressure/propellant, increased risk of explosion and possible cryo-pumping into air pockets within the laminate. Ultrasonic techniques have been shown capable of detecting the presence of microcracking and in this work they are used to quantify the level of microcracking. Resonance ultrasound methods are utilized with artificial neural networks to build a microcrack prediction/measurement tool. Two networks are presented, one unsupervised to provide a qualitative measure of microcracking and one supervised which provides a quantitative assessment of the level of microcracking. The resonant ultrasound spectroscopic method is made sensitive to microcracking by tuning the input spectrum to the higher frequency (shorter wavelength) components allowing more significant interaction with the defects. This interaction causes the spectral characteristics to shift toward lower amplitudes at the higher frequencies. As the density of the defects increases more interactions occur and more drastic amplitude changes are observed. Preliminary experiments to quantify the level of microcracking induced in graphite/epoxy composite samples through a combination of tensile loading and cryogenic temperatures are presented. Both unsupervised (Kohonen) and supervised (radial basis function) artificial neural networks are presented to determine the measurable effect on the resonance spectrum of the ultrasonic data taken from the samples.
Walker, James L.↗
Effect of Phenolic Matrix Microcracking on the Structural Response of a 3-D Woven Thermal Protection System
The effect of microcracking in the phenolic matrix of a three-dimensional woven thermal protection system (TPS) and the resulting material stiffness reduction was studied via a comparison of finite element analysis results from a linear analysis and an iterative linear analysis. A TPS is necessary to protect space vehicles from the aerodynamic heating of planetary entry. The Heatshield for Extreme Entry Environment Technology (HEEET) project has developed a TPS for use in high heat-flux and pressure missions. The material is a dual-layer continuous dry weave, which is then infiltrated with a low-density phenolic resin matrix to form a rigid ablator. The phenolic resin matrix does not have structural load transfer requirements, and testing has shown that the phenolic resin can fully satisfy thermal requirements when the matrix contains microcracks. Due to high stresses in the through-the-thickness direction of the material, phenolic microcracks may form in the matrix material, which would result in a reduction of stiffness. An exploratory study was conducted to determine if reduction in material stiffness would change the load paths and/or decrease the structural margins. A comparison was performed between a linear finite element analysis that did not take into account phenolic microcracking and an iterative linear finite element analysis that accounted for propagation of phenolic microcracking. Four subcases using varying assumptions were analyzed and the results indicate that the assumed strength at which the phenolic microcracking propagates was the critical parameter for determining the extent of microcracking in the phenolic matrix. Phenolic microcracking does not have an adverse effect on the structural response of the test article and is not a critical failure.
Langston, Sarah L.↗
Upscaling Reactive Transport and Clogging in Shale Microcracks by Deep Learning
Fracture networks in shales exhibit multiscale features. A rock system may contain a few main fractures and thousands of microcracks, whose length and aperture are orders of magnitude smaller than the former. It is computationally prohibitive to resolve all the fractures explicitly for such multiscale fracture networks. One traditional approach is to model the small-scale features (e.g., microcracks in shales) as an effective medium. Although this fracture-matrix conceptualization significantly reduces the problem complexity, there are classes of physical processes that cannot be accurately upscaled by effective medium approximations, e.g., microcrack clogging during mineral reactions. Here, we employ deep learning in place of effective medium theory to upscale physical processes in small-scale features. Specifically, we consider reactive transport in a fracture-microcrack network where microcracks can be clogged by precipitation. A deep learning multiscale algorithm is developed, in which the microcracks are upscaled as a wall boundary condition of the main fractures. The wall boundary condition is constructed by recurrent neural networks, which take concentration histories as input and predict the solute transport from main fractures to microcracks. The deep learning multiscale algorithm is firstly employed in specific scenarios, then a general model is developed which can work under various conditions. The new approach is validated against fully resolved simulations and an analytical solution, providing a reliable and efficient solution for problems that cannot be upscaled by effective medium models.
58 GEOSCIENCES↗
Analysis of autogenous shrinkage-induced microcracks in concrete from 3D images
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.
36 MATERIALS SCIENCE↗
The initiation and growth of delaminations induced by matrix microcracks in laminated composites
A recent variational mechanics analysis of microcracking damage in cross-ply laminates of the form /(S)/90n/s, where (S) is any orthotropic sublaminate much stiffer than /90n/, has been extended to account for the presence of delaminations emanating from the tips of microcracks in the /90 2n/T sublaminate. The new two-dimensional stress analysis is used to calculate the total strain energy, effective modulus, and longitudinal thermal expansion coefficient for a laminate having microcracks and delaminations. These results are used to calculate the energy release rate for the initiation and growth of a delamination induced by a matrix microcrack. At low crack densities, /(S)/90n/s laminates are expected to fail by microcracking and to show little or no delamination. At some critical crack density, which is a function of laminate structure and material properties, the energy release rate for delamination exceeds that for microcracking and delamination is predicted to dominate over microcracking. A quasi-three-dimensional model is used to predict the propagation of arbitrarily shaped delamination fronts. All predictions agree with experimental observations.
Nairn, J. A.↗
Reinforcement induced microcracking during the conversion of polymer-derived ceramics
This study investigates the role of discontinuous reinforcement on the microcracking of a preceramic polymer matrix during polymer to ceramic conversion. The material system comprised a carbosilane-based, preceramic polymer reinforced with mullite particles. The preceramic resin slurry was formulated for photopolymerization on a digital light projection 3D printer. Micro X-ray computed tomography, using a synchrotron light source, monitored a printed composite part during pyrolysis. The conversion of the carbosilane matrix into Si(O)C generated microcracks in the matrix that radially extended from particles. The likelihood of microcrack formation positively correlated with particle size. The largest particles (>10 4 µm 3 volume or >60 µm side length) always abutted microcracks, while the matrix surrounding smaller particles (<5 µm) was free of microcracks. Numerical calculations showed the particles resist the shrinking matrix during its conversion. This created tensile stresses within the matrix. The driving force for microcrack growth was also analyzed with regard to the influence of matrix material parameters, particle form-factor and crack length. These results reveal the need to consider the form factor of discontinuous reinforcements, with regard to the material properties of the polymer-derived ceramic, in order to reduce or eliminate defects in the final part.
36 MATERIALS SCIENCE↗
A Time-Dependent Directional Damage Theory for Brittle Rocks Considering the Kinetics of Microcrack Growth
In this work, a novel microcrack damage theory for describing the time-dependent behavior of brittle rocks is proposed. Instead of using scalar or tensorial variables to approximate the effect of microcracks, the concept of directional damage is introduced by upscaling the directional distribution density of microcracks through the noninteracting homogenization scheme. The contribution of an individual crack on global strain is first derived from the crack-opening displacements including sliding, closure, and dilation. The model is then cast in the free energy form, and the range of parameters ensuring compliance with the second law of thermodynamics is derived rigorously. Considering that the subcritical propagation of microcracks is the dominant mechanism behind the time-dependent deformation and failure of brittle rocks, the driving force for directional damage is defined as the corresponding energy release rate, and the effect of time is introduced through a damage evolution law inspired from the kinetics of subcritical crack growth. The model is applied to simulate the behavior of basalt rock under various loading conditions. In addition to predicting the stress–strain–time response, the model offers enhanced resolution in representing the anisotropic characteristics of microcrack-induced damage in brittle rocks and their time-dependent evolutions.
58 GEOSCIENCES↗
3D imaging techniques for characterising microcracks in cement-based materials
Concrete inherently contains pores and microcracks that can adversely impact its mechanical properties and long-term durability. However, characterising microcracks is difficult due to their complex, multiscale and three-dimensional (3D) nature. This paper presents an evaluation of 3D imaging techniques for characterising microcracks induced by different mechanisms. Seven cement pastes, mortars and concretes subjected to drying shrinkage, autogenous shrinkage and freeze-thaw cycles were investigated using focused ion beam nanotomography (FIB-nt), broad ion beam serial section tomography (BIB-SST), laser scanning confocal microscopy (LSCM) combined with serial sectioning and X-ray microtomography (μCT). The study shows that the characteristics of microcracks vary significantly depending on exposure conditions. Yet there is no single technique that can capture the entire size range of microcracks from sub to tens of μm within a sufficiently representative sampling volume. The achievable image volume and resolution, and the advantages and disadvantages of each technique are compared and discussed.
36 MATERIALS SCIENCE↗
Effect of autogenous shrinkage on microcracking and mass transport properties of concrete containing supplementary cementitious materials
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.
36 MATERIALS SCIENCE↗
Effects of Microstructural Composition, Porosity, and Microcracks on the Elastic Moduli of Nuclear Graphites
The elastic responses of nuclear graphite not only depend on the graphitic content itself but are largely dictated by the microstructural constitution of the material. The types of raw materials combined with the manufacturing processes used to produce the graphite yield the microstructural content that primarily includes graphite filler, graphitized pitch binder, and voids/defects that typically occupy approximately 20% of the volume. Among these microstructural components, porosity and microcracking (considered to be part of voids/defects) heavily influence the overall properties of the material, including the elastic moduli. It is widely accepted that the primary effect of oxidation is to increase porosity, but the related effect on the moduli cannot be explained satisfactorily by simply noting changes to porosity. Models describing the elastic moduli of porous, polycrystalline graphite materials have been developed to interpret experimental determinations of Young's modulus and shear modulus in oxidized graphites. Beyond porosity, the moduli are heavily influenced by microcracks, and their effects can be assessed using physical property models based on orientation distribution coefficients and microcrack-modified, single-crystal moduli to represent the combined effects of crystallite orientation and microcracking. This work demonstrates how most modulus measurements in nuclear graphites can be understood using relatively simple models that describe the effects of porosity and microcracking. We also present directions to be pursued to account for microstructure-related effects that occur as a result of neutron irradiation.
Spicer, James B.↗