Anisotropic Stress Research Articles

An anisotropic conductive hydrogel for strain sensing and breath detection

Conductive hydrogels, with their excellent conductivity and flexibility, are highly suitable for use as strain sensors. However, they often exhibit weak mechanical properties and isotropy, which can limit their application potential. Moreover, the incorporation of self-powering capabilities within hydrogels would provide a significant advantage for sensor applications. In this study, we utilized hydrophilic delignified wood as a scaffold and impregnated it with FeCl3 solution to fabricate conductive wood. Subsequently, a precursor solution of polyvinyl alcohol (PVA), chitosan (CS), and 2-acrylamido-2-methyl-1-propanesulfonic acid (AMPS) was prepared by heating and mixing. The conductive wood was then fully infiltrated with the precursor solution and transformed into a conductive wood-based hydrogel (CWH) using a freeze-thaw method. The aligned fibers in the conductive wood scaffold imparted anisotropic mechanical and electrical properties to the hydrogel, with a fracture stress anisotropy ratio of 47.5 (ratio of values parallel to the fiber direction to values perpendicular to the fiber direction) and an electrical conductivity anisotropy ratio of 1.55. The hydrogel remained soft after bonding with the wood scaffold, preserving its potential as a sensor. Experimental results demonstrated that the CWH sensor exhibited stable strain sensitivity (gauge factor of 0.2805 with R²=0.998 in the range of 0∼90°), enabling the monitoring of human joint bending and capturing facial smiles. The CWH also exhibited excellent resistance to expansion while maintaining high water content (79.4%), making it more suitable for use in humid environments compared to traditional hydrogels. Furthermore, we assembled the CWH into a humidity-driven generator and conducted power generation tests, revealing its promising power generation potential. The voltage significantly increased when exposed to humid air (from 6.2 mV to 66.1 mV). Lastly, we integrated the humidity-driven generator with a mask to create a breath detector, which was connected to an electrochemical workstation for testing. The test curve demonstrated the successful capture of orderly breathing activities from volunteers. The combination of these advantages positions CWH for a wide range of applications, including wearable flexible strain sensors, breath detection, bioelectrodes, and green energy generation devices.

Anisotropic stress mechanisms for different dielectric multi-layer films deposited by ion-beam assisted deposition on flexible substrates

This study simulates and tests various prototype multi-layer films on polyethylene terephthalate (PET) and polycarbonate (PC) substrates. The optical and stress response properties of three commonly used optoelectronic anti-reflector (AR) coatings (TiO2/SiO2)2, (Ta2O5/SiO2)2 and (Nb2O5/SiO2)2 were determined. A lab-designed phase-shifting shadow moiré interferometer and Mohr circle approach were used to collect and interpret data. Results showed that the refractive indices of the four different dielectric films were 2.24(TiO2) > 2.23(Nb2O5) > 2.1(Ta2O5) > 1.44(SiO2). The transmittances of the three different AR coatings, in decreasing order, were 95.28%(Ta2O5/SiO2)2 > 94.86%(TiO2/SiO2)2 > 94.03%(Nb2O5/SiO2)2. The maximum shear stress of three different AR coatings, in decreasing size, were (Nb2O5/SiO2)2 > (Ta2O5/SiO2)2 > (TiO2/SiO2)2, for both the PET and PC substrate; however, the maximum principal stresses of three different AR coatings were tensors for the PET substrate, and compressive for the PC substrate. The principal stresses recorded were -916 MPa (Nb2O5/SiO2)2 > 438 MPa (Ta2O5/SiO2)2 > 346 MPa (TiO2/SiO2)2 for PET, and -951 MPa (Nb2O5/SiO2)2 > -838 MPa (Ta2O5/SiO2)2 > -766 MPa (TiO2/SiO2)2 for PC. The different elasticity moduli (ΔE) and relative elasticity between the different film layers may potentially be used to mitigate stress relief in multilayer coatings.

Effects of consolidation conditions on the dynamic shear modulus of saturated coral sand over a wide strain range

The utilization of coral sand as a construction material for ports and other infrastructure systems in coral reefs is prevalent, wherein the soil elements within slopes and embankments typically experience an anisotropic stress state. It is imperative to accurately characterize the degradation behavior of the stratigraphic material's stiffness across a wide range of strains. In this study, the maximum and strain-dependent shear modulus (G0 and G) characteristics of saturated coral sand under isotropic and anisotropic consolidations were investigated by performing multi-stage stress-controlled undrained cyclic torsional shear tests with cyclic hollow cylinder shear apparatus. The experimental results indicated that G0 and G generally rose with increasing initial effective consolidation pressure but decreased with increasing inclination of initial major principal stress from the vertical (αc). In contrast, the effect of consolidation stress ratio (kc) on G0 and G was nonmonotonic, and that of kc and αc on the strain-dependent shear modulus reduction (G/G0) curve was slight. By defining anisotropic consolidation indexes δ0 and δr used for quantifying the effect of consolidation-induced anisotropy on the G0 and the G/G0, respectively. A unified formula of G0 obtained by multiplying Hardin's model by δ0, as well as a unique formula of G/G0 obtained by correcting γr in the Davidenkov skeleton curve expression as a linear function of δr were established under various consolidation conditions, respectively. The proposed G formula over a wide strain range is well validated by the experimental data for siliceous sandy soils from the literature.

A resolved CFD–DEM investigation into the onset of suffusion: effect of confining pressure and stress anisotropy

AbstractThe susceptibility of a granular soil to suffusion is strongly dependent on its grain size distribution (GSD) and the mechanical and hydraulic conditions it is subjected to. This study investigates the onset of suffusion considering the effect of confining pressure and stress anisotropy using a fully resolved computational fluid dynamics and discrete element method (CFD–DEM). Three benchmarks, including the sedimentations of single and two adjacent spheres and the classic one‐dimensional (1D) consolidation are performed to demonstrate the capability of this method for high‐fidelity particle‐fluid simulations. A modified hydraulic criterion for the onset of suffusion considering stress anisotropy is presented. The microstructural changes of soil specimens before and during global suffusion are inspected, with emphasis on the evolutions of particle kinetic energy and displacements, force chain networks, and stress anisotropy. We found that the critical hydraulic gradient is negatively correlated with the confining pressure and the degree of stress anisotropy. Fine particles in the soil matrix are locally detached at small hydraulic gradients before the apparent global suffusion, as manifested by the variation of particle kinetic energy and coordination numbers. The roles of different contact types on force transmission and stress anisotropy in eroded specimens are also examined.

Fixed-axis shear characteristics of marine coral sand under various consolidation conditions

Coral sand is commonly used to construct ports and other types of infrastructure in coral reefs, where soil elements within slopes and embankments are usually under anisotropic stress because anisotropy is inherent to coral sand. In this study, marine coral sand was subjected to undrained fixed-axis shear tests using a cyclic hollow-cylinder shear apparatus, and the results indicate that the undrained response of such sand is influenced significantly by the initial orientation angle of the major principal stress (α0) and the monotonic loading direction angle (αm). In all cases, the excess pore water pressure (ue) of the coral sand tended to increase and then decrease with increasing generalized shear strain (γg), implying that such sand exhibits shear shrinkage and then shear expansion under monotonic loading. Another finding was that in the case of isotropic consolidation, the phase-transition strength (SPT) and phase-transition internal friction angle (φPT′) of the marine coral sand tended to decrease and then increase with increasing αm, while those in the case of anisotropic consolidation were always maximum in the α0 direction. There is a linear relationship between the SPT of marine coral sand and a dimensionless parameter β, where β−1 varies cosinusoidally with α0 and αm.

4D printing of biomimetic anisotropic self-sensing hydrogel actuators

Organisms in nature, from plants, insects to mammals, have anisotropic and regularly arranged tissue structures, which are key to rapid and precise response to environmental stimuli. In this study, nature-inspired anisotropic hydrogel actuators are fabricated by 4D printing thermo-responsive composites of short carbon fibers (SCFs) and poly(N-isopropylacrylamide) (PNIPAM). The SCFs could be well aligned and programmed in hydrogel matrix, resulting in diverse precisely controlled anisotropic structures. The intrinsic anisotropy causes unbalanced swelling and shrinking upon thermo-stimulation, leading to reversible biomimetic shape morphing. Finite element analysis (FEA) simulations are used to estimate the internal anisotropic stress distribution and structure evolution. Biomimetic anisotropic butterfly-like, flytrap-like and starfish-like hydrogel actuators are fabricated by 4D printing. On the other hand, the anisotropic SCFs/PNIPAM hydrogels are conductive and could be used as wearable strain sensors with high sensitivity. The conductive anisotropic hydrogels can generate sensing signals when they are motivated by temperature changes. This self-monitoring soft actuator is promising for the development of soft robots with stimulation-sensing-actuation feedback loop, which has broad application prospects in artificial intelligent devices.

Experimental Investigation of Simultaneous and Asynchronous Hydraulic Fracture Growth from Multiple Perforations in Shale Considering Stress Anisotropy

Experimental Investigation of Simultaneous and Asynchronous Hydraulic Fracture Growth from Multiple Perforations in Shale Considering Stress Anisotropy

Multi-dimensional ultrasonic-assisted belt grinding on the surface integrity of Inconel 718

In order to meet the requirements of the isotropic high-performance machining of complex surfaces, this paper proposed three-dimensional ultrasonic assisted belt grinding (3D-UABG) method that integrates the advantages of surface strengthening and isotropic machining, analyzed the motion characteristics and surface formation laws. Then, the influence of ultrasonic vibrations on the surface integrity of Inconel 718 was studied by a self-designed 3D-UABG device. Finally, the surface formation mechanism was revealed combined with the surface integrity and abrasive grain motion characteristic. Results showed that compared with conventional abrasive belt grinding (CABG), the abrasive grain in normal-ultrasonic assisted belt grinding (N-UABG) reduced the height of texture peak formed an intermittent texture, which makes it have smallest surface roughness. At the same time, the high-frequency impact of abrasive grains not only increased the surface plastic deformation, but also realized the impact strengthening. Planar two-dimensional ultrasonic assisted belt grinding (2D-UABG) reduced the directionality difference of surface quality. However, the deflection characteristics of abrasive grains make it have a large surface roughness. The 3D-UABG surface has good comprehensive mechanical properties. The abrasive grains have three-dimensional dynamic characteristics in space, which effectively inhibit anisotropic stress state, promote uniform deformation, and helpful to obtain approximately isotropic surface texture and small surface roughness. On the one hand, the in-plane motion characteristics of planar two-dimensional ultrasonic vibration gave grinding surface more uniform surface integrity. On the other hand, the spatial motion trajectory of abrasive grains driven by three-dimensional ultrasonic vibration made it have a slow increased cutting depth, which avoided the tear damage caused by materials plastic accumulation and the large roughness caused by abrasive deflection under large cutting depth. In 3D-UABG, lower feed speed and amplitude and linear velocity matched to grinding parameters contribute to the improved surface integrity. This study has guiding significance for the development and engineering application of ultrasonic-assisted belt grinding technology.

Electro-metabolic coupling in multi-chambered vascularized human cardiac organoids.

The study of cardiac physiology is hindered by physiological differences between humans and small-animal models. Here we report the generation of multi-chambered self-paced vascularized human cardiac organoids formed under anisotropic stress and their applicability to the study of cardiac arrhythmia. Sensors embedded in the cardiac organoids enabled the simultaneous measurement of oxygen uptake, extracellular field potentials and cardiac contraction at resolutions higher than 10 Hz. This microphysiological system revealed 1 Hz cardiac respiratory cycles that are coupled to the electrical rather than the mechanical activity of cardiomyocytes. This electro-mitochondrial coupling was driven by mitochondrial calcium oscillations driving respiration cycles. Pharmaceutical or genetic inhibition of this coupling results in arrhythmogenic behaviour. We show that the chemotherapeutic mitoxantrone induces arrhythmia through disruption of this pathway, a process that can be partially reversed by the co-administration of metformin. Our microphysiological cardiac systems may further facilitate the study of the mitochondrial dynamics of cardiac rhythms and advance our understanding of human cardiac physiology.

Heterogeneous Swelling of an Isotropically Compacted Bentonite-Based Material: Experimental Observations and Modelling

This paper presents a comprehensive investigation of the swelling behaviour of a compacted bentonite–sand mixture subjected to hydration under constant volume conditions. Contrary to previous studies, the tested sample was isotropically compacted before being hydrated under constant volume conditions until full saturation was reached. The total axial pressure, total radial pressures at four different heights of the sample, and injected water volume were recorded over time. The experimental data reveal a complex and non-uniform evolution of the axial and radial stresses over time, as well as anisotropy of the total stresses, which persist at the saturated equilibrated state. To gain further insights, a numerical analysis was performed using an advanced hydromechanical framework for partially saturated porous media, accounting for the evolving microstructure of the material. The complex evolution of the total axial and radial pressures with time is attributed to the advancing hydration and swelling front in the sample, along with the development of irreversible strains. The good agreement between the numerical results and the experimental data enables validation of the developed framework. Implications for engineered barriers in deep geological disposal of radioactive waste are discussed.

Anisotropy in Additively Manufactured Concrete Specimens under Compressive Loading-Quantification of the Effects of Layer Height and Fiber Reinforcement.

This paper analyzes the effect of print layer heights and loading direction on the compressive response of plain and fiber-reinforced (steel or basalt fiber) 3D printed concrete. Slabs with three different layer heights (6, 13, and 20 mm) are printed, and extracted cubes are subjected to compression (i) along the direction of printing, (ii) along the direction of layer build-up, and (iii) perpendicular to the above two directions. Digital image correlation (DIC) is used as a non-contact means to acquire the strain profiles. While the 3D printed specimens show lower strengths, as compared to cast specimens, when tested in all three directions, this effect can be reduced through the use of fiber reinforcement. Peak stress and peak strain-based anisotropy coefficients, which are linearly related, are used to characterize and quantify the directional dependence of peak stress and strain. Interface-parallel cracking is found to be the major failure mechanism, and anisotropy coefficients increase with an increase in layer height, which is attributable to the increasing significance of interfacial defects. Thus, orienting the weaker interfaces appropriately, through changes in printing direction, or strengthening them through material modifications (such as fiber reinforcement) or process changes (lower layer height, enables attainment of near-isotropy in 3D printed concrete elements.

Quantitative assessment of the effect of in-situ stresses on blast-induced damage to rock

In-situ stress significantly affects rock blast damage but there is a paucity of quantitative assessments of damage evolution in rocks affected by confining pressure. The present paper analyses the effect of envelope pressure on blast-induced rock damage through theoretical analysis and numerical simulations. Damage clouds obtained from numerical simulations are processed using image processing techniques. The concept of the damage variable (η) is proposed to facilitate the presentation of the image processing results. The damage variable is found to be negatively correlated with the hydrostatic pressure (Px) at the same moment, in equiaxial in-situ stress fields. In contrast, in anisotropic in-situ stress fields, η is not negatively correlated with Px due to the presence of hoop tensile stresses in the rock. The mathematical relationship between η and Px in equiaxial and anisotropic stress fields are established. An anisotropic damage variable (ηk) is introduced to describe the effect of the anisotropy ratio (K) on rock damage, which is found to increase with increasing values of K. The sharp increase in K equal to 4 and 5 is explained in terms of the state of the rock stress distribution under static loading. This study provides insights into the effect of in situ stress on rock blast damage and presents new approaches for analyzing and presenting the data.

Feature importance in neural networks as a means of interpretation for data-driven turbulence models

This work aims at making the prediction process of neural network-based turbulence models more transparent. Due to its black-box ingredients, the model’s predictions cannot be anticipated. Therefore, this paper is concerned with the quantification of each feature’s importance for the prediction of trained and fixed NNs, which is one possible type of explanation for opaque models. Two conceptually different attribution methods, namely permutation feature importance and DeepSHAP, are chosen in order to assess global, regional and local feature importance. The neuralSST turbulence model, which serves as an example, will be investigated in greater detail. While the global importance scores provide a quick and reliable way to detect irrelevant features and may thus be used for feature selection, only the (semi-)local analysis provides meaningful and trustworthy interpretations of the model. In fact, the local importance scores suggest that hypotheses with a common high-level influence on the turbulence model, e.g. adjusting the net production of turbulent kinetic energy or the Reynolds stress anisotropy, are similarly affected by local mean flow structures such as attached boundary layers, free shear layers or recirculation zones.

About the role of the Hanratty correction in the linear response of a turbulent flow bounded by a wavy wall

Scallop patterns forming on erodible surfaces were studied historically using a linear analysis of the inner region of a turbulent boundary layer growing on a corrugated wall. Experimental observations show a phase shift between the shear stress at the wall and the wall oscillation that depends on the wavenumber. Anad hoccorrection applied to the turbulent closure and due to Hanrattyet al.(Thorsnesset al.,Chem. Engng Sci., vol. 33, issue 5, 1978, pp. 579–592; Abrams & Hanratty,J. Fluid Mech., vol. 151, issue 1, 1985, p. 443; Frederick & Hanratty,Exp. Fluids, vol. 6, issue 7, 1988, pp. 477–486) was systematically used to recover the reference experimental results. In this study, Reynolds-averaged Navier–Stokes (RANS) and direct numerical simulations (DNS) were performed and revealed the role of the Boussinesq assumption in the results obtained. We show that the Hanratty correction acts as a palliative to the misrepresentation of Reynolds stresses due to the use of the Boussinesq hypothesis. The RANS calculations based on a turbulence model using a second-order moment closure recovered the expected results obtained in the reference DNS calculations, in particular with respect to wall heat transfer. The analysis of these results highlights the critical importance of the anisotropy of the diagonal Reynolds stresses on the prediction of wall transfer under these conditions and their implication in the occurrence of scalloping.

A Hybrid Approach to Rock Pre-conditioning Using Non-explosive Demolition Agents and Hydraulic Stimulation

This study presents a novel approach to rock pre-conditioning to promote the sustainability of low-grade ore mining applications such as in-situ recovery and cave mining. The proposed method involves a two-stage hybrid approach, utilizing soundless cracking demolition agents (SCDAs) to initiate radial fractures in a predrilled host rock, followed by hydraulic stimulation to extend the fractures. SCDA injection in the first stage creates multiple radial fractures around the injection well. However, the extent of fractures is limited to the near vicinity of the injection well. To overcome this limitation, the second stage involves the application of hydraulic stimulation to extend the initiated fractures, which produces a greater fracture density compared to pure hydraulic stimulation. The concept was assessed using a fully coupled hydro-mechanical discrete element model that simulated the hybrid fracturing method on crystalline rock at the grain scale. The results indicate that the proposed method can create a high density of fractures around the injection well. Additionally, we identify and evaluate the key factors affecting the performance of the proposed method, including rock mass heterogeneity, stress anisotropy, and pre-existing defects, providing valuable insights for further experimental design and execution. Overall, the study offers promising results for a potential solution to enhance the efficiency of low-grade ore mining through the hybrid rock pre-conditioning method.

Solubility of NaCl under anisotropic stress state.

Salt solubility is generally determined under isotropic stress conditions. Yet, in the context of salt weathering of porous media, mechanical constraints on the in-pore growth of salt crystals are likely to be orientation-dependent, resulting in an anisotropic stress state on the crystal. In this paper, we determine by molecular simulation the solubility of NaCl in water when the crystal is subjected to anisotropic stress. Such anisotropy causes the chemical potential of the crystal to be orientation-dependent, and proper thermodynamic formulation requires describing the chemical potential as a tensor. The solute and crystal chemical potentials are computed from free energy calculations using Hamiltonian thermodynamic integration, and the usual condition of solubility is reformulated to account for the tensorial nature of the crystal chemical potential. We investigate in detail how the uniaxial compression of the crystal affects its solubility. The molecular simulation results led to revisiting the Correns law under anisotropic stress. Regarding the solute, the non-ideal behavior of the liquid phase is captured using Pitzer's ion interaction approach up to high concentrations of interest for in-pore crystallization and beyond the concentrations addressed in the existing literature. Regarding NaCl crystals, the validity of the generalized Gibbs-Duhem equation for a tensorial chemical potential is carefully verified, and it is found that crystallization progresses almost orthogonally to the crystal surface even under high shear stresses. Comparing uniaxial and isotropic compression highlights the major differences in solubility caused by stress anisotropy, and the revisited Correns law offers an appropriate framework to capture this phenomenon.

Present–day crustal deformation in the southeastern Tibetan Plateau: Insights from three–dimensional finite–element modeling

Quantifying the present–day kinematics of southeastern Tibet is important for understanding the tectonic evolution of the Tibetan Plateau. In this study, we established a three–dimensional finite element model to estimate fault slip and strain rates in the southeastern Tibetan Plateau based on Global Navigation Satellite Systems (GNSS) observations. Our model yields an overall good fit to the GNSS velocity field with residuals of 0.83 mm/yr and 0.85 mm/yr for the east and north components, respectively, comparable to the uncertainties of 0.67 mm/yr and 0.61 mm/yr. The model–derived strike–slip rates of the Xiaojiang fault, Nanhua–Chuxiong fault, Qujiang fault, central segment of Red River fault, southeastern segment of Red River fault and Dien Bien Phu fault are 13.7 ± 0.7 mm/yr, 1.9 ± 0.6 mm/yr, 3.4 ± 1.1 mm/yr, 1.5 ± 0.5 mm/yr, 1.2 ± 0.4 mm/yr and 1.6 ± 0.4 mm/yr, respectively, which are consistent with previous geological results, implying that the short–term fault motions estimated from GNSS data can reflect the long–term fault slip in the southeastern Tibetan Plateau. The shear strain rate is localized along the Xiaojiang fault, which agrees with predictions of the tectonic extrusion model (i.e., the lateral extrusion of internally rigid blocks along strike-slip faults). Strain orientations in the western part of southeastern Tibetan Plateau are characterized by clockwise rotation. Comparison of the surface strain rates, crustal stress, and seismic anisotropy reveals general consistency between deformation of the surface and upper crust. The eastern part of southeastern Tibetan Plateau has small residuals, and the present–day crustal deformation can be explained by rigid block motion. However, the western part of the study area has relatively large residuals, implying that other processes, such as gravitational spreading, may influence deformation in the area. We propose a hybrid model that combines rigid block motion with continuum deformation to explain the contemporary crustal deformation of southeastern Tibetan Plateau.

High-throughput characterization of cortical microtubule arrays response to anisotropic tensile stress

BackgroundPlants can perceive and respond to mechanical signals. For instance, cortical microtubule (CMT) arrays usually reorganize following the predicted maximal tensile stress orientation at the cell and tissue level. While research in the last few years has started to uncover some of the mechanisms mediating these responses, much remains to be discovered, including in most cases the actual nature of the mechanosensors. Such discovery is hampered by the absence of adequate quantification tools that allow the accurate and sensitive detection of phenotypes, along with high throughput and automated handling of large datasets that can be generated with recent imaging devices.ResultsHere we describe an image processing workflow specifically designed to quantify CMT arrays response to tensile stress in time-lapse datasets following an ablation in the epidermis — a simple and robust method to change mechanical stress pattern. Our Fiji-based workflow puts together several plugins and algorithms under the form of user-friendly macros that automate the analysis process and remove user bias in the quantification. One of the key aspects is also the implementation of a simple geometry-based proxy to estimate stress patterns around the ablation site and compare it with the actual CMT arrays orientation. Testing our workflow on well-established reporter lines and mutants revealed subtle differences in the response over time, as well as the possibility to uncouple the anisotropic and orientational response.ConclusionThis new workflow opens the way to dissect with unprecedented detail the mechanisms controlling microtubule arrays re-organization, and potentially uncover the still largely elusive plant mechanosensors.

Study on Laser Scan Strategy for Correcting Anisotropic Residual Stress Distribution and Reducing Warpage in Structures Fabricated by PBF-LB/M

Metal-based powder bed fusion with a laser beam (PBF-LB/M) can be applied to fabricate high-accuracy structures compared with other metal additive manufacturing (AM) methods. The rapid solidification of metal powder formed by laser irradiation introduces heterogeneous residual stress, which causes deformation and cracking of the structure. This, in turn, results in the deterioration of quality. In this study, the influence of the laser scan strategy on the residual stress distribution and warpage of the structure was investigated. Using maraging steel powder with an average particle size of 32.5 μm, the structures were constructed using several laser scan strategies at a wavelength of 1070 nm. The residual stress distributions on the surface of the structures were measured by the cosα method by applying X-ray diffraction (XRD). In addition, the warpage of the reverse side of the substrate as a foundation of the structure was measured by a stylus-type surface roughness measuring instrument. The results clarified that the structures constructed by unidirectional scan directions had a tensile residual stress that was generated parallel to the laser scan direction. Meanwhile, the compressive residual stress was generated perpendicular to the laser scan direction. The large warpage was aligned with the laser scan direction and tensile residual stress. When the laser scan direction was rotated by 90° for each layer, the residual stress distribution was generated with a cruciform shape. It was indicated that this residual distribution was caused by a laser scan on the top surface and a lower layer. The anisotropic residual stress distribution and reduction of warpage could be corrected by rotating the laser scan direction by 15° in each layer.

Crack deflection in shale-liked layered rocks under three-point bend loading

The bedding angle has a significant influence on the fracturing of anisotropic geomaterials, such as shale rock, and crack deflection usually takes place during crack propagation. To better understand and estimate the tensile crack deflection in shale, 35 large notched deep beam (NDB) specimens with different bedding angles—0° (Short-Transverse), 15°, 30°, 45°, 60°, 75°, and 90° (Arrester)—were tested under three-point bend (3PB) loading. For mode I dominated loadings, significant expected anisotropies in both fracture toughness and crack deflecting behavior were observed. The nominal mode I fracture toughness showed a progressive decrease from the arrester to the short-transverse orientation, with values from 1.371 MPa·m1/2 to 0.731 MPa·m1/2. When the bedding angle was less than or equal to 60°, the crack deflection induced the difference between the nominal and actual fracture toughness. By introducing the weak plane model to describe the fracture toughness of shale, an anisotropic K-type maximum tangential stress criterion (KMTS criterion) was presented. Using the KMTS criterion, the deflection angle and fracture load for an arbitrary bedding angle could be obtained conveniently with fracture toughness values in both arrester and short-transverse orientations. The comparison between theoretical predictions and experimental data demonstrated that the KMTS criterion could provide a dependable prediction, particularly for the slight deflection when the crack propagates within the matrix.