Stress Boundary Research Articles

Phase Field Modeling of Hydraulic Fracturing with Length-Scale Insensitive Degradation Functions

A length-scale insensitive degradation function is applied to extend the cracks during hydraulic fracturing under stress boundary conditions in this study. The phase field method is an effective modeling technique that has great potential for use in hydraulic fracturing. Nonetheless, current hydraulic fracturing research is still concentrated on small scales. The phase field model employs a degradation function that is insensitive to length scale, allowing for the decoupling of the phase field length scale from the physical length scale. This facilitates the simulation of hydraulic fracturing crack extensions in larger structures with a consistent mesh density. The correctness of the phase field method is verified firstly by comparing with the experimental results, and the accuracy and efficiency of the proposed method are further verified through a series of numerical calculations.

Influence of roof confined water drainage on stress distribution in coal seam

Coal and gas outbursts, along with rock bursts, are common dynamic disasters in coal mining, threatening the safety and green production of coal mines. The distribution of coal seam stress is an external factor contributing to coal mine power disasters. The drainage of confined water in coal seam roof is the primary factor of coal seam stress changes. Using theoretical analysis and numerical simulations, the influence of roof confined water on coal seam stress by looking at the law of stress and stress conservation transfer in the drainage layer is investigated. Our results show that: (1) after drainage, there is an increase in the local stress within the coal seam, with a stress concentration factor of 1.35. The influence range of theoretically calculated stress is consistent with the measured results. (2) the maximum value of drainage boundary stress correlated positively with the angle of the water-rich abnormal area, with a linear fitting of R2 = 0.98. These findings hold significant theoretical and practical implications for preventing and controlling dynamic disasters during the mining of water-rich coal seams.

Nonmonotonic rheology and stress heterogeneity in confined granular suspensions

We systematically investigated the impact of boundary confinement on the shear-thickening rheology of dense granular suspensions. Under highly confined conditions, dense suspensions were found to exhibit size-dependent or even rarely reported nonmonotonic (S-shaped) flow curves in steady states. By performing in situ boundary stress microscopy measurements, we observed enhanced flow heterogeneities in confined suspensions, where concentrated high-stress domains propagated stably either along or against the shear direction. By comparing the boundary stress microscopy results with macroscopic flow responses, we revealed the connection between nonmonotonic rheology and stress heterogeneity in confined suspensions. These findings suggest the possibility of controlling suspension rheology by imposing different boundary confinements.

A DSMC-CFD coupling method using surrogate modelling for low-speed rarefied gas flows

A new Micro-Macro-Surrogate (MMS) hybrid method is presented that couples the Direct Simulation Monte Carlo (DSMC) method with Computational Fluid Dynamics (CFD) to simulate low-speed rarefied gas flows. The proposed MMS method incorporates surrogate modelling instead of direct coupling of DSMC data with the CFD, addressing the limitations CFD has in accurately modelling rarefied gas flows, the computational cost of DSMC for low-speed and multiscale flows, as well as the pitfalls of noise in conventional direct coupling approaches. The surrogate models, trained on the DSMC data using Bayesian inference, provide noise-free and accurate corrections to the CFD simulation enabling it to capture the non-continuum physics. The MMS hybrid approach is validated by simulating low-speed, steady-state, force-driven rarefied gas flows in a canonical 1D parallel-plate system, where corrections to the boundary conditions and stress tensor are considered and shows excellent agreement with DSMC benchmark results. A comparison with the typical domain decomposition DSMC-CFD hybrid method is also presented, to demonstrate the advantages of noise-avoidance in the proposed approach. The method also inherently captures the uncertainty arising from micro-model fluctuations, allowing for the quantification of noise-related uncertainty in the predictions. The proposed MMS method demonstrates the potential to enable multiscale simulations where CFD is inaccurate and DSMC is prohibitively expensive.

Mechanical Simulation and Optimization Analysis of Slab Continuous Casting Process for Automobile

Abstract With the development trend of automobile lightweight, the continuous casting process of automobile slab is more and more demanding. In this paper, the stress conditions and boundary conditions in the deoxidizer of the continuous casting process were analyzed, and a contact mechanics model was established between the cast slab and the copper plate. The deformation laws of the slab shell under different amplitude and frequency were simulated and analyzed, and the amplitude and frequency parameters that minimize the impact of slag marks on the slab shell were determined, providing a basis for selecting reasonable vibration parameters.

An alternative stress boundary condition in small deformations and its application to soft elastic composites and structures

Linear elasticity theory has been used extensively in the study of the elastic behavior of various perforated structures and composite materials requiring the accompaniment of appropriate boundary conditions to derive qualitatively correct and quantitatively referential solutions. When incorporating conventional boundary conditions, however, linear elasticity theory fails to predict certain essential phenomena associated with perforate structures and composite materials even when they undergo small deformations. For example, a soft elastic porous medium is appreciably stiffened when inflated despite the fact that the internal air pressure is significantly lower than the modulus of the medium itself. In this paper, we propose an improved stress boundary condition by simply incorporating a small change in the normal to the boundary during deformation. We show via numerical examples that in the context of linear elasticity theory, the use of this improved boundary condition offers the possibility of predicting the influence of initial or residual stress in a perforated structure on the elastic response of the structure to external loadings (which can never be captured with the use of conventional boundary conditions). We perform also large-deformation-based finite element simulations to verify the accuracy of the closed-form results obtained from the improved boundary condition for a soft elastic perforated structure with initial internal pressure. We believe that the idea presented in this paper will extend the applicability of linear elasticity theory and yield more accurate referential analytic results for soft elastic structures and composites.

Physics-Informed Holomorphic Neural Networks (PIHNNs): Solving 2D linear elasticity problems

We propose physics-informed holomorphic neural networks (PIHNNs) as a method to solve boundary value problems where the solution can be represented via holomorphic functions. Specifically, we consider the case of plane linear elasticity and, by leveraging the Kolosov–Muskhelishvili representation of the solution in terms of holomorphic potentials, we train a complex-valued neural network to fulfill stress and displacement boundary conditions while automatically satisfying the governing equations. This is achieved by designing the network to return only approximations that inherently satisfy the Cauchy-Riemann conditions through specific choices of layers and activation functions. To ensure generality, we provide a universal approximation theorem guaranteeing that, under basic assumptions, the proposed holomorphic neural networks can approximate any holomorphic function. Furthermore, we suggest a new tailored weight initialization technique to mitigate the issue of vanishing/exploding gradients. Compared to the standard PINN approach, noteworthy benefits of the proposed method for the linear elasticity problem include a more efficient training, as evaluations are needed solely on the boundary of the domain, lower memory requirements, due to the reduced number of training points, and C∞ regularity of the learned solution. Several benchmark examples are used to verify the correctness of the obtained PIHNN approximations, the substantial benefits over traditional PINNs, and the possibility to deal with non-trivial, multiply-connected geometries via a domain-decomposition strategy.

Laser energy-dependent processability of non-equiatomic TiNbMoTaW high-entropy alloy through in-situ alloying of elemental feedstock powders by laser powder bed fusion

Pre-alloyed powder, which is primarily used in laser powder bed fusion (LPBF), has the disadvantages of requiring time and high manufacturing costs. To overcome these limitations, in-situ alloying, which mixes pure elemental powders and alloys them in real-time during the LPBF process, has attracted attention. In particular, manufacturing high entropy alloys (HEA) containing high-melting-point refractory elements through in-situ alloying presents considerable challenges. In this study, a non-equiatomic single body-centered cubic (BCC) solid-solution HEA was fabricated via in-situ alloying with Ti, Nb, Mo, Ta, and W powders through the LPBF process. Specifically, by applying a high volumetric energy density (VED), we successfully mitigated the segregation of constituent elements, leading to an enhanced crystallographic texture. Consequently, the reduction in the residual stress and high-angle grain boundary (HAGB) density progressed, contributing to an increased relative density. Thus, this study marks a pioneering endeavor for in-situ alloyed HEA fabrication via LPBF, illustrating the efficacy of in-situ alloying utilizing mixed powders.

Radiation in holography

We show how to encode the radiative degrees of freedom in 4-dimensional asymptotically AdS spacetimes, using the boundary Cotton and stress tensors. Background radiation leads to a reduction of the asymptotic symmetry group, in contrast to asymptotically flat spacetimes, where a non-vanishing news tensor does not restrict the asymptotic symmetries. Null gauges, such as Λ-BMS, provide a framework for AdS spacetimes that include radiation in the flat limit. We use this to check that the flat limit of the radiative data matches the expected definition in intrinsically asymptotically flat spacetimes. We further dimensionally reduce our construction to the celestial sphere, and show how the 2-dimensional celestial currents can be extracted from the 3-dimensional boundary data.

Process-based reconstruction of digital rock based on discrete element method considering thermal-mechanical coupling effect and actual particle shape

The digital rock is a crucial platform for numerical simulations of pore-scale flow in various fields such as geo-energy, carbon (CO2) sequestration, and hydrogen (H2) storage. Under these conditions, rocks deform, and pore structures change due to temperature and stress effects. However, existing methods for reconstructing digital rocks, such as physical experimental, stochastic simulation, and machine learning, can not consider the influence of high temperature and stress. Therefore, a process-based reconstruction method based on the discrete element method (DEM) considering the thermal-mechanical coupling effect is proposed in this paper. Initially, the computed tomography (CT) images are segmented based on the watershed algorithm, and a contour database is established using the spherical harmonic analysis method. A clump template library is then constructed in PFC3D (Particle Flow Code in 3 Dimensions). Subsequently, the DEM model is established using clumps from the template library according to porosity and particle radius distribution, and the model's accuracy is evaluated based on two-point and linear path correlation functions. Micro-mechanical and thermal parameters between particles are calibrated, and different temperature and stress boundary conditions are applied to obtain digital rocks under varying conditions. Finally, digital rocks' geometric and topological structures under different conditions are analyzed, and permeability and relative permeability are calculated. Using Bentheim sandstone as an example, digital rocks are constructed under various temperature and stress conditions. The research findings indicate that high temperatures and stress result in decreased pore and throat radii, elongated throats, deteriorated connectivity, reduced porosity, and permeability, making the digital rocks more water-wet. This study provides theoretical guidance for the accurate pore-scale flow simulation of geo-energy fluids, CO2, and H2.

Effects of irradiation plus thermal aging on the phase boundary microstructure of austenitic stainless steel welds

Irradiation damage and thermal aging greatly affect the phase boundary microstructure and stress corrosion cracking of austenitic stainless steel weld metals (ASSWMs) in water-cooled nuclear reactors. However, the effects of irradiation plus thermal aging (I + A) on the phase boundary segregation and phase changes remain unclear. Phase changes and elemental segregation at the carbide and carbide-free phase boundaries of 308 L ASSWMs after I + A treatment were investigated using atom probe tomography and transmission electron microscopy. The I + A treatment induced Si depletion at the phase interfaces of δ-ferrite/austenite (δ/γ) and δ-ferrite/carbide (δ/C) and also induced Ni enrichment and Cr depletion with concentrations having the order Ni/Cr(δ/γ) > Ni/Cr(δ/C) > Ni/Cr(γ/C). The solute-defect binding model and the vacancy mechanism were applied to explain the phase boundary segregation. Furthermore, the I + A treatment affected microstructural evolution near the phase boundaries; this reduced spinodal decomposition and inhibited G-phase and Ni/Si-rich-cluster formation. The phase separation of δ-ferrite near δ/γ and δ/C phase boundaries differed with the distance from the boundary, forming a gradient microstructure from phase boundaries to δ-ferrite internally. The gradual precipitation of the G-phase was observed beyond about 15 and 10 nm from the δ/γ and δ/C interfaces, respectively; moreover, the growth of α'-phase in the δ-ferrite was accelerated with increasing distance from the δ/γ and δ/C interfaces.

The mechanical coupling effect of α and β phases in Ti6Al4V alloy undergoing laser shock peening: A molecular dynamics study

In the dual- or multi-phase metallic materials, the influence of different microstructural constituents on the plastic strain/stress distribution is still an area of great controversy. Herein, the heterogeneous deformation behavior of α and β phases in Ti6Al4V duplex titanium alloy undergoing laser shock peening (LSP) has been investigated by molecular dynamics simulations, and the corresponding typical microstructural features are characterized at varied strains. Also, the relationship between the theoretical microstructural morphologies and the micro stress is revealed. It evidently indicates that, the grain refinement process can be summarized as: (i) dislocation motions1 interacting with deformation twins in α phases, (ii) a combination of dislocation propagations and the deformation-induced phase transition from β phase to α phase. In addition, unlike the α single-phase titanium alloy, the representative stress – strain curve of α + β titanium alloy presents a gentle fluctuation trend with smaller amplitude value, suggesting an occurrence of the coupling deformation behavior between α and β phases. The initial interfacial dislocation nucleation prefers to site in the α/α interface rather than the α/β interface, then emitting to the interior of α grains. Features of dislocation slip, twin growth, stacking fault, and phase transformation dominate the release of LSP-generated micro stress, while grain and interphase boundaries, as well as dislocation locks, contribute to the increment of the LSP-generated micro stress.

Elasticity solutions of clamped laminated arches with temperature-dependent material properties under thermo-mechanical loading

The mechanical behaviors of the clamped laminated arch with temperature-dependent material properties under the thermal and mechanical loadings are studied in this paper. An analytical method based on the theory of thermoelasticity is proposed for predicting the exact solutions of stresses and displacements in the arch with arbitrary thickness and layer numbers. The clamped support is equivalent to a simply support with a support reaction with the unit pulse function and the Dirac function. The space state method is utilized to establish the state equation by employing the displacements and stresses as the state variables. A slice model is introduced to simplify the coefficient matrix. Based on the continuities at the interfaces, the displacement and stress relationships between the internal and external surfaces of the laminated arch are derived with the transfer matrix method. Exact solutions for the displacements and stresses can be obtained according to the stress boundary conditions on the surfaces of the laminated arch. Finally, convergence and comparison studies demonstrate the excellent efficiency and accuracy of the present method. The influences of material dependency with temperature, thermal load, and thickness-to-radius ratio on the distributions of displacements and stresses are discussed in detail.

Stress and flow inhomogeneity in shear-thickening suspensions

HypothesisThe viscosity of dense suspensions surges when the applied stress surpasses a material-specific critical threshold. There is growing evidence that the thickening transition involves non-uniform flow and stress with considerable spatiotemporal complexity. Nevertheless, it is anticipated that dense suspensions of calcium carbonate particles with purely repulsive interactions may not conform to this scenario, as indicated by local pressure measurements with millimeter spatial resolution. ExperimentHere we utilize Boundary Stress Microscopy (BSM), a technique capable of resolving stresses down to the micron scale, to search for evidence of stress heterogeneity. In addition, we measure the flow field at the lower boundary of the suspension where the boundary stress is measured. FindingsWe find localized regions of high-stresses that are extended in the vorticity direction and propagate in the flow direction at a speed approximately half that of the rheometer's top plate. These high-stress regions proliferate with the applied stress accounting for the increased viscosity. Furthermore, the velocity of particles at the lower boundary of the suspension shows a significant and complex nonaffine flow that accompanies regions of high-stresses. Hence, our findings demonstrate that stress and flow inhomogeneity are intrinsic characteristics of shear-thickening suspensions, regardless of the nature of interparticle interactions.

Investigating corrosion-induced deterioration in bolted steel plate joints using guided wave ultrasonic inspection

AbstractBolted steel plate joints encounter challenges posed by joint corrosion, which impact the quality of interfacial contact among the bolted components. Unfortunately, no correlation between corrosion-induced joint damage and preload, nor an existing numerical model capable of capturing such effects, has been identified. This study aims to utilize guided wave ultrasonic investigation to examine the deterioration of interfacial contact caused by corrosion in bolted joints. Additionally, a contact modification-based numerical approach is presented to capture the effects of changing interfacial stress during joint corrosion. Guided wave mode selection was conducted with some preliminary experiments supplemented with the theory of wave mode dispersion, hence leading to the selection of S0 and A0 mode existing at 300 kHz. The joint was then corroded in a controlled manner using an electrochemical process while simultaneous ultrasonic measurements were taken. The experimental observations highlighted the progressive dispersion in the transmitted A0 mode across the bolted joint, potentially due to changing interfacial stress boundaries between the plates. A damage parameter, termed the dispersion index, was developed based on the energy ratio of different signal sections. A linear change in the dispersion index was observed with the increase in corrosion-induced mass loss. The insight was further established through a numerical investigation by studying the effect of changing bolt preload and the corresponding interfacial stress distribution. The findings revealed that monitoring the changes in the stress distribution at the bolted interface can provide insight into interfacial corrosion. Eventually, destructive tension test results confirmed the effect of joint corrosion on the load-bearing capacity of the joint. The change in failure mode of the pristine and corroded specimen is observed. The reported approach establishes the potential of ultrasonic inspection to investigate the interfacial health of a bolted joint in corroding conditions.

The virtual stress boundary method to impose nonconforming Neumann boundary conditions in the material point method

The virtual stress boundary method to impose nonconforming Neumann boundary conditions in the material point method

Renormalization group flows in AdS and the bootstrap program

We study correlation functions of the bulk stress tensor and boundary operators in Quantum Field Theories (QFT) in Anti-de Sitter (AdS) space. In particular, we derive new sum rules from the two-point function of the stress tensor and its three-point function with two boundary operators. In AdS2, this leads to a bootstrap setup that involves the central charge of the UV limit of the bulk QFT and may allow to follow a Renormalization Group (RG) flow non-perturbatively by continuously varying the AdS radius. Along the way, we establish the convergence properties of the newly discovered local block decomposition of the three-point function.

Modeling the Hydraulic Fracturing Processes in Shale Formations Using a Meshless Method

Complex bedding properties and in situ stress conditions of shale formation lead to complex hydraulic fracturing morphologies. However, due to the limitations of traditional numerical methods, the simulation of hydraulic fracturing in shale formation still needs further development. Based on this, the liquid–solid interaction modes and the SPH governing equations considering liquid–solid interaction force have been introduced. The smoothing kernel function in the traditional SPH method is improved by introducing the fracture mark ξ, which can realize the simulation of rock hydraulic fracturing processes. The stress boundary of the SPH method is applied by stress mapping of “stress particles”, and the feasibility and correctness of the method are verified by two numerical examples. Then, the simulation of hydraulic fracturing processes of bedding shale formations are carried out. With the increase of horizontal stress ratio, the total number of damaged particles decreases, but the initiation and extension pressure increase gradually. The initiation stress of small bedding dip angles (θ < 45°) is larger than that of big bedding dip angles (θ > 45°). The hydraulic fracture propagation range at low horizontal stress ratio is wider and the fracture is along the direction of maximum principal stress, while the hydraulic fracture propagation range at high horizontal stress ratio is limited to the perforation. The hydraulic fracture will propagate through the bedding with small dip angles. However, when the bedding dip angle is larger, the hydraulic fracture will propagate along the bedding direction.

PERSPECTIVE: Interfacial stresses in thin film drainage: Subtle yet significant

Film drainage, essential in droplet and bubble coalescence and surface wetting, is influenced strongly by the stress boundary condition, in particular, when interfacial stresses are present. These stresses, caused by ubiquitous surface-active components, significantly impact the dynamics of liquid films. Through dynamic thin film balance experiments, we compare the effects of Marangoni stresses, interfacial viscosity, and interfacial viscoelasticity on the drainage of free-standing thin liquid films. These data serve to demonstrate that film deformation intricately depends on the interplay between these stresses and capillarity, resulting in widely varied drainage times. Seemingly subtle changes, especially in the local stress-carrying capacity of the interface, can lead to significant differences in film dynamics. This makes it a promising area for research into interfacial-rheologically active materials for stabilizing potentially more sustainable multiphase materials.

Insensitivity of Grain boundary Stress Fields to Area Variations

The atomistic simulations in this article substantiate that grain boundary stress fields remain unaffected by changes in their area, aligning with the Olson–Cohen theory which supports that such area insensitivity is an inherent outcome of the combined effect of coherency and anti‐coherency dislocations. Twist grain boundaries are employed in α‐iron as a model in atomistic simulations, revealing and contrasting the dislocations and stresses of these grain boundaries when their area varies from infinity to a few square nanometers. It is discovered that the grain boundary stresses remain relatively constant, always short‐ranged. Furthermore, within the framework of the Frank–Bilby equation, the line directions and spacing of coherency and anti‐coherency dislocation arrays in a grain boundary are predicted, the stresses of these dislocations are subsequently calculated numerically, and these stresses are superimposed together to form the grain boundary stress field. The numerical calculations verify that stress fields of grain boundaries are not sensitive to changes of their area, corroborating our atomistic simulations. The preliminary atomistic simulations of various homophase and heterophase boundaries further affirm this area insensitivity.