Three-dimensional Stress Research Articles

Failure mechanism and control technology of soft-rock roadways subjected to high structural stress

The prevention and control of deformation and instability in high-stress soft rock roadways hold significant value for ensuring normal mine production and the safety of personnel and equipment. This study focuses on the pedestrian descent from the 11th mining area of the Yindonggou Mine, providing a thorough elucidation of the internal mechanisms leading to large deformation and instability in the roadway. It accounts for the influences of surrounding rock lithology, geological structure, and support measures. Consequently, based on the theory of rock instability, corresponding tunnel repair measures and control strategies were proposed and verified through field application. The results indicate that: (1) High strength dispersion and insufficient support resistance of the expansive weak and fractured surrounding rock sections are critical factors inducing significant deformation in the soft rock roadway of Yindonggou Mine. (2) The primary factor contributing to the large deformation disaster in the Yindonggou Mine roadway is the disturbance caused by proximate coal seam mining, which exacerbates the conflict between the high structural stress in the strata and the low strength of the surrounding rock. High-level stress initially leads to deformation in the weakly supported floor, followed by deformation and instability of the surrounding rock, ultimately culminating in the collapse of the entire roadway section. (3) Soft rock support should be designed with varying schemes tailored to the rock type and structural stress of the surrounding rock in the tunnel. For tunnels with carbon mudstone and expansive soft rock as the main roof and floor components, the support plan should primarily focus on enhancing the support stiffness of the tunnel wall. Conversely, for tunnels where sandstone predominates as the roof and floor material, the support plan should aim to restore the three-dimensional stress state of the surrounding rock and fully utilize its self-supporting capacity. (4) Based on the engineering conditions of pedestrian downhill in No.11 mining area of Yindonggou Mine, a differentiated support scheme is proposed. The feasibility and effectiveness of each support scheme are verified by numerical simulation, so as to provide valuable reference and enlightenment for similar projects.

Asymmetric deformation and failure behavior of roadway subjected to different principal stress based on biaxial tests

The magnitude and direction of stress will affect the failure of roadway. The impact of stress magnitude and direction on roadway failure was investigated using a rock failure system equipped with true triaxial loading, acoustic emission (AE), and digital image correlation (DIC) technologies. The system allowed for the simulation of rock sample failures under various three-dimensional stress conditions, while real-time monitoring was conducted using a high-precision microseismic system. By prefabricating rectangular holes at different angles in sandstone specimens, roadways under different stress effects in engineering can be simulated. Biaxial loading tests were then performed on these prefabricated sandstone cube specimens to observe external fracture characteristics and internal fracture information using acoustic emission equipment. The peak strength of samples with holes is approximately 38–56% of that of intact samples. In the early and middle loading stages, the strain on the surface is on the order of 10-3. In the later loading stage, the strain on the surface is on the order of 10-2. The findings indicate that roadway failure primarily involves local particle ejection, fragment spalling, large-scale particle ejection, plate crack buckling, and eventual failure. The ultimate failure mode varies based on stress deflection angles: with no included angle, the roadway exhibits a ’V’ shaped failure zone on both sides, predominantly experiencing tensile failure. At included angles of 30°, 45°, and 60° between stress and roadway axis, the roadway displays a “—” failure pattern along the diagonal, characterized by a combination of tension and shear failure. The extension angle of the“—” failure zone varies depending on the stress deflection angle. At a 90° included angle, the roadway shows a ’V’ shaped failure in the roof and floor, primarily undergoing tensile failure. Real-time monitoring of the strain field evolution around the roadway during failure using DIC method revealed valuable insights. AE events at different deflection angles reflect the progression of micro cracks in the specimen, showing a strong correlation with macro failure. The research outcomes elucidate the mechanisms behind various forms of roadway failure induced by stress deflection and shed light on the failure mechanism at different stress deflection angles.

A critical review on free edge delamination fracture criteria

Laminates experience three-dimensional singular stress near their free edges due to elastic mismatches between layers, which can cause delamination. This paper critically evaluates methods for predicting free edge delamination and highlights the limitations of conventional strength-of-materials and fracture mechanics approaches. The Theory of Critical Distances (TCD) uses a material-dependent critical distance parameter, while Finite Fracture Mechanics (FFM) employs a combined stress-energy criterion without needing a predefined length parameter. This review compares TCD and FFM, also discussing Cohesive Zone Models and Phase-Field Models, and aims to guide the selection of appropriate methods for analyzing free edge delamination.

Determination and Application of Stress States Based on Finite Element Techniques: A Case Study of the Longmaxi Formation in the Luzhou Block, Sichuan Basin.

Knowledge of the present-day in situ stress field (PIS) has important theoretical and practical significance for shale gas exploration and development. The Wufeng-Longmaxi Formation in the Luzhou Block serves as the main reservoir of marine shale production in southern China. However, there is no clear understanding of PIS in the Luzhou area, which leads to a series of production problems. To investigate the PIS of deep shale reservoirs in Luzhou, experimental and finite element methods (FEMs) were used. Data obtained from imaging logging data, well deviation data, multipole array acoustic logging (XMAC), and world stress map were used to determine the orientation of the horizontal maximum principal stress (S Hmax). Additionally, acoustic emission experiments were employed to determine the magnitude of three principal stresses. Based on FEM, with the stress of a single well as a constraint, a three-dimensional (3D) stress field model was developed. The results show that the orientation of S Hmax varies from 90 to 120 °E. Further, there are significant differences in stress regimes across the region, with strike-slip/reverse faulting stress regime (S Hmax > S v ≈ S hmin) in the northern region and strike-slip stress regime in the southern region (S Hmax > S v > S hmin). In addition, geomechanical evaluations of wellbore stability and natural activation of fractures were performed. The Luzhou Block mainly develops two groups of natural fractures (NE-SW trending and NW-SE trending), with NW-SE trending being the dominant fracture development orientation. During the fracturing operation, a pore pressure increment larger than 50 MPa is conducive to maintaining a high opening ratio of the reservoir and improving the gas production efficiency. Horizontal wells drilled in the direction of maximum horizontal principal stress in the Wufeng-Longmaxi Formation reduce the probability of wellbore instability. The research results provide a reference for the effective development of deep shale gas reservoirs in southern Sichuan.

An Enhanced Progressive Damage Model for Laminated Fiber-Reinforced Composites Using the 3D Hashin Failure Criterion: A Multi-Level Analysis and Validation.

This paper presents a progressive damage model (PDM) based on the 3D Hashin failure criterion within the ABAQUS/ExplicitTM 2021 framework via a VUMAT subroutine, enhancing the characterization of the mechanical performance and damage evolution in the elastic and softening stages of composite materials via the accurate calculation of damage variables and accommodation of non-monotonic loading conditions. In the subsequent multi-level verification, it is found that the model accurately simulates the primary failure modes at the element level and diminishes the influence of element size, ensuring a reliable behavior representation under non-monotonic loading. At the laminate level, it also accurately forecasts the elastic behavior and damage evolution in open-hole lamina and laminates, demonstrating the final crack band at ultimate failure. This paper also emphasizes the importance of correct characteristic length selection and how to minimize mesh size impact by selecting appropriate values. Compared to ABAQUS's built-in 2D model, the 3D VUMAT subroutine shows superior accuracy and effectiveness, proving its value in characterizing the mechanical behavior and damage mechanisms of fiber-reinforced polymer (FRP) materials. The enhanced 3D PDM accurately characterizes the softening processes in composite materials under simple or complex stress states during monotonic or non-monotonic loading, effectively minimizes the mesh dependency, and reasonably captures failure crack bands, making it suitable for future simulations and resolutions of numerical issues in composite material models under complex, three-dimensional stress states.

Study on the effect of variable laser power on residual stress distribution in laser directed energy deposition of Ti6Al4V

In the laser directed energy deposition (LDED) process, cyclic thermal stress loading induces significant temperature variations on the surface and subsurface of the workpiece during repeated heating, leading to the formation of residual tensile stress during cooling. This adversely affects the mechanical properties of the parts, causing deformation and defects. In this study, a heat transfer model and a three-dimensional stress model were established based on finite element analysis. A variable laser power (VLP) deposition strategy was proposed to dynamically simulate the temperature and stress fields of Ti6Al4V titanium alloy under different deposition strategies. The model was validated by collecting substrate temperature variations using thermocouples and measuring residual stress with an X-ray diffractometer (XRD). Experimental results showed that the temperature error between the simulation and the experiment ranged from 6.25 % to 10.12 %, with an average stress simulation error of 6.92 %. Among the four strategies, the samples using the VLP strategy showed a reduction in the average substrate temperature by 12.68 % to 15.08 % compared to the other three strategies. The maximum principal stress in the layer was reduced by 7.8 % to 32.14 %, and the residual stress distribution was more uniform in all directions. The microstructure of the deposition layer further indicated that the VLP strategy improves residual stress distribution and leading to better deposition quality.

Modelling of cracking during beam oscillation laser welding of a creep-resistant nickel alloy

During high power laser welding of Inconel 740H, horizontal solidification cracks form at locations between approximately 70–80% of the weld depth. With the integration of circular beam oscillation, the laser energy density distribution and underlying thermo-mechanical conditions were altered. By coupling three-dimensional heat transfer, fluid flow, and stress modelling tools, the role that circular beam oscillation plays in the formation of the strain rates and stresses driving this cracking phenomenon was identified. While the addition of a circular oscillation pattern appeared to lower the stress levels along the solidification front, it did not eliminate the appearance of horizontal cracking. Only when the beam amplitudes reached 1.6 mm did solidification cracking disappear, but the weld depths were also significantly reduced.

Three-dimensional fracture modes decoupling by means of invariant integrals in wood under mixed mode loading

This paper addresses the determination of the energy release rate in an orthotropic elastic material such as wood with a three-dimensional view of the problem. The mixed mode loading associated with the anisotropy of the material required mode decoupling by isolating the energy release rates in mode I, mode II and in mode III. These energy release rates are calculated using the invariant integral M of Linear Elastic Fracture Mechanics (LEFM). This decoupling has necessitated the introduction of kinetically and statically admissible three-dimensional virtual displacement and stress fields in the vicinity of the crack front. The fracture mode decoupling strategy is presented and implemented through finite element modelling of a Mixed Mode Crack Growth (MMCG) specimen. Different thicknesses are investigated to highlight the 3D effects. The modelling highlighted the effect of Mode II at the edges of free surfaces for mixed loadings including mode III (mode III, mode (II+III) and mode (I+II+III)), while mode III was the predominant at the middle of the specimen. In cases of mixed mode (I+II), the energy release rate GI was highest at the middle of the specimen and lowest at the edges of the free surfaces, regardless of the degree of mixing for a given thickness. The correlation between the results obtained using the proposed approach and the non-dependence of the integration domain, as well as with the usual approaches employed in the literature, is demonstrated.

Internal radiation effect on semiconductor β-Ga2O3 crystals grown by the VB Method and anisotropic thermal stress

Gallium oxide crystals are semitransparent semiconductors with good optical and electrical properties, which allow their use for several technological applications. During the growth process of β-Ga2O3 crystals, internal radiation plays a crucial role that affects the growth process and then the crystal quality. In this work, the effect of the melt and the crystal transparency on the vertical Bridgman growth of β-Ga2O3 oxide is thoroughly studied. Using a global 2D/3D finite element model, temperature, melt flow, melt-crystal interface, and three-dimensional anisotropic thermal stress are computed at different growth stages. At each stage, four cases are considered, namely, opaque melt and crystal, semi-transparent melt and opaque crystal, semitransparent crystal and opaque melt, and finally semitransparent melt and crystal. The role of internal radiation in each case at different growth stages is then highlighted separately and then coupled together. It was found that the melt-crystal interface is shifted from a convex shape at the early stage to a nearly plane and then to a concave shape at the last stage. The melt flow is then changed from two rolls pattern at the beginning to a single-roll structure at the last stage. Thermal stress of the as-grown ingot is decreased during the growth due to the decrease of temperature non-linearities. Internal radiation inside the crystal acts to increase the melt-crystal interface convexity at the early and middle stages of the growth process and leads to a decrease in its concavity at the final stage. However, the melt transparency leads to the opposite effects, i.e., it decreases the interface convexity at the early stage and increases the interface concavity at the final stage. As a result, for semitransparent crystal and melt, the interface is between the two previous cases. The calculated thermal stresses are found to be more affected by the transparency of the crystal than the melt as the absorption coefficient of β-Ga2O3 crystal is smaller than that of the melt. At all stages, the thermal stresses are found to be larger for the opaque case due to the increase of temperature non-linearities in the crystal. Large values are found at the bottom and the lower part of the periphery. Furthermore, internal radiation inside the melt plays a major role during the early growth stage due to the large liquid volume. It reduces the melt flow intensity close to the free surface where the shear stress is combined with the buoyant force and leads to the flattening of the interface decreasing then the radial temperature gradients, which leads to small attenuation of the thermal stress. At the final stage, the transparency of the melt plays the opposite role due to the increase of the interface concavity which leads to an increase in both of the temperature gradients and the thermal stress inside the crystal. Due to the crystal anisotropy, and especially to the large thermal expansion coefficient in the [010] direction, the 3D thermal stress values are found to be larger in this direction, especially in the bottom part of the ingot. Comparisons with available experimental and numerical works are provided in this paper.

Development of high-efficient asphalt pavement modeling software for digital twin of road infrastructure

To develop digital twin (DT) of road infrastructure, one critical element is computation of pavement responses (strains, stresses, and deflections) under traffic and environmental loading. This study aims to develop high-efficient asphalt pavement modeling software based on semi-analytical finite element method (SAFEM) for DT application. The algorithms address important aspects in vehicle-tire-pavement interaction modeling, such as dynamic vehicular loading, three-dimensional (3-D) non-uniform tire contact stress, viscoelastic behavior of asphalt material, and interface bonding condition. The simulation accuracy is verified by comparison with full-scale test and field measurements, and the relative differences are around 5 % to 20 %. Techniques including optimized discrete Fourier transform, parallel computing, graphics processing unit (GPU) acceleration, and sparse matrices are implemented for computation efficiency. As compared to the traditional 3-D FEM, SAFEM shows significant savings in computation time and storage usage. The high efficiency and accuracy make the software full of potential to be applied for DT of roadway infrastructure.

Three-dimensional elasticity solutions for doubly-curved composite shells by extended differential quadrature method

This paper presents the three-dimensional (3D) stress analysis of doubly-curved composite shells with general boundary conditions using the strong sampling surfaces (SaS) formulation. The SaS method is based on the choice of SaS parallel to the middle surface and located at Chebyshev polynomial nodes to introduce the displacements of these surfaces as unknown functions that leads to a non-conventional shell formulation, in which strain–displacement and stress–strain relationships are represented in terms of SaS displacements. This is due to the use of Lagrange polynomials in approximating displacements, strains and stresses in the thickness direction. The outer surfaces are not included into a set of SaS that makes it possible to uniformly minimize the error ca used by Lagrange interpolation. The strong SaS formulation, based on direct integration of elasticity equilibrium equations in the thickness direction by the extended differential quadrature (EDQ) method, can be applied efficiently for high-precision calculations of doubly-curved composite shells with clamped and free edges. This is because in the SaS/EDQ formulation, displacements, strains and stresses of SaS are interpolated in a rectangular domain specified in a curvilinear coordinate system using a Chebyshev-Gauss-Lobatto grid and Lagrange polynomials are also used as basis functions. The proposed approach deals with equilibrium equations in terms of SaS stresses, avoiding the integration of second order differential equations in terms of SaS displacements, that greatly simplifies the implementation of the EDQ method.

The effect of rock mechanical heterogeneity on induced stress and initiation pressure of multi-cluster fracturing

The stress interference between fracturing clusters in horizontal wells is key in affecting the initiation and propagation of multi-cluster fractures. However, in reservoirs such as shale, there are often changes in the mechanical properties of the rock along the direction of the wellbore. Such changes are often not considered in models for multi-fracture propagation. As a result, the impact of rock mechanical heterogeneity on induced stress is not fully understood. Therefore, in this paper, a prediction model of the three-dimensional induced stress field of hydraulic fractures is established, taking into account mechanical heterogeneity. Combined with the prediction model of fracturing pressure, the changes in induced stress and initiation pressure under different conditions are analyzed. The results indicate a significant difference between the induced stress results considering mechanical heterogeneity and those considering only a single homogeneous region. The change in elastic modulus has a profound influence on induced stress and initiation pressure. Perforating at locations with low elastic modulus in situ can help reduce initiation pressure. Additionally, temporarily blocking the wellbore and reducing the flow rate to decrease the net pressure in the fractures can facilitate more fractures to initiate.

Simulation of the Die and Punch Behavior During the Compaction Process of Alumina-Based Matrix Composite Using Finite Element Analysis

Background: Compaction in the powder metallurgy process typically involves using a die and punch, applying high pressure to mixed powder to achieve product quality, such as geometry, density, and porosity. This step is critical in the powder metallurgy process. Objective: This study aims to systematically design and manufacture a die and punch for compacting an Alumina-based matrix composite. Specimens were selected according to ASTM C 1421-10 guidelines, and the die and punch were constructed using AISI D3 tool steel alloy. Methods: To ensure satisfactory compaction, the design underwent virtual testing using Finite Element Analysis (FEA) with compaction loads ranging from 2.5 to 20 tons in 2.5-ton increments. The simulation results were validated through experimental testing. Results: The die parts were analyzed for three-dimensional stress and deformation during compaction. Maximum stress distribution was observed in the Alumina powder, followed by the punch, plate, and die. Additionally, compaction behavior and density tests confirmed that a compaction pressure of 548 MPa or more results in high relative density in the Alumina-based matrix composite powder during the compaction process. Conclusion: Both simulation and experimental results indicate that a compaction pressure of 548 MPa or more is necessary to achieve satisfactory compaction of the Alumina-based matrix composite. These findings offer practical implications for optimizing the powder metallurgy compaction process and reducing costs.

An online prediction method of three-dimensional machining residual stress field based on IncepU-net

The magnitude and distribution of residual stress field inside thin-walled parts is a critical factor influencing machining deformation. Traditional methods relying on offline data struggle to rapidly and accurately predict evolutionary state of residual stress fields, due to the time-varying and nonlinear characteristics in machining. This paper presents an online prediction method for residual stress in machining thin-walled parts based on deep learning. The multi-channel vector model is proposed to incorporate geometric, physical, and process information as input for deep learning models. A deep learning framework utilizing the IncepU-net network is developed and trained using both experimental and finite element simulation data. Results indicate a mean error of 6.2 MPa compared to experimental values, with an overall prediction time of 0.17 s. The proposed method can online predict the magnitude and distribution of residual stress field in machining, which offers cost-effectiveness and strong generalization capabilities.

Experimental study on the deformation and failure characteristics of cement stone under true triaxial stress state

The cement stone is widely utilized to fill the gap between the formation and the casing in wells. A clear understanding of the deformation and failure mode of cement stone under true triaxial stress state is necessary to ensure the safety and stability of wells. To analyze the three-dimensional deformation and failure characteristics of cement stone, the loading paths with constant Lode angle were employed in conducting true triaxial tests on cement stone. The stress-strain curve and failure mode of cement stone are first analyzed. Then, the three-dimensional deformation characteristics are discussed in meridian and deviatoric planes. Both peak strength and deformability increase with minimum principal stress, but show a tendency to increase and then decrease with intermediate principal stress coefficient. With the increase of minimum principal stress and intermediate principal stress coefficient, the failure mode of cement stone transforms from brittle to ductile behavior. Under elastic stage, the strain path in the meridian plane is a straight line, and is under constant Lode angle within the deviatoric plane. Due to the existence of plastic strain, the strain path in the meridian plane displays a downward convex shape. The strain path in the deviatoric plane deviates from the reference of constant Lode angle for stress, directly reflecting the Lode angle dependence of deformation. Both deformation and failure characteristics of cement stone are dominated by the three-dimensional stress state. Besides, deformation of cement stone is closely related to the failure characteristics of cement stone.

Examination of flow birefringence induced by the shear components along the optical axis using a parallel-plate-type rheometer

In this study, the concept of rheo-optics was applied to explore the flow birefringence induced by the stress components along the camera’s optical axis since it is often overlooked in the traditional theories of photoelastic flow measurement. A novel aspect of this research is that it involved conducting polarization measurements on simple shear flows, specifically from a perspective in which a shear-velocity gradient exists along the camera’s optical axis. A parallel-plate-type rheometer and a polarization camera are employed for these systematic measurements. The experimental findings for dilute aqueous cellulose nanocrystal suspensions demonstrate that the flow birefringence can be expressed as a power law based on the power of the second invariant of the deformation-rate tensor. This suggests that flow birefringence can be universally characterized by the coordinate-independent invariants and a pre-factor determined by the direction of polarization measurement. By adjusting the nonlinear term in the stress-optic law, its applicability could be expanded to include three-dimensional fluid stress fields in which the stress is distributed along the camera’s optical axis.

On stress ratio equations in three-dimensional stress space for modelling soil behaviour

On stress ratio equations in three-dimensional stress space for modelling soil behaviour

On anisotropic local bifurcation based on hypoplastic model

The incipience of shear band in homogeneous granular materials is well captured by the bifurcation analysis. Most bifurcation analyses are based on isotropic plastic constitutive models. In this paper, a hypoplastic constitutive model is presented by considering a fabric tensor for inherent anisotropy. Based on this model, we carry out bifurcation analysis for the plane strain case, and then extend the analysis to consider general three-dimensional stress state. The theoretical results are compared with experiments on sand conducted using a plane strain device and a true triaxial device. It's indicated the salient features of stress-strain behaviour and shear band formation are well captured by our analyses.

Three-dimensional phase field modeling, orientation prediction and stress field analyses of twin-twin, twin-grain boundary reactions mediated by disclinations in hexagonal close-packed metals

Crystalline defects, such as dislocations, disclinations, twins and grain boundaries, play critical roles in determining the mechanical properties of metals and alloys. In particular, with multiple competitive deformation modes activated, the mechanical behaviors of hexagonal close-packed metals are strongly influenced by the interactions and reactions of various types of defects. Despite extensive studies on the elastic interactions of defects, a theoretical framework capturing crystallographic reactions, especially reaction products and associated local stress concentration, is still unavailable. Here we suggest a disclination-based method to quantify defect reactions. By using a combination of crystallographic calculations and phase field modeling/simulations, twin-twin and twin-grain boundary reactions in hexagonal close-packed metals have been quantitatively analyzed. It has been found that partial disclinations, accompanied with other defects (e.g., {112¯6} and {112¯2} high-index twins), can be generated by defect reactions as typical byproducts. The orientation change and stress fields caused by disclination formation have been systematically calculated, which offers a rigorous mathematical foundation to explore twin-twin, twin-grain boundary reactions. By quantitatively determining defect reactions and local stress fields, our work provides new insights into the deformation mechanism and microstructure-property relationship in metallic materials.

Mesoscale mechanism of damage in fracture process zone of CFRP laminates simulated with triaxial stress state-dependent constitutive equation of matrix resin

The three-dimensional failure process experimentally observed by synchrotron radiation X-ray computed tomography (SR X-CT) regarding the influence of the interfiber distance is discussed on the basis of the results of numerical experiments. Triaxial stress states in the fracture process zone of carbon fiber reinforced polymers were analyzed on the mesoscale under mode I and mixed-mode (mode I + II) loading. Yield and damage models depending on stress triaxiality were used to accurately simulate three-dimensional stress states in the damage zone around the crack tip. Owing to the heterogeneity of composites, deviatoric stress is prominent in the thin resin region where the interfiber distance is small under mode I loading. On the other hand, matrix resin is triaxially stressed in the middle point between carbon fibers in the thick resin region where the interfiber distance is large. Under mode II loading, the shapes of fiber/matrix debonding depended on the interfiber distance. Areas with stress concentration were found owing to a large debonding area in the thick resin region resulting in a matrix cracking-prone stress state. These findings explain the damage and failure processes well observed by SR X-CT and provide a fundamental understanding of the damage mechanism at a mesoscale.