Principal Stress Research Articles

Polyaxial failure criteria for in situ stress analysis using borehole breakouts: Review of existing methods and development of an empirical alternative

Analysis of compressive wellbore failure, or breakouts, is one of the primary methods of constraining the maximum horizontal stress in deep boreholes. To estimate stress using the observation of breakouts, one needs to measure the breakout width from image logs and use a failure theory to predict the stress that led to the development of the measured breakout. Most commonly, Mohr–Coulomb failure criterion has been used which disregards the influence of intermediate stress on strength. Hence, various polyaxial criteria have been proposed to include this effect. Here, we first review some selected polyaxial criteria: Drucker–Prager, Mogi, Modified Wiebols–Cook, and Modified Lade, and we conclude that their application in breakout analysis may be cumbersome and often unreliable. One reason for these problems is that the criteria are defined using stress invariants, while the stress estimation is most easily performed and analyzed in the principal stress space. Therefore, an alternative is to define the polyaxial criterion as a simple relation between maximum and intermediate stresses. We propose to define such an empirical criterion as a second order polynomial which fits trends observed in polyaxial laboratory strength data. Such approach allows to limit strength overestimation, often associated with the use of previous polyaxial criteria, and to easily relate uncertainties in strength estimation to uncertainty in maximum horizontal stress prediction.

Effect of the Material Properties and Knee Position to the Bone Bruise Pattern in Skeletally Mature and Immature Subjects.

A bone bruise is generated by a bony collision that could occur when the ACL is injured, and its pattern supposedly depends on the injury mechanism and level of skeletal maturity. The objective of this study was to determine the effect of material properties and knee position on the bone bruise pattern in skeletally mature and immature subjects using finite element analysis. Finite element models were created from an MR image in the sagittal plane of a skeletally mature and immature male subject. The femur and tibia were collided at 2 m/s to simulate the impact and determine the maximum principal stress. The analysis was performed at 15, 30 and 45 degrees of knee flexion, and neutral, 10 mm anterior and posterior translated position at each flexion angle. Although high stress was distributed toward the metaphysis area in the mature model, the stress did not cross the growth plate in the immature model. The size of the stress area was larger in the mature model than those in the immature model. The location of the stress area was dependent on the joint position as well as Young's modulus of cartilage and trabecular bone. Thus, the bone bruise pattern was affected by the knee position and tissue quality. In conclusion, although the bone bruise distribution was generally called footprint of the injury, the combined evaluation of the quality of the structure and the bone bruise distribution is necessary for properly diagnosing tissue injury based on the MR imaging.

Compressive failure of thermally strengthened glass spheres — Why are Prince Rupert's drops so strong?

This paper aims to elucidate the exceptional high strength of Prince Rupert's Drops (PRDs). PRDs are idealized as thermally strengthened Glass Spheres (SGSs), and their compressive failure mechanisms are investigated experimentally and numerically. The distributions of residual stress within SGS specimens are quantitatively characterized using an integrated photo-elastic method. Uniaxial compression tests conducted on these specimens reveal that the compressive residual stress present on the sphere's surface significantly enhances its strength. High-speed video images demonstrate that SGSs fail at the equatorial region, in contrast to annealed glass spheres (AGS) which typically fracture near the Hertzian contact zone. Numerical simulations suggest that the residual stress mitigates the maximum principal stress on the surface of SGSs, thereby impeding the development of flaws on the surface of the specimens. Ultimately, failure of SGS specimens under pressure occurs due to the “squeezing” effect, in contrast to AGSs which commonly fail due to contact indentation.

Stress Characteristics and Mechanical Behavior of Rock Masses with an Opening under Complex Deep Underground Stress Conditions

In this study, the impact of principal stress states on the stress characteristics and initial failure of the rock mass surrounding a three-center arch opening was investigated using complex variable function methods and Discrete Element Method (DEM) numerical modeling. First, the mapping function of the opening was determined using the trigonometric interpolation method, and the influence of the number of terms in the mapping function on its accuracy was revealed. Based on this, the far-field stress state of the underground rock mass was characterized by the ratio of the minimum to maximum principal stress (λ) and the angle (β) between the principal stress and the vertical direction. This stress state was then converted into normal and shear stresses. Using complex variable function theory, the stress characteristics at the boundary of the opening under different stress states were analyzed. Finally, DEM numerical modeling was employed to study the initial failure characteristics at the boundary of the opening and its relationship with the stress distribution. The results indicate that the lateral pressure coefficient significantly affects the stability of the opening by influencing stress concentration around the surrounding rock. Low lateral pressure coefficients lead to tensile stress concentration at the boundary perpendicular to the maximum principal stress. As the coefficient increases, tensile stress decreases, and compressive stress areas expand. While the principal stress direction has a minor effect on stress concentration, it notably impacts stress distribution at the boundary. When λ < 1.0 and β = 45°, stress distribution asymmetry is most pronounced, with the highest compressive stress. The early failure distribution aligns with stress concentration areas, validating the use of stress analysis in predicting opening stability and failure characteristics.

Comparison of implant placement at crestal and subcrestal levels in aesthetic zone: A finite element analysis.

The success rate of the implant treatment, including aesthetics and long-term survival, relies heavily on preserving crestal peri-implant bone, as it determines the stability and long-term outcomes. This study aimed to demonstrate the stress differences in the crestal bone resulting from dental implant placement at various depths relative to the crestal bone level using finite element analysis. Three study models were prepared for implant placement at the crestal bone level (CL), 1 mm depth (SL-1),and 2mm depth (SL-2). Implants were placed in the maxillary central incisor region of each model, and 100 N vertical and oblique forces were applied. The von Mises, maximum principal (tensile), and minimum principal (compressive) stresses were evaluated. The CL model exhibited the highest stresses on the implant, abutment, and abutment screws under vertical and oblique forces. For maximum principal stress in the crestal bone under vertical force, the SL-2, SL-1, and CL models recorded values of 6.56, 6.26, and 5.77MPa, respectively. Under oblique forces, stress values for SL-1, SL-2, and CL were 25.3, 24.91, and 23.76MPa, respectively. The CL model consistently exhibited the lowest crestal bone stress at all loads and the highest stress values on the implant and its components. Moreover, considering the yield strengths of the materials, no mechanical or physiological complications were noted. Placing the implant at the crestal level or subcrestally beyond the cortical layer could potentially reduce stress and minimize crestal bone loss. However, further studies are warranted for confirmation.

Full-field stress-strain analysis of octagonal shape PMMA using reflection photoelasticity

This research involves stress-strain analysis in poly(methyl methacrylate) (PMMA) octagonal shape compressed by hydraulic system. The observation of uniaxially stressed samples was carried out using reflection photoelasticity technique. The results of fringe order number and principal stress angle were used to determine stress and strain distribution in the samples by shear difference method. It was found that high stress-strain region was close to the contact point where compressive force was applied but it was zero at the edge of the samples. The area of high strain region increased as the magnitude of force was increased but it decreased as the dimension of octagonal shape was increased.

Strength and fabric anisotropy of granular materials under true triaxial configurations using DEM

This paper investigates the strength and fabric anisotropy of granular materials under true triaxial configurations using the discrete element method. A clump logic based on the multi-sphere approach was utilized to replicate realistic particle shapes. The evolutions of deviatoric stress and volumetric strains were found to be independent of mean effective stress, and intermediate principal stress parameter (b). From a macroscopic viewpoint, all samples exhibited initial strain hardening followed by softening behaviour, stabilizing at large deviatoric strains due to the dense state of assemblies. The peak state friction angles showed dependency on the b-value, aligning closely with experimental findings. Microscopic parameters such as mechanical coordination number and sliding fraction were found to be approximately independent of b-values. Additionally, non-coaxiality was observed for various b-values except for specific shear modes, aligning with previous findings using spherical particles. These results highlight the capability of clumped particles to simulate the true mechanical behaviour of granular materials and contribute to our understanding of their complex response under different loading conditions.

True-triaxial strength characteristics of cement stone subjected to sulfuric acid corrosion: An experimental and theoretical study

True triaxial tests were conducted to investigate the effect of sulfuric acid corrosion on the true triaxial strength of cement stone under different acid immersion times, including the common loading path and novel loading path with constant Lode angle. The chemical composition and microstructure of cement stone under different acid immersion times (0, 7, 14, and 28 d) were examined via X-ray diffraction and scanning electron microscopy. As the duration of acid immersion increases, the concentrations of portlandite (Ca(OH)2) and calcium silicate hydrate (C-S-H) within the cement stone exhibit a gradual decline, while the presence of calcium sulfate (CaSO4) progressively rises. The microstructure of the cement stone was primarily affected by two factors: the damaging and strengthening effects of sulfuric acid and CaSO4, respectively. The damaging effects of the acid were dominant for days 0–14 of immersion, with continuous increase in microstructure damage. Subsequently, the strengthening effect of CaSO4 became apparent for days 14–28 of immersion, with continuous improvement in microstructure integrity. Consequently, the strength of cement stone exhibited a diminishing trend during the initial immersion period of 0–14 days, followed by an enhancement in strength from 14 to 28 days of immersion. Furthermore, a three-dimensional strength criterion was proposed by combining the Hoek–Brown and Matsuoka–Nakai criteria. The failure envelope first shrank and then expanded with increasing immersion time, accurately describing the variation in strength in the three-dimensional principal stress space.

Impacts of the mechanical connectors on seismic performance of the restored masonry Plaka Bridge using experimental and numerical studies

The use of clamp and dowel materials in the arch of the masonry bridges holds pivotal significance in enhancing the seismic resilience of these structures, as these elements contribute crucially to the structural integrity and dynamic response of these venerable structures. For this reason, the seismic performance of the restored historic Plaka Bridge, originally constructed in 1866 in Arta, Greece, and later restored in 2015 after flooding, was investigated considering the dowels and clamps in the arch section of this study. A combination of experimental and numerical analyses was conducted and verified to understand the in-situ interface behavior of the arch stones. In the first phase of the study, the mechanical properties of the dowels and clamps were characterized by the experimental tests. Compression and tension tests were conducted on the stone samples containing dowel bars and clamps respectively to determine the mechanical properties, The experimental outcomes were subsequently validated through Three-Dimensional (3D) Finite Difference Models (FDM). It was obtained that the dowels and clamps represent the bi-linear material model at the interfaces. Finally, the idealized interface behavior was constructed with normal and tangential spring stiffness properties in 3D-FD Models. These springs successfully simulate the interface delamination failure of the stones in all directions. In the final phase of the study, a 3D-FD model of the Plaka Bridge was constructed employing the previously validated normal and tangential stiffness elements in the arch of the bridge. A free-field non-reflecting boundary condition was imposed on the base and lateral boundaries of the bridge model. Seismic analyses were conducted utilizing the significant seismic events including 2023 Kahramanmaraş earthquakes. The results revealed significant alterations in the structural behavior of the bridge under considered earthquakes. Furthermore, the displacements, principal stresses and tensile-compressive damages in the main arch significantly reduced with the adopted stiffness values. This study proposes the undeniably realistic and efficient implementation of interface material modeling for the mechanical connections as opposed to the traditionally assumed mortar properties in literature. Furthermore, the combined behavior of the dowel, clamp, and Khorasan mortar proposes non-linear interface material model to the existing literature by invalidating commonly assumed linear interface behavior in masonry structures.

Rayleigh-type wave in non-planar pre-stressed nearly incompressible elastic structure

The primary objective of the current work is to establish the impacts of planar boundary and non-planar boundary on the displacement components (DCs) of Rayleigh-type wave propagation in an elastic structure. The elastic structure, precisely, incorporates a pre-stressed nearly incompressible elastic material in the half-space along with the non-planar boundary at the free surface. The methodology applied features variable separable technique and Taylor’s series expansion along with substitution method to establish the expressions for DCs and frequency relation. The frequency relation of Rayleigh-type wave is obtained for the situation considering planar free surface, which is further reduced as a special case of the study and validated with the classical result present in the literature. The DCs of Rayleigh-type wave have been numerically computed, and their reliance on wave number have been exhibited graphically. In addition to this, the influences of affecting parameters viz., hydrostatic stress, principal Cauchy stress and curvature parameter on DCs have been traced out. The computational result also manifests the domain of existence of Rayleigh-type wave propagating in the considered model in the presence of planar free surface.

Design and Development of Combined Mechanical and Pneumatic Valve Spring Remover

A combined mechanical and pneumatic valve spring remover is used to remove or install valve springs from an engine while the cylinder head is mounted on the engine or supported on a workbench (off the head). The designed tool was adjustable and mounted over the cylinder head by a stud. It can operate manually to depress the spring or by using an air compressor for a pneumatic actuator. The model of the tools is done by SOLIDWORK 2021 and we selected the stainless steel AISI grade-304(12) material. Tools were made following the calculations that have been done on valve springs. From the data calculation, the force required to depress the valve spring is 1350 N but the tools were designed to produce 1962.5 N by considering some friction loss. The analysis of the pneumatic system done by ANSYS software shows acceptable results like, Von Mises stress (20.036 MPa), maximum principal stress (26.426 MPa), and the total deformation becomes 1.6029×10-3. The prototype was built, and the test was carried out in time efficiently during the removal or installation of the valve spring on Engine YaMZ-238. The test result shows that to remove 4 springs, the designed tool is very effective to use by optimizing the difference in time savings of an average of 1 minute and 17 seconds when removing the spring valve, and 1 minute and 26 seconds when installing the valve, even when we use it mechanically. The developed valve spring remover has several advantages over the standard C-clamp tools, such as greater precision and accuracy in removing valve springs, reduced labor and time required for the task, and Increased safety with minimal human force.

Characterization and modeling of biaxial plastic anisotropy in metallic sheets

The anisotropic behavior of cold-rolled sheet metals has been extensively studied, typically characterized by uniaxial loading tests in different directions to determine yield strengths and plastic flow (Lankford r-values). However, biaxial principal stress states often focus solely on yield loci in the RD/TD (rolling/transverse) directions, with limited studies on other loading directions. This study analyzes the relationship between the principal stress yield loci and the material principal anisotropic stress directions based on the Hill48 yield function. Biaxial tensile tests are conducted on DP590 high-strength steel using cruciform specimens cut in various directions different from the sheet RD/TD directions. The evolution of the anisotropic yield locus and plastic flow of DP590 under biaxial tensile directions beyond the traditional RD/TD anisotropic directions is revealed. Furthermore, a modified Hill48 model that considers any principal stress direction of loading is proposed, accurately describing the continuous evolution of equi-biaxial tension stress, near-plane strain stress, and plastic flow direction for different principal stress directions of loading. The issues of failing to predict plastic flow under biaxial loadings in the original Hill48 model, and the degraded representation of existing constitutive models when accounting for out-of-plane anisotropy are addressed by decoupling the relationship between anisotropic parameters and stress state. In addition, the proposed calibration strategy of anisotropic parameters, using experimental data from various principal stress directions of loading, effectively captures the anisotropic evolution caused by changes in principal stress directions. Comprehensive evaluation and verification of the plasticity model should consider yield locus for any principal stress directions of loading, and also the normal and shear planes.

Blast resistance of 3D-printed Bouligand concrete panels reinforced with steel fibers: Numerical investigations

3D-printed concrete structures inspired by Bouligand architecture with helically twisted sequences exhibit excellent mechanical performance owing to its aligned fiber orientation. In this study, 3D-printed concrete panels with different numbers of layers (five, ten, and 15 layers) and spiral angles (0°, 15°, 30°, and 45°) are designed for numerical investigations of their blast-resistant capacity. A multi-scale model is developed to capture the isotropic and anisotropic properties of the fiber-concrete composite. The adequacy and accuracy of the model are evaluated and validated by experimental data in the literature. Blast resistance of different types of panels in terms of time histories of central-point deflection, contact explosion-induced plastic dissipation energy, stress propagation, and principal stress distribution is examined. It is found that extrusion-based concrete panels with aligned fiber orientation substantially enhance the blast resistance compared to traditional cast concrete panels with random fiber orientation. Furthermore, more layers of printed concrete panels prove to be more efficient in filtering blast waves. In particular, shifting a pitch angle of 30° after printing each layer plays an important role in reducing the maximum deflection. Meanwhile, 3D-printed concrete panels with a pitch angle of 0° can better mitigate blast-induced damage. Through parametric studies, the intrinsic mechanism of steel fibers aligned in 3D-printed panels is numerically analyzed to support the conclusions.

Experimental study of the end effect on the mechanical behaviors of rocks under true 3D compressions

AbstractIn true triaxial compression tests, all three principal stresses are imposed independently. This allows for a more comprehensive analysis of the material's mechanical properties. The end effect in true triaxial compression tests is a crucial phenomenon that impacts the accuracy and reliability of the test results. In this study, a series of true triaxial compression tests is conducted to examine the influence of the end friction on the mechanical properties. The laboratory results show that the presence of the end friction could bring about an apparent increase in rock strength and also restrict the deformation in each direction showing that the stiffness (the slope of the curves) increased slightly. The rock strength could be enhanced from 24.7 to 90.7 () when the end friction is increased, which is mainly caused by the lateral interface friction. The failure mode and fracture angle of the specimen are also influenced by the end effect, showing that under high friction conditions, the failure is more ductile, and a larger fracture angle is observed. At last, in comparison with the published experimental data, the actual specific friction angle (corresponding friction coefficient is about 0.19) for the direct specimen–metal contacts in a true 3D test is numerically identified, which is empirically reasonable and higher than the tested range 0.146–0.157 obtained from double‐shear test system.

Unveiling the mechanisms behind texture formation and its impact on the torsional performance of cold-drawn pearlitic steel wires

High carbon pearlitic steel wires are widely used in the industry, such as for producing tyre cords and steel cables due to its excellent mechanical properties. Cold drawing is a crucial step in steel wire production. Due to the loading state during the cold drawing process, pearlitic wires tend to exhibit a <110> fiber texture. The non-uniform texture distribution on the cross-section of steel wires has been observed experimentally. The mechanisms yielding this non-uniformly distributed texture are carefully investigated in this study using a multi-scale computational approach. Firstly, a macroscale finite element model is established to simulate the deformation behaviour of pearlitic steel wires during cold drawing, with the aim of thoroughly investigating the inhomogeneous elastic-plastic deformation behaviours. Secondly, the macro mechanical responses are incorporated into the mesoscale representative volume element model as boundary conditions to comprehensively study the effect of inhomogeneous deformation characteristics on texture formation. The results present a significant advancement by revealing that the non-uniform texture distribution in a steel wire can primarily be attributed to the multiaxial stress state on the cross-section. Notably, at the center of the steel wire, the maximum principal stress aligns with the drawing axis, resulting in a dominant <110> fiber texture. Conversely, at the subsurface, the maximum principal stress progressively shifts towards the circumferential direction, yielding an evolving texture characterized by a {110}<110> circumferential texture. Furthermore, the research uncovers a crucial finding that it is the {110}<110> circumferential texture that significantly weakens the torsion ability of the wires. This is due to the limited activation of slip systems, marking a key advancement in understanding the mechanical properties of steel wires.

Designing 3D-printed concrete structures with scaled fabrication models

This article proposes using scaled fabrication models to assist the design research of 3D-printed discrete concrete structures where full-scale fabrication tests are costly and time-consuming. A scaled fabrication model (SFM) is a scaled model 3D-printed the same way as in actual construction to reflect its fabrication details and acquire alike layer line textures. The components of a 1:10 SFM can be easily produced by consumer-level desktop 3D printers with minimal modification. SFMs assist the design communication and make possible quick tests of distinct fabrication designs that are hard to assess in digital modeling during the conceptual design phase. A case study of a discrete compression-dominant funicular floor derived from graphic statics is presented to illustrate the contribution of SFM to the design research of force-informed toolpathing where the printing direction of a component is aligned to the principal stress line. The design iterations encompass a sequence of component, partial, and full model SFM printing tests to explore and optimize the fabrication schemes where parallel, non-parallel, and creased slicing methods to create toolpaths are compared and chosen to adapt different discrete components.

Tectonic Stress Analysis of Shivnath-Salena Area, Using Stress Response Structure

The geological mapping of the Shivnath-Salena area and structure analysis of the same area were conducted in the LesserHimalayan sequence, Far West Nepal, unveiling the characteristics of kinematics and the associated stress field in the region. Thearea comprises of the Salena Formation and Chachura Formation. The Salena Formation is sandwiched between the PachkoraThrust and Dudulakhan Thrust, and the Chachura Formation occurs between the North Dadeldhura Thrust and Pachkora Thrust.The Salena Formation is composed of light grey and white quartzite and black slates that are intensely deformed, with folds. The Malena Anticline and the Lamalek Syncline are the intraformational folds observed in the study area. Superimposed folding was also observed. The Chachura Formation comprises Paleocene to Late Eocene green sandstone, grey and purple shale, and approximately 1 m thick grey fossiliferous limestone. This study interprets stress-response structures to show the tectonic stress field in the Salena Formation. Twenty-seven fault slip data (slickenside) were collected in the field and used to determine the stress regime by applying the stress inversion technique. The direction of the maximum principal stress axes is interpreted as NE-SW. The average value of the stress index R' is about 0.30, indicating an extensional tectonic stress regime in the study area. As σ1 is vertical, R = R' in the study area suggests normal faulting in an extensional regime.

Research on the evolutionary patterns and control of surrounding rock superimposed stress field local area loading in double-layer Island face main roadway

Double-layer island working face main roadway coal pillars are affected by complex mining stress superposition, when different coal pillar width combinations, the surrounding rock stress field will produce different degrees of regional loading increase effect; the study of the surrounding rock stress field regional superposition loading increase law is meaningful to explaining the failure mode of the roadway and determining the critical control area. This study combines numerical simulation with on-site monitoring and other methods and draws the following conclusions: The superimposed loading increase law (“decreasing” → “increasing”) of the abutment pressure and deviatoric stress in the lower coal seam of the double-layer island working face during the mining; the type of the principal stress deflection in the advance working face region; and by obtaining the three types of development morphology of the deviatoric stress peak zone of the roadway and its corresponding nine evolution modes (one type of circular tube → four types of inverse hyperbolic body → four types of hyperbolic body) in the double-layered island working face mining. Indicated the critical reinforcement area corresponding to the main roadway when at different combinations of coal pillar widths; determined the main track roadway protective coal pillars width for 40 m and the shape of the roadway peak deviatoric stress zone is the inverse class hyperbolic body mode; according to the evolution mode of the peak deviatoric stress zone, determined the synergistic failure control program for the asymmetric critical zone of the roadway surrounding rock which is a targeted scientific support method; after the feedback of on-site monitoring and, the support program is reasonable and effective.

In-situ stress field simulation and fracture distribution prediction of middle lower Ordovician in Zone B of Tahe Oilfield, Tarim Basin

This study constructed a heterogeneous rock mechanics model through well seismic joint inversion, set up a dual cycle statement to optimize the application of boundary loads, and obtained the current stress field distribution in Zone B. At the same time, we preferred the rock fracture criterion, carried out the quantitative characterization of different natures of fractures, and used the integrated fracture development rate to portray the integrated fracture development situation. Finally, the horizontal stress difference, stress heterogeneity coefficient, and comprehensive fracture rate were proposed to define the development index of fractured reservoirs. The results show that (1) the maximum horizontal principal stress is 102–144 MPa, and the minimum horizontal principal stress is 85–125 MPa; (2) the development rate of tension fractures is 0.03–0.23, the development rate of shear fractures is 0.15–0.54, and the integrated fracture development rate is 0.28–0.79; (3) the development index of fracture-type reservoirs is >2.3, Class I; 1.8–2.3, Class II; When it is lower than 1.8, Grade III. This article attempts to apply the stress field simulation results to the quantitative prediction of reservoir fractures, adding new ideas for the practical application of stress field results.

Multiscale-mechanical analysis on self-healing microcapsules under asphalt pavement

To investigate the stress state of self-healing microcapsules in asphalt pavement during their operational phase, this study utilizes the finite difference method to establish a macroscopic structural model of asphalt pavement and a multi-scale model of representative volume elements (RVE)containing self-healing microcapsules. It systematically analyzes the effects of microcapsule content, capsule wall modulus, and wall thickness on the its mechanical performance under different asphalt pavement. Experimental findings indicate that an increase in microcapsule content initially increases and subsequently decreases the maximum principal stress and shear stress of the capsule wall, suggesting an optimal content range for achieving optimal mechanical response. Moreover, an increase in capsule wall modulus results in increased maximum principal stress, minimum principal stress, and maximum shear stress borne by the capsule wall, underscoring the importance of capsule wall modulus for the mechanical properties of microcapsules. The impact of increasing wall thickness on minimum principal stress shows an initial increase followed by a decrease, emphasizing the critical role of appropriate wall thickness selection in facilitating prompt response of microcapsules to pavement cracks. This research provides essential theoretical foundations for the design and application of microcapsules, thereby enhancing the self-healing capability of asphalt pavement.