Three-dimensional Stress Tensor Research Articles

Flank fractures on spiral bevel gears—transfer of analytical methods for the estimation of residual stresses from cylindrical gears to bevel gears

The classic flank and root load capacity calculation on the component surface forms the basis for the design of power gears today. However, flank fractures also occur in practice, particularly with large-module gears and/or low case-hardening depths. It is a fatigue damage with crack initiation in the tooth interior, its prevention requires the calculation of the stresses below the surface. In addition to understanding the load stresses, the inhomogeneous load bearing capacity and the residual stress profile in case-hardened gears are also of great importance. There are various calculation approaches for this in the area of cylindrical gears, but these have not yet been transferred to the complex geometry of spiral bevel gears. The focus of this publication is on estimating the residual stresses in the tooth volume by generating a three-dimensional residual stress tensor field in the bevel gear tooth based on the two-dimensional calculation approaches used to date on cylindrical gears. In combination with the stress tensor-time curves from a tooth contact simulation with the LTCA tool BECAL, this can be fed into different failure hypotheses, which is illustrated using an example.

Stress-based dimensional reduction and dual-mixed hp finite elements for elastic plates

Starting from the linearized weak forms of the kinematic equation and the angular momentum balance equation of three-dimensional non-linear elasticity, a stressbased dimensional reduction procedure is presented for elastic plates. After expanding the three-dimensional non-symmetric stress tensor into power series with respect to the thickness coordinate, the translational equilibrium equations, written in terms of the expanded stress coefficients, are satisfied by introducing first-order stress functions. The symmetry of the stress field is satisfied in a weak sense by applying the material rotations as Lagrangian multipliers. The seven-field plate model developed in this way employs unmodified three-dimensional strain-stress relations. On the basis of the dimensionally reduced plate model derived, a new dual-mixed plate bending finite element model is developed and presented. The numerical performance of the hp-version plate elements is investigated through the solutions of standard plate bending problems. It is shown that the modeling error of the stress-based plate model in the energy norm is better than that of the displacement-based Kirchhoff- and Reissner-Mindlin plate models. The numerical solutions and their comparisons to reference solutions indicate that the dual-mixed hp elements are free from locking problems, in either the energy norm or the stress computations, both for h- and p-extensions, and the results obtained for the stresses are accurate and reliable even for extremely thin plates.

Evaluation of the Behavior of Carbon Short Fiber Reinforced Concrete (CSFRC) Based on a Multi-Sensory Experimental Investigation and a Numerical Multiscale Approach.

Carbon fiber reinforcement used in concrete has become a remarkable alternative to steel fibers. Admixing short fibers to fresh concrete and processing the material with a 3D printer leads to an orientation of fibers and a material with high uniaxial strength properties, which offers an economic use of fibers. To investigate its mechanical behavior, the material is subjected to flexural and tensional tests, combining several measuring techniques. Numerical analysis complements this research. Computed tomography is used with several post-processing algorithms for separating matrix and fibers. This helps to validate fiber alignment and serves as input data for numerical analysis with representative volume elements concatenating real fiber position and orientation with the three-dimensional stress tensor. Flexural and uniaxial tensional tests are performed combining multiple measuring techniques. Next to conventional displacement and strain measuring methods, sound emission analysis, in terms of quantitative event analysis and amplitude appraisal, and also high-resolution digital image correlation accompany the tests. Due to the electrical conductibility of carbon fibers, the material’s resistivity could be measured during testing. All sensors detect the material’s degradation behavior comparably, showing a strain-hardening effect, which results from multiple, yet locally restricted and distributed, microcracks arising in combination with plastic deformation.

Intragranular three-dimensional stress tensor fields in plastically deformed polycrystals.

The failure of polycrystalline materials used in infrastructure and transportation can be catastrophic. Multiscale modeling, which requires multiscale measurements of internal stress fields, is the key to predicting the deformation and failure of alloys. We determined the three-dimensional intragranular stress tensor fields in plastically deformed bulk steel using a high-energy x-ray microbeam. We observed intragranular local stresses that deviated greatly from the grain-averaged stresses and exceeded the macroscopic tensile strength. Even under deformation smaller than the uniform elongation, the intragranular stress fields were in highly triaxial stress states, which cannot be determined from the grain-averaged stresses. The ability to determine intragranular stress tensor fields can facilitate the understanding and prediction of the deformation and failure of materials through multiscale modeling.

Three-dimensional extent of flow stagnation in transcatheter heart valves.

The recent unexpected discovery of thrombosis in transcatheter heart valves (THVs) has led to increased concerns of long-term valve durability. Based on the clinical evidence combined with Virchow's triad, the primary hypothesis is that low-velocity blood flow around the valve could be a primary cause for thrombosis. However, due to limited optical access in such unsteady three-dimensional biomedical flows, measurements are challenging. In this study, for the first time, we employ a novel single camera volumetric velocimetry technique to investigate unsteady three-dimensional cardiovascular flows. Validation of the novel volumetric velocimetry technique with standard planar particle image velocimetry (PIV) technique demonstrated the feasibility of adopting this new technique to investigate biomedical flows. This technique was used to quantify the three-dimensional velocity field in the vicinity of a validated, custom developed, transparent THV in a bench-top pulsatile flow loop. Large volumetric regions of flow stagnation were observed in the neo-sinus throughout the cardiac cycle, with stagnation defined as a velocity magnitude lower than 0.05 m s-1. The volumetric scalar viscous shear stress quantified via the three-dimensional shear stress tensor was within the range of low shear-inducing thrombosis observed in the literature. Such high-fidelity volumetric quantitative data and novel imaging techniques used to obtain it will enable fundamental investigation of heart valve thrombosis in addition to providing a reliable and robust database for validation of computational tools.

CONTACT FABRIC CHARACTERISTICS OF GRANULAR MATERIALS UNDER THREE DIMENSIONAL STRESS PATHS

Macroscopic mechanical characteristics of granular materials are closely related to the microscopic contact force and fabric. Generally speaking, the strong contact system contributes to the force transmission of internal granular system, and then its corresponding fabric tensor has important influence on the macroscopic stress. Microscopic numerical methods, such as discrete element method, can reproduce the laboratory tests with reasonable macroscopic responses and extract macro- and micro-data conveniently for investigating the underlying mechanism of the granular system. Based on discrete element method (DEM), a series of true triaxial tests for granular materials under constant $p$ and constant $b$ stress paths are carried out, and the evolutions of macro- and micro-mechanical parameters of granular materials, the multiple relationship between three-dimensional fabric tensor and stress tensor and the macro-stress characteristics reflected by strong contact system are studied. The results demonstrate that some macro- and microscopic parameters at the stress peak and critical state in the granular system are independent on the loading path. Non-coaxiality between fabric tensor and stress tensor is observed under three-dimensional stress path, but the evolution of the joint invariant of the two tensors is independent on the 3D loading path. Compared to fabric tensor of weak contact system, the fabric tensor of strong contact system reflects better the characteristics of macroscopic stress tensor. Fabric tensors of strong and weak contact systems contribute differently to the granular macroscopic response. To divide the strong and weak contact system, there is a range for the threshold, however adopting the average contact force is relatively simple and reasonable.

Numerical study of optical trapping properties of nanoparticle on metallic film with periodic structure**Project supported by the National Natural Science Foundation of China (Grant Nos. 61701382, 61601355, and 61571355), the China Postdoctoral Science Foundation (Grant No. 2016M602770), and the Xi’an Technological University Principal Foundation Key Project, China (Grant No. XAGDXJJ18001).

Based on the three-dimensional dispersive finite difference time domain method and Maxwell stress tensor equation, the optical trapping properties of nanoparticle placed on the gold film with periodic circular holes are investigated numerically. Surface plasmon polaritons are excited on the metal-dielectric interface, with particular emphasis on the crucial role in tailoring the optical force acting on a nearby nanoparticle. Utilizing a first order corrected electromagnetic field components for a fundamental Gaussian beam, the incident beam is added into the calculation model of the proposed method. To obtain the detailed trapping properties of nanoparticle, the selected calculations on the effects of beam waist radius, sizes of nanoparticle and circular holes, distance between incident Gaussian beam and gold film, material of nanoparticle and polarization angles of incident wave are analyzed in detail to demonstrate that the optical-trapping force can be explained as a virtual spring which has a restoring force to perform positive and negative forces as a nanoparticle moves closer to or away from the centers of circular holes. The results of optical trapping properties of nanoparticle in the vicinity of the gold film could provide guidelines for further research on the optical system design and manipulation of arbitrary composite nanoparticles.

Asymmetric tensor representations in micropolar continuum mechanics theories

Получены новые представления трехмерного асимметричного тензора напряжений и соответствующие им формы дифференциальных уравнений равновесия. Асимметричные теории механики деформируемого твердого тела по прежнему привлекают пристальное внимание в связи с необходимостью математического моделирования механического поведения современных материалов (например, ауксетиков с помощью теорий гемитропной микрополярной упругости). Исследование ограничивается только такими асимметричными тензорами второго ранга, для которых удается сохранить понятие о вещественных собственных значениях, но отказаться от взаимной ортогональности направлений главного триэдра. Обсуждается точная алгебраическая формулировка указанных условий асимметричности. В статье обобщаются тензорные представления симметричного тензора напряжений, основанные на естественном репере асимптотических направлений. Полученные результаты являются ярким свидетельством в пользу алгебраической «гиперболичности» симметричных и асимметричных тензоров второго ранга в трехмерном пространстве.

Effect of nanoscale roughness on optical trapping properties of surface plasmon polaritons exerted on nanoparticle

Based on the three-dimensional dispersive finite difference time domain method and Maxwell stress tensor equation, the effect of nanoscale surface roughness on the optical trapping properties of nanoparticle in a vicinity of the composite gold film with periodic structure is investigated numerically. The periodic structure is observed as circular holes which can excite the surface plasmon polaritons on the metal-dielectric interface with particular emphasis on its crucial role in tailoring the optical force acting on a nearby nanoparticle. Utilizing the Monte-Carlo method, the surface roughness is added into the calculation model of the proposed method to accurately investigate the optical performance of the film-tuned nanoparticle system. Selected calculations on the effects of root mean square height and correlation length of rough surface are analyzed in detail to demonstrate that the negative effect of the surface roughness on the optical trapping force can be eliminated when the ratio of correlation length to root mean square height is equal to 10. Accurate investigation of optical trapping properties of nanoparticle in a vicinity of the composite gold film could provide guidelines for further research on the optical system design and manipulation of arbitrary composite nanoparticles.

Controllable trapping and releasing of nanoparticles by a standing wave on optical waveguides.

Based on the balance between the scattering force and the trapping force of an evanescent field of a standing wave on silicon waveguides, we propose a structure for controllable trapping and releasing of nanoparticles, which can act as pause operation for nanoparticle flow control. The design is realized by the cascade of an optical switch with a structure of a ring-assisted Mach-Zehnder interferometer (RAMZI) and a Sagnac loop reflector which connects to one output of the switch. Through thermal tuning, with a tiny refractive index change of 4.3×10-4 on a ring resonator, the output of a RAMZI can be switched between two ports. As for the release state of the nanoparticle flow, the light is guided to the port without a reflector. There is no standing wave or traps formed on a waveguide. Therefore, the scattering force dominates, which drives particles moving forward to output ports. Otherwise, for trapping a state, the light will be reflected by the Sagnac loop and form a stationary standing wave which provides an array of traps for nanoparticles. Most importantly, the structure can switch its state to trap or sequentially release particles without losing the control of samples which, to the best of our knowledge, has not been realized before. With the statistical description of particle motion, the balance between trapping and releasing is distinguished by the trapping time and tuned by reflectance. The feasibility of our design is verified using the three-dimensional finite-difference time domain and Maxwell stress tensor methods. Our structure possesses the merits of high compactness and time effectiveness and, thereby, it is highly suitable for on-chip optical manipulation of nanoparticle flow control, which brings great potential in integrated on-chip optofluidics.

A novel triaxial failure model for adhesive connections in structural glass applications

Structural adhesive connections for glass applications have been widely investigated in the past years, because of their enhanced mechanical performance when compared to bolted connections. However, due to the lack of established design methods and failure criteria, laboratory tests must always be performed, when adhesive connections are used in real-world structural applications. Because of the above, this work presents the analytical development of a Generalized Triaxial Model (here called GTM) that describes a novel failure criterion for adhesive materials in structural glass applications. This is done developing a generalized triaxial model defined over the three-dimensional stress space, which accounts for the non-linear effects of strain rate and temperature variation. The main output of this work is a five-dimensional formulation that allows to account for a generic stress state by a governing equation expressed as a function of the three-dimensional stress tensor. Both deviatoric and hydrostatic energetic components are taken into consideration by means of a non-linear function of the two contributions. The governing equation is represented in the stress space by a revolution surface that is axial-symmetric with respect to the hydrostatic axis, thus independent of the third stress invariant. The proposed model is suitable for isotropic materials and it is here applied to SentryGlas and TSSA, two adhesive materials used in structural glass applications, for which extensive test campaigns have been performed but for which no failure criteria are available yet in literature. Firstly, the proposed model is analytically compared to other existing general failure criteria. It is shown that some of the existing models that can be found in literature can be seen as a particular case of the proposed model. Then, the model is compared with the experimental results under different loading conditions, strain rates and temperatures. The results are found to be in line with the model predictions for both materials. Additional tensile-torsion tests are also performed to validate the proposed model at varying values of the hydrostatic angle.

Quantifying the effect of hydrogen on dislocation dynamics: A three-dimensional discrete dislocation dynamics framework

We present a new framework to quantify the effect of hydrogen on dislocations using large scale three-dimensional (3D) discrete dislocation dynamics (DDD) simulations. In this model, the first order elastic interaction energy associated with the hydrogen-induced volume change is accounted for. The three-dimensional stress tensor induced by hydrogen concentration, which is in equilibrium with respect to the dislocation stress field, is derived using the Eshelby inclusion model, while the hydrogen bulk diffusion is treated as a continuum process. This newly developed framework is utilized to quantify the effect of different hydrogen concentrations on the dynamics of a glide dislocation in the absence of an applied stress field as well as on the spacing between dislocations in an array of parallel edge dislocations. A shielding effect is observed for materials having a large hydrogen diffusion coefficient, with the shield effect leading to the homogenization of the shrinkage process leading to the glide loop maintaining its circular shape, as well as resulting in a decrease in dislocation separation distances in the array of parallel edge dislocations. On the other hand, for materials having a small hydrogen diffusion coefficient, the high hydrogen concentrations around the edge characters of the dislocations act to pin them. Higher stresses are required to be able to unpin the dislocations from the hydrogen clouds surrounding them. Finally, this new framework can open the door for further large scale studies on the effect of hydrogen on the different aspects of dislocation-mediated plasticity in metals. With minor modifications of the current formulations, the framework can also be extended to account for general inclusion-induced stress field in discrete dislocation dynamics simulations.

Analysis of monitored ground support and rock mass response in a longwall tailgate entry

A comprehensive monitoring program was conducted to measure the rock mass displacements, support response, and stress changes at a longwall tailgate entry in West Virginia. Monitoring was initiated a few days after development of the gateroad entries and continued during passage of the longwall panels on both sides of the entry. Monitoring included overcore stress measurements of the initial stress within the rock mass, changes in cable bolt loading, standing support pressure, roof deformation, rib deformation, stress changes in the coal pillar, and changes in the full three-dimensional stress tensor within the rock mass at six locations around the monitoring site. During the passage of the first longwall, stress measurements in the rock and coal detected minor changes in loading while minor changes were detected in roof deformation. As a result of the relatively favorable stress and geological conditions, the support systems did not experience severe loading or rock deformation until the second panel approached within 10–15 m of the instrumented locations. After reaching the peak loading at about 50–75 mm of roof sag, the cable bolts started to unload, and load was transferred to the standing supports. The standing support system was able to maintain an adequate opening inby the shields to provide ventilation to the first crosscut inby the face, as designed. The results were used to calibrate modeled cable bolt response to field data, and to validate numerical modeling procedures that have been developed to evaluate entry support systems. It is concluded that the support system was more than adequate to control the roof of the tailgate up to the longwall face location. The monitoring results have provided valuable data for the development and validation of support design strategies for longwall tailgate entries.

Analytical investigation for stress measurement with the rheological stress recovery method in deep soft rock

Due to the difficulty and weakness of current stress measurement methods in deep soft rock, a new rheological stress recovery method of the determination of the three-dimensional (3D) stress tensor is proposed. It is supposed that rock stresses will recovery gradually with time and can be measured by embedding transducers into the borehole. In order to explore the applicability and accuracy of this method, analytical solutions are developed for stress measurement with the rheological stress recovery method in a viscoelastic surrounding rock, the rheological properties of which are depicted as both the Burger’s model and a 3-parameter solid model. In such conditions, explicit analytical expressions for predicting time-dependent pressures on the transducer are derived. A parametric analysis is then adopted to investigate the influences of the grout solidification time and the mechanical properties of the grout layer. The results indicate that this method is suitable for stress measurement in deep soft rock, the characteristics of which are soft, fractured and subjected to high geo-stress.

Failure Criteria for SentryGlas® Ionomer and TSSA Silicon: A Theoretical Introduction to a Novel Generalized Triaxial Model (GTM)

SentryGlas® (SG) (a transparent ionomer from Kuraray) and Transparent Structural Silicon Adhesive (TSSA) (a transparent silicon from Dow Corning) are two of the adhesive materials used in laminated adhesive connections for structural glass applications. Although they have been used in several projects worldwide, failure criteria for these materials are currently not available in literature. This work gives an introduction to the theoretical development of a novel failure a criterion for TSSA and SG under varying stress state conditions. The main output of this work is a four-dimensional Generalized Triaxial Model (GTM) that accounts for a generic stress state by a governing equation expressed as a function of the three-dimensional stress tensor. Both deviatoric and hydrostatic energetic components are taken into consideration by means of a non-linear function of the two contributions. The effects of the model parameters are investigated by a parametrical study. The proposed model is then analytically compared to existing failure criteria. It is shown that many of the existing models available in the literature can be seen as particular cases of the proposed model. Although the GTM was theoretically developed specifically for SG and TSSA, the model can be generically used as failure criterion for many isotropic materials.

Experimental Investigation on the Mechanical Behavior of a New Three-Dimensional Pressure Transducer

Accurate measurements of in situ stress in deep soft rocks are needed to design the tunnel support system and to evaluate the stress redistribution process. Due to the difficulty and weakness of current methods in deep soft rock stress measurement, a new one, rheological stress recovery method to determine the three-dimensional stress tensor is proposed. It is supposed that rock stresses will recover gradually with time and can be measured by embedding transducers into the borehole. According to this method, an original three-dimensional pressure transducer to measure rock stresses is designed and manufactured. In order to investigate the accuracy of the measurement, calibration test and model test have been performed. Both uniaxial and tri-axial calibration tests are conducted to evaluate the transducer performance. For model test, the cement mortar was used to simulate the effect of the surrounding materials. This test considered different rock strengths as well as different types of loading. The results indicate that this transducer is good for stress measurement.

Stress and pore pressure histories in complex tectonic settings predicted with coupled geomechanical-fluid flow models

Most of the methods currently used for pore pressure prediction in sedimentary basins assume one-dimensional compaction based on relationships between vertical effective stress and porosity. These methods may be inaccurate in complex tectonic regimes where stress tensors are variable. Modelling approaches for compaction adopted within the geotechnical field account for both the full three-dimensional stress tensor and the stress history. In this paper a coupled geomechanical-fluid flow model is used, along with an advanced version of the Cam-Clay constitutive model, to investigate stress, pore pressure and porosity in a Gulf of Mexico style mini-basin bounded by salt subjected to lateral deformation. The modelled structure consists of two depocentres separated by a salt diapir. 20% of horizontal shortening synchronous to basin sedimentation is imposed. An additional model accounting solely for the overpressure generated due to 1D disequilibrium compaction is also defined. The predicted deformation regime in the two depocentres of the mini-basin is one of tectonic lateral compression, in which the horizontal effective stress is higher than the vertical effective stress. In contrast, sediments above the central salt diapir show lateral extension and tectonic vertical compaction due to the rise of the diapir. Compared to the 1D model, the horizontal shortening in the mini-basin increases the predicted present-day overpressure by 50%, from 20 MPa to 30 MPa. The porosities predicted by the mini-basin models are used to perform 1D, porosity-based pore pressure predictions. The 1D method underestimated overpressure by up to 6 MPa at 3400 m depth (26% of the total overpressure) in the well located at the basin depocentre and up to 3 MPa at 1900 m depth (34% of the total overpressure) in the well located above the salt diapir. The results show how 2D/3D methods are required to accurately predict overpressure in regions in which tectonic stresses are important.

Nano-optical conveyor belt with waveguide-coupled excitation.

We propose a plasmonic nano-optical conveyor belt for peristaltic transport of nano-particles. Instead of illumination from the top, waveguide-coupled excitation is used for trapping particles with a higher degree of precision and flexibility. Graded nano-rods with individual dimensions coded to have resonance at specific wavelengths are incorporated along the waveguide in order to produce spatially addressable hot spots. Consequently, by switching the excitation wavelength sequentially, particles can be transported to adjacent optical traps along the waveguide. The feasibility of this design is analyzed using three-dimensional finite-difference time-domain and Maxwell stress tensor methods. Simulation results show that this system is capable of exciting addressable traps and moving particles in a peristaltic fashion with tens of nanometers resolution. It is the first, to the best of our knowledge, report about a nano-optical conveyor belt with waveguide-coupled excitation, which is very important for scalability and on-chip integration. The proposed approach offers a new design direction for integrated waveguide-based optical manipulation devices and its application in large scale lab-on-a-chip integration.

Analytical Investigation for In Situ Stress Measurement with Rheological Stress Recovery Method and Its Application

In situ stress is one of the most important parameters in underground engineering. Due to the difficulty and weakness of current stress measurement methods in deep soft rock, a new one, rheological stress recovery (RSR) method, to determine three-dimensional stress tensor is developed. It is supposed that rock stresses will recover gradually with time and can be measured by embedding transducers into the borehole. In order to explore the relationship between the measured recovery stress and the initial stress, analytical solutions are developed for the stress measurement process with RSR method in a viscoelastic surrounding rock. The results showed that the measured recovery stress would be more close to the initial stress if the rock mass has a better rheological property, and the property of grouting material should be close to that of rock mass. Then, the RSR method, as well as overcoring technique, was carried out to measure the in situ stresses in Pingdingshan Number 1 coal mines in Henan Province, China. The stress measurement results are basically in the same order, and the major principal stresses are approximately in the direction of NW-SE, which correlates well with the stress regime of Pingdingshan zone known from the tectonic movement history.

Testing of a single-polarity piezoresistive three-dimensional stress-sensing chip

A new piezoresistive stress-sensing rosette is developed to extract the components of the three-dimensional (3D) stress tensor using single-polarity (n-type) piezoresistors. This paper presents the testing of a micro-fabricated sensing chip utilizing the developed single-polarity rosette. The testing is conducted using a four-point bending of a chip-on-beam to induce five controlled stress components, which are analyzed both numerically and experimentally. Numerical analysis using finite element analysis is conducted to study the levels of the induced stress components at three rosette-sites and the levels of the stress field non-uniformities, and to simulate the extracted stress components from the sensing rosette. The experimental analysis applied tensile and compressive loads over three rosette-sites at different load increments. The experimentally extracted stress components show good linearity with the applied load and values close to the numerical model.