Components Of Stress Field Research Articles

Constraint on the background stress in the source region of the 2016 Kumamoto earthquake sequence based on temporal changes in elastic strain energies and coseismic stress rotation

SUMMARY We investigated the deviatoric stress magnitude of the background stress fields before the 2016 Kumamoto earthquake sequence in Japan based on temporal changes in elastic strain energies caused by the mainshock and coseismic stress rotation. We modelled the six components of background stress fields from stress orientations together with the parameter of effective friction coefficients (μ’ = 0.3, 0.15, 0.1, 0.05 and 0.03) using the 3-D Mohr diagram. We computed the absolute stress fields immediately following the primary events (the largest foreshock and mainshock) of the earthquake sequence by combining coseismic stress change fields with background stress fields. The total amount of elastic strain energy released by the mainshock increased with the effective friction coefficient. Considering the energy balance in which some part of the released energy must be consumed as radiated energy, we understood that the model with μ’ = 0.03 was unrealistic. We also examined the dependence of coseismic stress rotation on the effective friction coefficient. Furthermore, we applied a stress inversion method to moment tensor data of earthquakes to directly estimate coseismic stress rotation. Comparing the theoretical and estimated coseismic stress rotations, we concluded that the models with μ’ = 0.3 and 0.15 were more consistent with the observations than those with μ’ < 0.1. In the reasonable models, the deviatoric stress magnitudes were 37–65 and 39−70 MPa at a depth of 10 km on the northern and southern source faults, respectively.

Couple-stress thermoelasticity of three-dimensional multilayered composites

This work presents a comprehensive analysis of field solutions for three-dimensional multilayered composites within the framework of the couple-stress thermoelasticity. Using double Fourier series expansion solutions, the powerful and elegant mathematical Stroh formalism is extended to include the thermal coupling with the couple-stress elasticity theory to capture small-scale microstructural effects. The size-dependent layered approach leads to concise and general eigenrelations for each homogeneous orthotropic plate, while the unconditionally stable dual-variable technique is used to propagate the extended displacement/temperature fields and force-/tangential couple-tractions through the internal interfaces of the multilayered structures. Closed-form expressions are derived for the recursive layer-to-layer relations, as well as for the temperature, heat flux, displacement, stress and couple-stress field components, with respect to simply-supported structures subjected to combined thermal and mechanical loading. Application examples, including highly anisotropic fiber-reinforced composites, show significant deviations from the classical thermoelasticity, demonstrating the critical importance of considering the microstructural characteristics of interface-dominated materials. The results result come from a series of scenarios, covering mechanical and thermomechanical loading conditions, changes in aspect ratios and stacking sequences within multilayered systems, and the consequences of varying the number of sandwich plates.

Статистичний метод визначення параметрів поля зсувних напружень в площині ковзання в багатокомпонентному сплаві

A method has been developed in which atomic sizes misfit and elastic modulus misfit at crystal lattice nodes are considered as discrete random variables and the definition of their dispersion allows to obtain analytical expressions for standard deviations and correlation lengths of the short- and long-wave components of stochastic shear stress field created by solute atoms in the glide plane in a multicomponent alloy. This makes it possible to significantly reduce the amount of calculations when determining the shear stress field parameters. The developed method was applied to calculate these parameters for the CrCoNiFeMn alloy. The calculated parameters were well correlated with similar parameters determined from the analysis of shear stress distributions in the glide plane, which were calculated by the method of direct summation of solute atoms contributions. In addition, it was found that there are separate effective crystal lattice distortions for the short- and long-wave components that differ from the average distortion that was proposed earlier. This results from the fact that these components are determined by solute atoms with different distance from the glide plane. Effective distortion is greater, the greater this distance from the glide plane. In addition, there is no single empirical constant for all alloy to determine the yield strength as a function of their shear modulus and average distortion. But the proposed method makes it possible to determine the main parameters of the shear stress field in a specific multicomponent alloy. These parameters can be used to calculate the yield strength of this alloy. Keywords: shear stress, multicomponent alloy, glide plane, solid solution.

Stress field model for bond in reinforced concrete ties

The interaction of the reinforcing bars and the surrounding concrete plays an important role in structural concrete as it is decisive for the reinforcing bar anchorage and the load-deformation behaviour, including stiffness and deformation capacity. Therefore, understanding this interaction – commonly known as bond – is highly relevant to a safe and efficient structural concrete design. Bond depends on many parameters, which affect the local reinforcing bar-concrete interface as well as the global load transfer between the reinforcing bars and the surrounding concrete. The latter governs the formation of transverse and longitudinal cracks and the activation of transverse confinement, which are as decisive for bond as the local interface characteristics. Nonetheless, most bond models and code provisions focus on the local interface and merely account for the global configuration by means of empirically calibrated factors accounting, e.g. for good or bad bond conditions in confined or unconfined situations, respectively.This study investigates the potential of stress fields for modelling bond based on the lower-bound theorem of plasticity theory. Stress fields facilitate the investigation of the local interface and the global load transfer consistently in one model, providing valuable insight into the flow of forces. For simplicity, the fundamental case of a concrete tie reinforced with one deformed steel bar is studied in this paper, superimposing axisymmetric discontinuous stress fields originating at each reinforcing bar rib. Each stress field consists of a triaxial nodal zone adjacent to a rib and a conical compression field that spreads the bond force radially, and is equilibrated along its outer perimeter by axial tensile stresses and confining hoops. The model relies on geometric parameters and basic material properties. The validation against experiments on reinforced concrete ties shows a good correlation between the predicted and observed bond strength and the crack spacing. The predictions can be improved by assigning stiffnesses to the stress field components and requiring interface compatibility, i.e. ensuring contact between the concrete and the reinforcing bar at every rib. Even when assuming a simplified, linearly elastic constitutive behaviour for concrete, the consideration of interface compatibility allows for reproducing the steel strain dependency of the local and average bond stresses and the occurrence and impact of splitting cracks.

Дві компоненти поля зсувних напружень в площині ковзання в багатокомпонентних сплавах

It was found that dissolved atoms in the two nearest atomic planes on each side of the glide plane in the multicomponent alloy CrCoNiFeMn create a short-wave component of the shear stress field in the glide plane. This component is characterized by greater standard deviation and shorter correlation length in comparison with the long-wave component. The long-wave component of the stress field is created by dissolved atoms that are located farther from the glide plane. This component has a correspondingly smaller standard deviation and longer correlation length than the short-wave one. Both components depend on the test segment length of dislocation. The stress calculated for a certain test segment length is actually averaged over this segment. The standard deviations of the short-wave and long-wave components of the stress field are complex functions of the test segment length. They generally decrease with increasing this length. The reduction of the short-wave component is especially noticeable at short test segment lengths. The correlation lengths opposite almost do not depend on the test segment length. The ratio between the standard deviations of the short-wave and long-wave components becomes such that it does not allow to neglect the long-wave one, when the test segment length is approximately equal to the full correlation length of the long-wave component. Two components of the shear stress field could explain the thermal and athermic components of the solid solution strengthening of multicomponent alloy. Keywords: shear stresses, solid solution, glide plane.

Evaluating tectonic dislocations formation under the action of stresses at the Upper Kama potassium salt deposits

Introduction. The studies of the tectonic structure, dynamic behavior and prediction of the areas of the most probable manifestation of hazardous dynamic events at the Upper Kama potassium salt deposits (VKMKS) revealed that active faults, nodal structures, fracture zones and individual fractures in the oversalt, salt and subsalt rocks exercise a decisive influence on the violation of the steady state of geological structure. The regional stress field and a large number of local factors caused by folding, basement tectonics (catagenetic and supergene leaching), exogenous (weathering and unloading) and endogenous (halokinesis) processes in the oversalt strata, the growth of dome structures, etc. cause tectonic dislocations in the VKMKS. Cracks and fissure zones have currently been incidentally mapped and quantitatively studied mainly in mine workings in the productive part of the deposit, to a lesser extent in the oversalt rock, and scarcely in subsalt deposits. A detailed high-precision gravity prospecting along with other geophysical methods is currently the only effective method for tectonic dislocations mapping in the rock mass of the VKMKS. Methods for the widespread and systematic mapping of tectonic dislocations both in plan and in section within the VKMKS have not been developed yet. However, the evaluation of kinematic tectonic dislocations development in bulk can be obtained to some extent by analyzing the qualitative and quantitative characteristics of the natural stress field. It is due to the fact that dislocations are formed only when the acting stress exceeds the limit of the corresponding longterm strength of rocks forming the object under study. Methods of research. Tectonic dislocations of various kinematic types are formed under the action of stresses. Kinematic dislocations depend on the relationships between the stress principal values. Therefore, to solve the problem of kinematic type in the Solikamsk depression (SD) and VKMKS, the data of natural stress field components measurement in Ural mine workings were analyzed, the regularities of its behavior in plan and depth were determined, which served as the basis for two mathematical models, regional and local. Research results. Mathematical modeling was carried out, giving a quantification of stress components behavior regularities with the depth for the tectonic and physical-geological conditions of SD and VKMKS. Conclusions. The data on the change in stress components, obtained from mathematical modeling for two models of the geological environment, made it possible to predict the regularities in formation of tectonic dislocations of various kinematic types at different depths in SD and VKMKS at the regional and detailed scale levels.

CREEP OF A THICKWALLED QUASILINEAR VISCOELASTIC TUBE UNDER A CONSTANT EXTERNAL AND INTERNAL PRESSURE

We consider the creep problem for a quasilinear viscoelastic model of a thickwalled tube, loaded with constant internal and external pressure; the material is supposed to be incompressible. An exact solution to this problem was received by one of the authors in previous papers, assuming the state of a tube to be plain deformation; hereby we study properties of this solution for arbitrary material functions of quasilinear viscoelasticity constitutive relation. A criterion of stress stationarity is derived; the stress field of a thickwalled tube under a constant pressure evolves in time in the case of unbounded creep function and arbitrary nonlinearity function, except some particular types. The monotonicity of stress field components is studied: the radial stress monotonicity depends only on internal and external pressure values (for internal pressure, greater than an external one, it is negative and increases in radii). For other stress components, there are derived sufficient conditions of monotonicity. For an exponential nonlinearity function and unbounded creep function, a creep curve is determined to be concave up at the initial moment, and concave down during prolonged observation; the creep curve of a bipower nonlinearity function model may change its convexity. The stressstrain state of a model with a bounded creep function is proved to be bounded.

Substantiating the optimal type of mine working fastening based on mathematical modeling of the stress condition of underground structures

Purpose. Predicting the formation of a stress-strain state (SSS) in the rock mass within the boundaries of influence of stope operations on the horizon -480 m in axes 2028 at the 10th Anniversary of Kazakhstans Independence (DNK) Mine. Methodology. An engineering-geological data on the host rocks properties are analyzed based on the international ISRM standard. Numerical modelling of the rock mass stress-strain state and the calculation of the load-bearing capacity of the compound support (roof-bolt+shotcrete+mesh) and arch support used at the mine are performed with the help of the RS2 software. This program, based on the Finite Element Method in a two-dimensional formulation, makes it possible to take into account a significant number of factors influencing the rock mass state. Findings. The calculations performed indicate that the support resistance is incommensurably low in comparison with the values of the initial stress field components in the rock mass. In such conditions, it may be more effective to strengthen the mass in the vicinity of mine working than setting more frames or using more massive support profiles. Originality. The paper presents the results of mathematical modeling and calculation of the stress-strain state of the underground supporting aquifer rock mass structures developed for complex mining-and-geological and geomechanical conditions of driving, supporting and operating mine workings on deep horizons of the mines at Donskoy Ore Mining and Processing Plant. Based on the performed research, the preliminary (advanced) strengthening of the border rock mass in the zone of inelastic (destructive) deformations has been substantiated, as a priority method to control the stability of mine workings. Practical value. The research results can be used when creating a geomechanical model of the field and designing stable parameters of mine working support.

A micromechanical model for overlapped short platelet-reinforced composites

An analytical model was developed for rectangular overlapped platelet reinforced composites subjected to unidirectional axial load. Two sets of the matrix/platelet displacement solutions (far-field and transient), were exactly derived based on the theory of elasticity. These displacement solutions were then superposed for achieving analytical expressions for the matrix/platelet 3D stress field components over the entire composite system including the platelet end region, using the adding imaginary fiber technique. The platelet/matrix components could exactly satisfy the equilibrium and compatibility conditions and satisfy the equilibrium requirements and the overall boundary conditions. The obtained analytical results were then validated by the Shear-lag model.

Characteristic analysis of inductor in pulsed power supply changing with shape ratio

Solenoid inductor is an important component of pulse power source, its volume, electrical performance, stress and magnetic field generated during discharge directly affect the relevant parameters and performance of pulse power source. This paper presents a calculation model for solenoid inductor in pulsed power supply, given the inductance value and the wire, the volume, stress, resistance and external magnetic intensity of the five inductance values inductor under different shape ratio are calculated by changing the number of turns, and discusses and analyzes the changes and extremum in the volume, resistance, stress, and magnetic intensity of inductor with shape ratio. This article has certain guiding significance for the design of solenoid inductors.

GENERAL SOLUTION OF ELASTICITY PROBLEMS IN TWO DIMENSIONAL POLAR COORDINATES USING MELLIN TRANSFORM

Abstract In this work, the Mellin transform method was used to obtain solutions for the stress field components in two dimensional (2D) elasticity problems in terms of plane polar coordinates. the Mellin transformation was applied to the biharmonic stress compatibility equation expressed in terms of the Airy stress potential function, and the boundary value problem transformed to an algebraic problem which was solved to obtain the Mellin transformed Airy stress potential function. The Mellin transform was similarly used to obtain the Mellin transformed stress field components. The use of Mellin transform inversion formula yielded the solutions to the 2D elasticity problem in the physical space domain variables. Specific illustration was considered of the solution by using the Mellin transform method for the Flamant problem and the Mellin transform solutions found to agree with solutions from the literature.

Natural stress estimation by solving inverse problem using acoustic sounding data

Under consideration is the approach allowing quantitative estimation of natural stress field components in the vicinity of underground objects based on solution of an inverse boundary-value problem using the data on acoustic sounding in an extended mine working. To ensure solvability of an inverse problem, the optimal sonic transmitter–receivers positioning and the limiting nominal error of measurements are determined. The objective function is set as a root-mean-square difference between the theoretical and actual head P-wave arrival times at the receivers; unimodelity of the objective function is illustrated using synthetic input data.

Stress distribution in laser metal deposited multi-layer thick-walled parts of Ti-6Al-4V

The laser metal deposition is an additive manufacturing technology enabling the production of large scale complex parts without additional treatment like welding or machining. The study of the origin of the stress field during laser metal deposition is essential for solving a number of problems, including: the assessment of cold and hot cracking; prediction of the fatigue resistance, and the stress corrosion cracking. The quantitative study of transient and residual stresses in build parts is necessary for optimising the parameters of processing and post-production stress relieving heat treatment. Residual stress field in laser metal deposited 50-layer (4-pass per layer) wall of Ti-6Al-4V was analysed experimentally using neutron diffraction and numerically using finite element simulation. Long dwell time between passes and a rigid substrate was used in order to simulate conditions of large scale parts fabrication. An analysis of the calculated and experimentally measured residual stress field showed that near the edges of the buildup there is a region where all three components of stress field are tensile, and normal stress exceeds the yield stress by more than 25%. Moreover, normal plastic strain in this area are also tensile and reaches 2.5-3%. The longitudinal tensile stress closes to yield stress on almost the entire length of the several last layers near the top of the buildup. Residual stress field calculated using neutron diffraction data according to interplanar lattice distance obtained assuming plane stress approach has a satisfactory agreement with FE simulated results.

Compressional stability of optical fibres: a combined experimental and computer study

Compressional stability is an important mechanical factor that influences the overall performance of a fibre. Assessment of the compressive stability and internal-stress distribution of a fibre must be performed to determine the effect of stress-induced birefringence due to the high deformation gradients in an unstable fibre. The purpose of this study is to combine experimental and finite element investigations of stress evolution and large post-buckling fibre deformations. The results of this study show that stability is greatly influenced by the initial curvature of the fibre. Increasing the deformation of the fibre leads to post-buckling behaviour that results in a fibre taking a complex shape with altered stress-field components. The results are compared with the analytical relation given by Euler’s theory of a thin beam and show that the simple analytical formula cannot predict the complicated post-buckling states and stresses.

A thermodynamic framework to analyze the thermal shock response in an anisotropic hollow cylinder with energy dissipation

PurposeThe purpose of this paper is to analyze the thermal shock response on the deformation of circular hollow cylinder in a thermodynamically consistent manner.Design/methodology/approachThe investigation is carried out under the light of generalized thermoelasticity theory with energy dissipation. In order to obtain the analytical expressions of the components of stress and strain fields, appropriate integral transform technique is adopted and the salient features are emphasized.FindingsIt has been observed that the existence of energy dissipation can minimize the development of the stress components into the cylindrical wall. Since more amount of heat is propagate into the medium in a short period of time consequently, the medium deformed in a high rate in presence of energy dissipation. Two special phenomena are also revealed in the particular cases.Originality/valueThe numerical simulated results are demonstrated through a numerous diagrams and some important observations are explained. This work may be helpful for those researchers who are devoted on several types of heat or fluid flow into the pipeline made with anisotropic solids.

Three-dimensional singular elastostatic fields in a cracked Neo-Hookean hyperelastic solid

The boundary-value problem of Neo-Hookean incompressible hyperelastic cracked solid under a superposition of a plane deformation to an anti-plane one is formulated. An asymptotic analysis is then employed to compute the elastostatic fields near the crack front and their principal properties are illustrated. In a particular basis, the crack is bound to open independently of the magnitude and the mode of the boundary conditions at infinity. The stress field components have different singularities and each one can posses more than one singular term. Some disagreements with the linear theory are evidenced.

Improving the accuracy of derivation of the Williams’ series parameters under mixed (I+II) mode loading by compensation of measurement bias in the stress field components data

A new method for compensation of bias in the stress field components measurement data used for Williams’ series parameters derivation was presented. Essential increase of accuracy of derivation of SIF-related leading terms in series under mixed (I+II) mode loading was demonstrated. It was shown that a relatively low value of bias in the stress field components data error could result in the essential deviation of the values of derived Williams’ coefficients and the crack tip coordinates.

Electric field dependence of optical phonon frequencies in wurtzite GaN observed in GaN high electron mobility transistors

Due to the high dissipated power densities in gallium nitride (GaN) high electron mobility transistors (HEMTs), temperature measurement techniques with high spatial resolution, such as micro-Raman thermography, are critical for ensuring device reliability. However, accurately determining the temperature rise in the ON state of a transistor from shifts in the Raman peak positions requires careful decoupling of the simultaneous effects of temperature, stress, strain, and electric field on the optical phonon frequencies. Although it is well-known that the vertical electric field in the GaN epilayers can shift the Raman peak positions through the strain and/or stress induced by the inverse piezoelectric (IPE) effect, previous studies have not shown quantitative agreement between the strain and/or stress components derived from micro-Raman measurements and those predicted by electro-mechanical models. We attribute this discrepancy to the fact that previous studies have not considered the impact of the electric field on the optical phonon frequencies of wurtzite GaN apart from the IPE effect, which results from changes in the atomic coordinates within the crystal basis and in the electronic configuration. Using density functional theory, we calculated the zone center E2 (high), A1 (LO), and E2 (low) modes to shift by −1.39 cm−1/(MV/cm), 2.16 cm−1/(MV/cm), and −0.36 cm−1/(MV/cm), respectively, due to an electric field component along the c-axis, which are an order of magnitude larger than the shifts associated with the IPE effect. Then, we measured changes in the E2 (high) and A1 (LO) Raman peak positions with ≈1 μm spatial resolution in GaN HEMTs biased in the pinched OFF state and showed good agreement between the strain, stress, and electric field components derived from the measurements and our 3D electro-mechanical model. This study helps to explain the reason the pinched OFF state is a suitable reference for removing the contributions of the electric field and the IPE-induced stress from the temperature rise in the ON state and suggests that the IPE-induced stress in the GaN buffer is an order of magnitude smaller than previously believed. Our analysis and experimental results support previous theoretical studies discussing the electric field dependence of optical phonon frequencies apart from the IPE effect and suggest that this is a general phenomenon occurring in all wurtzite and zincblende crystals. The total electric field dependence of the optical phonon frequencies in piezoelectric crystals is a critical consideration in accurately characterizing the stress, strain, electric field, and temperature distributions in microelectronic devices via micro-Raman spectroscopy.

Reconstruction of 3D stress field in coal–rock mass by solving inverse problem using tomography data

The theoretically evaluated multi-disciplinary approach enables determination of stress state of a coal–rock mass in the area of coal cutting using a package of geomechanical and geophysical information. The approach is based on successive solutions of two inverse problems in the framework of a geomechanical model: coal-bed tomography and assessment of horizontal components of external stress field. The numerical experiments demonstrate resolvability of the inverse problems given appropriate monitoring system ensures sufficient seismic coverage of a coal-bed in the domain of steep spatial gradients of elastic waves and the presence of regular composition in the frequency range of the order of hundreds of hertz in the sounding signal generated by a cutter–loader and/or other coal-face work machinery.

Contributed Review: Experimental characterization of inverse piezoelectric strain in GaN HEMTs via micro-Raman spectroscopy

Micro-Raman thermography is one of the most popular techniques for measuring local temperature rise in gallium nitride (GaN) high electron mobility transistors with high spatial and temporal resolution. However, accurate temperature measurements based on changes in the Stokes peak positions of the GaN epitaxial layers require properly accounting for the stress and/or strain induced by the inverse piezoelectric effect. It is common practice to use the pinched OFF state as the unpowered reference for temperature measurements because the vertical electric field in the GaN buffer that induces inverse piezoelectric stress/strain is relatively independent of the gate bias. Although this approach has yielded temperature measurements that agree with those derived from the Stokes/anti-Stokes ratio and thermal models, there has been significant difficulty in quantifying the mechanical state of the GaN buffer in the pinched OFF state from changes in the Raman spectra. In this paper, we review the experimental technique of micro-Raman thermography and derive expressions for the detailed dependence of the Raman peak positions on strain, stress, and electric field components in wurtzite GaN. We also use a combination of semiconductor device modeling and electro-mechanical modeling to predict the stress and strain induced by the inverse piezoelectric effect. Based on the insights gained from our electro-mechanical model and the best values of material properties in the literature, we analyze changes in the E2 high and A1 (LO) Raman peaks and demonstrate that there are major quantitative discrepancies between measured and modeled values of inverse piezoelectric stress and strain. We examine many of the hypotheses offered in the literature for these discrepancies but conclude that none of them satisfactorily resolves these discrepancies. Further research is needed to determine whether the electric field components could be affecting the phonon frequencies apart from the inverse piezoelectric effect in wurtzite GaN, which has been predicted theoretically in zinc blende gallium arsenide (GaAs).