Calculation Of Stress Field Research Articles

The Equilibrium Condition of a Non-Thin Screw Wedge-Shaped Twin Located in the Distance from the Surface of an Undeformed Crystal

The equilibrium condition for a non-thin helical wedge-shaped twin located far from the surface of the crystal is obtained. The case of an undeformed solid is considered. It is established that under such conditions a helical twin can not twin can not exist under such conditions. The result is in full conformity with generally known results for dislocation walls from helical dislocations. An approximation for continuous distribution of twinning dislocations at twin boundaries has been used in methodology for deriving an equilibrium condition. The shape of the twin boundaries has been described by functions that depend on density of the twinning dislocations at the twin boundaries. It has been assumed that the forces acting on the twin boundaries from the side of the twin dislocations are equal to zero. One degree of freedom along a twinning direction has been presupposed for twinning dislocations. Dislocation creeping effects have been excluded in the model. A calculation of stress fields for a twin has been carried out within the framework of an elasticity theory. In this case a superposition of stresses from each twin boundary has been considered. The solution of equations has been sought in the form of a polynomial. A linear approximation of such solution is considered in detail. The ем resulting equilibrium condition is satisfied for two values equal to zero that is a twin length and its width at the mouth. The result is important in the field of mechanics for twinning materials, shape memory materials, and in the development of techniques for predicting destruction and functioning of twinning materials.

Distribution and magnitude of stress due to lateral variation of gravitational potential energy between Indian lowland and Tibetan plateau

Magnitudes of differential stress in the lithosphere, especially in the crust, are still disputed. Earthquake-based stress drop estimates indicate median values ca. 180 MPa, corresponding to a friction angle of ca. 10° to maintain the topographic relief between lowland and plateau for >10 Ma. The relative contribution of crustal strength to total lithospheric strength varies considerably laterally. In the region between lowland and plateau and inside the plateau the depth-integrated crustal strength is approximately equal to the depth-integrated strength of the mantle lithosphere. Simple analytical formulae predicting the lateral variation of depth-integrated stresses agree with numerically calculated stress fields, which show both the accuracy of the numerical results and the applicability of simple, rheology-independent, analytical predictions to highly variable, rheology-dependent stress fields. Our results indicate that (1) crustal strength can be locally equal to mantle lithosphere strength and that (2) crustal stresses must be at least one order of magnitude larger than median stress drops in order to support the plateau relief over a duration of ca. 10 Ma.

Discrete Loading Ring-Core Method for Nonuniform In-Plane Residual Stress Analysis in Micro Area

The ring-core method is often used in residual stress analysis. It is applied to macro- and microscale stress analysis and has a unique advantage of releasing the residual stress across the core instead of at a single point, which makes it possible to measure an uneven residual stress field within a limited area, especially when the area is too small to be measured by other techniques. We developed a new layer-by-layer stress analysis method based on the ring-core method to retrieve the uneven in-plane stress, in which a nonuniform load that surrounds the core is approximated by discrete loading and then used to reveal the stress distribution within the core. The displacement–stress relationship is calibrated through finite element simulation. Because of the difficulty of preparing a standard specimen with an accurate high-gradient in-plane field stress in an area of several micrometers, the performance of the method was tested by a finite element simulation experiment. Good matches were achieved when comparing the calculated stress fields and the stress fields in the simulation experiments, including the biaxial, uniaxial and high-gradient cases. The method was applied to a piece of superconductor stand with a highly nonuniform stress by using a 4 μm-diameter-area ring core cut with focused ion beam.

A bi-criteria combined evaluation approach for reinforcement effect of gravity dam with cracks

The reinforcement measures, such as pre-stressed anchor cable and concrete anti-seepage layer covering original dam body, are often used to improve the structural stability, control the crack development and advance the carrying capacity of concrete dam engineering. This paper focuses on the reinforcement effect evaluation problem of gravity dam with cracks. Some mechanical and mathematical methods, such as the J integral and interaction integral methods in fracture mechanics, the support vector machine (SVM) method, are combined. According to the integrated criteria on crack behavior improvement and carrying capacity advancement, the implementation approach for reinforcement effect identification and long-term forecast of gravity dam with cracks is investigated. Firstly, considering the effect of reinforcement practice on structural behavior, stress field and strain field of original crack tip zone in gravity dam, the stress intensity factor (SIF) is taken to represent the combined action response of reinforcement practice and loads. To improve the computation efficiency and accuracy, which are the shortcomings existing in the conventional methods applied to the calculation of stress field with complex crack surface and crack tip, the improved J integral method is combined with the interaction integral method to calculate the SIF of crack tip in gravity dam after the reinforcement implementation. Then, the cracking safety of gravity dam is regarded as a goal, the SIF is regarded as a control index. A SVM method is proposed to determine the critical loads ensuring the cracking safety of gravity dam. An approach using two criteria on SIF and critical load is developed to implement the reinforcement effect evaluation of gravity dam with cracks. Lastly, an actual gravity dam undergoing reinforcement practice is taken as an example. The approach proposed in this paper is used to calculate the SIF of crack tip and the critical loads of cracking safety. The reinforcement effect identification and long-term forecast of gravity dam are fulfilled by analyzing the development of SIF and critical load.

Stresses in Circular Plates with Rigid Elements

Calculations of residual stress fields are carried out by numerical and static methods, using the flat cross-section hypothesis. The failure of metal when exposed to residual stresses is, in most cases, brittle. The presence in the engineering structures of rigid elements often leads to the crack initiation and structure failure. This is due to the fact that rigid elements under the influence of external stresses are stress concentrators. In addition, if these elements are fixed by welding, the residual welding stresses can lead to an increase in stress concentration and, ultimately, to failure. The development of design schemes for such structures is a very urgent task for complex technical systems. To determine the stresses in a circular plate with a welded circular rigid insert under the influence of an external load, one can use the solution of the plane stress problem for annular plates in polar coordinates. The polar coordinates of the points are the polar radius and the polar angle, and the stress state is determined by normal radial stresses, tangential and shearing stresses. The use of the above mentioned design schemes, formulas, will allow more accurate determination of residual stresses in annular welded structures. This will help to establish the most likely directions of failure and take measures at the stages of designing, manufacturing and repairing engineering structures to prevent these failures. However, it must be taken into account that the external load, the presence of insulation can lead to a change in the residual stress field.

An improved stress recovery technique for low‐order 3D finite elements

SummaryIn this paper, we propose a stress recovery procedure for low‐order finite elements in 3D. For each finite element, the recovered stress field is obtained by satisfying equilibrium in an average sense and by projecting the directly calculated stress field onto a conveniently chosen space. Compared with existing recovery techniques, the current procedure gives more accurate stress fields, is simpler to implement, and can be applied to different types of elements without further modification. We demonstrate, through a set of examples in linear elasticity, that the recovered stresses converge at a higher rate than that of directly calculated stresses and that, in some cases, the rate of convergence is the same as that of the displacement field.

Pressurized Thermal Shock analysis of the reactor pressure vessel

PTS analysis is a substantial part of the technical analyses supporting the license application for operation beyond design life. Guidance for the analysis’ concept is given by the Hungarian nuclear regulator which is in line with the relevant international rules. Involving technical support organizations and independent consultants as well as taking into account the changes in fuel management Paks NPP, Hungary, compiled a new PTS analysis. Subjects of the analysis were the RPV belt line region components as well as other circumferential welds of the RPV including nozzle region. Beyond the PTS initiating events selected on the basis of engineering judgment a PSA provided additional transients which showed a higher frequency than 10-5 /year. Thermal-hydraulic calculations completed for each selected PTS initiating event provided the necessary input for the structural analysis. Based on core configurations end-of-life fluence were calculated. Neutron dosimetry surveillance results were used to verify the calculations. Temperature and stress field calculations were performed by solving the system of equations of elasticity. Underclad crack was postulated for fracture mechanics calculation. KI was calculated at the crack tip and the boundary between the cladding and base / weld metal; KIc was calculated on the basis of the reference curve. Comparison of these two parameters (KI ≤KIc), i.e. evaluation of whether the postulated defect stability criteria was met, gave the result.

The assessment of the impact of natural and anthropogenic factors on the current stressstrain state of rock massif of burst-hazardous ore deposits in the East of Russia

This paper does a case study of endogenous deposits located in the zone of influence of convergent (converging, colliding) boundaries of tectonic plates in the zone of the continent-ocean transition, where there is increased present seismic and geodynamic activity, covers the issues of the ratio of natural and anthropogenic components of the stress-strain state (SSS) in rock massifs. It has been shown that, despite the confinement of the studied deposits to a single rock structure, as well as the proximity of their common neotectonic position, the SSS of the rock massifs containing them varies significantly. Based on a comprehensive analysis of geological and geophysical data with the use of space data about the Earth (GRACE mission data for calculation of stress fields and radar images of the Earth's surface), the kinematics of the process of modern deformation of the upper part of the Earth's crust within the studied area is specified. It is established that the peculiarity of the region is the pronounced contribution of the natural component to the general present SSS of rock massifs of impactthreatening deposits. On a real example, the possibility of a predictive assessment of SSS has been shown, which is important at the stages of designing and conducting underground mining operations in severe mining-geological and burst -hazardous conditions.

Origin of the Dongsha Event in the South China Sea

Post-rift tectonic activities have been widely observed in the northern continental margin of the South China Sea, especially during the late Miocene. Large numbers of faults became active. Unconformities, uplift of faulted blocks, sequence tilting, erosion along the Dongsha massif and canyon incision were also discriminated at this stage in the Pearl River Mouth basin (PRMB) and the area to the east. This tectonism has been named Dongsha Event. A number of hypotheses have been put forward to explain the mechanism of the Dongsha Event, such as high-velocity lower crustal flow, magmatic underplating, and arc–continent collision. To investigate the tectonic dynamics, sequence contact relationships, fault activities, and magmatism were analyzed along large numbers of seismic profiles that cover the eastern PRMB and Southwest Taiwan Basin. The timing, affected regions, and differences in the intensity of tectonic deformation were assessed, upon which the plate bending model was favored. In order to check the reasonableness of plate bending model, effective elastic thickness and other geodynamic parameters were calculated constrained by uplift area width and regarding the trench as sediment filling. A maximum Te value of ~27 km and a minimum value of ~4 km were obtained. Integrating with the former stress field calculation, we conclude that the Dongsha Event was mainly affected by subduction and collision of the South China Sea toward the Philippine Sea plate. This event commenced at about 10 Ma and peaked at around 3.6 Ma. Although the high effective elastic thickness required is a problem to be addressed, this research provides by far the most comprehensive evidences to the mechanism of the Dongsha Event.

Experimental characterization of dynamic behaviour of gelatin-based material using DIC

In this paper, the dynamic response of gelatin-based soft material under impact loading is investigated. The dynamic tests are principally performed by the classical SHPB (Split Hopkinson Pressure Bars) technique. However, due to the very low mechanical impedance of the specimen compared with the Hopkinson bars, the feeble impact forces are measured by highly sensitive piezoelectric polyvinylidene fluoride (PVDF) pressure sensors instead of SHPB measurement system. The PVDF pressure sensors are placed on the interfaces between the specimen and the bars. During the impact test, the non-equilibrium stress state and inhomogeneous strain fields are developed in the specimen; a digital image correlation (DIC) technique is proposed to identify the inhomogeneous displacement fields using high speed photography. A non-parametric approach based on the DIC technique is developed to deduce the transient stress fields in the longitudinal and transverse directions from the displacement fields measured by DIC. The validation of the calculated stress fields is performed by comparing them with the stress measurements from the PVDF pressure sensor at the bottom end of the specimen. Furthermore, stress-strain response is carried out using this approach throughout the specimen. It is clearly shown that the average highest strain rate varies with position in the specimen. This lead to multiple stress-strain relations determined at different strain rates by only one impact test. The significant strain rate sensitivity is observed at the tested rate range from 81/s to 269/s. Under compression loading, the axial stress state is developed as a simple compression only in the central part of the specimen due to the friction at the interfaces between the specimen and the bars. According to the calculated results based on movement of “long waves”, the region of the simple compression stress state in the central part of the specimen is localized. It is observed that the axial stress is much more important than the transverse stress in the central part and this confirms the assumption of uni-axial compression stress state in the specimen.

Stress, Strain-Rate Analysis of Sub-Surface Driveway Plants

Sub-surface driveway plants are strong enough to penetrate a macadam surface of thickness 7 – 9 cm. The mechanics of how the Taraxacum officinale accomplishes this feat remain a mystery. Using the Maxwell model for pavement yielding over time, data are presented which may shed some light on this phenomenon. The post-buckling behavior of the plant stalk is quantified. Euler bending and buckling theory enables calculation of the cellular stress field, compared to turgor pressure, indicating impending cell buckling. Post-buckling plastic strain of the plant stem is 19%. At the cell wall, the stress concentration factor is 3-times greater than the applied external field, so the cell’s internal turgor pressure is overwhelmed by imposed external stress. An Impulse Integral is developed for the surface whereby the product of applied FORCE times TIME is CONSTANT, in order to produce a given amount of surface deflection. Taraxacum officinale stems and leaf stalks are strong enough, in buckling mode, to lift and push apart the fractured macadam crater through which they erupt, but not strong enough to initially crack the surface. The purpose of this work is to determine the mechanisms underlying this unusual plant survival phenomenon, backed by quantified data.

Experimental investigation of the acoustic anisotropy field in the sample with a stress concentrator

The behavior of acoustic anisotropy and the longitudinal wave velocity in the case of multiaxial stress-strain state of the plate under inelastic deformation has been studied experimentally. The plate had a stress concentrator in the form of the central hole. The results for several deformation levels, and the results of finite element analysis of active stresses were presented. The qualitative agreement between the calculated stress fields and the distribution fields of acoustic anisotropy was revealed. It was found that the absolute magnitude maximum of acoustic anisotropy fell on the areas with the biggest stresses near the concentrator. It was supposed that the non-uniform distribution of acoustic anisotropy in the material testified to a possible stress concentration at the corresponding points.

Practical aspects of welding residual stress simulation

The interest on calculating welding residual stresses from the welding process, through finite element (FE) simulation, has increased in the last decades. The prediction of residual stresses and strains is important for the industry, as it can ensure more efficient mechanical design and manufacturing process, reducing as well the time of post weld treatments. More specifically, in structural engineering, the residual welding stresses may have detrimental effect on earthquake, fatigue or stability behaviour. Weld simulation is a complex subject and the application of simplified models, for calculating the residual stresses, is quite usual in practice. For this reason, the results quite often deviate significantly from the experimentally measured residual stresses on real welds. This paper reports on a straightforward but robust engineering approach for the calculation of the residual welding stress field. State of the art methods are applied in some parts, whereas a new engineering approach is proposed, for modelling the material behaviour during a thermal cycle. Aim of the current work is to provide a calculation method for the engineers, which is repeatable for any material and weld geometry, using only material data easily found in literature. The proposed approach is validated with experimental results, which were found in older published work. The approach was modelled in the finite element software ANSYS [1]. The calculated and the measured residual stresses show good agreement. The approach was validated for a single-pass weld with material HT-36 steel (Swedish steel grade HT-36 with yield stress 355MPa) [2] and S355J2 [3].

An Effective Way to Control Numerical Instability of a Nonordinary State-Based Peridynamic Elastic Model

The constitutive modeling and numerical implementation of a nonordinary state-based peridynamic (NOSB-PD) model corresponding to the classical elastic model are presented. Besides, the numerical instability problem of the NOSB-PD model is analyzed, and a penalty method involving the hourglass force is proposed to control the instabilities. Further, two benchmark problems, the static elastic deformation of a simple supported beam and the elastic wave propagation in a two-dimensional rod, are discussed with the present method. It proves that the penalty instability control method is effective in suppressing the displacement oscillations and improving the accuracy of calculated stress fields with a proper hourglass force coefficient, and the NOSB-PD approach with instability control can analyze the problems of structure deformation and elastic wave propagation well.

Stress interference calculation model and its application in volume stimulation of horizontal wells

A new model for calculating stress fields of fractured media was established by incorporating stress correction factor based on displacement discontinuity boundary element method. The accuracy of the new model is close to 3D displacement discontinuity model, and its calculation is significantly simplified. An algorithm for multi-fracture propagation geometry was proposed based on fracture criterion and fracture growth rate law, which was used to investigate multi-fracture stress interference and propagation geometry. The results show that the size of stress interference is determined by the shortest dimension of fracture face, which is 1.2−1.5 times fracture height when fracture length is longer than fracture height, and 1.2−1.5 times fracture length when fracture length is shorter than fracture height. The larger the ratio of fracture spacing to fracture height, or the smaller the ratio of net pressure to the differential principle stress, the more close to well-bores the deviation position is, and the larger the deviation angle is. The middle fracture propagates to the fracture at a further distance and one dominating fracture propagates longest when three-cluster fractures are not equally spaced, while the middle fracture propagates straightly when three-cluster fractures are equally spaced.

Central-force decomposition of spline-based modified embedded atom method potential

Central-force decompositions are fundamental to the calculation of stress fields in atomic systems by means of Hardy stress. We derive expressions for a central-force decomposition of the spline-based modified embedded atom method (s-MEAM) potential. The expressions are subsequently simplified to a form that can be readily used in molecular-dynamics simulations, enabling the calculation of the spatial distribution of stress in systems treated with this novel class of empirical potentials. We briefly discuss the properties of the obtained decomposition and highlight further computational techniques that can be expected to benefit from the results of this work. To demonstrate the practicability of the derived expressions, we apply them to calculate stress fields due to an edge dislocation in bcc Mo, comparing their predictions to those of linear elasticity theory.

A new calculation model for the stress field of hydraulic fracture propagation at the formation interface

Reservoirs with different formation interfaces are becoming increasingly common in the exploitation of unconventional oil and gas reservoirs, such as shale oil and gas. Therefore, it is essential to calculate the stress field of fracture propagation to understand the mechanism of propagating hydraulic fractures near formation interfaces. This study adopts the superposition principle of same-type fractures and considers the model propagating hydraulic fractures at interfaces as the superposition of three issues: actuating the fluid pressure inside the fracture without far-field stress, analysis with far-field stress and without fractures, and calculating the self-balancing surface force effect on the surface of fractures without far-field stress. Then, the study establishes the stress field calculation model for propagating hydraulic fractures at the formation interfaces, which considers different rock properties on both sides of the formation interfaces, as well as the influence of the dip angle based on the complex variable function method and fracture mechanics theory. Finally, this paper proposes corresponding numerical methods. It is determined by analyzing different stress concentration which occurs around the fractures and stress singularity which occurs at the hydraulic fracture tips, analyzing the plastic zone at hydraulic fracture tips which propagates contacts with formation interfaces; the maximum compressive stress and normal stress change gradually from tensile stress to compressive stress as the distance between the interface and the hydraulic fracture tip increases, and the exhibiting stress reverses on the formation interfaces.

METHOD FOR CALCULATION OF STRESS-STRAIN STATE DUE TO SINGLE TWIN IN GRAIN OF VARIOUS FORMS

The paper investigates a stress-strain state in a polycrystalline grain due to presence in its body of a single micro- twin in case of various grain boundary forms. A methodology for calculation of displacement and stress fields for the specified stress-strain state of a polygon-shaped grain has been developed in the paper. Nodal points in a polycrystalline grain that have a maximum stresses contributing to initiation of destruction have been revealed in the paper. The aim of this work has been to study the stress-strain state due to a single micro-twin in the polycrystalline grain and form of grain boundaries. The paper describes polycrystalline grains having a regular polygon shape and containing a single wedge twin in their body. Polycrystalline grain boundaries are presented as walls with complete dislocation. The investigated grains are located far from the surface of twinning material. The developed methodology for calculation of displacement and stresses created by wedge twin is based on the principle of superposition. Calculations on stress tensor components have been carried out for iron (Fe). The presented results of calculations for stress fields have indicated to validity of the used dislocation model. Twin and grain boundaries being stress concentrators are clearly visible on the obtained distributions of stress fields. Maximum normal stresses are observed on the twin boundaries; σ xy maximum shear stresses are located at nodal points of the twin; σ zy and σ xz shear stresses are maximum on the grain boundaries. The conducted investigations have resulted in study of the stress-strain state due to a single wedge-shaped micro-twin in the polycrystalline grain and form of the grain boundaries. Zones of stress concentration in the polycrystalline grain have been identified in the presence of residual mechanical wedge twin. A method for evaluation of the given state has been developed in the paper.

Locally Exact Homogenization of Unidirectional Composites With Cylindrically Orthotropic Fibers

The elasticity-based, locally exact homogenization theory for unidirectional composites with hexagonal and tetragonal symmetries and transversely isotropic phases is further extended to accommodate cylindrically orthotropic reinforcement. The theory employs Fourier series representations of the fiber and matrix displacement fields in cylindrical coordinate system that satisfy exactly equilibrium equations and continuity conditions in the interior of the unit cell. Satisfaction of periodicity conditions for the inseparable exterior problem is efficiently accomplished using previously introduced balanced variational principle which ensures rapid displacement solution convergence with relatively few harmonic terms. As demonstrated in this contribution, this also applies to cylindrically orthotropic reinforcement for which the eigenvalues depend on both the orthotropic elastic moduli and harmonic number. The solution's demonstrated stability facilitates rapid identification of cylindrical orthotropy's impact on homogenized moduli and local fields in wide ranges of fiber volume fraction and orthotropy ratios. The developed theory provides a unified approach that accounts for cylindrical orthotropy explicitly in both the homogenization process and local stress field calculations previously treated separately through a fiber replacement scheme. Comparison of the locally exact solution with classical solutions based on an idealized microstructural representation and fiber moduli replacement with equivalent transversely isotropic properties delineates their applicability and limitations.

Investigating the change in surface acoustic wave velocity due to the change in adhesion of a SU-8 thin film using a SU-8/AlN/Si SAW sensor

This study investigates the change in surface acoustic wave (SAW) phase velocity due to the change in adhesion of a SU-8 thin film using an Aluminum Nitride (AlN)/Silicon (Si) SAW sensor. The variation in the stress field at the SU-8/AlN interface at different levels of SU-8 adhesion is also investigated and correlated to the change in SAW phase velocity. A theoretical model is developed to determine the change in wave dispersion profile due to the change in adhesion of the SU-8 film on the surface of the AlN/Si sensor. The interface of the SU-8/AlN layers is represented by a layer of massless springs with interface stiffness K (N/m3). The results illustrate that as the adhesion of the SU-8 film weakens on the surface of the AlN/Si SAW sensor the velocity dispersion profiles fluctuate. The calculated stress field at the SU-8/AlN interface also fluctuates because the weakened interface cannot sustain the increased stress due to the confinement of the wave near the interface. Therefore, the mode of wave propagation varies between the perfect bond case where the SU-8 layer is perfectly bonded to the AlN/Si surface and when the SU-8 is completely de-bonded. Four SAW sensor designs operating in the frequency range of 84–208MHz are developed to measure the shift in the center frequency values and the corresponding change in SAW phase velocities due to the change in adhesion of the SU-8 layer. The adhesion of the SU-8 film on the surface of the AlN/Si SAW sensor is changed by using different adhesion layers. The adhesion layers used are a gold film and an omnicoat coated gold film. Omnicoat is an adhesion promoter used to improve the adhesion of SU-8. The results illustrate that as the adhesion of the SU-8 film improves for the sensors with omnicoat the wave velocity shifts to a lower value. The wave velocity values are fitted with the wave dispersion profiles for different values of the interface spring stiffness K. The interface spring stiffness values for the SAW sensors with omnicoat coated gold and gold films are 8.1×109N/m3 and 7.95×109N/m3, respectively. The use of omnicoat improves the adhesion of the SU-8 film and corresponds to a higher interface spring stiffness value. The stress and displacement fields generated in the SU-8 layer for different values of the interface spring stiffness K are plotted. The results illustrate that as the adhesion of the SU-8 layer improves the stress transmitted to the SU-8 layer increases and the wave is more confined in the SU-8 layer, which justifies the drop in wave velocity since the Rayleigh wave velocity in SU-8 is much lower in comparison to AlN and Silicon; 1166, 5600, 5000m/s, respectively.