Distribution Of Tangential Stresses Research Articles

Stress Analysis of a Three-Layer Metal Composite System of Bearing Assemblies During Grinding

A mathematical model of the stress state of a three-layer metal composite system caused by cutting forces during grinding the working layer of the system is elaborated. The implementation of the model by using the finite-element method made it possible to assess the effect of structure of the system, the deformation properties of layer materials, and grinding conditions on the distribution and level of normal and tangential stresses in layers, which determine the load-carrying capacity of the system. The results of an analysis of stress fields can serve as a basis for determining the grinding conditions ensuring retention of the load-carrying capacity of the metal composite system.

Plotting of Rational Sections of Hydrotechnical Tunnels

Results of solution of problems related to the plotting of rational cross-sectional shapes of hydrotechnical tunnels with respect to a given normal tangential-stress distribution on its perimeter are presented as a function of the depth of embedment of the tunnel and values of the coefficient of thrust of the enclosing rock. It is demonstrated that the condition whereby there are no points on the perimeter of the tunnel at which values of the tangential normal stresses exceed the ultimate tensile and compressive strengths of the enclosing rock may serve as a criterion for this purpose. Examples of the problem’s solution are presented.

The Effect of Specimen Size on the Determination of Residual Stress in Polymer Pipe Wall

As a result of the production process, there are axial and tangential residual stresses present in pressure pipes made of polymer materials such as polyethylene or polypropylene. The residual stress magnitude and distribution have a significant influence on the pipe lifetime. In this contribution the results from experiments focused on determining the tangential residual stress distribution in the walls of polypropylene pipes of different dimensions are compared. The experimental method used involves measuring the deformation of ring shaped specimens that were slit in the axial direction. Measured deformation of the ring specimen is a result of the tangential and axial stress superposition. However, the effect of the axial residual stress depends on the specimen axial dimension and tangential residual stress estimated basing on experimental data should be corrected according to axial dimension of the specimen used. The correction suggested in this article is determined based on three-dimensional FEM simulations of the experiment.

Analytic solutions of stress and displacement for a non-circular tunnel at great depth including support delay

The stress and displacement field for a non-circular supported tunnel subjected to in situ stress is derived based on the conformal transformation method. The basic equations for solving the stress and displacement solutions were obtained according to the boundary conditions on the inner boundary of lining and the liner-surrounding rock–mass interface. If the analytic function was represented in terms of series expression, the coefficients in the series expressions were undetermined. Combining with the basic equations, linear equations for solving the coefficients can be derived. The stresses and displacements in the surrounding rock–mass and lining were calculated with support delay taken into consideration. If it is assumed to be a plane strain problem and the displacement completed in the surrounding rock–mass before support installation is given, the stress and displacement solutions for a tunnel at great depth can be obtained. The distributions of tangential stresses on the excavation boundary, the inner and outer boundaries of lining, of contact stresses on the lining-surrounding rock–mass can be obtained. If the number of terms in the series exceeds 100, the boundary conditions can be well satisfied and the stresses, displacements results will be accurate.

Numerical Analysis of the Effect of Slip Ratio on the Fatigue Crack Initiation Life in Rolling Contact

This paper presents a numerical analysis of the effect of slip ratio on the fatigue crack initiation life, considering the tangential traction on the rolling contact surface. The distribution of tangential traction and contact stresses on the contact surface, when rolling contact occurs between two cylindrical test specimens, are obtained using three-dimensional finite element analysis. The effect of slip ratio on the fatigue crack initiation life was evaluated by applying multiaxial fatigue criteria based on critical plane approaches. As a result, the 3D-FE model developed well represent the distribution of tangential traction and contact stresses on the contact surface at stick-slip condition, which is differ from the static or full sliding contact condition. As the slip ratio increases, the maximum tangential traction also increases in slip zone and the location of maximum stress closer to the contact surface in stick zone. The fatigue strength decreased with the increase in the slip ratio. Therefore, it is clear that the slip ratio has an important role in prediction of fatigue crack initiation life on the rolling contact surface.

Numerical Analysis of Fretting-Wear With a Hybrid Elastoplastic Friction Model

Fretting-wear is a common problem in different industries, especially when it comes to interactions between metallic components. Flow-induced excitation forces in heat exchangers for instance cause tube-support interactions. The long-term interaction is an important phenomenon, which may cause fretting-wear of the tubes. Experimental tests of the interaction show the occurrence of stick–slip intermittent behavior in the tube response. To precisely simulate the intermittent stick–slip behavior, it is crucial to refine the conceptual model of the coefficient of friction for the entire motion from absolute zero velocity to gross slip phase. The incorporated friction model plays an important role in the determination of the level of fretting-wear in the system. The friction model should satisfy two important criteria. The first important aspect is the strategy of the friction model to detect the cessation of sticking, the beginning of partial-slipping, and establishment of the sliding region. The second important aspect is defining a friction coefficient function for the entire system response to precisely represent the transient stick–slip regions. In the present work, the velocity-limited friction model was compared with the LuGre model, which is a rate-dependent friction model. The effect of varying the break-away force and Stribeck effect on the stick–slip region were also investigated. Furthermore, the criteria to demarcate the stick–slip region in the LuGre model are discussed, and a different method to incorporate the Stribeck effect and presliding damping in the Dahl friction model is proposed. Using the tangential stress distribution in the contact area, a new hybrid spring-damper friction model is developed. The model is able to estimate the elastic, plastic, and partial-slipping distances during the relative motion. The ability of the model to reproduce experimental tests is investigated in the present work.

Twist Springback of Asymmetric Thin-walled Tube in Mandrel Rotary Draw Bending Process

This paper aims to develop an effective numerical model and analyse the twist springback behaviour of asymmetric thin-walled tube in mandrel rotary draw bending. Yld2000-2d anisotropic yield criterion integrated with mixed isotropic and kinematic hardening model was used to describe the material properties including anisotropy and Bauschinger effect. The corresponding mechanical experiments such as uniaxial tension, monotonic and forward-reverse shear tests were performed to obtain the material parameters. A three-dimensional elastic-plastic finite element model was developed, and its validity was assessed by comparing the predicted twist springback with experiment one. Based on the present FE model, the tangential stress distribution during different bending steps were analysed to explore the source of twist springback. The results indicate that the torsion moment of cross sections caused by the non-homogenous stress states play a considerable role in twist springback prediction.

Investigation on the Stress Behaviour of Coating-Substrate Interface under Contact Loading

This study is intended to predict the stress behavior of thick hard coating at the interface with the changes of coating stiffness and thickness to the substrate of Ti-6Al-4V and SCMV. The elastic mismatch between the coating and the substrate is presented in the value of Dundurs parameter α. The prediction is done using simple geometry of a cylinder-on-flat model in 2D analysis subjected to normal and tangential loading. Tangential stress distribution along the coating-substrate interface is then obtained from the FE modelling after a finite sliding of the cylinder. It is predicted that the maximum tangential stress value predicted at the interface which relates to coating fracture failure is increasing as stiffer coating is used on compliant substrate (i.e. increasing α values). The location of the maximum tangential stress predicted also changes from the trailing edge to the center of contact with increasing α values. Effect of changes of coating thickness on the predicted maximum tangential stress value is more significant for high positive α values. Risk of coating fracture at the interface is therefore predicted to increase with the increase of coating thickness and stiffness.

Modeling of Strain and Stress States for Straight Rods with Particular Cross Sections Subjected to Torsion

In the case of shaft-hub joints with cylindrical pins found in both macro and micro-devices, a longitudinal gutter with an almost half-circular cross section is practiced along the length of the shaft segment. The center of the circular arc is placed on the circular edge of the cross section. The present paper aims to model strain and stress states within such a shaft, when the material elastic properties are known along with shaft segment length and applied torque. Using the MathCad environment, 3D and constant stress level plots were obtained for the distribution of tangential stresses over the cross section. After application of torque, the transverse cross sections shift and become anti-symmetric as illustrated by the obtained 3D and constant strain plots.

Detailed Crack-Tip Stress Field Description in a Specimen Subjected to Mixed-Mode Loading

A mixed-mode cracked configuration is investigated using the multi-parameter fracture mechanics concept based on the analytical description of the stress/displacement field near a crack tip by means of the Williams series expansion. It is shown that using only one (singular) parameter as it is usual for brittle materials is not sufficient if the accurate stress distribution also further from the crack tip shall be known. Tangential stress distribution in various distances from the crack tip is presented and importance of the higher-order terms of the Williams expansion emphasized. Moreover, initial crack propagation direction is investigated by means of the MTS criterion and utilization of its generalized form is discussed.

Materials Testing under Mechanical Stress, Pressure and Turbulent Flow of Impure Supercritical CO2

Abstract The climate change necessitates measures to reduce carbon dioxide (CO2) emissions in the atmosphere, one of which is carbon dioxide capture and storage (CCS). Transmission of pressurized liquid or supercritical CO2 containing residual flue gas constituents in pipelines is an important component of CCS systems. Material testing under conditions as close as possible to real conditions is a prerequisite for reliable and safe implementation of CCS. A novel pipeline corrosion test facility was developed, accounting for major mechanical, physical and chemical influencing factors: elastic deformation, pressure, temperature, gas composition and flow velocity can be independently adjusted. Radial and tangential stress distributions on a round sample were experimentally investigated, indicating a good accordance with expected theoretical values. In this contribution the idea of the novel corrosion test facility and the assembled equipment as well as first results are presented and discussed.

Contact mechanics in fretting fatigue

This paper studies the contact mechanics in a line contact during fretting fatigue conditions. Inliterature one can find numerical and analytical solutions of normal and tangential stresses for a variety ofloading cases. However, a unified solution valid for all loading cases during fretting fatigue conditions is notavailable. We present in this paper a strategy to combine existing contact mechanics theories into a unifiedcalculation procedure. Therefore, the relevant contact mechanics theories for an idealized cylinder-on-flatcontact are selected and bundled. Two clear flowcharts group the existing theories, which results in aunified strategy that can easily be implemented in a programming language. A Matlab script wasprogrammed and calculates the normal and tangential stress distribution based on the applied forces, thegeometry of the contact, the coefficient of friction and the material properties. The present theory can beused to automate the calculation of the stress distributions, or as validation of new numerical techniques.The script is modular and can be extended to calculate the lifetime of a component, by adding lifetimecriteria.

Finite Element Simulation on Stress of Steel Sphere Shell

In order to verify correctness of two-dimensional axisymmetric finite element model, this paper carries out axial symmetry analysis of the steel ball shell by ANSYS software and 2-D finite element model is established. The radial and tangential stress distribution is acquired, through comparison with the theoretical solution, both are in good agreement. So it is feasible to simulate the three-dimensional model by finite element axisymmetrical two-dimensional model.

Influence of Speed-up and Speed-down on Internal Stresses of Wound Rolls in Web Handling Process

In web winding process, the effects of speed-up and speed-down on internal stresses of wound roll have been investigated. The air-entrainment can be obtained theoretically using the modified nonlinear Hakiel model. In this research work, air-entrainment model established by Hamrock and Dowson was applied to estimate the initial air film layers into a wound roll in the winding system with a nip-roller. Moreover, the characteristics of a wound roll were examined under varying tension and varying speed conditions. The numerical results showed the radial stress, tangential stress, and friction force distributions at central inside a wound roll under the condition for a wound roll without wrinkle and slippage phenomena.

Influence of Speed-up and Speed-down on Internal Stresses of Wound Rolls in Web Handling Process

In web winding process, the effects of speed-up and speed-down on internal stresses of wound roll have been investigated. The air-entrainment can be obtained theoretically using the modified nonlinear Hakiel model. In this research work, air-entrainment model established by Hamrock and Dowson was applied to estimate the initial air film layers into a wound roll in the winding system with a nip-roller. Moreover, the characteristics of a wound roll were examined under varying tension and varying speed conditions. The numerical results showed the radial stress, tangential stress, and friction force distributions at central inside a wound roll under the condition for a wound roll without wrinkle and slippage phenomena.

Modeling of contact-fatigue damage accumulation in a two-layer half-space with incomplete adhesion between the layers

A method is proposed for calculating the stress state and fatigue damage accumulation in a two-layer elastic half-space with a system of defects between the layers under the action of normal and tangential distributed forces. The problem is solved by the boundary element method and the double Fourier transform. The effects of the surface layer thickness, degree of imperfection of the intermediate defective layer, and interlayer friction on the distribution of the maximal tangential stresses are analyzed. An example of studying the damage accumulation kinetics taking into account the change in the layer thickness due to surface fracture.

Stress analysis of functionally graded rotating discs: analytical and numerical solutions

This study deals with stress analysis of annular rotating discs made of functionally graded materials (FGMs). Elasticity modulus and density of the discs are assumed to vary radially according to a power law function, but the material is of constant Poisson’s ratio. A gradient parameter n is chosen between 0 and 1.0. When n = 0, the disc becomes a homogeneous isotropic material. Tangential and radial stress distributions and displacements on the disc are investigated for various gradient parameters n by means of the diverse elasticity modulus and density by using analytical and numerical solutions. Finally, a homogenous tangential stress distribution and the lowest radial stresses along the radius of a rotating disc are approximately obtained for the gradient parameter n = 1.0 compared with the homogeneous, isotropic case n = 0. This means that a disc made of FGMs has the capability of higher angular rotations compared with the homogeneous isotropic disc.

Velocity-dependent friction in a model of wheel–rail rolling contact and wear

Models of rolling contact are used to predict the wear of the railhead due to passing wheels. It is commonly assumed in such models that material is worn away in proportion to the frictional work done in the slip zone of each contact patch. Moreover, a constant coefficient of friction is usually assumed. However, it is known that the friction coefficient between sliding surfaces decreases as the velocity of sliding increases. This paper describes a technique for including more sophisticated friction laws in a model of wheel–rail rolling contact. A non-Hertzian model is used based on a variational method. The resulting tangential stress distribution and slip velocity in rolling contact are examined and compared with results calculated using a constant coefficient of friction. For conditions of rolling contact with partial slip a stick–slip oscillation is found to occur when a velocity-dependent friction law is used. The pattern of material removed along the rail in rolling contact is also investigated. For low creep values and for existing broadband roughness, the inclusion of velocity-dependent friction does not result in significantly different predictions of wear. For higher creep values, velocity-dependent friction results in an unstable force–friction relationship which could lead to high variable wear.

Viscoelastic wrinkling in compression-stressed metal film-polymer sublayer system

The laws of corrugation (wrinkling) that takes place in thin aluminum films on silicon substrates with styrene sublayers under the conditions of thermal treatment have been studied using atomic force microscopy techniques. Measurements of the amplitude and period (wavelength) of wrinkles revealed stages in the viscoelastic corrugation process at various temperatures. It is established that the evolution of wrinkles in the course of annealing is controlled by the periodic distribution of normal and tangential stresses at the film-sublayer interface.

Closed-Form Elastoplastic Solution for the Wellbore Problem in Strain Hardening/Softening Rock Formations

This paper proposes an analytical approach predicting the development and progress of the plastic zone around a wellbore drilled in linear hardening or softening Drucker-Prager rocks in a theoretically consistent way. With some reasonable assumptions and simplifications on the definitions of stress invariants as well as the equivalent plastic strain, the wellbore boundary value problem is fully linearized, which leads to a simple ordinary differential equation with the radial displacement being the basic unknown. Explicit solutions for the stress and displacement fields due to wellbore drilling can thus be easily obtained. Comparisons between the analytical solution and the ABAQUS numerical simulation verify the reliability and applicability of the present closed-form solution. Extensive numerical results for the tangential and radial stress distributions are then provided to explore the influences of the friction angle and the plastic tangential modulus, for both strain hardening and softening cases. The important issue of critical mud density equivalent to wellbore radial controlled stresses that is required to maintain wellbore stability is also addressed.