Distribution Of Tangential Stresses Research Articles

Modeling of bending characteristics of symmetric tri-layer laminated Sheet materials

Bending of sheet materials is widely applied to shaping many automotive, aerospace and other industrial components. Tailored laminate sheet materials are desirable in bending applications where monolithic sheets do not meet the design requirements or manufacturing demands. An accurate analytical model can be effectively utilized for rapid design of components for laminated sheet materials for a given application. Many analytical models based on advanced theory of bending have been proposed in the literature to predict plane strain bending characteristics of monolithic sheet materials. However, there are very few such models for laminated sheet materials. In this study, an analytical model for tri-layer laminated sheet material is developed based on advanced theory of bending. The model considers Mises yielding and Ludwik non-linear plastic hardening with Bauschinger effect for various laminate thickness ratios. Also, a 3D FE model based on Marciniak-Kuczynski (MK) bend test design is developed to assess pure bending characteristics of a symmetric tri-layer aluminum sheet laminate with softer and thinner clad layers on both surfaces and a harder thicker core in the middle. The through-thickness tangential stresses from the analytical model are compared with those from FE model for different clad to matrix thickness ratios. The tangential stresses decrease in magnitude with increasing aluminum clad thickness ratios in the analytical model. This behavior is in good general agreement with the results from the mid-width section for the FE model. The analytical and FE models also yield similar order trend in relative thickness change with increasing clad thickness ratios and with increasing specimen radius of curvature. The 3D FE model exhibited anticlastic curvature at the edges as a result of strain inhomogeneity across the width. Unlike the tangential stress distribution, the tangential strain is maximum at the specimen edges than at the mid-width. The inhomogeneity in stress and strain across the bend line shows that plane strain condition is not consistent across the width of the sheet.

Analytical description of the flow of the newtonian liquid in a round tube and on a horizontal plate

The object of research is obtaining general integrals and some particular solutions for two common flow conditions of incompressible liquid – laminar and averaged turbulent flow. Mathematical description is based on the system of equations of motion in stresses (Navier) and its special case for the Newtonian liquid. A condition of integrating the equations is the constancy of pressure drop and viscosity along the flow. The block schemes of obtaining the general integrals for flow in a pipe and turbulent flow on a plate are represented. Are as a result, three new general integrals and four particular solutions, which are compared with the known equations, were found. It was shown that the integrals of the Navier equation describe the distribution of tangential stress for turbulent flow. An analysis of solutions for the distribution of velocity showed that the Poiseuille equation for laminar flow in a pipe and the Blasius curve for laminar flow on a plate are particular solutions of one general integral. An analysis of the particular solutions made it possible to estimate the thickness of the laminar sublayer under turbulent flow condition. The results of the work create prerequisites for a more detailed further analysis of laminar and turbulent flows.

Finite-Layer Method: Evaluation of Stresses and the Modal Components of Energy Release Rate on the Midplane of Edge-Cracked Composite Specimens

On the basis of the finite-layer method, a technique for calculating the two-dimensional stress-strain state and interlaminar stresses in edge-cracked specimens in tests on determination of the Mode I, II, and III fracture toughnesses of composites is proposed. Taking into account the symmetry and antisymmetry of specimens, the calculation is reduced to a boundary-value problem for a system of partial differential equations describing the deformation of one of the layers. Using the method of straight lines, the two-dimensional problem is reduced to a one-dimensional boundary-value problem, which is solved by the stable Godunov–Grigorenko numerical method. Calculations for specimens subjected to three types of the tests are performed, and the distributions of normal and tangential stresses on the specimen midplane and the distributions of modal components of the fracture toughnesses GI, GII, and GIII along the delamination front line are presented. Comparisons with results of the one-dimensional solution and with known results obtained by the virtual crack closure technique are presented.

Finite-Layer Method: Exact Numerical and Analytical Calculations of the Energy Release Rate for Unidirectional Composite Specimens in Double-Cantilever Beam and End-Notched Flexure Tests

Based on the finite-layer method, a method for evaluating the stress-strain state and energy release rate for specimens with delaminations in double-cantilever beam and end-notched flexure tests is proposed. Exact numerical solutions of boundary-value problems for the “stiff” systems of differential equations describing deformations of test specimens are obtained. The distributions of forces, moments, displacements, and rotations in the specimens and the distributions of normal and tangential stresses on their midline are presented. New closed-form expressions for these functions and for compliance of the specimens are developed. Calculation results for the energy release rate obtained by a numerical differentiation and from analytical relations are presented. Two new techniques for estimating the energy release rate are proposed: (1) using the calculated values of peak stress and jumps of displacements at the tip of delamination; (2) by evaluation of indeterminacy at the tip of delamination with the use of stresses and derivatives of stresses and displacements. The effect of the transverse shear and Poisson ratio on the results is estimated. A comparison of the numerical and analytical solutions obtained with known results and the ASTM standard is presented.

Growth of HVPE-GaN on native seeds – numerical simulation based on experimental results

Investigation of source of stress in HVPE-GaN grown in c-direction on native seeds is reported. The study was based on experimental results. Ammonothermally grown GaN seed was used for growth of a thick HVPE-GaN layer in the c-direction. Deterioration of quality of the HVPE-GaN layer appeared. Numerical simulations were used for determining and examining radial, tangential, and axial stress distributions in the grown GaN crystal and the seed. The maximum equivalent stress (von Mises stress) was calculated and analyzed. It was shown that growth in non-polar and semi-polar directions, which appears on the edges of the crystal during crystallization process, can generate a very large tensile stress in GaN growing in the c-direction. This stress is much larger than the one generated due to a lattice mismatch between the ammonothermal seed and the deposited HVPE layer.

Springback analysis of AA5754 after hot stamping: experiments and FE modelling

In this paper, the springback of the aluminium alloy AA5754 under hot stamping conditions was characterised under stretch and pure bending conditions. It was found that elevated temperature stamping was beneficial for springback reduction, particularly when using hot dies. Using cold dies, the flange springback angle decreased by 9.7 % when the blank temperature was increased from 20 to 450 °C, compared to the 44.1 % springback reduction when hot dies were used. Various other forming conditions were also tested, the results of which were used to verify finite element (FE) simulations of the processes in order to consolidate the knowledge of springback. By analysing the tangential stress distributions along the formed part in the FE models, it was found that the springback angle is a linear function of the average through-thickness stress gradient, regardless of the forming conditions used.

Viscous stress distribution over a wavy gas–liquid interface

Viscous stress contributes to momentum transfer between two phases, which plays an important role in both industrial applications and environmental processes. Near a wavy interface, the flow is modulated and produces a spatially non-uniform normal and tangential viscous stress. This study presents measurements of these stresses at a liquid–gas interface populated with two-dimensional millimeter scale waves performed with multiphase particle image velocimetry. Large datasets enable conditional phase-averaging of the data based on wave steepness, which increases the precision of the results and allows statistical analysis. For the first time at this scale, the spatial distribution of normal and tangential viscous stress is obtained for a large range of wave steepness (ak = 0–1, with a the amplitude and k the wavenumber). As the steepness increases, the mean shear stress over a wavelength decreases in magnitude, while the normal viscous stress increases. These trends are linear for ak < 0.6, and correlations are proposed. At ak > 0.7, flow separation is observed in the gas phase near the troughs and drastically alters the viscous stress distribution.

Improving the flexural rigidity of cold-finished steel

The influence of reduction on the distribution of axial, tangential, and radial residual stress over the cross section of cold-finished steel rods is experimentally studied. Computer modeling of the flexural rigidity of the rods indicates that, with 5–34% reduction, which is the range used in practice, the rigidity of the metal may be almost doubled. It is inexpedient to increase the rigidity of the rods by additional slight reduction, since that would lower the residual tensile stress.

Distribution of friction tangential stresses in the Courtney-Pratt experiment under Bowden’s theory

This article describes the calculation-experimental approach to determining friction stresses based on an experimental dependence of friction force on the displacement of compressed surfaces. As an example of the approach application, analysis of Bowden’s mechanical model of friction is presented. In the approach implementation, we use the results of Courtney-Pratt experiment. Solutions are given in the power form.

A fast wheel–rail contact model for application to damage analysis in vehicle dynamics simulation

A novel wheel–rail contact model is proposed to be implemented for multi-body dynamics simulation, in order to facilitate accurate online calculation of damage phenomena such as wear and rolling contact fatigue. The normal contact, i.e. contact patch and pressure distribution, is calculated using a fast non-elliptic algorithm called ANALYN. The tangential contact, i.e. tangential stress distribution, stick–slip division and creep force calculation, is treated using an alternative to the FASTSIM algorithm that is based on a strip theory which extends the two-dimensional solution of rolling contact to three-dimensional contacts. The proposed contact model is compared to the Hertz+FASTSIM model and evaluated using the CONTACT code in terms of contact patch and stress distribution as well as creep force curves. The results show that the proposed model can significantly improve the estimation of the contact solution both in terms of creep force estimation and contact details, such as stress distribution, needed for damage predictions.

Imperfect bonding effect on dynamic response of a non-circular lined tunnel subjected to shear waves

Combining the wave function expansion method and conformal transformation method, the dynamic stress around a non-circular tunnel with imperfect interface subjected to anti-plane shear waves is derived. The non-circular tunnel is mapped into an annular region, and the analytic solutions of stress and displacement solutions are expanded in terms of wave functions. By introducing the spring-type interface model, the coefficients are determined by satisfying the imperfect bonding conditions around the concrete lining. The distribution of tangential stresses on the imperfect interface is graphically illustrated, and the interacting effect of imperfect interface and incident wavelength is discussed in detail. The imperfect interface is revealed as a key factor dominating the seismic responses of a tunnel.

Frictional shakedown and ratcheting of an oscillating cylindrical, elastic contact with coulomb friction

We examine frictional shakedown of an elastic contact of a cylinder pressed on a flat substrate. Slight oscillatory rolling of the cylinder varies the pressure distribution and the contact region. Together with the tangential load, this rocking motion causes incremental sliding processes and a macroscopic rigid body motion. In case that the oscillation amplitude is sufficiently small, the slip ceases after the first few periods and a safe shakedown occurs: the residual force in the contact withstands the tangential load. Otherwise ratcheting occurs: one side of the contact alternately sticks, while the other slips. This leads to a continuing rigid body motion. By derivation of the tangential stress distribution and use of the Boussinesq and Cerruti potential functions, we find approximations for the shakedown limits for the tangential load and the oscillation amplitude. This allows the accurate prediction of the displacement and the reduced tangential load capacity in the shakedown state. The results show strong agreement with numerical and experimental data.

Stress analysis of borehole subjected to fluid injection in transversely isotropic poroelastic medium

This paper proposes an analytical solution, using the combined Laplace–Fourier integral transform technique, for a borehole drilled in transversely isotropic porous medium and subjected to a fluid discharge over a finite length of its surface. Especially, the coupled boundary condition between the total radial stress and injection-induced pore pressure at the borehole surface is addressed in a rigorous fashion, which leads essentially to a set of dual integral equations that can be solved through standard numerical procedure. The study focuses on the calculation of stress fields around the borehole with particular attention given to the time-dependent effective tangential stress and pore pressure distributions. Numerical solutions are presented for verification with those recently derived for the limiting case of an isotropic medium and, more importantly, to investigate the influences of material anisotropy on the stress responses of the borehole and porous medium.

Stress analysis of a cylindrical composition-gradient electrode of lithium-ion battery in generalized plane strain condition

A novel cylindrical composition-gradient electrode is considered to be one of most potential structures in lithium-ion battery. To investigate the mechanism of a cylindrical composition-gradient electrode under potentiostatic operation, we take Li1.2(Mn0.62Ni0.38)0.8O2 for example. The effects of the three main factors, i.e., diffusion coefficient, Youngs modulus, partial molar volume of solute, on the stress field in the cylindrical electrode are discussed. Each of the three material parameters is assumed to be a linear function of the distance from the center to surface. The small deformation theory and thermodynamic theory are employed to establish the mathematical model of composition-gradient cylindrical electrode. The mechanics equations and diffusion equation of cylindrical electrode are derived for an inhomogeneous material in plane strain condition. By comparing with single-phase electrode, it is found that Youngs modulus increasing from the center to the surface greatly reduces the max tensile radial stress and tensile hoop stress and changes the location of max radial stress since the radial displacement of the center is restricted. The time for the lithium-ions to reach the center is longer and the tensile stress near the center decreases at dimensionless time =0.0574 when diffusion coefficient decreases along the radial direction. Owing to the smaller diffusion coefficient at the surface, there is a reduction in the number of lithium-ions through the unit area in unit time when their corresponding concentration gradients are the same. The variation of partial molar volume means that the volume expansion caused by the intercalation of lithium-ions decreases along the radial direction. Therefore the partial molar volume decreasing along the radial direction considerably reduces the radial stress and the distribution of tangential stress becomes flat. The center point is picked, showing the development of hoop stress. The results show that the hoop stress increases and reaches a maximal value close to the dimensionless time =0.0574. Maximal tensile hoop stress at the center is reduced in an inhomogeneous material. The tensile hoop stress turns into compressive stress over time when elastic modulus and partial molar volume are denoted with E(r) and (r) respectively. The results indicate that the cylindrical composition-gradient electrode with core enriched Ni and edge enriched Mn reduces the max tensile radial stress and tensile hoop stress. It is an efficient way to avoid mechanical fracture in electrode since evidence has accumulated that tensile stress is the lead cause of crack in electrode. The result also provides useful guidance for mitigating the stresses in a cylindrical electrode.

Stress Distribution of Bolted Joints With Different Lay-Up Types

A parametric study of the stress distribution in the composite plates is undertaken to show the effect of different lay-ups. Full 3-D elastic properties are required in the modelling. These properties are calculated using equations taken from the literature and derivation from simple Classical Laminate Plate Theory (CLPT). In previous experimental work, it was shown that tensile failure involved the development of a damage zone at the edge of the hole. In a double-lap joint, it is assumed that uniform stresses are exhibited throughout the plate thickness. Different lay-ups system give different tangential stress distributions and insignificant variation in the radial stress distribution along the hole boundary.

DYNAMICS OF H-BEAM CAPTURE BY ROLLERS OF BREAK-DOWN STAND 1300 OF THE UNIVERSAL-BEAM MILL

The paper considers the condition features of the H-beam capture grooved with rolls and break-down stand 1300 of a universal-beam mill of Nizhny Tagil Metallurgical Plant. The authors have carried out the study of the stress-strain state of metal arising in the deformation zone during rolling of the beam in the calibers of rolls of a breakdown stand. The results of the calculation of the rolling process are presented in the form of plots of the distribution of contact normal and tangential stresses in the deformation zones as the rolls grip the H-beam. The value of normal tensile stresses arising in the wall of the H-beam does not exceed 52 MPa. In the deformation zones the shelf and the zone of interface the shelves with the wall are normal contact compressive stresses, indicating a favorable position of the beam quality of the scheme of stress state with a predominance of high compressive stress. The paper also presents the developed calculation method of dynamic loads in drive line of a breakdown stand 1300 considering the gaps in the spindle connection.

The Research of Stresses in the Molds of Injection Molding Machines

The article presents the analysis of casting molds failure under pressure. It was found that the main causes are physical and chemical activity of the casting alloy, the nature of the used materials and the intensity of the cyclic temperature-power loading. The technique of the stress assessment in the molds is presented. The schedule of distribution of axial and tangential stresses in the cross section of the sprue bushing in various stages of compression is made up. It is found that the maximum level of stress occurs at the contact surfaces during the filling and the subsequent brief exposure of the melt in the mold.

Thermomechanical interactions due to laser pulse in microstretch thermoelastic medium

The present investigation deals with deformation in microstretch generalized thermoelastic medium subjected to thermomechanical loading induced by thermal laser pulse. The Laplace and Fourier transform techniques are used to solve the problem, and concentrated normal force and thermal source describe the application of this approach. The closed form expressions of normal stress, tangential stress, couple stress, microstress and temperature distribution are obtained for the transferred domain. The numerical inversion technique of Laplace transform and Fourier transform has been applied to obtain the resulting quantities in the physical domain after developing a computer program. Normal stress, tangential stress, coupled stress and microstress temperature distribution are depicted graphically to show the microstretch effect. Some particular and special cases of interest are gathered and presented in the investigation.

Effect of Yield Strength of a Circular Saw Blade on the Multi-spot Pressure Tensioning Process

In this study, a numerical model of the tangential tensioning stress distribution of a circular saw blade tensioned by multi-spot pressure was established using theoretical analysis, and the tangential tensioning stress distribution of the circular saw blade calculated by the model was shown to be true and reliable. The effect of yield strength of the circular saw blade on the distribution of tangential tensioning stress was studied using the numerical model. The research achievements showed that a circular saw blade made with high-strength or ultra-high-strength steel yielded a better tensioning effect during the multi-spot pressure tensioning process, which could promote the application of a circular saw blade made by high-strength or ultra-high-strength steel.

A numerical simulation on multi-spot pressure tensioning process of circular saw blade

The multi-spot pressure tensioning process of circular saw blade was built by dynamic/explicit solution module of the finite element software called ABAQUS for avoiding non-convergence and improving the computational efficiency. The stress field of circular saw blade during loading process was calculated based on the finite element model. The model which could both meet the requirement of computational efficiency and accuracy was established by adjusting the step time and density of circular saw blade. The unloading process of circular saw blade was built by static/general solution module of ABAQUS using the stress field of loading process calculated by dynamic/explicit finite element method as initial conditions. The tangential tensioning stress field of circular saw blade tensioned by multi-spot pressure which showed the same trend with the measured result was calculated based on the two above-mentioned models. A more ideal distribution of tangential tensioning stress could be produced by the multi-spot pressure tensioning process. The feasibility of multi-spot pressure tensioning process was theoretically proved in this paper.