Radial Stress Distribution Research Articles

Mechanical Stress Distribution inside Dry Capacitor Elements

Many power products are produced by winding paper, polymer film or metal foils around an electrically active or passive core, like cables, bushings and capacitor elements. The mechanical stress distribution inside the product has high impact on its final performance. The stress distribution will be determined by the selected materials, winding parameters, and the ambient temperature. In this work the stress distribution inside dry metallized film capacitor elements for HV applications has been investigated using multiple experimental methods: Parotester, Smith needle, Pressure sensors and X-ray computed tomography. The results showed that the tested methods were unable to provide exact values of the radial stress distribution inside the capacitor element. As a continuation, the nonlinear material properties of the biaxially oriented polypropylene capacitor film were characterized. This work indicated that the temperature and the initial film stress will have an effect on the resulting tightness of the capacitor element.

Displacements, Strains, and Stresses Investigations in an Inhomogeneous Rotating Hollow Cylinder Made of Functionally Graded Materials under an Axisymmetric Radial Loading

In this paper, an analytical and numerical study of strain fields, stress fields and displacements in a rotating hollow cylinder, whose walls were completely made in Functionally Graded Materials (FGM), was conducted. We have considered the rotating hollow cylinder submitted to an asymmetric radial loading. It is assumed that, because of the functional graduation of the material, the mechanical properties such as Young elastic modulus and the density varies in the radial direction, in accordance with a the power law function. The inhomogeneity parameter was selected between -1 and 1. On the basis of the second law of Newton, Hooke’s law and the strain-stress relationship, we established the differential equation which governs the equilibrium for a rotating hollow cylinder. We found the analytical solution and compared to the numerical solution obtained by using the shooting method and the fourth order Runge-Kutta algorithm. The analytical and numerical results lead to the conclusion that the magnitude of the tangential stresses is greater than that of the radial stresses. The changes due to the graduation of FGM does not produce consistent variations in the distribution of radial stresses, but strongly affects the distribution of tangential stresses. The tangential stresses, tangential strains and displacements are much higher at the inner surface of the cylinder wall. The internal radial pressure intensely affects the radial stresses and the radial strain.

From experimental data, the mechanics relationships describing the behaviour of four different low alloyed steel powders during uniaxial cold compaction

ABSTRACTThis work aims at determining the constitutive model of four commercial water atomised low alloyed steel powders during cold compaction. Single-action experiments were performed, obtaining cylindrical specimens with different H/D ratios. The distribution of axial and radial stresses was investigated, and the relationships describing both the radial stress transmission coefficient and the flow stress as functions of the relative density were determined. The radial stress transmission coefficient also confirmed the hypothesised value of Poisson’s coefficient. The friction coefficient between the powder column and the die wall was determined, also highlighting the influence of the H/D ratio. Measuring the axial and radial strains due to spring-back, the axial and radial elastic moduli were determined, as functions of the relative density. The results obtained for the four materials were compared, also highlighting both differences and similarities.

Dynamic Interaction of Interfacial Point Source Loading and Cylinder in an Elastic Quarter with Anti-plane Shear

Theoretical steady state solution of a semi-circular cylinder impacted by an anti-plane point loading in a vertical bound of an elastic quarter is formulated in this paper through using image method and wave function expansion series. The elastic quarter is extended as a half space, and the semi-circular interfacial cylinder is extended as a circular cylinder. Displacement field is constructed as series of Fourier-Hankel and Fourier-Bessel wave functions. At last, circular boundary is expanded as Fourier series to determine coefficients of wave function. Numerical results show that material parameters have two widely divergent effects on the radial and circumferential dynamic stress distribution.

Parametric study of the deformation of transversely isotropic discs under diametral compression

The displacement field in a circular disc made of a transversely isotropic material is explored in a parametric manner. The disc is assumed to be loaded by a parabolic distribution of compressive radial stresses along two finite arcs of its periphery in the absence of any tangential (frictional) stresses. Advantage is here taken of a recently introduced closed-form analytic solution for the displacement field developed in an orthotropic disc under diametral compression which was achieved adopting the complex potentials technique for rectilinear anisotropic materials as it was formulated in the pioneering work of S.G. Lekhnitskii. The analytic nature of this solution permits thorough, indepth exploration of the influence of some crucial parameters on the qualitative and quantitative characteristics of the deformation of transversely isotropic circular discs compressed between the jaws of the devise suggested by the International Society for Rock Mechanics for the standardized implementation of the Brazilian-disc test. The parameters considered include the anisotropy ratio (i.e., the ratio of the two elastic moduli characterizing the disc material), the angle between the loading axis and the planes of transverse isotropy and the length of the loaded arcs. Strongly non-linear relationships between these parameters and the components of the displacement field are revealed.

Transient thermoelastic analysis of FGM rotating thick cylindrical pressure vessels under arbitrary boundary and initial conditions

Assuming arbitrary boundary and initial conditions, a transient thermo-elastic analysis of a rotating thick cylindrical pressure vessel made of functionally graded material (FGM) subjected to axisymmetric mechanical and transient thermal loads is presented. Time-dependent thermal and mechanical boundary conditions are assumed to act on the boundaries of the vessel. Material properties of the vessel are assumed to be graded in the radial direction according to a power law function. The Poisson’s ratio is assumed to be constant. Method of separation of variables has been used to analytically calculate the time dependent temperature distribution as a function of radial direction. In a case study, the distribution of radial and hoop stresses along the thickness is derived and plotted. In order to validate the model, the analytical results have been compared with finite element method modeling results presented in literature. Any arbitrary boundary and initial conditions can be handled using the equations derived in the present research. In order to investigate the inhomogeneity effect on time dependent stress distribution and displacements, values of the parameters have been set arbitrary in the present study. To the best of the authors’ knowledge, in previous researches, transient thermo-elastic analysis of thick cylindrical FGM pressure vessels is investigated by numerical methods, while in the present research, an exact solution is derived for the same problem.

3D thermo-mechanical bending solution of functionally graded graphene reinforced circular and annular plates

• 3D thermo-elastic bending solutions are obtained for functionally graded circular and annular plates reinforced with GPLs. • Thinner GPLs are preferred to achieve better enhancement in bending stiffness hence reduced bending deflection. • The parabolic GPL distribution offers the best reinforcing effect, followed by uniform then linear distribution patterns. • For plates reinforced by uniformly distributed GPLs, the temperature field and radial stress distribution are not affected by GPL's total content. Within the framework of three-dimensional elasticity theory, this paper investigates the axisymmetric bending of novel functionally graded polymer nanocomposite circular and annular plates reinforced with graphene nanoplatelets (GPLs) whose weight fraction varies continuously and smoothly along the thickness direction. The generalized Mian and Spencer method is utilized to obtain the analytical solutions of nanocomposite circular and annular plates under a combined action of a uniformly distributed transverse load and a through-thickness steady temperature field. Three different distribution patterns of GPLs within the polymer matrix are considered. The present analytical solutions are validated through comparisons against those available in open literature for the reduced cases. A parametric study is conducted to examine the effects of GPL weight fraction, distribution pattern, plate thickness to radius ratio, and boundary conditions on the stress and deformation fields of the plate. The results show that GPL nanofillers with a low content can have a significant reinforcing effect on the bending behavior of the thermo-mechanically loaded plate.

The multi-layered ring under parabolic distribution of radial stresses combined with uniform internal and external pressure

A recently introduced solution for the stress- and displacementfields, developed in a multi-layered circular ring, composed of a finite number of linearly elastic concentric layers, subjected to a parabolic distribution of radial stresses, is here extended to encompass a more general loading scheme, closer to actual conditions. The loading scheme includes, besides the parabolic radial stresses, a combination of uniform pressures acting along the outer- and innermost boundaries of the layered ring. The analytic solution of the problem is achieved by adopting Savin’s pioneering approach for an infinite plate with a hole strengthened by rings. Taking advantage of the results provided by the analytic solution, a numerical model, simulating the configuration of a threelayered ring (quite commonly encountered in practical applications) is validated. The numerical model is then used for a parametric analysis enlightening some crucial aspects of the overall response of the ring.

Experimental analysis of axial and radial stress distribution in soft materials used for petrochemical valve stem sealing package

Paper presents experimental results obtained by authors regarding pressure values and distribution, by using a special pressure sensitive paper, type FujiFilm and adequate hardware equipment and a soft program FPD810 Win. Was obtained the proper axial force related for different materials in order to respect the valves sealing demands. Were showed that, pressure maps obtained depends of the construction of sealing package, density of the preformed band rings and corrected sealing replacing on location in case of square braided cord used.

The displacement field in an orthotropic disc under parabolic pressure. Application to the case of transverse isotropy

Abstract: An analytic solution for the displacement field developed in a circular disc made of an orthotropic material is presented assuming that the disc is loaded by a distribution of radial stresses varying according to a parabolic law and acting along two finite arcs of the disc's periphery, antisymmetric with respect to its center. The solution is achieved with the aid of the complex potentials technique for rectilinear anisotropic materials as it was formulated by Lekhnitskii. The complex potentials and the general expressions for the displacement components are obtained at any point of the disc for the general case of orthotropy and then they are particularized for a transversely isotropic disc, due to its increased importance in practical engineering applications.

The excitation mechanism of a shear stress induced rotary wave

AbstractThe free surface flow in a vertical, cylindrical, rotating container will be considered when axis‐symmetric angular and radial shear stress distributions are applied on the free surface. It is well known that in the inviscid case a rotary wave which can be described by a flow potential exists. We want to determine the stability limit of the axis‐symmetric base state with respect to the rotary wave for small Ekman and Froude numbers. Under the above assumption, the critical flow conditions can be determined analytically. The results can be verified experimentally using a vertical, cylindrical container partially filled with water where the top lid rotates with a given angular velocity. Thus, the induced air flow will exert shear stresses in the angular and radial direction onto the water surface. Above a certain threshold, rotary waves can be observed. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Mathematical Modelling of Thermo-Elasto-Plastic Problems and the Solving Methodology on the Example of the Tubular Section Forming Process

Abstract The paper presents the results of numerical studies based on a mathematical model determined by the stress-strain state examination method. Numerical computations for two steel grades, namely H40 and C45, were made at similar strain and process rate parameters. As a result of the studies, the distribution of elastic and plastic zones was obtained, while the tube hollow drawing force was verified experimentally. The distribution of longitudinal, radial and circumferential stresses and, after the drawing operation, the distribution of residual stresses in the tube cross-section were also obtained.

Exact and Numerical Elastic Analysis for the FGM Thick-Walled Cylindrical Pressure Vessels with Exponentially-Varying Properties

Abstract Assuming exponential-varying properties in the radial direction and based on the elasticity theory, an exact closed-form analytical solution is obtained to elastic analysis of FGM thick-walled cylindrical pressure vessels in the plane strain condition. Following this, radial distribution of radial displacement, radial stress, and circumferential stress are plotted for different values of material inhomogeneity constant. The displacements and stresses distributions are compared with the solutions of the finite element method (FEM).

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.

Effect of thermal loading on sealing behavior of single and twin-gasketed flange joints

Gasketed flange joints are usually subjected to internal pressure at high temperature. The most important requirement of flange joint is to provide leak-free joint under operating condition. In the present study, temperature-dependent nonlinear gasket properties of spiral-wound gasket at elevated temperatures are obtained experimentally and included in the analysis. The relaxation of gasket contact stress in both single and twin-gasketed joints at elevated temperatures is compared. It is observed that the ability to withstand internal pressure decreases with increase in temperature in both single and twin-gasketed flange joints. But, the twin-gasketed flange joint is found to withstand higher internal pressure than single-gasketed joint at a given bolt preload and temperature. The influence of gasket seating surface rotation on the distribution of gasket radial contact stress at elevated temperature is studied. The effect of elevated temperature on flange stresses of twin-gasketed joint is also examined.

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.

Analysis of Temperature and Stress in Differential Temperature Reverse Deep Drawing of 5A06 Aluminum Cup

The warm reverse deep drawing process is proposed to form cylindrical cups with greater drawing depths. Experimental and numerical investigations were conducted to analyze the effect of the temperature field on the drawing depth limit and the stress distribution during the warm reverse deep drawing process of a 5A06 aluminum plate. The effects of the punch temperature and initial flange temperature on the temperature gradient in the blank are discussed. The drawing depth limits for the different temperature gradients in the blank were determined. In addition, the effect of the temperature field on the radial stress distribution was analyzed. A 180°C temperature gradient occurs when the punch temperature is room temperature. When the temperature field generated in the blank is uniform, a fracture occurs, and the drawing depth limit (72 mm) is only 20% of the desired depth. When the temperature gradient is 100°C, the drawing depth limit increases by 400%. Fracture occurs for a uniform temperature field because the radial stresses at the inside corner are larger than those at the punch corner. As the temperature gradient increases, the radial stress at the inside corner is lower than that at the punch corner, which prevents fracture. A deep cup with a 375-mm drawing depth was produced when the temperature gradient exceeded 100°C.

Assessment of Analytical Models of Pure Bending of Sheet Materials Using the Digital Image Correlation Method

Bending of sheet materials is a common forming mode for shaping sheet components. Although many numerical models of bending, both analytical and numerical simulations based, are available in the literature, extensive experimental validations have been rather limited. A new bend test method and complementary three-dimensional finite element (FE) simulation of the experiments are employed to assess the predictions from an advanced analytical and FE model of pure bending of aluminium sheet materials. The experimental set-up developed and utilised is an open concept design that allows access to the tensile surface and through-thickness region in the vicinity of the specimen bend line to continuously record images of the deforming specimen with two cameras. The specimen images are analysed for strains using an online strain mapping system based on digital image correction method. Tangential strain distribution results from the models in terms of material thinning in the bend region are compared with those from the experiments on AA2024 aluminium sheet material by considering the responses from the specimen edges and mid-width regions at the bend line. Furthermore, the tangential and radial stress distributions on the through-thickness section of the specimen from the analytical model are compared with those from the FE model. The results from experiments, FE model and analytical model are compared and discussed in the light of the experimental data and the assumptions involved in the development of the models.

Effect of local velocity on diffusion-induced stress in large-deformation electrodes of lithium-ion batteries

In this work, the contribution of local velocity to the resultant flux of lithium in lithium-ion battery is introduced into the diffusion equation to describe the migration of lithium in the active material of electrodes. The effect of the local velocity on the stress evolution in a spherical electrode made of silicon is analyzed, using the derived diffusion equation and nonlinear theory of elasticity. Two boundary conditions at the surface of the electrode, which represent two extreme conditions of real electrode materials, are used in the stress analysis: one is stress-free, and the other is immobile. The numerical results with the stress-free boundary condition suggest that the effect of the local velocity on the distribution of radial stress and hoop stress increases with the increase of time and the effect of the local velocity on the distribution of lithium is relatively small. In comparison with the results without the effect of the local velocity, the effect of the local velocity is negligible for the immobile boundary condition. The numerical result shows that the use of the immobile boundary condition leads to the decrease of von-Mises stress, which likely will retard the mechanical degradation of electrode and improve the electrochemical performance of lithium-ion battery.

Spatial distribution of residual stresses in glass-ZrO2 sphero-cylindrical bilayers

Residual stresses arising from inhomogeneous cooling after sintering have shown to play a preponderant role in the higher incidence of chippings observed for glass-zirconia dental prostheses. Still, current descriptions of their nature and distribution have failed to reconcile with clinical findings. Therefore, an axisymmetric sphero-cylindrical bilayer model was used in this study to determine the effect of the cooling rate on the final spatial distribution of residual stresses. Zirconia frameworks with two different radii (1.6 and 3.2mm) were CAD/CAM fabricated. Subsequent glass overlays with two different thickness ratios (1:1 and 2:1) were generated and heat pressed onto the zirconia substrates. The obtained structures were submitted to a last firing process and fast- (45°C/s) or slow-cooled (0.5°C/s) to room temperature. Unbonded bilayers were produced by firing glass overlays onto boron nitride coated zirconia. Thin sagittal and transversal sections were obtained from the specimens to assess residual stress distribution by means of light birefringence. The applied cooling rates did not affect distribution or magnitude of radial residual stresses (sagittal sections), whereas increased hoop stress magnitudes were measured (transversal sections) in fast-cooled specimens. A distinct stress nature was observed for the hoop stress component of unbonded overlays after fast cooling. Interaction between stress components seems to govern the final stress distribution, highlighting the importance of a multiaxial assessment of this problem in three-dimensional structures.