Terms Of Normal Stresses Research Articles

A New Critical Plane Multiaxial Fatigue Criterion with an Exponent to Account for High Mean Stress Effect

The mean stress effect remains a critical aspect in multiaxial fatigue analysis. This work presents a new criterion that, based on the classical Findley criterion, applies a material-dependent exponent to the mean normal stress term and includes the ultimate tensile stress as a fitting parameter. This way of considering the non-linear effect of the mean stress, with a material-dependent rather than a fixed exponent, is totally innovative among the multiaxial fatigue criteria found in the literature. In order to verify its accuracy, the new criterion has been checked against an extended version of the Papuga database of multiaxial experimental tests with 485 results, and compared with the criteria by Findley, Robert, and Papuga. The new criterion provides outstanding results for pure uniaxial cases, with multiaxial performance similar to the Robert criterion with a smaller range of error and a conservative trend, even surpassing the popular Papuga method in several relevant loading scenarios. These features enhance the applicability and versatility of the criterion for its use in the fatigue design of structural components.

The Role of Turbulence in an Intense Tropical Cyclone: Momentum Diffusion, Eddy Viscosities, and Mixing Lengths

Abstract Improved representation of turbulent processes in numerical models of tropical cyclones (TCs) is expected to improve intensity forecasts. To this end, the authors use a large-eddy simulation (with 31-m horizontal grid spacing) of an idealized category 5 TC to understand the role of turbulent processes in the inner core of TCs and their role on the mean intensity. Azimuthally and temporally averaged budgets of the momentum fields show that TC turbulence acts to weaken the maximum tangential velocity, diminish the strength of radial inflow into the eye, and suppress the magnitude of the mean eyewall updraft. Turbulent flux divergences in both the vertical and radial directions are shown to influence the TC mean wind field, with the vertical being dominant in most of the inflowing boundary layer and the eyewall (analogous to traditional atmospheric boundary layer flows), while the radial becomes important only in the eyewall. The validity of the downgradient eddy viscosity hypothesis is largely confirmed for mean velocity fields, except in narrow regions which generally correspond to weak gradients of the mean fields, as well as a narrow region in the eye. This study also provides guidance for values of effective eddy viscosities and vertical mixing length in the most turbulent regions of intense TCs, which have rarely been measured observationally. A generalized formulation of effective eddy viscosity (including the Reynolds normal stresses) is presented. Significance Statement This study uses a turbulence-resolving simulation of a category 5 tropical cyclone to understand the role of turbulence in intense storms. Results show that turbulence clearly modulates storm structure and intensity. This study provides guidance for the values of turbulent quantities (which are usually parameterized in comparatively coarse operational TC forecast models) in scarcely observed regions of intense storms. Furthermore, a complete formulation of the effective eddy viscosities is proposed, incorporating contributions from typically ignored Reynolds normal stress terms.

Rarefaction effect on the aerodynamics of bristled wings in miniature insects

All previous studies on the aerodynamics of bristled wings in miniature insects are based on continuum flows. However, the diameter of the bristle is very small, and the diameter-based Knudsen number (Kn) is approximately between 0.03 and 0.11, indicating that the flow around the bristle is in the slip-flow regime and rarefaction effect will be present. To investigate how the rarefaction will affect the aerodynamic force and flow field of the bristled wing, we calculated and analyzed the flow around a model bristled wing under two conditions: the continuum flow and the slip flow. The following is shown. Within the range of Kn considered in this study (0.01 ≤ Kn ≤ 0.1), the rarefaction has a very small effect on the aerodynamic force of the bristled wing: it decreases the aerodynamic force by less than 0.5% compared with that of the continuum flow. However, the rarefaction has a significant effect on the contributions of the viscous tangential and normal stress terms to the aerodynamic force: in the continuum flow, the force contribution of the viscous tangential stress is 50.7% and that of the viscous normal stress is zero, whereas in the slip flow, e.g., at Kn = 0.08, the contribution of the viscous tangential stress is only 37.7% and that of the viscous normal stress is 12.9% instead of zero; this is because the rarefaction-induced slip velocity in the slip flow changes the normal derivative of the velocity on the bristle surface compared with that of the continuum flow. Since the rarefaction has only a slight effect on the aerodynamic force, the results on the aerodynamic force of the bristled wing obtained based on continuum flows in previous studies are very good approximations to the correct results.

Discontinuous bifurcation of FRCC with zero-thickness interface modeling

In this work, firstly a fracture-based interface constitutive theory, aimed at simulating the cracking mechanisms of Fiber Reinforced Cementitious Composites (FRCCs), is presented. The discontinuous formulation assumes a hyperbolic maximum strength criterion in terms of normal and shear joint stresses. The latter are evaluated on each crack front to simulate the failure behavior of plain and FRCC systems. A non-associated plastic flow rule, in conjunction with a post-cracking softening law, is defined to complete the modeling approach. On the other hand, the use of the most-classical Mixture Theory is followed for taking into account the actions of fibers in concrete matrix. The bridging mechanisms between fibers and active cracks are defined in terms of fiber-to-concrete bond–slip rule and dowel effects. Secondly, a normalized Cracking Indicator (CI) for discrete crack is proposed in the spirit of Hill’s indicator for loss of stability of inelastic continua, to effectively evaluate the most critical direction for further loading in terms of the resulting energy release and crack opening, while accounting for the fiber direction and content. After presenting the constitutive theory and, particularly, the novel concept of the CI, numerical analyses at constitutive level are performed to evaluate the evolution of the fracture energy, post-peak strength, and critical cracking directions under variable fiber contents. Different load scenarios are evaluated, and the numerical predictions are compared with experimental data.

Seismic response of shallow circular openings to Rayleigh waves

Closed-form solutions are presented for an unsupported shallow circular opening subjected to Rayleigh waves. It is assumed that the ground is homogeneous and elastic, that the wave motion is perpendicular to the tunnel axis, with motions on the plane of the cross section of the tunnel. Thus, plane strain conditions apply. A quasi-static analysis is taken because Rayleigh waves have a large wavelength, arguably of the order of kilometers and velocities about 10% smaller than that of shear waves. Complex variable theory and conformal mapping are used to reach the solution, which is given as a system of equations that provides the parameters of the complex analytic functions needed to compute stresses and displacements. Solutions are found for drained and undrained loading conditions. For the latter, the principle of effective stresses is assumed, which requires no volume change of the ground during the passage of the Rayleigh wave. Because the vertical and horizontal free-field motions of the Rayleigh waves are out of phase, the stresses and displacements induced are also out of phase and cannot be superimposed. Thus, stresses and displacements obtained from the free-field motions are also out of phase, uncoupled and treated separately. The results show that the normal stress terms induced by the free-field motions dominate the response of shallow tunnels and that stresses and tunnel distortions decrease with tunnel depth. An additional solution for a deep circular tunnel subjected to Rayleigh waves is also proposed. A comparison between stresses and displacements obtained with the assumption of shallow or deep tunnel suggests that the largest demand on the tunnel can be approximated with the solution for a deep tunnel, for tunnels at depths larger than about five to six times their radius.

Transverse Wave Propagation in a Thin Isotropic Plate Part I

This article deals with the propagation of a transverse wave in a thin rectangular isotropic plate, which is fixed around the perimeter. The transverse wave is generated by an impact falling on the geometric center of the plate. The solution is performed analytically in the MATLAB software environment for Kirchhoff and Rayleigh geometric models and Hooke’s model. The introduction to the article outlines a very brief history of the solution, followed by a general analytical solution. The basic relations for displacements and velocities in the direction of the x, y, z axes are derived. Under the defined assumptions, the deformations in the individual axes and the rotation of the axes are also solved. Part of the general solution is the derivation of relations for normal and shear stresses, as well as the magnitudes of shear and normal forces and bending moments. Attention is also paid to determining the relationships for different types of excitation loads of the board. The relations for Kirchhoff’s and Rayleigh’s model are derived, as well as the results of the analytical solution at selected points of the plate. A comparison of the results of the solution of both models, i.e., Kirchhoff’s and Rayleigh’s, is performed, both in terms of displacements, velocities, and normal stresses.

Shear Rate–Dependent Frictional Properties of a Wet Granular Layer

Granular materials are a system of discrete particulates found practically in a variety of applications. Gouge particles along earthquake faults and rock joints behave as a granular material. In this article, the frictional properties of a wet granular layer are studied experimentally on a rock surface. Slide–hold–slide (SHS) tests show that static, steady, and residual stresses of the wet layer depend on the shear rate for a fixed hold time. Using Coulomb’s law of friction, adhesive stress and coefficient of friction are determined for all three stresses. Both components of friction are found to increase with shear rate. A friction model for soft solids is used to predict static friction of the granular layer. The scaling laws are also proposed for static friction concerning chain density, relaxation time, and extension of the molecular chains in terms of normal stress, and these results are justified.

Modeling Soil-Metal Sliding Resistance

HighlightsA model was developed to express soil-metal sliding resistance in terms of normal stress and sliding path length.Soil-metal sliding resistance data, different from those used to develop the model, were acceptably simulated.The model is expected to be useful in the design and development of soil-engaging equipment.Abstract. Most previous soil-material sliding resistance studies have focused on the measurement and formulation of only qualitative relationships between sliding resistance and the material type, applied normal stress, sliding path length, and/or soil-properties. Few studies have attempted to formulate quantitative mathematical relationships between soil-material sliding resistance and these factors, or to mathematically express the relative contributions of the frictional and adhesive components to the total sliding resistance. In this study, a mathematical model was developed to express the components of soil-metal sliding resistance for a clay soil as functions of applied normal stress and sliding path length. The model is restricted to soil containing enough moisture to exhibit cohesive strength, but not so much moisture to exhibit gross plastic behavior. Soil-metal sliding resistance data, different from those used to develop the model, were acceptably simulated, as the mean square error between the simulated sliding resistance and the measured sliding resistance ranged from 0.653 to 2.44. Keywords: Adhesion, Friction, Normal stress, Sliding path length, Sliding resistance.

Bond Behavior in Flexural Members: Numerical Studies

Adhesive bonding has recently emerged as an alternative to shear stud connection in steel–concrete composite flexural members. Research on adhesive-bonded steel–concrete composite flexural members is in a preliminary stage, and the behavior of the bond layer in these structures is not well understood yet. A three-dimensional finite element model is developed and used to conduct the parametric investigations. The developed model is validated with experimental results available in the literature. The behavior of the bond layer is defined in terms of normal stress, normal strain, shear stress, and shear strain. Seven different parameters are studied regarding their effect on the behavior of the bond layer. The parameters include load proportion factor, longitudinal distribution of load, transverse distribution of load, width of concrete slab, depth of the concrete slab, Young’s modulus of the adhesive and transverse location of the adhesive fiber. Parametric investigations are carried out to establish the relevance of parameters in terms of their effect on the behavior of the bond layer. The most significant parameters are identified as load proportion factor, longitudinal distribution of load, and Young’s modulus of adhesive.

Drivers for mass and momentum exchange between the main channel and river bank lateral cavities

Large-Eddy Simulations (LES) are used to investigate the governing processes involved in mass and momentum transfer between the flow in the main channel and symmetrically-distributed lateral bank cavities. In-cavity free-surface velocities, based on laboratory measurements made in an open channel, are used to validate the numerical results. A main vortical structure dominates the in-cavity flow which, despite the shallow nature of the flow, features a remarked three dimensional dynamics. LES results outline the largest velocities through the mouth of the cavity are attained in two thin regions near the bottom-bed and free-surface. In the shear layers established between the main channel and cavities is where the main transfer of turbulent momentum is made between these two flow regions, and the numerical simulations capture well the instantaneous coherent flow structures, e.g. Kelvin-Helmholtz vortices. LES captures a low-frequency standing wave phenomenon even with a rigid-lid approximation adopted at the free-surface boundary. Momentum exchange between cavities and main channel is analysed using the Reynolds Averaged momentum equation in the transverse direction, revealing that the pressure gradient term is the unique contributor to flushing momentum out of the cavities whilst convection and Reynolds normal stress terms are responsible for its entraining into the cavity. Furthermore, sediment deposition areas documented in the laboratory experiments are linked with the simulated hydrodynamics, which correlate with regions of low turbulent kinetic energy and vertical velocities near the bottom of the channel. Overall, the results shed new light into the complex mechanisms involved in mass and momentum transfer; this will aid to design embayments more efficiently regarding sediment transport processes.

Solution for cross- and angle-ply laminated Kirchhoff nano plates in bending using strain gradient theory

The static analysis of Kirchhoff nano plates subjected to uniformly (UDL) and sinusoidally (SSL) distributed load is computed. The strain gradient nonlocal theory has been employed in order to involve the size effects of nanostructures in classical continuum theory. The governing equation of motion of Kirchhoff in weak form are applied to nano plates, involving second-order strain gradient nonlocal theory. Thus, the obtained partial differential equations have an increased order of derivation respect to the classical theory, from the fourth to the sixth. The displacements are carried out following the Navier procedure for simply supported boundary conditions. Isotropic and antisymmetric orthotropic laminates, both cross- and angle-ply are studied, for different layouts involving different material properties. Dimensionless outcomes in terms of transverse displacements, and normal and shear stresses, are given to changing aspect ratio and non local ratio, also making a comparison with the classical theory.

Influence of the distribution shape of porosity on the bending FGM new plate model resting on elastic foundations

The functionally graded materials (FGM) used in plates contain probably a porosity volume fraction which needs taking into account this aspect of imperfection in the mechanical bahavior of such structures. The present work aims to study the effect of the distribution forms of porosity on the bending of simply supported FG plate reposed on the Winkler-Pasternak foundation. A refined theory of shear deformation is developed to study the effect of the distribution shape of porosity on static behavior of FG plates. It was found that the distribution form of porosity significantly influence the mechanical behavior of FG plates, in terms of deflection, normal and shear stress. It can be concluded that the proposed theory is simple and precise for the resolution of the behavior of flexural FGM plates resting on elastic foundations while taking into account the shape of distribution of the porosity.

Determination of critical velocity of gelatin hydrogel sliding on a smooth glass substrate

Soft solids such as rubbers, elastomers, gels show jerky or intermittent motion called as stick slip while sliding on a hard surfaces such as glass, metals or rocks. Stick slip causes friction induced vibration, squeaking or squealing sound, loss of energy and loss in positional accuracy. Stick slip exists for low sliding velocities and disappears above a certain velocity known as a critical velocity above which steady sliding exists. Critical velocity depends upon the properties of soft solids, properties of substrate, normal stress, specimen height, stiffness of sliding system, surrounding temperature and humidity etc. Hence understanding the effect of these parameters is extremely important to avoid or minimize the effects of stick slip in sliding systems. In the present study, quadratic model is generated for critical velocity in terms of gelatin concentration, normal stress and specimen thickness. Effect of these parameters on the response is discussed in detail and the results are validated with the established trends mentioned in the literature. Finally the spatio-temporal analysis of sliding interfaces has been performed to understand the rupture and healing of the interface during the stick slip as well as steady sliding.

Thermoelastic analysis of temperature-dependent functionally graded rectangular plates using finite element and finite difference methods

ABSTRACTTwo-dimensional thermoelastic analyses of fully clamped functionally graded rectangular plates (FGRPs) by applying a constant in-plane heat flux from one edge were studied by using Finite Difference Method (FDM) and Finite Element Method (FEM) with temperature-dependent material properties. Some differences about 1.5 to 2 times between FDM and the FEM solutions in terms of normal strain, equivalent strain, shear stress, and equivalent stress levels are observed. However, similar distribution characteristics from FDM and FEM analyses are obtained for temperature, displacement, strain, and stress components.

Instability analysis of a pump-turbine in vaneless space by turbulence kinetic energy production term

Unsteady flow in a high head pump-turbine was simulated using the Partially-Averaged Navier-Stokes (PANS) method. To study the improvement of “S” characteristics of a pump-turbine with misaligned guide vanes (MGV), turbulence kinetic energy production term and pressure fluctuations are numerical studied, comparing with results of pump-turbine with synchronized guide vane (SyV). Instability in the vaneless space of the model pump-turbine is analyzed based on turbulence kinetic energy equation. The maximum value of turbulence kinetic energy production(Pk) with MGV is doubled compared with the maximum value with SyV, which are in accordance with the increase of the amplitude of pressure fluctuation compared with SyV. The change of Pk is determined by the change of the normal stress term. The change of normal stress term will influence the amplitude of pressure fluctuation. The maximum value of 3D term with MGV increases compared with the result with SyV. It may be caused by the nouniform flow with MGV.

Early fretting crack orientation by using the critical plane approach

In the present paper, the novel critical direction method by Araújo et al. and the multiaxial critical plane-based criterion by Carpinteri et al. are combined together to estimate early crack orientation in configurations involving high stress gradients, as fretting fatigue configurations. More precisely, the first method is used to compute the input data for the second one, in terms of normal and shear stresses over a line with a characteristic length. The experimental data herein analysed are related to an Al7050 T7451 aluminium alloy, the fretting tests related to a cylinder-on-plane configuration being performed by the Research Group of Fatigue, Fracture and Materials at the University of Brasilia. Results show that the estimated values of the crack initiation plane fall in the interval defined by the mean experimental values and the standard deviation for each test configuration examined.

Bending behaviour of two directional functionally graded sandwich beams by using a quasi-3d shear deformation theory

This paper presents the static behaviour of two-directional functionally graded (FG) sandwich beams subjected to various sets of boundary conditions by using a quasi-3D shear deformation theory and the Symmetric Smoothed Particle Hydrodynamics (SSPH) method. The SSPH code, which is developed based on the present formulation of the FG sandwich beam, is validated by solving a simply supported conventional functionally graded beam problem. Numerical results which are in terms of maximum dimensionless transverse deflections, dimensionless axial, normal and shear stresses are compared with the analytical solutions and the results from previous studies. Various FG sandwich beam structures are investigated by considering different aspect ratios (L/h) and sets of boundary conditions and using power-law distribution.

Application of the critical plane approach to the torsional fatigue assessment of welds considering the effect of residual stresses

This study aims to investigate how the welding residual stresses affect the fatigue life of steel tubular joints. A single pass weld with filler material is created on the tubular specimens made of structural steel S355J2H. At first, welding residual stresses are calculated numerically by means of FE simulations. The validity of the results is verified experimentally by means of diffraction measurement techniques. Then, an uncoupled damage model based on the critical plane approach is utilized in order to calculate the fatigue life and the initial crack orientation. The as-welded specimens were subjected to cyclic torsional loading with constant stress amplitudes. The Fatemi-Socie (FS) damage parameter is used which is interpreted as the cyclic shear strain damage modified by the normal stress to include the crack closure effect. The stable portion of welding residual stresses is accounted for by the normal stress term of the model. It was observed that despite the common understandings about the critical weld notches, the crack initiation sites under torsional loading have been shifted from the weld toe and from the surface to the heat affected zone and beneath the surface where high tensile residual stresses exist. Then the initial cracks propagated toward the surface whose orientations were influenced by the presence of compressive residual stresses on the surface.It was generally found that the Fatemi-Socie parameter is capable of torsional fatigue damage assessment of welded tubular specimens which contain residual stresses since this critical plane parameter is based on the maximum shear strain plane.

Effect of Fast Constant Loading Rates on the Global Behavior of Sand in Triaxial Compression

Abstract Loading rate effects on the global stress-strain behavior of sand were investigated by performing triaxial compression tests on air-dried sand specimens. Siliceous and calcareous sands were subjected to triaxial compression at various constant strain rates to investigate the rate effects, initial density, confining pressure, shape and size of grains, as well as type of sand on the mechanical behavior of granular materials. The results indicate that silica sand and coral sand exhibit different rate dependency in terms of stiffness and peak normal stress. In general, strain rate effects are highly dependent on confining stress and relative density, with dense samples subjected to the highest employed confining stress exhibiting the most pronounced effects to variation in strain rates. Calcareous sand also exhibited a higher strain rate dependency than silica sand.

Comparison between SSF and Critical-Plane models to predict fatigue lives under multiaxial proportional load histories

Materials can be classified as shear or tensile sensitive, depending on the main fatigue microcrack initiation process under multiaxial loadings. The nature of the initiating microcrack can be evaluated from a stress scale factor (SSF), which usually multiplies the hydrostatic or the normal stress term from the adopted multiaxial fatigue damage parameter. Low SSF values are associated with a shear-sensitive material, while a large SSF indicates that a tensile-based multiaxial fatigue damage model should be used instead. For tension-torsion histories, a recent published approach combines the shear and normal stress amplitudes using a SSF polynomial function that depends on the stress amplitude ratio (SAR) between the shear and the normal components. Alternatively, critical-plane models calculate damage on the plane where damage is maximized, adopting a SSF value that is assumed constant for a given material, sometimes varying with the fatigue life (in cycles), but not with the SAR, the stress amplitude level, or the loading path shape. In this work, in-phase proportional tension-torsion tests in 42CrMo4 steel specimens for several values of the SAR are presented. The SSF approach is then compared with critical-plane models, based on their predicted fatigue lives and the observed values for these tension-torsion histories. KEYWORDS. Multiaxial fatigue life prediction; Critical-plane approach; Polynomial stress scale factor approach.