Normal Stress Components Research Articles

Multiscale failure analysis of fiber reinforced concrete based on a discrete crack model

In this work the capabilities of an interface model to predict failure behavior of steel fiber reinforced cementitious composites (SFRCCs) are evaluated at both macro and mesoscale levels of observation. The interface model is based on a hyperbolic maximum strength criterion defined in terms of the normal and shear stress components acting on the joint plane. Pre-peak regime is considered linear elastic, while the post-peak behavior is formulated in terms of the fracture energy release under failure mode I and/or II. The well-known “Mixture Theory” is adopted for modeling the interactions between fibers and the surrounding cementitious composite. The effects of both the axial forces on the fibers induced by normal relative displacements, as well as the dowel action due to tangential relative displacements in the interfaces are considered in the formulation of the interaction mechanisms between fibers and cementitious composites. After describing the interface model, this work focuses on numerical analyses of SFRCC failure behavior. Firstly, the validation analysis of the interface model is performed at the constitutive level by comparing its numerical predictions against experimental results available in scientific literature. Then, the sensitivity of the interface theory for SFRCC regarding the variation of main parameters of the composite constituents is evaluated. Finally, the attention is focused on Finite Element (FE) analysis of SFRCC failure behavior at meso and macroscopic levels of observation. The results demonstrate the capabilities of the interface theory based on the Mixture Theory to reproduce the main features of failure behavior of SRFCC in terms of fiber content and involved fracture modes.

Fatigue routing of container ships–assessment of contributions to fatigue damage from wave-induced torsion and horizontal and vertical bending

The traditional method for assessing fatigue damage of ship structures assumes moderate wave amplitudes and linear responses. This method can be questioned when applied to container ships which are characterised by large deck openings that cause low torsion rigidity of the structure. Depending on the heading of the vessel in relation to the wave encounter direction, container ships can therefore be sensitive to, for example, oblique waves. In the current investigation, SESAM software with the three-dimensional hydrodynamic code WASIM is used to simulate a 4400 TEU container ship operating in the North Atlantic. Non-linear wave loads are utilised for the direct calculation of stress histories under severe sea states using the finite element software in SESAM. A method for the separation of normal stress components in an arbitrary cross section and location of the ship is proposed: warping stress from wave-induced torsion and stress components from horizontal and vertical bending. The strain (stress) response calculated using the models in one location is verified against full-scale measurements made on a similar type of container vessel in the same location. A case study is presented for fatigue damage assessment in two cross sections of the container ship. The contributions to fatigue damage from wave-induced torsion and horizontal and vertical bending are calculated and presented in a fatigue damage routing tool by means of polar diagrams, which includes the effects of heading and ship speed on fatigue damage.

Interaction of Lamb modes with an inclusion

The interaction of Lamb modes propagating in a steel plate containing a thin inclusion is analyzed for cases where the inclusion material has elastic parameters similar to the ones of the plate, and where the inclusion is in perfect mechanical contact with the surrounding plate material. A modal decomposition method is used to calculate the conversion of an incident Lamb mode to other modes. Hence, the influence of the type of incident mode, of the location and geometry of the inclusion, and of the elastic parameters of the inclusion and plate material on the mode conversion coefficients is analyzed. Besides the expected increase of the conversion efficiency with increasing cross section of the inclusion, it is found that due to reasons of symmetry, the presence of an inclusion leads to an efficient conversion of an incident S0 mode into reflected and transmitted A0 modes, unless the inclusion is located very close to the plate center. On the other hand, the conversion efficiency of an incident A0 mode into a reflected A0 mode is found to be strongly dependent on the depth of the inclusion, this conversion even disappearing for some location depths. For the cases studied, the inclusion location dependence of the mode conversion seems to be correlated with the normal profile of the longitudinal normal stress component σyy(y). As intuitively expected, the mode conversion efficiency increases with the mismatch of an acoustic impedance like factor between the uniform plate and the inclusion region.

LDA Measurement in Cylindrical Containers without Using Planar Secondary Units

To measure velocity components using the laser Doppler anemometry (LDA)in a cylindrical surface, as in a hydrocyclone, traditionally, one encloses the top circular tube of the hydrocyclone with a flat surface box to minimize the refraction effects of laser beams caused by the curved solid walls. In this brief study, an alternative procedure is suggested to reorient the laser beams to measure the mean and fluctuation velocity components. Adopting the beam orientation suggested—at a single point in the flow field—the axial and circumferential mean velocity components, along with the corresponding turbulent normal and shear stress components, can be determined. Test results confirm that the proposed method is valid to get data related to the mean velocities and the Reynolds stresses at a single point in the flow field of a hydrocyclone. The suggested procedure with slight modifications can be applied to measure velocities in the flow field formed by other circular surfaces, such as cones.

Numerical Analysis of Viscoelastic Fluids in Steady Pressure-Driven Channel Flow

The developing steady flow of Oldroyd-B and Phan-Thien-Tanner (PTT) fluids through a two-dimensional rectangular channel is investigated computationally by means of a finite volume technique incorporating uniform collocated grids. A second-order central difference scheme is employed to handle convective terms in the momentum equation, while viscoelastic stresses are approximated by a third-order accurate quadratic upstream interpolation for convective kinematics (QUICK) scheme. Momentum interpolation method (MIM) is used to evaluate both cell face velocities and coefficients appearing in the stress equations. Coupled mass and momentum conservation equations are then solved through an iterative semi-implicit method for pressure-linked equation (SIMPLE) algorithm. The entry length over which flow becomes fully developed is determined by considering gradients of velocity, normal and shear stress components, and pressure in the axial direction. The effects of the mesh refinement, inlet boundary conditions, constitutive equation parameters, and Reynolds number on the entry length are presented.

A BOUNDARY-LAYER APPROACH TO STRESS ANALYSIS IN THE SIMPLE SHEARING OF RUBBER BLOCKS

Abstract Rubbers are usually modeled as being perfectly incompressible. In the simple shear of rubber blocks, the normal stress components, therefore, contain an arbitrary constant pressure term to be determined from the boundary conditions. There is therefore a fundamental ambiguity in the determination of this pressure because the normal stresses are expected to be identically zero on different faces of the sheared block. It is proposed here that the stress distribution near a face should be determined by the normal stress boundary condition at that face and that this distribution is valid only within a short distance from the face, giving rise to boundary layers at the faces of the sheared block. At the intersection of these boundary layers it will be assumed that the stress is additive. It is further assumed that the stresses within the bulk of the material should be determined by treating the perfectly incompressible material as equivalent to a slightly compressible material. The form of slight compressibility adopted here is that usually assumed in the finite element simulation of rubbers. These reasonable assumptions give rise to a complex stress pattern within the block. The results are qualitatively similar to results obtained by other authors on using a finite element approach for a neo-Hookean material. The possible occurrence of cavitation at the corners of the block is also examined.

Nonlinear micromechanics-based bond–slip model for FRP/concrete interfaces

Various experimental studies in the literature have reported that the local bond–slip profiles for fibre reinforced polymer (FRP)/concrete joints subjected to direct shear loading and the associated local bond strength values vary along the bonded length. This peculiarity of the local bond–slip curves has apparently not yet been considered in any of the available interface models.In this work, a procedure is developed for deriving a nonlinear bond–slip model for FRP/concrete interfaces that accounts for the variation of local bond strength along the bonded length. The bond–slip law was developed based on 3D nonlinear micromechanics-based finite element results using the microplane theory for concrete. In the finite element analysis, the microplane constitutive law is implemented as a user-defined subroutine in the ADINA finite element package to run the simulations. Subsequently, the finite element results have been used to develop the nonlinear bond–slip constitutive law for the FRP/concrete joints. This constitutive relation is developed considering the interaction between the interfacial normal stress components along the bonded length and local bond strength. Then a new mathematical approach is proposed to describe the entire local bond–slip relationship. The proposed interface law accounts for the nonlinear contributions of the FRP laminates, adhesive and concrete layers.Finally, to assess the efficacy of the proposed bond–slip model, validations are carried out using a large experimental database (results of 118 specimens). The predicted ultimate load carrying capacities show a satisfactory agreement with the test data. Furthermore, comparisons are made among the characteristics and predictions of the proposed model and those of two bond–slip models from the literature.

Preferred hydride growth orientations on oxide-coated gadolinium surfaces

The initial development of hydrides on polycrystalline gadolinium (Gd), as on some other hydride forming metals, is characterized by two sequential steps. The first step involves the rapid formation of a dense pattern of small hydride spots (referred to as the “small family” of hydrides) below the native oxidation layer. The second stage takes place when some of the “small family” nucleants (referred to as “growth centers”, GCs) break the oxide layer, leading to their rapid growth and finally to the massive hydriding of the sample.In the present study, the texture of the two hydride families was studied, by combining X-ray diffraction (XRD) analysis with a microscopic analysis of the hydride, using scanning electron microscopy (SEM) and atomic force microscopy (AFM). It has been observed that for the “small family”, a preferred growth of the (100)h plane of the cubic GdH2 takes place, whereas for the GCs, a change to the (111)h plane of the cubic hydride dominates. These preferred growth orientations were analyzed by their structure relation with the (00.1)m basal plane of the Gd metal.It has been concluded that the above texture change is due to the surface normal compressive stress component exerted by the oxidation overlayer on the developing hydride, preventing the (00.1)m||(111)h growth orientation. This stress is relieved upon the rupture of that overlayer and the development of the GCs, leading to the energetically favorable mode of growth.

Piezoresistive CMOS sensor for out-of-plane normal stress

A piezoresistive sensor for measuring the temperature compensated sum (σxx+σyy)/2−βσzz of the three mechanical normal stress components, where σxx+σyy, σzz, and β denote the in-plane normal stress sum, the out-of-plane normal stress, and a numerical factor close to 1 is presented. The device is based on CMOS-compatible diffusions and exploits the piezoresistive effect acting on vertical current components. The sensor signal and resulting possibilities to extract mechanical stress components are analyzed. Experimental results illustrate the influence of design parameters and operating conditions on the sensor performance and are compared to a simple analytical sensor model. A second-order cross-sensitivity to in-plane shear stresses is discussed and determined experimentally. The temperature compensation is demonstrated by a force measurement with a deviation between the numerically expected and the experimentally extracted value smaller than 15% over the temperature range from 10°C to 60°C.

Grain Boundary Structure Dependence of Extrinsic Grain Boundary Dislocation Emission Phenomena: A Molecular Dynamics Study

Recently, it has been reported that extrinsic grain boundary dislocations (EGBDs) are often present in the grain boundaries of ultrafine-grained (UFG) metals produced by severe plastic deformation; therefore, the emission of EGBDs from the grain boundaries could afect the mechanical characteristics of UFG metals. In this paper, we use molecular dynamics to simulate the emission of EGBDs from grain boundaries, and we examine the grain boundary structure dependence of the emissions. Then we apply J-integral analysis to evaluate the Peach–Koehler force required for the grain boundaries to emit the EGBD. It can be confirmed that the Peach–Koehler force required to emit the EGBD is highly dependent on the relationship between the Burgers vector components of the EGBD and intrinsic grain boundary dislocations (IGBDs), which form the equilibrium grain boundaries. Comparing analyses of the linear elastic theory with atomic simulations, we confirm that nonlinear structural changes in the dislocation cores of the EGBD and IGBDs, which can only be expressed by atomic scale resolution, are responsible for such strong grain boundary structural dependence. We also verify that normal stress components perpendicular to the slip plane of EGBDs have a significant effect on the emission of EGBDs.

On elastic deformation of radially prestressed incompressible spherical shells

We formulate and study inflation of radially prestressed incompressible spheres and annular spherical shells. We find that radially prestressed Neo-Hookean spheres subjected to tensile radial component of normal stress at the outer boundary admit deformations fields such that a cavity forms at the center of the sphere and that for a critical value of this radial component of the normal stress at the outer boundary, \(\mathcal{P}_{o}^{cr}, \) the surface of the cavity becomes traction free. This is the cavitation problem first studied by Ball [Phil Trans Royal Soc London A 306(1496): 557–611 (1982)]. Our studies show that the value of \(\mathcal{P}_{o}^{cr}\) depends on the prestress. While some prestress distributions requires the radial component of the normal stress at the outer surface to increase in value, at least initially, for the cavity to grow, for others, like in the stress free case, requires this normal stress to decrease monotonically. Consistent with the observation of Saravanan [ Int J Non-Linear Mech 46(1): 96–113 (2011)] we also find that the boundary traction required to engender a given deformation field in a prestressed annular spherical shell depends on the prestresses.

Elastic-Plastic and Residual Stresses in Clamped Thermoplastic Composite Laminates Loaded Transversely

In this study, an elastic-plastic stress analysis was carried out in woven steel fibers- thermoplastic clamped composite laminates. The stacking sequences were chosen as [0/0]2, [15/-15]2, [30/-30]2 and [45/-45]2 for woven steel fibers – thermoplastic composites plates. The layers were chosen for symmetric and antisymmetric cases. The finite element solution was performed by using the ANSYS software. Solid 186 element was utilized in the solution. Normal stress components at the clamped edges were found to be higher than that at the mid point of the laminated plates. Normal stresses are tensile at the mid point of the clamped edges and compressive at the mid point of the laminated plates. Then, the residual stress components were calculated in the critical points of the composite laminates.

The linear stability of plane Poiseuille flow of Burgers fluid at very low Reynolds numbers

The linear stability of plane Poiseuille flow of Burgers fluid at very low Reynolds numbers is studied. In the previous works, it was shown that plane Poiseuille flows of UCM and Oldroyd-B fluids at very low Reynolds numbers are linearly stable. However, in the present work, unstable modes for Burges fluid are detected with some special value of parameters. In critical stable condition, there are two kinds of perturbation waves. One travels downstream with the name of forward wave, while the other travels upstream with the name of reverse wave. The mean value of the two wave speeds is independent of the characteristic velocity of flow, while the difference between the wave speeds reflects the equivalent velocity of flow. By comparing the perturbation modes for Newtonian fluid and Burgers fluid under critical stable conditions, it can be found that although the shapes of their amplitudes are basically the same, their phase diagrams are significantly different. The neutral curve of Burgers fluid is also different from that of Newtonian fluid. Unstable modes can still be found at high wave numbers. The flow instability is induced due to the phase difference between the perturbation strain and stress. The perturbation energy caused by the forward wave, which is dissipated by the effects of the component of perturbation normal stress in the streamwise direction, is transported by the effects of both the perturbation normal stress in the wall-normal direction and the perturbation shear stress. The converse is true for the reverse wave.

Plane-strain state of an elastoplastic body with a crack under mixed-mode loading

A mixed-mode (I + II) crack model with a plastic strip on its continuation under plane strain is proposed. The stress components within the strip are determined from the yield conditions, stress limitation, and relationship between the normal stress components defined via the principal stress state. The crack parameters are analyzed for the Mises yield condition. In the quasibrittle case, the governing system of equations includes stress intensity factors K I, K II, and T-stresses

Estimating fatigue damage under variable amplitude multiaxial fatigue loading

The present paper is concerned with the use of the modified Wohler curve method (MWCM) to estimate both lifetime and high-cycle fatigue strength of plain engineering materials subjected to complex load histories resulting, at critical locations, in variable amplitude (VA) multiaxial stress states. In more detail, when employed to address the constant amplitude (CA) problem, the MWCM postulates that fatigue damage reaches its maximum value on that material plane (i.e. the so-called critical plane) experiencing the maximum shear stress amplitude, fatigue strength depending on the ratio between the normal and shear stress components relative to the critical plane itself. To extend the use of the above criterion to those situations involving VA loadings, the MWCM is suggested here as being applied by defining the critical plane through that direction experiencing the maximum variance of the resolved shear stress. Such a direction is used also to perform the cycle counting: because the resolved shear stress is a monodimensional quantity, stress cycles are directly counted by the classical rain-flow method. The degree of multiaxiality and non-proportionality of the time-variable stress state at the assumed critical sites instead is suggested as being measured through a suitable stress ratio which accounts for the mean value and the variance of the stress perpendicular to the critical plane as well as for the variance of the shear stress resolved along the direction experiencing the maximum variance of the resolved shear stress. Accuracy and reliability of the proposed approach was checked by using several experimental results taken from the literature. The performed validation exercise seems to strongly support the idea that the approach formalized in the present paper is a powerful engineering tool suitable for estimating fatigue damage under VA multiaxial fatigue loading, and this holds true not only in the medium-cycle, but also in the high-cycle fatigue regime.

Dugdale-type model for a mixed-mode crack: plane stress state

Amixed-mode (I + II) crack model with a plastic strip on its continuation is proposed. The three unknown stress components within the strip are determined from the yield conditions, stress limitation, and relationship between the normal stress components defined via the principal stress state. The crack parameters are analyzed for the Mises yield condition

FEA of Stress behavior in the Single-Lap Adhesive Joint

This paper deals with the effects of bending and boundary condition on the stress distribution of a single-lap adhesive joint under tension using the three-dimensional finite element analysis technique. The numerical results obtained from the finite element analysis show that both the left and right hand regions of the adhesive layer are subjected to high stresses. The numerical results also show that most of the extreme stresses occur at interface which is between the adhesive and the upper adherend. It is clear that the stresses are concentrated near the left and right free ends of the adhesive layer while the centre region of the adhesive layer is mostly stress-free. It is also clear that the stress state in this case is mainly dominated by the normal stress components.

Buckling analysis of double-walled carbon nanotubes embedded in an elastic medium under axial compression using non-local Timoshenko beam theory

Using the non-local elasticity theory, Timoshenko beam model is developed to study the elastic buckling of double-walled carbon nanotubes (DWCNTs) embedded in an elastic medium under axial compression. The non-local effects in the normal and transverse shear stress components are considered. The effects of the surrounding elastic medium based on a Winkler model and van der Waals' (vdW) force between the inner and outer nanotubes are taken into account. Considering the small-scale effects, the governing equilibrium equations are derived and the critical buckling loads under axial compression are obtained. The numerical results are reported using the non-local Timoshenko beam theory and compared with those obtained using the non-local Euler—Bernoulli beam theory. The results show that the critical buckling load can be overestimated by the local beam model if the small-scale effect is overlooked for long nanotubes. Furthermore, in order to estimate the non-local critical buckling load of DWCNTs under axial compression, a simplified analysis is carried out and the results are compared with those obtained using molecular mechanics.

Elasto-Viscoplastic Response of Silicon to Femtosecond Laser Heating at Elevated Temperature

The elasto-viscoplastodynamics of single-crystalline silicon in response to femtosecond laser pulsing at elevated temperature is studied. Hyperbolic energy transport dynamics is considered in conjunction with the Haasen–Sumino constitutive law to explore the thermo-elasto-visco-plastic response of the silicon material subjected to ultrafast optical heating. A computational scheme with staggered-grids is developed to time-integrate the coupled thermal-mechanical responses of silicon wafer at annealing temperatures up to 1,100 K. Non-thermal melting fluence threshold is examined favorably against published physical data. The elasto-viscoplastic response at high annealing temperature is characterized by thermal stress waves that propagate with increased oscillation amplitude and modified frequency spectrum. It is shown that the induced transverse and longitudinal displacements along with the normal stress components all establish well-defined relations with temperatures, suggesting that they may be utilized for the thermometric profiling of silicon wafers undergoing Rapid Thermal Processing (RTP) with desired thermal resolution.

Finite element analysis of functionally graded plates under transverse load

The nonlinear behaviors of functionally graded material (FGM) plates under transverse distributed load are investigated here using a high precision plate bending finite element. Material properties of the plate are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of volume fractions of the constituents. The effective material properties are then evaluated based on the rule of mixture. The formulation is developed based on the first-order shear deformation theory considering the physical/exact neutral surface position. The shear correction factors are evaluated employing the energy equivalence principle. The transverse shear stresses and transverse normal stress components are obtained using the in-plane stresses evaluated from the constitutive equations and the three-dimensional equilibrium equations. The nonlinear governing equations are obtained following a standard finite element procedure and solved through Newton–Raphson iteration technique to predict the lateral pressure load versus central displacement relationship.