Axial Normal Stress Research Articles

Closed-form solutions for inhomogeneous states of a slender 3-D SMA cylinder undergoing stress-induced phase transitions

This paper considers the isothermal stress-induced phase transitions of shape memory alloys (SMAs), based on a two variant model with an internal variable. More specifically, we study analytically the inhomogeneous states of a slender SMA cylinder under uniaxial tension/extension in a three-dimensional (3-D) setting. By utilizing two small quantities, the complex 3-D mechanical system is reduced to three linear systems for three different regions (austenite, martensite and phase transition regions). Then, we concentrate on the inhomogeneous states with only one phase transition region which is far away from the two ends. For the case of planar and general interfaces among three regions, we construct closed-form solutions and semi-analytical solutions, respectively. Theoretically, the present analytical study generalizes the classical Ericksen’s 1-D results. First, unlike the 1-D case, for which there are infinitely many equally stable states, the current 3-D problem has only one optimal state (by the energy criterion). Second, in the optimal state the average axial stress on the cross section is still the 1-D Maxwell stress, although there is a nonuniform distribution. Physically, the analytical solutions clearly reveal the roles of material and geometrical parameters. The localized inhomogeneous deformation is due to the structural effect and the strain softening behavior, and an explicit formula for the width of the transition region is deduced. We also make a comparison of our 3-D analytical results with those of a 1-D gradient model, which leads to a plausible choice of the gradient parameter.

Normal stress‐induced permeability hysteresis of a fracture in a granite cylinder

AbstractThe paper examines the influence of axial stress‐induced closure of a fracture on its permeability. The experiments were conducted on a cylinder of Barre Granite measuring 457 mm in diameter and 510 mm in height, containing a central cylindrical cavity of diameter 75 mm. Radial flow hydraulic pulse tests were conducted in a previous research investigation (Selvadurai et al., PAGEOPH, 2005) to determine the permeability characteristics of the intact granite. In the continuation of the research, a fracture was introduced in the cylinder with its nominal plane normal to the axis of the cylinder. Axial compressive stress was applied normal to the plane of the fracture. An increase in the compressive normal stress acting on the fracture caused a reduction in the aperture of the fracture, which resulted in the reduction in its permeability. Steady state radial flow tests were conducted on the fractured axially stressed sample to determine the variation of fracture permeability with axial normal stress. The analytical developments also take into account flow through the matrix region as the normal stress increases. The results of the experimental investigations indicate that the complete stress relief of a fracture previously subjected to a normal stress of 7.5 MPa can result in a permeability increase of approximately three orders of magnitude. These findings are relevant to shallow depth geotechnical construction activities where enhanced fluid flow can be activated by stress relief. As the fracture aperture closes with high normal stress, the flow through the matrix can be appreciable and if this factor is not taken into consideration the interpretation of fracture permeability can be open to error. This factor can be of interest to the interpretation of permeability of fractures in deep crustal settings where the stresses acting normal to the fracture surface can inhibit flow in the fracture.

Experimental investigation on anisotropic turbulent flow in a 6 × 6 rod bundle with LDV

The five-beam three-component laser Doppler velocimetry (LDV) is applied to investigate the turbulent flow in a 6×6 rod bundle installed with simple grid spacers. LDV measurement has been conducted at four cross sections downstream a grid spacer at five Reynolds numbers ranging from 6600 to 70,300. The flow evolution downstream of the grid spacer is demonstrated through the comparison of the axial mean velocity and Root Mean Square (RMS) velocity at the three cross sections downstream of the grid spacer. All the three components of the flow velocity are measured in the selected subchannels at the outlet cross section of the rod bundle which is dedicated to provide more information on the turbulence statistics in the rod bundle flow. Remarkably high ratio of axial normal stress to the turbulent kinetic energy, vv¯/k, is observed even in the subchannel center, which indicates that the turbulence in the rod bundle is anisotropic. Comparing experiment results at the five Reynolds numbers, the low Reynolds number effect is found in the case with Re=6.6×103. The experiment results also imply that the Reynolds number effect in the tight-lattice bundle is weak compare to that in the loose one.

Effective flange width of steel–concrete composite beam with partial openings in concrete slab

Openings often existed in the concrete flange of steel–concrete composite floors in practical structures, affecting the mechanical behavior of composite floors, such as bearing capacity, rigidity and stability. In this paper, the effective flange width of steel–concrete composite beams with openings in the concrete slab was studied by finite element method. The predicted results for the entire loading history of composite beams with openings in the concrete slab were verified by test results, and the axial normal stress distribution was analyzed in detail based on finite element analysis results. Then the parametric analysis was carried out for obtaining the practical simplified design method for calculating the effective width of steel–concrete composite beams with openings in the concrete slab. At last, the predicted deflection of composite beams with openings in the concrete slab was compared with test results and finite element analysis results, showing that the simplified method for calculating the effective flange width of steel–concrete composite beams with openings in concrete slab had enough precision and was suitable for practical design.

Dynamic Stress Analysis of Battery Tabs Under Ultrasonic Welding

Ultrasonic metal welding is widely used for joining multiple layers of dissimilar metals, such as aluminum/copper battery tabs welding onto copper busbars. It is therefore important to have a robust product/process design using ultrasonic metal welding that ensures consistent welds with desired quality. In this work, the effects of longitudinal and flexural vibrations of the battery tab during ultrasonic welding on the development of axial normal stresses that occasionally cause cracks near the weld area are studied by applying a one-dimensional continuous vibration model for the battery tab. Analysis results indicate that fracture could occur near the weld area, due to low cycle fatigue as a result of large dynamic stresses induced by resonant flexural vibration of the battery tab during welding. This study provides a fundamental understanding of battery tab dynamics during ultrasonic welding and its effects on weld quality, and can be used to develop guidelines for product/process design of ultrasonically welded battery tabs.

Analysis of a three-dimensional FEM model of a thin piezoelectric actuator embedded in an infinite host structure

In this paper, we adopted a two-dimensional analytical electro-elastic model to predict the stress distributions of the piezoelectric actuator in 3D case. The actuator was embedded in an elastic host structure under electrical loadings. The problem is reduced to the solution of singular integral equations of the first kind. The interfacial stresses and the axial normal stress in both plane stress state and plane strain state were obtained to study the actuation effects being transferred from the actuator to the host. The stress distributions of the PZT actuator in different length and different thickness were analyzed to guarantee the generality. The validity of the present model has been demonstrated by application of specific examples and comparisons with the corresponding results obtained from the Finite Element Method.

CFD investigating the flow characteristics in a triangular-pitch rod bundle using Reynolds stress turbulence model

With the dramatic progress in the computer processing power, computational fluid dynamics (CFD) methodology can be applied in investigating the detailed knowledge of thermal–hydraulic characteristics in the rod bundles. These localized information, including flow, turbulence, and heat transfer characteristics, can assist in the design and the improvement of rod bundles for nuclear power plants. In this paper, a three-dimensional (3-D) CFD model with the Reynolds stresses turbulence model is proposed simulating the flowing characteristics within the rod bundles and subsequently to investigate the effects of different mesh distributions and pressure–strain models on the turbulent mixing. Based on the CFD simulations, the secondary flow can be reasonably captured in the rod bundle. However, different pressure–strain models would affect the distributions of normal stresses and lead to be non-uniform distribution for using Linear Pressure–Strain (LPS) model. In addition, the predicted results with RSM–LPS model would be larger than that using other models for axial velocity and normal stresses. The main reason is the wall-reflection effect added on RSM–LPS model. The wall-reflection effect also would affect the position of the vortex center. The predicted position with the Quadratic Pressure–Strain (QPS) model has good agreement compared with the experiments.

Semi-analytically presenting the creep strain rate and quasi shear-lag model as well as finite element method prediction of creep debonding in short fiber composites

In this research work, semi-analytical method (SAM) is presented to predict composite creep strain rate and quasi shear-lag (QSL) formulation directly, as well as, finite element method (FEM) is employed for predicting partial creep debonding at the interface in steady state creep of short fiber composites under tensile axial stress. Also, new formulation QSL is introduced to obtain the average axial stress in fiber which its results are similar to the results of shear lag (SL) model. Then, it is shown that FEM can approximately predict the partial debonding in some regions of the interface. As a result, interfacial debonding can be caused by high tensile axial and circumferential stresses, high shear and equivalent stresses, and low compressive radial stresses with considering stress concentration. The results obtained from SAM are in good agreement with the available experimental results. Finally, it is concluded that FEM simulation can be useful for predicting some defects such as interfacial debonding and also better designing the fibrous composites.

Thermal residual stresses in SiC particle reinforced aluminium composites: a study by the Taylor-based nonlocal theory of plasticity

Strain gradient theories have been considered to be an effective means for capturing the size effects on ceramic particle-reinforced metal-matrix composites (MMCp), but the results predicted by them are significantly lower than the corresponding experimental data. One reason might be, that the thermal residual stresses caused by thermal contraction mismatch between the metal matrix and the ceramic particle were neglected in the numerical models. By incorporating the Taylor-based nonlocal theory (TNT) of plasticity, the finite element method (FEM) is applied in the present research, to investigate the effect of thermal residual stresses on the yield stress and average axial stresses of the aluminium matrix reinforced by silicon carbide particles (SiCp/Al). The elements of the matrix have been implemented in the ABAQUS finite element code through its USER-ELEMENT (UEL) interface for TNT plasticity. Some comparisons with the associated literature demonstrate that the numerical model with the thermal residual stresses is more in agreement with the experimental results.

Stress Analysis of Carbon Nanotubes Reinforced Nanocomposites

Stress transfer in the carbon nanotube reinforced nanocomposites is investigated in this work. The model consists of two concentric cylinders, namely, a single-walled carbon nanotube cylinder (SWCNT) and a matrix cylinder, as the representative volume element (RVE). The stress analysis is performed using the shear lag model for the axisymmetric RVE. Analytical solutions for the axial normal stresses in the SWCNT and matrix, and the interfacial shear stress across the SWCNT/matrix interface are obtained. Numerical results show that using a large volume fraction improves the efficiency of the stress transfer from the matrix to the carbon nanotubes.

Turbulence of a Fin Trailing Vortex in Subsonic Compressible Flow

minimalcouplingbetweenturbulentvelocitycomponents.Thevortexturbulenceisstronglyanisotropicinamanner that varies greatly with spatial position. As the vortex strength is reduced, the axial turbulent normal stress diminishesmore sharply than the twocross-plane turbulent normal stresses, possibly because the latter components are influenced by external turbulence spiraling towards the vortex core. The turbulent shear stresses do not show discernable reductions in magnitude with lower vortex strength.

A study of the blast‐induced brain white‐matter damage and the associated diffuse axonal injury

PurposeBlast‐induced traumatic brain injury (TBI) is a signature injury of the current military conflicts. Among the different types of TBI, diffuse axonal injury (DAI) plays an important role since it can lead to devastating effects in the inflicted military personnel. To better understand the potential causes associated with DAI, this paper aims to investigate a transient non‐linear dynamics finite element simulation of the response of the brain white matter to shock loading.Design/methodology/approachBrain white matter is considered to be a heterogeneous material consisting of fiber‐like axons and a structure‐less extracellular matrix (ECM). The brain white matter microstructure in the investigated corpus callosum region of the brain is idealized using a regular hexagonal arrangement of aligned equal‐size axons. Deviatoric stress response of the axon and the ECM is modeled using a linear isotropic viscoelastic formulation while the hydrostatic stress response is modeled using a shock‐type equation of state. To account for the stochastic character of the brain white matter microstructure and shock loading, a parametric study is carried out involving a factorial variation of the key microstructural and waveform parameters.FindingsThe results obtained show that the extent of axon undulations and the strength of axon/ECM bonding profoundly affect the spatial distribution and magnitude of the axonal axial normal and shear stresses (the stresses which can cause diffuse axonal injury).Originality/valueThe present approach enables a more accurate determination of the mechanical behavior of brain white matter when subjected to a shock.

Steady state creep behavior of short fiber composites by mapping, logarithmic functions (MF) and dimensionless parameter (DP) techniques

A new mathematical insight based on logarithmic, polynomial mapping functions (MF), and dimensionless parameter (DP) models is presented for determination of some unknowns in the steady state creep stage of short fiber composites subjected to axial loading. These unknowns are displacement rate in outer surface of the unit cell, shear and equivalent stresses at interface and outer surface of the unit cell, and average axial stress in fiber. Dimensionless parameter technique is presented for determination of displacement rate and equivalent stress in outer surface of the unit cell. However, the polynomial mapping function is presented for determination of average axial stress in fiber. Most important novelty of the present research work is determination of the mentioned unknowns in steady state creep by DP and MF techniques without using the shear-lag theory unlike the previous researches. Good agreements are found among the new approaches and previous analytical results based on the shear-lag theory and also numerical solutions (FEM) for predicting the steady state creep behavior in short fiber composites.

Studies on FRP-concrete interface with hardening and softening bond-slip law

This latest experimental study proposes a theory that the bond-slip law for a FRP-concrete interface contains linear hardening and exponential softening. On the basis of this law, the paper studies the mechanic behavior and debonding process of a FRP-concrete interface. Firstly, through nonlinear fracture mechanics, the analytical solutions of the interface shear stress, the axial normal stress of FRP and the load–displacement relationship at the loaded end with the single shear test model of FRP-concrete are acquired. The shear stress propagation as well as the debonding process of the whole interface for different bond lengths could be predicted. Secondly, a simplified interface bond-slip law is used by changing the exponential softening law into a linear softening law. In addition, the analytical solutions for the simplified interface bond-slip law could also be obtained. Finally, based on the analytical solutions of the two bond-slip laws, the influences of the FRP bond length and stiffness on load–displacement curve and the ultimate load, as well as stiffness on effective bond length were discussed, with the similarities and differences between the two bond-slip laws also being studied.

Ultra‐High‐Speed Full‐Field Deformation Measurements on Concrete Spalling Specimens and Stiffness Identification with the Virtual Fields Method

Abstract: For one decade, spalling techniques based on the use of a metallic Hopkinson bar in contact with a concrete sample have been widely employed to characterise the dynamic tensile strength of concrete at strain rates ranging from a few tens to hundreds of s−1. However, the processing method based on the use of the velocity profile measured on the rear free surface of the sample (Novikov formula) remains quite basic. In particular, the identification of the whole softening behaviour of the concrete material is currently out of reach. In the present paper, a new processing technique is proposed based on the use of the virtual fields method (VFM). First, a digital ultra‐high‐speed camera is used to record the pictures of a grid bonded onto the specimen. Then, images of the grid recorded by the camera are processed to obtain full‐field axial displacement maps at the surface of the specimen. Finally, a specific virtual field has been defined in the VFM equation to use the acceleration map as an alternative ‘load cell’. This method applied to three spalling tests with different impact parameters allowed the identification of Young's modulus during the test. It was shown that this modulus is constant during the initial compressive part of the test and decreases in the tensile part when microdamage exists. It was also shown that in such a simple inertial test, it was possible to reconstruct average axial stress profiles using only the acceleration data. It was then possible to construct local stress–strain curves and derive a tensile strength value.

Effects of the axial in situ stresses on the zonal disintegration phenomenon in the surrounding rock masses around a deep circular tunnel

A new non-Euclidean model in which effects of the axial in-situ stress with arbitrary value on the zonal disintegration phenomenon in the surrounding rock masses around a deep circular tunnel is taken into account is established. The total elastic stress-field distributions of the surrounding rock around a deep circular tunnel including effects of the axial in-situ stress were given out. The strength criterion of the deep rock masses is applied to determine the occurrence of disintegration zones. The numerical computation was carried out. It is found from numerical results that number and size of fractured and nonfractured zones are sensitive to the axial in-situ stress, tangential, radial and axial normal stress, the intermediate principal stress coefficient and the rock mass rating classification RMR.

The virtual fields method applied to spalling tests on concrete

For one decade spalling techniques based on the use of a metallic Hopkinson bar put in contact with a concrete sample have been widely employed to characterize the dynamic tensile strength of concrete at strain-rates ranging from a few tens to two hundreds of s −1 . However, the processing method mainly based on the use of the velocity profile measured on the rear free surface of the sample (Novikov formula) remains quite basic and an identification of the whole softening behaviour of the concrete is out of reach. In the present paper a new processing method is proposed based on the use of the Virtual Fields Method (VFM). First, a digital high speed camera is used to record the pictures of a grid glued on the specimen. Next, full-field measurements are used to obtain the axial displacement field at the surface of the specimen. Finally, a specific virtual field has been defined in the VFM equation to use the acceleration map as an alternative ‘load cell’. This method applied to three spalling tests allowed to identify Young’s modulus during the test. It was shown that this modulus is constant during the initial compressive part of the test and decreases in the tensile part when micro-damage exists. It was also shown that in such a simple inertial test, it was possible to reconstruct average axial stress profiles using only the acceleration data. Then, it was possible to construct local stress-strain curves and derive a tensile strength value.

Contact analysis of thin films bonded to graded coatings

In this study, the contact mechanics of thin films bonded to graded coatings is investigated both analytically and numerically. In these problems, the stresses may be arisen due to uniform temperature changes and temperature excursions, far field mechanical loading, and residual stresses resulting from film processing or manufacturing process of the graded coatings. The primary interest in this study is the examination of the stress concentrations or singularities near the film ends. The underlying mechanics problem is formulated by assuming the film acts as a “membrane” and the graded coating as a functionally graded material (FGM). In the analytical formulation, the problem is reduced to a singular integral equation for the unknown interfacial shear stresses through an asymptotic expansion and then solved numerically using a suitable collocation technique. Finite Element Method (FEM) is utilized in the computational studies. The calculated results include interfacial shear stress between the film and the graded coating, strength of stress singularity at the film ends and the axial normal stress in the film. This study reveals that both mechanical and geometrical parameters of the system as well as the loading type have a great effect on the stress distribution and the strength of shear stress singularity at the film ends. Adjusting these parameters and selecting the appropriate type of grading will reduce these stresses that may have a bearing on the failure of the coating.

Drag Reduction of Biopolymer Flows

Drag reduction of rigid and semi-rigid biopolymers – scleroglucan (0.005% and 0.01% w/w) and xanthan gum (0.0124% and 0.07% w/w) – in a circular pipe and a concentric annular pipe (radius ratio  = 0.5) have been investigated experimentally. The objective here is to assess and study the behaviour of these polymers and compare to the drag reduction by flexible polymers, available in the literature. Pressure-drop, mean axial and complete Reynolds normal stress data measurements on the polymer solutions were conducted using laser Doppler anemometry. Measurements were also performed on the Newtonian solvent (water) for comparison. Rheological characterization of the polymers conducted over a wide range of concentrations (0.005% - 0.75% w/w) showed increased shear-thinning ability of the polymer solutions with increasing solution concentration. The pressure-drop measurements indicate that the effectiveness of these polymers as drag-reducing agents is only mildly dependent on the Reynolds number. Qualitative assessment of the turbulent peak values in the circular pipe flow shows behaviour resembling that of low drag-reducing (DR 40%) flexible polymer solutions data available in the literature such as carboxymethylcellulose with increases in u'+ and decreases both in w'+ and v'+ generally when compared to that of the Newtonian flow at the same Reynolds number. The peak values of the turbulent fluctuation levels (normalized with UB) in the annular pipe, however, shows a decreasing trend of the axial component below 40% drag reduction. Above this drag-reduction “limit”, the peak levels seemed to increase, generally, with drag reduction. Decrease in both w'/UB and v'/UB when compared to that of the Newtonian flow are observed at the same Reynolds number for all drag-reducing flows, similar to what is observed in the pipe-flow study.

Continuum and multi-scale simulation of mixed kinematics polymeric flows with stagnation points: Closure approximation and the high Weissenberg number problem

Abstract It is a well known fact that the upper We limit encountered in continuum level viscoelastic flow simulations with typical constitutive equations for dilute polymeric solutions that predict bounded extensional viscosities in geometries with internal stagnation points on solid surfaces is a strong function of the strain hardening nature of the fluid. Specifically, the upper We limit decreases as the level of strain hardening of the fluid is increased. To provide further insight into the high We limitations in continuum level computations of this class of flows, we have performed extensive continuum and multiscale flow simulations in two benchmark flow problems, namely sedimentation of sphere in a tube and flow past a cylinder in a channel, utilizing the FENE-P (continuum and Brownian Configuration Fields (BCF)) and Giesekus (continuum) constitutive equations as well as the FENE (BCF) dumbbell micromechanical model. Extremely large stress gradients in the axial normal stress along the plane of symmetry in the wake of the cylinder and sphere are observed in FENE-P and Giesekus predictions using both multiscale and continuum numerical techniques at We of O(1) where the numerical simulations begin to breakdown for significantly strain hardening fluids, i.e., b > 300, α < 0.005. The existence of very large localized polymeric stresses and stress gradients is shown to be the consequence of significant over prediction of macromolecular extension by the closed form constitutive equations in the extensionally dominated region of the flow. The inability of the aforementioned constitutive equations to accurately describe the flow microstructure coupling downstream of stagnation points in complex kinematics flows should motivate use of regularization techniques for the polymeric stress or utilization of more sophisticated constitutive equations in flows with strong straining components.