Thermoelastic behavior of a thermoelectric thin-film attached to an infinite elastic substrate

Abstract

This paper examines the thermoelectric behaviour of a thermoelectric thin film bonded to an elastic substrate. A calculation model for thermoelectric thin films is developed based on the singular integral equation method. The interface shear stress is found to exhibit singular behaviour at the ends of the films. Numerical results for the thermal stress distribution in the film and the film/substrate interface are obtained. Effects of film thickness and the substrate to film stiffness ratio on the stress of the film and the stress intensity factor of the interface are identified. The effects of interface electricity conductivity and the elastic–plastic deformation of the film are discussed.     

Effects of charge-density-wave depinning on the low frequency shear compliance of NbSe3

We report on measurements of the voltage dependence of the complex shear compliance of two crystals of the charge-density-wave (CDW) conductor NbSe₃, for torsional frequencies between 1 Hz and 71 Hz. For both samples, there is a frequency independent, ∼1% increase of the magnitude of the compliance when the voltage exceeds the threshold for CDW depinning, but the internal friction has a striking sample dependence which we do not understand. For one sample, there is a frequency independent decrease in internal friction with CDW depinning, suggesting that the elastic changes are not relaxational and might reflect changes in the screening of the crystal strain by the CDW. For the second sample, the sign and magnitude of the change in internal friction is strongly frequency dependent, which we associate with a change in screening due to the finite electron diffusion time. The second sample also exhibits a frequency dependent peak in internal friction near threshold that may reflect relaxation of the CDW phase. Received 14 August 2001 and Received in final form 3 October 2001     

How does the structural inhomogeneity influence the shear band behaviours of metallic glasses

ABSTRACT

Here we propose a model to understand the influence of structural inhomogeneity on the shear band behaviours of metallic glasses. By considering the inhomogeneous structure and stress concentration, the model predicts that the strain for shear band nucleation in metallic glasses can be variable and far below the theoretical elastic limit. During sliding, the shear band will approach a dynamic equilibrium state of balanced free volume generation and annihilation. By considering the accumulation of irreversible structure change, the shear band will finally develop into fracture. Under fluctuating load, the shear band shows an ‘activate-arrest’ behaviour, which results from a delayed response to the external load change. These results reasonably explain and correlate the physics behind the elastic limit, stick-slip shear band behaviour, implicit shear events, and shear band fracture in metallic glasses. The study can provide another perspective and platform to understand the correlations between structural inhomogeneity and shear band behaviours in metallic glasses, and further explore other shear band related phenomena not only in metallic glasses but also in the class of shear-softened materials.     

Frictional shear cracks

We discuss crack propagation along the interface between two dissimilar materials. The crack edge separates two states of the interface, “stick” and “slip.” In the slip region, we assume that the shear stress is proportional to the sliding velocity; i.e., the linear viscous friction law is valid. In this picture, the static friction appears as the tile Griffith threshold for crack propagation. We calculate the crack velocity as a function of the applied shear stress and find that the main dissipation comes from the macroscopic region and is mainly due to the friction at the interface. The relevance of our results to recent experiments, Baumberger et al., Phys. Rev. Lett. 88, 075509 (2002), is discussed.     

A model of a belt chamber cracking based on crack profiles calculations

Abstract

The problem of a Belt chamber matrix cracking is presented. The influence of crack surface quality on the effective values of near crack tip stress is discussed. It is shown that under working conditions of the vessel, the existing shear friction between upper and lower crack surfaces caused by crack surface roughness can prevent the crack surface sliding displacement. Therefore, the control variable for matrix cracking is the value of stress intensity factor K_I corresponding to normal node of loading only. The calculations are performed by finite element method within the range of linear elastic fracture mechanics.     

Nonlinear shear wave interaction at a frictional interface: energy dissipation and generation of harmonics

Analytical and numerical modeling of the nonlinear interaction of shear wave with a frictional interface is presented. The system studied is composed of two homogeneous and isotropic elastic solids, brought into frictional contact by remote normal compression. A shear wave, either time harmonic or a narrow band pulse, is incident normal to the interface and propagates through the contact. Two friction laws are considered and the influence on interface behavior is investigated: Coulomb's law with a constant friction coefficient and a slip-weakening friction law which involves static and dynamic friction coefficients. The relationship between the nonlinear harmonics and the dissipated energy, and the dependence on the contact dynamics (friction law, sliding, and tangential stress) and on the normal contact stress are examined in detail. The analytical and numerical results indicate universal type laws for the amplitude of the higher harmonics and for the dissipated energy, properly non-dimensionalized in terms of the pre-stress, the friction coefficient and the incident amplitude. The results suggest that measurements of higher harmonics can be used to quantify friction and dissipation effects of a sliding interface.     

Finite strain stress fields near the tip of an interface crack between a soft incompressible elastic material and a rigid substrate

We present a numerical study of finite strain stress fields near the tip of an interface crack between a rigid substrate and an incompressible hyperelastic solid using the finite element method (FEM). The finite element (FE) simulations make use of a remeshing scheme to overcome mesh distortion. Analyses are carried out by assuming that the crack tip is either pinned, i.e., the elastic material is perfectly bonded (no slip) to the rigid substrate, or the crack lies on a frictionless interface. We focus on a material which hardens exponentially. To explore the effect of geometric constraint on the near tip stress fields, simulations are carried out under plane stress and plane strain conditions. For both the frictionless interface and the pinned crack under plane stress deformation, we found that the true stress field directly ahead of the crack tip is dominated by the normal opening stress and the crack face opens up smoothly. This is also true for an interface crack along a frictionless boundary in plane strain deformation. However, for a pinned interface crack under plane strain deformation, the true opening normal stress is found to be lower than the shear stress and the transverse normal stress. Also, the crack opening profile for a pinned crack under plane strain deformation is completely different from those seen in plane stress and in plane strain (frictionless interface). The crack face flips over and the tip angle is almost tangential to the interface. Our results suggest that interface friction can play a very important role in interfacial fracture of soft materials on hard substrates.     

On the dynamics of sliding elastic manifolds with random interaction

The friction dynamics of contacting D-dimensional disordered elastic manifolds, driven by external forces, is studied, and the existence of a zero-temperature depinning transition below some critical dimensionality is demonstrated for different kinds of elastic response. It is shown that this model falls into the universality class of single interface depinning in a 2D-dimensional random medium. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 8, 532–537 (25 October 1996) Published in English in the original Russian Journal. Edited by Steve Torstveit.     

Ice internal friction: Standard theoretical perspectives on friction codified,adapted for the unusual rheology of ice,and unified

Sea ice contains flaws including frictional contacts. We aim to describe quantitatively the mechanics of those contacts, providing local physics for geophysical models. With a focus on the internal friction of ice, we review standard micro-mechanical models of friction. The solid's deformation under normal load may be ductile or elastic. The shear failure of the contact may be by ductile flow, brittle fracture, or melting and hydrodynamic lubrication. Combinations of these give a total of six rheological models. When the material under study is ice, several of the rheological parameters in the standard models are not constant, but depend on the temperature of the bulk, on the normal stress under which samples are pressed together, or on the sliding velocity and acceleration. This has the effect of making the shear stress required for sliding dependent on sliding velocity, acceleration, and temperature. In some cases, it also perturbs the exponent in the normal-stress dependence of that shear stress away from the value that applies to most materials.

We unify the models by a principle of maximum displacement for normal deformation, and of minimum stress for shear failure, reducing the controversy over the mechanism of internal friction in ice to the choice of values of four parameters in a single model. The four parameters represent, for a typical asperity contact, the sliding distance required to expel melt-water, the sliding distance required to break contact, the normal strain in the asperity, and the thickness of any ductile shear zone.     

On the nature of low-temperature anomalies of the anelastic properties of metallic glasses

In Memory of A. M. Roshchupkin The low-temperature (30<T<300 K) internal friction and elastic modulus of the metallic glass (MG) Ni₆₀Nb₄₀ subjected to preliminary cold working by rolling, high-temperature uniform straining, or electrolytic hydrogenation is investigated. It is established that cold rolling, which induces localized plastic flow, or hydrogenation radically alters the temperature dependences of the internal friction and elastic modulus: hysteresis appears in the background damping and intense relaxational peaks arise in the internal friction, accompanied by a defect of the elastic modulus. A uniform strain does not affect the low-temperature anelastic behavior of MGs. Microplastic deformation is observed to accompany the hydrogenation of weakly loaded samples. It is asserted that localized microplastic deformation also occurs on hydrogenation with no load. Plastic flow accompanying both rolling and hydrogenation occurs by the formation and motion of dislocationlike defects, which in the presence of an external load of alternating sign give rise to the observed anelastic anomalies. It is concluded that the low-temperature internal-friction peaks, described in the literature, in the “as-quenched,” cold-deformed, or hydrogenated MGs are all of a dislocation nature. Zh. Tekh. Fiz. 67, 35–46 (October 1997) In Memory of A. M. Roshchupkin     

The influence of a magnetic field on the inelastic properties of LiF crystals

The effect of weak magnetic fields (0.1–0.8 T) on the internal friction and Young’s-modulus defect of LiF crystals is investigated over a range of relative strain amplitudes ɛ ₀ from 10⁻⁶ to 10⁻⁴ at frequencies of 40 and 80 kHz. Experiments with these fields show that the internal friction increases and the effective elastic modulus decreases, indicating an increase in the plasticity of the samples. Plots are obtained of the internal friction versus the magnitude of the magnetic field at various values of the strain amplitude ɛ ₀. Fiz. Tverd. Tela (St. Petersburg) 41, 1035–1040 (June 1999)     

Variations in,and Relationships of Surface Area,internal angle of friction and compact diametral fracture strength with degree of compaction

The progress of the compaction process to produce from an assembly of particles a coherent mass can be achieved by the application of shear and normal stress. The achievement of a densified coherent mass necessitates, together with the yielding of material, the movement of particles over and between each other. In uniaxial compaction the angle of internal friction, δ_E, is a projection of the unique critical state line which divides a three dimensional relationship between volume change (V), shear stress (?) and normal stress (σ) into yield domains and surfaces. There is one region for failure and flow (the Hvorslev surface) and another region for failure and consolidation (the Roscoe surface). In this paper the concepts of the Roscoe and Hvorslev surfaces together with the Coulomb yield criterion have been applied to the uniaxial compaction, over a range of compactable stresses, of titanium dioxide (20–2000 kPa). The characteristics of applied and shear stress, angle of internal friction (δ_E), angle of shearing resistance (?) and surface area (S_BET) were measured and correlated with the compaction stress (σ_c) and diametral strength (σ_f) of the compacts to investigate the phenomena of uniaxial compaction.     

Elasticity and inelasticity of silicon nitride/boron nitride fibrous monoliths

A study is reported on the effect of temperature and elastic vibration amplitude on Young’s modulus E and internal friction in Si₃N₄ and BN ceramic samples and Si₃N₄/BN monoliths obtained by hot pressing of BN-coated Si₃N₄ fibers. The fibers were arranged along, across, or both along and across the specimen axis. The E measurements were carried out under thermal cycling within the 20–600°C range. It was found that high-modulus silicon-nitride specimens possess a high thermal stability; the E(T) dependences obtained under heating and cooling coincide well with one another. The low-modulus BN ceramic exhibits a considerable hysteresis, thus indicating evolution of the defect structure under the action of thermoelastic (internal) stresses. Monoliths demonstrate a qualitatively similar behavior (with hysteresis). This behavior of the elastic modulus is possible under microplastic deformation initiated by internal stresses. The presence of microplastic shear in all the materials studied is supported by the character of the amplitude dependences of internal friction and the Young’s modulus. The experimental data obtained are discussed in terms of a model in which the temperature dependences of the elastic modulus and their features are accounted for by both microplastic deformation and nonlinear lattice-atom vibrations, which depend on internal stresses.     

Synthesis and physical properties of the ferroelectric magnet SrBi3Nb2FeO12

The dielectric, elastic, and inelastic properties of a ceramic ferroelectric SrBi₃Nb₂FeO₁₂ are studied over the temperature range 300–900 K. The observed anomalies in the temperature dependences of the permitivity, dielectric loss, shear modulus, and internal friction indicate the occurrence of a structural phase transition in the compound at ～700 K. It is suggested that the transition is a proper ferroelectric and improper ferroelastic second-order phase transition.     

Elastic waves in non-Newtonian (Maxwell) fluid-saturated porous media

Abstract

This paper studies the elastic waves in non-Newtonian (Maxwell) fluid-saturated porous media with the nonzero boundary slip velocity for pore size distribution. The coefficient bF _m (ω) that measures the deviation from Poiseuille flow friction in such media is presented. Based on this coefficient, we investigate the properties of elastic waves by calculating their phase velocities and attenuation coefficients as functions of frequency and the behaviour of the dynamic permeability. The study shows that the pore size distribution removes oscillations in all physical quantities in the non-Newtonian regime. Consideration of the nonzero boundary slip effect in non-Newtonian (Maxwell) fluid-saturated porous media results in (a) an overall increase of the dynamic permeability, (b) an increase of phase velocities of fast Biot waves and shear waves except in the low frequency domain and an overall increase of phase velocity of slow Biot waves and (c) an overall increase of the attenuation of three Biot waves in the intermediate frequency domain except in the deeply non-Newtonian regime. The study also shows that the attenuation coefficient of slow Biot waves is small in the deeply non-Newtonian regime at higher frequency, which encourages us to detect slow Biot waves in oil-saturated porous rock.     

NiTi合金相变过程中界面动力学的内耗研究

本文采用同时测量内耗、模量及电阻的方法,对NiTi合金变温过程中所发生的正、反马氏体相变及可逆I/C相变进行了系统的研究。结果表明,变温马氏体相变及I/C相变过程中内耗均为粘弹性型内耗,是相界面在克服粘滞性阻力而运动时引起的。从界面动力学出发,研究了相变过程中界面的运动动力学行为。由实验数据求得了马氏体相变过程中界面动力学关系的具体表达式为:V=V^*exp(—△G^*/△G—△G_R);相变过程内耗表达式为:Q^-1=(n²)/2·(μ△G^*)/((△G—△G_R)²)·(dF)/(dT)·T/ω;相变阻力△G_R约为10cal/mol的数量级。讨论了相变过程中的“软模”效应。马氏体相变过程中的模量“软化”来自声子模的软化和界面运动引起的附加模量亏损两个方面。 关键词：     

Local friction at a sliding interface between an elastomer and a rigid spherical probe

This paper reports on spatially resolved measurements of the shear stress distribution at a frictional interface between a flat rubber substrate and a glass lens. Silicone rubber specimens marked close to their surface by a colored pattern have been prepared in order to measure the surface displacement field induced by the steady-state friction of the spherical probe. The deconvolution of this displacement field then provides the actual shear stress distribution at the contact interface. When a smooth glass lens is used, a nearly constant shear stress is achieved within the contact. On the other hand, a bell-shaped shear stress distribution is obtained with rough lenses. These first results suggest that simple notions of real contact area and constant interface shear stress cannot account for the observed changes in local friction when roughness is varied.     

Elestic constants in the interfacial layer at the nematic-liquid-crystal-vapour interface

Summary Close to the interface between a nematic liquid crystal (NLC) and another medium, the elastic constants become functions of distancez from the interface and of angle θ between the directorn and the unit vectork orthogonal to the interface. Furthermore, due to the breaking of the translation symmetry at the interface, a lot of new subsurface elastic contributions can appear. In a previous paper we investigated these subsurface anomalies by using a simple molecular model based on induced-dipole-induced-dipole interactions and by making numerical calculations in the special case of a planar director distortion. In this way, only the numerical values of some effective subsurface elastic constants that characterise planar director distortions could be obtained. In this paper we make a more complete analytical calculation of all the subsurface elastic constants by using a microscopic model and a more general theoretical procedure. The microscopic interaction energy is written in a general form that allows us to investigate different kinds of intermolecular interactions (induced diple-induced dipole, quadrupole-quadrupole and so on). Both thez-dependence and the θ-dependence of the subsurface elastic constants are obtained in a closed analytical form. In the special case of induced-dipole-induced-dipole interactions and for planar director distortions, our analytical results are shown to agree with the previous numerical results. The important macroscopic effect of these elastic subsurface anomalies is discussed.     

In situ observation of interfacial debonding process induced by matrix crack propagation in two-dimensional unidirectional model composites

Interfacial debonding behavior is studied for unidirectional fiber reinforced composites from both experimental and analytical viewpoints. A new type of two-dimensional unidirectional model composite is prepared using 10 boron fibers and transparent epoxy resin with two levels of interfacial strength. In situ observation of the internal mesoscopic fracture process is carried out using the single edge notched specimen under static loading. The matrix crack propagation, the interfacial debonding growth and the interaction between them are directly observed in detail. As a result, the interfacial debonding is clearly accelerated in specimens with weakly bonded fibers in comparison with those with strongly bonded fibers. Secondary, three-dimensional finite element analysis is carried out in order to reproduce the interfacial debonding behavior. The experimentally observed relation between the mesoscopic fracture process and the applied load is given as the boundary condition. We successfully evaluate the mode II interfacial debonding toughness and the effect of interfacial frictional shear stress on the apparent mode II energy release rate separately by employing the present model composite in combination with the finite element analysis. The true mode II interfacial debonding toughness for weaker interface is about 0.4 times as high as that for a stronger interface. The effect of the interfacial frictional shear stress on the apparent mode II energy release rate for the weak interface is about 0.07 times as high as that for the strong interface. The interfacial frictional shear stress and the coefficient of friction for weak interface are calculated as 0.25 and 0.4 times as high as those for strong interface, respectively.     

The effect of dissipation on the resistive admittance of an elastic medium

The effect of dissipation on the real part of the admittance of an elastic half-space is typically thought to be unimportant if the loss factor ζ of the elastic medium is small. However, dissipation induces losses in the near field of the source and, provided the size of the source is small enough, this phenomenon can be more important than elastic wave radiation. Such losses give rise to a fundamental limit in the quality factor of an oscillator attached to a substrate. Near field losses associated with strains in the elastic substrate can actually be larger than intrinsic losses in the oscillator itself if the internal friction of the substrate is larger than the internal friction of the oscillator. For a uniform stress applied to a disk of radius a, a monopole source, such phenomena become significant for k(L)a<ζ, while for higher order multipole sources of order l, near field losses are important for (k(L)a)(l+1)<ζ, a far less restrictive constraint.