Low Temperature Electronic Transport in RuO2-Based Cermet Resistors

We have studied the temperature (T) dependence of resistance (R) of RuO₂-based thick films down to 1.2 K. Samples were prepared from inks containing conductive RuO₂ powders (<-10% wt.), high lead-silicate glass particles and Mn (≤1.4% wt.). We found that the resistance fits the exponential lawR=R ₀ exp (T ₀/T)^x with x=1/4 and the most resistive samples show a cross-over to the x=1/2 regime as the temperature decreases. Both the fitting parametersR ₀ andT ₀ scale down as the RuO₂ fraction increases and they are affected in a similar way by a change of the Mn content. The presence of the two regimes is similar to that observed inn-type GaAs [Phys. Rev. B39, 8059 (1989)] andn-type CdSe [Phys. Rev. Lett.64, 2687 (1990)] whilst it disagrees with the behaviour predicted for grain to grain hopping [Phys. Rev. B27, 2583 (1983)] and with that expected for resonant tunneling between metallic particles [J. Appl. Phys.48, 5152 (1977)]. We conclude that in our systems the driving charge transport mechanism is electron hopping within the glassy matrix. Since in our case the hopping length is of the same order of the localization length, the puzzling questions arising from our experiments are whether and how the variable range hopping model can be extended beyond its conventional limits.     

Implementation of stress-dependent resilient modulus of asphalt-treated base for flexible pavement design

Abstract

Asphalt-treated base (ATB) is a widely used base course material in flexible pavements. Due to its lower binder content and lower quality granular material, resilient modulus (M_R) of ATB exhibits a stress dependent property. While most of the pavement analysis software used in the current routine design tasks is based on Burmister’s multi-layer elastic theory, in which the M_R is the primary fundamental material property, the software cannot truly deal with the stress-dependent M_R of paving material. In this study, M_R model in the Mechanistic Empirical Pavement Design Guide was adopted to accommodate the stress-dependent M_R of ATBs and the model was implemented in pavement mechanistic analyses through Abaqus finite element software and its user programmed subroutine. The comparison of critical pavement responses was made among pavements with three types of ATBs. Pavement responses obtained using the multi-layered elastic theory and based on resilient moduli recommended by Alaska Department of Transportation & Public Facilities, were also included for comparison.     

Dependence of the microwave surface resistance on the structure and thickness of superconducting cuprate films

An investigation is made of the microwave surface resistance R _s measured at 10 GHz and 77 K, as a function of the thickness of superconducting epitaxial films of yttrium barium cuprate grown on lanthanum aluminate substrates by magnetron sputtering. Films between 200 and 1800 nm thick have low values R _s (0.3–0.5) mΩ and do not show any deterioration. The level of R _s achieved in films of comparatively large thickness is mainly attributable to the low rate of film growth (0.8 nm/min). Pis’ma Zh. Tekh. Fiz. 25, 79–88 (August 12, 1999)     

Size effect in the low-field Hall coefficient of single-crystal copper films

Measurements of the low-field Hall coefficientR _H of single-crystal copper films were made at 4.2 K by the use of a SQUID. The surface normaln of the samples was directed in the [100], [110], and [111] directions and the ratio of the thickness to the mean free path ranged from 0.1 to 0.7. It is found that the effect of surface scattering causesR _H to decrease whenn [100], whereas it causesR _H to increase whenn [110] and [111]. This behavior is interpreted in terms of the geometrical characteristics of the Fermi surface.     

The Gap-to- Tc Ratio of a van Hove Superconductor

We give an analytical expression for the gap-to-T _c ratio (R) of a superconductor with a van Hove singularity in the density of states. Our calculation yields R in very good agreement with the results obtained numerically by S. Ratanaburi et al. [J. Supercond. 9, 485 (1996)].     

Effect of orthorhombic distortion and second-nearest neighbor hopping on gap-to-T cratio

Within the framework of the BCS theory, we perform a numerical study of the effect of orthorhombic distortion and second nearest neighbor hopping on the ratioR = 2δ(0)/T _c based on the van Hove singularity scenario. We find that the gap-to-T _c ratio depends on the distortion and hopping parameters, in contradiction to the recent conclusion of Sarkaret al. [Phys. Rev. B 51, 12854 (1995)]. In particular, the introduction of orthorhombic distortion increases the value ofR, and with decreasing second neighbor hopping,R decreases.     

Theory of thermohyperelasticity for near-incompressible elastomers

Summary Elastomers are often used in hot and confining environments in which thermomechanical properties are important. It appears that published constitutive models for elastomers are mostly limited to isothermal conditions. In this study, athermohyperelastic constitutive model for near-incompressible elastomers is formulated in terms of the Helmholtz free energy density . Shear and volume aspects of the deformation are decoupled. Thermomechanical coupling occurs mostly as thermal expansion. Criteria for thermodynamic stability are derived in compact form. As illustration, a particular expression for is presented which represents the thermomechanical counterpart of the conventional two-term incompressible Mooney-Rivlin model. It is used to analyze several adiabatic problems in a rubber rod.List of symbols A _i matrices appearing inD - c _e, _e, c _e specific heat at constant strain - C Cauchy strain tensor - C _R reduced Cauchy strain tensor - C ₁,C ₂ coefficients of Mooney-Rivlin model - c vectorial counterpart ofC: VEC (C) - c ₂ vectorial counterpart ofC ²: VEC (C ²) - D isothermal tangent stiffness matrix - e vectorial counterpart of : VEC () - deviatoric Lagrangian strain tensor - e _R reduced deviatoric Lagrangian strain tensor - e volume strain - e _T reduced volume strain - f thermal expansion function,=[1+(T–T ₀)/3]^–1 - F, F _T deformation gradient tensor - F _R reduced deformation gradient tensor - H Hessian matrix for the Gibbs free energy density - H related toH - I ₁,I ₂,I ₃ invariants ofC - I _1R,I _2R,I _3R invariants ofC _R - I, I ₉ identity matrix - i vectorial counterpart ofI: VEC (I) - J determinant ofF - J _R determinant ofF _R - J _T determinant ofF _T - J ₁,J ₂ invariants of /J _{R 2} ³ - J _1R,J _2R invariants of _R /R _J ^2/3 - k thermal conductivity coefficient - K ₁,K ₂,K ₃ invariants of /J ^2/3 - K _1R,K _2R,K _3R invariants ofe _R/J^2/3 - p hydrostatic pressure - s vectorial counterpart of stress : VEC () - s isotropic stress - T (absolute) temperature - T ₀ reference temperature - conventional (isothermal) strain energy density (per unit volume) - volumetric thermal expansion coefficient - thermal expansion vector - strain, Lagrangian strain - entropy density - isothermal bulk modulus - Lagrange multiplier - _i extension ratio - shear modulus - stability coefficient - mass density - stress, 2nd Piola-Kirchhoff stress - _i principal stress - Cauchy stress - _d deviatoric Cauchy stress - , _{M C T 0} Helmholtz free energy density - _i /I _i - _ij ²/I _i I _j - Gibbs free energy density - (.) variational operator - VEC (.) vectorization operator - operator for Kronecker product     

Finite element method for thermomechanical response of near-incompressible elastomers

Summary The present study addresses finite element analysis of the coupled thermomechanical response of near-incompressible elastomers such as natural rubber. Of interest are applications such as seals, which often involve large deformations, nonlinear material behavior, confinement, and thermal gradients. Most published finite element analyses of elastomeric components have been limited to isothermal conditions. A basic quantity appearing in the finite element equation for elastomers is thetangent stiffness matrix. A compact expression for theisothermal tangent stiffness matrix has recently been reported by the first author, including compressible, incompressible, and near-incompressible elastomers. In the present study a compact expression is reported for the tangent stiffness matrix under coupled thermal and mechanical behavior, including pressure interpolation to accommodate near-incompressibility. The matrix is seen to have a computationally convenient structure and to serve as a Jacobian matrix in a Newton iteration scheme. The formulation makes use of a thermoelastic constitutive model recently introduced by the authors for near-incompressible elastomers. The resulting relations are illustrated using a near-incompressible thermohyperelastic counterpart of the conventional Mooney-Rivlin model. As an application, an element is formulated to model the response of a rubber rod subjected to force and heat.Notation A _i n _i /c - C Cauchy strain tensor - c VEC (C) - C ₁,C ₂ constants in Mooney-Rivlin model for elastomer - c ₂ VEC (C ²) - c _i eigenvalues ofC - c _e ,c _e , _e specific heat at constant strain - D _nl stiffness matrix due to the geometric nonlinearity - D _T ,D _T isothermal tangent modulus matrices - e VEC () - e _d VEC ( _d ) - f, f(T) thermal expansion function, =1/[1+(T-T ₀)/3] - f combined vector of nodal forces and heat fluxes - f _M consistent nodal force vector - f _T ,f _1T ,f _2T ,f _3T ,f _4T consistent heat flux vector - F deformation gradient tensor - g related tof _T - h time step - I _i invariants ofC - I 9×9 identity tensor - I identity tensor - i vectorial counterpart ofI:VEC(I) - J the Jacobian matrix in Newton iteration scheme - J determinant ofF - J _i invariants ofI ₁ ^–1/3 C - k, k(T) thermal conductivity - K tangent stiffness matrix - K _MM ,K _MT ,K _MP tangent stiffness submatrices - L,L _M ,L _P ,L _S lower triangular matrices related toLU decomposition ofK - M ₁,M ₂ strain-displacement matrices - N interpolation matrix - n surface normal vector - n _i (I _i /c) ^T - P matrix arising in theLU decomposition ofK - P the tension applied to the rubber rod - p (true) pressure - Q heat flux - q heat flux vector - r,r _M ,r _T ,r residual vectors - R,R ₁,R ₂,R ₃ matrices from thermal boundary conditions - R _s 1/2(R+R ^T ) - R _a 1/2(R–R ^T ) - R –R ₁+R ₂+R - R _s 1/2(R+R ^T ) - R _a 1/2(R-R ^T ) - s VEC() - S surface in undeformed configuration - t time - t traction referred to undeformed configuration - T, T ₀ temperature, reference temperature - T upper-shelf temperature in the surface convective relation - U upper triangular matrix inLU decompositionK - u displacement vector - v combined vector of nodal parameters - v _n value ofv at thenth time step - V volume in undeformed configuration - w strain energy density per unit undeformed volume - x position vector in deformed configuration - X position vector in undeformed configuration - volumetric thermal expansion coefficient - _c coefficient in the surface convective relation - ₁ strain-displacement matrix - _T interpolation matrix for thermal gradient: T - vector of nodal displacements - Lagrangian strain tensor - _d deviatoric Lagrangian strain tensor - interpolation function for - entropy per unit mass in the undeformed configuration - vector of nodal temperatures - þ isothermal bulk modulus - interpolation function forT - temperature-adjusted pressure,p/f ³(T) - mass density in the undeformed configuration - matrix arising inLU decomposition ofK - 2nd Piola-Kirchhoff stress - Cauchy stress tensor - , _M , _T , _c , ₀ Helmholtz free energy density function per unit mass - _i - _ij - vector of nodal values of - matrix arising in theLU decomposition ofK - near-incompressibility constraint function - internal energy density per unit mass - (·) variational operator - VEC(·) vectorization operator - symbol for Kronecker product of two tensors - tr(·) trace of a tensor - det(·) determinant of a tensor     

On R ratio dependence of threshold stress intensity factor range for fatigue crack growth in type 316(N) stainless steel weld

Abstract

The influence of R ratio in the range 0·05–0·4 on the ambient temperature fatigue crack growth behaviour of an austenitic stainless steel weld, SS 316(N), has been studied. Results indicate that the cyclic threshold stress intensity factor ΔK_th increases with decreasing R ratio. The data are compared with those for SS 316, SS 316L and SS 316L(N) base materials from the literature, and various approaches dealing with the R ratio effects are examined. Zhang’s model considering the contribution of the crack tip plasticity to the fundamental fatigue crack propagation process does provide a consistent interpretation for the data.     

Computer Reconstruction of a Random Rough Surface in the Presence of Higher Diffraction Orders

Abstract

The profile of a random rough surface (RRS), whose mean roughness R_a is greater than the light wavelength, is visualized by computer processing. The surface is presented as a sum of sinusoidal gratings. The light diffracted from this surface field is registered by a photodiode array. The second and third diffraction orders from each grating are taken into account in computer processing of the diffracted field and the mixing field–the field obtained at the mixing of the reference and the diffraction fields. The criterion for taking into account higher diffraction orders is the asymmetry of the diffraction pattern to the left and to the right relative to the central peak (the field of zero diffraction orders obtained from each grating) The number of the diffraction orders higher than the first is defined from the average intensity distribution between the central peak and the diffraction orders to the left and to the right at arbitrary light wavelength. The surface profile is reconstructed by a computer program and the mean roughness R_a is calculated. The obtained value of R_a is in satisfactory agreement with that measured by the contact pin method.