Normalized Free Energy and Normalized Entropy Applied to Some Lambda (λ) Transitions

The λ-anomaly occurs for a system that can undergo a boson – fermion thermodynamic equilibrium. It is shown that a λ-transition figure can be interpreted in terms of the normalized Gibbs–Helmholtz equation, the Maxwell–Boltzmann energy distribution function, and properties of the statistics of the relevant species. There are three variations of a “λ-transition” curve. These are: (A) the classical λ curve, (B) a saw-tooth line shape that is characteristic of the Bardeen–Cooper–Schrieffer theory of superconductivity, and (C) a single line δ type figure. The low temperature He-4 transition, and Type II superconductor transitions are typical of the line shape A. Type I superconductors typically have type B line shapes. The line shapes for variations A and C result from classical thermodynamic equilibria. The type B line shape occurs in systems that do not have a classical thermodynamic equilibrium at the superconducting transition. Analysis of type B line shapes provides interesting concepts and data for some low- and high-temperature superconductors. Several applications and physical property consequences of these line shapes are discussed.     

Experimental determination of solid–liquid interfacial energy for succinonitrile solid solution in equilibrium with the succinonitrile–(D) camphor eutectic liquid

The equilibrated grain boundary groove shapes for Succinonitrile (SCN) solid solution in equilibrium with the Succinonitrile (SCN)–D Camphor (DC) eutectic liquid were directly observed. From the observed grain boundary groove shapes, the Gibbs–Thomson coefficient and solid–liquid interface energy for SCN solid solution in equilibrium with the SCN–DC eutectic liquid has been determined to be (5.39 ± 0.27) × 10⁻⁸ K m and (7.88 ± 0.79) × 10⁻³ J m⁻² with present numerical method and Gibbs–Thomson equation, respectively. The grain boundary energy of SCN rich phase of the SCN–DC eutectic system has been determined to be (14.95 ± 1.79) × 10⁻³ J m⁻² from the observed grain boundary groove shapes. Thermal conductivity ratio of the liquid phase to the solid phase for SCN–0.16 mole % DC alloy has also been measured.     

Designing cutouts for optimum residual strength in plane structural elements

The paper presents a new approach for shape optimisation of structures with residual strength as the design objective. It must be emphasized that flaws are inevitably present in most structures, and hence the influence of cracks on optimised shapes needs to be investigated. Numerical simulation of cracks using the finite element method requires a very fine mesh to model the singularity at crack tip. This makes fracture calculations computationally intensive. Furthermore, for a damage tolerance based optimisation numerous cracks are to be considered along the structural boundary, and fracture analysis needs to be repeated for each crack at every iteration, thus making the whole process extremely computationally expensive for practical purpose. Moreover, the lack of information concerning crack size, orientation, and location makes the formulation of the optimisation problem difficult. As a result, little attention has been paid to date to consider fracture parameters in the optimisation objective. To address this, the paper presents a methodology for the shape optimisation of structures with strength and durability as the design objectives. In particular, the damage tolerance optimisation is illustrated via the problem of optimal design of a ‘cutout in a rectangular block under biaxial loading’. A parametric shape representation has been used to describe the problem geometry. Damage tolerance based optimisation was performed using nonlinear programming algorithms, and NE-NASTRAN was used for finite element analysis. The first order mathematical programming algorithms, viz: the Broydon–Fletcher–Goldfarb–Shanno (BFGS) and the Fletcher–Reeves (Conjugate Direction) Methods were evaluated as the potential algorithms for optimising the residual strength in the presence of flaws. Another recently developed Sequential Unconstrained Minimisation Technique (SUMT), based on an exterior penalty function method and especially suited for large problems, was also investigated for fracture based optimisation. The effects of the orientation and the number of boundary cracks on the optimal solutions were also studied. It has been shown that the residual strength optimised shapes can be different from the corresponding and commonly adopted stress optimised solution. This emphasises the need to explicitly consider residual strength as the design objective. In all cases a significant reduction in the maximum stress intensity factor was achieved with the generation of a ‘near’ uniform fracture critical surface. The design space near the optimal region was found to be relatively flat. This is beneficial as a significant structural performance enhancement is important rather than precise identification of the local/global optimum solution. The optimal solutions obtained using the nonlinear programming algorithms were compared against those obtained in the literature using a heuristic optimisation method (Biological algorithm). The results obtained using the two methods, employing inherently different (gradient-based and gradient-less) algorithms, were found to agree very well.     

Investigation into nonlinear vibrations of composite plates using the <Emphasis Type="Italic">R</Emphasis>-function theory

We have developed an effective approach to the solution of problems on geometrically nonlinear vibrations of orthotropic multilayer plates of irregular shapes in a classical statement based on the use of the R-function theory, Ritz variational method and Bubnov-Galerkin method. Using the proposed method, problems of vibrations of both multilayer rectangular plates and plates of complex geometries have been solved. The effect of the domain geometry and boundary conditions on the amplitude-frequency characteristics has been investigated. __________ Translated from Problemy Prochnosti, No. 5, pp. 101–113, September–October, 2007.     

Quasistationary Model of Electromagnetic Fields for a Piecewise-Homogeneous Body

We consider a two- or three-dimensional body of arbitrary shape containing foreign inclusions. These inclusions are in perfect electromagnetic contact with the matrix. A boundary condition of the third kind is imposed on the surface of the body. We propose a method of combined application of the fundamental solution of the nonstationary of heat-conduction equation, near-boundary and contact elements, and a step-by-step time scheme of common initial condition for the construction of integral transformations of the components of the vectors of electromagnetic-field intensity at an arbitrary point of space and time. In the case of perfect electromagnetic contact between the zones, the application of contact elements on the interface of the media (instead of boundary or near-boundary elements) enables one to automatically satisfy the first condition of contact (the equality for the components of the vector of electric-field intensity). As a result, the number of unknown fictitious current sources decreases as compared with the case of application of traditional indirect methods of boundary and near-boundary elements. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 41, No. 2, pp. 89–96, March–April, 2005.     

Effects of bondline thickness on Mode-II interfacial laws of bonded laminated composite plate

For a variety of modern industries, interfacial delamination is a critical issue for the design and application of laminated composite structures. Numerous global experimental studies have been conducted to characterize the toughness of adhesively bonded composite structures. In the recent two decades, cohesive zone models (CZMs) have been receiving intensive attentions. The local interfacial traction–separation laws as the fundamental input are crucial for the successful applications of CZMs. Several local tests have also been conducted to determine the interfacial traction–separation laws in adhesively bonded joints. However, very few tests have been employed to investigate the dependency of the local interfacial traction–separation laws on the bondline thickness, particularly, for the laminated composite joints under Mode-II loading conditions. In this work, the effects of bondline thickness on the interfacial behavior have been systematically investigated at various typical bondline thicknesses (from 0.1 to 0.8 mm). The effects of adhesive thickness on the interfacial toughness, interfacial strength, and shapes of the local interfacial traction–separation laws have also been evaluated. The test results indicated that the measured Mode-II (shear test) interfacial shear strength of the composite joints increases as the adhesive layer becomes thicker. It was found a significant dependency of the measured shapes of the Mode-II interfacial laws on the bondline thickness. Several other interesting issues were also reported in this work. This work may provide valuable baseline test data for analytical and numerical modeling of fracture and failure of laminated composite structures.     

Homogenization of viscoelastic composites with fibres of diamond-shaped cross-section

The present paper provides details on the application of asymptotic homogenization techniques to the analysis of viscoelastic composite materials with fibres of diamond-shaped cross-section. The Correspondence principle allows transforming the governing boundary value problems to quasistatic ones. Then, we apply the homogenization approach. For solving the cell problem for small volume fractions, the boundary shape perturbation procedure and the composite cylinder assemblage model are used. For a volume fraction equal to 1/2, we use the Dykhne–Keller–Mendelson formula. Matching of limit solutions by two-point Padé approximants gives a formula for the effective properties valid for any volume fraction from the interval [0, 0.5].     

In vitro corrosion behaviour of Ti–Nb–Sn shape memory alloys in Ringer’s physiological solution

The nearly equiatomic Ni–Ti alloy (Nitinol) has been widely employed in the medical and dental fields owing to its shape memory or superelastic properties. The main concern about the use of this alloy derives form the fact that it contains a large amount of nickel (55% by mass), which is suspected responsible for allergic, toxic and carcinogenic reactions. In this work, the in vitro corrosion behavior of two Ti–Nb–Sn shape memory alloys, Ti–16Nb–5Sn and Ti–18Nb–4Sn (mass%) has been investigated and compared with that of Nitinol. The in vitro corrosion resistance was assessed in naturally aerated Ringer’s physiological solution at 37°C by corrosion potential and electrochemical impedance spectroscopy (EIS) measurements as a function of exposure time, and potentiodynamic polarization curves. Corrosion potential values indicated that both Ni–Ti and Ti–Nb–Sn alloys undergo spontaneous passivation due to spontaneously formed oxide film passivating the metallic surface, in the aggressive environment. It also indicated that the tendency for the formation of a spontaneous oxide is greater for the Ti–18Nb–5Sn alloy. Significantly low anodic current density values were obtained from the polarization curves, indicating a typical passive behaviour for all investigated alloys, but Nitinol exhibited breakdown of passivity at potentials above approximately 450 mV(SCE), suggesting lower corrosion protection characteristics of its oxide film compared to the Ti–Nb–Sn alloys. EIS studies showed high impedance values for all samples, increasing with exposure time, indicating an improvement in corrosion resistance of the spontaneous oxide film. The obtained EIS spectra were analyzed using an equivalent electrical circuit representing a duplex structure oxide film, composed by an outer and porous layer (low resistance), and an inner barrier layer (high resistance) mainly responsible for the alloys corrosion resistance. The resistance of passive film present on the metals’ surface increases with exposure time displaying the highest values to Ti–18Nb–4Sn alloy. All these electrochemical results suggest that Ti–Nb–Sn alloys are promising materials for biomedical applications.     

A method for the determination of the elastic equilibrium of isotropic bodies with curvilinear inclusions. Part 2. Plane problem

Within the framework of the approach proposed in the first part of the work, the two-dimensional boundary-value problem for an isotropic body with noncanonical elastic inclusion is reduced to a finite system of linear algebraic equations. It is shown that the solution of this problem for elastic inclusions with small radius of curvature at the tip and/or cusps describes the intensity and concentration of stresses in the composition. For some special examples, we reveal the influence of elastic properties of the components of the composition and configuration of the inclusions on its local stress-strain state. It is also established that, unlike the method of perturbation of the shape of the boundary, this method is applicable to the determination of the concentration and intensity of stresses in the vicinity of the tips of elastic inclusions with small radii of curvature, including the inclusions whose elastic properties are close to the elastic properties of the matrix. Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 35, No. 1, pp. 16–26, January–February, 1999.