Nondestructive Evaluation of <Emphasis Type="Italic">Corymbia citriodora</Emphasis> Logs by Means of the Free Transverse Vibration Test

The bending modulus of elasticity has been used as a wood quality predictor due to the good correlation between bending stiffness and strength. In recent years, there has been an increasing use of nondestructive testing techniques based on dynamic tests to assess wood quality. The objective of this study is to evaluate the results obtained with the application of transverse vibration test to measure the bending modulus of elasticity of Corymbia citriodora logs. The approach used estimated the log cylinders with the diameter equal to the diameter measured at half-length. A sample of 38 C. citriodora logs was tested in free transverse vibration and static bending tests, their diameter measured at half-length ranged from 13.6 to 20 cm and the length ranged between 4 and 4.4 m. A strong correlation (\(\hbox {R}^{2} = 0.92\)) was found between static and dynamic bending modulus of elasticity. The transverse vibration test was faster than the static bending test. The results indicate that the free transverse vibration test provides accurate measurements of bending modulus of elasticity of C. citriodora logs.     

Non-destructive evaluation of the bending behaviour of in-service pine timber structural elements

An essential step while assessing the performance of existing timber structures is the allocation of strength and stiffness values to the timber members. In spite of the importance of this step and the research effort already made, the evaluation of timber structural members in-service is still performed in most cases based only on visual strength grading rules. This paper addresses the possibility of applying a procedure based on visual assessment and ultrasonic testing for predicting the bending strength and stiffness of timber elements in-service. This possibility can support a more accurate structural performance analysis of timber structures. The basis of the procedure is explained and the results of its application to maritime pine timber (Pinus pinaster Ait.) beams are shown. The setting-up of the procedure includes data from former studies and new experimental data. A validation is carried out on two extra samples (not used in the setting-up process) by comparing the global modulus of elasticity and the bending strength of maritime pine timber obtained following EN 408 with the predicted value given by the proposed procedure. The application of this procedure provided a good agreement between the predicted and the experimental values of global modulus of elasticity. Regarding the bending strength, the results indicate that more precise parameters, or choice of parameters, need to be defined in order to address the real effect of knots.     

Effects of grading procedures on the scatter of characteristic values of European grown sawn timber

The natural scatter in mechanical properties of sawn timber must be reduced by grading the material either visually or mechanically. Depending on the grading procedure, the scatter of these properties varies. This study deals with their variation as influenced by the grading procedure. The effect of the grading principle is analyzed based on 4,893 sawn timber specimens from several European natural forests with widths up to 167 mm and depths up to 284 mm and using the method given in EN 14081-2:2010, CEN, Brussels (2010). Grading models for visual grading and machine grading are derived considering different source countries, strength classes and strength class combinations. Material safety factors for the graded material are then estimated in accordance with ISO 2394 (1998) to evaluate the grading outcomes. Analyzing and comparing the lower 5th-percentile to the requirements of EN 384: 2009, CEN, Brussels (2009), it is found that the actual strength for class C24 can be up to 20 % lower than required by the standard. This is true, regardless of whether the timber is graded visually or by an advanced grading machine using dynamic modulus of elasticity and knots. Low strength values can be expected especially in cases where a batch of timber is graded into a single strength class and reject only. High coefficients of variation of the graded material lead to the conclusion that high material safety factors are needed. On the contrary, if the material is graded by a machine and into more than two strength classes in one pass, it can be shown that the required material safety factors can be lower.     

Structural characteristics analysis of the hind wings in a bamboo weevil (Cyrtotrachelus buqueti)

The finite element method is a powerful tool for evaluating the experimental results. It can help to study the flight mechanism of insects and the structural characteristics of flying wings. Therefore, the research object based on the hind wings of Cyrtotrachelus buqueti (C. buqueti) was completed here. A finite element model with a length of 45 mm in the spanwise direction and a 16 mm width in the chordwise direction were established. We used a three‐dimensional (3D) scanner to scan a real hind wing to obtain point cloud images. The physical model of the hind wing was carried out by using both the software Imageware and Unigraphics NX. To quantify the quality of the finite element model of the hind wing, the material properties of the wing membranes and veins were conducted by the tensile testing machine. The structural static properties of the hind wing, including static characteristics analysis and natural vibration modal analysis, were analysed by ANSYS; the stress and deflection under uniformly distributed load, bending moment, and torque were, respectively, shown. It was found that the model only had a small deformation, which shows that the hind wings of C. buqueti have excellent structural properties.Inspec keywords: mechanical engineering computing, finite element analysis, bending, solid modelling, vibrations, modal analysis, aerospace components, tensile testing, test equipmentOther keywords: hind wing, cyrtotrachelus buqueti, finite element model, static characteristics analysis, natural vibration modal analysis, bamboo weevil, flight mechanism, structural characteristics, C. buqueti, bending moment, torque, software Imageware, Unigraphics NX, three‐dimensional scanner, ANSYS, size 45.0 mm, size 16.0 mm     

Simulation of transport properties in Nb3Sn strand under bending

Superconducting performance of a large-scale Nb₃Sn cable-in-conduit conductor (CICC) is degraded by periodic bending of strands subjected to a distributed transverse electromagnetic force during operation. The current transport in a single strand depends mainly on the bending strain and transverse resistivity. In particular, in the case of high-level strain and/or crack occurring among the filaments in the strain-sensitive Nb₃Sn strand, these two parameters are required for better understanding of the critical current I_c degradation of a single strand. We use finite element method to simulate transport properties of a single Nb₃Sn strand under bending. The simulation allows treating a wider range of transverse resistivity of strand, compared with our previous analytical method (Cryogenic, 58, 2013). Also, the present simulation incorporates the change of the area of strand cross section due to filament fracture into the boundary of the current transport, rather than simply imposes the condition of vanishing current on the filament fracture region as in the previous analytical method. We show the current/field profiles in the strand for various bending loads and transverse resistivities, as well as the I_c degradation of several types of strands under bending.     

Reliability of timber structures under long term loads

The strength of timber is significantly reduced under sustained load. Existing experimental data give a reasonable estimate of the strength reduction as a function of time under constant load. In practice, however, the load level is variable in time. For this situation the strength reduction must be estimated on the basis of so called damage theories. In engineering design, effects of load duration are accounted for by a strength reduction factor, k_mod, which depends on the type of load acting on the structure. The loads are classified in terms of their duration time. In a load combination the value of k_mod is based on the load with shortest duration. For several reasons the scientific basis to determine k_mod is rather uncertain. In this paper a probabilistic analysis is made with the purpose to calibrate k_mod for timber structures under combination of permanent load and snow load. The analyses are based on Swedish data for snow. A theoretical model proposed in [1] describes the damage accumulation. The analyses show that k_mod is of the order 0.8 for geographic locations with heavy snow loads as well as for locations with moderate snow loads. The factor k_mod was also found independent of the two practically relevant load combinations studied. The results can be used as recommendations for appropriate choice of k_mod in engineering design.

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Résumé La résistance du bois de construction diminue significativement sous la pression de charge. Les données expérimentales qui existent, donnent une estimation raisonnable de la réduction de la résistance du bois comme étant une fonction du temps sous une charge constante. Dans la réalité, le niveau de charge est néanmoins variable dans le temps. Pour cette raison la réduction de la résistance doit être estimée sur la base de ce que l’on appelle la théorie des dommages. En design de construction, les effets de la durée d’une charge sont représentées par un facteur de la réduction de la résistance, k_mod, qui dépend du type de la charge pesant sur la structure. Les charges sont classifiées en terme de leur durée de temps. Lorsque les charges sont variables, la valeur k_mod est basée sur la charge ayant la plus courte durée. Pour plusieurs raisons la base scientifique qui détermine k_mod est assez incertaine. Dans cet article, nous réalisons une analyse de probabilité ayant pour but de calibrer k_mod en ce qui concerne le bois de construction subissant des combinaisons de charges permanentes et de charges neigeuses. Les analyses sont basées sur des données suédoises sur la neige. Un modèle théorique proposé [1] décrit. l’accummulation des dommages. Les analyses montrent que k_mod est de l’ordre de 0,8 aussi bien dans les zones géographiques ayant de lourdes charges de neige que dans les zones ayant des charges modérées. Le facteur k_mod se révèle donc être indépendant des deux principales combinaisons de charges étudiées. Ces résultats peuvent être utilisés comme recommandation pour le choix approprié de k_mod en design de construction.

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Editorial Note Prof. H. J. Lorsen and Prof, S. Thelandersson are RILEM Senior Members This anide has been published in RILEM Proceedings International RILEM Symposium on Timber Engineering.     

Nonlinear thermal bending response of FGM plates due to heat conduction

Nonlinear thermal bending analysis is presented for a simply supported, shear deformable functionally graded plate without or with piezoelectric actuators subjected to the combined action of thermal and electrical loads. Heat conduction and temperature-dependent material properties are both taken into account. The temperature field considered is assumed to be a uniform distribution over the plate surface and varied in the thickness direction and the electric field considered only has non-zero-valued component E_Z. The material properties of functionally graded materials (FGMs) are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents, and the material properties of both FGM and piezoelectric layers are assumed to be temperature-dependent. The governing equations of an FGM plate are based on a higher order shear deformation plate theory that includes thermo-piezoelectric effects. A two step perturbation technique is employed to determine the thermal load–deflection and thermal load–bending moment curves. The numerical illustrations concern nonlinear bending response of FGM plates without or with surface bonded piezoelectric actuators due to heat conduction and under different sets of electric loading conditions. The results reveal that for the case of heat conduction the nonlinear thermal bending responses are quite different to those of FGM plates subjected to transverse mechanical loads, and the temperature-dependency of FGMs could not be neglected in the thermal bending analysis.     

Nonlocal plate model for nonlinear analysis of thin films on elastic foundations in thermal environments

Postbuckling, nonlinear bending and nonlinear vibration analyses are presented for a simply supported stiff thin film resting on a two-parameter elastic foundation in thermal environments. The stiff thin film is modeled as a nonlocal orthotropic plate which contains small scale effects. The elastomeric substrate with finite depth is modeled as a two-parameter elastic foundation. The thermal effects are included and the material properties of the substrate are assumed to be temperature-dependent. The governing equation that includes plate-foundation interaction is solved by a two-step perturbation technique. The numerical results reveal that the small scale parameter e₀a reduces the postbuckling equilibrium paths, the static large deflections and natural frequencies, but increases the nonlinear to linear frequency ratios of the thin film slightly. The results also reveal that the effect of the small scale parameter is significant for compressive buckling, but less pronounced for static bending and marginal for free vibration of the thin film resting on an elastic foundation.     

Nonlocal beam model for nonlinear analysis of carbon nanotubes on elastomeric substrates

Postbuckling, nonlinear bending and nonlinear vibration analyses are presented for single-wall carbon nanotubes (SWCNTs) resting on a two-parameter elastic foundation in thermal environments. The SWCNT is modeled as a nonlocal nanobeam which contains small scale effects. The elastomeric substrate with finite depth is modeled as a two-parameter elastic foundation. The thermal effects are included and the material properties of both SWCNTs and the substrate are assumed to be temperature-dependent. The governing equation that includes beam–foundation interaction is solved by a two-step perturbation technique. The numerical results reveal that the small scale parameter e₀a reduces the postbuckling equilibrium paths, the static large deflections and natural frequencies of SWCNTs resting on an elastic foundation. The results also reveal that the effect of the small scale parameter is significant for compressive buckling, but less pronounced for static bending and marginal for free vibration of SWCNTs resting on an elastic foundation.     

Steady state thermoelastic contact problem in a functionally graded material

This paper is concerned with the stationary plane contact of a functionally graded heat conducting punch and a rigid insulated half-space. The frictional heat generation inside the contact region due to sliding of the punch over the half-space surface and the heat radiation outside the contact region are taken into account. Elastic coefficient μ, thermal expansion coefficient α_t and coefficient of thermal conductivity k are assumed to vary along the normal to the plane of contact. With the help of Fourier integral transform the problem is reduced to a system of two singular integral equations. The equations are solved numerically. The effects of nonhomogeneity parameters in FGMs and thermal effect are discussed and shown graphically.     

Modeling of functionally graded sandwich shells accounting for variation in transverse displacement

In this study, a simple C₀ isoparametric finite element formulation based on higher-order shear deformation theory is presented for static analysis of functionally graded material sandwich shells (FGMSS). To characterize the membrane-flexure behavior observed in a functionally graded shell, a displacement field involving higher-order terms in in-plane and transverse fields is considered. The proposed kinematics field incorporates for transverse normal deformation, transverse shear deformation, and nonlinear variation of the in-plane displacement field through the thickness to predict the overall response of the shell in an accurate sense. To develop the efficient C₀ formulation, the derivatives of transverse displacement are treated as independent field variables (nodal unknowns). Voigt's rule of mixture is employed to ascertain the mechanical properties of each layer's constituents along the thickness direction. A wide range of numerical problems are solved assuming various parameters: side-thickness ratio, curvature-side ratio, and gradation parameter, and their interactions with regard to static analysis of FGMSS are discussed in brief. Deflection and stresses incorporating different thickness schemes of sandwich shells are presented in the form of figures. To validate the results, a functionally graded shell without sandwich arrangement is considered. Since no results are available on static analysis of FGMSS, the present 2D model based on the finite element method might be helpful in assessing the applicability of other analytical and numerical models in this area in the future.     

New weld toe magnification factors for semi-elliptical cracks in double-sided T-butt joints and cruciform X-joints

British Standard BS7910:2005 has a single set of equations for estimating the weld toe magnification factor (M_k) of different types of welded joints containing a surface crack. The equations are based on the finite element (FE) results of single sided T-butt joint. In this study, extensive FE analyses are carried out to determine the M_k of double-sided T-butt joint and cruciform X-joint. Both the joints are subjected to axial and bending loading, and M_k at crack ends and deepest points of the surface crack are determined. It is found that M_k results for cruciform X-joint differ with those of double-sided T-butt joint with percentage difference in values being as high as 136% and 76% for axial and bending loading cases, respectively. Finally, a new set of M_k equations for cracked double-sided T-butt joint and X-joint are proposed based on multiple regression analyses.     

Manifestation of the Transition Semiconductor-Semimetal and Intrinsic Interface State in Band Structure and Magneto-Transport Properties in Nanostructure Superlattice

We report here G carrier??s magneto-transport properties and the band structure results for II-VI semiconductors. HgTe is a zero gap semiconductor and when it is sandwiched between CdTe layers yield a small gap HgTe/CdTe superlattice which is the key to development of an infrared detector. Our sample, grown by MBE, had a period d (100 layers) of 18?nm (HgTe)/4.4?nm (CdTe). Calculations of the spectra of energy E(k _z ) and E(k _p ), respectively, in the direction of growth and in the plane of the superlattice were performed in the envelope-function formalism. The angular dependence of the transverse magnetoresistance follows the two-dimensional (2D) behavior with Shubnikov?Cde Haas oscillations. At low temperature, the sample exhibits p-type conductivity with a hole mobility of 900?cm²/V?s. A reversal of the sign of the weak-field Hall coefficient occurs at 25?K with an electron mobility of 3×10⁴?cm²/V?s. In the intrinsic regime, the measured E _g ??38?meV agrees with the calculated E _g (??, 300?K) =34?meV, which coincide with the Fermi level energy. The formalism used here predicts that this narrow gap sample is semi-metallic, quasi-two-dimensional and far-infrared detector.     

Influence of the film thickness on structural and optical properties of CdTe thin films electrodeposited on stainless steel substrates

CdTe thin films of different thicknesses were deposited by electrodeposition on stainless steel substrates (SS). The dependence of structural and optical properties on film thickness was evaluated for thicknesses in the range 0.17–1.5 μm. When the film is very thin the crystallites lack preferred orientation, however, thicker films showed preference for (111) plane. The results show that structural parameters such as crystallite size, lattice constant, dislocation density and strain show a noticeable dependence on film thickness, however, the variation is significant only when the film thickness is below 0.8 μm. The films were successfully transferred on to glass substrates for optical studies. Optical parameter such as absorption coefficient (α), band gap (E_g), refractive index (n), extinction coefficient (k_e), real (?_r) and imaginary (?_i) parts of the dielectric constant were studied. The results indicate that all the optical parameters strongly depend on film thickness.     

Immobilization of lanthanum,cerium, and selenium into ceramic matrix of sodium zirconium phosphate

The crystallographic nature of NaCe_0.2Zr_1.8P₃O₁₂, NaSe_0.2Zr_1.8P₃O₁₂, and NaLa_0.13Ce_0.14Se_0.15·Zr_1.58P₃O₁₂ phases has been investigated with the aim of developing methods for radionuclide immobilization into sodium zirconium phosphate (NZP) phase. The phases have the NZP structure, space group \(R\bar 3c\) , Z = 6. Powder diffraction data have been subjected to Rietveld refinement, and satisfactory structural convergence of R-factors was achieved. The PO₄ stretching and bending vibration bands in the IR region have been assigned.     

Transverse Acoustic Impedance Measurements for Surface States of Superfluid 3He A1 and A2 Phases

We measured the complex transverse acoustic impedance in both superfluid ³He A₁ and A₂ phases. This impedance is sensitive to surface states. In our preliminary results, the temperature dependence of the impedance in the A₁ phase is similar to that in A phase, and the imaginary part shows an anomaly in the A₂ phase. These anomalies occurred at the temperature defined as T _k , which is lower as the frequency gets higher. The similar frequency dependence of T _k in each phase suggests that the anomaly is attributed to the same origin. The frequency dependence of the T _k /T _c indicates that the shape of the surface density of each spin pair state did not greatly change in the present experimental temperature range.     

Representative indentation elastic modulus evaluated by unloading of nanoindentation made with a point sharp indenter

The conventional method to extract elastic modulus from the nanoindentation on isotropic linearly elastic solids is based on Sneddon’s solution (1965). However, it is known that the solution is valid only for incompressive elastic solids with the Poisson’s ratio ν of 0.5. This paper first proposes the modification of the solution in a wide range of ν from 0 to 0.5 through the numerical analysis on the unloading behavior of a simulated conical nanoindentation with a finite element method. As a result of the modification, the coefficient of linearity between the indentation elastic parameter k_e and Young’s modulus E is empirically given as a function of ν and the inclined face angle of the indenter, β, where k_e is defined as k_e ≡ P/h² with the indentation load P and penetration depth of the indenter h. According to the linear relationship between k_e and E, it is found that elastic rebound during unloading of a nanoindentation is uniquely characterized by a representative indentation elastic modulus E¹ defined in terms of E, ν and β, and that the value of E¹ can be evaluated from the P–h relationship with k_e and β. For an isotropic elastoplastic solid, the indentation unloading parameter k₂ defined as k₂ ≡ P/(h–h_r)² for a residual depth h_r is different from k_e even though a linearly elastic solid with k_e and elastoplastic solid with k₂ have a common E¹. In order to evaluate E¹ of an elastoplastic solid, the corresponding k_e is estimated from k₂ with an empirical equation as a function of the relative residual depth ξ defined as ξ ≡ h_r/h_max for the maximum penetration depth h_max. A nanoindentation experiment confirmed the validity of the numerical analysis for evaluating the elastic modulus.     

Prediction for Ic degradation of superconducting strand under bending

Nb₃Sn strand critical current (I_c) degradation is a basic issue strongly related to ITER operating performance. The developed analytical scheme predicting I_c degradation takes into account transverse resistivity and irreversibility of strand composite. Once compared to the measurements on three types of strands in periodic bending tests, this analytical prediction almost eliminates the difference between the measurements and widely existing previous models. As transverse resistivity gets closer to the experimental value, the prediction approaches the measurement remarkably.Additionally the classical outstanding experiment for strand in a steel tube simulating the practical operating situation is interpreted with this improved scheme. It is concluded that the discrepancy between Ekin’s model result and the measurement is primarily due to the intrinsic transverse resistivity and irreversibility limit.     

Dielectric behaviour and improved anisotropy in piezoelectric properties of modified lead titanate ceramics

Polycrystalline samples of the nominal composition Pb_0.76−xSm_xCa_0.24Ti_0.98Mn_0.02O₃ were prepared using a solid state reaction technique. Single-phase formation was checked through X-ray diffraction. Dielectric properties were studied as a function of frequency and temperature. The transition temperature determined from dielectric constant vs. temperature plots was found to decrease with increasing Samarium substitution. Poling field was optimized to achieve maximum piezoelectric properties. Piezoelectric coefficients e.g. d₃₃, d₃₁, g₃₃, g₃₁, g_h, d_h, k_t and k_p were measured. The experimental results successfully showed that samarium substitution is helpful to obtain a much higher value of thickness electromechanical coupling coefficient, k_t (∼ 57%) while maintaining a smaller planar electromechanical coupling coefficient, k_p in PCT ceramics.     

Nonlinear bending of FGM plates subjected to combined loading and resting on elastic foundations

A nonlinear bending analysis is presented for a simply supported, functionally graded plate resting on an elastic foundation of Pasternak-type. The plate is exposed to elevated temperature and is subjected to a transverse uniform or sinusoidal load combined with initial compressive edge loads. Material properties are assumed to be temperature-dependent, and graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The formulations are based on a higher-order shear deformation plate theory and general von Kármán-type equation that includes the plate-foundation interaction and thermal effects. A two step perturbation technique is employed to determine the load–deflection and load–bending moment curves. The numerical illustrations concern nonlinear bending response of functional graded plates with two constituent materials resting on Pasternak elastic foundations from which results for Winkler elastic foundations are obtained as a limiting case. The results reveal that the characteristics of nonlinear bending are significantly influenced by foundation stiffness, temperature rise, transverse shear deformation, the character of in-plane boundary conditions and the amount of initial compressive load. In contrast, the effect of volume fraction index N becomes weaker when the plate is supported by an elastic foundation.