A comparative study of guided wave propagation in timber poles with isotropic and transversely isotropic material models

Guided wave (GW) has been used for many years in non-destructive testing (NDT). There are various ways to generate the guided wave, including impact or impulse either manually or using devices. Although the method of impact or impulse is considered to be simple and practical in guided wave generation, it produces waves with broadband frequencies, which often make analysis much more difficult. The frequency bandwidth produced by manual impacts is usually at the low end, and is therefore justified when dealing with one dimensional wave propagation assumption in low strain integrity testing of cylindrical structures. Under such assumption if the velocity is known accurately, NDTs can produce reasonably good results for the condition assessment of the structure. However, for guided wave propagation in timber pole-like structures, it is rather complicated as timber is an orthotropic material and wave propagation in an orthotropic medium exhibits different characteristics from that in isotropic medium. It is possible to obtain solutions for guided wave propagation in orthotropic media for cylindrical structures, even though the orthotropic material greatly complicates GW propagation. In this paper, timber has been considered as a transversely isotropic (i.e. simplified orthotropic) material and a comparative study of GW propagation in a timber pole is conducted considering isotropic and transversely isotropic modelling. Phase velocity, group velocity and attenuation are the main parameters for this comparative study. Moreover, tractionfree situation and embedded geotechnical condition are also taken into consideration to evaluate the effect of boundary. Displacement profile, wave propagation pattern and power flow at particular frequency are utilized to determine different displacement components of longitudinal and flexural waves along and across the timber pole. Effect of temperature and moisture content (in terms of modulus of elasticity) in timber pole is also compared to show the variation in phase velocity.

Effect of elastic modulus and poisson's ratio on guided wave dispersion using transversely isotropic material modelling

Timber poles are commonly used for telecommunication and power distribution networks, wharves or jetties, piling or as a substructure of short span bridges. Most of the available techniques currently used for non-destructive testing (NDT) of timber structures are based on one-dimensional wave theory. If it is essential to detect small sized damage, it becomes necessary to consider guided wave (GW) propagation as the behaviour of different propagating modes cannot be represented by one-dimensional approximations. However, due to the orthotropic material properties of timber, the modelling of guided waves can be complex. No analytical solution can be found for plotting dispersion curves for orthotropic thick cylindrical waveguides even though very few literatures can be found on the theory of GW for anisotropic cylindrical waveguide. In addition, purely numerical approaches are available for solving these curves. In this paper, dispersion curves for orthotropic cylinders are computed using the scaled boundary finite element method (SBFEM) and compared with an isotropic material model to indicate the importance of considering timber as an anisotropic material. Moreover, some simplification is made on orthotropic behaviour of timber to make it transversely isotropic due to the fact that, analytical approaches for transversely isotropic cylinder are widely available in the literature. Also, the applicability of considering timber as a transversely isotropic material is discussed. As an orthotropic material, most material testing results of timber found in the literature include 9 elastic constants (three elastic moduli and six Poisson's ratios), hence it is essential to select the appropriate material properties for transversely isotropic material which includes only 5 elastic constants. Therefore, comparison between orthotropic and transversely isotropic material model is also presented in this article to reveal the effect of elastic moduli and Poisson's ratios on dispersion curves. Based on this study, some suggestions are proposed on selecting the parameters from an orthotropic model to transversely isotropic condition.

Reducing the effect of wave dispersion in a timber pole based on transversely isotropic material modelling

Round timbers are used for telecommunication and power distribution networks, jetties, piles, short span bridges etc. To assess the condition of these cylindrical shape timber structures, bulk and elementary wave theory are usually used. Even though guided wave can represents the actual wave behaviour, a great deal complexity exists to model stress wave propagation within an orthotropic media, such as timber. In this paper, timber is modelled as transversely isotropic material without compromising the accuracy to a great extent. Dispersion curves and mode shapes are used to propose an experimental set up in terms of the input frequency and bandwidth of the signal, the orientation of the sensor and the distance between the sensors in order to reduce the effect of the dispersion in the output signal. Some example based on the simulated signal is also discussed to evaluate the proposed experimental set up.

Secondary bonding in para-substituted diphenyltellurium dichlorides (p-XC6H4)2TeCl2 (X = H, Me, MeO) probed by 125Te MAS NMR spectroscopy. Crystal and molecular structure of (p-MeC6H4)2TeCl2

The solid-state structures of the previously known para-substituted diphenyltellurium dichlorides, (p-XC₆H₄)₂TeCl₂ (X=H (1), Me (2), MeO (3)) were investigated by ¹²⁵Te MAS NMR spectroscopy and in case of 2 by single crystal X-ray diffraction. The ¹²⁵Te-NMR shielding anisotropy (SA) was studied by tensor analyses based on relative intensities of the observed spinning sidebands. Solid-state NMR parameters, namely the isotropic chemical shift (δ_iso), anisotropy (ζ) and asymmetry (η), were discussed in relation to the molecular structures established by X-ray crystallography. The asymmetry (η) was found to be particularly sensitive to structural differences stemming mostly from the diverse secondary Te...Cl interactions, but no correlation with geometric parameters could be established.

Direct current electric potential in an anisotropic half-space with vertical contact containing a conductive 3D body

Detailed studies of anomalous conductors in otherwise homogeneous media have been modelled. Vertical contacts form common geometries in galvanic studies when describing geological formations with different electrical conductivities on either side. However, previous studies of vertical discontinuities have been mainly concerned with isotropic environments. In this paper, we deal with the effect on the electric potentials, such as mise-`a-la-masse anomalies, due to a conductor near a vertical contact between two anisotropic regions. We also demonstrate the interactive effects when the conductive body is placed across the vertical contact. This problem is normally very difficult to solve by the traditional numerical methods. The integral equations for the electric potential in anisotropic half-spaces are established. Green’s function is obtained using the reflection and transmission image method in which five images are needed to fit the boundary conditions on the vertical interface and the air-earth surface. The effects of the anisotropy of the environments and the conductive body on the electric potential are illustrated with the aid of several numerical examples.

Some aspects of numerical simulation for lamb wave propogation in composite laminates

Some aspects of numerical simulation of Lamb wave propagation in composite laminates using the finite element models with explicit dynamic analysis are addressed in this study. To correctly and efficiently describe the guided-wave excited/received by piezoelectric actuators/sensors, effective models of surface-bounded flat PZT disks based on effective force, moment and displacement are developed. Different finite element models for Lamb wave excitation, collection and propagation in isotropic plate and quasi-isotropic laminated composite are evaluated using continuum elements (3-D solid element) and structural elements (3-D shell element), to elaborate the validity and versatility of the proposed actuator/sensor models.

Application of radial return mapping algorithm for finite strain elastoplasticity in a hybrid finite element and particle-in-cell model

The radial return mapping algorithm within the computational context of a hybrid Finite Element and Particle-In-Cell (FE/PIC) method is constructed to allow a fluid flow FE/PIC code to be applied solid mechanic problems with large displacements and large deformations. The FE/PIC method retains the robustness of an Eulerian mesh and enables tracking of material deformation by a set of Lagrangian particles or material points. In the FE/PIC approach the particle velocities are interpolated from nodal velocities and then the particle position is updated using a suitable integration scheme, such as the 4th order Runge-Kutta scheme[1]. The strain increments are obtained from gradients of the nodal velocities at the material point positions, which are then used to evaluate the stress increment and update history variables. To obtain the stress increment from the strain increment, the nonlinear constitutive equations are solved in an incremental iterative integration scheme based on a radial return mapping algorithm[2]. A plane stress extension of a rectangular shape J2 elastoplastic material with isotropic, kinematic and combined hardening is performed as an example and for validation of the enhanced FE/PIC method. It is shown that the method is suitable for analysis of problems in crystal plasticity and metal forming. The method is specifically suitable for simulation of neighbouring microstructural phases with different constitutive equations in a multiscale material modelling framework.

Texture and mechanical anisotropy in three extruded magnesium alloys

One ZM61 alloy (6·2%Zn, 1·2%Mn) and two magnesium alloys containing nominally 3% of neodymium and yttrium respectively have been prepared in the form of hot extruded flat strips. Their textures and microstructures have been quantified and series of mechanical tests were carried out to determine plane stress yield loci in both the solution treated and aged conditions. The ZM61 alloy had a sharp texture and marked anisotropy of strength that could be rationalised in terms of deformation by basal <a> slip and {1012}<1011> twinning. This material was much weaker in compression than in tension. Precipitation hardening on aging caused a greater impedance to twinning than to slip with the result that the anisotropy was somewhat reduced. The Mg–3Nd alloy had a very weak and different texture but nevertheless demonstrated a pronounced anisotropy of strength. Aging increased the yield stress by about 80% and also inhibited twinning to some extent although the degree of anisotropy remained almost unaffected. The Mg–3Y alloy which showed a texture of intermediate strength was different in type from either of the others. Its strength behaviour was close to isotropic; in particular, no difference existed between tensile and compressive loading, and aging produced only a marginal increase in strength. Twins were relatively infrequent in the deformed Mg–3Y alloy but its mechanical behaviour could not be rationalised according to simple models.

Inspection of drop-weight impact damage in woven CFRP laminates fabricated by different processes

The influence of manufacturing process on the drop-weight impact damage in woven carbon/epoxy laminates was inspected by visual observation, dyepenetrant X-ray technique, and optical microscopy observation. The MTM56/ CF0300 woven quasi-isotropic laminates were fabricated by two processes: the autoclave and the Quickstep processes. Quickstep^TM is a novel composite manufacturing process, which was designed for the out-of-autoclave production of high-quality composite parts at lower cost. It utilizes higher heat conduction of fluid other than gas to transfer heat to components, which results in much shorter cure cycles. The laminates cured by this fast heating process showed different impact failure modes from those cured by the conventional autoclave process. The residual indentation in the top side of the Quickstep-cured laminates had a bigger diameter, but a smaller depth at the same impact energy level. Dye-penetrant X-ray revealed more intense and connected impact damage regions in the autoclave-cured laminates. Optical micrography as a supplementary method showed less severe matrix damage in the quickstep-cured laminates indicating a more ductile property of the resin matrix cured at a faster heating rate.

Deep drawing behaviour of ultrafine grained copper : modelling and experiment

Ultrafine grained materials produced by severe plastic deformation methods possess attractive mechanical properties such as high strength compared with traditional coarse grained counterparts and reasonable ductility. Between existing severe plastic deformation methods the Equal Channel Angular Pressing is the most promising for future industrial applications and can produce a variety of ultrafine grained microstructures in materials depending on route, temperature and number of passes during processing. Driven by a rising trend of miniaturisation of parts these materials are promising candidates for microforming processes. Considering that bi-axial deformation of sheet (foil) is the major operation in microforming, the investigation of the influence of the number of ECAP passes on the bi-axial ductility in micro deep drawing test has been examined by experiments and FE simulation in this study. The experiments have showed that high force was required for drawing of the samples processed by ECAP compare to coarse grained materials. The limit drawing ratio of ultrafine grained samples was in the range of 1.9–2.0 with ECAP pass number changing from 1 to 16, while a higher value of 2.2 was obtained for coarse grained copper. However, the notable decrease in tensile ductility with increase in strength was not as pronounced for bi-axial ductility. The FE simulation using standard isotropic hardening model and von Mises yielding criterion confirmed these findings.

Rotational and translational mobility of a highly plastic salt : Dimethylpyrrolidinium thiocyanate

Thermal analysis, impedance spectroscopy, NMR and Raman spectroscopy have been used to investigate the plastic crystal dimethylpyrrolidinium thiocyanate in order to gain further insight into the properties of organic ionic plastic crystals. This compound has a solid–solid phase transition at 82 °C, and melts at 122 °C. A step increase in conductivity of about one order of magnitude is observed at the phase transition, followed by a decrease in activation energy for conduction. A large entropy gain occurs at the II → I transition, and ¹H NMR linewidth measurements together with second moment calculations showed that the dimethylpyrrolidinium cation goes from a static state, to full isotropic tumbling. Raman measurements confirm that the cation as well as the anion exhibit increased rotational mobility when entering phase I.

Plastic crystal behaviour in tetraethylammonium dicyanamide

The plastic crystal tetraethylammonium dicyanamide ([N_2,2,2,2][dca]) has been investigated with an emphasis on structure and dynamics in the plastic phase. It was found that almost all of the volume expansion occurs at the II → I transition, with no volume expansion at the melt transition (as normally observed for crystals). The conductivity of this material shows a rapid increase at temperatures below the II → I transition, reaching values ~ 10^{− 3} S/cm in Phase I, and 0.1 S/cm in the melt. The NMR measurements show that there is a sudden onset of rotational motions of the cations at the plastic transition; below this temperature the cations appear static. The rotational motion of the cation in Phase I has been discussed in terms of isotropic tumbling.