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Pulse and flash thermography are experimental techniques which are widely used in the field of non-destructive testing for materials characterization and defect detection. We recently showed that it is possible to determine quantitatively the thickness of semitransparent polymeric solids by fitting of results of an analytical model to experimental flash thermography data, for both transmission and reflection configuration. However, depending on the chosen experimental configuration, different effective optical absorption coefficients had to be used in the model to properly fit the respective experimental data, although the material was always the same. Here, we show that this effect can be explained by the wavelength dependency of the absorption coefficient of the sample material if a polychromatic light source, such as a flash lamp, is used. We present an extension of the analytical model to describe the decay of the heating irradiance by two instead of only one effective absorption coefficient, greatly extending its applicability. We show that using this extended model, the experimental results from both measurement configurations and for different sample thicknesses can be fitted by a single set of parameters. Additionally, the deviations between experimental and modeled surface temperatures are reduced compared to a single optimized effective absorption coefficient.
Multilayer graphene/chlorine-isobutene-isoprene rubber nanocomposites: the effect of dispersion
(2016)
Multilayer graphene (MLG) is composed of approximately 10 sheets of graphene. It is a promising nanofiller just starting to become commercially available. The Dispersion of the nanofiller is essential to exploit the properties of the nanocomposites and is dependent on the preparation method. In this study, direct incorporation of 3 parts per hundred of rubber (phr) MLG into chlorine-isobutene- isoprene rubber (CIIR) on a two-roll mill did not result in substantial enhancement of the material properties. In contrast, by pre-mixing the MLG (3 phr) with CIIR using an ultrasonically assisted solution mixing procedure followed by two-roll milling, the properties (rheological, curing, and mechanical) were improved substantially compared with the MLG/CIIR nanocomposites mixed only on the mill. The Young’s moduli of the nanocomposites mixed in solution increased by 38%. The CIIR/MLG nanocomposites produced via solution showed superior durability against weathering exposure.
In this paper we propose an algorithm to compute specific parts of the dispersion curves for elastic waveguides. The formulation is based on an axisymmetric representation of the Scaled Boundary Finite Element Method, where the wavenumbers of propagating modes are obtained as solutions of a Hamiltonian eigenvalue problem. The novel solution procedure involves tracing selected modes over a given frequency range and computing the corresponding solutions by means of inverse iteration. The resulting algorithm is applied in the context of material characterization, where the efficiency of the computation is crucial.
This paper addresses the computation of dispersion curves and mode shapes of elastic guided waves in axisymmetric waveguides. The approach is based on a Scaled Boundary Finite Element formulation, that has previously been presented for plate structures and general three-dimensional waveguides with complex cross-section. The formulation leads to a Hamiltonian eigenvalue problem for the computation of wavenumbers and displacement amplitudes, that can be solved very efficiently. In the axisymmetric representation, only the radial direction in a cylindrical coordinate system has to be discretized, while the circumferential direction as well as the direction of propagation are described analytically. It is demonstrated, how the computational costs can drastically be reduced by employing spectral elements of extremely high order. Additionally, an alternative formulation is presented, that leads to real coefficient matrices. It is discussed, how these two approaches affect the computational efficiency, depending on the elasticity matrix. In the case of solid cylinders, the singularity of the governing equations that occurs in the center of the cross-section is avoided by changing the quadrature scheme. Numerical examples show the applicability of the approach to homogeneous as well as layered structures with isotropic or anisotropic material behavior.
In this paper, a numerical approach for the computation of dispersion relations for three-dimensional waveguides with arbitrary cross-section is proposed. The formulation is based on the Scaled Boundary Finite Element Method (SBFEM). It is an extension of the approach previously derived for plate structures. It is shown that the wavenumbers of guided waves in a waveguide can be obtained as the eigenvalues of the Z matrix, which is well known in the SBFEM. The Hamiltonian properties of this matrix are utilized to derive an efficient way to compute the group velocities of propagating waves as eigenvalue derivatives. The cross-section of the waveguide is discretized using higher-order spectral elements. It is discussed in detail how symmetry axes can be utilized to reduce computational costs. In order to sort the solutions at different frequencies, a mode-tracking algorithm is proposed, based on the Padé expansion.
The simulation of Lamb waves in a cracked plate using the scaled boundary finite element method
(2012)
The scaled boundary finite element method is applied to the simulation of Lamb waves for ultrasonic testing applications. With this method, the general elastodynamic problem is solved, while only the boundary of the domain under consideration has to be discretized. The reflection of the fundamental Lamb wave modes from cracks of different geometry in a steel plate is modeled. A test problem is compared with commercial finite element software, showing the efficiency and convergence of the scaled boundary finite element method. A special formulation of this method is utilized to calculate dispersion relations for plate structures. For the discretization of the boundary, higher-order elements are employed to improve the efficiency of the simulations. The simplicity of mesh generation of a cracked plate for a scaled boundary finite element analysis is illustrated.
In this paper, a method is presented for the numerical computation of dispersion properties and mode shapes of guided waves in plate structures. The formulation is based on the Scaled Boundary Finite Element Method. The through-thickness direction of the plate is discretized in the finite element sense, while the direction of propagation is described analytically. This leads to a standard eigenvalue problem for the calculation of wave numbers. The proposed method is not limited to homogeneous plates. Multi-layered composites as well as structures with continuously varying material parameters in the direction of thickness can be modeled without essential changes in the formulation. Higher-order elements have been employed for the finite element discretization, leading to excellent convergence for complex structures. It is shown by numerical examples that this method provides highly accurate results with a small number of nodes while avoiding numerical problems and instabilities.
In this paper a numerical approach, based on the Scaled Boundary Finite Element Method (SBFEM), is described to obtain dispersion relations for propagating modes in wave guides. While the formulation is developed for plate structures, it can easily be extended to wave guides with arbitrary cross-section. The cross-section is discretized in the Finite Element sense while all equations remain analytical in the direction of propagation. The wave numbers of all propagating modes are obtained as the solutions of a standard eigenvalue problem. The group velocities can be calculated accurately as the eigenvalue derivatives. The use of higher-order elements drastically increases the efficiency and accuracy of the computation. This approach can be used for wave guides with arbitrary distribution of material parameters.
In this paper, a method to determine the complex dispersion relations of axially symmetric guided waves in cylindrical structures is presented as an alternative to the currently established numerical procedures. The method is based on a spectral decomposition into eigenfunctions of the Laplace operator on the cross-section of the waveguide. This translates the calculation of real or complex wave numbers at a given frequency into solving an eigenvalue problem. Cylindrical rods and plates are treated as the asymptotic cases of cylindrical structures and used to generalize the method to the case of hollow cylinders. The presented method is superior to direct root-finding algorithms in the sense that no initial guess values are needed to determine the complex wave numbers and that neither starting at low frequencies nor subsequent mode tracking is required. The results obtained with this method are shown to be reasonably close to those calculated by other means and an estimate for the achievable accuracy is given.