Analytische Chemie
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The one-phase methods described in Chapter 2 were shown to be able to predict casting to some extent, but could not depict segregation, sedimentation and blockage occurring during flow. On the other hand, the distinct element methods described in Chapter 3 did not take into account the presence of two phases in the system and describes concrete as distinct elements interacting through more or less complex laws. A reliable numerical model of a multiphase material behaviour shall take into account both phases (solid and liquid). From the numerical point of view, concrete flow shall be seen therefore as the free surface flow of a highly-concentrated suspension of rigid grains.
The application of waveguides for acoustic measuring technologies and the development of non-destructive evaluation techniques with guided ultrasonic waves for plate like materials like carbon fiber reinforced plastic shells and layered structures require a good understanding of acoustic wave propagation inside the material. The well-known Finite Element Method can be used for simulations, however at least for higher frequencies, the ratio of wavelength and geometrical dimension demands a time-consuming fine grid. Using commercial simulation tools the computational costs increase considerably for ultrasonic frequencies.
In the recent years, the Federal Institute for Materials Research and Testing has developed a very efficient alternative for simulating acoustic wave propagation particularly in wave guides by extending the Scaled Boundary Finite Element Method (SBFEM). The SBFEM as a semi-analytical method has one main advantage over the classical Finite Element Method: It only demands a discretization of the boundary instead of the whole domain. This is pictured in the figures below. The method is still related to the Finite Element Method and uses their well-known solving strategies. SBFEM is shown to be highly efficient, especially in the frequency domain. Additionally, the efficiency can be increased by using higher-order spectral elements. In plates and cylinders, the SBFEM can be used to animate propagating modes and computes their wavenumber.
In this contribution, we present a short introduction into the basics of SBFEM formulation of the dynamic elastic wave equation. The applicability and efficiency of the approach is demonstrated by applying the method to layered structures and different wave guide geometries. As one example we present the wave propagation in a typical adhesive joint of different metal sheets as common in new designs in automotive industry. The analysis comprises the computation of dispersion curves as starting point of every development of non-destructive testing techniques for inspecting such structures as well as the analysis of the propagating modes. Additional examples presented handle special cases for axis-symmetric geometries, such as pipes and cylindrical rods which are common in various acoustic measurement applications.
Pulsed thermography is a well-known non-destructive testing technique and has proven to be a valuable tool for examination of material defects, to determine thermal material parameters, and the thickness of test specimens through calibration or mathematical models. However, the application to semitransparent materials is quite new and demanding, especially for semitransparent materials like epoxy, polyamide 12, or glass fiber reinforced polymers with epoxy or polyamide matrix.
In order to describe the temporal temperature evolution in such materials, which are recorded with an infrared camera during pulse thermography experiments, much more influences have to be considered, compared to opaque materials:
- The wavelength of the excitation source and the spectral range of the infrared camera
- The angles between the specimen, the excitation source and the infrared camera
- The area behind the specimen
- The roughness of the material surface
- The scattering mechanism within the material
Here, we will consider all these influences and describe how they can be treated mathematically in analytical or numerical models (using COMSOL Multiphysics software). These models describe the temperature development during the pulse thermography experiment in reflection and transmission configuration. By fitting the results of the mathematical models to experimental data it is possible to determine the thickness or the optical and thermal properties of the specimen.
The quality of additively manufactured (AM) parts is determined by the applied process parameters used and the properties of the feedstock powder. The influence of inner gas pores in feedstock particles on the final AM product is a phenomenon which is difficult to investigate since very few non-destructive measurement techniques are accurate enough to resolve the micropores.
3D X-ray computed tomography (XCT) is increasingly applied during the process chain of AM parts as a non-destructive monitoring and quality control tool and it is able to detect most of the pores.
However, XCT is time-consuming and limited to small amounts of feedstock powder, typically a few milligrams. The aim of the presented approach is to investigate digital radiography of AM feedstock particles as a simple and fast quality check with high throughput. 2D digital radiographs were simulated in order to predict the visibility of pores inside metallic particles for different pore and particle diameters. An experimental validation was performed. It was demonstrated numerically and experimentally that typical gas pores above a certain size (here: 3 to 4.4 µm for the selected X-ray setup), which could be found in metallic microparticles, were reliably detected by digital radiography.
Material defects in fiber reinforced polymers such as delaminations can rapidly degrade the material properties or can lead to the failure of a component. Pulse thermography (PT) has proven to be a valuable tool to identify and quantify such defects in opaque materials. However, quantification of delaminations within semitransparent materials is extremely challenging. We present an approach to quantify delaminations within materials being semitransparent within the wavelength ranges of the optical excitation sources as well as of the infrared (IR) camera. PT experimental data of a glass fiber reinforced polymer with a real delamination within the material were reconstructed by one dimensional (1D) mathematical models. These models describe the heat diffusion within the material and consider semitransparency to the excitation source as well to the IR camera, thermal losses at the samples surfaces and a thermal contact resistance between the two layers describing the delamination. By fitting the models to the PT data, we were able to determine the depth of the delamination very accurately. Additionally, we analyzed synthetic PT data from a 2D simulation with our 1D-models to show how the thermal contact resistance is influenced by lateral heat flow within the material.
In non-destructive testing and structural health monitoring, ultrasonic guided waves (UGWs) are of great interest for finding and characterizing structural flaws. The interaction of the waves with the flaws can often not be described analytically due to waves’ complexity. This makes numerical simulations and experiments indispensable. However, mentioned field of research is still relatively young and most of the methods focus on flaw localization, using time of flight of the reflected signal. This leaves many possibilities for further research, especially when it comes to separate analysis of different propagating modes.
It is well-known that ultrasonic wave modes convert when interacting with flaws. When a fundamental mode (A0 or S0) encounters a notch, it interacts and converts to another fundamental mode. In this contribution, this effect is used to analyze the depth of a notch. Firstly, numerical simulations are presented, which show notch depth proportionality to amplitude ratio of fundamental modes. To validate these results, experiments were carried out on a metal plate with a shallow notch which was gradually deepened. UGWs were excited using a polymer-based interdigital transducer (IDT) and detected with a 3D laser Doppler vibrometer. The IDT is employed to ensure excitation of a single mode and thus to reduce the complexity of the analysis. Good agreement between numerical and experimental results has been found. The results show the potential of UGWs not only for defect reconstruction and localization, but also its precise sizing.