Problems on the identification of two-dimensional spatial domains arising in the detection and characterization of structural flaws in materials are considered. For a thermal diffusion system with external boundary input, observations of the temperature on the surface are used in a output least-squares approach. Parameter estimation techniques based on the 'method of mappings' are discussed and approximation schemes are developed based on a finiteelement Galerkin approach. Theoretical convergence results for computational techniques are given and the results are applied to experimental data for the identification of flaws in thermal testing of materials.
Dynamic dielectric analysis (DDA) has been used to study curing polymer systems and thermoplastics. Measurements have been made over a frequency range of six decades. This wide range of frequencies increases the amount of information which can be obtained. The data is analyzed in terms of the frequency dependence of the complex permittivity ε*, specific conductivity σ(ohm−1 cm−1), and the relaxation time τ, parameters which are characteristic of the cure state of the material and independent of the size of the sample. Dynamic dielectric measurements have been used to monitor polymer processing in UDEL‐P1700, LARC‐160, polyphenyl quinoxaline (PPQ), and Epon 828 cured with Agent U. Dynamic dielectric measurements have been correlated with viscosity for the polysulfone thermoplastic UDEL‐P1700 and with viscosity and ultrasonic measurements on the DGEBA type epoxy Epon 828 cured with Agent U. The experimental results suggest that when ionic processes dominate the dielectric response, the intensive property σ is a good monitor of the resin's viscosity. The results show that the dielectric relaxation time τ can be used to monitor the state of the system and the extent and rate of the reaction. Solvent evolution can also be easily observed.
We report here on the use of the heat equation to simulate a thermal interrogation method for detecting damage in a heterogeneous porous material. We first use probability schemes to randomly generate pores in a sample material; then we simulate flash heating of the compartment along one of its boundaries. Temperature data along the source and back boundaries are recorded and then analyzed to distinguish differences between the undamaged and damaged materials. These results suggest that it is possible to detect damage of a certain size within a porous medium using thermal interrogation.
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Principal Component Analysis (PCA) has been shown effective for reducing thermographic NDE data. This paper will discuss an alternative method of analysis that has been developed where a predetermined set of eigenvectors is used to process the thermal data from both reinforced carbon-carbon (RCC) and graphite-epoxy honeycomb materials. These eigenvectors can be generated either from an analytic model of the thermal response of the material system under examination, or from a large set of experimental data. This paper provides the details of the analytic model, an overview of the PCA process, as well as a quantitative signal-to-noise comparison of the results of performing both conventional PCA and fixed eigenvector analysis on thermographic data from two specimens, one Reinforced Carbon-Carbon with flat bottom holes and the second a sandwich construction with graphite-epoxy face sheets and aluminum honeycomb core.
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