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Elastic waves in inhomogeneous meshes avoiding numerical artifacts
Elastic waves in solids resulting from damage processes, e.g. microcracking are used to monitor the integrity of structures. The numerical modelling of these acoustic Emission processes is hindered by the different scales involved. Crack opening is a fast process and the size of the damaged zone is small, leading to small time steps and fine meshes in a numerical finite element simulation. On the other hand the relevant wave Propagation takes place on a much larger spatial scale, e.g covering the distance between Emission source and sensor.
To avoid numerical oscillations, the mesh size at the emission source has to be coupled to its time scale. Using higher order spectral elements can be beneficial with respect to the needed number of degrees of freedom. To make the computation of an acoustic emission process feasible one is lead to coarsening the mesh for larger distances to the source. Solution components with a higher frequency will be reflected at mesh density steps. The mesh coarsening has to be done in a way to avoid or minimize this kind of reflections.
To get more insight into the propagation characteristics of the numerical solution, dispersion curves are calculated for different element types assuming a structured mesh with constant element size. Coupling two meshes with different mesh densities will then lead to frequency dependent reflections at the boundary similar to the coupling of different materials.
The starting mesh density is dictated by the acoustic emission source time scale. The largest allowable mesh size needs to resolve the components of propagating signal with the highest frequency, smallest wavelength which is given by the bandwidth of the sensor.
Still coarser meshes may be used when high frequency components are propagated by a different method.
Crack detection in metallic samples at high surface temperature, hostile and hazardous environments, etc. is challenging situation in any manufacturing industries. Most of the present NDE methods are suitable only for lower surface temperatures, especially room temperature. In this situation, we need a fast and non-contact NDT method which can be applied even in high sample surface temperature. Laser thermography is one of the techniques having a high potential in non-contact inspection. As a preliminary investigation, in this article, we have studied the potentiality of laser line thermography in crack detection at room temperature. In laser line thermography, a continuous wave (CW) laser is used to generate a laser line, which in turn is used to scan the metal surface. The heat distribution over the sample surface is recorded by an infrared thermal (IR) camera. Two different approaches are reported in this work. Firstly, a stationary laser line source and its interaction with cracks; secondly, moving laser line source scanning over a surface with crack. When the distance between crack centre to laser line centre increases, crack detectability will decrease; and when laser power increases, crack detectability will increase. A dedicated image processing algorithm was developed to improve the detectability of the cracks. To understand the heat transfer phenomenon, a simplified 3D model for laser thermography was developed for the heat distribution during laser heating and was validated with experimental results. Defects were incorporated as a thermally thin resistive layer (TTRL) in numerical modeling, and the effect of TTRL in heat conduction is compared with experimental results.