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The amount of absorbed energy in the keyhole as well as its spatial and temporal distribution is essential to model the laser beam welding process. The recoil pressure, which develops because of the evaporation process induced by the absorbed laser energy at the keyhole wall, is a key determining factor for the macroscopic flow of the molten metal in the weld pool during high-power laser beam welding. Consequently, a realistic implementation of the effect of laser radiation on the weld metal is crucial to obtain reliable and accurate simulation results. In this paper, we discuss manyfold different improvements on the laser-material interaction, namely, the ray tracing method, in the numerical simulation of the laser beam welding process. The first improvement relates to locating the exact reflection points in the ray tracing method using a so-called cosine condition in the determination algorithm for the intersection of reflected rays and the keyhole surface. A second correction refers to the numerical treatment of the Gaussian distribution of the laser beam, whose beam width is defined by a decay of the laser intensity by a factor of 1/e2, thus ignoring around 14% of the total laser beam energy. In the third step, the changes in the laser radiation distribution in the vertical direction were adapted by using different approximations for the converging and the diverging regions of the laser beam, thus mimicking the beam caustic. Finally, a virtual mesh refinement was adopted in the ray tracing routine. The obtained numerical results were validated with experimental measurements.
The amount of absorbed energy in the keyhole as well as its spatial and temporal distribution is essential to model the laser beam welding process. The recoil pressure, which develops because of the evaporation process induced by the absorbed laser energy at the keyhole wall, is a key determining factor for the macroscopic flow of the molten metal in the weld pool during high-power laser beam welding. Consequently, a realistic implementation of the effect of the laser radiation on the weld metal is crucial to obtain reliable and accurate simulation results.
In this paper, we discuss manyfold different improvements on the laser-material interaction, namely the ray-tracing method, in the numerical simulation of the laser beam welding process. The first improvement relates to locating the exact reflection points in the ray tracing method using a so-called cosine condition in the determination algorithm for the intersection of the reflected rays and the keyhole surface. A second correction refers to the numerical treatment of the Gaussian distribution of the laser beam, whose beam width is defined by a decay of the laser intensity by a factor of 1/e2 thus ignoring around 14 % of the total laser beam energy. In a third step, the changes in the laser radiation distribution in the vertical direction were adapted by using different approximations for the converging and the diverging regions of the laser beam thus mimicking the beam caustic. Finally, a virtual mesh refinement was adopted in the ray tracing routine. The obtained numerical results were validated with experimental measurements.
The amount of absorbed energy in the keyhole as well as its spatial and temporal distribution is essential to model the laser beam welding process. The recoil pressure, which develops because of the evaporation process induced by the absorbed laser energy at the keyhole wall, is a key determining factor for the macroscopic flow of the molten metal in the weld pool during high-power laser beam welding. Consequently, a realistic implementation of the effect of laser radiation on the weld metal is crucial to obtain reliable and accurate simulation results. In this paper, we discuss manyfold different improvements on the laser-material interaction, namely, the ray tracing method, in the numerical simulation of the laser beam welding process. The first improvement relates to locating the exact reflection points in the ray tracing method using a so-called cosine condition in the determination algorithm for the intersection of reflected rays and the keyhole surface. A second correction refers to the numerical treatment of the Gaussian distribution of the laser beam, whose beam width is defined by a decay of the laser intensity by a factor of 1/e2, thus ignoring around 14% of the total laser beam energy. In the third step, the changes in the laser radiation distribution in the vertical direction were adapted by using different approximations for the converging and the diverging regions of the laser beam, thus mimicking the beam caustic. Finally, a virtual mesh refinement was adopted in the ray tracing routine. The obtained numerical results were validated with experimental measurements.
The present work is devoted to the numerical analysis of the high-power laser beam welding of thick sheets at different welding speeds. A three-dimensional transient multi-physics numerical model is developed, allowing for the prediction of the keyhole geometry and the final penetration depth. Two ray tracing algorithms are implemented and compared, namely a standard ray tracing approach and an approach using a virtual mesh refinement for a more accurate calculation of the reflection points. Both algorithms are found to provide sufficient accuracy for the prediction of the keyhole depth during laser beam welding with process speeds of up to 1.5 m/min. However, with the standard algorithm, the penetration depth is underestimated by the model for a process speed of 2.5 m/min due to a trapping effect of the laser energy in the top region. In contrast, the virtually refined ray tracing approach results in high accuracy results for process speeds of both 1.5 m/min and 2.5 m/min. A detailed study on the trapping effect is provided, accompanied by a benchmark including a predefined keyhole geometry with typical characteristics for the high-power laser beam welding of thick plates at high process speed, such as deep keyhole, inclined front keyhole wall, and a hump.
Ray tracing boudary value problems: simulation and SAFT reconstruction for ultrasonic testing
(2016)
The application of advanced imaging techniques for the ultrasonic inspection of inhomogeneous anisotropic materials like austenitic and dissimilar welds requires information about acoustic wave propagation through the material, in particular travel times between two points in the material. Forward ray tracing is a popular approach to determine traveling paths and arrival times but is ill suited for inverse problems since a large number of rays have to be computed in order to arrive at prescribed end points. In this contribution we discuss boundary value problems for acoustic rays, where the ray path between two given points is determined by solving the eikonal equation. The implementation of such a two point boundary value ray tracer for sound field simulations through an austenitic weld is described and its efficiency as well as the obtained results are compared to those of a forward ray tracer. The results are validated by comparison with experimental results and commercially available UT simulation tools. As an application, we discuss an implementation of the method for SAFT (Synthetic Aperture Focusing Technique) reconstruction. The ray tracer calculates the required travel time through the anisotropic columnar grain structure of the austenitic weld. There, the formulation of ray tracing as a boundary value problem allows a straightforward derivation of the ray path from a given transducer position to any pixel in the reconstruction area and reduces the computational cost considerably.
Ray tracing boundary value problems: simulation and SAFT reconstruction for ultrasonic testing
(2016)
The application of advanced imaging techniques for the ultrasonic inspection of inhomogeneous anisotropic materials like austenitic and dissimilar welds requires information about acoustic wave Propagation through the material, in particular travel times between two Points in the material. Forward ray tracing is a popular approach to determine traveling paths and arrival times but is ill suited for inverse problems since a large number of rays have to be computed in order to arrive at prescribed end points.
In this contribution we discuss boundary value problems for acoustic rays, where the ray path between two given points is determined by solving the Eikonal equation. The implementation of such a two Point boundary value ray tracer for sound field simulations through an austenitic weld is described and its efficiency as well as the obtained results are compared to those of a forward ray tracer. The results are validated by comparison with experimental results and commercially available UT simulation tools.
As an application, we discuss an implementation of the method for SAFT (Synthetic Aperture Focusing Technique) reconstruction. The ray tracer calculates the required travel time through the anisotropic columnar grain structure of the austenitic weld. There, the formulation of ray tracing as a boundary value Problem allows a straightforward derivation of the ray path from a given transducer Position to any pixel in the reconstruction area and reduces the computational cost considerably.
Implementation of soilcrete columns via jet grouting or deep soil mixing to stabilize problematic subsurface soils is common in underground construction. However, industry is faced with limited options to characterize column geometry and quality of the resulting soilcrete without excavation or destructive testing. Laboratory-scale experiments were conducted on simulated soilcrete columns using crosshole ultrasonic testing to evaluate the feasibility of acoustic tomography to characterize soilcrete geometry and quality. Data were acquired on multiple columns immediately after placement up to a curing time of 120 hours. Jet grout compressional wave velocity (VP) was estimated using a first arrival time approach and inverted to construct acoustic tomograms. Acoustic tomograms indicate that crosshole ultrasonic testing is able to characterize the changes in acoustic properties that result from jet-grout curing, locate contrasts between weaker/stronger regions in the jet grout, and estimate geometry of the column.
The synthetic aperture focusing technique (SAFT) is an imaging technique commonly used in ultrasonic inspection. In order to apply SAFT to the inspection of austenitic welds, the inhomogeneous anisotropic nature of the weld structure has to be taken into account. A suitable approach to accomplish this, is to couple the SAFT-algorithm with a ray tracing program (RT-SAFT). While SAFT-imaging of cracks in austenitic welds by use of ray tracing has been carried out before, all attempts so far were limited to longitudinal cracks which usually allows a treatment as 2-dimensional problem. In case of transverse cracks, a full 3-dimensional ray tracing is necessary in order to perform a SAFT-reconstruction. In this paper, we give an outline of our attempts to reconstruct images of transverse cracks in austenitic welds, utilizing 3-dimensional ray tracing and a layered structure model derived from an empirical model of grain orientations in welds. We present results of this RT-SAFT on experimental data taken from transverse cracks in different austenitic welds, which show that size and position of the cracks can be estimated with good accuracy, and compare them to images obtained by assuming an isotropic homogeneous medium which corresponds to the application of the classical SAFT-algorithm.
Up to now there is no sufficient technique to detect transverse cracks in austenitic and dissimilar welds which recently are of increasing interest in the integrity surveillance of nuclear power plants as well as in quality control of longitudinally welded pipes. Weld inspection by interpretation of single A-scans will lead to erroneous results due to effects caused by anisotropy and in worst case might leave flaws undetected. Therefore, imaging techniques such as the synthetic aperture focusing technique (SAFT) should be used. If the SAFT algorithm is applied on data taken from austenitic welds, the inhomogeneous, anisotropic structure of these welds has to be taken into account in order to properly attribute amplitudes measured in A-scans to the corresponding coordinates in the region of interest. While this has been investigated in the past, all attempts so far were limited to the imaging of longitudinal cracks which requires a less complicated setup than the imaging of transverse cracks. In this paper we give an outline of our attempts to reconstruct images of transverse cracks in different welds. For this purpose a SAFT program based on ray tracing and a layered structure weld model derived from an empirical model of grain orientations in welds are used. The results of the image reconstruction on experimental data are shown and compared to images obtained by assuming an isotropic homogeneous model. Root reflection and crack tip echo are clearly visible which allows an estimation of size and position of the crack with good accuracy.
Ultrasonic examination of anisotropic inhomogeneous austenitic welds is challenging, because of the columnar grain structure of the weld leads to beam skewing and splitting. Modeling tools play an important role in understanding the ultrasound field propagation and optimization of experimental parameters during the ultrasonic testing of austenitic welds as well as the interpretation of the test results. In this contribution, an efficient theoretical model based on the ray tracing concepts is developed to calculate the ultrasonic fields in inhomogeneous austenitic welds quantitatively. The developed model determines the ultrasound fields by taking into account the directivity of the ray source, the inhomogenity of the weld as well as ray transmission coefficients. Directivity of the ray source in columnar grained austenitic materials (including layback orientation) is obtained in three dimensions based on Lamb's reciprocity theorem. Ray energy reflection and transmission coefficients at an interface between two general columnar grained austenitic materials are calculated in three dimensions. The ray tracing model predictions on inhomogeneous austenitic weld material are compared against those from CIVA, a commercial non-destructive modeling and simulation tool. The ultrasonic modeling tools in CIVA are based on semi-analytical solutions. For beam propagation simulation, a so-called 'pencil method' is used, which involves modeling the probe as a set of individual source points, each radiating 'a bundle' of diverging rays into the medium and integrating those elementary contributions. Inhomogenity in the weld region is approximated by mapping the grain orientations on weld macrograph. Simulation results for ultrasonic field profiles for an austenitic weld are shown to be in good agreement with the corresponding experimental results.