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The present Ph.D. thesis provides a comprehensive experimental and theoretical study of the bulging-cracking relationship in laser beam welding of thick unalloyed steel sheets. It focuses on experimentally proving the existence of the bulging region and on developing a coupled multiphysics mathematical framework to analyze its influence on the three critical factors controlling the susceptibility to solidification cracking, namely the thermal, metallurgical, and mechanical factors.
The research employs a novel experimental setup, utilizing a combination of transparent quartz glass and thick unalloyed steel sheet, enabling real-time visualization of the weld pool geometry and confirming the existence of a distinctive bulging region. To deepen the understanding of these experimental insights, an extensive multiphysics mathematical framework was developed and rigorously verified and validated. This framework introduces an innovative approach using Lamé curves for accurately describing complex three-dimensional weld pool geometries, including the bulging region's characteristics. Through analytical solutions and numerical procedures, it facilitates the computation of solidification parameters, which are crucial for understanding the metallurgical aspects of crack formation. The framework also incorporates a mechanical model to assess and evaluate the local stress distribution within the bulging region.
The findings indicate that an elongated, sharply shaped bulging region significantly increases the susceptibility to solidification cracking. This is attributed to its adverse impact on the distribution and local dwell time of liquid metal residing at grain boundaries during solidification, combined with the localized tensile stresses identified in the bulging region.
In essence, this research contributes to the broader understanding of solidification cracking in laser beam welding of thick unalloyed steel sheets, with a particular focus on the bulging region. The insights and methodologies developed in this thesis are valuable for future research and advancements in the application of the laser beam welding technology for joining high-thickness unalloyed steel components.
It is proposed to model the experimentally observed weld pool boundary with superellipses (Lamé curves) and to find the unknown parameters of the curves using optimization methods. It has been shown experimentally that during laser welding of austenitic stainless steel with a thickness of 2 mm at a speed of 20 mm/s, the rear weld pool part has a shape close to triangular which can be accurately approximated by a superellipse. Analytical dependences of the trajectory and growth rate of the crystal and its cross-sectional area on the geometry of the rear weld pool part are obtained.
A method of solving the thermo-fluid dynamics problem is presented, enabling the prediction of the shape and dimensions of the weld pool during keyhole laser welding of thick plates. It is shown that the rear weld pool boundary can be satisfactorily approximated by a set of superellipses (Lamé curves). The presence of a convex rear weld pool boundary in the mid-plane has been observed experimentally and reproduced numerically. It was shown that in this zone the concentration of liquating impurities increases and the local solidification temperature decreases, contributing to the susceptibility to hot cracking.
The main solidification parameters, namely the crystal axis, the growth rate, and the cross-sectional area of the columnar crystal control the primary microstructure and thus the final weld seam properties.
Limited understanding of solidification parameters due to complexities in experimental and theoretical weld pool boundary determination and
its mathematical description.
Application of local Lamé curves for efficient weld pool boundary reconstruction Derivation of general analytical solutions for the main solidification parameters of a two-dimensional columnar crystal growth during laser beam welding of thin steel sheets.
The Lamé curves approximation technique was successfully applied for the reconstruction of the rear part of the two-dimensional steady-state weld pool boundary. General analytical expressions for the main solidification parameters, namely the crystal axis, the growth rate and the cross-sectional area of the crystal were derived.
The derived expressions and herewith obtained results were verified and validated by comparing them to known theoretical solutions and experimental measurements. Dimensionless analysis of the influence of the size and shape of the rear weld pool boundary on the solidification parameters was provided.
The derived general solutions and the analysis provided allow for critical welding parameters to be estimated and adapted accordingly to improve the welding process.
The effect of the oscillating metal vapor plume on the keyhole and molten pool behavior during the laser beam welding of AlMg3 aluminum alloys is investigated by the experimental and numerical method. The real-time height of the metal vapor plume is measured by high-speed camera observation. The obtained experimental results are used to evaluate the additional heating source and laser beam attenuation caused by the scattering and absorption based on the Beer-Lambert theory. Furthermore, the dynamic behavior of the metal vapor plume is incorporated into a 3D transient heat transfer and fluid flow model, coupled with the ray tracing method, for the laser beam welding of the AlMg3 alloy. It is found that the additional heating resulting from the scattered and absorbed laser beam energy by the metal vapor plume significantly expands the shape of the molten pool on the top region. Moreover, the oscillating metal vapor plume caused the fluctuation of the molten pool shape. The probability of keyhole collapse at the bottom increases significantly to 72% due to the oscillating laser power induced by the laser beam attenuation. The internal interplay between the metal vapor plume, molten pool shape, and the keyhole collapse are obtained. The developed model has been validated by the experiments, which shows a good agreement.
The weld quality and the possible defect formation are directly determined by the weld pool shape and the thermo-fluid dynamics therein. In this paper, an untypical weld pool profile, i.e., elongated at its top and bottom but narrowed at the middle, is found experimentally and numerically in the wire feed laser beam welding. The detrimental influence of the weld pool narrowing on the element transport is analyzed and discussed. A magnetohydrodynamic technique is utilized to suppress the narrowing, aiming at a more homogenous element distribution. It is found that a low-temperature region is formed in the middle of the weld pool due to the interaction of the two dominant circulations from the top and bottom regions. The weld pool is significantly narrowed due to the untypical growth of the mushy zone in the low-temperature region, which results in a direct blocking effect on the downward flow and the premature solidification in the middle region. The Lorentz force produced by a transverse oscillating magnetic field shows the potential to change the flow pattern into a single-circulation type and the low-temperature-gradient region is mitigated.
Therefore, the downward transfer channel is widened, and its premature solidification is prevented. The numerical results are well validated by experimental measurements of metal/glass observation and X-ray fluorescence element mapping.
The contactless magnetohydrodynamic technology has been considered as a potential and promising method to improve the weld qualities of deep penetration laser beam welding. In this paper, numerical investigations are conducted to study the influence of the auxiliary oscillating magnetic field on the porosity suppression in laser beam welding of 5754 aluminum alloy. To obtain a deeper insight into the suppression mechanism, a three-dimensional transient multi-physical model is developed to calculate the heat transfer, fluid flow, keyhole dynamic, and magnetohydrodynamics. A ray tracing algorithm is employed to calculate the laser energy distribution on the keyhole wall. A time-averaged downward Lorentz force is produced by an oscillating magnetic field. This force acts in the molten pool, leading to a dominant downward flow motion in the longitudinal section, which blocks the bubble migration from the keyhole tip to the rear part of the molten pool. Therefore, the possibility for the bubbles to be captured by the solidification front is reduced. The electromagnetic expulsive force provides an additional upward escaping speed for the bubbles of 1 m/s ~ 5 m/s in the lower and middle region of the molten pool. The simulation results are in a good agreement with experimental measurements. Based on the results obtained in this study, a better understanding of the underlying physics in laser beam welding enhanced by an auxiliary oscillating magnetic field can be provided and thus the welding process can be further optimized reducing the porosity formation.
A three-dimensional numerical model was developed to accurately predict the steady-state weld pool shape in full penetration laser beam welding. The model accounts for the coupling between the heat transfer and the fluid dynamics by considering the effects of solid/liquid phase transition, thermo-capillary convection, natural convection, and phase-specific and temperature-dependent material properties up to the evaporation temperature. A fixed right circular cone was utilized as a keyhole geometry to consider the heat absorbed from the laser beam. The model was used to analyze the influence of the thermodynamic activity of solutes and turbulence on the weld pool shape. A mesh sensitivity analysis was performed on a hybrid mesh combining hexahedral and tetrahedral elements. For the case of full penetration laser beam welding of 8 mm thick unalloyed steel sheets, the dependence of the weld pool shape on the surface-active element sulfur was found to be negligible. The analysis of the results showed that a laminar formulation is sufficient for accurately predicting the weld pool shape since the turbulence has a minor impact on the flow dynamics in the weld pool. The validity of the numerical results was backed up by experimental measurements and observations, including weld pool length, local temperature history, and a range of metallographic crosssections.
Numerical study on the formation of a bulging region in partial penetration laser beam welding
(2023)
A transient three-dimensional thermo-fluid dynamics numerical model was developed to study the formation of a bulging region in partial penetration laser beam welding. The model accounts for the coupling between the fluid flow, the heat transfer, and the keyhole dynamics by considering the effects of multiple reflections and Fresnel absorption of the laser beam in the keyhole, the phase transitions during melting and evaporating, the thermo-capillary convection, the natural convection, and the phase-specific and temperature-dependent material properties up to the evaporation temperature. The validity of the model was backed up by experimentally obtained data, including the drilling time, the weld pool length, the local temperature history outside the weld pool, the process efficiency, and a range of metallographic crosssections.
The model was applied for the cases of partial penetration laser beam welding of 8 mm and 12 mm thick unalloyed steel sheets. The obtained experimental and numerical results reveal that the bulging region forms transiently depending on the penetration depth of the weld, showing a tendency to transition from a slight bulging to a fully developed bulging region between penetration depths of 6 mm and 9 mm, respectively.
The present work deals with the recently confirmed widening of the weld pool interface, known as a bulging effect, and its relevance in high power laser beam welding. A combined experimental and numerical approach is utilized to study the influence of the bulge on the hot cracking formation and the transport of alloying elements in the molten pool. A technique using a quartz glass, a direct-diode laser illumination, a high-speed camera, and two thermal imaging cameras is applied to visualize the weld pool geometry in the longitudinal section. The study examines the relevance of the bulging effect on both, partial and complete penetration, as well as for different sheet thicknesses ranging from 8 mm to 25 mm. The numerical analysis shows that the formation of a bulge region is highly dependent on the penetration depth and occurs above 10 mm penetration depth. The location of the bulge correlates strongly with the cracking location. The obtained experimental and numerical results reveal that the bulging effect increases the hot cracking susceptibility and limits the transfer of alloying elements from the top of the weld pool to the weld root.
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.
Laser beam welding is a widely used joining technique in many industrial applications. This is mainly due to its many unique advantages, especially compared to conventional arc welding processes. These advantages include, among others, highly concentrated energy deposition, low total heat input and a capacity to penetrate deep into the material while causing only small welding distortions.
However, at the same time, the small dimension of the laser spot, high solidification rates, and small dimensions of the weld pool itself can provoke issues regarding the assembly tolerances of the workpiece, the hot-cracking phenomena, as well as keyhole-induced bubbles escaping from the melt.
Weld pool shapes in laser beam welding are elongated at the external, free surfaces under the action of the main driving forces in the melt – such as recoil pressure and surface tension forces – while being shorter in the internal areas of the weld pool. This leads to a regular solidification sequence from the internal zones toward the free surfaces, e.g. from the bottom to the top in partial penetration welding. However, in recent studies reported in the literature and seen in the experimental and numerical investigations of BAM Bundesanstalt für Materialforschung und -prüfung in Berlin, it was found that an internal narrowing phenomenon can occur that is often accompanied by a distinct bulging of the weld bead in deeper zones.
As the internal behaviour of the melt during the process is hardly optically accessible, several numerical models and experimental techniques were established to visualise the mechanisms of the formation of the bulging and the narrowing phenomenon and to reveal the consequences on the solidification sequence, pore formation, and filler metal dilution.
An accurate and efficient description of the spatial distribution of laser energy is a crucial factor for the modeling of laser material processing, e.g., laser welding, laser cutting, or laser-based additive manufacturing. In this study, a 3D heat transfer and fluid flow model coupled with the volume-of-fluid algorithm for free surface tracking is developed for the simulation of molten pool dynamics in high-power laser beam welding. The underlying laser-material interactions, i.e., the multiple reflections and Fresnel absorption, are considered by a ray-tracing method. Two strategies of free surface reconstruction used in the ray-tracing method are investigated: a typical piecewise linear interface calculation (PLIC)-based method and a novel localized Level-Set method. The PLIC-based method is discrete, resulting in non-continuous free surface reconstruction. In the localized Level-Set method, a continuous free surface is reconstructed, and thus the exact reflection points can be determined. The calculated spatial laser energy distribution and the corresponding molten pool dynamics from the two methods are analyzed and compared. The obtained numerical results are evaluated with experimental measurements to assure the validity of the proposed model. It is found that distinct patterns of the beam multiple reflections are obtained with the different free surface reconstructions, which shows significant influence not only on the molten pool behaviors but also on the localized keyhole dynamics.
This study presents mechanisms of the evolution of a narrowed region in the weld pool center during deep penetration laser beam welding. In numerous numerical studies presented in this study, it was also found that the local reduction of the weld pool size can cause detrimental effects on the melt flow behavior and the resulting properties of the welds. A particularly large influence of this effect was identified in three aspects. Firstly, the local variation of the solidification sequence of the weld pool causes an increase in the hot-cracking susceptibility due to a locally delayed solidification. Secondly, it was proven that a change in the local length and width of the weld pool is associated with an adverse impact on the potential flow routes of the molten material that induces stronger local variations of its solidification. Thus, the element mixing, e.g. during the welding with filler materials, is blocked. This leads to a non-homogeneous chemical composition of the final weld and can cause undesired effects on the final material properties. Finally, another observed effect is related to the reduced ability of process pores to reach the top surface. As this type of porosity is usually produced around the keyhole tip, the change of the fluid flow regime above this area plays a significant role in determining the final path of the pores until the premature solidification in the middle of the weld pool captures them. This study summarizes mainly numerical results which were supported by selected experimental validation results.
Numerical study on the formation of a bulging region in partial penetration laser beam welding
(2022)
A transient three-dimensional thermo-fluid dynamics numerical model was developed to study the formation of a bulging region in partial penetration laser beam welding. The model accounts for the coupling between the fluid flow, the heat transfer, and the keyhole dynamics by considering the effects of multiple reflections and Fresnel absorption of the laser beam in the keyhole, the phase transitions during melting and evaporating, the thermo-capillary convection, the natural convection, and the phase-specific and temperature-dependent material properties up to the evaporation temperature. The validity of the model was backed up by experimentally obtained data, including the drilling time, the weld pool length, the local temperature history outside the weld pool, the process efficiency, and a range of metallographic cross-sections. The model was applied for the cases of partial penetration laser beam welding of 8 mm and 12 mm thick unalloyed steel sheets. The obtained experimental and numerical results reveal that the bulging region forms transiently depending on the penetration depth of the weld, showing a tendency to transition from a slight bulging to a fully developed bulging region between penetration depths of 6 mm and 9 mm, respectively.
A mathematical model for physical processes in fusion welding has been developed. It is based on the equivalent heat source concept and consists of two parts: thermo-hydrodynamics of the weld pool and heat conduction in the weldment outside the pool. In thermo-hydrodynamic problem, temperature – dependent material properties, keyhole shape, thermo-capillary and natural convection, phase transformations and other physical phenomena are taken into consideration.
Solution of the thermo-hydrodynamic problem by the finite element method is demonstrated with keyhole laser beam welding of a 15 mm thick steel plate. Thermo-capillary convection is primarily responsible for the intricate convex-concave melt pool shape and pool enlargement near the plate surfaces. The calculated and experimental molten pool dimensions are in close agreement.
Mathematical analysis of the bulging effect in high power laser beam welding of thick steel sheets
(2021)
The present work is devoted to the mathematical analysis of the bulging effect in high-power laser beam welding of thick steel sheets. The numerical results are based upon experimental results from previous studies, revealing the relationships between the bulging effect, the hot cracking formation, and the distribution of alloying elements in the weld pool. The widening of the molten pool in its middle area is observed for both complete and partial penetration welding of 8 mm - 15 mm thick structural steel sheets. The weld pool shape is extracted from the simulations to evaluate the extent of the necking and bulging of the solidification isotherm and their influence on the hot cracking formation and the mixing behavior of the weld pool. Relying on an earlier numerical study utilizing a fixed keyhole, simulation models considering a dynamic keyhole are developed thereto. The link between the bulge and the studied phenomena is found to be significant.
This article is devoted to the study of the bulging effect in deep penetration laser beam welding. The numerical results of the investigations are based upon experimental results from previous studies to reveal the relationship between the bulging effect and the hot cracking formation, as well as the mixing of alloying elements in the weld pool. The widening of the molten pool in its center area can be observed in full penetration as well as in partial penetration welds on 8 mm and 12 mm thick structural steel plates, respectively. The weld pool shape is extracted from the simulations to evaluate the extent of the necking of the solidification line as well as the bulging phenomena and its influence on the hot cracking phenomena. Relying on an earlier numerical study utilizing a fixed keyhole, simulation models considering a dynamic keyhole are developed thereto. Additionally, the mixing behavior of alloying elements during partial penetration is investigated. The link between the bulge and the studied phenomena is found to be significant.
This article is devoted to the study of the bulging effect in deep penetration laser beam welding. The numerical results of the investigations are based upon experimental results from previous studies to reveal the relationship between the bulging effect and the hot cracking formation, as well as the mixing of alloying elements in the weld pool. The widening of the molten pool in its center area can be observed in full penetration as well as in partial penetration welds on 8 mm and 12 mm thick structural steel plates, respectively. The weld pool shape is extracted from the simulations to evaluate the extent of the necking of the solidification line as well as the bulging phenomena and its influence on the hot cracking phenomena. Relying on an earlier numerical study utilizing a fixed keyhole, simulation models considering a dynamic keyhole are developed thereto. Additionally, the mixing behavior of alloying elements during partial penetration is investigated. The link between the bulge and the studied phenomena is found to be significant.
The transport phenomena in the wire feed laser beam welding are investigated numerically. A three-dimensional transient heat transfer and fluid flow model coupled with free surface tracing and element transport is developed. A ray-tracing method with local grid refinement algorithm is used to calculate the multiple reflections and Fresnel absorption on the keyhole wall. The filler material flows backward along the lateral side of the weld pool, and subsequently flows forward along the longitudinal plane. The occurrence of the bulging phenomenon may further prevent the downward transfer of the additional elements to the root of the weld pool.