Molten Metal Oscillatory Behaviour in Advanced Fusion-based Manufacturing Processes

Research output: ThesisDissertation (TU Delft)

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The growing demand for manufactured products with complex geometries requiring advanced fusion-based manufacturing techniques emphasises the importance of process development and optimisation to reduce the risk of adverse outcomes, which is currently impeded with traditional approaches (trial and error experiments). Development, optimisation and qualification of such procedures are often expensive and time-consuming, particularly when new materials or new material combinations are involved. Process stability is intrinsically linked to the stability of the molten metal melt-pool, which ideally should solidify in a smooth and continuous manner to produce a consistent product, free of undesirable geometric and metallurgical defects. The influence of material properties and process conditions on melt-pool stability are generally difficult to derive from experimental observations; hence process optimisation is often reliant on a trial-and-error approach, mitigated to a large extent by a considerable body of industrial experience.
The challenge addressed in this research is to develop a simulation-based approach to assess the stability of oscillating melt-pools in fusion welding and additive manufacturing, to minimise the number of trial-and-error experiments required for process development and optimisation, which ultimately will lead to shortening the time between design and production. The computational model developed in the present work has a generic construction with specific process influences addressed through appropriate boundary conditions, avoiding the necessity to integrate melt pool and detailed process descriptions in a single simulation. The model is therefore capable of representing a wide range of welding and additive manufacturing technologies through selection of appropriate material properties and boundary conditions. The robustness of the present computational model in predicting the melt-pool behaviour is demonstrated by comparing the numerical predictions with experimental, analytical and numerical data.
Focusing on numerical simulations of solidification and melting using the enthalpy-porosity method, the influence of the permeability coefficient (also known as the mushy-zone constant) on the numerical predictions, which is employed to dampen fluid velocities in the mushy zone and suppress them in solid regions, is systematically analysed for both isothermal and non-isothermal phase-change problems. For isothermal phase-change problems, reducing the cell size diminishes the influence of the mushy-zone constant on the results and the solution becomes independent of the mushy-zone constant for fine enough meshes. Numerical predictions of non-isothermal phase-change problems are inherently dependent on the mushy-zone constant. A method is proposed, based on a Péclet number, to predict and evaluate the influence of the permeability coefficient on numerical predictions of solidification and melting problems.
In many numerical studies in the literature, the transport coefficients of the material, specifically thermal conductivity and viscosity, are artificially increased by a so-called `enhancement factor' to achieve agreement between experiments and numerically predicted melt-pool sizes and solidification rates. However, the use of an enhancement factor has little physical meaning, does not represent the physics of complex transport phenomena and can significantly affect the numerical predictions. The effects of using enhancement factors on the numerical predictions of melt-pool behaviour in fusion welding and additive manufacturing are studied in detail. Moreover, the effects of employing temperature-dependent material properties on the numerical predictions are discussed in the present thesis.
Melt pools in fusion welding and additive manufacturing exhibit highly non-linear responses to variations of process parameters and are very sensitive to imposed boundary conditions. Temporal and spatial variations in the energy-flux distribution, which are often neglected in numerical simulations, are taken into account in the present work. It is shown how deformations of the melt-pool surface, due to fluid motion as well as changes in the system orientation, affect the numerical predictions of thermal and fluid flow fields. The effects of joint shape design on melt-pool behaviour during fusion welding is also studied in the present work.
Changes in power-density and force distributions affect the thermal and fluid flow fields on the melt-pool surface, which in turn can influence the pool shape. Oscillations strongly relate to shape and size of the melt-pool and the surface tension distribution on the molten material surface. Using the simulation-based approach developed in the present work, the frequency and amplitude of melt-pool oscillations and changes in the oscillation modes are predicted, which are not accessible using published analytical models and are generally difficult to measure experimentally. Additionally, using the proposed simulation-based approach, the need for triggering of the melt-pool oscillations is obviated, since even small surface displacements are detectable, which are not sensible to the current measurement devices employed in experiments.
The dynamic features of the oscillation signals cannot easily be derived employing conventional Fourier transform (FT) analysis since the oscillation signals are assumed to be stationary (i.e. the behaviour of the system is linear and time-invariant), which is often not the case in fusion welding and additive manufacturing. The continuous wavelet transform (CWT) has been employed in the present work to overcome the shortcomings of the conventional fast Fourier transform (FFT) analysis in characterising the non-stationary features of the surface oscillation signals received from the melt pool. Employing the continuous wavelet transform, the time-resolved melt-pool surface oscillation signals obtained from the numerical simulations can be decomposed into time and frequency spaces simultaneously.
The simulation-based approach developed in the present work addresses some of the significant challenges involved in assessing the melt-pool stability for process development and optimisation. The numerical predictions of the present computational model enhances the current understanding of the process behaviour, which is often very challenging to achieve from experiments alone. Moreover, the present simulation-based approach can be employed to explore the design space and reduce the costs associated with process development and optimisation.
Original languageEnglish
QualificationDoctor of Philosophy
Awarding Institution
  • Delft University of Technology
  • Richardson, I.M., Supervisor
  • Kleijn, C.R., Supervisor
Thesis sponsors
Award date30 Mar 2022
Print ISBNs9789464237412
Publication statusPublished - 2022


This research was carried out under the project number F31.7.13504 in the framework of the Partnership Program of the Materials innovation institute M2i ( and the Foundation for Fundamental Research on Matter (FOM) (, which is part of the Netherlands Organisation for Scientific Research (


  • Materials processing
  • Fusion welding and additive manufacturing
  • Process design and optimisation
  • Melt pool behaviour
  • Computational modelling


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