Operando X-ray diffraction during laser 3D printing: from machine design to experiments and computer simulations

The importance of additive manufacturing, also known as 3D printing, has grown exponentially in the recent years thanks to its high flexibility to manufacture intricate parts. This process can be divided into many different sub-categories, depending on the feedstock form and the source used. However, the principle stays the same: building the part one layer after another.

Selective Laser Melting (SLM) is one them, combining between a fine metallic powder bed and a laser beam scanning the surface to selectively fuse the particles together. SLM is already used in the medical field where custom shapes implants are needed, or in the automotive and aerospace industries where it eases the production time of certain parts. SLM exhibits very high heating and cooling rates, up to 105-106 K/s as demonstrated in this work. Therefore, it poses several challenges such as the formation of pores, the accumulation of residual stresses and the creation of metastable phases in the microstructure. Post-processing techniques such as long heat treatments are used to counter the effect of these problems. A better way to address these different issues would be to adapt the processing parameters to reduce or remove the generation of such unwanted features. To do so, it is necessary to understand the underlying causes creating these defects. Ex situ characterisation of SLM-printed parts can be done using microscopy techniques. It consists in exploring the microstructure changes for a certain range of parameter values (laser power, scanning speed, etc). However, this is very time consuming. Simulations could be used as a prediction tool, but the degree of complexity needed here is quite high, which makes them computationally expensive.

This PhD thesis is part of the CCMX-Challenge AM3 (Additive Manufacturing and Metallic Microstructures) and is dedicated to the development of a new device reproducing the SLM manufacturing process to characterise the phase evolution of metallic microstructures in real time, or operando, by X-ray diffraction (XRD) techniques. A Ti-6Al-4V (wt%) alloy is used to demonstrate the capabilities of this new device, thanks to its compatibility with the X-ray energies available at the Swiss Light Source (SLS) synchrotron beamlines of the Paul Scherrer Institut (PSI).

This dissertation introduces the design of the machine and its software, as well as a characterisation of the printed Ti-6Al-4V samples to determine the optimum printing parameters. To demonstrate the measurement capabilities of the machine, different operando XRD experiments will then be presented, giving new insights into the phase evolution during SLM processing. These observations will be linked to the sample microstructure after printing. Additionally, the unique properties of this setup allow to capture the rapid temperature evolution within the probed materials during the XRD measurement. The obtained temperature profile will be compared to some results derived by Finite Elements Method (FEM) analysis on already existing models established for Ti-6Al-4V.

Modélisation des transformations de phase à l'état solide dans les aciers et application au traitement thermique par induction

Alain Jacot

In the first part of this work a comprehensive model of the continuous hardening of 3D-axisymmetric steel components by induction heating has been developed. In the model, the Maxwell and heat flow equations are solved using a mixed numerical formulation : the inductor and the workpiece are enmeshed with finite elements (FE) but boundary elements (BE) are used for the solution of the electromagnetic equations in the ambient air. This method allows the inductor to be moved with respect to the workpiece without any remeshing procedure. The heat flow equation is solved for the workpiece using the same FE mesh. For the thermal boundary conditions, a net radiation method has been implemented to account for grey diffuse bodies and the viewing factors of the element facets are calculated using a "shooting" technique. These calculations have been coupled to a metallurgical model describing the solid state transformations that occur during both heating and cooling. From the local thermal history, the evolution of the various phase fractions are predicted from TTT-diagrams using an additivity principle. A micro-enthalpy method has been implemented in the heat flow calculations in order to account for the latent heat released by the various transformations. At each time step, the local properties of the material, in particular its magnetic permeability, are updated according to the new temperatures and magnetic field. Special attention has been taken for the description of the boundary conditions associated with the water spraying below the inductor. The heat transfer coefficient has been deduced from the inverse modelling of temperatures measured at various locations of a test piece. This preliminary work has been complemented with measurements of the magnetic permeability of the 42CrMo4 steel from which the workpieces are made. This part of the study also includes dilatometric measurements for the verification of the additivity principle used in the simulation. The model has been applied to three cases of increasing complexity : induction stream heating of a steel cylinder without quenching, stream quenching of a steel cylinder and, finally, stream quenching of a non-cylindrical workpiece. The results of the simulation have been compared with experimental cooling curves, microstructures and hardness profiles. In the second part of this work, the phase transformations that occur in hypoeutectoid steels during heating have been investigated at the scale of the microstructure according to a microscopic approach. Several models have been developed in order to describe the various steps of the austenitisation process : (i) pearlite dissolution, (ii) transformation of ferrite into austenite and homogenization, (iii) grain growth in austenite. In a first approach, each step has been modeled separately. The dissolution of pearlite has been described using a two-dimensional finite element model with a deforming mesh and a remeshing procedure. The diffusion equation has been solved in austenite (γ) for a typical domain representative of a periodic structure of ferrite (α) and cementite (θ) lamellae. The α/γ and θ/γ interfaces are allowed to move with respect to the local equilibrium condition, including curvature effects via the Gibbs-Thompson coefficient. The model has been used to predict the concentration field and the shape of the interface at different stages of the pearlite dissolution. Maps representing the steady state dissolution rate as a function of the temperature and lamellae spacing have been obtained for small values of overheating. The appearance of a non-steady state regime at higher temperature has been discussed. The transformation of ferrite into austenite has been described using a pseudo-front tracking finite volume approach for solving the diffusion equation in a 1D, 2D or 3D domain. At the start of the computation, the volume is made of ferritic particles and austenitic zones resulting from the pearlite dissolution. The model allows to calculate the kinetics of the phase transformation as a function of the temperature and the initial microstructure. Although the comparison of the transformation kinetics with experimental results was quite satisfactory, it appeared that the calculated kinetics were slightly slower. This effect has been attributed to the other alloying elements which are contained in the Ck45 steel used for the experiments. This discrepancy has also been explained by a stereological effect which is due to the calculation in a 2D section instead of a 3D domain as demonstrated by a comparison of 2D and 3D simulations. The austenitic grain growth has been described with two models based respectively on a Monte Carlo technique and a mechanical approach. A methodology for obtaining a correspondence between the simulation time scale and real time has been presented and applied to the Ck45 steel. The value of the exponent n of the grain growth law d = Κ t1/n (where d is the mean diameter and t the time) has been determined for both models. The mechanical model (n=2) turned out to describe perfectly the case of normal grain growth as it occurs in liquid-gas systems. However the results of the Monte Carlo simulation (n=2.3) are in better agreement with the non-ideal behaviour of the Ck45 steel. The influence of the impurities and particles which are present in real materials should be taken into account in both models if a more quantitative agreement is to be obtained. Finally, a combined model coupling the various steps of the austenitisation process has been proposed. It allowed to show that the assumption consisting in dividing the process in three separate steps is valid in most cases. This combined model is a first attempt for a comprehensive modelling of the austenitisation process.

EPFL1997

Measurements and modelling of residual stresses during quenching of thick heat treatable aluminium components in relation to their precipitation state

Nicolas Paul Henry Chobaut

In the fabrication of heat treatable aluminium parts, solutionising and quenching are key steps in order to obtain the required mechanical characteristics. Fast quenching is necessary to avoid coarse precipitation as this one reduces the mechanical properties after heat treatment. However fast quenching gives birth to high residual stresses, which cause unacceptable distortions during machining and can reduce service life drastically. For this reason, plates and forgings such as those considered in this thesis are subjected to a stress relieving operation, removing most of the residual stresses after quenching. For thick products, fast quenching throughout the thickness is no longer possible owing to the high but still limited thermal diffusivity of aluminium alloys, but residual stress occurrence remains problematic. The objective of this work is to develop a comprehensive model of quenching including precipitation effects for understanding the development of residual stresses in thick heat treatable aluminium components. Two industrial contexts are studied in this work: - the cold-water quenching of hot-rolled AA7040 and AA7449 thick plates for aerospace applications, - the boiling-water quenching of large AA2618 compressor wheel forgings used in turbochargers. Besides an accurate knowledge of the thermal field in the components during quenching, this work has involved an extensive thermo-mechanical characterisation of the three alloys in different precipitation states by interrupted quench-tests achieved in a Gleeble machine. Plastic strain recovery at high temperature is considered in a simple way in the description of the material behaviour and the Bauschinger effect is neglected as suggested by dedicated experiments. Three numerical models are developed to predict as-quenched residual stresses: - a thermo-mechanical model ignoring precipitation, - a physically-based thermo-metallurgical-mechanical model where a yield strength model is coupled with a precipitation model, - a thermo-mechanical model accounting for precipitation in a simple but realistic way. Instead of modelling precipitation that occurs during quenching, the model parameters are identified using a limited number of tensile tests achieved after representative interrupted cooling paths in a Gleeble machine. The results are compared to as-quenched residual stress measurements achieved by neutron diffraction and layer removal in thick AA7449 and AA7040 plates and in large AA2618 forgings. The thermo-mechanical model ignoring precipitation is found to be sufficient for relatively thin products. For thicker products, precipitation hardening by small precipitates is found to increase as-quenched residual stresses. Since the thermo-mechanical model ignoring precipitation underestimates these residual stresses, precipitation must thus be accounted for. The second model gives an excellent agreement between measurements and simulations provided that the precipitation model is well calibrated. This physically-based model is necessary for modelling complex parts with different thicknesses. Nevertheless, a lot of effort has to be dedicated to the characterisation and modelling of the precipitation of metastable non-stoichiometric phases and GP zones during quenching. This tedious work is not needed for the third model which requires only a few interrupted quench-tests while giving an excellent agreement between measurements and simulations for all the investigated components. In particular, it is verified that the two models taking into account precipitation give identical residual stress profiles in thick AA7449 plates.

EPFL2015

A miniaturized selective laser melting device for operando X-ray diffraction studies

Nicola Casati, Samy Hocine, Steven Van Petegem, Helena Van Swygenhoven

We report on the development of a miniaturized device for operando X-ray diffraction during laser 3D printing. The printing chamber has a size of only 130 x 135 x 34 mm(3) and is optimized to be installed at synchrotron beamlines. We describe the design considerations, details on the setup and the implementation at two different beamlines of the Swiss Light Source. Its capabilities are demonstrated by ex situ printing of complex shapes and operando X-ray diffraction experiments using Ti-6Al-4V powder. It is shown that the beamline characteristics have an important influence on the X-ray footprints of the microstructural evolution during 3D printing. From the intensity of the diffraction peaks, the evolution of the different phases can be followed during printing. Furthermore, the diffuse scattering signal provides information on the precise location of the laser beam on the sample and the scanning head settling time.