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Modelling is the mathematical description of various natural processes, be it thermophysical (e.g. heat transfer), chemical (e.g.combustion), or mechanical (e.g bending of a component). The aim of a modeling activity is to calculate output parameters and the development of these parameters with time, to both describe experimental observations and predict behaviour. The model output can be an analytical or numerical solution (which depends on the set of equations that are available to describe the process). Therefore, formal descriptions have to be developed that approximate a real process as close as possible. This is the basic work during modelling, which always involves alternating simplification and optimization approaches. Output parameters that are of interest in in the IP Nanoker project are: electric current density in advanced sintering technologies, component temperature, induced and residual stress, thermal spray particle properties, atomistic description of ceramic microstructures and grain boundaries. The processes modelled in IP Nanoker are not only manufacturing processes but also physical processes, like transmittance of light through matter, which are related with material properties.
Simulation is the application of these models to produce information about process results or component behaviour under specific parameters or conditions that represent possible variations in the real process. Therefore, a simulation calculation is also called a simulation experiment as various conditions can be explored by calculation as in experimental approaches.. By using specific parameters during simulation, the results can be compared with experimental results, and thus, the model can be validated in a specific parameter region and can be refined and optimised so that it describes as closely as possible the experimental data. Models that have been proven to represent the real world with adequate accuracy can be used for parameter variation in order to save time and material and, of course, cost. In this sense, modelling and simulation is a very valuable tool for process development and research, where large numbers of parameter variations are applied and compared to each other. It also enables to very specifically change single parameters and analyse their effect on the process or material, whereas in real experiments, parameters often interact and show strong interdependency. Moreover, simulation results often contain information that can not be measured experimentally, e. g. because process times are too short, temperatures are too high, systems are encapsuled, or the system dimensions are too small for observation of any phenomena during real manufacturing processes (e. g., processes on the atomistic scale). That means, modelling and simulation activities in science and technology aim at a fundamental understanding of processes and mechanisms in order to guide experimental work.
In IP Nanoker, modelling and simulation is characterized by strong cooperation between the modelling scientists and the groups working on process development, manufacturing engineering, and materials characterisation. Modelling work was planned in order to provide additional information from simulation experiments about the processes and materials to enable the development of materials with new or adapted manufacturing processes and with optimized material properties. Therefore, objectives defined at the beginning of the project were:
- Modelling of particle interaction and manufacturing processes
- Modelling of sintering processes
- Experimental measurement of material properties
- Model verification and simulation experiments; feedback into processes
- Modelling of component behaviour
The guideline for these objectives were practical, taking into account a typical project development during a 3 or 4 year period, which very roughly consists of basic research, transfer towards application and finally optimization. In terms of modelling and simulation, an analogical path would consist of modelling, model verification and improvement, simulation experiments, and transfer of simulation results into process development or industrial process optimisation. That means, in order to help experimental process development with simulation results, basic research has to be performed at the same time in both kinds of groups (experimental and simulation) in order to be able to verify models with the first experimental results and then, during the transfer of processes into application, the use of information from parameter variation in simulation experiments. The first two objectives reflect the basic modelling work that is curently being done at the academic research institutions (with sintering modelling as a separate task because it started later than powder processing but is performed by a number of groups working with different methods). The next two objectives are performed with a close collaboration between academic scientists working on both modelling and experimental process development together with industrial partners that support process development. Modelling of component behaviour is mainly performed by industry during optimization of component design, taking into account results from process optimization and material properties measurements.
The modelling projects launched in the first 18 months of IP Nanoker were mainly related with the open questions that occur during the processing of nano sized powders when compared to standard micron scale materials (grain size effect) and with basic process models, e. g. the spark plasma sintering process or thermal spray processes. These different modelling approaches are listed in table 1, including the modelling methods that are being applied for the different topics.
Tab. 1: Overview about process modelling activities in IP Nanoker
|
modelling approach / research area |
modelling method |
| Colloidal stability of suspensions, taking into account spherical particles’ overall interaction energy depending on a large number of suspension parameters |
analytical calculation based on the DLVO model and others |
| Optical transmittance (real in-line transmittance) of ceramics depending on wavelength, grain size, pore / second phase volume fraction and size distribution, and dopant segregation |
analytical calculation based on extended mean field model + coated sphere model |
| Atomistic diffusion coefficient calculations |
metadynamics |
| Grain boundary and surface segregation of yttrium, magnesium and lanthanide dopants in alumina and of neodymium in YAG |
atomistic energy minimisation techniques |
| Analysis of grain size for optimized laser efficiency |
analytical model based on atomistic data |
| Temperature and stress distribution in nano coatings during deposition with atmospheric plasma spraying (APS) |
finite elements (FEM) |
| Particle in-flight properties during thermal spraying of nano coatings with the high-velocity suspension flame spraying (HVSFS) method |
finite volumes (CFD) |
| Fluid-structure coupling at spray jet / coating interface to analyse heat, mass and momentum transfer during coating deposition with HVSFS |
finite elements / finite volumes |
| Geometries of injection nozzle, combustion chamber and expansion nozzle for HVSFS |
finite volumes (CFD) |
| Optimization of sintering programmes (temperature-time-profile) for pressureless sintering (e. g. rate controlled sintering) |
thermokinetic modelling based on dilatometry data |
| Current density, temperature, and pressure distribution during SPS processes |
finite elements (FEM) |
| Tool design (punch and die) for SPS processes |
finite elements (FEM) |
| Sintering of complex shapes for dental applications by SPS, HIP, and pressureless sintering with minimal geometry distortion and homogeneous microstructure |
finite elements (FEM) |
In some cases of the modelling problems listed in table 1, mathematical descriptions or sets of interacting mathematical formulations exist that can be solved analytically, although there may be large numbers of parameters that can be varied. In this case, special simulation applications can be created, applying a user interface for definition of the parameters and a system of equations that is solved by the application depending on these parameters. Examples are the Hamaker software for colloidal stability calculation of suspensions and the GB Optics software for calculatioin of the real in-line transmittance of transparent ceramics. Both applications were written in Java for user -friendliness, see figure 1.
Fig. 1: GB Optics programme; real in-line transmittance of alumina depending on grain size (Uli Aschauer, EPFL)
However, most process descriptions include non-linear equations that have to be solved numerically and with large computational effort. One example are atomic scale problems like dopant segregation which are solved by atomistic simulation. Thereby, the lowest energy arrangement has to be calculated from interatomic potentials for all possible surface terminations and different interface concentrations of dopant ions. This is achieved by calculating a large number of configurations in order to find a global minium in energy. An example for a mirror twin grain boundary exhibiting a minimum energy configuration in the Nd:YAG system is given in figure 2. Atomistic simulations yield predictions on the proportion of dopants that segregate from the bulk to the surfaces and grain boundaries as a function of the population of surfaces and interfaces present in the powder or ceramic. These data are relevant for the optical properties of materials, like transmittance or laser effciency, for the creep resistance of materials, and for the choice of the powder and the sintering technique, because dopant segregation kinetics are governed by sintering conditions. Along with atomistic simulations, an extended molecular dynamics scheme called metadynamics is used for the simulation of diffusion coefficients, which will allow the simulation of grain boundary diffusion in different doped environments, and thereby, be a valuable input parameter for sintering simulations in the future.
Fig. 2: Nd dopant segregation in YAG (Al = blue, Y = dark green, O = red, Nd = light green); most stable doped mirror twin grain boundary (Uli Aschauer, EPFL)
On the macroscopic scale, the interesting process parameters for analysis and planning of sintering processes are temperature and pressure distribution in the green body for fast sintering processes (SPS) as well as mass loss and sintering activity of the material for pressureless sintering. The latter can be modeled by a mathematical approximation of experimentally measured data from thermal analysis (dilatometry and DTA/TG) for the definition of optimized temperature/time profiles that lead to uniform mass loss and shrinkage as well as controlled densification (and thus, avoiding early closure of pores before the volatile fractions are removed).
Simulation of the current density, temperature and pressure distribution during SPS processes is aimed at providing spatial information that depend on the geometries of tools and components. Therefore, the tool/component system is modelled as a multi continuum body system with the finite element method (FEM). There are a number of commercial software packages for the design, discretization, numerical solving, and post-processing of thermophysical, electrophysical, or mechanical problems with finite elements. An example for a system containing an alumina pellet, a die, and punch with the electrical current density distribution in different cross sections of the system is given in figure 3. This modelling approach can be used for easy calculation of parameter variations (e. g., different punch pressure or heating current) as well as analysis of the effect of geometry on the distribution of pressure and temperature in the sample.
Fig. 3: Current density distribution (max. red: 1.6×107 A/m2; min. blue: 0 A/m2); SPS system (alumina pellet, die, and punch) finite element model (Zhao Zhe, USTOCK)
The last field, in which intensive modelling activities are carried out in IP Nanoker, is the deposition of nano coatings by thermal spray techniques. Here the modelling of the heat and mass transfer processes and the particle behaviour in the flame or plasma during thermal spraying can yield a variety of beneficial effects on process development and optimisation. This then can be used to improve the properties of the manufactured coatings. Thermal spray processes in general can be divided in two main sections, which are the spray jet and the coating/substrate system. Due to the nature of the physical processes involved, the spray jet is described by computational fluid dynamics (CFD) which is based on the finite volume method, and the coating/substrate system is approximated as a continuum by finite elements during the modelling.
The CFD approach couples the processes of energy transfer from the fuel gases to the spray jet by combustion and energy transfer from the expanding combustion gases to the spray particles by solving the respective partial differential equations (combustion process and Navier-Stokes equations of the gas and the particles with turbulent flow model). Figure 4 shows the computational domain of the HVOF process model, which is an axisymmetric problem, and therefore, enables reduction of the computation time by solving only a section of the full spatial process extent. Fluid dynamics calculation yields the particle properties, i. e. velocity and temperature, at the time of impact on the substrate. These data are used as process inputs (thermal, momentum) in FEM modelling of the coating build-up. The finite element approach is suitable for simulation of temperature distribution in the component during the coating process as well as development of thermal residual stresses which can have a large influence on the coating properties. Microscopic finite element modelling of thermal spray coatings can lead to prediction of fracture behaviour and coating adhesion. However, this is not part of the current work in IP Nanoker.
Fig. 4: Computational domain (3D symmetrical segment) of HVOF/HVSFS process model including combustion chamber, expansion nozzle and free jet (Esther Dongmo, USTUTT)
At the current state of work in IP Nanoker, the process models described are evaluated by comparison with experimental results. The experience coming from this work will be used for improvement of the models and furthermore, in closer cooperation with the industrial partners in the project, for optimization of the respective manufacturing processes. Future work on modelling will also include further contributions of the industrial partners in terms of finite element modelling of components’ behaviour under operational conditions. |