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Reference : UMR7649-DANWEI-001
Workplace : PALAISEAU
Date of publication : Friday, June 4, 2021
Scientific Responsible name : Daniel Weisz-Patrault, Grégoire Allaire, Jean-Yves Hascoet
Type of Contract : PhD Student contract / Thesis offer
Contract Period : 36 months
Start date of the thesis : 1 September 2021
Proportion of work : Full time
Remuneration : 2 135,00 € gross monthly
Description of the thesis topic
A- General objective
Process parameters in additive manufacturing have a significant influence on the microstructure and residual stresses . The objective of this PhD is to propose an optimization strategy of process parameters in directed energy deposition additive manufacturing (DED), which enables us to minimize the fabrication time and ensures that residual stresses remains limited during the fabrication and at the final stage of the process. To do so, we propose to use already existing fast thermal simulations of the process and to develop a new unidimensional multi-thread mechanical model for the efficient computation of residual stresses. On this basis, an optimization strategy will be proposed and tested on real parts printed by DED.
B- State of the art
1- Numerical simulation of DED and WAAM processes
For numerical simulation of additive manufacturing processes the most common approach is to develop very comprehensive simulation with a particular focus on the melt pool at the mesoscopic [2-5]. These approaches provide very rich information and enable to accurately quantify residual [6- 9]. The main drawback of such approaches is their computation. Indeed, the computation cost is so high that a single track of a few centimeters can only be simulated in most cases, which hinders the development of parametric studies enabling to correlate process parameters and residual stresses in the entire part body.
Regarding thermal aspects, recent works in LMS enable to release this usual limitation and give the possibility to consider more complex geometries with arbitrary laser paths . Furthermore, in-situ measurements enabled to validate this results for various conditions.
2- Constrained optimization for additive manufacturing
Within the framework of selective laser melting additive manufacturing a few optimization of the laser path in order to minimize the fabrication time under the constrain of a maximal temperature have been proposed on the basis of different thermal models (steady state of unsteady state) [11, 12]. Furthermore topologic optimizations (part shape)  or substrate shape  enabled to reduce residual stresses. An optimization strategy to minimize residual stresses has also been proposed . These works rely on the optimization of only a few layers because of the computation cost. However, few studies have been conducted for DED or WAAM with thin-walled structures, for which the computation of residual stresses on a large number of layers is needed because of buckling issues. This issue makes necessary the development of very fast simulation tools in order to make the optimization possible.
C- Proposed works
1- Adapt the existing model for constrained optimization
All strategies of process parameters optimization necessitate predictive simulations of temperature kinetics in order to quantify residual stresses in the entire part. This PhD relies on an existing model which is sufficiently fast at the scale of the entire part. However, this model has not been developed by aiming an efficient optimization scheme. One issue is therefore to adapt this existing model so that it can be used not as a black box but in such a way that we can exploit the equations that are solved in order to accurately compute the minimization function gradients.
2- Fast multi-thread model for residual stresses
This PhD also relies on the development of a mechanical model at the scale of the entire part in order to compute residual stresses on the basis of the temperature kinetics obtained from the existing model. Most common approaches rely on FEM in 3D or in 2D, which is computationally costly, because meshes of very thin to discretize the layer height (around 0.2mm). An alternative approach is to develop 1D multi-thread models discretize with FEM. Such models are not limited by the layer height, which becomes a model parameter that does not drive the choice of the mesh size. On the other hand, such a 1D model should be enriched to be sufficiently representative of the stress field complexity, and have therefore more degrees of freedom per node. However, we can show that the gain on the mesh size widely exceeds the addition cost due to the additional degrees of freedom. The coupling between thermal and mechanical problems is done as follows. First the temperature history is computed, which enables to compute at each time step a field of thermal expansion. Then, the mechanical problem is solved with an imposed strain (eigenstrain) composed of the thermal expansion.
3- Adjoint state for the optimization
In order to include thermal and mechanical models in the optimization scheme, it is necessary to compute the minimization function gradient. Since all equations to be solved are available, one can establish an adjoint state problem in order to compute the gradient. Thus, a problem should be solved in addition to the mechanical problem. This adjoint state problem will inherit of the 1D multi-thread structure of the mechanical model so that the computational cost remains limited.
The thesis will mainly take place at the École Polytechnique in the solid mechanics laboratory (LMS) and in the Applied Mathematics Center of the École Polytechnique (CMAP). Trips to GeM at École Centrale Nantes are planned.
Constraints and risks
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