Estimation des contraintes internes dans les pièces composites imprimés par dépôt de filament polymère

This thesis deals with the study of residual stresses in a polymer matrix composite part obtained using the High Temperature Fused Deposition Modeling (HT-FDM) manufacturing process. This type of 3D printing uses high performance polymers as the primary material. During the printing process, several types of defects are observed due to the strong thermal gradient that the part under construction undergoes, generally representing the lack of dimensional accuracy with respect to the 3D model used to encode the printing paths. This distortion is in fact a residual deformation associated with residual stresses in the part in response to the temperature distribution during printing until each point of the material reaches room temperature.

Estimating residual stresses in a printed polymer composite is not trivial because the material contains multiple scales of heterogeneity. If we want to treat the multiscale problem in a deterministic way using a generic computational method such as Finite Element Analysis (FEA), we observe that the phenomenon of scale separation imposes characteristic mesh sizes that are beyond the scope of a reasonable computational approach in terms of time versus current computational resources, and in such an approach we have to take into account that the cost of simulations increases exponentially due to the total volume of the part studied. For this reason, we propose a methodology based on homogenization in the mechanics of materials \cite{Bornet01, Mura1987, milton2002theory} to trace back to the macroscopic behavior, which allows to consider the printed part as represented by a continuous model that, at the scale of the observer, behaves equivalently to its heterogeneous counterpart, which we treat through a two-stage homogenization methodology.

The first scale, the microscale, is treated using a mean-field homogenization method described in a previous publication by the authors \cite{Suarez22_1}, where the estimation is obtained by extending conventional mean-field homogenization methods (derived from the Eshelby problem in the context of thermoelasticity) using the extension of the correspondence principle \cite{Mandel66} in continuous temperature variations for a thermo-viscoelastic material known as \textit{thermorheologically simple}, and using a probabilistic description of the microstructural parameters associated with the fibers. It should also be mentioned that we have dedicated a chapter to the estimation of the effective behavior in the case of \textit{thermorheologically complex} materials by a model reduction technique of the mean-field homogenization problem being already published in \cite{Suarez2023}. The mesoscale is treated by a full-field numerical homogenization method based on conventional finite elements, the calculation of the effective thermo-viscoelastic properties is carried out by steady-state dynamic simulations over a frequency space relevant to the part's operating conditions of the part, and then undergoes an identification procedure according to \cite{JALOCHA15}, which maintains a conventional representation of the functions characterizing the material's response in an experimental identification context.

After checking the quality of the approximations obtained with purely numerical comparisons, we compare what we have obtained with physical reality. The reference experiment is that of cooling a thin plate obtained by superimposing unidirectional printing layers, the orientation of the layers being [0,0,90,90]. The part is cooled in the printing chamber and the deflection of the plate is measured, as a consequence of the temperature evolution and the asymmetric distribution of the porosities aligned in the printed layers. The objective is therefore to predict the plate deflection using a numerical model with properties obtained using the methodology proposed in this thesis. Since we are confronted with reality, several experimental measurements have been carried out to identify the necessary parameters, as well as microtomographic analysis of the two characteristic scales.