Computed tomography-based modeling of structured polymers

Because of their excellent specific strength and energy absorption properties, polymeric foams find their application in a wide range of engineering areas. Their specific mechanical response results from a subtle interplay between the intrinsic material response of the polymer base material and the complex microstructure related to their process history. In order to optimize foam products, the macroscopic mechanical response of foams should be predictable for multiple and mixed loading conditions. In other words the central question concerns the extent to which the structure of a foam and the material constituting the structure contribute to the final properties. To address this topic an understanding of the underlying deformation and failure mechanics is required. In this thesis an approach which combines X-ray Computed Tomography (CT) and Finite Element (FE) simulations is evaluated. X-ray CT is a technique that enables the detailed description of the foam’s microstructure up to a resolution of 1 µm. The first part focuses on the effects of modeling structured polymers, i.e. honeycomb and foam structures, with this technique. A regular honeycomb structure is modeled with a perfect RVE exposed to periodic boundary conditions and compared with a model based on CT-images exposed with symmetry boundary conditions. A nonlinear elasto-viscoplastic constitutive model is used to describe the intrinsic response of the polycarbonate base material. The highly non-linear response of the structure is captured and contact phenomena in the large strain regime, leading to densification, are incorporated. The comparison with a fully hyper elastic description of the base material revealed that the mechanical response can be explained in terms of a rate dependent onset of plasticity, causing a deviation from a non-linear elastic response. A discrepancy between the ideal RVE and CT model is assigned to the absence of imperfections in the ideal RVE compared with the more realistic CT model. To study the influence of the irregular microstructure in case of X-ray CT-based moddeling on the predicted mechanical response, an irregular closed-cell foam structure is characterized and converted into a 2D FE model where the model size (number of cells in the model) and discretization (number of elements over the thickness of a cell wall) are varied. The results show that, in case of an elastic material response, the RVE-model should contain a minimum of 12 cells to correctly represent the bulk mechanical response. On the other hand, the influence of discretization show a stiffening of the response when increasing the element size in the small strain regime. When the element size becomes larger than the size of the smallest details, this results in loss of local connectivity and stiffness reduction. The applicability of the developed micromechanical modeling is demonstrated on a Rapid Prototyped (RP) foam structure. This foam structure, based on the scaled-up microstructure of a real foam, is created using stereo lithography RP. The RP structure is characterized with X-ray CT and converted into a FE model, based on quadratic tetrahedral elements. For proper characterization of the base material, compression samples are made with RP and the intrinsic response is determined just above its glass transition temperature Tg. The mechanical response of the RP structures is experimentally characterized at different temperatures and strain rates. FE simulations are in good qualitative agreement with the experimental observations. Although the mechanical response is over predicted by the FE simulations, it is demonstrated that this is likely to be related to small temperature variations. Also for the RP structures a comparison with between a hyperelastic and viscoplastic description of the base material revealed that due to rate dependent plasticity the response deviates from a non-linear elastic response. Finally, the mechanical response of an open-cell polyurethane foam is determined with the microstructural simulations in five loading conditions: uniaxial compression and tension, simple shear and hydrostatic compression and tension. In uniaxial loading the response corresponds to the experimental results in the elastic regime, where the deviation beyond this regime is due to the viscous response of the foam. Similar to elasto-viscoplastic foams, it is believed that the response to loads at different rates, approaches the hyperelastic response for high strain rates and that the viscous behavior at low strain rates originates from the base material. The typical volumetric response is analyzed using compression and tensile experiments and 3D FE simulations on a microstructural level. In compression, the volume decreases and the apparent Poisson’s ratio decreases gradually from 0.3 to 0. This mechanism is confirmed by in-situ compression experiments and FE simulations. The microstructural origin is bending of cell struts followed by the collapse of the foam’s microstructure through buckling. In tension, however, an increase of the volume is found up to a maximum, after which it decreases as well. The microstructural simulations show that this decrease is related to buckling of the struts oriented pendicular to the loading direction. Based on the experimental observations and the X-ray CT-based FE simulations, three macroscopic hyperelastic constitutive models are tested on their ability to describe the non-linear elastic response as well as the volume response of the foam in the five loading conditions. The main conclusion is that existing macroscopic models are of limited use. Since none of them is able to describe hydrostatic loading situations and, as a consequence, also behave moderately in shear, they all lack predictive power in more complex loading situations. The importance of including all loading conditions for material parameter fitting is clear, when compared to only incorporate the data of uniaxial compression, resulting in a significantly over predicted response in shear.