Küresel mikro yapı morfolojili yarı kristal polimerlerin mikromekanik modellenmesi

In this study, a micromechanical constitutive model for semicrystalline polymers is developed. The proposed model considers interactions among the adjacent regions at the same length scale. The neighborhood information is obtained from the well characterized spherulite morphology of polyethylene. Deformation characteristics of a disk-like spherulite model that has similarities with the considered modeling approach are studied using the finite element method. The model discretizes a disk-like spherulite into amorphous and crystalline slices, separated by planar interfaces. Consistent deformation of the amorphous and crystalline phases of semircystalline polymers at the spherulite length scale is the distinctive feature of the model. A three-dimensional spherulite is also modeled, and it is found that the employment of the crystallographic slip as the only plastic deformation mode of crystalline phase leads to plastically soft polar regions in spherulites, and therefore contradicts with the experimental observations. This simplification is employed in all semicrystalline polymer models that we are aware of in literature. In order to obtain a simplified disk-like spherulite model, a set of methods that consider the neighborhood information is developed by extending the rank-1 laminates to support an arbitrary number of lamination directions. The equilibrium and compatibility conditions are not exactly satisfied together on the interfaces, as a consequence of the uniform strain field assumption of rank-1 laminates. The methods are consistent averaging schemes, and satisfy the Hill's energy criterion and the separation of length scales principle. According to these qualities, they could be employed in micromechanical constitutive models. Disk-like spherulite and twisted lamellar microstructure of the spherulites are modeled with the methods. Approximately transversely isotropic responses are obtained in the disk-like spherulite, and a desired tension-compression asymmetry is observed in the twisted lamellar microstructure model. Additionally, without uniform strain field assumption, another simplified disk-like spherulite model is obtained by connecting non-parallel rank-1 laminates with compatible strain fields in cylindrical coordinates, which may enable application of non-local constitutive models in rank-1 laminates. The disk-like spherulite models are considered as the analogous of the symmetric crystals with many common slip systems that are known to be good candidates for Taylor-type homogenization. A constitutive model for high density polyethylene is obtained with Taylor-type homogenization of randomly oriented realizations of the disk-like spherulites, where the elasto-viscoplastic constitutive models of the phases and their parameters are adopted from the literature. The stress-strain response and texture evolution of the model are in line with the literature. An attempt to obtain a micromechanical constitutive model for ultra high molecular weight polyethylene is also presented, and the influence of surface texture on the friction coefficient is studied using the finite element method and a constitutive model from literature.