Multiscale Constitutive Modeling of Heterogeneous Engineering Materials

Sammanfattning: This work deals with different methods used to determine heterogeneous constitutive model parameters for macro-scale finite element models, based on microstructural variations, caused by the manufacturing process. These methods could be applied to decrease modeling errors associated with the material behavior, improving the predictive capabilities of structural analyses in simulation-driven industrial product development. By providing engineers with more sophisticated tools and methods which lets them consider the complex relationships between the manufacturing process, the resulting microstructure and the final properties, manufactured components have the potential to be further optimized with respect to both weight and performance, reducing their cost and environmental impact.An empirical approach for cast components is presented in Papers I & II, where material testing is used as a basis for constitutive model parameter extraction via optimization. Linear models were created for both thermo-mechanical and thermo-physical material properties, by characterizing specimens extracted from different regions in a lamellar graphite cast iron cylinder head. These models were used to generate heterogeneous constitutive model parameters for the cylinder head, based on the solidification time as predicted by casting process simulations. The influence of several commonly made casting-specific engineering simplifications were investigated, and it was shown that non-trivial errors of a potentially large magnitude are introduced by not considering e.g. the compressive behavior of the material, residual stresses from the casting process, the temperature dependency of the material, or the process-induced heterogeneity.Paper III describes a statistical homogenization-based method, for modeling of anisotropic fiber reinforced materials. A non-linear anisotropic constitutive model was developed and implemented in commercial finite element codes, which is able to consider heterogeneous fiber orientations using only one material definition. The anisotropic elastic constitutive tensor is determined from fiber-matrix homogenization, and orientation averaging using second- and fourth order fiber orientation tensors provided by injection molding simulations. The plastic constitutive parameters are determined by optimization against experimental tensile tests using specimens with different fiber orientations. The method was demonstrated using a injection molded 50 wt.% short glass fiber reinforced plastic.A pixel/voxel-based method is presented in Papers IV (2D) & V (3D), for simple and efficient generation of reduced numerical microstructure models using imaging data as input. The input micrograph or image stack is split into subdomains, which are evaluated individually using numerical or semi-analytical homogenization. The constitutive tensor of each subdomain is mapped to a new, reduced numerical model. The purpose of this approach was to support component level analyses, by representing process-induced microstructural imperfections like e.g. porosity on the macro-scale, in a computationally efficient way. The geometrical description of the microstructure can be retrieved from experimental imaging methods like Scanning Electron Microscopy (SEM) or X-ray based Computed Tomography (CT). Alternatively, it can be approximated from phase field or manufacturing process simulations. The method was demonstrated by reducing a 2D aluminium micrograph by 99.89%, with material property errors of less than 0.5% in Paper IV. Also, in paper V by reducing a complex high-resolution 3D aluminum shrinkage porosity by 99.2%, with a material property error of approximately 1%. The method significantly reduces the complexity of building finite element models of complex microstructures, where the pre-processing step is replaced by image segmentation.