ABSTRACT of the Doctoral Thesis
Even though they have been commercially important for several decades heterogeneous nonlinear materials such as highly alloyed steels and light metal alloys are at present still not fully understood with respect to their material behavior at length scales much smaller than those of typical samples or components. Especially "limit" material properties such as the overall strength and fracture toughness are strongly influenced by the morphological situation found in the material under consideration. Due to the complexity of the material morphologies particularly of such "natural" composites, standard micromechanical material descriptions are of limited suitability for predicting the overall material response to statically applied thermomechanical overall loads. In the present work these difficulties are overcome by developing continuum mechanics based multiscale modeling approaches that can account explicitly for rather complex material morphologies in an appropriate way.
First some principal notes on the research field of Micromechanics of Materials are given, and some analytical methods are discussed that can be used as constitutive laws for inhomogeneous materials. Using these, a semi--analytical incrementally formulated mean field based constitutive law, i.e. a mean field based version of the Transformation Field Analysis (M/TFA), for thermoelastoplastic multiphase composites is developed which is implemented in a Finite Element code as a material description at integration point level. The applicability of this method is verified by performing material characterization of continuously reinforced metal matrix composites under various loading conditions and comparing the results to those obtained with another incremental mean field method and to Finite Element based periodic microfield approaches. The M/TFA model is then used to study mesoscale unit cell models containing inclusion clusters, which represent real material structures typically found in high speed steels produced by electro--slag remelting. Results obtained by this hierarchical approach are compared to predictions from another multiscale model based on statistical micromechanics as well as an advanced periodic microfield approach, both of them accounting explicitly for generic graded phase arrangements in the materials under investigation. This way insight can be gained into local phenomena such as fluctuations in local stress and strain fields as well as initiation and evolution of local damage in nonlinear multiphase materials.