Computational Multiscale Modeling of Pearlitic Steel

Licentiatavhandling, 2012

The objective of this thesis is to investigate the possibilities to describe the mechanical behavior of a pearlitic steel by using computational homogenization, or multiscale modeling. The proposed model contains three scales: the engineering macroscale, the mesoscale representing the colonies of the pearlite and the microscale containing the individual cementite lamellae and the ferrite matrix. On the mesoscale of a pearlitic steel, two constituents can be identified in the form of cementite lamellae embedded in a ferrite matrix. These lamellae appear in domains, referred to as colonies, within which the corresponding orientation is ideally constant. The different domains, with their cementite (morphological) orientations but also with their crystallographic orientations of the ferrite, are homogenized in the modeling to obtain a macroscopic behavior of the pearlite. In the appended papers, different orientation distributions have been assumed and their influence on the macroscopic response has been studied. In addition, the number of orientations that should be included in the mesomodel to obtain a representative response has been investigated. To capture the mechanical behavior of the constituents and their orientations, the mesomodel is linked to a micromodel using different prolongation conditions (both Taylor, Dirichlet and periodic). In the micromodel the ferrite is modeled by using crystal plasticity while the cementite is assumed to behave elastically. The micromodel is rotated depending on what cementite lamella orientation/colony it should represent. In addition, the crystallographic orientations of the ferrite are chosen depending on what colony that is modeled. The influence on the macroscopic response of the size of the micromodel and the prolongation condition from the mesomodel to the micromodel has been examined. A number of numerical examples are presented within the appended papers illustrating the overall possibility of using the proposed multiscale model to predict the behavior of a pearlitic steel. In particular, both 2D and 3D models are used to show different sources of anisotropy. Finally, it is shown how the proposed multiscale model can be used to predict macroscopic yield surfaces.