The present work aims at the investigation of residual stresses in a component on several scales. For this purpose, a numerical simulation tool is developed using the Finite Element Method. An essential aspect of this approach, besides the discretization of the geometry to be investigated and the definition of the algebraic system of equations to be solved, is the definition of a suitable material model. The microheterogeneous structure of materials such as steel must be taken into account during the analysis.
Since this work focuses on the numerical investigation of the evolution of residual stresses in hot bulk forming processes of steel components, a model for the representation of occurring phase transformation on the microscale is additionally required. To this end, a single-scale finite element model in combination with its constitutive equations is introduced, which is used to calculate effective material properties and resulting stresses especially during cooling of a hot bulk forming component.
Different cooling routes influence the stress development in the component on all scales. Thus, multi-scale methods are a valuable tool for the analysis of macroscopic and microscopic residual stresses. Subsequently, different representative volume elements are discussed, which are used to describe a phase transformation in a microscopic boundary value problem within a multi-scale finite element method. This approach enables to calculate stresses during the cooling process as well as the final residual stress states at the different scales.