Section 6: Material modelling in solid mechanics - GAMM 2012

Section 6: Material modelling in solid mechanics 13
Heat treatment is an indispensable part of the manufacturing of metallic products, especially in
powder coating process. It provides an efficient way to manipulate the properties of the metal as
e.g. hardness, yield stress and tensile stress by controlling the rate of diffusion and the rate of
cooling within the microstructure.
The process-integrated powder coating by radial axial rolling of rings is a new hybrid production
technique which is introduced in [1]. It takes advantage of the high temperatures and high
forces of the ring rolling process not only to increase the rings diameter, but also to integrate
the application and compaction of powder metallurgical multi-functional coatings to the solid
substrate rings within the same process [2]. The applied temperatures in hot rolling are within
the range of austenitizing temperatures for the investigated steels. Therefore, controlled cooling
can be conducted directly from process heat subsequent to the deformation process.
The talk is concerned with the finite element (FE) simulation of the process-integrated powder
coating by radial axial rolling of rings and the integration of heat treatment of the rolled ring
into the subsequent cooling process. Finally parameter studies are performed to analyse the
temperature profile and phase transformation in the rings cross-section.
[1] J. Frischkorn, S. Reese, Modelling and Simulation of Process-integrated Powder Coating by
Radial Axial Rolling of Rings, Archive of Applied Mechanics 81 (2011)
[2] R. Kebriaei, J. Frischkorn, S. Reese, Influence of Geometric Parameters on Residual Porosity
in Process-integrated Powder Coating by Radial Axial Rolling of Rings, Steel Research
International 163 (2011)
Simulation of phase-transformations based on numerical minimization of intersecting
Gibbs energy potentials
Richard Ostwald, Thorsten Bartel (TU Dortmund), Andreas Menzel (U Dortmund / Lund University)
We present a novel approach for the simulation of solid to solid phase-transformations in polycrystalline
materials. To facilitate the utilization of a non-affine micro-sphere formulation with
volumetric-deviatoric split, we introduce Helmholtz free energy functions depending on volumetric
and deviatoric strain measures for the underlying scalar-valued phase-transformation model.
As an extension of affine micro-sphere models [3], the non-affine micro-sphere formulation with
volumetric-deviatoric split allows to capture different Young’s moduli and Poisson’s ratios on the
macro-scale [1]. As a consequence, the temperature-dependent free energy assigned to each individual
phase takes the form of an elliptic paraboloid in volumetric-deviatoric strain space, where
the energy landscape of the overall material is obtained from the contributions of the individual
constituents.
For the evolution of volume fractions, we use an approach based on statistical physics—taking
into account actual Gibbs energy barriers and transformation probabilities [2]. The computation
of individual energy barriers between the phases considered is enabled by numerical minimization
of parametric intersection curves of elliptic Gibbs energy paraboloids. The framework provided
facilitates to take into account an arbitrary number of solid phases of the underlying material,
though we restrict ourselves to the simulation of three phases, namely an austenitic parent phase
and a martensitic tension and compression phase. It is shown that the model presented nicely
reflects the temperature-dependent effects of pseudo-elasticity and pseudo-plasticity, and thus
captures experimentally observed behaviour at different temperatures.