Formability of polycrystals on the macroscale is defined by deformation and damage mechanisms on the microscale. While micromechanical deformations, e.g. those resulting from dislocations, can be sufficiently modeled by crystal plasticity formulations for many applications, the incorporation of damage in polycrystals on the microscale has not yet been widely discussed in the literature. This is especially true for the interaction of plastic deformation and damage mechanisms. However, this interaction is fundamental in order to understand, quantify, and ultimately control the relevant macroscopic behavior of polycrystals – here, using the examples of the dual phase steel DP800 and the case-hardening steel 16MnCr55.

In the present project an extended crystal plasticity model is to be developed. In this extended theory the consistent integration of material degradation into plasticity theory will be elaborated. One of the main tasks is to model damage only as accurately as necessary to provide for a numerically efficient scheme. This can only be accomplished in close collaboration with material characterization on the microscale. For the coupling of crystal plasticity and damage models, equivalence principles will be applied (e.g. principle of energy equivalence). In a second step, the coupled model will be formulated using variational principles (incremental energy minimization) to render the possibility of developing an efficient finite-element implementation using so-called variational constitutive updates.

The damage on the macroscale is, on the one hand, influenced by damage mechanisms inside the grains. On the other hand, it is influenced by relative slip at the grain boundaries (e.g. separation of grains). To incorporate the latter damage mechanism, suitable interface models are to be developed and implemented. Due to the expected finite deformations, this task is far from trivial. To name one major issue, classic cohesive zone elements in a geometrically exact formulation neither fulfill the conservation law of angular momentum nor the second law of thermodynamics. Analogously to the intra-grain damage model, the development of the inter-grain cohesive zone model can only be realized in cooperation with partners from material characterization. The interface model will also be embedded into a variationally consistent implementation on the basis of incremental energy minimization.

Interface elements for modelling damage at the grain boundaries

Using the described material models, finite-element-models of representative volume elements (RVEs) are generated – again in collaboration with material characterization – and numerically analyzed. This serves at two purposes: The validation of the developed material model and the quantification of influence of damage mechanisms on the microscale on the macroscopic behavior. This, in turn, is relevant for the development of macroscopic constitutive models. Furthermore, the dependence of load-paths on the damage evolution can be investigated – on the microscale as well as on the macroscale. Based on these investigations, optimal load paths can be identified, which is of utmost importance for the actual technological process.

 

 

 

 

 

 

 

 

Simulated textur evolution of an initially
quasi-isotropic RVE of a polycrystal
under simple shear stress

Project leaders
Jun.-Prof. Dr.-Ing. Sandra Klinge
Institute of Mechanics (IM), TU Dortmund University

Prof. Dr.-Ing. Jörn Mosler
Institute of Mechanics (IM), TU Dortmund University

Project coordinator
Volker Fohrmeister M. Sc.
Institute of Mechanics (IM), TU Dortmund University