Entwicklung und Validierung einer skalenüberbrückenden Methode zur Beschreibung von Verformung und interkristallinem Bruch in Molybdän
Final Report Abstract
Ductile fracture comprises the very localized event of bond stretching and ultimate breaking, the strength of which can be accurately assessed by ab-initio electronic structure calculations. However, a major point of concern in the simulation community is that the substantial computational effort involved in determining corresponding traction–separation laws prohibits the sampling of the many different microstructural features found in a real microstructure. Furthermore, experimentally measured fracture strengths can so far only be “predicted” by continuum models of plasticity if the traction–separation law is (arbitrarily) rescaled to mimic local stress concentrations. Both these obstacles have by and large been overcome by the developments in our project. First, we could show that sampling the grain boundary parameter space of different geometries or chemical compositions is actually not as time consuming as feared, since the tensile behaviour of (structurally or chemically) different materials obeys a scaling law in the spirit of the universal binding energy relationship (UBER). This means that only three equilibrium properties of an interface or single crystal plane are necessary to obtain the full traction–separation law for interplanar decohesion, which drastically reduces the computational effort to establish a corresponding database by ab-initio methods. Second, taking the example of a pre-existing crack, we could demonstrate that consideration of actual dislocation flux in a (then non-local) continuum model results in dislocation depletion around the crack tip leading to a strong stress concentration with peak values for the atoms immediately ahead of the crack reaching the theoretical fracture strength determined ab-initio. The latter effect cannot be observed for (classical) crystal plasticity models that are formulated in a purely local fashion, that is, neglecting dislocation transport through the crystal. We could further demonstrate that the presence of a grain boundary in the non-local simulations decisively influences the ability of a micro-beam to accommodate plastic strain such that the simulations predict fracture for the bicrystal while not for the singlecrystal; this is in agreement with results obtained from micro-beam bending experiments. In summary, the direct combination of ab-initio calculated traction–separation laws with a continuum model of plastic deformation seems now feasible, but only with a crystal plasticity model that captures the dislocation transport inherent in plastic deformation.
Publications
- Ab-initio investigation of the influence of C on the mechanical properties of the sigma- 5 symmetrical tilt grain boundary in Mo. European Congress on Advanced Materials and Processes, Montpellier, France, 12.–15.09.2011
A. Tahir, R. Janisch, A. Hartmaier
- Dislocation flux in three-dimensional crystal plasticity. 9th International Conference of Numerical Analysis and Applied Mathematics, Halkidiki, Greece, 18.–25.09.2011
C. Kords, P. Eisenlohr, F. Roters, D. Raabe
- A nonlocal crystal plasticity model used to solve heterogeneous boundary value problems for 3D microstructures. 18th International Symposium on Plasticity & Its Current Applications, San Juan, Puerto Rico, 03.–08.01.2012
C. Kords, P. Eisenlohr, F. Roters
- DAMASK: the Düsseldorf Advanced Material Simulation Kit for studying crystal plasticity using FEM and FFT based numerical solvers. 18th International Symposium on Plasticity & Its Current Applications, San Juan, Puerto Rico, 03.–08.01.2012
F. Roters, P. Eisenlohr, D.D. Tjahjanto, C. Kords, M. Diehl, D. Raabe
- Multiscale modeling of the influence of C on intergranular fracture strength of bcc Mo, W and Fe. 6th International Conference on Multiscale Materials Modeling, Singapore, 15.–19.10.2012
A. Tahir, R. Janisch, A. Hartmaier
- A high-resolution look at crack tip deformation. Spring meeting of the german physical society (DPG), Regensburg, 10.–15.03.2013
C. Kords, P. Eisenlohr, A. Tahir, R. Janisch, F. Roters
- Ab-initio calculation of traction separation laws for a grain boundary in molybdenum with segregated C impurities, Modelling Simul. Mater. Sci. Eng. 21 (2013) 075005
A. M. Tahir, R. Janisch, and A. Hartmaier
(See online at https://doi.org/10.1088/0965-0393/21/7/075005) - Modelling and understanding the strength of grain boundaries based on abinitio results. Spring meeting of the german physical society (DPG), Regensburg, 10.–15.03.2013
R. Janisch
- On the role of dislocation transport in the constitutive description of crystal plasticity. PhD thesis, RWTH Aachen, 2013
C. Kords
- Development and Validation of a Scale-Bridging Method for Simulation of Intergranular Fracture in Body Centered Cubic Metals. PhD thesis, Ruhr-Universität Bochum, 2014
A. Tahir
- Dislocation density distribution around an indent in single-crystalline nickel: Comparing nonlocal crystal plasticity finite-element predictions with experiments, Acta Materialia 71 (2014) 333 – 348
C. Reuber, P. Eisenlohr, F. Roters, and D. Raabe
(See online at https://doi.org/10.1016/j.actamat.2014.03.012) - Hydrogen embrittlement of a carbon segregated
Σ5 (310)[001] symmetrical tilt grain boundary in α-Fe. MSE-A, Volume 612, 26 August 2014, Pages 462-467
A. M. Tahir, R. Janisch, and A. Hartmaier
(See online at https://doi.org/10.1016/j.msea.2014.06.071)
