## Multiscale modelling of fracture at grain boundaries

Fracture is a multi-scale phenomenon in which the process starts at atomistic level by breaking of bonds in front of the crack tip. Subsequently this damage progression leads to macroscopic failure modes such as plastic yielding and large cracks formation and eventually total failure of the material. Multi-scale modelling strategies are therefore needed for the description of the hierarchy of material processes that govern the fracture [1].

In the present project work, the aim is to develop a scale bridging method to predict the deformation and inter-granular fracture in body centered cubic (bcc) metals through ab-initio calculations of the density functional theory and continuum scale finite element modelling. For this purpose, the fracture process is divided into two parts i.e. pure brittle fracture along the grain boundary and plastic dissipation in the two adjacent grains. The plastic deformation in the individual grains will be described by the crystal plasticity model specifically designed for body centered cubic metals by P. Eisenlohr, F. Roters, and C. Kords from Max Planck Institute for Iron Research Düsseldorf Germany. Along the grain boundary cohesive zone elements will be used to account for crack initiation and growth. The cohesive zone model will be directly parameterized with material parameters derived from ab-initio calculations. The model system chosen as a first case is bcc Molybdenum (Mo) with varying Carbon (C) concentration since the positive influence of carbon on the mechanical properties of Mo has been studied by fracture experiments, transmission electron microscopy and ab-initio calculations [2-6]. The simulation results will be validated with experimental results for e.g. by performing three point bending tests using Mo bi-crystal samples with different carbon contents.

[1] Y. Yamakov, E. Saether, E.H. Glaessgen., J. Mat. Sci. 43, 7488-7494 (2008).

[2] A. Kumar, B. L. Eyre., Acta metall., 26, 567, (1978).

[3] A. Kumar, B. L. Eyre., Proc. R. Soc. Lond. A, 370, 431, (1980).

[4] J. M. Pénisson, M. Bacia, M. Biscondi., Phil. Mag. A, 73, 859, (1996).

[5] R. Janisch, C. Elsässer., Phys. Rev. B, 67, 2241101, (2003).

[6] R. Janisch, C. Elsässer., Physical Review B 77, 094118 (2008).