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Microscopic Origins of Fracture Toughness

Periodic Reporting for period 3 - microKIc (Microscopic Origins of Fracture Toughness)

Reporting period: 2020-05-01 to 2021-08-31

The resistance to crack propagation is undoubtedly one of the most important properties of structural materials. However, our current mechanistic understanding of the fracture processes in typical semi-brittle materials like steels, refractory metals or semiconductors is not sufficiently advanced to predict the fracture toughness KIc and its dependence on the microstructure, temperature and strain rate. Therefore, KIc is commonly regarded as a phenomenological material parameter for fracture mechanics models that requires experimental calibration.
The aim of microKIc is to study fracture in model materials in order to gain a detailed understanding of the microscopic crack-tip processes during fracture initiation, propagation and arrest, and to systematically study the interactions of cracks with constituents of the microstructure like dislocations, voids, precipitates and grain boundaries. To this end, we will perform fully 3D, large-scale atomistic simulations on cracks in bcc- based materials with varying crack orientation, crack front quality, and in the presence of dislocations and microstructural obstacles. The obtained criteria for crack advance and dislocation nucleation at crack tips will be implemented in a novel coupled finite element - discrete dislocation dynamics code, which will allow for the first time a fully 3D study of fracture and crack-tip plasticity at the mesoscale. The simulations will be compared to in-situ micro-mechanical tests on well-characterized fracture specimens produced by focused ion beam milling.
The ultimate goal of microKIc is to use this experimentally validated multiscale modelling framework to develop a microstructure-sensitive, physics-based micromechanical model of the fracture toughness, which will be tested against macroscopic fracture experiments. Such predictive models are crucial for the development of new failure-resistant materials and for improved design guidelines for safety-relevant structures and components.
The project is organized along five work packages (WPs):
WP1: Atomistic Simulations of Static and Dynamic Cracks
WP2: Development of a Discrete Dislocation - Crack Dynamics (DDD+C) Model
WP3: Micromechanical Fracture Testing
WP4: Development of a Continuum-Scale Micromechanical Fracture Model
WP5: Macroscopic Fracture Testing

In WP1, different types of interatomic potentials for bcc metals were evaluated and compared to DFT calculations, and the crack initiation toughness was determined for perfect and kinked crack fronts in bcc metals as well and in stoichiometric and off-stoichiometric B2 NiAl. Furthermore, the interaction of propagating cracks with voids of different sizes, shapes and inter-void distances were studied in detail and first simulations on cracks interacting with dislocations were performed.

In WP2, the DD code TRIDIS was adapted to B2 ordered alloys. In this initial version for BCC metals, dislocation lines are gliding in {110} planes with <111> Burgers vectors. The <001> direction has been added to the list of Burgers vectors. Furthermore, the XFEM-enabled Finite Element code CAST3M has been coupled with TRIDIS. That way dislocation motion and crack propagation can now for the first time be simulated simultaneously.

In WP3, microbending tests were performed on FIB-milled notched cantilever beams of NiAl, W, and Cr to determine the fracture toughness for different crack orientations and deformation rates. Together with atomistic simulations in WP1 the role of atomic scale heterogeneities on fracture toughness could be elucidated using off-stoichiometric NiAl as a model system. The effect of pre-deformation on fracture toughness and its rate dependence were studied on W and Cr. Using eutectic NiAl-Cr(Mo) with a bcc respectively B2 crystal structure interface fracture was studied. Additional fracture tests on cracks crossing from one phase into the other were also performed. Furthermore, complementary fracture test methods like pillar splitting and bulge test on slit containing thin films were established within microKIc. In combination with atomistic simulations (WP1) we could explain the size and microstructure dependence of the fracture behavior of thin Ag films.

Regarding WP4, together with activities in WP1 a new scaling relation was developed that allows to directly parameterize continuum scale fracture models based on atomistic simulations. This important step was actually reached ahead of the schedule.

No work was planned or performed on WP5 during this reporting period.

Dissemination-wise we organized a well-attended international symposium on the fundamentals of fracture at Europe’s largest Physics conference, the joint DPG and EPS Spring Meeting 2018, and a media campaign resulted in a TV report and a whole page feature in the regional newspaper.
On the atomic scale, a novel benchmark has been developed to quickly assess the usability of interatomic potentials modelling bcc metals for fracture simulations. Various potentials, including EAM, MEAM, ADP and BOP, for different metals were tested and compared to DFT calculations. Including the benchmark in the fitting procedure of potentials should improve the applicability of new potentials to fracture simulations.
Furthermore, we performed the first simulations of dislocation-crack interactions in bcc metals, the first studies of the effect of off-stoichiometric composition in NiAl and on the role of the resulting atomic-scale heterogeneities, as well as the systematic study of crack-void interactions in intermetallics

On the mesoscale dislocation as well as cleavage crack propagation can now be modelled within the same framework, opening up completely new possibilities to study crack tip plasticity.

Micromechanical fracture tests were performed for the first time on the eutectic NiAl-Cr(Mo) nanocomposite – an ideal model system to study fracture in the crystallographically related bcc and B2 phases and to study the role of combining these phases and of the interphase boundary on crack propagation. Furthermore, first micromechanical tests on pre-deformed samples were performed, using a novel approach to attain different degrees of plastic strains.

One further highlight of the first reporting period is the development of a novel scaling method that enables a direct parameterization of traction separation laws for cohesive zone or XFEM methods from atomistic calculations of the forces necessary to break atomic bonds. We furthermore confirmed the applicability of linear elastic fracture mechanics in the nanometer range close to crack tips in brittle materials and demonstrated for the first time the ability to model the bonding situation at a crack tip by performing calculations of rigid body separation.
Crack in off-stoichiometric B2 NiAl - micro mechanical testing and atomistic simulation