The Failure Mechanisms and Mechanics Laboratory at Cornell
Fracture at the Atomic Scale
Crack growth is inherently an atomic‐scale process as it entails the breaking of atomic bonds to create new surface area. However, bond breaking at the tip of a crack constitutes only a small portion of the energy dissipation associated with crack growth in a typical structural metal as the majority of energy dissipation is linked to continuum plasticity. Nonetheless, bond breaking at a crack tip often plays a governing role in the fracture process. For instance, consider the limiting case when the surface energy goes to zero. In this case a crack will grow under infinitesimal loading.
With continually increasing computational resources and improving algorithms, atomistic modeling is well positioned to contribute to our understanding of atomic‐scale crack tip processes. However for atomic simulations to serve as more than a source of inspiration for understanding, several long‐standing challenges must be addressed. Specifically, (1) the limited spatial domain associated with atomistic modeling must be reconciled with the long range character of relevant elastic fields, (2) the interatomic interactions must be computed in an accurate, yet computationally feasible way, and (3) the short temporal domain inherent to direct atomistic simulations must be reconciled with the thermally activated nature of many crack tip processes.
To overcome the challenges mentioned above we employ a concurrent multiscale approach that directly couples an atomistic region to a continuum region. This allows for the examination of a sufficiently large domain with no artificial boundary effects while at the same time reducing the number of degrees of freedom in the system. The small atomistic region facilitates the use of high fidelity quantum mechanics based interatomic force computations. This permits complex multi‐element bonding interactions to be accurately calculated, and thus, enables simulations involving real materials with impurities in real non‐vacuum environments.
The reduced number of degrees of freedom associated with the multiscale approach can also be utilized to permit longer timescale simulations using empirical potentials. To extend to experimental timescales, we combine this approach with other accelerated atomistic simulation techniques such as parallel replica dynamics and hyperdynamics.
Using the previously described framework we have been able to demonstrate that the abbreviated timescale, typical of traditional direct atomistic simulations of crack tip processes, can lead to not only quantitative, but qualitative differences compared to experiment, i.e. entirely different deformation mechanisms can be active. This finding motivated us to thoroughly investigate a variety of alternative indirect atomistic approaches that use transition state theory (TST) to overcome the challenge of timescale. Our investigations revealed that some advanced TST approaches are capable of accurately predicting atomic‐scale crack tip processes, while simpler more commonly used approaches can lead to significant errors. Presently, we are harnessing the methodologies mentioned on previously to directly simulate fatigue crack growth at the same loading rate as ultra‐high cycle fatigue experiments.
To date, our quantum mechanics based crack tip simulations have led to two noteworthy findings. The first is that crack tip predictions from two commonly used interatomic Al potentials compare well with quantum mechanical results, thus, providing confidence in the outcome of previously performed (and to be performed) simulations that use these potentials. The second entails new insight into the role of hydrogen and oxygen at an Al crack tip surface. Our preliminary results indicate that both H and O can increase the load needed for crack tip nucleated plasticity and thus the presence of these elements can favor a more brittle response.
Overall our efforts are aimed at two broad goals. The first is to illuminate new (and examine existing) routes for improving the accuracy of atomistic simulations of deformation and fracture processes. The second is to uncover and understand the controlling physical mechanisms of these processes. Both goals are necessary steps towards improving failure prognosis of existing materials and towards the development of novel bottom‐up designed materials with outstanding properties.
- A.K. Nair, D.H. Warner, R.H. Hennig, W.A. Curtin, “Coupling Quantum and Continuum Scales to Predict Crack Tip Dislocation Nucleation.” Scripta Materialia 63(2010)(12), p. 1212‐1215
- L.D. Nguyen, K.L. Baker, D.H. Warner, “Atomistic Predictions of Dislocation Nucleation with Transition State Theory.” Submitted to Physical Review B
- D.H. Warner, W.A. Curtin, and S. Qu. “Rate Dependence of Crack‐Tip Processes Predicts Twinning Trends in FCC Metals.” Nature Materials 6(2007), p. 876‐881
- D.H. Warner and W.A. Curtin. “Origins and Implications of Temperature Dependent Activation Energy Barriers for Dislocation Nucleation in FCC Metals.” Acta Materialia 57(2009)(14), p. 4267‐4277