Making Ends Meet – Bringing MD Simulations and Experiments Together

Principal Investigator:
Martin Hummel

Local Project ID:

HPC Platform used:

Date published:

Although MD is a widely used and accepted method, there is often the need of comparison to experiment to validate the reliability of the findings. The development of supercomputers as well as the optimization of the used simulation code led to enormous changes in the achievable dimensions. Nevertheless, the simulation of an aluminum cube of 1 µm side length would contain about 60 billion atoms. To simulate this for a duration of 1 µs simulated time, with time step 1 fs, it would take 47,248 core years on a Cray XT5 system, based on the 1.49e-6 sec/atom/time step determined at the benchmark on the LAMMPS webpage [2].

Our approach was to separate the tensile rate and the size of the specimen. Finding suitable experimental results of an Aluminum alloy AD1 with 99.3 wt% aluminum gave us the opportunity to start a direct comparison. The spall strength in these experiments for the strain rate of 1.1 x 104 s-1 is 1.06 GPa on the lower end and 1.38 GPa at the high strain rate of 8.8 x 105 s-1[3]. Simulations have been carried out for a cubic aluminum polycrystal containing 642,000 atoms at strain rates from 1.0 x 108 s-1 to 1.0 x 105 s-1, depicted in figure 1 left. To be honest, these calculations do not require a super computer rather than a lot of computational time, e.g. 150 days of computation for the slowest strain rate. These results are plotted together with the experimental results in figure 1 right hand side. One can see the quite smooth transition from the experimental to the simulation data, especially when taking into account, that in both regimes these are extreme simulations. Extreme slow for the simulations, extreme fast for experiments.

For the variation in the size of the simulated crystal, there definitely is the necessity of a supercomputer. The largest simulated single crystal in Figure 2 is of the size 450 x 224 x 153 nm³ and contains 909 million aluminum atoms. The five different sizes, which have been simulated indicate the transition from the inverse-Hall-Petch effect into the Hall-Petch effect. The maximum stress for the largest specimen was 1535 MPa. Luckily, we did as well find an experimental work of Huang et al. [4] who investigated the influence of the system sizes of aluminum. Their experimental setup sizes went down to lengths of 400±100x200±50x150±50 nm³ and therefore are of the same size like our simulations. The Yield stress went up to 750 MPa for their smallest size. The simulation result with 1535 MPa are double, but it has to be be considered, that the experiment took place at a strain rate of 1x10-3 s-1 and the simulation at 1x107 s-1. If one would take the findings of figure 1 on the right hand side, and extrapolate and transfer the calculated values of the large system to the experimental strain rate it would be a maximum stress of 586 MPa, which is in quite good agreement to the experimental value of 750 MPa.

Summarizing, MD simulations lead to the same results as experiments, when they are carried out at the same scales. Nevertheless, one has to be careful when transferring results from one scale to another and it is of great importance which material is used.

References and Publications

[1] https://doi.org/10.1007/978-3-030-66792-4_9

[2] Sandia National Laboratories, LAMMPS Molecular Dynamics Simulator. [Online] Available: http://lammps.sandia.gov.

[3] G. I. Kanel et al., “Spall fracture properties of aluminum and magnesium at high temperatures,” Journal of Applied Physics, vol. 79, no. 11, pp. 8310–8317, 1996.

[4] J. H. Wu, W. Y. Tsai, J. C. Huang, C. H. Hsieh, and G.-R. Huang, “Sample size and orientation effects of single crystal aluminum,” Materials Science and Engineering: A, vol. 662, pp. 296–302, 2016.