Combining a series of atomistic simulations with fracture mechanics theory, we systematically investigate the crack growth stability of graphene under tension and indentation, with a pre-existing crack made by two methods: atom removal and (artificial) bonding removal. In the tension, the monotonically increasing energy release rate G is consistent with the unstable crack growth. In contrast, the non-monotonic G with a maximum for indentation explains the transition from unstable to stable crack growth when the crack length is comparable to the diameter of the contact zone. We also find that the crack growth stability within a stable crack growth regime can be significantly affected by the crack tip sharpness even down to a single atom scale. A crack made by atom removal starts to grow at a higher indentation force than the ultimately sharp crack made by bonding removal, which leads to a large force drop at the onset of the crack growth that can cause unstable crack growth under indentation with force control. In addition, we investigate the effect of the offset distance between the indenter and the crack to the indentation fracture force and find that the graphene with a smaller initial crack is more sensitive. The findings reported in this study can be applied to other related 2D materials because crack growth stability is determined primarily by the geometrical factors of the mechanical loading.
Bibliographical noteFunding Information:
This work is supported by the Basic Science Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Science and ICT (NRF-2019R1A2C4070690). NMP is supported by the European Commission under the Graphene Flagship Core 2 Grant No. 785219 (WP14 “Composites”) and FET Proactive “Neurofibres” Grant No. 732344 as well as by the Italian Ministry of Education, University and Research (MIUR) under the “Departments of Excellence” Grant L.232/2016 and ARS01-01384-PROSCAN Grant.
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