Modelling fracture of graphene using Griffith’s criterion and quantized fracture mechanics

In armchair graphene sheets, crack propagates perpendicular to the applied strain, whereas crack propagation in zigzag sheets occurs at an angle to the straining direction. This occurs due to different bond structure along armchair and zigzag directions as shown in Fig. 1. Videos 1 and 2 show the fracture of armchair and zigzag sheets, respectively.

Fig. 1: Armchair and zigzag directions of graohene

Video 1: Fracture of an armchair graphene sheet. The colour of atoms indicates the out of plane (z) movement of atoms.

Video 2: Fracture of a zigzag graphene sheet. The colour of atoms indicates the out of plane (z) movement of atoms.

In our recent study, published in Int. J. Fract., we found that quantized fracture mechanics theory [1] is more accurate compared to Griffith’s energy balance criterion in predicting the fracture strength of graphene. Figure 2 compares the fracture strength of armchair (2a) and zigzag (2b) graphene given by molecular dynamics, quantized fracture mechanics theory, and Griffith’s criterion.

Fig. 2: Comparison of the ultimate strength of (a) armchair and (b) zigzag sheets given by molecular dynamics, Griffith, and quantized frature mechanics.

Reference
[1] Pugno NM, Ruoff RS (2004) Quantized fracture mechanics. 
Philos Mag 
84:2829-2845