Crack Interaction at the Nanoscale

In continuum fracture mechanics, it has been well established that the interaction between a crack and a micro defect plays an important role in the overall failure mechanism of quasi-brittle materials. However, the applicability continuum mechanics concepts at the nanoscale is questionable because they do not take into account the discrete nature of matter and the quantum manifestations at the nanoscale.

In one of our recent work, we focused our attention on exploring the influence of interactions between existing edge cracks in graphene (a two-dimensional hexagonal lattice of carbon) and a nano-crack. We conducted molecular dynamics simulations and compared the results with a continuum-based model. Figure 1 shows a typical simulation sample of graphene containing a nano-crack interacting with an edge crack.

Figure 1 A typical molecular dynamics simulation sample of graphene.

Figures 2a and 2b show the stress distributions at the armchair and zigzag crack-tips, respectively. Figures 2c-2g demonstrate that the presence of nano-cracks greatly influences the stress field at the crack-tips. An article based on this work has been published in Computational Materials Science. The submitted version is available here.

Figure 2 The effect of atomic vacancies on the crack-tip stress field. Figures (a) and (b) show averaged stress distributions at the tips of armchair and zigzag cracks at the incipient crack propagation, respectively. Figures (c-g) show variation of the normalized crack-tip stress with r, θ, and ?. Figures (c), (d), and (e) are for the collinear (θ = ? = 0), oriented (r is fixed and ? = 0), and oblique (r and θ are fixed) nano-cracks, respectively. Figures (f) and (g) are for the collinear and oriented circular vacancies, respectively. Insets in Figures (c-g) show the stress distribution at an armchair crack-tip due to an applied tensile strain of 1% in the presence of an atomic vacancy at the specified location.