Graphene Design with Parallel Cracks: Abnormal Crack Coalescence and Its Impact on Mechanical Properties

TL;DR

This study investigates how two preexisting parallel cracks in graphene interact under uniaxial tension and how their spacing $W_{\text{gap}}$ governs fracture behavior. Using molecular dynamics with ReaxFF, AC and ZZ graphene with varying crack gaps are simulated to map transitions between crack coalescence and independent propagation. The results show that coalescence lowers strength at small $W_{\text{gap}}$, while larger gaps increase peak stress and energy absorption, indicating a brittle-to-ductile transition; an effective stress intensity factor $K^{\text{eff}}_{\mathrm{IC}}$ rises with gap. A design relation for peak stress as a function of $W_{\text{gap}}$ is proposed, and a lever-type fracture mechanism is identified that enhances toughness, offering practical guidelines for defect-tolerant graphene components.

Abstract

Graphene is a material with potential applications in electric, thermal, and mechanical fields, and has seen significant advancements in growth methods that facilitate large-scale production. However, defects during growth and transfer to other substrates can compromise the integrity and strength of graphene. Surprisingly, the literature suggests that, in certain cases, defects can enhance or, at most, not affect the mechanical performance of graphene. Further research is necessary to explore how defects interact within graphene structure and affect its properties, especially in large-area samples. In this study, we investigate the interaction between two preexisting cracks and their effect on the mechanical properties of graphene using molecular dynamics simulations. The behavior of zigzag and armchair graphene structures with cracks separated by distances ($W_\text{gap}$) is analyzed under tensile loading. The findings reveal that crack coalescence, defined as the formation of a new crack from two existing crack tips, occurs for lower values of the distance between cracks, $W_\text{gap}$, resulting in a decline in the strength of structures. As $W_\text{gap}$ increases, the stress-strain curves shift upward, with the peak stress rising in the absence of crack coalescence. The effective stress intensity factor formulated in this study exhibits a clear upward trend with increasing $W_\text{gap}$. Furthermore, an increase in $W_\text{gap}$ induces a transition in fracture behavior from crack coalescence to independent propagation with intercrack undulation. This shift in fracture behavior demonstrates a brittle-to-ductile transition, as evidenced by increased energy absorption and delayed failure. A design guideline for the initial crack geometry is suggested by correlating peak stress with the $W_\text{gap}$, within a certain range.

Figures (9)

• Figure 1: Geometry and structure of graphene: (a) pristine graphene, (b) graphene with a single crack of length $2a_0$ and width $2b$, and (c) graphene with two cracks, each of length $2a_1$ and width $2b$, separated by a distance $W_\text{gap}$. A magnified view of a portion of the crack is provided to show its local structure. Cyan (blue) represents carbon (hydrogen) atoms in the structure.
• Figure 2: Effect of boundary conditions in tensile MD simulations of monolayer graphene with and without initial cracks at strain rate of $10^7/$s. Normalized von Mises stress distribution under a tensile strain of 0.06 for (a) pristine graphene and (b) precracked graphene. (c) Stress-strain curves. The correction for the stress values due to the use of Voronoi method was not applied here.
• Figure 3: Stress-strain curves for different strain rates for the precracked graphene structure with $W_\text{gap}=1.228$ nm. The correction for the stress values due to the use of Voronoi method was not applied here.
• Figure 4: Comparison of stress versus strain curves at the linear elastic regime, obtained by using Voronoi (solid line) and Common (dashed line) volume methods for (a) armchair and (b) zigzag structures. Pristine graphene (blue curves) and the graphene with the initial crack ($W_\text{gap}$=0, magenta curves) are examined for both structures.
• Figure 5: Results of armchair (AC) structures with crack lengths of $2a_0 = 5.388$ nm and $2a_1 = 2.836$ nm (AC1 to 5), and zigzag (ZZ) structures with $2a_0 = 5.281$ nm and $2a_1 = 2.825$ nm (ZZ1 to 5). (a, b) Stress versus strain curves for armchair and zigzag, respectively, graphene structures with different values of $W_\text{gap}$, at a strain rate of $10^8$ s$^{-1}$. The vertical lines at strain values of 0.075 and 0.1 are references for the next two figures. (c) Young's modulus versus $W_\text{gap}$ for both AC and ZZ structures. (d) Peak stress and effective stress intensity factor versus $W_\text{gap}$, respectively, corresponding to the stress-strain curves shown in (a) and (b). (e) Energy absorption under the stress-strain curve. Lines are guides to the eye. See the legends for the different symbols and lines.