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Griffith's equation

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

Submitted by Nuwan Dewapriya on
research
fracture mechanics
molecular dynamics
nanomechanics
continuum mechanics
graphene
crack propagation
Griffith's equation
quantized fracture mechanics
fracture of graphene
armchair
zigzag

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

Griffith

Submitted by Rajesh Prasad on
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Griffith's equation

I teach Materials Science to undergraduate engineering students. We devote 2 or 3 lectures on Fracture where we mainly introduce Griffith's formula and the stress intensity formula. I face a difficulty in reconciling the two which I would lke to present here.

The Griffiths equation gives the fracture stress s for a given crack size c:

s=sqrt[2 E g/ (p c)] (1)

The stress concentration formula gives the max stress at the crack tip as

s=s0 [1+2 sqrt (c/r)] (2)

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