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Why Griffith's Law of fracture does not hold at the nanoscale
We know from fracture mechanics theories that fracture instability in a perfectly brittle material occurs when energy release rate (G) becomes equal or more than two times the surface energy (γ) of that material. The value of G = 2γ is known as fracture toughness Gc. This is the classical Griffith criteria of brittle fracture. Experimentally, however, we know that plasticity becomes eminent for most materials and this criteria does not work.
With the use of atomistic calucations (e.g. Molecular Dynamics), we have the "luxury" to choose a "perfectly" brittle material (e.g. sodium chloride) so that we can revisit whether Griffith's theory works. I have found a bunch of recent literatures and found that Gc = 2γ does not work either in MD - they vary by 20% - 40% or more.
I would like to learn why Griffith's Law does not work in Molecular Dynamics calculation. Is this because of some "nanoscale" effect, inadequecy of MD potentials to reveal the correct physics, nonexistence of perfectly brittle materials (that can be simulated in MD) or Griffith's Law is just a "theory". I look forward to hearing some comments from our fellow mechanicians.
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Ashfaq,
The question you asked is interesting. It may be helpful for the discussion if you would list a few example papers that simulated perfectly brittle materials but "violated" Griffith's fracture criterion. Thanks.
RH
re: your list
Dear Rui:
Here are few references that you may want
to read. I can add more. I am including some relevant information from each of
these papers. Karimi et al [1] studied crack propagation of Ni with/
without defects and attempted to find Critical Energy release rate under plane
strain condition. They choose (001)[100] as the crack system and assumed that
under plane strain condition, the material would mimic brittle crack
propagation. Their calculated critical energy release rate Gc
was ~20% more than what Classical Griffith’s criterion predicts. Swadener et al
[2], however, found that Griffith’s criterion fits quite well with brittle
3C-SiC system as long as the strain energy release rate is small. For higher
value of energy release rates, they found that simulation results diverge from
Griffith’s criterion. Kikuchi et al [3] observed that Mode I crack propagation in
single crystal brittle SiC
system is direction dependent and some cases crack branching occurs instead of
cleavage crack. In this system, estimated critical energy release rate is also
higher than Griffiths Criteria. Instead of remote stress loading, Instread of remote boundary loading, Xu et al [4]
employed near-tip displacement as the applied deformation. They
found that the resulted stress intensity factor is overestimated by ~40%.
References
“Molecular Dynamics Simulation of crack propagation in Ni with defects”,
Modeling and Simulation in Materials Science and Engineering, 14:
1409-20, 2006.
M., “Molecular Dynamics Simulation of Brittle Fracture in Silicon”, Physical
Review Letters, 89(8) 085503-1-4, 2002.
Vashistha, P., Branicio, P.S., Shimojo, F., “Brittle dynamic fracture of
crystalline cubic silicon carbide (3C-SiC) via molecular dynamics simulation”,
Journal of applied physics, 98:103524, 2005.
Z., “Stepwise-quilibrium and Adaptive Molecular Dynamics Simulation for Fracture
Toughness of Single Crystals”, Journal of Intellegent Material Systems and
Structures, 15:933939, 2004.
Ashfaq Adnan
Post Doctoral Fellow, Mechanical Engineering
Northwestern University, Evanston, Illinois 60208