Dynamic fracture is a never-ending story. In 1951, EH Yoffe obtained an analytical solution for a crack of constant length travelling at constant speed along a plane. She used a Galilean transformation to get a solution for arbitrary speeds. The situation seems strange with a crack tip where the material breaks and a lagging tip where the material heals. However, there are applications. One that I encountered was several mode II cracks that travel in the contact plane between a brake pad and a brake disc. The moving cracks were blamed for the causing squeaking noise when braking.
A step towards a more versatile solution was given by KG Broberg in 1960 for crack growth with both tips moving apart from each other at the same speed. The self-similar state leads to simplifications while all coordinates are scaled with speed and time. The solution suffers from the crack growth rate instability that is expected as long as the crack growth rate is less than the speed of the Rayleigh wave, i.e. always as long as you don’t push the crack tip with something. I can recall an epoxy experiment and a high-power laser that gave the crack tip a push.
Finally in 1972 LB Freund solved the problem of a semi-infinite crack and an arbitrary crack growth rate which more or less culminated the entire subject. Another milestone is the incorporation of plastic strain rate dependencies, dealt with LB Freund and JW Hutchinson in 1989, that explained the observed sudden arrest from a finite crack growth speed.
These are a few milestones as regards the mathematical physics of dynamic fracture. Maybe a new milestone is reached with the article,
that begins with a brilliant and detailed review of three successful models for the initiation of crack growth in brittle materials. The first is AA Griffith’s theory from 1920, for the initiation of crack growth, which has served us well for decades. The limitation is that it only applies to stable quasistatic crack growth. The second model is due to LB Freund and his work from 1972. This certainly put the subject and us on a different level. The third model is based on molecular dynamics. Here the present paper gives much insight and could be a springboard for initiates.
Observations and results are based on data from fracture mechanical testing of brittle single-crystal silicon samples. The focus is on the relationship between the energy balance and the crack tip speed. Also, the details of the crack front contribute. Analysis of fracture processes on a microscopic scale enabled the development of an interesting model for the required binding energy. The involved mechanisms are the low-energy migration and high-energy kink nucleation along the crack front.
In particular, the energy release rate at crack initiation, and its derivative with respect to the crack length, play an important role. The macroscale experiments, the microscale atomistic model and the energy release rate gradient lead to several conclusions. A primary conclusion is that the energy release rate required for breaking the bonding in the crack plane is not constant. Instead, it is limited by the classical Griffith energy and an upper limit, related to the lattice trapping at as much as 3 times the Griffith energy. Also an interesting transition phase between breaking up from the virgin crack and growth. During this phase, the sequence of bond-breaking mechanisms varies, leading to an increase in the cleavage energy.
Also, the variation of the cleavage energy shows that shorter cracks require higher energy to grow, and are stronger than what is predicted by the classic Griffith’s surface energy.
I consider this to be an interesting and important paper. This is why I only have two questions. First, were there ever any dislocations that were nucleated and thrown out from the crack tip? Second, there is of course no such thing as a pure mode for a kink but is the kink propagating under mixed mode closer to mode I or possibly closer to mode II?
It would be interesting to hear from the author or anyone else who would like to discuss or provide comments or thoughts, regarding the subject, the method, or anything related. If you do not have an iMechanica account and fail to register, please email me at per.stahle@solid.lth.se and I will post your comments in your name. The paper will be open-access in a couple of days.
Per Ståhle
Leave a Reply