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Naming the SI Unit for Fracture Toughness (KIC)

To: Engineers, Fracture Analysts, Mechanicians, Physicists...

In science and engineering, we have an excellent tradition: naming a physical unit using the name of a prominent personality from the concerned field. For example, in SI system, we measure force in newton, work in joule, power in watt...

But the unit of fracture toughness, i.e. KIC, is too lengthy to pronounce: (mega) pascal-underoot-meter. Further, it has also been in use for something like half a century by now, perhaps more. So, how do you like the idea of giving a name to this unit?

As far as I can see, the possible choices are:

-- Griffith (G)
-- Irwin (I)
-- Some other person (Please specify)
-- None. The physical quantity KIC is not necessarily the best measure of toughness... We should wait for the research to evolve a better measure.
-- Something else (though I fail to see what it could be)

Please note, this is not a suggestion for a poll. (I mean, rather, that things like this should never be finalized purely by polls alone!) 

But anyways, I would appreciate knowing what you think... Please leave your comment below...


ramdas chennamsetti's picture



Yes, why not.

The units of KiC (i=I, II and III) look odd - MPa.m^0.5.

I feel Griffith may be a good choice, because, the Fracture Mechanics starts with Griffith's theory and we encounter KIC there at the first time.

     1 Griffth = 1 MPa.m^0.5

 - Ramdas. 


Dear Ramdas,

Thanks for your feedback. I very much appreciate it.

I do have an opinion on the matter, but would like to reserve it for the time being. ... I would rather that others, too, expressed what they felt about the issue...

Once a few more comments come in, I will sure go ahead and add my view of the matter below here. Anyways, special thanks to you, once again, for being the lone commenter for something like a week by now!!






Hello sir,

I have confusion between strain energy release rate, critical energy release rate and fracture toughness. All are the same or different? because some of the researchers have mentioned fracture toughness with unit J/m2.


Thanks in advance. 

Matt Pharr's picture

       The energy release rate is the reduction in elastic energy associated with a crack increasing per unit area of crack. Its dimensions are energy per length^2 or units of J/m^2. If we think about progressively increasing an external load on the material (e.g. hang a progressively heavier weight from the material), the energy release rate will increase. When the energy release rate value reaches some critical value, the crack will grow. This critical value is known as the fracture energy (also with dimensions of energy/length^2 or units of J/m^2). So, the energy release rate is the driving force for the advancement of the crack whereas the fracture energy is some sort of resistance to the growth of the crack.

       There is another quantity denoted by K (also written as KI KIIor KIII depending on the mode of crack opening), which is known as the stress intensity factor. The crack tip field in an elastic body takes the form σ=K/(2*π*r)^(1/2) where r is the distance from the crack tip. K is undetermined in the solution of the crack tip field and is a loading quantity that depends on the geometry of the boundary value problem. K has the dimensions of stress*(length)^(1/2) or units of MPa*(meters)^(1/2). As with the energy release rate, if we progressively increase an external load on the material, the stress intensity factor will increase. When this value reaches a critical value, the crack will grow. This critical value is known as the critical stress intensity factor (very original, I know). As we can see, the stress intensity factor and the energy release rate are very similar conceptually. In fact, Irwin showed that they are mathematically related by the expression G=K^2/E (for plane stress). For further details on these topics, please see the following two sets of notes:

Energy Release Rate
Stress Intensity Factor


Hi all,


0. It's been a long while since we discussed this issue.


1. My own opinion has always been that the unit should be named in honour of Griffith. As a pioneer of this field, he deserved it more than any one else.

However, in my above reply (to Ramdas, some 12+ years ago!) I had kept my opinion reserved---mainly because I wanted to hear others' opinion first.

Then, sorry to say, in the pursuit of other topics and all, I came to completely forget about this thread! (I don't even remember checking it back again. If I were to do that, I would sure have added my opinion.)


2. Cut to the present, there is a pleasant reason to revive this thread.

Recently, I received an email from Pedro Rivero Antunez, a PhD student at the University of Seville (Spain). Let me copy-paste the relevant part from his email here, so you know the exact story. I quote Pedro:

>> quote

Some months ago my director and I thought that the unit used for Fracture toughness, MPa·m1/2, was awkward and odd. Searching on the internet for someone who realized this point before, we found your comments on a thread/post about this topic on Recently, we published a paper on Ceramics International where we used the new unit based on your suggestions: ``Griffith'' (Gf) is proposed in substitution of the awkward classical magnitude Pa·m1/2, where 1 Gf = 1 Pa·m1/2, as a tribute to the mechanical engineer Alan Arnold Griffith (1893–1963). ``Mega-Griffiths'' (MGf) will be the tipical order of magnitude for the fracture toughness of ceramics.

Attached, you can find the mentioned article, and in this link you can access to the online version:

<< unquote.


3. Needless to add, I was very happy to find that someone else not only thought of this idea independently, but even began putting it to use---right in a journal paper. That's how it should proceed.

I am also grateful to iMechanica for providing a perfct forum for putting forth suggestions and discuss ideas like this.


4. In my email reply to Pedro, I confirmed that I would be happy to assist in anyway if there is any initiative to have the unit approved by the relevant national and international standards committees.

But of course, a widespread usage is only going to help.

So, my request to all mechanicians, and especially iMechanicians: Please start using the unit of griffith (Gf) in your work.

(Following the SI convention, we use lowercase letter while identifying the full form of the unit; e.g., newton, joule, ... griffith. However, while using the abbreviated form of the unit, the beginning letter is capitalized, as in N, J, ..., Gf.)


Thanks for your time and attention.




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