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Fracture Criterion

Arash Karpour's picture

 This is either a wage question I am asking or a stupid one...

How many fracture criterion do we have and what are they? some of these criterion that I am reading are related or a form of others...For example CTOD (crack tip opening displacement) criterion is related to energy release rate in

" A CTOD-Based Mixed-Mode Fracture Criterion" by Fashang Ma et al.

Any guid or direct help would be much appreciated.


   Thanks for your time



Arash Karpour's picture

Mastery on others is Force
Mastery on self is Strength

Well, related to fracture criterion, there is another very common method which is, Displacement Extrapolation Method (DEM). It`s one of the most accurate method used in Linear Elastic Fracture Mechanics (LEFM) as would be applied in Mode I and Mixed mode as well.

Dear All;

I have drawn the relation between dynamic stress intensity factor and crack tip velocity under mode-I impact loading for brittle material. In my research, some specimens were give nice results and I want to know:

Why is the dynamic stress intensity factor (DSIF) at initiation point not same DSIF at arrested point?

Why are almost the DISFs at arrested point always less than DSIF at initiation point of crack?

Why are DSIFs difference although they are same crack tip velocity?

I am very glad when give your comments;




Henry Tan's picture

What kind of criterion to use depends on what kind material you are fracturing?

msd.jacob's picture

As MR. Henry Tan ...

Mateial are clasifies as Ductile and Britlle. So in general the failure creterion is classified based these two materials. Again the criterion is based on energy method, stress concentration method.......... 

To add on above comments,

CTOA(Critical tip opening angle) can be used as a fracture criterion for ductile material. In ductile material, SIF is found to be dependent on a/W ratio, but CTOA remains constant. The following paper gives a fair idea about this approach(Look at the Fig.3)

"A review of the CTOA/CTOD fracture criterion" :JC Newman, M James - Engineering Fracture Mechanics, 2003 

Arash Karpour's picture


I am using brittle material with small scale of yelding...(small plastisity at the tip of the crack) 


Dan Cojocaru's picture

I think that (hypothetically) any quantity involved in describing the response of a given structure under a certain set of loading conditions can be used as a propagation criterion as long as a relation between the variation of that quantity and the crack propagation can be established.

Arash Karpour's picture



Maybe it is my lack of understanding of fracture...I found many fracture criterion and I don't know what would be the reason to apply each criterion...what are the general criterion? (that is for brittle material with small yeilding condition)  

Mastery on others is Force
Mastery on self is Strength

yoursdhruly's picture


I will take a "crack" at this, with a disclaimer at the outset: Smile my opinions are derived only from the few texts and one class I have taken. If any of my arguments are incorrect or outdated, I would appreciate them being pointed out as such.

For a globally brittle material with small scale yielding, such as you describe, you should not have trouble applying K based criteria, or, as we have been discussing in the other thread, the SED theory. In general, I imagine these are the relevant questions you need to resolve, listed below. Of course after you answer each question, there may be sub-issues to deal with.

1.  Is your material considered generally ductile or brittle? This you have answered. If your material is ductile, you cannot apply G or K based criteria. 

2. Assuming your material is "generally brittle" and you have conditions of small-scale yielding, you still must ask: Are your cracks self-similar? In other words, is the increment of the crack similar to the pre-existing one? If not, again you may not be able to apply the above criteria and will have to, in all likelihood, resort to another approach - SED may be of use to you here.

3. Finally, generally speaking, if you have significant plasticity, you may want to use the J-integral approach, provided that your loading conditions are monotonic. The J-integral approach is essentially based on a "deformation Plasticity" model, which is essentially a nonlinear elastic model - so no history is kept track of, which may be a problem for materials and loading conditions that need this (e.g. fatigue in viscoplastic materials like solder).

4. If all else fails, you need to enter the domain that some people call "Nonlinear Fracture Mechanics" (I think the J-integral is included in this group when applied to nonlinear materials). Here you can use the CTOA and CTOD methods, but there is a lot of skepticism about their generality, including the issues Prof. Chao mentioned. The more promising approach is that of the Cohesive Zone Models (CZM), which actually has a critical "separation". This approach is almost a back door approach to solving the problem, but a very powerful one and there are several review papers (including one by Ingo Scheider that you can google for).

I hope that sums up the criteria for you. My point really is this: the kind of problem helps you select the criteria. It is a true (and somewhat unsatisfying) fact that almost every theory in fracture seems to come with its cautionary list of limitations. Fortunately, there are several approaches out there and you should find one to fit your need.

With regard to the second question you bring about, regarding the relationship between different criteria, the K-G-J-SED equivalence is well known for elastic materials, Anderson's text can help with the K-G-J equivalence. SED can be written in terms of Ks quite easily too. The problems start to arise for nonlinear materials. Hopefully someone can shed some light on this. 

I think it would make sense for us to reach some sort of summary at the end of threads of this nature - perhaps the author of the thread can summarize the points learnt so that a quick read of the summary can help future readers.


Arash Karpour's picture


Thank  you so much for your explanations. It is been most helpful for me. I just couldn't relate one criterion to another before. Thanks again 

Mastery on others is Force
Mastery on self is Strength

You can read some papers of Prof. Nishioka (Kobe University, Japan) on some Journal webs, you can get your answer.

Good luck,


Arash Karpour's picture


Thank you for your response 

Mastery on others is Force
Mastery on self is Strength

Zhigang Suo's picture

This thread of discussion is related to another thread.

Arash Karpour's picture


I am reading your review aritcle on why K works. It is helping with some of my questions.

Thank you for you help. 

Mastery on others is Force
Mastery on self is Strength

chao's picture

Hi, this is my 2nd visit to iMechanics and found it interesting.  Prof. Suo’s effort in making this happen should be commended.


Let’s get back to fracture criterion.  In the early development of fracture mechanics, a critical stress or strain at the crack tip was used as fracture criterion similar to those used in strength of material for judging failure w/o cracks.  The problem associated with this criterion is the difficulty to “measure” the critical stress or strain.   Irwin proposed the K (which is the strength of the crack tip stress) so a “global” parameter can then be used to quantify the fracture event.  The critical K then became the fracture toughness of the material.   Similarly, J is used for ductile materials.  However, one needs to remember all theories have limitations, e.g. path-dependence of J in crack propagation.  While you are reading Suo’s article on “why K works”, you need to be aware that there are situations where K does not work, e.g. crack curving under mode I conditions..


The advantage of the “critical CTOA/CTOD criterion” is that they directly address what’s happening right near the crack tip.  The disadvantage of it is that it may not be a “material property”, e.g. it is thickness dependent.    Furthermore, it may not work for thick plate (see recent article by Lam, et al in EFM).

De Xie's picture

I think, as the spread of virtual crack closure technique (VCCT) and cohesivze zone model(CZM), CTOD will finally be aborted. The energy related criteria (e.g. strain enery released rate, G) will predominate the fracture mechanics.

The reasons are
(1) G can be very easily computed by VCCT in conjuction with FEA.
(2) no singular element nor collapsed element is required to achieve accurate results
(3) not mesh sensitive, even coarse mesh can work.
(4) physical meaning is clear: energy to create new surfaces. It combines both force and displacement opening.

So, engineers can easily use G to do some facture analysis at structral level with FEA.

CTOD requires very fine mesh around the crack tip and only displacement opening is taken into acount,no force is considered. Therefore, its physical meaning is not strong.

The only advantage is its easy computation. However, by VCCT, G can be compuated in a manner just as simple as CTOD if not simpler, then how can CTOD survive?

CZM is the nonlinear version of VCCT. Or VCCT is the linear version of CZM.

Now, more and more criteria (fracture and fatigue) are being developed directly based on G.

This is my prediction.


Hi De Xie 

 I am working on crack propagation problem using cohesive elements but I really do not know how to choose the properties of cohesive element. Can you tell me how to choose it??




I am trying to calculate K values for a double tip crack orientated at 45 deg in a rectangular plate in ansys.I am stuck with a strange problem. When i give the Kcal command it says the crack face is not parallel to the active x axis. But i have checked the cordinates of the keypoints that i have used to create the crack. The crack is perfectly symetric about the active cordinate system  about the crack tip.Can somebody help me please.

Hello friends

I am doing my research in fracture mechanics. Presently I am working on crack propagation FE model using ABAQUS software. I am new user for the software. Can any body tell me that where I can find the interactive tutorials for crack propagation problems or any idea, how to proceed for the same using ABAQUS software? I heard that there is a node release technique in ABAQUS software to solve such problems, but not able to use it. 

Dear vcvikas,

The node release method available in Abaqus is Virtual Crack Closure Technology (VCCT). You can use too the cohesive elements. One of the differences between theses 2 methods is that VVCT method assume that you have an initial crack.

Theses methods assume that you know the crack path (for example delamination). If you want to study the bifurcation of the crack, you must use remeshing tecnique and crack font advance. XFEM method are very efficient to study this kind of problem.





Dear Sir

Can we use VCCT in GYFM? 

Sorry what's means GYFM


GYFM means Gerenal yielding fracture mechanics. in this cateragy there is large plastic zone ahead of crack tip and it is applicable for thin sheets. 

Hi Panierstef

I am modeling a crack propagation problem using cohesive elements. But I really don't know, how to choose the properties of cohesive elements? Can you help me in this regards.



AS's picture


I find this topic pretty interesting. A broad
literature has been devoted to it and to a similar one (see Myself as well gave a small
contribution recently published in Journal of the Mechanics and
Physics of Solids, 56 (2008)
2092–2116. A few mistakes and some further developments have been
considered in another note, submitted presently to Engineering Fracture
Mechanics. My conclusion is that most criteria for crack propagation in
the small scale yielding range, and SED among them, have several
weaknesses and should be carefully considered. But of course I
can be wrong.

Any comment on this is sincerely appreciated.

Hope it helps!

I have prepared FE model for crack growth analysis in ABAQUS. I want to know that how can we get out put results? e.g. CTOD or J- intergral values. I am getting LLD. Plz help me.

Dear Vikas,

You can get J-Integral directly from 'History output requests'. Select  History output requests and Contour integral domain. and for the second one CTOD can be evaluated from finite element displacement and 45 degree intercept concept.

can you tell me how to evaluate LLD..?pls..



Dear All,

I am using ABAQUS/EXPLICIT for analysing a cracked body.Is there any way to calculate crack growth in EXPLICIT.? somewhere I have seen that " priciple stress/strain element failure approach" can be used. if it is so how to implement it..?

Can anybody help me in this regard.



Salamander777's picture

 In order to optimize the blanking processes, it is important to
identify the conditions within the deforming workpiece which may lead
to fracture initiation and propagation. Within this framework,
numerical simulations are widely used in industries to optimize sheet
metal forming processes. However, in order to have a confidence in the
results of such simulations, an accurate material model is required.
The accuracy of a material model is affected by the constitutive
equations and the values of the material parameters. In order to reduce
the danger of fracture of metal parts during manufacturing processes,
advanced optimal design requires knowledge of critical values of some
fracture criteria of the material used.
There are some good reads in pdf on this topic on the web. Might be useful for
the readers.

Dear friends,

I am writing an XFEM code fordynamic crack propagation and interested in using the Interaction Integral method(as in Rethore et al. (2005)) for computation of Stress Intensity Factors(SIFs). I wonder if anyone knows what kind of dynamic asymptotic crack tip auxiliaryfields could be applied to the method for computation of SIFs for a dynamicallypropagating crack.




Have you resolved these problems yet and could you give me some details about the auxiliary fields, including the auxiliary velocity fields, the auxiliary displacement fields and the auxiliary stress fields. Thank you very much.


 Zhi-Yong Wang PhD candidate Center for Composite Materials and Structures Harbin Institute of Technology Harbin, Heilongjiang 150080, P. R. China Tel: +86-013904656487,+86-45186402739,Fax: +86-45186402739 Email:

HussamNasreddin's picture

Hello all,

I am trying to model concrete as an elastic material in ABAQUS. The
model can be any simple structure (cube, beam or column) but the main
feature is that concrete behaviour is elastic up to a limiting strain
(St. Venant's theory). Which of the  Failure criteria in ABAQUS i should
be using (Elasticity or brittle cracking)? if neither would you mind
explaining other options?




i am a new learner of using abaqus.i would like to know whether there is a possibility of simulating a brittle material until cracks appear? i have read that we need to introduce an initial crack?are we not possible to simulate a solid brittle material without having initial crack?

i hope someone out there can advice me on this matter. your help is much appreciated.


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