The J integral

Hi Zhigang,

Thanks a lot for this handy and useful lecture notes on J-integral.

In engineering applications, we often need to calculate stress intensity factors
for a corner crack. A convenient approach is to deduce them from J- or similar
integrals. Numerically, such integral does not appear to be path-independent.
And I read somewhere (unfortunately cannot recall where) that theoretically the
path-independence can only be guaranteed for a 2-D crack.

Do you have any comments on the 3-D J-integral?

Xiaobo

Thanks Prof. Suo. It is a very good lecture. For a nonhomogenous material, the J integral is path-dependent. In this case, how to use J integral to calculate the energy release rate?

Dear zhigang

I have read the article (J.R. Rice, Mathematical analysis in the mechanics of fracture, Chapter 3)  that proves G=J for elastic materails. and I faced a problem,  why in two-dimensional crack we take A* any finite region in which the crack tip is imbedded?

can you please help me.

Sh.Eskandari

Please help, i am in rush.

Dear Everyone

I am working on Fracture Mechanics, and facing problem to evaluate  J-Integral in 2D and 3D crack model and as well as in composite model by ANSYS.

If anyone have idea about it please send me tutorials or steps for the same problem.

Your help will be heartly appreciated.

Thanks.........

email ID: himanshu [at] iitp.ac.in

               hpiitp [at] gmail.com

Michele Ciavarella, Politecnico di BARI - Italy, Rector's delegate.
http://poliba.academia.edu/micheleciavarella
Editor, Italian Science Debate, www.sciencedebate.it
Associate Editor, Ferrari Millechili Journal, http://imechanica.org/node/7878

soton.ac.uk
[PDF]S Filippi, M Ciavarella, P Lazzarin -
International Journal of Fracture, 2002 - Springer

S.
FILIPPI1, M. CIAVARELLA2 and P. LAZZARIN3,∗ 1Department of Mechanical
Engineering

- University of Padova, Via Venezia 1, 35100 Padova (Italy); 2CNR-IRIS,
Computational Mechanics

of Solids, Str. Crocefisso 2B, 70125 Bari (Italy); 3Department of
Management and ...

Michele Ciavarella, Politecnico di BARI - Italy, Rector's delegate.
http://poliba.academia.edu/micheleciavarella
Editor, Italian Science Debate, www.sciencedebate.it
Associate Editor, Ferrari Millechili Journal, http://imechanica.org/node/7878

Duality and symmetry lost in solid mechanics

Comptes
Rendus Mécanique, Volume 336, Issues 1-2, January-February
2008, Pages 12-23

Huy Duong Bui

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Michele Ciavarella, Politecnico di BARI - Italy, Rector's delegate.
http://poliba.academia.edu/micheleciavarella
Editor, Italian Science Debate, www.sciencedebate.it
Associate Editor, Ferrari Millechili Journal, http://imechanica.org/node/7878

Dear all,

I am a new Abaqus user. My work involve with fracture modelling by using Abaqus.

For 2D Edge Crack problem, I have requested 5 values of J contour integral in abaqus, but i can not plot the J-integral path (J - integral versus Radius). I know abaqus will choose the path of each contour integral automatically. But How to show the path of each contour integral?

Thank you so much,

Sutham A.

Dears

I found in XFEM J-integral is little bit path dependent for three dimensionalcracks. its value changes up to 8%for penny crack with path.

Hi All,

I have a question in mind for a while and unfortunately

have not yet found a clear answer to it. I would highly appreciate if you

provide me with your idea about this question:

 Is J-integral valid inside the process zone ahead of a

sharp crack? and if is valid, Is it equal to the value obtained from a contour

outside the process zone?

 Thanks

Ahmad Khayer D.

To be precise the J-integral is only path independent for isothermal, non-linear elastic problems where there are no body forces. For monotonic loading where there is plasticity then it is path independent only under deformation plasticity. For in-elastic problems where there you hasve cyclic loading the J-integral is  not path dependent. In such situations the crack tip can be described by a related path integral called T*, that was first formulated by Satya Atluri. When J is path independent then J=T*. The importance of the J integral is related to its ability to characterise the near tip stresses and strains for a non-linear elastic material. The so called HRR solution. The experimental work of Professor Albert Kobayashi has shown that this is not true for cyclic loading.

 As an aside many people mistakenly think that the J-Integral was developed by Jim Rice. This is not true. It was first proposed in the early 50's by Professor Eshelby at the University of Sheffield. Prof Rice popularised it many years later. The 3D variant was first developed in a joint paper by Professors George Sih and George Irwin, both at Lehigh, shortly thereafter. You can chase down the relevant references with a simple Google search. The reference to the original Sih-Irwin paper is in one of Professor Sih's papers in his Journal, viz: Theoretical and Applied Fracture Mechanics.

 Hope this helps

Rhys  Jones

if you can just read this part of the article and help with this?

Dear Colleagues,

My problem is that if I define a zero-area path around the crack tip of the mode-II ENF specimen and
calculate the traction vectors, there is a negative sign (2nd page)
that I do not understand and this is what leads to the wrong result. Can
You take a look at my note and tell me what is wrong?

page 1

page 2

Thanks

Andras

Hi

i'm modeling crack with EFG method and using M-integral to calculate stress intensity and i have some quastions:

 is domain integral form of j-integral still path-independence?

what is the best 'q' function?

what domain size is good for the M-integral?

i found diffrence between answers with several domain size is it mean that m-integral is path-dependence?

and my bigest problem is sometimes i got worse answer with finer mesh!!! (also with uniform distribution)

and in some domain size  my enriched basis got worse answer than the ordinary basis!!!

is my model unstable or something like that???

what should i do???

i checked everything!!! my code works well what do you suggest????

Dear Prof. Suo,

I have read your posted outlines for fracture meachanis and they are really helpful. Thank you for sharing them! But one problem is that I couldn't find all the outlines for all the listed topics. I could not find any pdf file for this one, for example. Are you still posting those outline?

Best,

Hi Zhigang,

Thank you for the useful explanation. I would like to ask you if you can model a crack on a 3D curved surface like a pipe. How could this be modeled ? can i still use the contour integral method?

Thank you,

Diana.

Dear Prof. Suo,

Rice introduced the J integral concept which is equal to the energy release rate for a uniform, linear or nonlinear elastic material free of body forces and subjected to a 2d deformation field (plane strain, plane stress etc.).

In ANSYS and Abaqus, the implementation is always referenced to the work of Shih (1986). There has been numerous publications on the use of J-integral to estimate Gc (critical energy release rate) for cracks which are located at the interface of dissimilar materials.

I could not find the relevant information if this approach is applicable, if yes, under what  circumstances? Could you please give me some information or references about the implementation of Jintegral at the interface of two materials?

I am looking forward to hearing from you,

Yalcin