# Question regarding applicability of J-integral in LEFM

hi,

I am a Student of 2 year M. Tech. studying in S. V. National Institute of Technology, Surat. My name is Zoeb K Lakdawala. My topic for disseration is ''Implemenation of Fracture Mechanics on Pressure Vessels". In my disseration I want to develop a code on fracture mechanics and compare it with standard Packages like ANSYS & ABAQUS

However, going through the books I have found that in

1. Plane Strain Mode the thickness of the material is very high

2. In Plane Stress Mode the thickness of Material is thin but the exact thickness of the material about which, one should consider Plane strain Problem or Plane stress Problem is not given in any of this books nor it is cited in any material

3. In LEFM (Linear Elastic Fracture Mechanics) it is desired to calculate Stress Intensity Factors KI, KII, KIII according to size of the crack and other geometries whereas in EPFM (Elastic Plastic Fracture Mechanics) it is always advisable to calculate J-integral which a path depended approach. My question is why one cannot calculate J-integral in LEFM and Stress Intensity Factors in EPFM and vice versa what are the restriction in each case.

Regards

Zoeb Kaizar Lakdawala
M. Tech (Industrial Process Equipment Design)
S. V. National Institute of Technology, Surat
Mobile : 09925207052

### As for your third question

Dear Zoeb,

I would like to comment on your third question. First, you may use the J-integral in LEFM calculations. It is widely used for this kind of problems.

As for elasto-plastic materials, for simplicity, I think that we shall restrict our discussion to a case of a Ramberg-Osgood material law with a proportional loading, so that the deformation theory can be assumed. For this case, it may be shown that the plastic zone near the crack tip (HRR zone) is governed by the J-integral, rather than a stress intensity factor. Although Hutchinson (Hutchinson JW, Singular behavior at end of a tensile crack in a hardening material, Journal of the Mechanics and Physics of solids 16: 1-13, 1968)  used a "plastic" stress intensity factor, it is easier to describe this zone using the J-integral, which plays a role of an "amplitude" of the HRR zone. In other words, J is not only the energy release rate, but also the amplitude of the stresses in this region.

In addition, traditionally, K_I, K_II and K_III are associated with a square-root singularity. However, a crack in an elasto-plastic medium does not experience a square-root singularity. Therefore, in my opinion, the J-integral is used in the text books for this case.

A word of caution. The applicability of the J-integral should be examined carefully. For more information, I'm directing you to:

Rice Jr, McMeeking RM, Parks DM and Sorensen EP, Recent finite element studies in plasticity and fracture mechanics, Computer Methods in Applied Mechanics and Engineering 17/18: 411-442 (1979).

--
Yuval