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# J integral variation through thickness in tubes with through-wall circumferential crack, calculated with Abaqus/CAE

Dear friends: I am a PhD candidate studying fracture problems in tubes. I am doing J integral calculations in Abaqus, for tubes with through-wall circumferential cracks subjected to tensile and bending loads. I am using quadratic 20 nodes isoparametric elements with reduced integration (C3D20R), ranging from two to five elements through the wall thickness mesh. The singularity is modeled with midside node parameter t=0.3 (not 0.25 because the 3D elements planes are not perpendicular to the crack line) and collapsed element side, duplicate nodes, to create a combined square root and 1/r singularity for hardening materials (the material is modeled as elastic-plastic, with a stress-strain curve introduced with a data table). The results show that the J integral varies through the thickness of the tube. Up to now we have only one reference showing this kind of J integral behavior through thickness for tubes (see attachment 1). This reference shows a variation of J with the highest value at the mid-thickness of the wall, and depends on the number of elements through thickness: the question is if this is a numerical artifact or has some physical meaning. Our results also show J variation through thickness, but with the higher J values at the wall surfaces for high loads (see attachment 2). Obviously, the comparison between these results is not direct due to the fact that both problems have different geometry, material properties and loading conditions. From the earlier, I have the following questions: 1) Are there more references regarding the J variation through thickness for tubes with through-wall circumferential cracks? 2) The high J variation through thickness, is it a physical or numerical result? 3) The singularity modeling in our case (t=0.3 and collapsed duplicated nodes), is it adequate? 4) Abaqus calculates a J integral in each element face, where are located the nodes. In the case of quadratic elements, Abaqus also calculates the J integral in the middle of the element, using the midside nodes. Are the last J integral values comparable with the J integral values obtained in the element faces? I mean if the J values have the same “weight” in an averaging process, for instance, or if there is some difference in the accuracy depending if the nodes used to calculate J are in the faces or in the mid-face of the element. Is it better to calculate element averages than individual values in each face and mid-face?Thank you very much for your comments!Best regards, Marcos

Attachment | Size |
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Attachment 1.pdf | 257.9 KB |

Attachment 2.pdf | 127.6 KB |

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## Comments

## abaqus

Hi Marcos

I studying throughwall circumferential cracked pipes in Abaqus. I wanted to know what is the strategy to partition the cell in abaqus to get a crack tip. What should be the radius of the circle where we want to mesh finer around the crack tip.

thanks in advance!!

## J-int should vary due to

J-int should vary due to through-the-thickness constrain.

Same case as plane strain or plane stress conditions.

I have performed similar calculations and found same results but with ANSYS