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through-wall circumferential crack

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.

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