Line Spring elements errors

Hello, All

***Problem ***

Failure pressure for Steam generator tube having 2 axial cracks. I am following one paper in that paper they found failure pressure by finding J and K values for line spring elements for different pressure. The pressure at which it approach material JIC(92N/mm) and KIC(65Mpa*sqrt(m)) value is considered as failure pressure or coalescence pressus

**Modelling** 

I modeled steam generator tube having diameter of 22mm and thickness of 1.27 mm. It has 2 axial cracks of 6.35mm and lengths between cracks is 0.254mm. Length of the tube is 220mm, so I can assume it as a infinite cylinder.I modeled quarter symmetry of tube. I modified input file to create crack as a line spring elements, 31 line spring elements are created on crack. The tube has S8R shell elements.

**Material Property**

 Material is Alloy 600.

Material property (Entered in ABAQUS): Elastic Modulus : 200 Gpa, Poission ratio : 0.3 

                                    Plastic property :  Stress(MPa)Strain(mm/mm)

                                                                             300                            0

                                                                             512                           0.09274

                                                                             687                         0.178865

                                                                             840                         0.2582

                                                                             946                         0.33177

                                                                            1125                          0.5

                                                                            1700                         1.05

**Questions**

When I ran the analysis for 33Mpa my J reached value of 95 N/mm.And it shows 2 warnings.

1>The line spring elasticity predicts closing of the flaw at 2 points

2>The line spring plasticity theory is intended for tensile and opening moment loading of a flaw. 2 points have elastic stress states which violate this condition

Thank you for comment and advice on my post (crack using line spring elements)

I have one node that is showing stress singularity and it did't show up in warning when I monitor result. However when I went into job diagnostic it shows that one node has stress singularity I found that node and the node has boundary condition of Y symmetry. I am attaching image where node is located at. When i fixed that node it don't show any warnings in Job diagnostic but fixing the node is not realistic I think as I am using quarter symmetry.

 if you have any another advice why this is happening or what else I can do to remove this warning I would really appreciate your help.

Thank you again.