Elastoplastic three dimensional crack border field—I. Singular structure of the field

✍ Scribed by Wanlin Guo

• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 957 KB
• Volume: 46
• Category: Article
• ISSN: 0013-7944
• DOI: 10.1016/0013-7944(93)90306-d

✦ Synopsis

The structure of stress and strain fields at the border of three dimensional cracks in a tension field is investigated for elastoplastic materials treated by a deformation theory. The investigation is based upon the physics of the problem and is conducted with mathematical rigour. It is found that the character of singular stresses is as follows: c,, = rfl+*d,,(O, Tz) (i,j = x,y), where/(z) is a function of triaxial stress constraint Tz. The transverse shear stresses Q,, and cc are of the order of unity. The corresponding in-plane strains E,, (i.j = x, y) have singularity of order n(/(z) -2).

while E,, and E,, are of the order of unity. E,, has the same order as in-plane strains at comer points but may be much weaker in the interior of the crack border. Further, it is argued that the problem can be simplified to a quasi-planar problem with the triaxial stress constraint Tz being considered.

When the solution is degenerated into a plane problem by enforcing the confinement, the exact solution for a plane strain crack is obtained and some interesting phenomena are discussed in detail.