Cracks with small-scale yielding SSY

Plane-strain and plane-stress plastic zones 

In SSY, a plastic zone surrounds the crack tip, inside of which the material has yielded as the equivalent stress Ce has reached the yield stress and has strained plastically. Depending on the thickness of the plate in comparison with the size of the plastic zone, the plastic zone develops two different limiting forms. When the 

7 (a) Plastic-zone shapes in SSY under an applied K, in a thin plate in plane stress (v = 0) (P is the finite specimen factor of eqs. (12.6)) and in a thick plate in plane strain for values of Poisson s ratio of 1/3 and 1/2. (b) The shape of the plane-strain plastic zone in a thick plate, changing from a plane-stress character near the surfaces to plane-strain character in the interior (after Williams (1984) courtesy of Wiley). 

Moreover, inside the plane-strain plastic zone of two lobes, the constraint traction o- along the border establishes in the interior of the zone an area-averaged triaxial tensile stress 

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