Analysis of plastic zone of mode I crack tip by GM yield criterion

Based on GM (geometrical midline) yield criterion, the analytical solutions for the shape and size of a mode I crack tip plastic zone are derived. Comparing the solutions with those based on Mises and Tresca criteria shows that under a plain strain condition the area of a plastic zone on GM is between both on Tresca and Mises criteria, and very close to Mises one. Among the areas, Tresca's is the largest and Mises is the smallest and all three zones are dumbbell shaped. However, for plane stress, the plastic zones based on GM and on Mises criteria are also proximal but with a bean-spout shape, while the area on Tresca is still the largest. Whenever plane stress or plane strain conditions the result calculated by GM criterion is always an optimal approximation to that calculated by Mises criterion.