Pseudo plane stress mode II crack growth in plastic materials

The near tip field of mode II crack that grows in thin bodies with power hardening or perfectly plastic behavior is analyzed. It is shown that for power hardening behavior, the pseudo plane stress field possesses the logarithm singularity, i.e. σ (ln r)²/(n−1), (ln r)^{2n/(n − 1)}, where r is the distance from the crack tip, n the hardening exponent is σⁿ. When n → ∞ the solution reduced to that for the perfectly plastic case.