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Abstract The asymptotic analysis of near tip field of plane stress mode II cracks growing quasi-statically in steadiness in power lawhardening solids has been performed. Attention was focused on the behavior of the asymptotic solutions as hardening exponent n → ∞.Analytical expressions of the dominant terms of velocities and now factor in centered fan sectors were obtained by expanding them in seriesof the small parameter s = 2/(n - 1). Results show that, as n→∞, all the expressions of dominant terms of quantities in near tip fieldtend to their corresponding ones for elastic-perfectly plastic materials. The effect of hardening exponent n on the angular variations ofstresses in near tip field is very weak. Analysis and discussion that related to plane stress mode Ⅰ crack problem is given in appendix forcomparison with results for mode Ⅱ.
Abstract The asymptotic analysis of near tip field of plane stress mode II cracks growing quasi-statically in steadiness in power lawhardening solids has been performed. Attention was focused on the behavior of the asymptotic solutions as hardening exponent n → ∞. An analysis of the dominant terms of velocities and now factor in centered fan sectors were obtained by expanding them in series of the small parameter s = 2 / (n - 1). Results show that as n → ∞, all the expressions of dominant terms of quantities in near tip The effect of hardening exponent n on the angular variations of stresses in near tip field is very weak. Analysis and discussion that related to plane stress mode I crack problem is given in appendix for comparison with results for mode Ⅱ.