On the second order term asymptotic solution for sharp V-notch tip field in elasto-viscoplastic solids

Abstract

A two-order asymptotic solution for sharp V-notch tip mechanics field in elasto-viscoplastic solids with power-law form under mode I loading is developed. The stress exponents and angular distributions for various notch angles and viscoplastic exponents for the second terms are reported. The stress exponent of the first order is singular and is non-singular except for low creep exponent with small notch opening angle. Compared with finite element results from several V-notched specimens, it is found that the two-order solution can have a better estimate for those cases with small notch opening angles, e.g., α = 30° under n = 5, than that of one-order solution regardless of viscoplastic extent, specimen type and loading level. One-order term solution is demonstrated to be sufficient to characterize the full field of sharp V-notch specimen for those conditions that elastic term is considered into higher order term, e.g., α = 60° under n = 5, in all specimens under various viscoplasticity extents.