Deformation limits on two-parameter fracture mechanics in terms of higher-order asymptotics

In recent years, there has been an increased interest in the influence that crack-tip constraint has on the ability to measure a materials geometry independent toughness. Loss of crack-tip constraint observed in several laboratory specimens geometries can occur for several reasons. The two most common are influences of near tip free boundaries and uncontained plasticity which can be directly associated with the free boundaries. Recent studies have addressed this issue by incorporating a second parameter into what has become known as classical single-parameter fracture mechanics.; In this thesis, a criteria is established by which it is possible to determine if a crack-tip stress field can be characterized by a two-parameter theory. An asymptotic analysis of the general power series representation of the stress potential was performed for a Ramberg-Osgood power hardening material. The independent coefficients in the series were determined as a function of deformation level for the single edge notch bend (SENB), center crack tension (CCT), double edge notch tension (DENT), and single edge notch tension (SENT) by matching the analytic solution with full field finite element results for a/W geometries of 0.1, 0.5, and 0.9. The evolution of these independent parameters was compared with the evolution of those found for the two-parameter modified boundary layer (MBL).; Results indicate that the near tip stresses in all but the SENB (a/W = 0.5, 0.9) and SENT (a/W = 0.9) lend themselves to a hyo-parameter characterization. Although the two SENB and one SENT do not evolve in a customary two-parameter sense, the difference between their results and those obtained for the single-parameter small scale yielding (SSY) solution for the MBL is in general not large for low to moderate deformation levels. Hence, the error field which is defined as the difference between the two-parameter MBL stress field and finite geometry stress field is less for an equivalent departure from the two-parameter description for the deep cracked SENB and SENT geometries as compared to the CCT or DENT at moderate deformation levels.