(A) dislocation theory of semi-brittle fracture

Abstract

The semi-brittle fracture of an isolated, internal, elastic-plastic, mole 1 crack in uniform tension is studied theoretically with continuum crack and lattice dislocations by inclined slip bands. The simultaneous, singular, integral equations of force equilibrium on the crack and lattice dislocations are solved by cancelling the singularity of stresses at the plastically relaxed crack tip with proper dislocation density functions. The square root term is found to be indispensible in the nonsingular part of the density functions. The validity of cancelling the singularity is confirmed by taking the plastic zone size as the reference of criterion. This confirmation is based on the coincidence in the plastic zone size of this study with that of generally accepted Rice``s T-stress approximation. The COD is found to vary linearly with $K^2/Eσ_Y$ even beyond the limit of small scale yielding. The J-integral based on this model is evaluated on a shrunk path in the form of ◁수식 삽입▷(원문을 참조하세요) The equation first gives a concrete statement of the Eshelby force concept of the J-integral in the inclined strip yield model : J is a hypothetical force acting at the plastic crack tip in the direction of crack propagation and the resorved force of one half of J on the slip plane is equal to the total shear force acting at all the lattice dislocations on one branch of the slip plane. The semi-brittle fracture instability is further studied in the inclined slip band model since the J-integral is a parameter describing fracture initiation only. The concept of the crack tip force which is the same as the J-integral in the elastic crack is extended to the elastic-plastic crack to derive sem-brittle fracture instability. The specific plastic work which has so far been treated experimentally is evaluated theoretically, where the average plastic shear strain in the slip band is assumed to be that corresponding to a 0.2% off-set yield strain. The validity of the assumption is checked ...