TRANSFORMATION TOUGHENING IN THE GAMMA-TIAL-BETA-TI-V SYSTEM .1. FINITE-ELEMENT ANALYSIS OF A CRACK TOUCHING THE INTERFACE

Atomistic simulation of transformation toughening due to martensitic t ransformation in Ti-V phase particles dispersed in a gamma-TiAl matrix containing cracks requires knowledge of the continuum elastic stress and displacement fields for the problem of a crack touching the gamma- beta interface. Because of the anisotropic characters of the two phase s, analytical solutions for these fields are not available and they mu st be determined numerically. In the present paper a finite element me thod-based eigenanalysis is developed and subsequently applied to the gamma-beta system to determine the order of the stress singularity and the angular dependences of the stress and displacement fields. These fields are subsequently used to enrich the finite elements surrounding the crack tip and, through the use of the general finite element code ABAQUS, to determine the generalized stress intensity factors and thu s the total singular crack-tip stress and displacement fields. It is f ound that there are two coupled singular terms in the singular stress and displacement fields, and consequently pure (uniaxial) mode I loadi ng gives rise to mixed modes I-II near-crack-tip behaviour.