Relating matrix stress to local stress on a hard microstructural inclusion for understanding cleavage fracture in high strength steel

Abstract

Macroscale cleavage fracture toughness of high strength steels is strongly related to the fracture of hard microstructural inclusions. Therefore, an accurate determination of the local stress on these inclusions based on the matrix stress is necessary for the statistical modelling of macroscale cleavage fracture. This paper presents analytical equations to quantitatively estimate the stress of the microstructural inclusions from the far-field stress of the matrix. The analytical equations account for the inclusion shape, the inclusion orientation, the far-field stress state and matrix material properties. Finite element modelling of a representative volume element containing a hard inclusion shows that the equations provide an accurate representation of the local stress state. The equations are implemented into a multi-barrier model and compared with CTOD experiments with two different levels of constraint.