# Grain boundary crack growth in metastable titanium $β$ alloys

### Abstract

Ductile crack growth in a grain boundary layer is modeled under mode I plane-strain, small-scale yielding conditions. The calculations are carried out for planar polycrystals using an elastic–viscoplastic constitutive relation for a progressively cavitating solid with two populations of void nucleating second-phase particles. The material properties in the grain boundary layers are taken to be representative of those for the α phase boundaries in metastable Ti β alloys, while the grain properties are homogenized representations of the grain properties in such alloys. Void nucleation is taken to occur rather early in the deformation history in the grain boundary α phase layers by a stress-controlled nucleation criterion. Subsequent strain-controlled void nucleation occurs within the grains as well as in the grain boundary α layers. The effects of grain flow strength, average grain size, grain morphology and grain boundary α layer continuity on the crack growth resistance and on the plastic dissipation during fracture are considered. The main effects on the crack growth resistance are found to be the grain morphology and the α layer continuity. The fracture surface roughness is characterized in terms of the fracture surface height fluctuations and the computed small-scale regime Hurst exponents in the crack growth direction are consistent with the “universal” values found for other materials and loading conditions. A model for the estimation of the crack growth resistance is also presented. The model gives a very good representation of the crack growth resistance when crack branching does not occur. The model also shows that the crack path taken in the calculations is not necessarily the path of least resistance.

Type
Publication
Acta Materialia
##### Shmuel Osovski
###### Asst. Prof.

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