Stress fields and geometrically necessary dislocation density distributions near the head of a blocked slip band

We have examined the interaction of a blocked slip band and a grain boundary in deformed titanium using high-resolution electron backscatter diffraction and atomic force microscopy. From these observations, we have deduced the active dislocation types and assessed the dislocation reactions involved within a selected grain. Dislocation sources have been activated on a prism slip plane, producing a planar slip band and a pile-up of dislocations in a near screw alignment at the grain boundary. This pile-up has resulted in activation of plasticity in the neighbouring grain and left the boundary with a number of dislocations in a pile-up. Examination of the elastic stress state ahead of the pile-up reveals a characteristic “one over the square root of distance” dependence for the shear stress resolved on the active slip plane. This observation validates a dislocation mechanics model given by Eshelby, Frank and Nabarro in 1951 and not previously directly tested, despite its importance in underpinning our understanding of grain size strengthening, fracture initiation, short fatigue crack propagation, fatigue crack initiation and many more phenomena. The analysis also provides a method to measure the resistance to slip transfer of an individual grain boundary in a polycrystalline material. For the boundary and slip systems analysed here a Hall–Petch coefficient of K = 0.41 MPa m½ was determined.