Extended Hall–Petch Relationships for Yield, Cleavage and Intergranular Fracture Strengths of bcc Steel and Its Deformation and Fracture Behaviors

Abstract

Extended Hall–Petch relationships for yield ($\sigma_{y}$), cleavage ($\sigma_{\text{cl}}$) and intergranular fracture ($\sigma_{\text{ig}} )$ strengths of pure iron have been established through the direct calculation of the proportional constant $(k)$ and the estimation of the friction stress $(\sigma_{0} )$. The magnitude orders of $k$ and $\sigma_{0}$ are generally $k_{y} < k_{\text{cl}} < k_{\text{ig}}$ and $\sigma_{y0} < \sigma_{\text{cl0}} < \sigma_{\text{ig0}}$, respectively. Based on the Hall–Petch relationships, micro-yielding in a bcc steel occurs at the instance that the pile-up dislocations within a specific grain showing the Schmid factor of 0.5 propagate into the neighboring grain. The initial brittle crack is formed at the instance that the flow strength exceeds the brittle fracture strength. Once the brittle crack is formed, it grows catastrophically. Due to the smallest and $k_{y}$ and $\sigma_{\text{y0}}$, the cleavage and the intergranular fracture occur always after micro-yielding. The {100} cleavage fracture of the steel is due to the lowest theoretical {100} cleavage strength. Due to the thermal components included in cleavage and intergranular fracture strengths, they show also the temperature and strain rate dependence observed in yield strength. The increase in susceptibility to brittle fracture with decreasing temperature and increasing strain rate is due to the increase in dislocation density which causes the high work hardening rate.