Scaling Theory of the Hall-Petch Relation for Multilayers

A scaling theory describing the strength of lamellar materials is developed. The theory is based on the premise that dislocation pileups are responsible for the yielding behavior of the lamellar material. The theory is developed in terms of four parameters: The pileup length, the exponent characterizing the divergence of the dislocation density at the interface, a critical distance between the lead dislocation and the interface, and a pinning stress at the interface which acts as an additional hindrance to dislocation motion.