Topological characteristics of grain boundary networks during severe plastic deformations of copper alloys

Abstract

The grain boundary character distribution strongly affects the properties of polycrystalline materials. Grain boundaries of similar characters form networks, whose topological invariants can be considered as distribution descriptors. Understanding the evolution of such descriptors during severe plastic deformations (SPD) can elucidate the evolution of properties and underpin the design of processing routes for target behaviour. For topological analysis of grain boundary networks, polycrystalline materials are considered here as polyhedral complexes with grain boundaries classified into two types — low-angle and high-angle. Changes of grain boundary types are calculated using sub-grain rotations, which reflects the physical mechanism of microstructure evolution during SPD. A non-physical approach, by direct conversions of low-angle to high-angle boundaries, is also explored as a reference to demonstrate the impact of the physical constraint imposed by rotations. Reported is the discovery of topological phase transitions in the grain boundary networks which might take place during severe plastic deformations of different copper alloys. Depending on the evolution approach, the transitions correspond to zeros of the Euler characteristic, or of the logarithm of the inverse connectivity, of the grain boundary network. The relations between these transitions and the fraction of high-angle grain boundaries, and between the fraction of high-angle grain boundaries and plastic strain obtainable experimentally, provide new perspectives for grain boundary engineering and network design. Determining the dominant evolution mechanism and critical accumulated strain for a given material and processing route requires further experimental studies of triple junction evolution.