Integrated Discrete Cell Complexes and Finite Element Analysis for Microstructure Topology Evolution during Severe Plastic Deformation

Microstructure topology evolution during severe plastic deformation (SPD) is crucial for understanding and optimising the mechanical properties of metallic materials, though its prediction remains challenging. Herein, we combine discrete cell complexes (DCC), a fully discrete algebraic topology model—with finite element analysis (FEA) to simulate and analyse the microstructure topology of pure copper under SPD. Using DCC, we model the evolution of microstructure topology characterised by Betti numbers ( ${\beta }_0$, ${\beta }_1$, ${\beta }_2$) and Euler characteristic ( $\chi$). This captures key changes in GBNs and topological features within representative volume elements (RVEs) containing several hundred grains during SPD-induced recrystallisation. As SPD cycles increase, high-angle grain boundaries (HAGBs) progressively form. Topological analysis reveals an overall decrease in ${\beta }_0$ values, indicating fewer isolated HAGB substructures, while ${\beta }_2$ values show a steady upward trend, highlighting new grain formation. Leveraging DCC-derived RVE topology and FEA-generated plastic strain data, we directly simulate the evolution and spatial distribution of microstructure topology and HAGB fraction in a copper tube undergoing cyclic parallel tube channel angular pressing (PTCAP), a representative SPD technique. Within the tube, the HAGB fraction continuously increases with PTCAP cycles, reflecting the microstructure’s gradual transition from subgrains to fully-formed grains. Analysis of Betti number distribution and evolution reveals the microstructural reconstruction mechanism underpinning this subgrain to grain transition during PTCAP. We further demonstrate the significant influence of spatially non-uniform plastic strain distribution on microstructure reconstruction kinetics. This study demonstrates a feasible approach for simulating microstructure topology evolution of metals processed by cyclic SPD via the integration of DCC and FEA.