Modeling GND-induced back stress and its role in tension-compression behavior of ultra-thin metal sheets

Accurate prediction of springback and reverse loading behavior in thin metal sheets requires a constitutive model that captures grain-size-dependent long-range dislocation interactions. In this study, a geometrically necessary dislocation (GND)-based back-stress formulation is developed by linking dislocation pile-ups and geometrically necessary boundaries (GNBs) to the generation of internal long-range stress fields. The model introduces a single grain-size-dependent parameter calibrated only from uniaxial tensile tests on two microstructures with different grain sizes, enabling prediction of reverse loading without tension-compression data. The approach accurately reproduces the tension-compression response of low-carbon steel (0.64 mm) and, when coupled with an anisotropic hardening model, captures the tension-bending behavior of ultra-thin SUS316 (0.083 mm). Parameter identifiability analysis confirms the uniqueness and stability of the calibrated values. This framework provides a practical route to predict load-path sensitivity and springback in thin metal sheets while reducing experimental demand. • GND-based back stress model with geometrically necessary boundaries proposed. • Reverse loading predicted using only tensile data from two grain sizes. • CPFEM reproduced Hall-Petch and Bauschinger effects, validated by T-C and T-B tests. • Model upscaled with anisotropic hardening for macroscopic forming simulations.