Quantitative analysis of bending hysteresis by real-time monitoring of curvature in flexible polymeric films

Flexibility, viscoelasticity and stress-strain relation in bending polymeric films are key factors in designing mechanically durable flexible electronic devices and soft robots. However, bending hysteresis, which appears as a precursor phenomenon of fracture and fatigue, remains unclear; no one quantitatively evaluated a bending curvature causing hysteresis. Herein, we report the bending hysteresis of polymeric films used as common substrates in flexible electronics by precisely monitoring bending curvatures. By real-time measuring curvatures of films upon bending and subsequent unbending, we have successfully determined the curvatures that cause the hysteresis. These curvatures also depend on a film thickness. Furthermore, we revealed that the occurrence of bending hysteresis is explained by bending strains that have a nonlinear relation with internal stresses. This enables us to predict strain limits that cause the bending hysteresis, based on a stress-strain curve of polymeric films.