Microscopic measurement of the local deformation field establishes the mechanistic origin of the fatigue threshold for soft brittle materials

Abstract

Fatigue fracture, whereby a material fails only under repeated loading cycles, depends strongly on load magnitude. In most materials, the applied load must exceed a threshold value - the fatigue threshold - for the crack to advance each cycle. While recent studies clarify the regimes of soft polymer response to cyclic loading, the interplay between crack tip strain fields, irreversible deformation, and energy dissipation remains unclear. Here, we subject polyacrylamide hydrogels and polydimethylsiloxane (PDMS) elastomers to controlled cyclic loading, while directly resolving crack tip strain fields with particle tracking microscopy. An irreversible deformation zone emerges at the crack tip with a load-amplitude dependent structure. Below the fatigue threshold, the zone is compressive, and progressively accumulates without crack advance; this demonstrates that sub-threshold deformation is not fully reversible. Above threshold, a tensile plastic zone grows and co-propagates with the crack tip. Crack tip opening displacement (CTOD) measurements of the energy release rate G show that the applied strain energy evolves with cycle count under constant stretch amplitude loading. Below threshold, G remains nearly constant; above threshold, expansion of the tensile plastic zone modifies the CTOD geometry, producing a measurable decrease in G. Consistent across both material systems in the brittle limit, these results suggest that irreversible deformation — shielding the crack below threshold and governing growth rate above it — may be a general hallmark of soft brittle material fatigue. These findings open pathways toward rational design of fatigue-resistant hydrogels and elastomers for soft robotics, biomedical devices, and stretchable electronics.