The Coulomb's failure criterion, which postulates that failure occurs along a fault plane when the applied shear stress overcomes a resistance made of two parts of different nature, cohesion, and friction, remains the standard conceptual framework of faulting mechanics. More recently, rate‐and‐state friction laws became the main modeling tool of the seismic cycle. These laws implicitly assume that only frictional resistance sets the fault strength and its evolution. We therefore raise the question of the role of cohesion and related healing/sealing mechanisms on fault mechanics. We designed an original laboratory experiment based on a model material, an ice thin layer sitting on top of a water tank and mechanically deformed at various rates with a circular Couette‐like geometry. This allowed sliding along the fault plane over arbitrarily large slip distances, and analyzing the competition between faulting and cohesion‐healing rates, whereas frictional resistance, resulting from the fault roughness, is limited in magnitude. We show that cohesion‐healing plays an essential role in the time evolution of the interface strength under constant loading rate. In particular, the magnitudes of shear stress fluctuations are observed to be temperature and velocity weakening. The present experiment shares several properties similar to that of active faults during seismic cycles, suggesting that cohesive healing could control some of these features: scale invariance properties, Gutenberg‐Richter law of rupture event size distribution, Omori's law of energy dissipation, at least after major ruptures, time asymmetry in energy dissipation, and periods of creep under high shear stress alternating with major earthquake‐like ruptures.