Fig. 4: Damage, quantified by dissipated energy.

a, Damage in each cycle D^cyc, defined as the stress (σ) versus strain (γ) loop area, as a function of strain cycle n_cyc. Insets: stress–strain loops at two different cycles across the failure. b, Accumulated damage D^acc against n_cyc for different \({\gamma }_{\max }\). The solid line for a representative \({\gamma }_{\max }\) indicates that D^acc increases roughly linearly with n_cyc until the failure initiation time t_fi. The crosses indicate the failure initiation time t_fi. The dashed line shows that the accumulated damage until the failure initiation time \({D}_{\mathrm{fi}}^{\mathrm{acc}}=A{t}_{\mathrm{fi}}^{0.8}\). c,d, \({D}_{\mathrm{fi}}^{\mathrm{acc}}\) grows with t_fi with a power of 0.8 for two different degrees of annealing: e_IS = − 7.00 (T_p = 0.435) (c) and e_IS = −6.96 (T_p = 0.5) (d). Symbols with the same colour indicate sample-to-sample data for a given \({\gamma }_{\max }\). e, Failure initiation time t_fi versus average damage per cycle \(\langle {D}_{{\rm{fi}}}^{\mathrm{cyc}}\rangle\) (computed up to t_fi) fitted as a power law for a subset (50%) of samples to estimate the parameter A = 0.036 for e_IS = −7.00. f, Predicted failure initiation time \({t}_{\mathrm{fi}}^{\mathrm{pred}}\) based on the estimated value of parameter A compared with the observed times \({t}_{\mathrm{fi}}^{\mathrm{real}}\) (for the remaining 50% of samples) for different \({\gamma }_{\max }\).