Dependence of Strength of Elastomers on Strain Rate and Type of Filler

Nonlinear Viscoelasticity and Generalized Failure Criterion for Polymer Gels

“…This appears to be the case for the brittle-like failure scenario of casein gels that are well modeled by Fiber Bundle Models that verify the former hypothesis [5,35,36]. The Bailey criterion reads cess σ(t), and F (σ) is the dependence of the time to rupture for creep experiments performed at a series of constant imposed stresses σ [17]. Independent creep tests have been performed on casein gels [5] and indicate that F (σ) = Aσ −β where A is a scale parameter, with A = (7.6 ± 0.1) × 10 13 s.Pa β and β = 5.5 ± 0.1 for the 4% wt.…”

“…cess σ(t), and F (σ) is the dependence of the time to rupture for creep experiments performed at a series of constant imposed stresses σ [17]. Independent creep tests have been performed on casein gels [5] and indicate that F = Aσ −β where A is a scale parameter, with A = (7.6 ± 0.1) × 10 13 s.Pa β and β = 5.5 ± 0.1 for the 4% wt.…”

“…This approach captures the strain-stiffening of the gel during start up of steady shear tests, up to the appearance of a stress maximum that is accompanied by the onset of the first macroscopic crack. In order to link the nonlinear viscoelastic response of the gel to its subsequent brittle-like rupture, we adopt the Bailey criterion, which describes the failure as arising from accumulation of irreversible damage. , The combination of the stress response predicted by the K-BKZ constitutive formulation with the Bailey criterion allows us to predict the scaling of the critical stress and critical strain at failure with the applied shear rate.…”

“…This appears to be the case for the brittle-like failure scenario of casein gels that are well modeled by Fiber Bundle Models, ,, which themselves verify such assumptions. The Bailey criterion reads ∫ 0 τ f d t / F [σ­( t )] = 1, where τ f denotes the sample lifespan under an arbitrarily given active loading process σ­( t ), and F (σ 0 ) is the dependence of the time to rupture for creep experiments under constant imposed stress σ 0 . Independent creep tests have been performed on the same casein gels and indicate that F (σ 0 ) = A σ 0 –β , where A = (7.6 ± 0.1) × 10 13 s·Pa β and β = 5.5 ± 0.1 for the 4% wt gel and A = (5.0 ± 0.1) × 10 18 s·Pa β and β = 6.4 ± 0.1 for the 8% wt gel (see Figure 3 in the SI].…”