Читать книгу The Rheology Handbook - Thomas Mezger - Страница 249

Also for the second test interval various denominations are used: creep recovery curve, re-formation curve, retardation curve, or rest phase.

Transient flow behavior during the re-formation occurs between the time points t2 and t3. Finally, the deformation value reached is Δγe. The latter represents the elastic proportion of the viscoelastic behavior. For a test being sufficiently long, a VE liquid will show a certain, permanently remaining deformation value then (which is γv = const), and therefore steady-state deformation behavior . For a VE solid, steady-state (equilibrium state) is reached when the material displays complete re-formation after all.

The creep recovery function, describing the time-dependent re-formation behavior during the rest phase, can be formulated as follows:

Equation 6.2

γ(t) = γmax – Δγ1 – Δγ2(t) = γmax – (τ0 / G1) – (τ0 / G2) ⋅ [1 – exp(-t/Λ)]

The following applies for t = 0:

γ(0) = γmax – (τ0 / G1) – (τ0 / G2) ⋅ [1 – e0] = γmax – (τ0 / G1) – (τ0 / G2) ⋅ (1 – 1)

thus: γ(0) = γmax – (τ0 / G1)

i. e., immediately after releasing the load, only the spring S1 recoils without any delay.

The following applies for t = ∞ (infinity), or for practical users, after a “very long” time:

γ(∞) = γmax – (τ0 / G1) – (τ0 / G2) ⋅ [1 – (1/e∞)] = γmax – (τ0 / G1) – (τ0 / G2) ⋅ (1 – 0)

thus: γ(∞) = γmax – (τ0 / G1) – (τ0 / G2)

i. e., S1 and S2, and therefore also D2 are fully reset; D3 however, remains deflected. At the very end of the creep recovery phase it is merely the deformation value γv which still occurs.

The following applies for t = Λ, i. e., when reaching the retardation time:

γ(Λ) = γmax – (τ0 / G1) – (τ0 / G2) ⋅ [1 – (1/e)]

thus: γ(Λ) = γmax – (τ0 / G1) – 0.632 ⋅ (τ0 / G2)

i. e., S1 is fully recoiled; and up to this time point, S2 and therefore also D2 is reset by 63.2 %.

D3 however, is still fully deflected as it was at the end of the creep phase.