Fluctuations and Scaling in Creep Deformation

Abstract

The spatial fluctuations of deformation are studied in creep in the Andrade's power-law and the logarithmic phases, using paper samples. Measurements by the Digital Image Correlation technique show that the relative strength of the strain rate fluctuations increases with time, in both creep regimes. In the Andrade creep phase characterized by a power law decay of the strain rate ǫt ∼ t −θ , with θ ≈ 0.7, the fluctuations obey ∆ǫt ∼ t −γ , with γ ≈ 0.5. The local deformation follows a data collapse appropriate for an absorbing state/depinning transition. Similar behavior is found in a crystal plasticity model, with a jamming or yielding phase transition.

Universal rescaling of flow curves for yield-stress fluids close to jamming

“…over sometimes remarkably long times t. Such behavior was already observed by Andrade for metals in 1910 and has since been reported, in the macroscopic rheology or in corresponding microscopic time scales, for, e.g., crystals [13,[22][23][24], glasses [25], polymers [26], emulsions [27,28], gels [27,28], foams [27,28], sand [29], paper [30], and even complex biomaterials [31]. The value of the creep exponent α equally remarkably then often falls in a narrow interval 0.5-0.7.…”

Predicting sample lifetimes in creep fracture of heterogeneous materials

“…We find a = 0.83 ± 0.01 [26] and a wide range of t c s spanning three orders of magnitude [ Fig. 2(a); see also SM, Figs.…”

“…This, however, is found not to be the case: The "activity spots" [40] detected by DIC during the early stages of creep are not significantly correlated with the final deformation localization and sample failure. In the experiments (material) at hand, typical fluctuations have a fairly large spatial scale compared to the sample size [24,26]. Also, the final crack is detectable using infrared thermography [41] only roughly 1 s before the sample failure (SM, Figs.…”

“…Upper inset: A data collapse of six creep curves after rescaling the time axis by the lifetime t c and the vertical axis by the minimum strain rate t (t m ) [9]. t m from the data-a posteriori or during an experiment-is somewhat complicated for two reasons: experimental noise and intrinsic fluctuations [24,26] in the instantaneous sample creep rate [see Fig. 3(a) for an example t (t) curve].…”

“…One can also consider the sample-dependent spatial strain [24] (as those shown in Fig. 1) or strain rate fluctuations [26] [ Fig. 3(c)] obtained by DIC [24,34] during the early stages of the creep process.…”