Predicting sample lifetimes in creep fracture of heterogeneous materials

Juha Koivisto, Markus Ovaska, Amandine Miksic, Lasse Laurson, and Mikko J. Alava

Phys. Rev. E 94, 023002 – Published 8 August 2016

Abstract

Materials flow—under creep or constant loads—and, finally, fail. The prediction of sample lifetimes is an important and highly challenging problem because of the inherently heterogeneous nature of most materials that results in large sample-to-sample lifetime fluctuations, even under the same conditions. We study creep deformation of paper sheets as one heterogeneous material and thus show how to predict lifetimes of individual samples by exploiting the “universal” features in the sample-inherent creep curves, particularly the passage to an accelerating creep rate. Using simulations of a viscoelastic fiber bundle model, we illustrate how deformation localization controls the shape of the creep curve and thus the degree of lifetime predictability.

Received 21 September 2015

DOI:https://doi.org/10.1103/PhysRevE.94.023002

Physics Subject Headings (PhySH)

Creep Fracture Mechanical deformation Viscoelasticity

Interdisciplinary PhysicsCondensed Matter, Materials & Applied PhysicsNonlinear Dynamics

Authors & Affiliations

Juha Koivisto, Markus Ovaska, Amandine Miksic, Lasse Laurson, and Mikko J. Alava

COMP Centre of Excellence, Department of Applied Physics, Aalto University, P. O. Box 11100, FIN-00076, Aalto, Espoo, Finland

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Vol. 94, Iss. 2 — August 2016

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Images

Figure 1
Experimental setup to study the spatiotemporal creep dynamics of paper samples. (a) The tensile testing machine where the paper sample, attached between two clamps, is subject to a constant applied force. (b) A typical creep curve and example strain maps computed by digital image correlation analysis for three times $t_{1}, t_{2}$ , and $t_{3}$ , showing how the strain fluctuations develop towards the localization of deformation leading finally to sample failure.
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Figure 2
(a) The time of the minimum creep rate $t_{m}$ as a function the sample lifetime $t_{c}$ for a large number of experiments, including different loading conditions and sample geometries, and also repeating the experiment several times using the same conditions. The data are well described by $t_{m} = 0.83 t_{c}$ . Lower inset: Time dependence of strain rate $ε_{t}$ for three example experiments, all exhibiting a minimum strain rate at time $t = t_{m}$ (shown with a red arrow in one case) before acceleration towards final failure at time $t = t_{c}$ . 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 $ε_{t} (t_{m})$ [9]. (b) Comparisons of lifetime predictions $(t_{c})$ to the actual values of lifetime, $t_{c}$ , with the black lines corresponding to a $10 %$ difference between the predicted and actual value of $t_{c}$ . Inset: Six different cases of actual prediction experiments. The full symbols correspond to minimum strain rate time $t_{m}$ estimates and the open ones to the corresponding $t_{c}$ predictions. The $ε_{t}$ data are shown with the curves. The six cases are also marked in the main figure with the correspondingly colored symbols.
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Figure 3
(a) Definition of the transient time $t_{trans}$ corresponding to the crossover from primary to secondary creep regime is here given by the point (blue dot) at which a fit (black line) corresponding to the typical Andrade or primary creep law, $ε_{t} = A t^{- 2 / 3}$ , deviates more than 10% from the data (shown in green). (b) $t_{c}$ as a function of the corresponding $t_{trans}$ , revealing a roughly exponential trend, $〈 t_{c} (t_{trans}) 〉 \sim exp (t_{trans} / t_{0})$ . (c) Shows that the relative spatial strain rate fluctuations, computed by DIC 128 s from the start of the experiment using a time window of 10 s (see the inset for an example of a map of the fluctuating local strain rates), exhibit an inverse correlation with the lifetime, $t_{c}$ .
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Figure 4
(a) The MG $[t_{m} (t_{c})]$ relation is depicted for three different geometries of the viscoelastic SFBM, i.e., different values of the number $N_{s}$ of bundles connected in series. For each $N_{s}$ (with $N_{s} = 1$ , 40, and 1000 shown in red, blue, and green, respectively), we consider also several load values (shown with different symbols) close to but above the critical load required to break the sample. (b) The evolution of $t_{m} / t_{c} \equiv a (N_{s})$ with $N_{s}$ . The solid line corresponds to a fit of the form of $a (N_{s}) = 1 - A e^{- {(N_{s} / B)}^{C}}$ , with $A = 0.69 \pm 0.01, B = 17.6 \pm 0.1$ , and $C = 0.26 \pm 0.01$ . (c) Examples of the scaled creep curves for the three $N_{s}$ values shown in (a). Notice how the minimun strain rate time $t_{m}$ moves towards the lifetime $t_{c}$ as $N_{s}$ is increased.
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Figure 5
Lifetime histograms shown for the experiments (a) and the model (b) using a “Weibull paper” [plotting the inverse cumulative lifetime distribution $1 - P_{cum} (t_{c})$ using a double logarithmic scale].
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