Load-Dependent Power-Law Exponent in Creep Rupture of Heterogeneous Materials

TL;DR

The study investigates how heterogeneities influence slow creep rupture under subcritical loading and shows that the power-law creep exponent $\alpha$ depends on both applied load and loading direction. Using a displacement-feedback experimental protocol on paper and PDMS, they observe primary creep with $\dot{\varepsilon}=\gamma\,t^{-\alpha}$ and a load-dependent evolution of $\alpha$ and $\gamma$, including material anisotropy effects. These findings are reproduced by a thermally activated, equal-load-sharing Disordered Fiber Bundle Model (DFBM), which also reveals that $\alpha$ decreases and $\gamma$ increases as $\sigma_t$ approaches $\sigma_r$, with $\alpha$ and $\gamma$ modulated by temperature $T$ and disorder $T_d$. The results indicate that load-dependent delayed rupture dynamics in heterogeneous materials can be captured by simple DFBMs, offering insights into rupture precursors and material reliability under subcritical loading.

Abstract

Creep tests on heterogeneous materials under subcritical loading typically show a power-law decaying strain rate before failure, with the exponent often considered material-dependent but independent of applied stress. By imposing successive small stress relaxations through a displacement feedback loop, we probe creep dynamics and show experimentally that this exponent varies with both applied load and loading direction. Simulations of a disordered fiber bundle model reproduce this load dependence, demonstrating that such models capture essential features of delayed rupture dynamics.

Figures (11)

• Figure 1: Experimental set-up: custom made tensile apparatus (a). On one side a motor pulls on the sample to impose a deformation $\varepsilon$, while a force sensor measures the resulting load $\sigma$ on the material. The force sensor can be used in a feedback loop to impose a constant load on average. The sample is maintained either by two cylindrical rollers in the case of paper samples (b) or by two self-locking jaws in the case of PDMS samples (c). The entire experimental setup is placed in a semi-hermetic box to control the air humidity.
• Figure 2: Comparison of the mechanical behavior in tensile test for fax paper in parallel direction (a) and in perpendicular direction (b), and for two kinds silicon elastomers from manufacturers Gteek (c) and GoodFellow Inc (d).
• Figure 3: Subcritical rupture process in paper. Here, the sample is loaded with a target stress of 16.87 (orange horizontal line), maintained at the target stress by a feedback mechanism until macroscopic failure at $\tau_{c}$$\sim$3000 (red vertical line). The inset shows a zoom on a few successive relaxations and the graphical definition of their duration $\Delta t$ and their amplitude $\Delta \sigma$.
• Figure 4: Duration of successive relaxations $\Delta t$ as a function of the normalized time $t/\tau_c$ for paper $\perp$ (top), PDMS 1 (bottom left), and PDMS 2 (bottom right). All samples show a near-linear increase in $\Delta t$ for at least 50% of the lifetime $\tau_c$. Paper and PDMS 1 also show a clear decrease before failure.
• Figure 5: Strain rate $\dot{\varepsilon}$ as function of time for paper (top), PDMS 1 (bottom left), and PDMS 2 (bottom right). For all samples, the primary creep regime follows $\dot{\varepsilon} = \gamma\times t^\alpha$. Fitted values of $\alpha$ and $\gamma$ are shown in each legend.