Creep Ruptures in Heterogeneous Materials

We present creep experiments on fiber composite materials with different controlled heterogeneity. All samples exhibit a power-law relaxation of the strain rate in the primary creep regime (Andrade's law) followed by a power-law acceleration up to rupture. We discover that the rupture time is proportional to the duration of the primary creep regime, showing the interplay between the two regimes and offering a method of rupture prediction. These experimental results are rationalized by a mean-field model of representative elements with nonlinear viscoelastic rheology and with a large heterogeneity of strengths.

Figure 1

Creep strain rate for all 15 samples: (a) linear time scale, with times renormalized by the rupture time $t_r$; (b) logarithmic time scale to test for the existence of Andrade's law in the primary creep; (c) logarithmic time scale in $t_c-t$ to test the time-to-failure power-law in the tertiary creep. The thick straight line in (b) [respectively, (c)] corresponds to the law $1/t$ [respectively, $1/(t_c-t)$].

Figure 2

Relation between the time $t_m$ of the minima of the strain rate and the rupture time $t_r$, for all samples.

Figure 3

Strain rate $dϵ/dt$ given by (1) for different values of the stress $\sigma$ (in MPa), and with parameters $E=20\mathrm{G}\mathrm{P}\mathrm{a}$, $\mu =1.2$, ${ϵ}_{01}=0.003$, ${ϵ}_{02}=0.015$, $\beta =50{\mathrm{G}\mathrm{P}\mathrm{a}}^{-1}$, and $K={10}^{-5}{sec}^{-1}$. (b) illustrates Andrade's law in the primary regime, with exponent $p\approx 1$ for $\sigma =22\mathrm{M}\mathrm{P}\mathrm{a}$ and $p\approx 0.8$ for $\sigma =25\mathrm{M}\mathrm{P}\mathrm{a}$. The dashed line is the approximate solution (2) of (1) with $\sigma =22\mathrm{M}\mathrm{P}\mathrm{a}$. (c) shows the power-law acceleration of $dϵ/dt$ before failure for $\sigma \ge 25\mathrm{M}\mathrm{P}\mathrm{a}$, with $p^{\prime }\approx 1$ asymptotically. In (a) and (c) the time is normalized by the rupture time for $\sigma \ge 25\mathrm{M}\mathrm{P}\mathrm{a}$, and by the time when $dϵ/dt$ decreases below ${10}^{-14}$ for $\sigma =22\mathrm{M}\mathrm{P}\mathrm{a}$.