Creep failure in heterogeneous materials from the barrier landscape

Abstract

Stressed under a constant load, materials creep with a final acceleration of deformation and for any given applied stress and material, the creep failure time can strongly vary. We investigate creep on sheets of paper and confront the statistics with a simple fiber bundle model of creep failure in a disordered landscape. In the experiments, acoustic emission event times $t_j$ were recorded, and both this data and simulation event series reveal sample-dependent history effects with log-normal statistics and non-Markovian behavior. This leads to a relationship between $t_j$ and the failure time $t_f$ with a power law relationship, evolving with time. These effects and the predictability result from how the energy gap distribution develops during creep.

Figures (5)

• Figure 1: a) Temporal evolution of the strain rate for different experiments and identification of the minimum strain rate (blue dots). b) Amplitudes obtained from the AE sensor (blue) and evolution of the displacement (red). The cyan dashed-line is the amplitude's threshold. Creep load: 0.27 kN.
• Figure 2: Universal lognormal probability distribution for the time $t_j$ in a set of a) experiments and b) FBM simulations. Both cases are represented in a normal probability plot where the x--axis represents the standard normal variable of the logarithm of $t_j$ and the y--axis are the quantiles represented as their respective cumulative probability. Non-Markovian trajectories for each individual c) experiment including $t_f$ (dashed line) and d) FBM simulation.
• Figure 3: Non-Markovian trajectories for the a) mean and b) minimum fiber strength in individual FBM simulations.
• Figure 4: Creep lifetime as a function of a $jth$-event times $t_j$ in a) experiments and c) FBM simulations. The evolution of the exponent $\theta_j$ for b) the experimental data, and d) the FBM results. The black dashed lines are the predicted values from Eq. \ref{['eq:t_f']}.
• Figure 5: a) Evolution of the mean multiplier $\langle r_j \rangle = \langle \Delta t_{j+1} / t_j \rangle$ for the experimental results (red points), numerical results (green points) and theoretical result obtained from Eq. \ref{['eq002']} in one FBM simulation (light green points). b) Evolution of the minimum value of the stress gap distribution for one simulation (light green points), and obtained solving $\Delta\sigma_{\mathrm{min},j}$ in Eq. \ref{['eq002']} from the experimental (red points) and numerical (green points) results. c) Evolution of the stress gap distribution for different values of $j$ in one simulation.