Early Prediction of Creep Failure via Bayesian Inference of Evolving Barriers

Abstract

Creep under a sustained load can persist for long times yet culminate in abrupt yielding or rupture, implying a finite lifetime even when the material appears solid. Here, we formulate lifetime prediction as Bayesian inference over an evolving activation-energy landscape. A time-dependent distribution of activation barriers controls deformation: stress lowers barriers, while irreversible rearrangements deplete the weakest sites and reshape the low-barrier tail. Using early-time acoustic emission data, Bayesian inference estimates the evolving barrier statistics in each sample and yields posterior predictive distributions for the time-to-failure. This approach provides uncertainty-aware lifetime forecasts that link microscopic barrier evolution to macroscopic creep dynamics.

Figures (3)

• Figure 1: A schematic description of the prediction process, where the top panel shows the continuous strain rate $\dot{\varepsilon}$ (blue) and the discrete accumulated number of events (red dots) as a function of time $t$. The data $\mathcal{D}$ consist of the strain data (blue) and discrete event times (red) read up to a time $t_{\rm obs}$, and based on this data, one tries to predict the failure time $t_{\rm f}$. For Bayesian inference, one needs a prior distribution $p(\theta)$, e.g., for the failure time (middle panel). By conditioning on the data $\mathcal{D}$, one obtains a posterior distribution $p(\theta \, | \, \mathcal{D})$ (bottom panel), which provides an estimate of the failure time and its associated uncertainty for each Bayesian inference approach.
• Figure 2: a) An example of the failure time prediction from the strain rate signal (Top panel). b) The evolution of the posterior distribution of the failure time (blue) as one changes the time $t_{\rm obs}$ (blue dashed line) for a representative example. The green symbols show the prior distributions for the failure time for comparison. c) The proportion of predicted experiments for a given tolerance and prediction time $t_{\rm obs}$, with a zoomed-in view below. Here a 10 % precision is chosen.
• Figure 3: a) Comparison of the evolution of the posterior distribution of the failure time as one changes the prediction time $t_{\rm obs}$ for one single experiment using either the master curve approach (blue) or the AE correlations (red). The gray dashed line corresponds to $t_{\rm obs}$b) Comparison of the prediction score (CRPS${_{\rm log}}$) for all the experiments using either the master curve approach (blue) or the AE correlations (red), where the blue dots and the red diamonds represent their mean value. Evolution of the power--law exponent c) $\theta_j$, and the prefactor d) $C_j$ for all the experiments taking just times at $t_{\rm obs} / t_f^{\rm true} \leq 0.9$, where the red diamonds represent the mean value.