Statistical dynamics of early creep stages in disordered materials

Abstract

When materials are loaded below their short-term strength over extended periods, a slow timedependent process known as creep deformation takes place. During creep deformation, the structural properties of a material evolve as a function of time. By means of a generic coarse-grained mesoscopic elastoplastic model which envisages deformation as a sequence of stochastically activated discrete events, we study the creep deformation of disordered materials. We find that the structural evolution of the material during creep modifies not only the average material properties but also changes the statistics of those properties. We analyze the emergence of correlations in the strain localization and deformation activity patterns, the variation of the event rate and the evolution of the interevent time distribution. We find that the event rate follows the Omori law of aftershocks, which is the discrete counterpart of Andrade's transient creep law, and that the exponent of these laws only depends on the microstructural heterogeneity. Finally, we find during the initial stages of transient creep a transition from Poisson distributed inter-event times towards a non-trivial power law distribution. arXiv:1903.00444v2 [cond-mat.soft]

Prediction of creep failure time using machine learning

“…Such damage localization induces a divergence of the strain rate which indicates catastrophic failure. The model has been successful in reproducing the temporal regimes of creep, the statistics of damage accumulation in the form of avalanches, and the observation of progressive strain localization in the approach to failure 2,3 . A detailed model description and default model parameters are provided in the "Methods" section.…”

“…The model produces, as raw data output, information that can be interpreted as a simulated Acoustic Emission time series: Deformation activity is characterized by the timings, locations, and amplitudes of deformation avalanches, as well as by the resulting spatio-temporal strain patterns. As shown in 2,3 , the corresponding time series exhibit correlations which evolve with time. Examples are the variation of the statistics of avalanches or the progressive localization of spatial activity (see Fig.…”

“…If one assumes the weakest-link hypothesis, then the local strength of a mesoscale region is essentially the strength of the weakest microscopic subregion. In this case, the mesoscale distribution function of the local strength is expected to follow a Weibull distribution 3 . We statistically distribute the local barriers according to a Weibull distribution with shape parameter k, which determines the width of the distribution and hence can be used to quantify the microstructural disorder.…”

“…Attributes (3) and (4) are calculated by taking the sum over the individual rows and columns of the matrices shown in Fig. 1a-d, and determining the magnitude of the maximum and minimum accumulated damage along a row or column, i.e.…”

“…Overall, creep deformation is generally known to have three temporal regimes. First, we observe a decelerating strain rate regime associated with (statistical) hardening or aging effects as the weakest elements of the microstructure deform first and become consequentially inactivated by internal back stresses 3 . The decelerating regime is followed by an intermediate regime of constant strain rate and a final accelerating strain rate regime, associated with damage accumulation and strain localization and leading to catastrophic breakdown 2 .…”