Material Grain Size Determines Relaxation-Time Distributions in Slow-Dynamics Experiments

By measuring the elastic slow dynamics behavior of various consolidated granular materials and metallic alloys, we show that the evolution of the wave velocity as a function of time can be reproduced by using a continuous relaxation-time spectrum, whose main features can be extracted from the experiments. Here we propose to adopt a Weibull distribution of the relaxation times, that we find to display a maximum, which is related to the material grain size and independent of the conditioning amplitude. These results show that the role of the grain-size distribution is fundamental to quantify slow dynamics effects, as well as to clarify its mesoscopic physical origin. Moreover, they can pave the way for the implementation of advanced characterization methods or nondestructive testing techniques capable of retrieving information on the different spatial scales or defects in the materials under investigation.