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Korchinski, Daniel

University of British Columbia

Amorphous solids are a diverse class of materials that have significant interest owing to their ubiquity in industry, yet a unifying theory to describe their mechanical response to load under temperature is lacking. Using a combination of highly parallelized numerical routines to simulate an elastoplastic model (EPM) of amorphous solids, as well the corresponding mean-field theory, I develop a scaling theory for the yielding of amorphous solids for non-zero temperature and driving rates. First, I simulate very large systems at zero temperature. Here, ductile yielding proceeds through localized rearrangements that, under sufficient load, self-organize into extended avalanches. I study the appearance of the recently described stability plateau, which violates the existing athermal scaling theories for amorphous yielding. Using finite-size scaling, I show that this deviation originates in the spatial extent of the largest avalanches, and that this plateau in turn affects the energy available to avalanches. Consequently, this changes the scaling description for amorphous yielding at zero temperature. Second, I introduce a temperature-dependent failure to the EPM. With extensive numerical simulations, as well as scaling arguments from mean-field theory, I map out a phase-diagram for different regimes of behaviour, depending on both temperature and the rate at which energy is loaded into the system. I verify the boundaries of the phase-diagram by showing changes in behaviour across each of the phase lines, test predictions for avalanche size and flow stress in each flow regime. Contrary to recently proposed theories based on mean-field modelling alone, I show that the competition between driving rate and temperature differs between the continuously flow regime (in which avalanches merge) and the intermittent flow regime. Finally, motivated by experimental data on the creep of disordered mylar sheets, I study creep-flow in amorphous solids by considering an EPM at fixed stress and non-zero temperature. Here, we show that creep proceeds through cascades of correlated activity that occur over extremely long timescales. These "thermal avalanches" have long periods of quiescence, yet I argue they obey the same scaling laws and underlying physics as the mechanical avalanches of the ductile yielding transition.

Text

2024-09-26

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/89302

Physics

University of British Columbia

UBCV

http://creativecommons.org/licenses/by-nc-nd/4.0/