Executive Summary : | Amorphous solids composed of a wide range of materials are of interest in diverse settings, ranging from hard glasses such as silica, chalcogenide glasses, metallic glass alloys to a range of soft materials such as polymeric glasses, emulsions, gels etc. These amorphous solids exhibit both elastic and plastic deformations, the latter being fundamentally important in describing both failure and elasto-plastic flow properties of amorphous solids. A common feature of all these materials is that their structure is disordered microscopically, which implies that (i) plasticity cannot be described in terms of microscopically well defined defects, (ii) the entropic aspects of the diversity of possible states enters essentially into the description of plasticity, and (iii) the mechanical response of an amorphous solid depends strongly on the preparation history of the amorphous solid. There has been significant activity in addressing various dimensions of the problem of yielding in amorphous solids, including under cyclic deformation. Under cyclic deformation, a phenomenon of immense practical importance is fatigue failure, which is the failure of a material with repeated cycles of loading. The present proposal aims to develop a theory of fatigue failure for amorphous solids based on recent advances and employing a range of theoretical and computational approaches. Computer simulations of athermal and thermal cyclic shear deformation of model glasses, carried out by the PI, reveal striking features of yielding behavior. These include a sharply defined, discontinuous yielding transition, a strong and qualitative dependence of yielding behavior on the preparation history of the glasses, mechanically induced aging or annealing below the yield point, and a nucleation like sudden failure after a large number of cycles that has the characteristics of fatigue failure. Several of the features of simulations are remarkably reproduced by a model that has been proposed by the PI, which, in its current form, does not include features of spatial variation and interactions. It thus provides the correct mesoscale description of the problem at hand but needs to be extended to include spatial heterogeneity. It is proposed to build on ongoing investigations in several directions, to address yielding behavior under cyclic loading, and to address the much more challenging problem of fatigue failure. These will include the investigation of idealized stochastic process models without and with activated events that may trigger fatigue failure, mean field and spatially extended coarse-grained elasto-plastic models, the formulation of a nucleation theory for fatigue failure, and extensive atomistic computer simulations that will be used both to inform and to validate the theoretical analysis. The goal is to arrive at a new unified, multi-pronged approach to fatigure failure in amorphous solids, and the outcomes of the investigations will be compared with experimental results. |