Yield-Surfaces of Glass Forming Fluids

Kurzfassung

The yielding of amorphous solids depends in principle on the geometry of the deformation applied to the solid. This defines a 'static' yield surface in the state of principal stresses that is typically described by empirical models (such as von Mises, Tresca, Drucker-Prager etc). In a similar vein, approaching the glass transition from the fluid side, the flow stresses approach a dynamical yield stress, defining the dynamical yield surface as the geometry of the flow is varied. Owing to the difficulty of imposing arbitrary steady deformation geometries, both experiment and simulation data are scarce. We will discuss an approach to model yield surfaces that is rooted in a first-principle theory originally developed by Fuchs and Cates, the combination of mode-coupling theory of the glass transition with the integration-through transients framework (ITT-MCT). Using suit- able simplifications, we recover some of the well-known empirical yield surface descriptions as limiting cases. It also sheds light on the qualita- tive differences arising between models of the upper-convected and the lower-convected type. We also performed non-equilibrium molecular- dynamics simulations of a model glass former to determine the dy- namical yield surface. Surprisingly, this attains a shape that is in qualitative agreement with the lower-convected model, although com- mon expectation is that upper-convected models are more canonical in emerging from microscopic descriptions of glass forming fluids.