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Register a new userThe yield of Amorphous Solids Under Stress Control at Low Temperatures
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The yield of amorphous solids like metallic glasses under external stress was discussed asserting that it is related to the glass transition by increasing temperature, or that it can be understood using statistical theories of various sorts. Here we study the approach to stress-controlled yield and argue that neither assertions can be supported, at least at low temperatures. The yield of amorphous solids at low temperatures is a highly structured phenomenon, characterized by a specific series of mechanical instabilities, and having no similarity at all to fluidization by increased temperature, real or fictive. The series of instabilities followed by stress controlled yield at low but finite temperature protocols can be predicted by analyzing athermal quasi-static strain controlled protocols, making the latter highly relevant for the deep understanding of the mechanical properties of amorphous solids.
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It is known by now that amorphous solids at zero temperature do not possess a nonlinear elasticity theory: besides the shear modulus which exists, all the higher order coefficients do not exist in the thermodynamic limit. Here we show that the same phenomenon persists up to temperatures comparable to the glass transition. The zero temperature mechanism due to the prevalence of dangerous plastic modes of the Hessian matrix is replaced by anomalous stress fluctuations that lead to the divergence of the variances of the higher order elastic coefficients. The conclusion is that in amorphous solids elasticity can never be decoupled from plasticity: the nonlinear response is very substantially plastic.
Amorphous solids yield at a critical value of the strain (in strain controlled experiments); for larger strains the average stress can no longer increase - the system displays an elasto-plastic steady state. A long standing riddle in the materials community is what is the difference between the microscopic states of the material before and after yield. Explanations in the literature are material specific, but the universality of the phenomenon begs a universal answer. We argue here that there is no fundamental difference in the states of matter before and after yield, but the yield is a bona-fide first order phase transition between a highly restricted set of possible configurations residing in a small region of phase space to a vastly rich set of configurations which include many marginally stable ones. To show this we employ an order parameter of universal applicability, independent of the microscopic interactions, that is successful in quantifying the transition in an unambiguous manner.
Normal stresses in complex fluids lead to new flow phenomena because they can be comparable to or even larger than the shear stress itself. In addition, they are of paramount importance for formulating and testing constitutive equations for predicting non-viscometric flow behavior. Very little attention has so far been paid to the normal stresses of yield stress fluids, mainly because they are very difficult to measure. We report the first systematic study of the first and second normal stress differences, N1 (>0) and N2 (<0), in both continuous and oscillatory shear of three model yield stress fluids. We show that both normal stress differences are quadratic functions of the shear stress both above and below the shear yield stress, leading to the existence of a yield normal stress.
We study the solid-to-liquid transition in a two-dimensional fully periodic soft-glassy model with an imposed spatially heterogeneous stress. The model we consider consists of droplets of a dispersed phase jammed together in a continuous phase. When the peak value of the stress gets close to the yield stress of the material, we find that the whole system intermittently tunnels to a metastable fluidized state, which relaxes back to a metastable solid state by means of an elastic-wave dissipation. This macroscopic scenario is studied through the microscopic displacement field of the droplets, whose time statistics displays a remarkable bimodality. Metastability is rooted in the existence, in a given stress range, of two distinct stable rheological branches as well as long-range correlations (e.g., large dynamic heterogeneity) developed in the system. Finally, we show that a similar behavior holds for a pressure-driven flow, thus suggesting possible experimental tests.
Soft glassy materials such as mayonnaise, wet clays, or dense microgels display under external shear a solid-to-liquid transition. Such a shear-induced transition is often associated with a non-monotonic stress response, in the form of a stress maximum referred to as stress overshoot. This ubiquitous phenomenon is characterized by the coordinates of the maximum in terms of stress $sigma_text{M}$ and strain $gamma_text{M}$ that both increase as weak power laws of the applied shear rate. Here we rationalize such power-law scalings using a continuum model that predicts two different regimes in the limit of low and high applied shear rates. The corresponding exponents are directly linked to the steady-state rheology and are both associated with the nucleation and growth dynamics of a fluidized region. Our work offers a consistent framework for predicting the transient response of soft glassy materials upon start-up of shear from the local flow behavior to the global rheological observables.
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