Continuum modeling of shear startup in soft glassy materials

Abstract

Yield stress fluids (YSFs) display a dual nature highlighted by the existence of a critical stress σ y such that YSFs are solid for stresses σ imposed below σ y , whereas they flow like liquids for σ > σ y . Under an applied shear rate γ , the solid-to-liquid transition is associated with a complex spatiotemporal scenario that depends on the microscopic details of the system, on the boundary conditions, and on the system size. Still, the general phenomenology reported in the literature boils down to a simple sequence that can be divided into a short-time response characterized by the so-called "stress overshoot," followed by stress relaxation towards a steady state. Such relaxation can be either (1) long-lasting, which usually involves the growth of a shear band that can be only transient or that may persist at steady state or (2) abrupt, in which case the solid-to-liquid transition resembles the failure of a brittle material, involving avalanches. In the present paper, we use a continuum model based on a spatially resolved fluidity approach to rationalize the complete scenario associated with the shear-induced yielding of YSFs. A key feature of our model is to provide a scaling for the coordinates of the stress overshoot, i.e., stress σ M and strain γ M as a function of γ , which shows good agreement with experimental and numerical data extracted from the literature. Moreover, our approach shows that the power-law scaling σ M ( γ ) is intimately linked to the growth dynamics of a fluidized boundary layer in the vicinity of the moving boundary. Yet such scaling is independent of the fate of that layer, and of the long-term behavior of the YSF, i.e., whether the steady-state flow profile is homogeneous or shear-banded. Finally, when including the presence of "long-range" correlations, we show that our model displays a ductile to brittle transition, i.e., the stress overshoot reduces into a sharp stress drop associated with avalanches, which impacts the scaling σ M ( γ ). This generalized model nicely captures subtle avalanche-like features of the transient shear banding dynamics reported in experiments. Our work offers a unified picture of shear-induced yielding in YSFs, whose complex spatiotemporal dynamics are deeply connected to nonlocal effects.

Stress Overshoots in Simple Yield Stress Fluids

“…2(b), which is composed of two power-law asymptotic limits, namely ðΣ M − 1Þ ∼ _ Γ 1=3 for _ Γ ≪ 1, and ðΣ M − 1Þ ∼ _ Γ 4=17 for _ Γ ≫ 1. These two limits are justified analytically in detail in the companion paper [39] and can be understood qualitatively as the signature of two different dynamical regimes for the nucleation and growth of a shear band of size l b ð tÞ at the moving wall. Indeed, upon shear startup, the initial fluidity remains negligible and the stress Σð tÞ grows roughly linearly up to Σð tM Þ ¼ Σ M where the lhs of Eq.…”

“…In the limit of large shear rates, the fluidity grows from the moving wall, triggering the formation of a fluidized front. Scaling arguments show that the characteristic length and time in the system are ξ= ffiffiffiffi m p and m −3 , respectively [34,39]. Hence, the shear band is expected to move with a velocity dl b =d t ∼ m equals the yield stress, i.e., Σð t1 Þ ¼ 1.…”

Determination of Static and Dynamic Yield Stress of Chengdu Clay Slurry

“…[48,49] described this change process: in viscoelastic thixotropic fluid or nonlinear viscoelastic fluid, there will be stress growth first, then stress attenuation, and then the stress change tends to be stable (equilibrium flow). Although the static yield stress of thixotropic fluid depends on the applied shear rate and sample age [20,21], it is one of the common methods to use the stress overshoot as the static yield stress of mud. In this paper, for the slurry with solid volume concentration greater than 35%, the peak stress (stress overshoot) in the process of accelerated shear is taken as its static yield stress.…”

“…In this case, the stress with deviation of stress response from linearity or maximum stress can be considered. The static yield stress thus determined depends on the shear rate applied and the "sample age" [20,21]. For dynamic yield stress, it is theoretically the shear stress value when the shear rate approaches zero, which represents that the material gradually enters the solid state from the flowing liquid state.…”

Finite-disorder critical point in the yielding transition of elasto-plastic models

“…It was then proposed that the brittle-toductile transition is a novel nonequilibrium phase transition, similar to that of an athermally driven random-field Ising model [19,20]. Further understanding the transformation from brittle to ductile yielding behavior appears as a major challenge in many fields, from materials science to statistical physics [21][22][23][24][25][26][27][28][29][30][31].…”