A comprehensive constitutive law for waxy crude oil: a thixotropic yield stress fluid

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Abstract

A constitutive model is developed that predicts the rheological response of waxy crude oil to a number of different flows.

Abstract

Guided by a series of discriminating rheometric tests, we develop a new constitutive model that can quantitatively predict the key rheological features of waxy crude oils. We first develop a series of model crude oils, which are characterized by a complex thixotropic and yielding behavior that strongly depends on the shear history of the sample. We then outline the development of an appropriate preparation protocol for carrying out rheological measurements, to ensure consistent and reproducible initial conditions. We use RheoPIV measurements of the local kinematics within the fluid under imposed deformations in order to validate the selection of a particular protocol. Velocimetric measurements are also used to document the presence of material instabilities within the model crude oil under conditions of imposed steady shearing. These instabilities are a result of the underlying non-monotonic steady flow curve of the material. Three distinct deformation histories are then used to probe the material's constitutive response. These deformations are steady shear, transient response to startup of steady shear with different aging times, and large amplitude oscillatory shear (LAOS). The material response to these three different flows is used to motivate the development of an appropriate constitutive model. This model (termed the IKH model) is based on a framework adopted from plasticity theory and implements an additive strain decomposition into characteristic reversible (elastic) and irreversible (plastic) contributions, coupled with the physical processes of isotropic and kinematic hardening. Comparisons of experimental to simulated response for all three flows show good quantitative agreement, validating the chosen approach for developing constitutive models for this class of materials.

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Dynamics of Viscoplastic Deformation in Amorphous Solids

M. L. Falk, J. Langer (1997)

We propose a dynamical theory of low-temperature shear deformation in amorphous solids. Our analysis is based on molecular-dynamics simulations of a two-dimensional, two-component noncrystalline system. These numerical simulations reveal behavior typical of metallic glasses and other viscoplastic materials, specifically, reversible elastic deformation at small applied stresses, irreversible plastic deformation at larger stresses, a stress threshold above which unbounded plastic flow occurs, and a strong dependence of the state of the system on the history of past deformations. Microscopic observations suggest that a dynamically complete description of the macroscopic state of this deforming body requires specifying, in addition to stress and strain, certain average features of a population of two-state shear transformation zones. Our introduction of these new state variables into the constitutive equations for this system is an extension of earlier models of creep in metallic glasses. In the treatment presented here, we specialize to temperatures far below the glass transition, and postulate that irreversible motions are governed by local entropic fluctuations in the volumes of the transformation zones. In most respects, our theory is in good quantitative agreement with the rich variety of phenomena seen in the simulations.