Yielding Behaviour of Viscoplastic Materials

J. Ind. Eng. Chem., Vol. 12, No. 5, (2006) 653-662 REVIEW Yielding Behaviour of Viscoplastic Materials C. Tiu†, J. Guo, and P. H. T. Uhlherr Department of Chemical Engineering, Monash University, Clayton 3800, Australia Received September 4, 2006 Abstract: Complex fluids exhibiting a yield stress have extremely variable shear properties ranging from elasto-plastic behaviour below the yield stress to viscous behaviour beyond that. The progressive elastic to plastic transition of viscoplastic materials can be explored by a number of rheological techniques including stress sweep, stress ramp, creep and strain recovery. The non-linear behaviour of such materials under different loading conditions can be investigated using a large amplitude oscillatory shear flow (LAOS) combined with Fourier-Transform (FT) harmonic analysis. Results from these rheological measurements provide a char- acteristic “rheological fingerprint” for complex materials exhibiting yield stress. Keywords: yield stress, viscoplasticity, creep, recovery strain, large amplitude oscillatory shear Introduction responding to the transition between plastic deformation 1) and purely viscous flow [4-6]. Although the yielding Many industrial materials, such as filled polymers, response is conventionally interpreted in terms of a polymer gels, thickeners, foodstuffs, cosmetics, concen- “critical stress”, measurements with highly-filled suspen- trated mineral suspensions, electro-rheological and mag- sions such as ER fluids have shown that it is equally neto-rheological fluids behave rheologically in a manner possible to consider the existence of a critical strain at that varies between elastic solid and viscous liquid any level of stress [7,8]. A fundamental interpretation of depending upon the processing conditions. The exis- this transition with respect to processing conditions is of tence of a “yield stress” is traditionally recognised to be great importance to industrial applications. responsible for the complicated transition between The techniques developed for measuring yield stress classical solid-like and liquid-like behaviour. Although can be categorized into two groups: indirect and direct the inadequacy of the rheological definition of this methods. The indirect methods involve the fitting of the property has generated worldwide debate on the exis- shear stress-shear rate data to rheological models such as tence of a true yield stress [1-3], the concept of the yield the Bingham, Casson and Herschel-Bulkley models, etc. stress remains an important parameter in rheological The yield stress is determined by the extrapolation of the characterisation of complex fluids and in understanding flow curve at low shear rates to zero shear rate [9]. The their processing characteristics in industrial applications. results obtained using indirect methods are very sensitive The yield stress is generally regarded as the transition to the models used for fitting the rheological data and the stress between elastic solid-like behaviour and viscous accuracy of the rheological measurement in the low shear liquid-like behaviour, and is related to the internal rate region. particulate network structure. However, this transition Over the last two decades, a variety of direct mea- typically occurs not at a single point, but instead over a surement techniques have been developed to obtain the range of stresses starting at a lower limit, corresponding yield stress based either on dynamic or static principles. to progressive transition between elastic and plastic de- Some examples of these techniques include the im- formation and ultimately ending at a higher limit, cor- mersed plate [10], vane torsion [11], falling and rolling ball [12], inclined plate [13,19], pendulum [14] and slotted plate [15], cylindrical penetrometer [17], and † To whom all correspondence should be addressed. falling needle [18] methods. Among these methods, the (e-mail: [email protected]) 654 C. Tiu, J. Guo, and P. H. T. Uhlherr vane torsion technique is probably the most recognized understand the creep behaviour of a complex material. In and accepted method for yield stress measurement [16]. order to elucidate the transition mechanisms, only the With this method, a well-designed four-bladed vane fully results obtained for a polymeric microgel dispersion are immersed in the test liquid or suspension is rotated at a discussed hereafter. The experimental techniques em- sufficiently low shear rate, and the torque generated is ployed are divided into two parts. Firstly, the transition recorded as a function of time. The vane torsion method behaviour of yield stress materials is fully explored using measures the dynamic yield stress as the sample is the experimental results obtained from various steady sheared from its rest period until the stress reaches its and transient shearing tests. The non-linearity of such peak. The yield stress is calculated from the peak torque materials is investigated in the second part under dif- measurement and the vane dimensions. Recently, the ferent loading conditions using the LAOS and Fourier- vane torsion device has been incorporated into a transform techniques. The large amount of information stress-controlled rheometer to carry out the stress ramp/ generated by LAOS measurements and subsequent FT sweep and creep tests for yield stress materials [6]. On harmonic analysis is represented by some less common the other hand, the static yield stress is the equilibrium formalisms including Pipkin diagrams, Lissajous figures, stress at which the viscoplastic material attains the static FT amplitude and phase angle spectra. This information equilibrium with the measuring devices. With the static provides a unique “rheological fingerprint” for charac- methods, the yield stress is usually approached from the terising the linear and nonlinear behaviour of any non-equilibrium stresses above it. complex fluid. Such rheological fingerprinting will shed Yield stress measurements are notoriously difficult to light on the structural changes from a linear elastic solid interpret. It is not surprising to see that vastly different to a non-Newtonian viscous liquid, occurring in complex values of yield stress of the same material are reported in materials exhibiting a yield stress under the action of an the literature. The variations may be attributed to the applied stress. differences in the measurement techniques, definition of the yield stress, sample preparation, time scale of measurement, and sample pre-sheared history, etc Steady and Transient Shear Flow [6,9,20]. A recent inter-laboratory study [21] was conducted to evaluate the reliability and reproducibility The progressive transition of rheological behaviour of of several common yield stress measuring devices. In viscoplastic materials can be revealed by the shear-stress general, yield stress obtained by the direct methods is sweep or ramp test using a stress-controlled rheometer. A more reliable than the indirect methods. A uniform stress plateau coincides with an unambiguous transition sample preparation, conditioning procedure and a well- from solid-like behaviour to liquid-like behaviour for controlled shear history are paramount in obtaining yield stress materials [6]. Figure 1 shows a typical plot of accurate and reproducible results by direct measurement shear stress versus shear strain and shear stress versus methods. shear rate obtained for a 0.5 % Carbopol gel. Carbopol is The yielding process of viscoplastic materials is closely a high molecular weight polyacrylic acid, cross-linking linked to the transition between linear and non-linear with polyalkenyl and polyester. In an aqueous solution, it rheological behaviour. In recent years, large amplitude takes the form of a microgel dispersion and is often used oscillatory shear (LAOS) flow has been used increas- as a model yield stress material because of its stability ingly to investigate the non-linear rheological responses and transparent nature. At lower stress values, the shear of complex materials such as polymer melts, ER fluids strain appears to be a unique function of the shear stress, and highly concentrated suspensions [8,22-24]. Sig- and is independent of the rate of stress increment, as seen nificant progress has been made in the application of a in Figure 1. A linear relation with a slope approximately methodology known as Fourier-Transform (FT) rheology equal to unity implies a Hookean solid-like behaviour. At [25,26]. The accurate acquisition and processing of large stress values, the shear stress is a unique function highly sensitive FT spectra enable one to systematically of strain rate, which represents a fluid behaviour. The quantify the non-linearity of materials by monitoring the transition from solid to liquid is not abrupt, but goes appearance and growth of higher harmonics. through a region of a stress plateau. The extent of the In this review paper, the yielding process of nonlinear stress plateau reflects the breaking process of the internal viscoplastic materials, covering the entire range of their structure of the material, the slope of which represents transition from elastic to plastic to viscous behaviour, is the uniformity of the molecular bonding strength, or explored using a variety of rheological techniques. A inter-particle forces for the case of a particulate system quantitative understanding of this progressive transition such as suspension. A large slope implies that the in rheological behaviour from linear elastic response to

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