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Nov 1987

Volume 31, Issue 8, pp. 635-834


Elasticity and Failure in Composite Gels

G. J. Brownsey, H. S. Ellis, M. J. Ridout, and S. G. Ring

J. Rheol. 31, 635 (1987); http://dx.doi.org/10.1122/1.549941 (15 pages)

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The mechanical behavior of composite gels consisting of spherical deformable filler particles (Sephadex beads) embedded in a gelatin gel matrix has been investigated. The shear modulus of composite gels is dependent on the shear modulus of the matrix, the deformability of the particles, and their volume fraction. Under uniaxial compression, at high strains, the importance of the filler‐matrix interface in influencing the strength of the composites was demonstrated. Failure properties of the composite were shown to be controlled by altering the chemical affinity between filler and matrix. Studies with a composite food starch gel showed similar dependence on the previously identified parameters.
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83.80.Ab Solids: e.g., composites, glasses, semicrystalline polymers
83.60.Uv Wave propagation, fracture, and crack healing

Effective Medium Approximation for an Elastic Network Model of Flocculated Suspensions

Sanjib Mall and William B. Russel

J. Rheol. 31, 651 (1987); http://dx.doi.org/10.1122/1.549954 (31 pages) | Cited 1 time

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Volume‐filling flocculated dispersions respond elastically to small deformations. We have modelled such systems as disordered elastic networks with statistically homogeneous structures. The disorder of the actual network is represented by a partially filled f.c.c. lattice and the elastic moduli calculated through an effective medium approximation. In this paper we present results for triangular networks in two dimensions with arbitrary combinations of central and bond bending forces for bond as well as site percolation. The moduli increase from zero above an apparent threshold value dependent on the type of percolation and the force law. However, these results are bounded by the isotropic and central force cases, both of which are known for three dimensions. Hence qualitative results for three‐dimensional networks can be obtained without further computations. The theory explains experimental results qualitatively but further refinement is needed to predict the moduli as well as the conductivity of the dispersions accurately.
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83.80.Hj Suspensions, dispersions, pastes, slurries, colloids
83.80.Iz Emulsions and foams
82.70.Kj Emulsions and suspensions

Linear Viscoelasticity at the Gel Point of a Crosslinking PDMS with Imbalanced Stoichiometry

Francois Chambon and H. Henning Winter

J. Rheol. 31, 683 (1987); http://dx.doi.org/10.1122/1.549955 (15 pages) | Cited 33 times

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The evolution of linear viscoelasticity during cross‐linking of a stoichiometrically imbalanced polydimethylsiloxane (PDMS) was measured by small amplitude oscillatory shear. At the gel point (GP), stress relaxation was found to follow a power law, St−n, as described by the previously suggested gel equation. However, while stoichiometrically balanced gels (PDMS, polyurethanes) gave the specific exponent value of n=1∕2, a higher exponent value, 1∕2<n<1, was measured on a stoichiometrically imbalanced PDMS sample. Transformation of the data from the frequency to the time domain required the hypothesis that the power law behavior extends over the entire frequency range, 0<ω<∞. The imbalanced gel exhibited a higher loss than storage modulus, G″(ω)>Gv′(ω), and a higher rate of stress relaxation. GP was found to occur before the crossover point of the loss and storage moduli, G″(ω0,t), and G′(ω0,t), as measured during the cross‐linking reaction (reaction time, t) at constant frequency, ω0. This suggests new methods for localizing GP, for instance by the detection of a loss tangent independent of the frequency. All the experiments were performed with end‐linking networks far above the glass transition temperature. The network junctions were assumed to be due to chemical cross‐links only and not due to any other association phenomenon such as crystallization or phase separation.
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83.60.Bc Linear viscoelasticity
83.80.Jx Reacting systems: thermosetting polymers, chemorheology, rheokinetics

A Comparison of Techniques for Measuring Yield Stresses

Ann S. Yoshimura, Robert K. Prud'homme, H. M. Princen, and A. D. Kiss

J. Rheol. 31, 699 (1987); http://dx.doi.org/10.1122/1.549956 (12 pages) | Cited 8 times

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Three techniques for measuring yield stresses are compared by performing parallel experiments on five model oil‐in‐water emulsions. The emulsions displayed yield stresses of 50–550 dynes∕cm2. The three techniques involved: (1) measurements of rotation rate and stress in a concentric‐cylinder geometry, (2) measurement of torque and apparent shear rate in a parallel disk geometry at two different gap heights, and (3) measurement of rotation under constant applied stress in a vane geometry previously described by Boger. Emulsions are prone to slip at solid boundaries; therefore, methods to assess wall slip contributions for techniques (1) and (2) are developed. The vane device eliminates the possibility of slip. The measurements give comparable results. The techniques are compared with respect to: precision, ease of implementation, information obtained, and sample requirements.
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83.85.Cg Rheological measurements—rheometry
83.60.La Viscoplasticity; yield stress
83.80.Hj Suspensions, dispersions, pastes, slurries, colloids
83.80.Iz Emulsions and foams

Effect of Strain Amplitude on Viscoelastic Properties of Concentrated Solutions of Styrene‐Butadiene Radial Block Copolymers

Yasuhiko Ohta, Takahiko Kojima, Toshikazu Takigawa, and Toshiro Masuda

J. Rheol. 31, 711 (1987); http://dx.doi.org/10.1122/1.549943 (14 pages) | Cited 3 times

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The dynamic viscoelastic properties of 30 wt% solutions of styrene (S)‐butadiene (B) radial (star) block copolymers were measured to investigate the effect of deformation history. The block structure for SBH1 examined was (S‐B‐)m and that for BSH1 (B‐S‐)n, where m and n are about 5. The solvents used were chlorinated diphenyl (KC4) and dibutylphthalate (DBP); the former is a good solvent for both polystyrene (PS) block and polybutadiene (PB) block, and the latter is a good solvent for PS block and a poor solvent for PB block. Both storage modulus G′ and loss modulus G″ vary little with maximum strain amplitude (γ0) for the solutions in KC4, or for those in DBP at 80°C. On the other hand, G′, and G″ depend significantly on γ0 for solutions in DBP at temperatures lower than 60°C, implying that the former systems are homogeneous solutions and the latter contain microdomain structure. G′ and G″ of DBP solutions of SBH1 are independent of γ0 for γ0⩽0.03,G′ decreases and G″ increases in the range 0.04<γ0<0.1, and both decrease for γ0>0.1. This increment in G″ with increasing γ0 is attributed to a domain structure existing in the solution which will be broken down gradually; correspondingly the relaxation time will be shortened. Reformation of the micro‐domain structure takes about 40 min at 60°C.
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83.80.Rs Polymer solutions
83.80.Sg Polymer melts

Fore‐and‐Aft Asymmetry in a Concentrated Suspension of Solid Spheres

F. Parsi and F. Gadala‐Maria

J. Rheol. 31, 725 (1987); http://dx.doi.org/10.1122/1.549944 (8 pages) | Cited 26 times

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Abstract Unavailable
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83.80.Hj Suspensions, dispersions, pastes, slurries, colloids
83.80.Iz Emulsions and foams

Slender Viscoelastic Fiber Flow

William W. Schultz

J. Rheol. 31, 733 (1987); http://dx.doi.org/10.1122/1.549957 (18 pages) | Cited 2 times

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The one‐dimensional equations describing Newtonian fiber flow have been derived previously using lubrication scaling of the axisymmetric equations of motion. Here, we present an extension of that analysis using a generalized convected Maxwell model. We find that the non‐Newtonian behavior of the fluid must be severely limited for the one‐dimensional equations to be determinate. In this sense, the primary effect of viscoelastic behavior is to make the flow more two dimensional. Limiting cases based on previous one‐dimensional models are shown to violate the axisymmetric equations of motion. In addition, questions are raised about the validity of elongational viscosity measurements of highly elastic fluids.
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83.50.Jf Extensional flow and combined shear and extension

The Use of Tensors to Describe and Predict Fiber Orientation in Short Fiber Composites

Suresh G. Advani and Charles L. Tucker

J. Rheol. 31, 751 (1987); http://dx.doi.org/10.1122/1.549945 (34 pages) | Cited 28 times

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The properties of a set of even‐order tensors, used to describe the probability distribution function of fiber orientation in suspensions and composites containing short rigid fibers, are reviewed. These tensors are related to the coefficients of a Fourier series expansion of the probability distribution function. If an n‐th‐order tensor property of a composite can be found from a linear average of a transversely isotropic tensor over the distribution function, then predicting that property only requires knowledge of the n‐th‐order orientation tensor. Equations of change for the second‐ and fourth‐order tensors are derived; these can be used to predict the orientation of fibers by flow during processing. A closure approximation is required in the equations of change. A hybrid closure approximation, combining previous linear and quadratic forms, performs best in the equations of change for planar orientation. The accuracy of closure approximations is also explored by calculating the mechanical properties of solid composites with three‐dimensional fiber orientation. Again the hybrid closure works best over the full range of orientation states. Tensors offer considerable advantage for numerical computation because they are a compact description of the fiber orientation state.
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83.50.-v Deformation and flow
83.80.-k Material type

Mathematical and Computational Aspects of a General Viscoelastic Theory

Alex Markovsky, Thomas F. Soules, Victor Chen, and Milan R. Vukcevich

J. Rheol. 31, 785 (1987); http://dx.doi.org/10.1122/1.549958 (29 pages)

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A discussion of mathematical aspects of general stress‐strain problems involving viscoelastic materials is given. Constitutive equations are presented in a general differential form. These equations generalize the Boltzmann constitutive relations and provide a convenient way to solve stress‐strain problems. A stable and efficient finite‐difference scheme is constructed and applied to the calculation of the residual stress distribution in a laminar viscoelastic‐elastic composite plate cooled by convection from both sides. In the appendices general relations among relaxation functions are discussed. The results can be used to determine the shift in average relaxation times depending on geometry of relaxation experiment.
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83.10.Gr Constitutive relations

Wall Slip and Extrudate Distortion in Linear Low‐Density Polyethylene

Douglass S. Kalika and Morton M. Denn

J. Rheol. 31, 815 (1987); http://dx.doi.org/10.1122/1.549942 (20 pages) | Cited 31 times

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The onset of extrudate distortion (sharkskin) in linear low‐density polyethylene is shown to coincide with the failure of adhesion at the polymer∕metal interface. The transition to slip‐stick melt fracture is characterized by a catastrophic failure of adhesion, with periodic nearly complete slip over a capillary residence time alternating with adhesion. The onset of sharkskin is in agreement with a calculation based on a stability theory of Pearson and Petrie.
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83.50.Lh Slip boundary effects (interfacial and free surface flows)
83.80.Rs Polymer solutions
83.80.Sg Polymer melts
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