Correlation of normal stresses in polystyrene melts and its implications

It is found that the principal normal stress difference, N₁, in commercial polystyrene melts is a unique function of shear stress σ₁₂, independent of temperature and molecular weight, An empirical expression representing this relationship is developed. The functional dependence reported does not represent data for narrow molecular weight distribution polystyrenes, generally significantly overpredicting N₁ values. The basis for this behavior is discussed. The implications of the N₁ ? σ₁₂ relationship to some rheological and processing problems are described.     

The yield stress of fibre suspensions

Yield stresses were determined for commercial wood pulp suspensions and synthetic fibre suspensions of low and medium mass concentration. The yield stresses measured represent interfibre failure of the network rather than failure between the suspension and a solid surface. The measurements were carried out in a rotary viscometer at low yield stresses and in a concentric rotary shear tester at yield stresses in excess of 2500 Pa. The experimental results were correlated with the volumetric concentration C_v in equations of the form τ_y = aC^b_v where a and b are constant for a given fibre type. It was found that b ? 3, in agreement with the predictions of a theoretical model of fibre network strength based upon the interlocking of elastically bent fibres. The dependence of the yield stress on the fibre properties of aspect ratio and modulus of elasticity was not adequately predicted by the model, suggesting that fibre bending alone did not account for the network strength over the concentration range studied.     

Stress growth and relaxation of a molten polyethylene in a modified weissenberg rheogoniometer

A Weissenberg rheogoniometer was modified^1-3 to improve sample temperature uniformity and constancy (to within ±0.5°C) and to give a quicker response to normal thrust changes (estimated gap change ≤0.1 μm/kg thrust; gap angle = 8.046°; gap radius = 1.2 cm; servomechanism replaced by an open-loop cantilever spring of 10 kg/μm stiffness). Low-density polyethylenes (IUPAC samples A and C, melt index at 190°C = 1.6) at 150°C were used in step-function shear rate experiments. Inspection of marked sectors in the samples showed substantial uniformity of shear at values of ? = 0.1, 2, and 5 sec^?1; for ? = 10 sec^?1 and S ≤ 2 shear units (S = ?t), the shear was highly nonuniform at and near the free boundary. Using selected premolded samples A, scatter in seven replicate tests at ? = 1.0 sec^?1 did not exceed ±6% for N₁(t) and ±5% for σ(t) (N₁ = primary normal stress difference; σ = shear stress; t = time of deformation from the initiation of experiment at zero time). N₁(t) and σ(t) data agreed with Meissner's¹; for ? = 0.1, 2.0, 5.0, and 10.0 sec^?1, torque maxima occurred at S = 6 shear units, and thrust maxima occurred in the range of 10 to 20 shear units. σ(t) and N₁(t) data do not satisfy the van Es and Christensen⁴ test for rubber-like liquids with strain rate invariants included in the memory function. On cessation of shear (after a shear strain S at constant shear rate ?), initial values of ?dσ(t)/dt and ?dN₁(t)/dt were found to depend strongly on S, in some cases passing through maxima as S was increased. After shearing at ? = 0.1 sec^?1 for 500 sec, such that stresses became constant, stress relaxation data satisfied Yamamoto's⁵ equation of dN₁(t)/dt = ?2?σ(t).     

A Survey of Rheological Properties of One-Component Epoxy Adhesives

Flow characteristics of seven commercially available one-component epoxy adhesive pastes were measured using a controlled shear stress rheometer and a controlled shear rate rheometer over a temperature range from 5°C to 60°C. Combining data obtained from both controlled rate and controlled stress experiments over a wide range of shear rates, we observed Newtonian flow (shear stress proportional to shear rate) at very low shear rates, a plateau “shear thinning” region at intermediate shear rates, and a second region of linear dependence of shear stress on shear rate at high shear rates. The adhesive pastes exhibited a very broad range of rheological behavior. Two flow parameters important to adhesive application technology, the plastic viscosity and the apparent yield stress, were measured for each adhesive. The plastic viscosity ranged from 11.6 to 329.5 Pa. s; the apparent yield stress ranged from 56.2 to 413 Pa. The temperature dependence of the rheological parameters of the epoxy adhesive pastes was also determined. The results are reported as the activation energies, E_η and E_σ , of plastic viscosity and apparent yield stress, respectively. The apparent yield stress of each adhesive paste was much less sensitive to changes in temperature than was the plastic viscosity. This suggests that the processing characteristics are likely to show qualitative as well as quantitative changes with temperature.     

Rheological characterization of carbon black/polystyrene solution systems

Steady‐shear measurements of suspensions of carbon blacks (CB) in polystyrene (PS)/di‐(butyl phthalate) (DBP) solution were investigated as a function of volume fraction (?) of CB to clarify the effect of the primary particle size and the structure of CB aggregates on the rheological properties. The suspensions show a typical shear‐thinning behavior in the range of a shear rate studied. The Casson model was applied to evaluate the viscosity at infinite of shear rate η_∞ and the yield stress σ_y for the suspensions. Relative viscosity η_∞/η_m, (η_m: medium viscosity) thus obtained was compared to the high‐frequency viscosity for the ideal hard‐sphere silica suspensions to evaluate the effective volume fraction ?_eff of CB aggregates. The ?_eff value was larger for the higher‐structure CB with higher DBP absorption value, irrespective of the primary particle size. The yield stress σ_y had almost the same ?_eff dependence for neutral furnace CB/(PS/DBP) suspensions, although it was larger for acetylene black (AcB)/(PS/DBP) suspensions. These results demonstrated that the effective volume fraction is the most important quantity to characterize the CB aggregates on the rheological properties. It was also found that the correction of the medium viscosity changes due to polymer adsorption on the CB surface is important since neutral furnace CB adsorbs PS polymers but AcB hardly adsorbs PS polymers in the solution. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Rheoiogical studies of compaction for polystyrene powder

Polystyrene powder was compacted in a cylindrical die at constant compaction speed. Compaction was found to be influenced by test temperature, compaction speed and void fraction of the powder bed. The stress reduction behavior of an axial stress σ₁ and a radial stress σ₂ was observed at constant void fraction after compaction. The stress reduction thus obtained was interpretable by adopting an octahedral normal stress σ_oct and an octahedral shear stress τ_oct which were converted from σ₁ and σ₂. This behavior was attributable to the deformation of polystyrene around contact points and to a sliding mechanism between particles. It was ascertained that the relation between a shear stress τ and a normal stress σ obtained on compaction differed from that obtained in shear by a mechanism involving movement between polystyrene particles.     

Effect of high shear stress on microbial viability

Escherichia coli and Saccharomyces cerevisiae suspensions were submitted to controlled shear stress. Above a threshold value shear stress induced a decrease in micro‐organism viability. The threshold of shear stress efficiency depended on the micro‐organisms, being between 1292 Pa and 2770 Pa for S cerevisiae, and about 1250 Pa for E coli. Above 1810 Pa, E coli cells were disrupted whereas the S cerevisiae cells remained intact. The higher the cellular concentration, the greater the rate of decrease in viability. Viability loss was influenced by the number of passages through the experimental shear stress device and by exposure time. © 2001 Society of Chemical Industry     

Effects of interlaminar stresses on damping of 0-degree unidirectional laminated composites

The principal aim of this paper is to formulate a general model for predicting damping in composites on the basis of the concept of strain energy-weighted dissipation. In this model, the effects of interlaminar stresses on damping have been included in addition to the effects of in-plane extension/compression and in-plane shear. Validation of the model was confirmed by performing damping measurements on 0° unidirectional composite beams with varying length and thickness. The results of theoretical predictions of damping in laminated composites were found to compare favorably with experimental data. The transverse shear (σ_xz) reveals to have a considerable effect on the damping mechanisms in 0° unidirectional polymer composites. However, the other interlaminar stresses (σ_yz, σ_z) were shown to have little influence on damping in composite beam.     

A Study of the Pull‐Out Performance of PPTA Fibres in Composites of Ethylene‐Type Ionomer Matrices/PPTA Fibres

The mean frictional shear stresses of six ionomer resins and sized Kevlar fibre were determined from fibre pull‐out tests. A study of the failure mechanisms occurring during pull‐out revealed that fibre delamination and fibre resin adhesion were factors which increased the measured frictional shear stresses and that there was a definite grouping of high and low frictional shear stress values. The low frictional shear stress values were used to calculate the mean frictional shear stress values, τ_B, because these were uncomplicated by fibre delamination and fibre resin adhesion, since these factors (delamination and adhesion) are certainly not unexpected in an ionomer/Kevlar composite. From these shear stress values, it was determined that critical fibre lengths should be between 35 and 72 mm for the high tensile strength Kevlar fibres within an ionomer matrix, for the composite to be used effectively. The ratio of the debonding force (F_B) to the frictional shear force (F_F), θ, did not vary significantly with the lengths of the embedded reinforcing fibres. Both debonding and frictional forces indicate increasing trends with the interfacial contact areas. The ratio of the interfacial bonding strength (τ_B) to the frictional shear stress (τ_F), ϕ, for the resin PEA‐6 compared to the surface modified poly(p‐phenylene terephthalamide) (PPTA) fibre ranged from 2 to 24. These ratios were grouped into two, viz: those where ϕ > 11 and those with ϕ < 7. Using only the τ_F where ϕ > 11 provided a mean frictional shear stress of 0.94 MPa and a standard deviation, s, of 0.23 MPa (the number of test samples, n, was 9). This value is little different from the frictional shear stresses measured for sized PPTA (0.84 MPa). The decrease in the values of ϕ is attributed to the decrease in τ_B, due to the surface modification reaction, without necessarily affecting the frictional shear stress, τ_F.     

Application of critical state to uniaxial compaction

From the radial stress σ_R and the normal stress σ_A, measured continuously during uniaxial loading and unloading on three compactable (sodium chloride, polyethylene and tartaric acid) and two non-compactable (polypropylene and polystyrene plastics) materials, characteristic compaction profiles of (σ_A ? σ_R) versus (σ_A + σ_R) can be observed. The uniaxial loading stress pathways for both compactable and non-compactable materials validated the assumption that the Coulomb yield criterion, which is usually applicable for the shear testing of soils, can be applied to the uniaxial compression of particulate materials. In addition, the unloading stress profiles for the compactable materials produced two characteristic parameters: a normal stress value at zero shear (σ_A + σ_R)_o and a minimum shear stress value (σ_A ? σ_R)_min. Correlation of (σ_A + σ_R)_o and (σ_A ? σ_R)_min values with either the tensile strength f_c or the Vickers hardness number H_V from the resultant compacts showed a linear logarithmic relationship. No such relationship was found, however, with non-compactable materials.     

Normal stresses in flow of polyvinyl chloride plastisols

In the steady state flow of many liquids, such as polymer solutions and melts, the first normal stress difference, N₁ = σ₁₁ ? σ₂₂, is positive. However, with liquid crystal systems and some colloidal suspensions, negative values of N₁ were reported in literature. In our past work with a commercial polyvinyl chloride plastisol, negative values were observed. During the steady state flow, the plastisol undergoes stress‐induced phase separation into an immobilized layer and a mobile phase. The concentration difference between the two phases gives a rise to an osmotic pressure difference, Δπ, which is countered by a normal stress, N, generated by the flow. Because N is balanced with Δπ, N cannot be observed directly. In this work, N is identified as an isotropic and N₁, directional. The disturbance among rotating particles in the mobile phase produces two effects; one is an increase of pressure, which is N; the other, N₁ is associated with a small volume increase, which is directed towards the opening of the rheometer. The directional expansion is caused by the shear‐stress gradient in the liquid between the rotating particles. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 103: 2769–2775, 2007     

Molecular weight distribution and rheological properties of polyisobutylene solutions

The molecular weight distribution of a series of polyisobutylenes was determined using osmotic pressure measurements, gel permeation chromatography, and intrinsic viscosity. All of the polymers except for one, a blend of the highest and lowest molecular weight constituents, had similar moderate molecular weight distributions. The “extended chain length” method of calibrating the gel permeation chromatograph for polyisobutylenes was found to be effective. Steady state and transient shear stresses and normal stresses were measured on 5% decalin solutions of these polymers. The zero shear viscosity increased with the 3.3 power of molecular weight, and the zero shear normal stress coefficient (σ₁₁ ? σ₂₂)/Γ² varied with the 7.5 power. Relative elastic memory as measured by (σ₁₁ ? σ₂₂)/σ₁₂ or stress relaxation increased with increasing molecular weight (and at constant number- or weight-average molecular weight) with breadth of distribution. Stress overshoot also correlated with this tendency.     

Rheological investigation of xanthan gum–chromium gelation and its relation to enhanced oil recovery

Xanthan gum–water solutions with polymer concentrations 0.05–1% w/w and chromium ion content 30–1200 ppm were being gelled at temperatures from 25 to 90°C. A control deformation test (CD test) at a constant shear rate 0.05 s^?1 was performed for all the specimens. Shear moduli of elasticity and in some cases yield stresses and yield strains were determined from these tests. The energy of activation E_a = 93 ± 6 kJ/mol was obtained. The dependence of the gelation rate on the ionic concentration followed a power law with a coefficient of 1.8. There was relatively small dependence of the gelation rate on the xanthan gum concentration. Surprisingly, the maximum obtainable moduli at complete gelation do not depend on xanthan gum concentration in the range 0.2–1% w/w and are about 2400 Pa. The number of the bound chromium ions per monomer unit of xanthan gum is changed from 0.64 to 0.16 for the above measured concentrations of the polymer. High moduli gels on the base of the lower concentrations of xanthan gum were practically not recoverable after mechanical destruction. The assumption was made that the main reason for the profile modification of the flow for enhanced oil recovery in porous media is the yield stress of the gels. The smaller capillaries can even be closed if the yield stress is higher than the maximum shear stress existing in the capillary. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 103: 160–166, 2007     

Entanglement network model relating tensile impact strength and the ductile-brittle transition to molecular structure in amorphous polymers

A model is presented to account for the large variations in tensile and tensile impact strength of amorphous polymers from a consideration of an idealized entanglement network. The material strength under tensile impact conditions is shown to be predictable and to increase with the “fineness” of the entanglement network; a higher entanglement density leading to more molecular chains supporting the stress. The entanglement density is, in turn, shown to increase with number-average molecular weight and the quotient of the length to the molecular weight of the chemical repeat unit (empirically found to be related to the critical enganglement molecular weight). Ductile behavior is demonstrated to occur under tensile impact conditions when the material strength σ_B exceeds the yield stress σ_y and brittle behavior when σ_y > σ_B. It is further demonstrated that the large variation in tensile impact strength among the amorphous polymers studied can be adequately accounted for in terms of the large and predictable variation in σ_B; the larger σ_B is relative to σ_y, the more the polymer can draw (absorbing energy in the process) until σ_B is reached. Surprisingly, the predictions of strength for high-molecular-weight polycrystalline materials also gave good agreement with experimental data.     

Shear viscosity of carbon black filled polypropylene at very low shear stresses

The shear viscosity of carbon black filled polypropylene with a range of different carbon blacks was investigated. This was accomplished using (a) a constant shear stress creep instrument, (b) a cone-plate rotational rheometer, (c) a capillary extrusion rheometer. It was found that stresses exist for these compounds below which there are only finite deformations and no steady flow, Much attention was given to measurements of creep at low stresses, especially in the neighborhood of yield values. The magnitudes of yield stresses obtained from such creep measurements are significantly lower than those obtained using standard extrapolation to zero shear rate of higher stress data from rotational instruments. The shear viscosity behavior near the yield value differs significantly depending upon the carbon black used. A high viscosity was observed (～10⁹ to 10¹⁰ Pa.s) plateau in some compounds.     

Effects of rigid segments on structure and properties of unoriented and oriented poly(p-phenylene terephthalamide-co-ethylene terephthalates)

In poly(p-phenylene terephthalamide-co-ethylene terephthalate) the rigid segments of p-phenylene terephthalamide are aggregated as crystalline domains above the weight fraction of the rigid segments, 6 wt%. The rigid segments disturb the crystallization of the flexible segments of poly(ethylene terephthalate) (PET) and are preferentially contained in the amorphous phase of the PET segments. The crystallinity of the PET segments decreased with increasing the content of the rigid segments in the copolymers and the glass transition temperature is decreased by the decrease of the crystallinity below the weight fraction of the rigid segments, 6 wt%, in spite of the depression of micro-Brownian motion of the PET segments due to the rigid segments. The values of Young's modulus E, yield stress σ_y and breaking stress σ_b for the zone-drawn copolymer were conspicuously increased by the rigid segments contained in it, in comparison with those of the zone-drawn PET homopolymer. Such higher values of E, σ_y, and σ_b of the copolymer are originated by greater increases in the orientation of amorphous chains in the copolymer. The rigid segments in the amorphous phase effectively depressed the thermal shrinkage of the zone-drawn and the zone-annealed copolymers.     

Rheological characterization of cellulose solutions in N‐methyl morpholine N‐oxide monohydrate

Three different modes of rheological properties were measured on 11 and 13 wt % solutions of cellulose in N‐methyl morpholine N‐oxide (NMMO) monohydrate, in which concentration range lyocell fibers of much reduced fibrillation are preferably produced. The dynamic rheological responses revealed that the Cox–Merz rule did not hold for these cellulose solutions. Both cellulose solutions showed a shear thinning behavior over the shear rate measured at 85, 95, 105, and 115°C. However, 13 wt % solution gave rise to yield behavior at 85ºC. The power law index ranged from 0.36 to 0.58. First normal stress difference (N₁) was increased with lowering temperature and with increasing concentration as expected. Plotting N₁ vs shear stress (τ_ω) gave almost a master curve independent of temperature and concentration, whose slope was about 0.93 for both cellulose solutions over the shear rate range observed (τ_ω > 500 Pa). In addition, the cellulose solutions gave high values of recoverable shear strain (S_R), ranging from 60 to 100. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 86: 216–222, 2002     

Elastic stresses in an adhesively-bonded functionally-graded tubular single-lap joint in tension

In this study, the elastic stress analysis of an adhesively-bonded tubular lap joint with functionally-graded Ni-Al₂O₃ adherends in tension was carried out using a 3D 8-node isoparametric multilayered finite element with 3 degrees-of-freedom at each node. Stress concentrations were observed along the edges of both outer and inner tubes in the overlap region. Thus, the outer tube region near the free edge of the inner tube and the inner tube region near the free edge of the outer tube experienced considerable stress concentrations. Normal σ_zz and shear σ_rz stresses were dominant among the stress components. In addition, both edges of the adhesive layer experience stress concentrations, and the von Mises σ _eqv stress decreases uniformly across the adhesive thickness at the free edge of the outer tube, whereas it increases at the free edge of the inner tube. However, different compositional gradients had only a small effect on the through-the-thickness normal and shear stress profiles of both outer and inner tubes, and the peak von Mises σ _eqv stresses occurred inside the tube walls. As the ceramic phase in the material composition of the outer and inner tubes was increased, peak von Mises σ _eqv stress appeared in the ceramic layer. However, its magnitude was increased 1.75-fold in both tubes. In addition, the peak adhesive stresses appeared at the edge of the outer tube–adhesive interface near the free edge of the inner tube and at the edge of the inner tube–adhesive interface near the free edge of the outer tube. Increasing the ceramic phase in the material composition caused 1.22–1.67-times higher von Mises stresses along the free edges of the adhesivetube interfaces. In addition, with increasing number of layers across the inner and outer tubes the profiles of the normal σ_zz , shear σ_r and von Mises σ _eqv stresses across the tube walls and adhesive layer become similar. Increasing the ceramic phase in the material composition of the tubes causes also evident increases in the normal σ_zz and von Mises stresses while it does not affect their through-the-thickness profiles. However, it affects only shear σ_r and von Mises stresses across the adhesive layer. Finally, the layer number and the compositional gradient do not affect considerably through-the-thickness normal and shear stress profiles but levels in a functionally graded plate subjected to structural loads.     

J-integral studies of crack initiation and crack tip-blunting of phenolphthalein polyether ketone

The J-integral is applied to characterize the fracture initiation of phenolphthalein polyether ketone (PEK-C) for which the concepts of linear elastic fracture mechanics (LEFM) are inapplicable at high temperatures for reasonably-sized specimens due to extensive plasticity. The multiple-specimen resistance curve technique recommended by the ASTM is the basic method employed. The values of J_IC increase with increasing temperature. The crack tipblunting of PEK-C is observed. The parameters, such as crack opening displacement (COD), δ₀, and the stretching increment Δa_b1 are introduced to describe the blunting phenomenon. The δ₀ increases with increasing temperature, as does Δa_b1. This indicates that the blunting occurs easily as the temperature increases; i.e., as the material's yield stress, σ_y steadily falls. The relationships between δ₀, Δa_b1, and σ_y are also discussed. © 1994 John Wiley & Sons, Inc.     

Effect of hydrostatic pressure on the deformation behavior of polyethylene and polycarbonate in tension and in compression

The stress-strain response of crystalline high density polyethylene and of amorphous polycarbonate has been determined in tension and in compression at superimposed pressures up to 1104 MPa(160 ksi). Strain softening occurred in the polycarbonate at low pressures but was inhibited by pressure. Tensile necking occurred in both materials, but was promoted by pressure in polyethylene and inhibited in polycarbonate. The initial modulus, E, and the flow stress, σ, at a given offset strain varied linearly with the mean pressure, P, with essentially the same pressure coefficient, α. Thus, E = (1+αP)E₀ and σ = (1+αP)σ₀, where E₀ and σ₀ are values at zero mean pressure. In polyethylene, the coefficient, σ₀, was the same in tension and compression, indicating that the strength differential between tension and compression was a simple manifestation of pressure-dependent yielding. In polycarbonate the coefficient, σ₀, was different in tension and in compression, implying an effect due to the third stress invariant or to anisotropy. The results suggest a constitutive model for polymers in which the flow stress is linearly dependent on mean pressure, but in which inelastic volume change is negligible. The results also suggest that the pressure dependence of flow stress in polymers is the same as that of the initial modulus.