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1.
Flow visualization experiments have been carried out on these melts flowing from a reservoir into a capillary die. The existence and magnitude of vortices at the die entrance have been determined over a range of extrusion conditions. The vortex size is interpreted in terms of the theory of viscoelastic fluid mechanics. It is found that the second-order fluid-perturbation solution cannot represent the observed experimental results. The data are correlated with (i) a Weissenberg number τch ≡ gt(w)w ≡ Ψ1w/2η (N1)w/ 2(σ12)w measured at the die wall and (ii) with the deformation-rate dependence of relaxation time. Interpretation of vortex formation and size in terms of elongational viscosity is offered.Several polystyrene and polyethylene melts have been rheologically characterized as part of this study with measurements of viscosity η and principal normal stress difference N1. The zero shear viscosity η0 of the polystyrenes varies with the 3.5 power of the weight-average molecular weight Mw while the principal normal stress difference coefficient Ψ1 varies with the sixth power of Mw when evaluated at a shear rate of 1 sec?1. 相似文献
2.
OFHC copper specimens of 39 μm grain size were deformed to small strains (up to 8%) in tension, torsion and combined tension-torsion at 300 K and the resulting dislocation structures, distributions and densities were determined using transmission electron microscopy. Employing the von Mises yield criterion and the plastic-work hypothesis good agreement was obtained for the three testing conditions for (i) equivalent stress gs vs equivalent strain g3p curves, (ii) the dislocation structure, distribution and density ρ as a function of g3p, and (iii) gs as a function of . Furthermore, upon comparing the gs vs curve for polycrystalline copper with the τRSS vs curve for single crystals, an average Taylor factor M= (σ/τRSS) of approximately 3.2 was obtained, which is in good accord with that predicted theoretically for FCC metals. Almost equally good correlations for the stressstrain curves and for the dislocation density were obtained on the basis of maximum shear stress τmax and maximum shear strain γpmax as on the basis of gs and g3P. Therefore, the present results do not permit a positive decision on the question whether the dislocation density correlates better with gs and g3P or with τmax and γPmax.A single test in which the direction of straining in torsion was reversed yielded a density and distribution of dislocations (and a corresponding value of gs) equivalent to those that developed at a smaller strain in unidirectional straining. 相似文献
3.
Properties of suspensions of spherical glass beads (25–38 μm dia.) in a Newtonian fluid and a non-Newtonian (NBS Fluid 40) fluid were measured at volume fractions, φ, of 0%, 10%, 20% and 30%. Measurements were made using a modified and computerized Weissenberg Rheogoniometer. Properties measured included steady shear viscosity, η(), first normal stress difference, N1(), linear viscoelastic properties, η′(ω) and G′(ω), shear stress relaxation, σ? (, t), and growth, σ+(, t) and normal stress relaxation, N1?(, t).For a the Newtonian fluid, increasing φ causes both η and η′ to increase, with η′ showing a slight frequency dependence. Both N1 and G′ are zero and stress relaxation and growth occur essentially instantaneously. For the NBS fluid, both η and η′ increse with φ at all and ω, respectively, the increase being greater as and ω approach zero. N1 and G′ are less affected by the presence of the particles than η and η′ with the effect on G′ being more pronounced than on N1. For fixed , stress relaxation and growth exhibit greater non-linear effects as φ is increased. A model for predicting a priori the linear viscoelastic properties for suspensions was found to yeild reasonable estimates up to φ = 20%. 相似文献
4.
We consider constitutive expressions which the stress σ(X, t) at a particle X at time t is given by σ (X, t) = [F[X, τ)] where [F(X, τ)] denotes a functional of the history of the deformation gradient matrix [F(X, τ)] from time τ = 0 unti τ = t. This expression is restricted by the requirement of invariance under a superposed rotation of the physical system and by the further requirement that the constitutive expression shall be invariant under the group of unimodular transformations, i.e. [F(X, τ)] = [F(X, τ) H] must hold for all matrices H such that det H - 1. We employ results from the classical theory of invariants in order to determine the general form of the expression [F(X, τ)] which is consistent with these restrictions. Special cases are considered where the functional is replaced by a function of the strain, rate of strain, ? matrices. The case of shear flow is briefly discussed. 相似文献
5.
Two methods for determining the initial coefficient of the first normal stress difference are presented. They are based on the evaluation of the steady viscosity function η() and the viscosity function η+(, t) at the start-up of a flow with a very small rate of deformation < 0. For the functions η() and η+(), equations are given which can be used for a simple evaluation of the integral relationships obtaiend for ψ10. The values for ψ10 calculated by the two methods are compared with values obtained by the well-known methods via measurement of the ψ1() or η″(ω)/ω functions and extrapolation to zero). Both methods give values which are in satisfactory agreement with the experimental values. 相似文献
6.
Jin-Woo Klm 《Journal of the mechanics and physics of solids》1985,33(2):141-152
A quasi-static linear viscoelastic model for the dart impact type test on toughened rigid plastics is proposed and analysed. Based on the modified Maxwell element model of viscoelastic behavior of material with relaxation modulus E(t) = Ef + (Eo ? Ef)e, some approximate computations are performed to assess the relative importance of various parameters such as the impact velocity, fracture initiation.energy and critical stress. 相似文献
7.
《International Journal of Solids and Structures》2003,40(2):251-269
The constitutive postulations for mixed-hardening elastoplasticity are selected. Several homeomorphisms of irreversibility parameters are derived, among which Xa0 and Xc0 play respectively the roles of temporal components of the Minkowski and conformal spacetimes. An augmented vector Xa:=(YQat,YQa0)t is constructed, whose governing equations in the plastic phase are found to be a linear system with a suitable rescaling proper time. The underlying structure of mixed-hardening elastoplasticity is a Minkowski spacetime on which the proper orthochronous Lorentz group SOo(n,1) left acts. Then, constructed is a Poincaré group ISOo(n,1) on space X:=Xa+Xb, of which Xb reflects the kinematic hardening rule in the model. We also find that the space (Qat,q0a) is a Robertson–Walker spacetime, which is conformal to Xa through a factor Y, and conformal to Xc:=(ρQat,ρQa0)t through a factor ρ as given by ρ(q0a)=Y(q0a)/[1−2ρ0Qa0(0)+2ρ0Y(q0a)Qa0(q0a)]. In the conformal spacetime the internal symmetry is a conformal group. 相似文献
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Oliver Arnolds Hans Buggisch Dirk Sachsenheimer Norbert Willenbacher 《Rheologica Acta》2010,49(11-12):1207-1217
Semi-dilute ( $c^\ast < c < c_{\rm e}$ ) as well as concentrated, entangled (c?>?c e) solutions of PEO yield uniformly thinning, cylindrical filaments in capillary breakup extensional rheometry (CaBER) experiments. Up to c?≈ c e thinning can be characterized by a single elongational relaxation time λ E. Comparison with the longest shear relaxation time, λ S reveals that λ E/λ S decreases with increasing concentration or molecular weight according to (c[η])???4/3. This is attributed to the large deformation the solutions experience during filament thinning. A factorable integral model including a single relaxation time and a Soskey or Wagner damping function accounting for the large deformation in CaBER experiments is used to calculate λ E/λ S and provides good agreement with experimental results. Irrespective of concentration or molecular weight a beads-on-a-string structure occurs prior to filament breakup at a diameter ratio D/D 0?≈ 0.01. This instability is supposed to be closely related to a flow-induced phase separation. 相似文献
10.
The transient elongation behavior of entangled polymer and wormlike micelles (WLM) solutions has been investigated using capillary breakup extensional rheometry (CaBER). The transient force ratio X = 0.713 reveals the existence of an intermediate Newtonian thinning region for polystyrene and WLM solutions prior to the viscoelastic thinning. The exponential decay of X(t) in the first period of thinning defines an elongational relaxation time λ x which is equal to elongational relaxation time λ e obtained from exponential diameter decay D(t) indicating that the initial stress decay is controlled by the same molecular relaxation process as the strain hardening observed in the terminal regime of filament thinning. Deviations in true and apparent elongational viscosity are discussed in terms of X(t). A minimum Trouton ratio is observed which decreases exponentially with increasing polymer concentration leveling off at Trmin = 3 for the solutions exhibiting intermediate Newtonian thinning and Trmin ≈ 10 otherwise. The relaxation time ratio λ e/ λ s, where λ s is the terminal shear relaxation time, decreases exponentially with increasing polymer concentration and the data for all investigated solutions collapse onto a master curve irrespective of polymer molecular weight or solvent viscosity when plotted versus the reduced concentration c[ η], with [ η] being the intrinsic viscosity. This confirms the strong effect of the nonlinear deformation in CaBER experiments on entangled polymer solutions as suggested earlier. On the other hand, λ e ≈λ s is found for all WLM solutions clearly indicating that these nonlinear deformations do not affect the capillary thinning process of these living polymer systems. 相似文献
11.
Using the criterion that a crack will extend perpendicular to the maximum circumferential stress,σ θ, we show that the directional stability of crack growth is governed by the location of microcrack initiation ahead of the crack tip. At distances greater than a geometrical radiusr o, the maximum value ofσ θ deviates from the position of symmetry. Thus, if we assume that the physical processes involved in fracture lead to crack initiation at a distancer c ahead of the crack tip, the criterion for directional stability isr o>r c. Experimental and theoretical values ofr o verify that, asr o becomes small, the crack's directional stability deteriorates. Observing that a lengthwise compressive stress increasesr o, a center-cracked specimen was developed which allows the application of controlled lengthwise compression independently of the opening-mode load. A detailed photoelastic analysis of the specimen has provided the value ofr o as a function of the crack length. The value ofr o is then compared with the expected microcrack initiation distances in ductile fracture. By applying sufficient lengthwise compression, we are able to make the crack grow straight and obtain numerous data points from this specimen which would otherwise be directionally unstable. The results indicate that, as the total lengthwise tensile stress at the crack tip increases, the fracture toughness also increases. Using this information we can then adjustK Ic for zero lengthwise loading and obtain a geometry independent fracture toughness. 相似文献
12.
We study the initial boundary value problem for the reaction–diffusion equation, in a bounded domain with periodic microstructure , where aε(x) is of order 1 in and κ(ε) in with κ(ε)→0 as ε→0. Combining the method of two-scale convergence and the variational homogenization we obtain effective models which depend on the parameter θ=limε→0κ(ε)/ε2. In the case of strictly positive finite θ the effective problem is nonlocal in time that corresponds to the memory effect. To cite this article: L. Pankratov et al., C. R. Mecanique 331 (2003). 相似文献
13.
Isothermal and non-isothermal flow rate-pressure drop data in turbulent flow through smooth pipes have been obtained for non-Newtonian fluids, including aqueous solutions of polymers and aqueous suspensions of titanium dioxide. It has been found that the friction factor, f, is a function of a new form of Reynolds number, ReB, based on the parameters A, x and w of Bowen's correlation, viz. where τw is the wall shear strees, ?u the mean velocity, D the pipe diameter; A, x and w are experimentally derived parameters which characterise the fluid. 相似文献
14.
Donald R. Childs 《International Journal of Non》1973,8(4):371-379
The non-linear equation is shown to represent simply periodic motion with a minimum at R1 and a maximum at R1R0 or a maximum at R1 and a minimum at R1R0?1. R0 is a function of the ratio and is greater than 1 for > 1 and less than 1 for > 1. The period of the motion satisfies the simple relation T(R0?1) = R0?1T(R0). The exact solution to the above equation is represented in terms of elliptic integrals of the first and second kinds and a simple algebraic function. 相似文献
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16.
R.P. Chhabra 《ournal of non Newtonian Fluid Mechanics》1983,13(2):225-227
Viscoelastic solutions were ejected vertically downwards into air and various Newtonian fluids. The measured swell increased significantly when ejected into a liquid rather than air. The observed increase is considered a result of both bouyancy and drag forces on the solution. The following dimensions expression relating the ratio of the swell diameter in liquid and air DL/DA to the elastic shear compliance of the ejected solution Je was experimentally observed.(DL/DA)6-1=30(Δ?/?s)?([g2η2N?s]Je), where Δ? is the density difference between the extruded and Newtonian fluid, ?s is the solution density, g is the gravitational constant, and ηN is the Newtonian fluid viscosity. Thus with this expression a simple extrudate swell technique exists to estimate the elastic shear compliance of a viscoelastic solution. 相似文献
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18.
We consider singular perturbation problems depending on a parameter ε?0 such that for ε>0 the solution uε belongs to a Sobolev space on a domain , but the limit u0 is not a distribution on . A very simple model problem, solvable by Fourier transform allows us to study the complexification process of uε as . The limit holds in the topology of a space of analytical functionals. To cite this article: C.A. De Souza, É. Sanchez-Palencia, C. R. Mecanique 332 (2004). 相似文献
19.
In this paper, a differentially heated square/cubic cavity is studied by performing three-dimensional direct numerical simulations. The first bifurcation observed at is due to the 3D vortex structures generated at the end regions of vertical boundary layers near the median plane. The main results of this Note are that the flow returns to a steady state for higher values of the Rayleigh number (7×107 and 108 for example) still exhibiting these 3D vortex structures, and that multiple steady flows which differ by their symmetry properties, are obtained for . However, the flow reverts to unsteadiness for . In this latter case, the instability is due to the vertical boundary layers. To cite this article: G. de Gassowski et al., C. R. Mecanique 331 (2003). 相似文献
20.
The rate at which energy is accumulated within a unit volume of material in fatigue is assumed to depend not only on load-time history but also on the specimen size and geometry in addition to material type. A threshold level for the hysteresis strain energy density function accumulated in the material is used for predicting macrocrack growth. This is accomplished by application of the incremental theory of plasticity for each increment of crack growth. The accumulated hysteresis strain energy density factor ΔS to crack growth increment Δa ratio is found to be constant for fixed specimen size and loading, i.e., . Results are obtained for the cylindrical bar specimens with a penny-shaped defect at the center subjected to a constant amplitude and frequency loading. The resistance curves in the ΔS versus Δa plot are parallel lines as specimen size is altered. This information provides a rational means for predicting the influence of specimen size on fatigue lifetime.The results are also compared with those found for geometrically similar plate specimens with line cracks. Cylinder bar specimens of the same material are found to sustain more load cycles prior to catastrophic failure. 相似文献