Study of magnetorheological fluids at high shear rates

The tunable rheological properties of magnetorheological (MR) materials at high shear rates are studied using a piston-driven flow-mode-type rheometer. The proposed method provides measurement of the apparent viscosity and yield stress of MR fluids for a shear rate range of 50 to 40,000 s⁻¹. The rheological properties of a commercial MR fluid, as well as a newly developed MR polymeric gel, and a ferrofluid-based MR fluid are investigated. The results for apparent viscosity and dynamic and static shear stresses under different applied magnetic fields are reported.     

Primary normal-stress coefficient prediction at high shear rates

On the basis of a brief analysis of well known normal-stress calculation methods, the necessity of improved models of prediction is elaborated. A modified form of the so-called mirror relation which meets these requirements is presented. In combination with the Carreau viscosity equation, an analytical solution is given which leads to a Carreau normal-stress coefficient equation and, thus, to a simple method of calculation. The comparison between measured normal stresses and those determined by experiments shows that the values calculated in accordance with the presented method agree well with the measured values, especially within the range of high shear rates. The parameters andK to be selected for this purpose are determined in dependence on the slope of the viscosity function ₁ at high shear rates for each polymer individually, using empirical relations so that the global selection of parameters, which is common practice with other methods, is obviated. In an appendix a method for deriving the relations between material functions on the basis of operator calculation is given.Extended version of a paper read at the 2^nd Symposium on Rheology of the GDR in Tabarz/Thuringia, December 7–11, 1987     

Use of a sliding plate rheometer to measure the first normal stress difference at high shear rates

The use of a sliding plate rheometer (SPR) to determine the first normal stress difference of molten polymers and elastomers at high shear rates is demonstrated. The simple shear flow in this instrument is not subject to the flow instabilities that limit the use of rotational rheometers to shear rates often below 1 s⁻¹. However, issues of secondary flow and wall slip must be addressed to obtain reliable data using an SPR. A highly entangled, monodisperse polybutadiene and a commercial polystyrene were the polymers studied. The inclusion of the polystyrene made it possible to compare data with those obtained by Lodge using a stressmeter, which is an instrument based on the measurement of the hole pressure. The data from the two instruments are in good agreement and are also close to the predictions of an empirical equation of Laun based on the storage and loss moduli.     

Techniques for measuring stress-strain relations at high strain rates

The qualitative dependence of the mechanical behavior of some materials on strain rate is now well known. But the quantitative relation between stress, strain and strain rate has been established for only a few materials and for only a limited range. This relation, the so-called constitutive equation, must be known before plasticity or plastic-wave-propagation theory can be used to predict the stress or strain distribution in parts subjected to impact stresses above the yield strength. In this paper, a brief review of some of the experimental techniques for measuring the stress, strain, strain-rate relationship is given, and some of the difficulties and shortcomings pointed out. Ordinary creep or tensile tests can be used at plastic-strain rates from 10^?8 to about 10^?1/sec. Special quasi-static tests, in which the stress- and strain-measuring devices as well as the specimen geometry and support have been optimized, are capable of giving accurate results to strain rates of about 10²/sec. At higher strain rates, it is shown that wave-propagation effects must be included in the design and analysis of the experiments. Special testing machines for measuring stress, strain and strain-rate relationships in compression, tension and shear at strain rates up to 10⁵/sec are described, and some of the results presented. With this type of testing machine, the analysis of the data requires certain assumptions whose validity depends upon proper design of the equipment. A critical evaluation of the accuracy of these types of tests is presented.     

Integral-based constitutive equation for rubber at high strain rates

High-speed experiments were conducted to characterize the deformation and failure of Styrene Butadiene Rubber at impact rates. Dynamic tensile stress–strain curves of uniaxial strip specimens and force–extension curves of thin sheets were obtained from a Charpy tensile impact apparatus. Results from the uniaxial tension tests indicated that although the rubber became stiffer with increasing strain rates, the stress–strain curves remained virtually the same above 280 s⁻¹. Above this critical strain rate, strength, fracture strain and toughness decreased with increasing strain rates. When strain rates were below 180 s⁻¹, the initial modulus, tensile strength and breaking extension increased as the strain rate increased. Between strain rates of 180 and 280 s⁻¹, the initial modulus and tensile strength increased with increasing strain rates but the extension at break decreased with increasing strain rates. A hyper-viscoelastic constitutive relation of integral form was used to describe the rate-dependent material behavior of the rubber. Two characteristic relaxation times, 5 ms and 0.25 ms, were needed to fit the proposed constitutive equation to the data. The proposed constitutive equation was implemented in ABAQUS Explicit via a user-defined subroutine and used to predict the dynamic response of the rubber sheets in the experiments. Numerical predictions for the transient deformation and failure of the rubber sheet were within 10% of experimental results.     

利用SHPB测定高应变率下冰的动态力学行为

利用分离式Hopkinson压杆(SHPB)实验装置,在-25和-10℃的低温下,对冰进行了应变率为500～2 000 s-1的动态压缩实验.制作了试样的模具和低温制冷保温装置,满足冰所需要的低温条件.SHPB实验中使用波形整形器消除波形振荡现象,并最大程度地实现恒应变率加载.实验表明,冰的动态应力应变呈非线性关系;在...     

Tensile testing of materials at high rates of strain

A tension version of the split Hopkinson bar or Kolsky apparatus is developed for conducting tests in tension at high rates of strain up to 10³ s^?1. A number of aluminum, titanium, and steel alloys tested in tension show increasing degrees of rate sensitivity above 10 to 10² s^?1. Tests on 6061-T651 and 7075-T6 aluminum show measurable strain-rate sensitivity in tension at the highest strain rates, although similar tests in compression in the literature show essentially no strain-rate sensitivity. Details of the apparatus and instrumentation and guidelines for its use are presented.     

A unit for testing materials at high strain rates

Some of the problems regarded as inherent in materials testing at high strain rates are associated with inertia effects, both in the loading mechanism and in the specimen itself. In fact, it has generally been difficult to ensure a homogeneous and uniaxial strain field. Some of these problems encountered in dynamic testing have, however, been circumvented in a simple testing unit, developed at the Technical University of Denmark and described in the present paper.     

Dynamic measurements of initiation toughness at high loading rates

An experimental method is described for measuring the dynamic initiation toughness of a sharp stationary crack. A plane specimen is utilized which consists of a central region 50-mm wide and 200-mm long with integral dog-bone ends. The loading is accomplished by the detonation of four small explosive charges which produce two tensile stress waves upon reflection from the dog-bone ends. The stress waves meet at the midpoint of the specimen and reinforce to produce a relatively large, uniformly stressed region with a very high loading rate. The crack is positioned at the midpoint of the specimen at the location where the reinforcing tensile stress waves meet. A series of photoelastic experiments were conducted using Homalite 100 as the model material to observe, in a full-field view, the arrival of the dilatational waves, the subsequent development of the stress field at the tip of the stationary crack and the initiation of the crack. The isochromatic fringe pattern was also used to determine the instantaneous value of the stress-intensity factorK(t) after the characteristic fringe loops developed in the region near the crack tip. Finally,K(t) was measured using a single strain gage positioned and oriented so that its signal output was proportional toK(t) and independent of the next two higher order terms in the series representation of the strain field. A method was developed to determine the instant of initiation from the strain-time trace. Results obtained from the photoelastic and strain measurements of the dynamic-initiation toughnessK _ID were consistently higher than the static value ofK _IC . Paper was presented at the 1987 SEM Fall Conference on Experimental Mechanics held in Savannah, GA on October 25–28.     

Determination of stress-strain characteristics at very high strain rates

A modified version of the Kolsky thin-wafer technique is described. The method permits one to obtain the dynamic plastic properties of materials at strain rates as high as 10⁵ sec^?1. Data obtained from compression tests on high-purity aluminum are presented for strain rates ranging from 4000 to 120,000 sec^?1 at room temperature. Specimen-size effects and the effect of lateral inertia are taken into account in analyzing the data. The results plotted as stress vs. strain rate at constant strains (5 to 20 percent) show that, at the highest strain rates, the stress rises very rapidly with strain rate suggesting that a limiting strain rate is being reached. At the lower strain rates (10³ to 10⁴ sec^?1), the stress is linearly proportional to the strain rate indicating that the material is deforming in a viscous manner.     

New method for testing composites at very high strain rates

A method was developed for testing and characterizing composite materials at strain rates in the 100 to 500 s^?1 regime. The method utilizes a thin ring specimen, 10.16 cm (4 in.) in diameter, 2.54 cm (1 in.) wide and 6–8 plies thick. This specimen is loaded by an internal pressure pulse applied explosively through a liquid. Pressure is measured by means of a calibrated steel ring instrumented with strain gages. Strains in the composite specimen are measured with strain gages. Strains in the calibration and specimen rings are recorded with a digital processing oscilloscope. The equation of motion is solved numerically and the data processed by the mini-computer attached to the oscilloscope. Results are obtained, and plotted by an X-Y plotter in the form of a dynamic stress-strain curve. Unidirectional 0-deg, 90-deg and 10-deg off-axis graphite/epoxy rings were tested at strain rates up to 690 s^?1. Times to failure ranged between 30 and 60 μs. The 0-deg properties which are governed by the fibers do not vary much from the static ones with only small increases in modulus. The 90-deg properties show much higher than static modulus and strength. The dynamic in-plane shear properties, obtained from the 10-deg off-axis specimens, are noticeably higher than static ones. In all cases the dynamic ultimate strains do not vary much from the static values.     

Semi-analytic inverse method for rubber testing at high strain rates

Because of their low mechanical wave speed, high strain rate testing of rubber is highly difficult. Indeed, stress and strain homogeneity is hard to achieve. In this paper, a semi-analytic inverse solution is proposed. This solution is based on a uni-axial stress state assumption in the specimen. Moreover, a new-Hookean law is assumed for rubber. The new method is successfully applied to a high strain rate test on a synthetic rubber.     

Experimental mechanics at velocity extremes —Very high strain rates

The early experimental work of Clark and Wood with regard to von Kármán's theory on the effect of material flow and fracture at high strain rates has led to many controversial issues on these effects. Interest has been greatly revived in recent years because of the increased emphasis on such high-velocity forming processes as explosive and capacitor discharge. Considerable new work has been performed by Ling-Temco-Vought, Inc., for the Air Force, the results of which are presented in this paper. Data have been accumulated on tensile and compression specimens, spherical bulging and cylindrical bulging for a wide variety of materials. This high-speed information has been generated with the use of a special projectile impact machine and special presses utilizing various combinations of explosive and capacitor-discharge energy, with strain rates to 10¹/sec. The effect of velocity on ductility is discussed for total strain distribution, uniform strain, double necking and critical impact velocity. The modes of failure for various part shapes are presented and related to the forming velocity.     

高应变率下航空透明聚氨酯的动态本构模型

采用低阻抗分离式霍普金森压杆对航空透明聚氨酯进行了高应变率下的动态力学性能测试,得到的应力应变曲线表现出了显著的非线性黏弹性特征。基于本构理论和实验数据,构建了航空透明聚氨酯的松弛时间应变相关的超黏弹性本构形式。该本构模型由2部分组成:一部分表征准静态下的超弹性行为,另一部分描述非线性应变率的相关特性。利用超黏弹性本构模型对不同应变率下航空透明聚氨酯的动态应力应变曲线进行拟合,拟合曲线与实验曲线一致性良好。     

Stress-strain data obtained at high rates using an expanding ring

Dynamic uniaxial tensile stress-strain data are obtained at high strain rates by measuring the kinematics of thin-ring specimens expanding symmetrically by virtue of their own inertia. Impulsively loaded to produce high initial radial velocities, expanding rings are decelerated by the radial component of the hoop stresses. Differential equations of motion are evaluated experimentally to obtain the stress-strain (constitutive) relationships which govern the magnitude of these stresses. Techniques have been developed for producing symmetric radial expansion and measuring resulting displacements precisely as a function of time. Dynamic stress-strain relationships have been obtained for 6061-T6 aluminum, 1020 cold-drawn steel, and 6Al-4V titanium. For each of these materials, displacement-time curves are observed to be parabolic within the resolution of the measurements. Results are presented as true-stress/true-strain relationships.     

Viscosity of some clay-based coating colors at high shear rates

The shear viscosity of clay-based coating colors containing latex and carboxymethyl cellulose (CMC) has been measured over a relatively large shearrate region. In the shear-rate range of 50–1500 s^–1 the measurements were performed using a rotational viscometer and, at higher shear rates extending into the region 10⁵ – 10⁶ s^–1, a high pressure capillary viscometer was employed. The viscosity of the clay colors increased with increasing CMC-concentration, but the influence of the CMC-content was less pronounced at higher shear rates. The apparent shear-thinning behavior of the investigated colors could, in part, be attributed to the shear-thinning of the corresponding polymer (CMC) solution constituting the liquid phase of the color, but the influence of another factor was also indicated. At low shear rates, the interaction between the color components can produce relatively high viscosity levels, but in the high shear rate region these interactions appear to be less important for the viscosity level. It is also of interest to note that the viscosity dependence on the solids content in the high shear-rate region could be described with reasonable accuracy using an empirical equation neglecting interactions between the color components.     

Phenomena of high polymer solutions while flowing through capillaries at high rates of shear

Generally solutions of high polymers show a shear-rate dependent flow behaviour and so the properties of these fluids have to be measured under conditions of shear corresponding to the practical service. Capillary viscometry is suitable for achieving high rates of shear but relaxation phenomena can effect the results, which is proved experimentally. The flow behaviour of a lubricant blended with a high polymer additive is measured and a graphical representation of the dependence of flow behaviour on temperature and rate of shear is recommended.     

Flow birefringence of dilute solutions of polyethyleneoxide of high molecular weight at high rates

Summary Birefringence and orientation angle of solutions of Polyox WSR 301 in the concentration range of 50 to 1350 ppm have been measured up to 8000 s^–1. A few marked differences with ordinary flexible polymers have been evidenced: (i) a very low value of the extinction angle at high shear rate, which could be attributed to an unusually high molecular weight; (ii) the independence of this angle on the concentration, which is due to the variation of the flexibility with the concentration, as shown by the study of the concentration dependence of the segmental optical anisotropy; (iii) the concentration dependence of the elongation shows a plateau value forc 150 ppm, which may come from a concentration dependent and reversible association process, as shown from reduced viscosity measurements.

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Zusammenfassung Es wurden die Doppelbrechung und der Orientierungswinkel von Polyox-WSR 301-Lösungen im Konzentrationsbereich 50–1350 ppm bis zu Schergeschwindigkeiten von 8000 s^–1 gemessen. Dabei wurden einige ausgeprägte Unterschiede gegenüber normalen flexiblen Polymeren gefunden: (i) ein sehr niedriger Wert des Auslöschwinkels, was auf ein ungewöhnlich hohes Molekulargewicht schließen läßt: (ii) die Unabhängigkeit dieses Winkels von der Konzentration, was von einer Änderung der Flexibilität mit der Konzentration herrührt, wie sie durch die Untersuchung der Konzentrationsabhängigkeit der optischen Anisotropie der Segmente aufgezeigt wird; (iii) die Existenz eines Plateaus in der Konzentrationsabhängigkeit der Streckung beic 150 ppm, welches auf einen konzentrationsabhängigen reversiblen Assoziationsvorgang hindeutet, der auch durch Messung der reduzierten Viskosität nahegelegt wird.

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With 5 figures