Rheo-optical measurements of the first and third normal stresses of homopolymer poly(vinyl methyl ether) melt

Normal stresses play a key role in polymer processing, yet accurate measurements are still challenging. Simultaneous rheo-optical measurements are conducted on a poly(vinyl methyl ether) homopolymer melt over a wide range of temperatures and oscillatory shear frequencies, in an effort to measure the normal stresses, by using quantitative flow birefringence measurements. The stress optical rule holds well for this polymer as expected, with the value of the stress optic coefficient of (6.38±0.19)×10⁻¹¹ cm²/dyn at 30°C. The first and third normal stress difference coefficients, calculated using a single memory constitutive equation applied to the stress and birefringence data, are in excellent agreement. The ratio of the measured third and first normal stress difference coefficients, (1−β)=0.71±0.05, agrees well with the result of the Doi–Edwards model with independent alignment approximation (β=0.28). The measurement of normal stress difference coefficients with such small deviations proves the robust nature of the improved rheo-optical instrument and its ability to measure complete stress tensor.     

A shear rheometer for measuring shear stress and both normal stress differences in polymer melts simultaneously: the MTR 25

The MTR 25 is a multitask rheometer (for shear and squeeze flow) with 25 kg of normal force and a partitioned plate. Torque and normal force are measured at both, the inner disk and the outer ring of the plate. The first and second normal stress differences can be determined from a single test. The axial stiffness is high (10⁷ N/m) by using rigid springs and strain gauges for the load cell. Monodisperse polystyrene (M _w = 206 kg/mol, 180°C) has been sheared in the range from 0.05 to 47 s^− 1. The viscosity and first normal stress difference are highly reproducible. The second normal stress difference scatters and mirrors the instability at the rim. A critical comparison is made between the MTR 25 method and the single transducer evaluation method (RMS 800 method, Schweizer, Rheol Acta 41:337–344, 2002): Both yield excellent and coinciding viscosity and first normal stress difference data. The RMS 800 method gives more stable second normal stress difference data, since the normal force from the outer ring, which is influenced by edge fracture, is not used. Data for the RMS 800 method can be acquired on the MTR 25. The high normal force capacity permits larger samples and higher shear rates than on the RMS 800.

Measurement of thermal expansion coefficients of composites using strain gages

The measurement of the coefficients of thermal expansion (CTEs) of composite materials using electrical resistance strain gages is addressed. Analytical expressions for the CTEs of an orthotropic lamina are derived, accounting for the effects of transverse sensitivity and possible misalignment of the gages. Experiments are performed for the characterization of the thermal expansion behavior of a fiber-glass-reinforced epoxy unidirectional lamina using an invar specimen as reference material. Preliminary training cycles are performed for the determination of an optimal heating rate for the measurements, which ensures thermal equilibrium conditions. Three measurement cycles yield the principal CTEs of the lamina α₁, α₂ and α₁₂ with repeatability within ±0.34×10⁻⁶, ±0.85×10⁻⁶ and ±2.8×10⁻⁶/°C, respectively. It is noted that inhomogeneity of the specimen and variation in thermomechanical properties of the gages can cause a noticeable spead in the measurements.     

The investigation on dynamic fracture behavour of materials under compressive-shear combined stress waves

In this paper, an improved plate impact experimental technique is presented for studying dynamic fracture mechanism of materials, under the conditions that the impacting loading is provided by a single pulse and the loading time is in the sub-microsecond range. The impacting tests are carried out on the pressure-shear gas gun. The loading rate achieved is dK/dt∼10⁸ MPa m^1/2s⁻¹. With the elimination of influence of the specimen boundary, the plane strain state of a semi-infinite crack in an infinite elastic plate is used to simulate the deformation fields of crack tip. The single pulses are obtained by using the “momentum trap” technique. Therefore, the one-time actions of the single pulse are achieved by eradicating the stress waves reflected from the specimen boundary or diffracted from the crack surfaces. In the current study, some important phenomena have been observed. The special loading of the single pulse can bring about material damage around crack tip, and affect the material behavior, such as kinking and branching of the crack propagation. Failure mode transitions from mode I to mode II crack are observed under asymmetrical impact conditions. The mechanisms of the dynamic crack propagation are consistent with the damage failure model. The project supported by the National Natural Science Foundation of China (No. 19672066 and 18981180-4) and the Key Project of Chinese Academy of Sciences (No. KJ951-1-20)     

Yield stress of structured fluids measured by squeeze flow

Various structured fluids were placed between the parallel circular plates of a squeeze-flow rheometer and squeezed by a force F until the fluid thickness h was stationary. Fluid thickness down to a few microns could be measured. Most fluids showed two kinds of dependence of f on h according to an experimentally-determined thickness h ^*. If h > h ^* then F varied in proportion to h ⁻¹ as predicted by Scott (1931) for a fluid with a shear yield stress τ₀. The magnitude of τ₀ from squeeze-flow data in this region was compared with the yield stress measured by the vane method. For some fluids τ₀ measured by squeeze flow was less than the vane yield stress, suggesting that the yield stress of fluid in contact with the plates was less than the bulk yield stress. If h < h ^* then F varied approximately as h ^−5/2 and the squeeze-flow data in this region analysed with Scott's relationship gave a yield stress which increased as the fluid thickness decreased. This previously unreported effect may result from unconnected regions of large yield stress in the fluid of size similar to h ^* which are not sensed by the vane and which become effective in squeeze flow only when h < h ^*. Received: 13 December 1999/Accepted: 4 January 2000     

Variation of the stress intensity factor along the crack front of interacting semi-elliptical surface cracks

Summary  In this study, the interaction between two semi-elliptical co-planar surface cracks is considered when Poisson's ratio ν = 0.3. The problem is formulated as a system of singular integral equations, based on the idea of the body force method. In the numerical calculation, the unknown density of body force density is approximated by the product of a fundamental density function and a polynomial. The results show that the present method yields smooth variations of stress intensity factors along the crack front very accurately, for various geometrical conditions. When the size of crack 1 is larger than the size of crack 2, the maximum stress intensity factor appears at a certain point, β₁=177^∘, of crack 1. Along the outside of crack 1, that is at β₁=0∼90^∘, the interaction can be negligible even if the two cracks are very close. The interaction can be negligible when the two cracks are spaced in such a manner that their two closest points are separated by a distance exceeding the small crack's major diameter. The variations of stress intensity factor of a semi-elliptical crack are tabulated and charted. Received 30 August 1999; accepted for publication 22 February 2000     

Prediction of flow and heat transfer in narrow rotating rectangular channels using Reynolds stress model

A computational study is performed on three-dimensional turbulent flow and heat transfer in a rotating rectangular channel with aspect ratio (AR) of 10:1, oriented 120° from the direction of rotation. The Focus is on high rotation and high-density ratios effects on the heat transfer characteristics of the 120° orientation. The Reynolds stress model (RSM), which accounts for rotational effects are used to compute the turbulent flow and heat transfer in the rotating channel. The effects of rotation and coolant-to-wall density ratio on the fluid flow and heat transfer characteristics is reported on a range of rotation numbers and density ratios (0 < Ro < 0.25 and 0.07 < Δρ/ρ < 0.4). The computational results are in good agreement with experimental data within ±15%. The results show that the density ratio, rotation number and channel orientation significantly affect the flow field and heat transfer characteristics in the rotating rectangular channel. Flow reversal occurs at high rotation number and density ratio.     

Dynamic stress intensity factor K III and dynamic crack propagation characteristics of anisotropic materials

Based on the mechanics of anisotropic materials, the dynamic propagation problem of a mode Ⅲ crack in an infinite anisotropic body is investigated. Stress, strain and displacement around the crack tip are expressed as an analytical complex function, which can be represented in power series. Constant coefficients of series are determined by boundary conditions. Expressions of dynamic stress intensity factors for a mode Ⅲ crack are obtained. Components of dynamic stress, dynamic strain and dynamic displacement around the crack tip are derived. Crack propagation characteristics are represented by the mechanical properties of the anisotropic materials, i.e., crack propagation velocity M and the parameter ~. The faster the crack velocity is, the greater the maximums of stress components and dynamic displacement components around the crack tip are. In particular, the parameter α affects stress and dynamic displacement around the crack tip.     

Experimental Investigation of Strain Rate Dependence of Nanocrystalline Pt Films

A new microscale uniaxial tension experimental method was developed to investigate the strain rate dependent mechanical behavior of freestanding metallic thin films for MEMS. The method allows for highly repeatable mechanical testing of thin films for over eight orders of magnitude of strain rate. Its repeatability stems from the direct and full-field displacement measurements obtained from optical images with at least 25 nm displacement resolution. The method is demonstrated with micron-scale, 400-nm thick, freestanding nanocrystalline Pt specimens, with 25 nm grain size. The experiments were conducted in situ under an optical microscope, equipped with a digital high-speed camera, in the nominal strain rate range 10⁻⁶–10¹ s⁻¹. Full field displacements were computed by digital image correlation using a random speckle pattern generated onto the freestanding specimens. The elastic modulus of Pt, E = 182 ± 8 GPa, derived from uniaxial stress vs. strain curves, was independent of strain rate, while its Poisson’s ratio was v = 0.41 ± 0.01. Although the nanocrystalline Pt films had the elastic properties of bulk Pt, their inelastic property values were much higher than bulk and were rate-sensitive over the range of loading rates. For example, the elastic limit increased by more than 110% with increasing strain rate, and was 2–5 times higher than bulk Pt reaching 1.37 GPa at 10¹ s⁻¹.     

The plane stress crack-tip field for an incompressible rubber material

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A blood-mimicking fluid for particle image velocimetry with silicone vascular models

For accurate particle image velocimetry measurements in hemodynamics studies, it is important to use a fluid with a refractive index (n) matching that of the vascular models (phantoms) and ideally a dynamic viscosity matching human blood. In this work, a blood-mimicking fluid (BMF) composed of water, glycerol, and sodium iodide was formulated for a range of refractive indices to match most common silicone elastomers (n = 1.40–1.43) and with corresponding dynamic viscosity within the average cited range of healthy human blood (4.4 ± 0.5 cP). Both refractive index and viscosity were attained at room temperature (22.2 ± 0.2°C), which eliminates the need for a temperature-control system. An optimally matched BMF, suitable for use in a vascular phantom (n = 1.4140 ± 0.0008, Sylgard 184), was demonstrated with composition (by weight) of 47.38% water, 36.94% glycerol (44:56 glycerol–water ratio), and 15.68% sodium iodide salt, resulting in a dynamic viscosity of 4.31 ± 0.03 cP.     

Micron-Scale Residual Stress Measurement by Micro-Hole Drilling and Digital Image Correlation

This paper reports a new technique, namely the incremental micro-hole-drilling method (IμHD) for mapping in-plane residual or applied stresses incrementally as a function of depth at the micron-scale laterally and the sub-micron scale depth-wise. Analogous to its macroscale counterpart, it is applicable either to crystalline or amorphous materials, but at the sub-micron scale. Our method involves micro-hole milling using the focused ion beam (FIB) of a dual beam FEGSEM/FIB microscope. The resulting surface displacements are recorded by digital image correlation of SEM images recorded during milling. The displacement fields recorded around the hole are used to reconstruct the stress profile as a function of depth. In this way residual stresses have been characterized around a drilled hole of 1.8microns. diameter, enabling the profiling of the stress variation at the sub-micron scale to a depth of 1.8 microns. The new method is used to determine the near surface stresses in a (peened) surface-severe-plastically-deformed (S²PD) Zr₅₀Cu₄₀Al₁₀ (in atomic percent, at.%) bulk metallic glass bar. In plane principal stresses of -800 MPa ± 90 MPa and −600 MPa ± 90 MPa were measured, the maximum compressive stress being oriented 15° to the axis of the bar.     

Determining the stress intensity factor by using the principle of minimum potential energy

Expressing the total potential energy of the system of a cracked body П by Williams’ infinite series solution of stress and displacement components containing coefficients A_n(n = 1,2,...), we obtain a set of simultaneous linear equations of unknown coefficients A_n by using the principle of minimum potential energy. When the set of equations is solved, the stress intensity factor K₁ can be easily determined. It is equal to √2πaA₁ Take a sample plate as an example. A single-edgc-cracked plate under tension, with the ratio of crack length to the width of the plate being 0.5 and the ratio of half plate height to the width of the plate being 2.0 and 2. 5, has been calculated. Only 20 - 30 coefficients are taken, and the errors in stress intensity factors are within 5%.     

The average stress tensor in systems with interacting particles

The derivation of an expression of the macroscopic stress tensor in terms of microscopic variables in systems of finite interacting particles is discussed from different points of view. It is shown that in volume averaging the introduction of a fictitious “interaction stress field”T ^I with special boundary conditions on the boundary of the averaging volume is needed. In ensemble averaging similar results are obtained by using a multipole expansion of the local stress and force fields. In the appropriate limiting cases, the obtained results are shown to be consistent with the results of kinetic theories of polymer solutions. Paper, presented at the First Conference of European Rheologists at Graz, April 14 – 16, 1982.     

A second-order dynamic subgrid-scale stress model

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Turbulent flow measurement in a square duct with hybrid holographic PIV

 A hybrid holographic system has been developed for three-dimensional particle image velocimetry. With unique high pass filters, the system combines advantages of both in-line and off-axis holography without having their draw-backs. It improves the signal to noise ratio of the reconstructed image, allows use of 3–15 μm particles in water at high population and achieves large dynamic ranges in both velocity and space. With an automated image acquisition and processing system it has been used for measuring the velocity distributions in a square duct at Re=1.23×10⁵. The data consists of 97×97×87 vectors (with 50% overlapping of adjacent interrogation windows). The quality of the results is evaluated using the continuity equation. The deviation from the equation decreases rapidly with increasing control volume and reaches a level of less than 10%. Mean velocities, r.m.s. velocity fluctuations and turbulence spectra are estimated using the data. Received: 16 December 1996/Accepted: 6 March 1997     

Testing Aluminum Alloy from Quasi-static to Dynamic Strain-rates with a Modified Split Hopkinson Bar Method

An aluminum alloy¹ was tested at quasi-static to dynamic strain-rates (from 10⁻¹ to 5 10³ s⁻¹), using a single measuring device, a modified Split Hopkinson Bar. A wave separation technique [Bussac et al., J Mech Phys Solids 50:321–350, 2002] based on the maximum likelihood method was applied to process the strain and velocity measurements recorded at various points on each bar. With this method, it is possible to compute the stress, strain, displacement and velocity at any point on the bar. Since the measurement time is unlimited, the maximum strain measured in a given specimen no longer decreases with the strain-rate, as occurs with the classical Split Hopkinson Bar method. ¹The authors wish to thank the automobile manufacturer who provided samples of the alloy used in this study. For reasons of commercial and industrial confidentiality, we were not informed about the composition of this alloy.     

The effect of 1,3:2,4-<Emphasis Type="Italic">bis</Emphasis>-<Emphasis Type="Italic">O</Emphasis>-(<Emphasis Type="Italic">p</Emphasis>-methylbenzylidene)-<Emphasis Type="SmallCaps">d</Emphasis>-sorbitol (PDTS) on uniaxial elongational viscosity of polypropylene

We investigated the dynamic viscoelasticity and elongational viscosity of polypropylene (PP) containing 0.5 wt% of 1,3:2,4-bis-O-(p-methylbenzylidene)-d-sorbitol (PDTS). The PP/PDTS system exhibited a sol–gel transition (T _gel) at 193 °C. The critical exponent n was nearly equal to 2/3, in agreement with the value predicted by a percolation theory. This critical gel is due to a three-dimensional network structure of PDTS crystals. The elongational viscosity behavior of neat PP followed the linear viscosity growth function 3η ⁺ (t), where η ⁺ (t) is the shear stress growth function in the linear viscoelastic region. The elongational viscosity of the PP/PDTS system also followed the 3η ⁺ (t) above T _gel but did not follow the 3η ⁺ (t) and exhibited strong strain-softening behavior below T _gel. This strain softening can be attributed to breakage of the network structure of PDTS with a critical stress (σ _c) of about 10⁴ Pa.     

Influence of molecular parameters on the stress dependence of viscous and elastic properties of polypropylene melts in shear

The stress dependencies of the steady-state viscosity η and, particularly, that of the steady-state elastic compliance J _e of various linear isotactic polypropylenes (PP) and one long-chain branched PP are investigated using creep-recovery tests. The creep stresses applied range from 2 to 10,000 Pa. In order to discuss the stress-dependent viscosity η and elastic compliance J _e with respect to the influence of the weight average molar mass M _w and the polydispersity factor M _w/M _n the PP are characterized by SEC–MALLS. For the linear PP, linear steady-state elastic compliances J_e⁰J_{\rm e}^0 in the range of 10^− 5–10^− 3 Pa^− 1 are obtained depending on the molar mass distribution. J_e⁰J_{\rm e}^0 of the LCB-PP is distinctly higher and comes to lie at around 10^− 2 Pa^− 1. J_e⁰J_{\rm e}^0 is found to be independent of M _w but strongly dependent on polydispersity. η and J _e decrease with increasing stress. For the linear PP, J _e as a function of the stress τ is temperature independent. The higher M _w/M _n the stronger is the shear thinning of η and the more pronounced is the stress dependence of J _e. For the LCB-PP, the strongest stress dependence of η and J _e is observed. Furthermore, for all PP J _e reacts more sensitively to an increasing stress than η. A qualitative explanation for the stronger stress dependence of J _e compared to η is given by analyzing the contribution of long relaxation times to the viscosity and elasticity.