Effects of strain rate and moisture content on the behaviour of sand under one-dimensional compression

The influence of strain rate and moisture content on the behaviour of a quartz sand was assessed using high-pressure quasi-static (10^?3 s^?1) and high-strain rate (10³ s^?1) experiments under uniaxial strain. Quasi-static compression to axial stresses of 800 MPa was carried out alongside split Hopkinson pressure bar (SHPB) experiments to 400 MPa, where in each case lateral deformation of the specimen was prevented using a steel test box or ring, and lateral stresses were recorded. A significant increase in constrained modulus was observed between strain rates of 10^?3s^?1 and 10³s^?1, however a consistently lower Poisson’s ratio in the dynamic tests minimised changes in bulk modulus. The reduction in Poissons ratio suggests that the stiffening of the sand in the SHPB tests is due to additional inertial confinement rather than an inherent strain-rate dependence. In the quasi-static tests the specimens behaved less stiffly with increasing moisture content, while in the dynamic tests the addition of water had little effect on the overall stiffness, causing the quasi-static and dynamic series to diverge with increasing moisture content.     

Miniaturized Compression Test at Very High Strain Rates by Direct Impact

A modified miniaturized version of the Direct Impact Compression Test (DICT) technique is described in this paper. The method permits determination of the rate-sensitive plastic properties of materials up to strain rate ∼10⁵ s⁻¹. Miniaturization of the experimental setup with specimen dimensions: diameter d _S = 2.0 mm and thickness l _S = 1.0 mm, Hopkinson bar diameter 5.2 mm, with application of a novel optical arrangement in measurement of specimen strain, makes possible compression tests at strain rates from ∼10³ s⁻¹ to ∼10⁵ s⁻¹. In order to estimate the rate sensitivity of a low-alloy construction steel, quasi-static, Split Hopkinson Pressure Bar (SHPB) and DICT tests have been performed at room temperature within the rate spectrum ranging from 5*10⁻⁴ s⁻¹ to 5*10⁴ s⁻¹. Adiabatic heating and friction effects are analyzed and the final true stress versus true strain curves at different strain rates are corrected to a constant temperature and zero friction. The results have been analyzed in the form of true stress versus the logarithm of strain rate and they show two regions of a constant rate sensitivity : relatively low up to the strain rate threshold ∼50 s⁻¹, and relatively high above the threshold, up to strain rate ∼4.5*10⁴ s⁻¹.     

High Strain Rate Torsion Properties of Ultrafine-Grained Aluminum

Mechanical properties of most metallic materials can be improved by reducing their grain size. One of the methods used to reduce the grain size even to the nanometer level is the severe plastic deformation processing. Equal Channel Angular Pressing (ECAP) is one of the most promising severe plastic deformation processes for the nanocrystallization of ductile metals. Nanocrystalline and ultrafine grained metals usually have significantly higher strength properties but lower tensile ductility compared to the coarse grained metals. In this work, the torsion properties of ECAP processed ultrafine grained pure 1070 aluminum were studied in a wide range of strain rates using both servohydraulic materials testing machines and Hopkinson Split Bar techniques. The material exhibits extremely high ductility in torsion and the specimens did not fail even after 300% of strain. Pronounced yield point behavior was observed at strain rates 500 s⁻¹ and higher, whereas at lower strain rates the yielding was continuous. The material showed slight strain softening at the strain rate of 10⁻⁴ s⁻¹, almost ideally plastic behavior at strain rates between 10⁻³ s⁻¹ and 500 s⁻¹, and slight but increasing strain hardening at strain rates higher than that. The tests were monitored using digital cameras, and the strain distributions on the surface of the specimens were calculated using digital image correlation. The strain in the specimen localized very rapidly after yielding at all strain rates, and the localization lead to the development of a shear band. At high strain rates the shear band developed faster than at low strain rates.     

Influence of Molecular Conformation on the Constitutive Response of Polyethylene: A Comparison of HDPE, UHMWPE, and PEX

The current work presents the characterization and comparison of the mechanical response of three different industrial forms of polyethylene. Specifically, high-density polyethylene (HDPE), ultra high molecular weight polyethylene (UHMWPE), and cross-linked polyethylene (PEX) were tested in compression as a function of temperature (−75 to 100°C) and strain-rate (10⁻⁴ to 2,600 s⁻¹). The responses of UHMWPE and PEX are very similar, whereas HDPE exhibits some differences. The HDPE samples display a significantly higher yield stress followed by a flat flow behavior. Conversely UHMWPE and PEX both exhibit significant strain hardening after yield. The temperature and strain-rate dependence are captured by simple linear and logarithmic fits over the full range of conditions investigated. The yield behavior is presented in terms of an empirical mapping function that is extended to analytically solve for the mapping constant. The power-law dependence on strain-rate observed in some polymers is explained using this mapping function.     

Effect of Mass Density on the Compressive Behavior of Dry Sand Under Confinement at High Strain Rates

Dynamic compressive behavior of dry quartz sand (Quikrete #1961 sand quarried in Pensacola, FL) under confinement was characterized using a modified long split Hopkinson pressure bar (SHPB). Sand grains were confined inside a hollow cylinder of hardened steel and capped by cemented tungsten carbide cylindrical rods. This assembly was subjected to repeated shaking to consolidate sand to attain precise bulk mass densities. It is then sandwiched between incident and transmission bars on SHPB for dynamic compression measurements. Sand specimens of five initial mass densities, namely, 1.51, 1.57, 1.63, 1.69, and 1.75 g/cm³, were characterized at high strain rates near 600 s⁻¹, to determine the volumetric and deviatoric behaviors through measurements of both axial and transverse responses of a cylindrical sand sample under confinement. The stress–strain relationship was found to follow a power law relationship with the sand initial bulk density, with an exponent of 8.25, indicating a behavior highly sensitive to mass density. The energy absorption density and compressibility of sand were determined as a function of axial stress.     

Effect of strain rate,moisture and temperature on the deformation behavior of polymer roll covers

Soft polymer roll covers, which are used in certain positions of paper manufacturing machines, have a vital role in the dynamics of two mating rotating rolls (i.e., nip dynamics). The polymer covers are often used in moist conditions where the loading rates are rather high and temperatures may vary from 45 to 60°C. In this paper, we study the dynamic mechanical behavior of two soft polyurethane composite roll covers under different conditions of temperature, moisture, and loading rate. For the tests in compression, both servohydraulic materials testing machines and the split Hopkinson pressure bar technique were used in the strain rate range of 0.001–1500 s⁻¹. The specimens, which were to be tested under moist conditions, were immersed in paper machine water (pH 4.5) until saturated moisture content was reached. The materials showed remarkable softening as well as decrease in the strain rate sensitivity in moist conditions.     

Determination of dynamic yield strengths with embedded manganin gages in plate-impact and long-rod experiments

The dynamic yield strengths of three steels were determined at strain rates of about 10³ s⁻¹ and 10⁶ s⁻¹. The measurements at 10³ s⁻¹ were obtained by a new technique based on measurements of large amplitude elastic waves in long bars struck by rigid flyer plates. Embedded manganin gages were used to measure stress, and the gage records were long enough to observe subsequent reverberations between the bar free end and the plastically deformed impact end. The measurements at 10⁶ s⁻¹ were made with a slightly modified version of a conventional flyer-plate impact configuration. The data are combined with static results to show the behavior of these steels at strain rates of 10⁻³ s⁻¹ to 10⁶ s⁻¹.     

Torsional split Hopkinson bar tests at strain rates above 104s−1

The torsional split Hopkinson bar is used for testing materials at strain rates above 10⁴s⁻¹. This strain rate, which is an order of magnitude higher than is typical with this technique, is obtained by using very short specimens. Strain rates of 6.4×10⁴s⁻¹ have been achieved with specimens having a gage length of 0.1524 mm. Results from tests on 1100 aluminum show an increase in rate sensitivity as the strain rate increases.     

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.     

High-rate decremental-strain-rate test

A modified torsional split-Hopkinson bar is intoduced and used to study material response associated with a sudden reduction of stain rate during high-rate plastic deformation. In tests on 1100-0 aluminum iniial deformation at a strain rate of approximately 2400 s⁻¹ is reduced by a factor of 15 after 200 μs of high-rate deformation. After the reduction, the deformation continues at the low rate for additional 550 μs. The change in the strain rate is obtained by using a stepped input bar. The results for 1100-0 aluminum show a decrease in the flow stress following the reduction in the strain rate. A short delay exists between the beginning of the strain-rate reduction and the response of the stress. The magnitude of the drop in the stress agrees with the difference in flow stress expected in constant-strain-rate tests in the corresponding high- and low-strain rates. Following the stress reduction. The stress remains essentially constant with no hardening during the subsequent deformation at the low rate.     

A crystallographic model for the orientation dependence of low cyclic fatigue property of a nickel-base single crystal superalloy

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Modeling of water transport in roof tiles by removal of moisture at isothermal conditions

The main objective of this article is to describe the drying process of ceramic roof tiles, shaped from red clay, using diffusion models. Samples of the product with initial moisture content of 0.24 (db) were placed inside an oven in the temperatures of 55.6, 69.7, 82.7 and 98.6°C; and the data of the drying kinetics were obtained. The analytical solutions of the diffusion equation for the parallelepiped with boundary conditions of the first and third kinds were used to describe the drying processes. The process parameters were determined using an optimization algorithm based on inverse method coupled to the analytical solutions. The analysis of the results makes it possible to affirm that the boundary condition of the third kind satisfactorily describes the drying processes. The values obtained for the convective mass transfer coefficient were between 8.25 × 10⁻⁷ and 1.64 × 10⁻⁶ m s⁻¹, and for the effective water diffusivity were between 9.21 × 10⁻⁹ and 1.80 × 10⁻⁸ m² s⁻¹.     

Thin-layer drying of tomato (<Emphasis Type="Italic">Lycopersicum esculentum Mill. cv. Rio Grande</Emphasis>) slices in a convective hot air dryer

The effects of different drying temperatures on the drying kinetics of tomato slices were investigated using a cabinet-type dryer. The experimental drying data were fitted best to the to the Page and Modified Page models apart from other theoretical models to predict the drying kinetics. The effective moisture diffusivities varied from 1.015 × 10⁻⁹ to 2.650 × 10⁻⁹ m² s⁻¹over the temperature range studied, and activation energy was 22.981 kJ mol⁻¹.     

Small and large strain rheology of wheat gluten

 The rheological properties of wheat gluten were studied under both small and large deformation and compared with those of the parent flours. The limiting strain of linear viscoelastic behaviour of gluten doughs, 3 × 10⁻², was an order of magnitude larger than that of the flour doughs, 10⁻³. The role of starch in the lower limiting strain of flour doughs was indicated by the exponential decrease in the limiting strain of gluten-starch mixtures with greater quantities of starch. Large strain measurements showed gluten doughs possessed greater shear and elongational viscosities than flour doughs and these differences were greatest at lower shear and elongation rates (0.01 and 0.1 s⁻¹). The larger viscosities of flour and gluten doughs at the low strain rates help to stabilise and prevent the collapse of gas bubbles during bread fermentation and baking. Increasing starch levels in gluten-starch mixtures, at either constant or optimal water levels, lowered the elongational viscosity. Dynamic measurements were, however, more sensitive to the level of water added to the gluten-starch mixtures. The storage modulus decreased with increasing starch levels when constant water levels were used to prepare the mixtures, but when optimal water levels were used the storage modulus increased. Gluten and starch are major contributors to the large and small strain rheological properties of flour doughs; however, gluten-starch mixtures were unable to duplicate exactly the rheological properties of flour doughs, indicating that other flour components such as pentosans, lipids and water soluble proteins also influence dough rheology. Received: 20 March 2001 Accepted: 11 July 2001     

A Kolsky bar: Tension,tension-tension

The present paper introduces a new technique which combines rotation disk and traditional Kolsky bar (often termed as split-Hopkinson bar). This technique can be employed to study the tension stress-strain relations and tension-unloading-tension strain-rate history effects of materials in the strain rate range from 10²–10³s⁻¹. The rise time of the incident wave is as short as 15 μs because of the particular design. An attempt is made to estimate strain error caused by the thread connection between the specimen and the bars, and stress error due to the mismatch of the cross section of the specimen and bars. A short rise-time incident wave appears to be most advantageous in view of maintaining the accuracy of the stress-strain curve obtained near the initiation. Preliminary tests are performed on the instrument. Comments are made for this design configuration. M. Li (Student Member of SEM), presently at the Department of Aerospace Engineering, Mechanics and Engineering Science, University of Florida, Gainesville, FL 32611, was Research Associate; R. Wang (formerly A.J. Wang) is Professor; and M.-B. Han is Associate Professor, Department of Mechanics, Peking University, Beijing 100871, P.R. China.     

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.     

Determination of the shear strength and modulus of water at low flow velocities

Damped inertial water flow in a cylindrical vessel is investigated. A return effect or "recoil" as the shear strain rate falks to a value of the order of 10⁻³s⁻¹ is observed. Over the range of low strain rates the water behaves like a medium with very low shear strength and a shear modulus of the order of 10⁻⁶ Pa. Ekaterinburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 3–7, January–February, 1997.     

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.     

High-strain-rate compressive behavior of a rigid polyurethane foam with various densities

The dynamic compressive stress-strain behavior of a rigid polyurethane foam with four values of density (78, 154, 299, and 445 kg/m³) has been determined in the strain-rate range of 1000–5000 s⁻¹. A pulse shaping technique was used with a split Hopkinson pressure bar to ensure homogeneous deformation in the foam specimens under dynamic compression. Dynamic stress equilibrium in the specimen was monitored during each experiment using piezoelectric force transducers mounted close to the specimen end-faces. Quasi-static experiments were also performed to demonstrate rate effects. Experimental results show that both the quasistatic and the dynamic stress-strain curves of the foam exhibit linear elasticity at small strains until a peak is reached. After the peak, the stress-strain curves have a plateau region followed by a densification region. The peak stress is strain-rate sensitive and depends on the square of the foam density.     

Strain-rate history effects and microstructural aspects in lithium fluoride and aluminium single crystals after dynamic loading

Single crystals of LiF and Al are deformed in shear at a number of constant strain-rates in the range 10^–4 to 1600 s^–1. These constant rate tests are supplemented by a series of jump tests in which a sharp increment in strain rate is imposed during the quasi-static straining. Dislocation arrangements are observed by etch-pits technique for LiF crystals and by TEM for Al crystals. It is shown that cell sizes vary inversely with flow stress and strain-rate sensitivity.