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.     

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.     

Strain-rate history and temperature effects on the torsional-shear behavior of a mild steel

Previous investigations on the effects of strain-rate and temperature histories on the mechanical behavior of steel are briefly reviewed. A study is presented on the influence of strain rate and strain-rate history on the shear behavior of a mild steel, over a wide range of temperature Experiments were performed on thin-walled tubular specimens of short gage length, using a torsional split-Hopkinson-bar apparatus adapted to permit quasi-static as well as dynamic straining at different temperatures. The constant-rate behavior was first measured at nominal strain rates of 10^?3 and 10³ s^?1 for ?150, ?100, ?50, 20, 200 and 400°C. Tests were then carried out, at the same temperatures, in which the strain rate was suddenly increased during deformation from the lower to the higher rate at various large values of plastic strain. The increase in rate occurred in a time of the order of 20 μs so that relatively little change of strain took place during the jump. The low strain-rate results show a well-defined elastic limit but no yield drop, a small yield plateau is found at room temperature. The subsequent strain hardening shows a maximum at 200°C, when serrated flow occurs and the ductility is reduced. The high strain-rate results show a considerable drop of stress at yield. The post-yield flow stress decreases steadily with increasing temperature, throughout the temperature range investigated. At room temperature and below, the strain-hardening rate becomes negative at large strains. The adiabatic temperature rise in the dynamic tests was computed on the assumption that the plastic work is entirely converted to heat. This enabled the isothermal dynamic stress-strain curves to be calculated, and showed that considerable thermal softening took place. The initial response to a strain-rate jump is approximately elastic, and has a magnitude which increases with decrease of testing temperature; it is little affected by the amount of prestrain. At 200 and 400° C, a yield drop occurs after the initial stress increment. The post-jump flow stress is always greater than that for the same strain in a constant-rate dynamic test, the strain-hardening rate becoming negative at large strains or low testing temperature. This observed effect of strain-rate history cannot be explained by the thermal softening accompanying dynamic deformation. These and other results concerning total ductility under various strain-rate and temperature conditions show that strain-rate history strongly affects the mechanical behavior of the mild steel tested and, hence, should be taken into account in the formulation of constitutive equations for that material.     

The effect of strain rate and heat developed during deformation on the stress-strain curve of plastics

Polymethylmethacrylate, cellulose acetate butyrate, polypropylene and nylon 6–6 have been characterized in compression at various strain rates from 10^?4 s^?1 to 10³ s^?1 at room temperature. A medium strain-rate machine and a split-Hopkinson-bar apparatus are used in conducting the experiments. The temperature rise developed during deformation is also measured by using a thermocouple. All four materials tested definitely show a viscous effect at the beginning of the deformation and a plastic flow follows thereafter. Test results also indicate that the temperature rise developed during deformation cannot be neglected in determining the dynamic response of those materials investigated in this study.     

Compression-impact testing of aluminum at elevated temperatures

This paper presents and experimental technique for determining compressive stress-strain curves well into the plastic range of relatively soft metals at strain rates from 300 to 2000 sec^?1 at six temperatures from 30 to 550° C. More than 100 curves were obtained on annealed 1100° F aluminum. The strain-rate dependence in these tests could be fitted quite well either by a power function (log-log plot) or by a semilogarithmic plot, but the power function gave a better correlation of the present data with that obtained at lower strain rates by Alder and Phillips.¹     

Annular Pulse Shaping Technique for Large-Diameter Kolsky Bar Experiments on Concrete

The goal of this study is to design a novel annular pulse shaping technique for large-diameter Kolsky bars for investigating the dynamic compressive response of concretes. The purpose of implementing an annular pulse shaper design is to alleviate inertia-induced stresses in the pulse shaper material that would otherwise superpose unwanted oscillations on the incident wave. This newly developed pulse shaping technique led to well-controlled testing conditions enabling dynamic stress equilibrium, uniform deformation, and constant strain-rate in the testing of a chosen concrete material. The observed dynamic deformation rate of the concrete is highly consistent (8 % variation) with the stress in the specimen well equilibrated confirming the validity of this new technique. Experimental results at both quasi-static (10^?4 s^?1) and dynamic (100 s^?1, 240 s^?1) strain rates showed that the failure strength of this concrete is rate-sensitive.     

A study of localisation in dual-phase high-strength steels under dynamic loading using digital image correlation and FE analysis

Tensile tests were conducted on dual-phase high-strength steel in a Split-Hopkinson Tension Bar at a strain-rate in the range of 150–600/s and in a servo-hydraulic testing machine at a strain-rate between 10^?3 and 10⁰/s. A novel specimen design was utilized for the Hopkinson bar tests of this sheet material. Digital image correlation was used together with high-speed photography to study strain localisation in the tensile specimens at high rates of strain. By using digital image correlation, it is possible to obtain in-plane displacement and strain fields during non-uniform deformation of the gauge section, and accordingly the strains associated with diffuse and localised necking may be determined. The full-field measurements in high strain-rate tests reveal that strain localisation started even before the maximum load was attained in the specimen. An elasto-viscoplastic constitutive model is used to predict the observed stress–strain behaviour and strain localisation for the dual-phase steel. Numerical simulations of dynamic tensile tests were performed using the non-linear explicit FE code LS-DYNA. Simulations were done with shell (plane stress) and brick elements. Good correlation between experiments and numerical predictions was achieved, in terms of engineering stress–strain behaviour, deformed geometry and strain fields. However, mesh density plays a role in the localisation of deformation in numerical simulations, particularly for the shell element analysis.     

Shear-strain-rate effects in a high-strength aluminum alloy

Methods of investigating the plastic flow of materials at high rates are reviewed, and experiments are described in which thin-walled tubular specimens were subjected to dynamic torsional loading. These experiments were performed using a modified version of a torsional Hopkinsonbar apparatus used in earlier work. The results show that, at strain rates of order 10³ sec⁻¹, the stress-strain curve of the alloy tested does not differ significantly from that found at 10⁻³ sec⁻¹. In tests involving the propagation of a stress increment, however, it was found that the speed of propagation was that of elastic shear waves, indicating that the initial response of the material is essentially rate dependent.     

Dynamic deformation of metals under high hydrostatic pressure

A method for investigating the static and dynamic deformation of materials subjected to hydrostatic confining pressures is described. Results of tests on high-purity (99.995 percent) copper in compression are given. These tests cover a range of hydrostatic pressures from one to 6,985 bars (100,000 psi) and strain rates from 0.001 to 10,000 sec^?1. The results show a definite strain-rate effect which is dependent on pressure.     

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.     

A Novel Image-based Ultrasonic Test to Map Material Mechanical Properties at High Strain-rates

An innovative identification strategy based on high power ultrasonic loading together with both infrared thermography and ultra-high speed imaging is presented in this article. It was shown to be able to characterize the visco-elastic behaviour of a polymer specimen (PMMA) from a single sample over a range of temperatures and strain-rates. The paper focuses on moderate strain-rates, i.e. from 10 to 200 s^?1, and temperatures ranging from room to the material glass transition temperature, i.e. 110^°C. The main originality lies in the fact that contrary to conventional Dynamic Mechanical Thermal Analysis (DMTA), no frequency or temperature sweep is required since the experiment is designed to simultaneously produce both a heterogeneous strain-rate state and a heterogeneous temperature state allowing a local and multi-parametric identification. This article is seminal in nature and the test presented here has good potential to tackle a range of other types of high strain-rate testing situations.     

High strain-rate crack growth in rate-dependent plastic solids

At high crack velocities in metallic materials nearly all plastic strain accumulates at very high strain-rates, typically in the range 10³ s^?1 to 10⁵ s^?1. At these rates, dislocation motion is limited by dynamic lattice effects and the plastic strain-rate increases approximately linearly with stress. The problem for a crack growing at high velocity is posed for steady-state, small scale yielding in elastic/rate-dependent plastic solids. A general expression is derived for the near-tip stress intensity factor in terms of the remote intensity factor, or equivalently for the near-tip energy release-rate in terms of the overall release-rate. An approximate calculation of the plastic strain-rates provides this relation in analytical form. Imposition of the condition that the near-tip energy release-rate be maintained at a critical value provides a propagation equation for the growing crack. A single, nondimensional combination of material constants emerges as the controlling parameter. Implications for dynamic crack propagation are discussed.     

High-strain-rate tests on titanium 6-6-2 utilizing a unique rate-testing machine

This paper presents the design of a unique materials-testing system capable of medium strain rates of from 10^?4 to 10²/s. The design incorporates both closed-loop hydraulic operation with that of open-loop pneumatic operation. A novel design permits accurate specimen alignment and a stiff frame which exceeds 17×10⁶ lb/in. (11.7×10⁴ MPa). The mechanine is able to perform conventional tension/compression tests, fatigue tests and, with slight modification, biaxial-stress-tube tests and triaxial-stress tests. The accurate alignment capability coupled with high frame stiffness and the pneumatic operation enables the testing of brittle materials with rigid grips. Titanium 6-6-2 was tested in both tension and compression at strain rates from 10^?4 to about 10/s at four selected temperatures. The material showed a slight strain-rate sensitivity. Yield stress was shown to increase with strain rate while ductility decreased at each test temperature.     

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.     

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.     

Characterization of Anisotropic Polymeric Foam Under Static and Dynamic Loading

An orthotropic polymeric foam with transverse isotropy (Divinycell H250) used in composite sandwich structures was characterized at various strain rates. Uniaxial experiments were conducted along principal material axes as well as along off-axis directions under tension, compression, and shear to determine engineering constants, such as Young??s and shear moduli. Uniaxial strain experiments were conducted to determine mathematical stiffness constants, i. e., C _ij . An optimum specimen aspect ratio for these tests was selected by means of finite element analysis. Quasi-static and intermediate strain rate tests were conducted in a servo-hydraulic testing machine. High strain rate tests were conducted using a split Hopkinson Pressure Bar system built for the purpose using polymeric (polycarbonate) bars. The polycarbonate material has an impedance that is closer to that of foam than metals and results in lower noise to signal ratios and longer loading pulses. It was determined by analysis and verified experimentally that the loading pulses applied, propagated along the polycarbonate rods at nearly constant phase velocity with very low attenuation and dispersion. Material properties of the foam were obtained at three strain rates, quasi-static (10^?4 s^?1), intermediate (1 s^?1), and high (10³ s^?1) strain rates. A simple model proposed for the Young??s modulus of the foam was in very good agreement with the present and published experimental results.     

Elasto-visco-plastic modeling of mild steels for sheet forming applications over a large range of strain rates

A physically based elasto-visco-plastic constitutive model is presented and compared to experimental results for three different mild steels. The experiments consist of tensile tests ranging from quasi-static conditions up to strain rates of 10³ s^?1 as well as quasi-static simple and reverse shear tests at different amounts of pre-strain. Additional two-step sequential mechanical tests (Bauschinger and orthogonal effects) have been performed to further evaluate the ability of the model to describe strain-path changes at moderate/large strains. The model requires significantly fewer material parameters compared to other visco-plasticity models from the literature, while being able to describe some of the main features of the strain-rate sensitivity of mild steels. Accordingly, the parameter identification is simple and intuitive, requiring a relatively small set of experiments. The strain-rate sensitivity modeling is not restricted to a particular hardening law and thus provides a general framework in which advanced hardening equations can be adopted.     

Measuring dynamic-strain profile and history with a drum camera

A low-speed drum camera has been used to continuously record the strain profile in several different types of impact tests. The drum camera was selected because it is inexpensive and simple to use, and it overcomes many of the inherent disadvantages of other dynamic-recording techniques. The use of the drum camera in recording the strain profile in tensile and torsional impact is illustrated, as well as the determination of impact velocity in collinear plastic impact of two bars. A detailed discussion of determination of the strain profile from the tensile-test film record is presented, including an analysis of the accuracy achieved. It was found that the drum camera is capable of measuring strains to an accuracy of approximately 1 percent for a gage length of 0.05 in. Strains varying from 1 to 100 percent were measured in the tensile test, with a nominal strain rate of 20 sec^?1. Strain rates of up to 2000 sec^?1 were successfully recorded in the torsional impact tests.     

Rubber-like behaviour of poly(ethylene oxide) solution in elongational flow

The behaviour of an aqueous poly(ethylene oxide) sucrose solution and of a suspension of glass beads in a similar solution has been examined in elongational flow using a spinline rheometer. Over the accessible strain-rate range of ca. 1 to 10 s^?1 these fluids behaved essentially as elastic materials whereas, at similar strain rates in shear, they show shear-thinning behaviour.     

Dynamic stress-strain characteristics of metals at elevated temperatures

A method for measuring the load, strain and strain rate inside a high-temperature environment is described. Results of tests on specimens of high-purity copper are reported. Results indicate that copper is strain-rate dependent within the temperature range 78°–1000° F up to strains of 0.6 percent and strain rates of 10³ sec^–1.Paper was presented at 1969 SESA Spring Meeting held in Philadelphia, Pa., on May 13–16.This work was sponsored by the Army Research Office (Durham) under Contract No. DA 31-124-ARO-D229.