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.     

Brittle fracture of precompressed steel as affected by hydrostatic pressure,temperature and strain concentration

Highly precompressed 1020 HR steel, 0.65 prestrain at 400°F (204°C), tested in nominally uniform tension at ?80°F (?62°C) fractures at about 110,000 psi (760 MN/m²) with less than 0.02 plastic strain. Yet the addition of a hydrostatic pressure of less than 7000 psi (48 MN/m²) converts this visually brittle fracture to a ductile one with appreciable necking. The explanation of this surprising experimental result is shown to follow directly and simply from the combination of a tensile stress criterion of fracture, strain concentration and the low tangent modulus of the stress-strain curve in tension beyond the Bauschinger transition region of a few percent of plastic strain. Temperature dependence and strain-rate dependence of brittle fracture similarly are predictable in an almost trivial manner from the appropriate stress-strain curves for different amounts of precompression. So also is the amazingly high ductility or fracture toughness of the most complex of perforated or notched statically loaded structures of mild steel in an undamaged or fully annealed state.     

Influence of Mass Ratio on Forward and Reverse Ballistic Impact Equivalence: Experiments,Simulations, and Mechanism Analysis

Reverse ballistic impact tests are widely used for studying dynamic responses because they provide more comprehensive and quantitative projectile/rod response results than forward impact tests. To examine equivalent forward and reverse conditions, a series of 8-cm length oxygen-free copper rods with varying length–diameter ratios was used in forward and reverse ballistic Taylor impact experiments with velocities and strain ratios of 104–215 m/s and 1.25?×?10³–2.5?×?10³ s^-1, respectively. Digital image correlation (DIC) and traditional optical measurements were used to determine instantaneous responses at the μs level. Based on DIC, transient structural deformation, and plastic wave propagation, the forward and reverse length difference at similar velocities ranges from 2 to 6.95 %. Rules governing deformation from the perspective of energy, along with rules for changes in energy and plastic wave propagation were determined. The relative deformation energy error was below 5 % for target projectile mass ratios above 20.     

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.     

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.     

45钢柱壳膨胀断裂的应变率效应

采用前照明高速分幅照相技术拍摄到在爆轰加载下45钢柱壳表面裂纹生成、扩展及产物泄漏过程的清晰图像,较准确地测量了膨胀断裂的时间与应变。 45钢柱壳在炸药爆轰加载下,断裂应变随应变率的增加而增加,当应变率达到一定值,断裂应变随应变率的增加而降低,出现了动态断裂中的塑性峰现象。     

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.     

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.     

Anomaly in the dynamic strength of austenitic stainless steel 12Cr19Ni10Ti under shock wave loading

Measurement results for the shock wave compression profiles of 12Cr19Ni10Ti steel and its dynamic strength in the strain rate range 10⁵–10⁶ s^?1 are presented. The protracted viscous character of the spall fracture is revealed. With the previously obtained data taken into account, the measurement results are described by a polynomial relation, which can be used to construct the fracture kinetics. On the lower boundary of the range, the resistance to spall fracture is close to the value of the true strength of the material under standard low-rate strain conditions; on the upper boundary, the spall strength is more than twice greater than this quantity. An increase in the temperature results in a decrease in both the dynamic limit of elasticity and the spall fracture strength of steel. The most interesting result is the anomaly in the dependence of the spall fracture strength on the duration of the shock wave compression pulse, which is related to the formation of deformation martensite near the growing discontinuities.     

On neck propagation in amorphous glassy polymers under plane strain tension

Unlike metals, necking in polymers under tension does not lead to further localization of deformation, but to propagation of the neck along the specimen. Finite element analysis is used to numerically study necking and neck propagation in amorphous glassy polymers under plane strain tension during large strain plastic flow. The constitutive model used in the analyses features strain-rate, pressure, and temperature dependent yield, softening immediately after yield and subsequent orientational hardening with further plastic deformation. The latter is associated with distortion of the underlying molecular network structure of the material, and is modelled here by adopting a recently proposed network theory developed for rubber elasticity. Previous studies of necking instabilities have almost invariably employed idealized prismatic specimens; here, we explicitly account for the unavoidable grip sections of test specimens. The effects of initial imperfections, strain softening, orientation hardening, strain-rate as well as of specimen geometry and boundary conditions are discussed. The physical mechanisms for necking and neck propagation, in terms of our constitutive model, are discussed on the basis of a detailed parameter study.     

Synchronous Full-Field Strain and Temperature Measurement in Tensile Tests at Low,Intermediate and High Strain Rates

Tensile tests with simultaneous full-field strain and temperature measurements at the nominal strain rates of 0.01, 0.1, 1, 200 and 3000 s^?1 are presented. Three different testing methods with specimens of the same thin and flat gage-section geometry are utilized. The full-field deformation is measured on one side of the specimen, using the DIC technique with low and high speed visible cameras, and the full-field temperature is measured on the opposite side using an IR camera. Austenitic stainless steel is used as the test material. The results show that a similar deformation pattern evolves at all strain rates with an initial uniform deformation up to the strain of 0.25–0.35, followed by necking with localized deformation with a maximum strain of 0.7–0.95. The strain rate in the necking regions can exceed three times the nominal strain rate. The duration of the tests vary from 57 s at the lowest strain rate to 197 μs at the highest strain rate. The results show temperature rise at all strain rates. The temperature rise increases with strain rate as the test duration shortens and there is less time for the heat to dissipate. At a strain rate of 0.01 s^?1 the temperature rise is small (up to 48 °C) but noticeable. At a strain rate of 0.1 the temperature rises up to 140 °C and at a strain rate of 1 s^?1 up to 260 °C. The temperature increase in the tests at strain rates of 200 s^?1 and 3000 s^?1 is nearly the same with the maximum temperature reaching 375 °C.     

Evaluation of the Material Properties of an OFHC Copper Film at High Strain Rates Using a Micro-Testing Machine

The material properties of an oxygen-free high thermal conductivity (OFHC) film with a thickness of 0.1 mm were evaluated at strain rates ranging from 10⁻³/s to 10³/s using a high-speed material micro-testing machine (HSMMTM). The high strain-rate material properties of thin films are important especially for an evaluation of the structural reliability of micro-formed parts and MEMS products. The high strain-rate material testing methods of thin films, however, have yet to be established to the point that the testing methods of larger specimens for electronics, auto-body, train, ship, and ocean structures are. For evaluation, a new type of HSMMTM was developed to conduct high-speed tensile tests of thin films. This machine is capable of testing at a sufficiently high tensile speed with an electromagnetic actuator, a novel gripping mechanism, and an accurate load measurement system. The OFHC copper film shows high strain-rate sensitivity in terms of the flow stress, fracture elongation, and strain hardening. These measures increase as the tensile strain rate increases. The rate-dependent material properties of an OFHC copper film are also compared with those of a bulk OFHC copper sheet with a thickness of 1 mm. The flow stress of an OFHC copper film is relatively low compared to that of a bulk OFHC copper sheet in the entire range of strain rates, while the fracture elongation of an OFHC copper film is much larger than that of a bulk OFHC copper sheet. A quantitative comparison would provide material data at high strain rates for the design and analysis of micro-appliances and different types of micro-equipment.     

Shear Failure of Inconel 718 under Dynamic Loads

Kinetics of deformation and fracture of nickel–iron alloy Inconel 718 under dynamic shear loading was measured using a split torsional Hopkinson bar facility and high-speed photography. Tubular specimens with a reduced gage length and a starter notch were sheared at strain rates up to 6 × 10³ s⁻¹. High-speed photographs of fiducial lines scribed on the specimen surface showed the development of local strains and cracking. This paper describes the experimental and analytical procedures, illustrates average and local plastic strain evolution, and presents shear crack initiation times and propagation speeds.     

Stress-strain relationships for spruce wood: Influence of strain rate,moisture content and loading direction

The influence of strain rate, moisture content and loading direction on the stress-strain relationships for spruce wood has been investigated. The strain rates were approximately 8×10⁻³ s⁻¹, 17s⁻¹ and 1000 s⁻¹, and the states of moisture content were those corresponding to oven dry, fiber saturated and fully saturated. Compressive loads were applied along the principal directions of the stem of the tree, i.e., radially, tangentially and axially. The low and medium strain-rate tests were performed with the aid of a servohydraulic testing machine, while the high strain-rate tests were carried out using the split Hopkinson pressure bar (SHPB) technique. Magnesium or steel bars were used in the different SHPB tests in order to reduce impedance mismatch for the different directions of the wood specimens. The strain rate was found to have large influence on the behavior of the wood, especially under the condition of full saturation, where water transport in the deforming specimen is of major importance.     

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.     

On the propagation and pulsation of Portevin-Le Chatelier deformation bands: An experimental study with digital speckle pattern metrology

The Portevin-Le Chatelier (PLC) effect is closely associated with inhomogeneous deformation, which is characterized by the band of strain localization. In this work, the spatio-temporal dynamics of the Portevin-Le Chatelier deformation bands are investigated by a novel digital speckle pattern metrology technique consisting of digital speckle pattern interferometry (DSPI) and digital speckle correlation (DSC). A series of tension process of a commercial aluminum alloy (A2017) under different imposed strain rates in a range from 10⁻⁶ to 10⁻³ s⁻¹ are monitored in real time with this technique. The formation of the PLC band, the evolution of the band structure and the propagation of the band are visualized and followed by fringe patterns. The distribution of the deformation in the specimen containing the band is measured precisely. It is shown that even for a tensile test, an elastic shrinkage deformation, which is caused by the avalanche-like shearing deformation within the band, occurs outside the band.     

A rigorous assessment of the benefits of miniaturization in the Kolsky bar system

A rigorous experimental and numerical assessment is made of the benefits and limits of miniaturization in the Kolsky bar system. The primary issues that arise in very high strain rate testing (stress equilibration, inertial effects, wave dispersion, friction, and controllability of deformations) are addressed through experiments coupled with explicit finite element analyses. A miniaturized Kolsky bar system that includes the input bar is developed, together with the use of the laser occlusive radius detector to obtain local measurements of specimen strain during the very high rate deformations. It is demonstrated that this miniaturized Kolsky bar system can be used to provide fully validated results, including the explicit determination of equilibration, over a very wide range of strain rates (1×10³ to 5×10⁴ s⁻¹). The desired high strain rate can be achieved even at low accumulated strains, and the total strain developed can be controlled very effectively. Specific conditions are developed for determining the range of utility of the technique for a given material. The technique is applied to the characterization of 6061-T651 aluminum, and the results are compared with the results obtained using a conventional Kolsky bar.     

Single bubble deformation and breakup in simple shear flow

Experiments in a parallel band apparatus and a transparent concentric cylinder device allow the observation of bubble deformation (shape and orientation) and breakup as a function of the viscosity ratio λ and the Capillary number Ca. For viscosity ratios between 3.1 × 10⁻⁷ and 6.7 × 10⁻⁸, critical Capillary numbers Ca _c for bubble breakup between 29 and 45 are found. It is furthermore shown that in the given parameter space no clear distinction between tip breakup and fracture can be made for bubbles. An erratum to this article can be found at     

The strain-rate effect and the incremental plastic wave in copper

An experimental investigation was conducted to determine the degree of sensitivity of commerically pure copper to strain rate and to note the effect of this sensitivity on the velocity of propagation of shearing strain in copper. Thin-walled cylindrical specimens of copper were loaded in torsion to eliminate the effects of radial inertia. All specimens were annealed and then cold worked in torsion to obtain necessary specimen uniformity. Quasi-static tests were performed on short-length specimens to determine the shearing stress-strain curve of copper at a very low strain rate. The strain-rate sensitivity of copper at low strain rates, from 3×10^?4/sec to 5/sec, was tested by loading short specimens at a very slow continuous rate and then suddenly increasing the strain rate. A quasi-static test was also performed to determine the effect of creep on prestressed copper. Dynamic tests involving strain rates up to 500/sec were performed on long specimens with a torsional impact machine. Specimens were tested under stress-free and prestressed initial conditions. The prestressed specimen was loaded at a slow, continuous rate before impact to avoid the undesirable effects of creep which would have occurred with a static preload. Results from the quasi-static tests showed that copper is noticeably sensitive to strain rate in the low strain-rate regions, but that the sensitivity becomes almost constant as the strain rate is increased. Results from the dynamic tests showed that large strains propagated at speeds which agreed well with speeds predicted by the strain-rate-independent theory of plastic-wave propagation. The lower-level strains in the prestressed specimen, however, propagated at much higher speeds than are predicted by the strain-rate independent. Because radial-inertia effects were not present, this discrepancy in measured and predicted speeds for low-level strains must be due to the strain-rate sensitivity of copper.     

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.