Load-Inversion Device for the High Strain Rate Tensile Testing of Sheet Materials with Hopkinson Pressure Bars

A high strain rate tensile testing technique for sheet materials is presented which makes use of a split Hopkinson pressure bar system in conjunction with a load inversion device. With compressive loads applied to its boundaries, the load inversion device introduces tension into a sheet specimen. Two output bars are used to minimize the effect of bending waves on the output force measurement. A Digital Image Correlation (DIC) algorithm is used to determine the strain history in the specimen gage section based on high speed video imaging. Detailed finite element analysis of the experimental set-up is performed to validate the design of the load inversion device. It is shown that under the assumption of perfect alignment and slip-free attachment of the specimen, the measured stress–strain curve is free from spurious oscillations at a strain rate of 1,000 s^?1. Validation experiments are carried out using tensile specimens extracted from 1.4 thick TRIP780 steel sheets. The experimental results for uniaxial tension at strain rates ranging from 200 s^?1 to 1,000 s^?1 confirm the oscillation-free numerical results in an approximate manner. Dynamic tension experiments are also performed on notched specimens to illustrate the validity of the proposed experimental technique for characterizing the effect of strain rate on the onset of ductile fracture in sheet materials.     

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.     

Specimen Size and Strain Rate Effects on the Compressive Behavior of Concrete

Three high-performance concrete (HPC) materials with different specimen geometries were characterized using Kolsky compression bar techniques to study the strain rate and specimen size effects on their uniaxial compressive strength. A large-diameter Kolsky bar and recently established annular pulse shaping technique were used to achieve dynamic stress equilibrium and constant strain-rate deformation in the experiments. A complimentary effort was conducted using a 19-mm-diameter Kolsky compression bar to understand the strain rate and specimen size effects on failure strength and dynamic increase factor (DIF) for concrete. It was found that, for all three concrete materials investigated, the failure strength is highly dependent on the specimen geometry, however such a relationship is not apparent for the DIF. The DIF observed in this study shows significantly lower values compared to historical data, which may indicate the importance of well-controlled dynamic testing conditions on the accuracy and validity of experimental results for concrete materials.     

The Effect of Grain Size on Deformation and Failure of Ti<Subscript>2</Subscript>AlC MAX Phase under Thermo-Mechanical Loading

An experimental investigation was performed to analyze the effects of grain size on the quasi-static and dynamic behavior of Ti₂AlC. High-density Ti₂AlC samples of three different grain sizes were densified using Spark Plasma Sintering and Pressureless sintering. A servo-hydraulic testing machine equipped with a vertical split furnace, and SiC pushrods, was used for the quasi-static experiments. Also, a Split Hopkinson Pressure Bar (SHPB) apparatus and an induction coil heating system were used for the dynamic experiments. A series of experiments were conducted at temperatures ranging from 25 °C to 1100 °C for strain rates of 10^?4 s^?1 and 400 s^?1. The results show that under quasi-static loading the specimens experience a brittle failure for temperatures below Brittle to Plastic Transition Temperature (BPTT) of 900–1000 °C and large deformation at temperatures above the BPTT. During dynamic experiments, the specimens exhibited brittle failure, with the failure transitioning from catastrophic failure at lower temperatures to graceful failure (softening while bearing load) at higher temperatures, and with the propensity for graceful failure increasing with increasing grain size. The compressive strengths of different grain sizes at a given temperature can be related to the grain length by a Hall-Petch type relation.     

Hopkinson拉杆的入射波波形整形实验研究

目前,分离式Hopkinson杆实验技术已经被广泛用于测试材料在10~2~10~4s~(-1)应变率范围内的动态力学特性。为了抑制入射波的高频振荡,实现恒定应变率加载,本文利用分离式Hopkinson拉杆(SHTB)实验装置,研究了加载金属短杆(2A12T4铝合金)及整形垫片(纸板、PVC软塑料及带磁性胶皮)对入射波波形的影响。实验结果表明,整形垫片降低了入射应力脉冲的高频振荡,获得了比较平滑的入射应力脉冲,延长了上升时间。同时,利用所得的波形整形结果,对2A12T4铝合金进行了拉伸应力波脉冲加载的拉伸和断裂实验测试。     

PLASTIC BEHAVIOR AND CONSTITUTIVE MODELING OF ARMOR STEEL OVER WIDE TEMPERATURE AND STRAIN RATE RANGES

Plastic behavior of 603 armor steel is studied at strain rates ranging from 0.001 s-1 to 4500 s-1 , and temperature from 288 K to 873 K. Emphasis is placed on the effects of temperature, strain rate, and plastic strain on flow stress. Based on experimental results, the JC and the KHL models are used to simulate flow stress of this material. By comparing the model prediction and the experimental results of strain rate jump tests, the KHL model is shown to have a better prediction of plastic behavior under complex loading conditions for this material, especially in the dynamic region.     

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.     

Dehydration characteristics and mathematical modelling of lemon slices drying undergoing oven treatment

In this study, the effect of drying temperature on drying behaviour and mass transfer parameters of lemon slices was investigated. The drying experiments were conducted in a laboratory air ventilated oven dryer at temperatures of 50, 60 and 75 °C. It was observed that the drying temperature affected the drying time and drying rate significantly. Drying rate curves revealed that the process at the temperature levels taken place in the falling rate period entirely. The usefulness of eight thin layer models to simulate the drying kinetics was evaluated and the Midilli and Kucuk model showed the best fit to experimental drying curves. The effective moisture diffusivity was determined on the basis of Fick’s second law and obtained to be 1.62 × 10^?11, 3.25 × 10^?11 and 8.11 × 10^?11 m² s^?1 for the temperatures of 50, 60 and 75 °C, respectively. The activation energy and Arrhenius constant were calculated to be 60.08 kJ mol^?1 and 0.08511 m² s^?1, respectively. The average value of convective mass transfer coefficient for the drying temperatures of 50, 60 and 75 °C was calculated to be 5.71 × 10^?7, 1.62 × 10^?6 and 2.53 × 10^?6 m s^?1, respectively.     

The development and use of a torsional Hopkinson-bar apparatus

A technique is described by means of which torsional waves of large, essentially constant amplitude can be generated in an elastic bar. Waves with rise times of order 25 μs and maximum angular velocities of order 10³ rad.s^?1 have been achieved and used to test tubular specimens at shear-strain rates up to 15×10³ s^?1. Results are presented for mild steel tested at 2×10³ s^?1, and it is shown that the flow stress correlates well with the trend found at lower rates using conventional methods. The measured drop of stress at yield, however, was considerably smaller in the present tests than in earlier work; this is attributed to the generation of flexural waves which reach the specimen at the same time as the torsional wave.     

Strain-Rate-Dependent Failure of a Toughened Matrix Composite

The strain-rate-dependent behavior of a toughened matrix composite (IM7/8552) was characterized under quasi-static and dynamic loading conditions. Unidirectional and off-axis composite specimens were tested at strain rates ranging from 10^?4 to 10³ s^?1 using a servo-hydraulic testing machine and split Hopkinson pressure bar apparatus. The nonlinear response and failure were analyzed and evaluated based on classical failure criteria and the Northwestern (NU) failure theory. The predictive NU theory was shown to be in excellent agreement with experimental results and to accurately predict the strain-rate-dependent failure of the composite system based on measured average lamina properties.     

The dependence of crack velocity on the critical stress in fracture

The constant velocity of crack propagation in PMMA is investigated in terms of the fracture stress for both continuously increasing loading (strain rate ?=0.59×10^?4 s^?1) and dynamic loading (strain rate ?=0.35 s^?1). It was found that the constant crack velocity increases with increasing fracture stress and that it depends on the loading conditions (continuously increasing or dynamic loading). In particular, it was found that the increase of the constant velocity for the static loading case is higher than for the dynamic one. However, in both cases, the constant velocity reaches a limiting value for stresses higher than a certain level.     

The Development of a High Rate Tensile Testing System for Micro Scaled Single Crystal Silicon Specimens

Structures have been built at micro scales with unique failure mechanisms that are not yet understood, in particular, under high-rate loading conditions. Consequently, microelectromechanical systems (MEMS) devices can suffer from inconsistent performance and insufficient reliability. This research aims to understand the failure mechanisms in micro-scaled specimens deforming at high rates. Single-crystal silicon (SCS) micro specimens that are 4 μm thick are subjected to tensile loading at an average strain rate of 92 s^?1 using a miniature Hopkinson tension bar. A capacitance displacement system and piezoelectric load cell are incorporated to directly measure the strain and stress of the silicon micro specimens. The average dynamic elastic modulus of the silicon micro specimens is measured to be 226.8?±?18.50 GPa and the average dynamic tensile strength of the silicon is measured to be 1.26?±?0.310 GPa. High-speed images show that extensive fragmentation of the specimens occurs during tensile failure.     

Thickness Effect of Pulse Shaper on Dynamic Stress Equilibrium and Dynamic Deformation Behavior in the Polycarbonate Using SHPB Technique

0Introduction Thehighstrainratestress strainresponsesofpolymersandpolymericcompositematerialshave receivedincreasedscientificandindustrialattentioninrecentyears.Polymericmaterialsaresubjected todynamicloadingandhighstrainratedeformationinavarietyofimporta…     

Pulse shaping techniques for testing elastic-plastic materials with a split Hopkinson pressure bar

We present pulse shaping techniques to obtain compressive stress-strain data for elastic-plastic materials with a split Hopkinson pressure bar. The conventional split Hopkinson pressure bar apparatus is modified by placing a combination of copper and steel pulse shapers on the impact surface of the incident bar. After impact by the striker bar, the copper-steel pulse shaper deforms plastically and spreads the pulse in the incident bar so that the sample is nearly in dynamic stress equilibrium and has a nearly constant strain rate in the plastic response region. We present analytical models and data that show a broad range of incident strain pulses can be obtained by varying the pulse shaper geometry and striking velocity. For an application, we present compressive stress-strain data for 4340 R_c 43 steel.     

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.     

Sedimentation and convective boiling heat transfer of CuO-water/ethylene glycol nanofluids

The convective boiling characteristics of dilute dispersions of CuO nanoparticles in water/ethylene glycol as a base fluid were studied at different operating conditions of (heat fluxes up to 174 kW m^?2, mass fluxes range of 353–1,059 kg m^?2 s^?1 and sub-cooling level of 343, 353 and 363 K) inside the annular duct. The convective boiling heat transfer coefficients of nanofluids in different concentrations (vol%) of nanoparticles (0.5, 1, and 1.5) were also experimentally quantified. Results demonstrated the significant augmentation of heat transfer coefficient inside the region with forced convection dominant mechanism and deterioration of heat transfer coefficient in region with nucleate boiling dominant heat transfer mechanism. Due to the scale formation around the heating section, fouling resistance was also experimentally measured. Experimental data showed that with increasing the heat and mass fluxes, the heat transfer coefficient and fouling resistance dramatically increase and rate of bubble formation clearly increases. Obtained results were then compared to some well-known correlations. Results of these comparisons demonstrated that experimental results represent the good agreement with those of obtained by the correlations. Consequently, Chen correlation is recommended for estimating the convective flow boiling heat transfer coefficient of dilute CuO-water/ethylene glycol based nanofluids.     

A Long Split Hopkinson Pressure Bar (LSHPB) for Intermediate-rate Characterization of Soft Materials

In this study, we developed a long split Hopkinson pressure bar (LSHPB) for mechanically characterizing soft materials at intermediate strain rates. Using a proper pulse shaper, a loading pulse over 3 ms was produced for compression experiments on a PMDI foam material at the strain rates in the order of 10/s. The pulse shaping technique minimized the dispersion effects of stress wave when propagating through such a long bar system. Consistency of stress–strain curves obtained from the LSHPB and an MTS in the same strain rate range shows that a gap currently existing in intermediate strain-rate range is closed by the introduction of the LSHPB.     

Drying characteristics of garlic (Allium sativum L) slices in a convective hot air dryer

The effects of drying temperatures on the drying kinetics of garlic slices were investigated using a cabinet-type dryer. The experimental drying data were fitted best to the Page and Modified Page models apart from other theoretical models to predict the drying kinetics. The effective moisture diffusivities varied from 4.214 × 10^?10 to 2.221 × 10^?10 m² s^?1 over the temperature range studied, and activation energy was 30.582 kJ mol^?1.     

Mass transfer kinetics during deep fat frying of wheat starch and gluten based snacks

Mass transfer (moisture loss and oil uptake) kinetics during deep fat frying of wheat starch and gluten based snacks was investigated. Both followed a modified first order reaction. Activation energies, z-value, and highest values of D and k for moisture loss and oil uptake were 28.608 kJ/mol, 129.88 °C, 490 and 0.0080 s^?1; and 60.398 kJ/mol, 61.79 °C, 1,354.71 and 0.0052 s^?1, respectively.     

Influence of Portevin-Le Chatelier Effect on Shear Strain Path Reversal in an Al-Mg Alloy at Room and High Temperatures

The main objective of this study is to characterize the mechanical behaviour of an Al-Mg alloy in conditions close to those encountered during sheet forming processes, i.e. with strain path changes and at strain rates and temperatures in the range 1.2×10^?3–1.2×10^?1 s^?1 and 25–200°C, respectively. The onset of jerky flow and the interaction of dynamic strain ageing with the work-hardening are investigated during reversed-loading in specific simple shear tests, which consist of loading up to various shear strain values followed by reloading in the opposite direction, combined with direct observations of the sample surface using a digital image correlation technique. Both strain path changes and temperature are clearly shown to influence the occurrence and onset of the Portevin-Le Chatelier (PLC) effect. Moreover, the Bauschinger effect observed in the material response shows that the PLC effect has a major influence on the kinematic contribution to work-hardening as well as its stagnation during the reloading stage, which could open up interesting lines of research to improve theoretical plasticity models for this family of aluminium alloys.