High Strain Rate Data Research Articles

Dynamic mechanical response of ABS polymer at elevated strain rates and temperatures

Acrylonitrile butadiene styrene (ABS) is an extensively used material for various applications from automobile to toys. The material is known to have good machinability along with toughness and thermal-stability. The present investigation is aimed at understanding the effect of high strain rate loading (>1000 /s) on the dynamic response of ABS for potential benefits in energy absorption in mechanical and structural applications. Considering this, uniaxial compression tests on ABS polymer have been performed at different high strain rates (1000 /s – 4000 /s) and temperatures (250C – 1100C) using split Hopkinson Bar (SHB) test setup. The results indicate that the material shows a linear relationship between the true stress and the true strain up to its yield point. High plastic deformation is observed at higher strain rates along with higher levels of stress. However, as the strain rate is increased, there is more evidence of collapse ultimately leading to the failure of the specimens. The material is not much sensitive to strain rate. These high strain rate data may be useful for safety and structural integrity assessment of structures subjected to dynamic loading.

Influence of strain rate on the mechanical response of nanostructured coppers elaborated by SPD and SPS

The influence of strain rate on the mechanical response of two different nanostructured pure coppers was investigated under uniaxial compression. The first nanostructured copper was elaborated by powder metallurgy using the Spark Plasma Sintering (SPS) process. The second nanostructured copper was elaborated by Severe Plastic Deformation (SPD). Conventional characterizations were conducted with quasi-static compression and tensile tests, hardness tests and, with microstructure analysis. The effect of strain rate was evaluated under uniaxial compression at strain rates varying from 10-4 to 10+4 s-1. The high strain rate data were generated with a direct Hopkinson impact technique. The increase of strength with strain rates was analysed and discussed from the Scanning Electron Microscope observations and grain size distribution. The mechanical properties are consequently dependent on the metallurgical history of these samples prepared according to two different routes.

An Alternate Approach to SHPB Tests to Compute Johnson-Cook Material Model Constants for 97 WHA at High Strain Rates and Elevated Temperatures Using Machining Tests

AbstractWith advances in computational techniques, numerical methods such as finite element method (FEM) are gaining much of the popularity for analysis as these substitute the expensive trial and error experimental techniques to a great extent. Consequently, selection of suitable material models and determination of precise material model constants are one of the prime concerns in FEM. This paper presents a methodology to determine the Johnson-Cook constitutive equation constants (JC constants) of 97 W Tungsten heavy alloys (WHAs) under high strain rate conditions using machining tests in conjunction with Oxley’s predictive model and particle swarm optimization (PSO) algorithm. Currently, availability of the high strain rate data for 97 WHA are limited and consequently, JC constants for the same are not readily available. The overall methodology includes determination of three sets of JC constants, namely, M1 and M2 from the Split-Hopkinson pressure bar (SHPB) test data available in literature by using conventional optimization technique and artificial bee colony (ABC) algorithm, respectively. However, M3 is determined from machining tests using inverse identification method. To validate the identified JC constants, machining outputs (cutting forces, temperature, and shear strain) are predicted using finite element (FE) model by considering M1, M2, and M3 as input under different cutting conditions and then validated with corresponding experimental values. The predicted outputs obtained using JC constants M3 closely matched with that of the experimental ones with error percentage well within 10%.

Mechanical behavior and texture evolution of WE43 magnesium-rare earth alloy in Split-Hopkinson Pressure Bar and Taylor Impact Cylinder Testing

Mechanical behavior and texture evolution of Mg rare-earth alloy WE43 is investigated for strain-rates 10−3/s to upwards of 105/s for the two material conditions - as-cast (AC) and T6 age hardened, rolled plate (RT6). The high strain-rate behavior is tested using both Taylor cylinder impact tests (TC) and split Hopkinson pressure bar tests (SHB) and bulk textures are obtained using neutron diffraction. Unlike the quasi-static strained material, AC and RT6 SHB retained high hardening rates throughout the test, even up to 30% true strain. Moreover, the high strain-rate data revealed that the RT6 material has a much higher strength than the AC material, but similar hardening rates despite significantly different initial texture. The flow stress near yield increased up to 10% for RT6 and up to 30% for AC as the strain-rate increased six orders of magnitude from quasi-static rates 10−3/s to 103/s. Neither material exhibited significant plastic anisotropy over the broad range of strain rates, despite the fact that the RT6 material had a moderately strong initial texture. In the TC tests, the geometric cross-sectional changes and texture along the cylinder from the cylindrical sample foot to head are measured and from the neutron diffraction texture analysis, upper-bound estimates of twin volume fraction are obtained as well as dislocation density from analyzing diffraction peak broadening. Recorded geometrical changes along several loading directions show that the material has deformed homogeneously under impact. Analysis of deformed textures indicates that {101¯2} extension deformation twinning occurred in the RT6 condition over the range of strain rates, with an upper bound estimate of 40% twin volume fraction for approximately 0.10-0.25 true strain. The peak texture components after the impact have their c-axes closely aligned with the impact direction. These observations are presented and rationalized in the paper.

Characterizing Strain Rate-Dependent Mechanical Properties for Bovine Cortical Bones.

Comprehensive knowledge of strain rate-dependent viscoelastic properties of bony materials is necessary to understand the mechanisms of bone fracture under impact loading conditions (e.g., falls, traffic accidents, and military environments). Although the mechanical properties of bones have been studied for several decades, the high strain rate data and corresponding material parameters of the rate-dependent constitutive models are still limited. In this study, split Hopkinson pressure bar technique was used to test bovine cortical bones, to obtain the rate-dependent stress-strain curves in two directions (along and perpendicular to the bone fibers). A constitutive relationship comprising two terms was then applied to identify the material constants with strain rate effect and viscoelastic properties. In this model, the linear elasticity was combined with nonlinear viscoelasticity components to describe the overall nonlinear strain rate dependence. The presented data give strong experimental evidence and basis for further development of numerical biomechanical models to simulate human cortical bone fracture.

A Simple Glassy Polymer Model

This work presents a simple and robust material model, suitable for dynamic simulations of glassy polymers such as Polycarbonate. The new model reduces the complex stress/strain behavior and its dependence on strain rate and temperature to a simple set of characteristics. Utilizing a time–temperature superposition principle, these characteristics serve as input for a purely empirical fitting approach, which provides an accurate representation of the material behaviour over a wide range of strain rates and temperatures. Calibration data including failure at high rates is obtained using a split Hopkinson tension bar. To demonstrate the applicability of the new model, it is parameterized using high strain rate data and its simulation predictions compared to a gas gun impact experiment wherein a Polycarbonate plate is subjected to the impact of a steel sphere at temperatures between 23–80 °C and 56–75 m/s.

Predicting the high strain rate response of plasticised poly(vinyl chloride) using a fractional derivative model

Polymers are frequently used in fields as diverse as aerospace, biomedicine, automotive and in-dustrial vibration damping, where they are often subjected to high strain rate or impact loading. Poly(vinyl chloride) (PVC), and its plasticised variants (PPVC), are just two examples of this broad category of materi-als. Since many polymers exhibit strong rate and temperature dependence, including a low temperature brittle transition, it is extremely important to understand their mechanical responses over a wide range of loading con-ditions.PVC with 60 wt% plasticiser is used in this study, as its highly rubbery nature lends itself well to being used in various load mitigation and energy absorption applications. It is challenging to obtain high strain rate data on rubbery materials using conventional techniques such as the split-Hopkinson (Kolsky) bar. Therefore, alternative approaches are required. Based on previous work developing a framework to predict high rate re-sponseusing a fractional derivative model, Dynamic Mechanical Analysis (DMA) experiments are conducted on the PPVC to construct a master curve of storage modulus. These data are used to part-calibrate a modified Mulliken-Boyce model which also takes into account specimen heating to derive stress-strain relationships at strain rates varying from 0.001 s_1 to 13 500 s_1. This model is further calibrated against experiments conducted in a previous study and shown to provide an excellent description of the behaviour at these rates.

A comparison of strain-rate enhancement approaches for concrete material subjected to high strain-rate

High strain-rate induced from intense dynamic loadings will cause an obvious enhancement of concrete material frequently used in civil and defense engineering, which plays an important role in correct numerical simulations of concrete members subjected to intense dynamic loadings. In this article, the existing three strain-rate enhancement approaches for concrete material are compared by three aspects, that is, flexibility of fitting data, consistency condition, and time-dependent behavior. The so-called “overstress approach” is found to be not flexible for fitting high strain-rate data and unable to well predict the strain-softening behavior but can capture the inherent viscidity of concrete material. The “consistency approach” can describe the strain-softening behavior and the inherent viscidity but may be inconvenient and time-consuming when fitting high strain-rate data. The “simplified approach” widely used in commercial concrete material models can describe the strain-softening behavior and fit high strain-rate data by a more convenient and direct way but cannot capture the inherent viscidity of concrete material. Examples of uniaxial stress including loading and unloading under constant and varying strain-rates are presented to demonstrate the above-mentioned findings, in which the updating algorithm of dynamic stress is presented in detail.

High Strain Rate Response of A356/Al2O3 Aluminum Alloy MMCs Using Ls-Dyna

Aluminum alloy Metal Matrix Composites (MMCs) have evoked a keen interest in recent times for potential applications in aerospace, defense, marine and automotive industries owing to their superior strength to weight ratio and high temperature resistance despite the higher manufacturing costs. The ability to withstand dynamic loading is an important design criteria for many structures in above applications. The Split Hopkinson Pressure Bar (SHPB) also referred to as Kolsky bar is a commonly used setup for high strain rate test in strain rate range from 102 to 104 s-1. The high strain rate data is required for safety and structural integrity assessment of structures subjected to dynamic loading. As high strain rate data is not easily available in open literature need was felt for setting up such high strain rate testing. Four distinctly different A356/Al2O3 Aluminum alloy MMCs reinforced with 0, 4, 8 and 12% fiber volume fraction of aluminum oxide (Al2O3) particles were prepared using stir casting process. These four different MMCs were numerically characterised with SHPB test setup using Ls-Dyna software. The compressive stress-strain behavior was obtained at different strain rates ranging from 100 to 1200 s-1. The high strain rate results of compressive SHPB for all specimens were obtained in the form of stress-strain graphs, which strongly indicates that the high strain rate affects on the dynamic mechanical behaviour of MMC materials. These results are helpful to select the MMCs for structural applications where materials go under dynamic loading.

Moisture, anisotropy, stress state, and strain rate effects on bighorn sheep horn keratin mechanical properties.

The horn of the bighorn sheep is an anisotropic composite composed of keratin that is highly sensitive to moisture content. Keratin is also found in many other animals in the form of hooves, claws, beaks, and feathers. Only one previous study contains high rate experimental data, which was performed in the dry condition and only in compression. Considering the bighorn sheep horns' protective role in high speed impacts along with the moisture and strain rate sensitivity, more high strain rate data is needed to fully characterize and model the material. This study provides high strain rate results demonstrating the effects of moisture, anisotropy, and stress state. As a result, the comprehensive data allows modeling efforts to be greatly improved.

Modeling the effect of laser heating on the strength and failure of 7075-T6 aluminum

The effect of rapid laser heating on the response of 7075-T6 aluminum has been characterized using 3-D digital image correlation and a series of thermocouples. The experimental results indicate that as the samples are held under a constant load, the heating from the laser profile causes non-uniform temperature and strain fields, and the strain-rate increases dramatically as the sample nears failure. Simulations have been conducted using the LLNL multi-physics code ALE3D, and compared to the experiments. The strength and failure of the material was modeled using the Johnson–Cook strength and damage models. In order to capture the response, a dual-condition criterion was utilized which calibrated one set of parameters to low temperature quasi-static strain rate data, while the other parameter set is calibrated to high temperature high strain rate data. The thermal effects were captured using temperature dependent thermal constants and invoking thermal transport with conduction, convection, and thermal radiation.

Prediction of flow stress of 7017 aluminium alloy under high strain rate compression at elevated temperatures

An artificial neural network (ANN) constitutive model and Johnson–Cook (J–C) model were developed for 7017 aluminium alloy based on high strain rate data generated from split Hopkinson pressure bar (SHPB) experiments at various temperatures. A neural network configuration consists of both training and validation, which is effectively employed to predict flow stress. Temperature, strain rate and strain are considered as inputs, whereas flow stress is taken as output of the neural network. A comparative study on Johnson–Cook (J–C) model and neural network model was performed. It was observed that the developed neural network model could predict flow stress under various strain rates and temperatures. The experimental stress–strain data obtained from high strain rate compression tests using SHPB over a range of temperatures (25°–300 °C), strains (0.05–0.3) and strain rates (1500–4500 s −1 ) were employed to formulate J–C model to predict the flow stress behaviour of 7017 aluminium alloy under high strain rate loading. The J–C model and the back-propagation ANN model were developed to predict the flow stress of 7017 aluminium alloy under high strain rates, and their predictability was evaluated in terms of correlation coefficient ( R ) and average absolute relative error (AARE). R and AARE for the J-C model are found to be 0.8461 and 10.624%, respectively, while R and AARE for the ANN model are 0.9995 and 2.58%, respectively. The predictions of ANN model are observed to be in consistent with the experimental data for all strain rates and temperatures.

Neural network modeling to evaluate the dynamic flow stress of high strength armor steels under high strain rate compression

Abstract An artificial neural network (ANN) constitutive model is developed for high strength armor steel tempered at 500 °C, 600 °C and 650 °C based on high strain rate data generated from split Hopkinson pressure bar (SHPB) experiments. A new neural network configuration consisting of both training and validation is effectively employed to predict flow stress. Tempering temperature, strain rate and strain are considered as inputs, whereas flow stress is taken as output of the neural network. A comparative study on Johnson–Cook (J–C) model and neural network model is performed. It was observed that the developed neural network model could predict flow stress under various strain rates and tempering temperatures. The experimental stress–strain data obtained from high strain rate compression tests using SHPB, over a range of tempering temperatures (500–650 °C), strains (0.05–0.2) and strain rates (1000–5500/s) are employed to formulate J–C model to predict the high strain rate deformation behavior of high strength armor steels. The J-C model and the back-propagation ANN model were developed to predict the high strain rate deformation behavior of high strength armor steel and their predictability is evaluated in terms of correlation coefficient (R) and average absolute relative error (AARE). R and AARE for the J–C model are found to be 0.7461 and 27.624%, respectively, while R and AARE for the ANN model are 0.9995 and 2.58%, respectively. It was observed that the predictions by ANN model are in consistence with the experimental data for all tempering temperatures.

The high strain rate response of Ultra High Molecular-weight Polyethylene: From fibre to laminate

The effect of strain rate upon the uniaxial response of Ultra High Molecular-weight Polyethylene (UHMWPE) fibres, yarns and laminates of lay-up [0/90]48 has been measured in both the 0/90° and ±45° configurations. The tensile strength of the matrix-dominated ±45° laminate is two orders of magnitude less than that of the fibre-dominated 0/90° laminate, and is more sensitive to strain rate. A piezoelectric force sensor device was developed to obtain the high strain rate data, and this achieved a rise time of less than 1 μs. It is found that the failure strength (and failure strain) of the yarn is almost insensitive to strain rate within the range (10−1–103 s−1). At low strain rates (below 10−1 s−1), creep of the yarn dominates and the failure strain increases with diminishing strain rate. The tensile strength of the dry yarn exceeds that of the laminate by about 20%. Tests on single fibres exceed the strength of the yarn by 20%.

Research on Numerical Algorithm of Constitutive Equation under High Speed Deformation in Hadfield Steel

The influence of the strain rate on the plastic deformation of the metals was significant during the high strain rate of loading. However, it was very difficult to obtain high strain rate data (≥ 104 s-1) by experimental techniques. Therefore, the finite element method and iterative method were employed in this study. Numerical simulation was used to characterise the deformation behavior of Hadfield steel during explosion treatment. Base on experimental data, a modified Johnson-Cook equation for Hadfield steel under various strain rate was fitted. The development of two field variables was quantified during explosion hardening: equivalent stress and strain rates.

Tension and Compression Behavior of Pre-Stressed Steel Strands at High Strain Rate

In this paper is described the mechanical characterization at high strain rate of the high strength steel usually adopted for strands. The experimental set-up used for high strain rates testing: in tension and compression was the Split Hopkinson Pressure Bar installed in the Laboratory of Dynamic Investigation of Materials in Nizhny Novgorod. The high strain rate data in tension was obtained with dog-bone shaped specimens of 3mm in diameter and 5mm of gauge length. The specimens were screwed between incident and transmitter bars. The specimens used in compression was a cylinder of 3mm in diameter and 5mm in length. The enhancement of the mechanical properties is quite limited compared the usual reinforcing steels.

Strong stabilization of the Rayleigh–Taylor instability by material strength at megabar pressures

Experimental results showing significant reductions from classical in the Rayleigh–Taylor (RT) instability growth rate due to high pressure effective lattice viscosity in metal foils are presented. Stabilization of RT instability (RTI) by ablation and density gradients has been studied for decades. The regime of stabilized RTI due to material strength at high pressure is new. On the Omega Laser in the Laboratory for Laser Energetics, University of Rochester, target samples of polycrystalline vanadium are compressed and accelerated quasi-isentropically at ∼1 Mbar pressures, while maintaining the samples in the solid-state. Provided strong shocks are avoided, the higher the applied peak pressure, the higher the predicted foil strength, and hence, the higher the degree of strength stabilization of RTI. Several experiments were conducted where the amount of RT growth is measured by face-on radiography. The vanadium samples are probed by a laser driven He-α x-ray backlighter which produced 5.2 keV radiation. Comparison of the results with constitutive models for solid state strength under these conditions show that the measured RT growth is substantially lower than predictions using existing models that work well at low pressures and long time scales. High pressure, high strain rate data can be explained by the enhanced strength due to a phonon drag mechanism, creating a high effective lattice viscosity.

In situ biomechanical properties of normal and diabetic nerves: An efficient quasi-linear viscoelastic approach

Biomechanical properties of nerves were investigated using the quasi-linear viscoelastic model. An improved parameter estimation technique based on fast convolution was developed and tested in sciatic nerves of normal and diabetic rats. In situ dynamic compression response of sciatic nerves was obtained by a modified custom-designed compression system. Six normal and five diabetic neuropathic Wistar rats were used. The model derived from the high strain rate (0.1 s −1) data could predict the responses of lower strain rates (0.05 and 0.01 s −1) satisfactorily. The computation time was cut down 49.0% by using the newly developed technique without increasing the root-mean-square error. The percentage of stress relaxation of the diabetic and normal rats, calculated directly from the experimental data, was not significantly different (51.03±1.96% vs. 55.97±5.89%, respectively; p=0.247). After model fitting, compared with the QLV parameters of normal nerves, the smaller parameter C for diabetic nerves (0.27±0.06 vs. 0.20±0.02, p < 0.05) indicated that diabetic nerves had a smaller amplitude of viscous response (stress relaxation). The larger parameter τ 2 of diabetic nerves (199±153 s vs. 519±337 s, p<0.05) implied that diabetic nerves needed a longer relaxation period to reach equilibrium.

Modeling and testing strain rate-dependent compressive strength of carbon/epoxy composites

A technique for testing high modulus fiber-reinforced composites in compression at different strain rates is investigated. The rate-dependent compressive behavior of unidirectional AS4/3501-6 carbon/epoxy composite is characterized by using off-axis specimens. It is found that, in the compression test, a titanium coating applied at the contact ends of the off-axis specimen can greatly reduce contact frictions, allowing a fully developed extension–shear coupling so that a state of uniform stress in the specimen can be achieved. A rate-dependent nonlinear constitutive model and a dynamic compressive strength model (fiber microbuckling model) for the unidirectional AS4/3501-6 composite are established based on the low strain rate off-axis test data. Model predictions and experimental data including high strain rate data are in very good agreement indicating that the constitutive model and compressive strength model obtained with low strain rate data are valid for high strain rates as well. A technique is also developed to extract the longitudinal compressive strength of the composite from those of the off-axis specimens.

Material characterization and constitutive modelling of ductile high strength steel for a wide range of strain rates

This paper presents results of a research program in progress to describe the behaviour of 35NiCrMoV109 high strength steel over a wide range of strain rates for numerical simulations of dynamic events. In the low strain rate regime tensile tests in combination with a numerical stress state correction in terms of necking have been carried out. In comparison to the common Bridgeman-analysis this procedure allows to determine reliable necking-corrected stress–strain curves in a shorter time with a high accuracy as well. These data have been linked to high strain rate data from a novel modified Taylor-impact test using VISAR technique and data from planar-plate-impact-tests. The yield-stress strain-rate dependency covering a strain rate range of 11 orders of magnitude (5×10 −5–1.78×10 6 s −1) have been measured. A bcc→hcp phase transition could be observed at pressures exceeding 13 GPa. A phenomenological material model including a strength model and an equation of state has been developed. The validation of the material model has been performed by numerical simulations of the modified Taylor-impact tests and the planar-impact-tests. In addition to common analysis by comparison of sample deformation, an enhanced model validation has been made by comparing the measured and calculated VISAR-signals while this technique is normally used for plate impact-test only. Agreement between the numerical simulations and the experimental results is found for the comparison of the deformation and the characteristic profile of the VISAR-curves.