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.     

New method for testing composites at very high strain rates

A method was developed for testing and characterizing composite materials at strain rates in the 100 to 500 s^?1 regime. The method utilizes a thin ring specimen, 10.16 cm (4 in.) in diameter, 2.54 cm (1 in.) wide and 6–8 plies thick. This specimen is loaded by an internal pressure pulse applied explosively through a liquid. Pressure is measured by means of a calibrated steel ring instrumented with strain gages. Strains in the composite specimen are measured with strain gages. Strains in the calibration and specimen rings are recorded with a digital processing oscilloscope. The equation of motion is solved numerically and the data processed by the mini-computer attached to the oscilloscope. Results are obtained, and plotted by an X-Y plotter in the form of a dynamic stress-strain curve. Unidirectional 0-deg, 90-deg and 10-deg off-axis graphite/epoxy rings were tested at strain rates up to 690 s^?1. Times to failure ranged between 30 and 60 μs. The 0-deg properties which are governed by the fibers do not vary much from the static ones with only small increases in modulus. The 90-deg properties show much higher than static modulus and strength. The dynamic in-plane shear properties, obtained from the 10-deg off-axis specimens, are noticeably higher than static ones. In all cases the dynamic ultimate strains do not vary much from the static values.     

Brittle and quasi-ductile damage at large strain rates

The present study suggests that molecular and particle dynamics simulations can provide the basis for estimates of qualitative and quantitative aspects of damage in materials with inferior cohesive strength subjected to high strain rate loading. Two examples demonstrate that the traditional continuum models are of limited value in modeling of the class of considered problems.     

A constitutive model for cold deformation of aluminium at large strains and high strain rates

A temperature-dependent constitutive model for viscoplastic deformation of aluminium based on a single, scalar internal variable is presented. The model is designed particularly for the strains, strain rates, and temperatures important for cold forging. Special attention is paid to the underlying physical processes that determine the flow stress in the metal. The kinetic constitutive equation is based on thermal activation of dislocations over an average potential barrier from various kinds of obstacles. Strain hardening is modelled through the internal variable which represents the increasing height of these barriers. The model is generalized to three dimensions, and it has been implemented in the finite-element code ABAQUS. Simulations of simple forging operations are presented.     

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.     

利用SHPB测定高应变率下冰的动态力学行为

利用分离式Hopkinson压杆(SHPB)实验装置,在-25和-10℃的低温下,对冰进行了应变率为500～2 000 s-1的动态压缩实验.制作了试样的模具和低温制冷保温装置,满足冰所需要的低温条件.SHPB实验中使用波形整形器消除波形振荡现象,并最大程度地实现恒应变率加载.实验表明,冰的动态应力应变呈非线性关系;在...     

Optical measurement of the specimen deformation at high strain rate

During recent years, the investigation of the strain-rate-dependent properties of materials has become more and more important. The experimental techniques used to establish the specific dynamic behavior of materials all have in common that the acquisition of information concerning the deformation of the specimen is cumbersone and often questionable. Mostly, only limited information on the spatial distribution and time evolution of the deformation in specimen can be obtained. In this paper, a non-contact, optical technique is presented, providing the time evolution and spatial distribution of the axial deformation in specimens during a high strain rate test. The deformation of a line grid attached to the specimen is recorded during an experiment by means of a rotating drum camera. The time history of the axial displacements is subsequently derived by an advanced technique based on digital geometric moiré combined with a phase-shift method, specially developed to this purpose. The technique can be applied to a wide range of materials and high strain rate tests, and is illustrated by means of a split Hopkinson tensile bar experiment on a steel sheet specimen.     

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.     

Integral-based constitutive equation for rubber at high strain rates

High-speed experiments were conducted to characterize the deformation and failure of Styrene Butadiene Rubber at impact rates. Dynamic tensile stress–strain curves of uniaxial strip specimens and force–extension curves of thin sheets were obtained from a Charpy tensile impact apparatus. Results from the uniaxial tension tests indicated that although the rubber became stiffer with increasing strain rates, the stress–strain curves remained virtually the same above 280 s⁻¹. Above this critical strain rate, strength, fracture strain and toughness decreased with increasing strain rates. When strain rates were below 180 s⁻¹, the initial modulus, tensile strength and breaking extension increased as the strain rate increased. Between strain rates of 180 and 280 s⁻¹, the initial modulus and tensile strength increased with increasing strain rates but the extension at break decreased with increasing strain rates. A hyper-viscoelastic constitutive relation of integral form was used to describe the rate-dependent material behavior of the rubber. Two characteristic relaxation times, 5 ms and 0.25 ms, were needed to fit the proposed constitutive equation to the data. The proposed constitutive equation was implemented in ABAQUS Explicit via a user-defined subroutine and used to predict the dynamic response of the rubber sheets in the experiments. Numerical predictions for the transient deformation and failure of the rubber sheet were within 10% of experimental results.     

A unit for testing materials at high strain rates

Some of the problems regarded as inherent in materials testing at high strain rates are associated with inertia effects, both in the loading mechanism and in the specimen itself. In fact, it has generally been difficult to ensure a homogeneous and uniaxial strain field. Some of these problems encountered in dynamic testing have, however, been circumvented in a simple testing unit, developed at the Technical University of Denmark and described in the present paper.     

Rheology and birefringence of Fomblin YR at very high shear rates

The rheological and structural properties of perfluoropolyether (PFPE) lubricant films including viscosity, shear stress, and birefringence were measured at relatively low to extremely high shear rates using a rotational optical rheometer. The viscosity of various films with different thicknesses exhibit Newtonian behavior up to a shear rate 1 × 10⁴ s⁻¹, with a transition to shear-thinning behavior obvious at higher shear rates. Birefringence of these films was also measured for the first time, and these results indicate chain alignment with shear in the shear-thinning regime. The shear rate at which alignment occurs is similar to that of the onset of shear thinning. This correlation between chain alignment and shear thinning provides direct evidence that the ability of PFPEs to lubricate hard drives at high shear rates is a direct consequence of the ability of the applied shear field to align the molecules on a molecular level.     

高应变率下航空透明聚氨酯的动态本构模型

采用低阻抗分离式霍普金森压杆对航空透明聚氨酯进行了高应变率下的动态力学性能测试,得到的应力应变曲线表现出了显著的非线性黏弹性特征。基于本构理论和实验数据,构建了航空透明聚氨酯的松弛时间应变相关的超黏弹性本构形式。该本构模型由2部分组成:一部分表征准静态下的超弹性行为,另一部分描述非线性应变率的相关特性。利用超黏弹性本构模型对不同应变率下航空透明聚氨酯的动态应力应变曲线进行拟合,拟合曲线与实验曲线一致性良好。     

Semi-analytic inverse method for rubber testing at high strain rates

Because of their low mechanical wave speed, high strain rate testing of rubber is highly difficult. Indeed, stress and strain homogeneity is hard to achieve. In this paper, a semi-analytic inverse solution is proposed. This solution is based on a uni-axial stress state assumption in the specimen. Moreover, a new-Hookean law is assumed for rubber. The new method is successfully applied to a high strain rate test on a synthetic rubber.     

Experimental mechanics at velocity extremes —Very high strain rates

The early experimental work of Clark and Wood with regard to von Kármán's theory on the effect of material flow and fracture at high strain rates has led to many controversial issues on these effects. Interest has been greatly revived in recent years because of the increased emphasis on such high-velocity forming processes as explosive and capacitor discharge. Considerable new work has been performed by Ling-Temco-Vought, Inc., for the Air Force, the results of which are presented in this paper. Data have been accumulated on tensile and compression specimens, spherical bulging and cylindrical bulging for a wide variety of materials. This high-speed information has been generated with the use of a special projectile impact machine and special presses utilizing various combinations of explosive and capacitor-discharge energy, with strain rates to 10¹/sec. The effect of velocity on ductility is discussed for total strain distribution, uniform strain, double necking and critical impact velocity. The modes of failure for various part shapes are presented and related to the forming velocity.     

Mechanical and optical characterization of an anelastic polymer at large strain rates and large strains

Two constitutive relations have been determined from test results that characterize, respectively, the uniaxial and photomechanical behavior of a polyester-styrene copolymer for strain rates from 10^?5 to 3×10³ in./in./s and strains up to 40 percent. The high-strain-rate data were obtained by means of a split-Hopkinson-bar apparatus. Intermediate-strain-rate tests, performed with the aid of a drop tower, were reported in an earlier paper. Quasi-static experiments were conducted on a standard testing machine. A nonlinear, four-parameter, elastic-viscoplastic model was constructed which describes the mechanical behavior. The parameters were determined by a least-mean-squares curve-fitting procedure. The viscoplastic parameters were found to obey a power law in strain rate. The photomechanical model was found to be linear with strain well into the plastic-deformation region, while the slope of the strain-birefringence curve for each strain rate also varied by strain rate to a power.     

Determination of tensile flow stress beyond necking at very high strain rate

The objective of this effort was to extend the Bridgman analysis of tensile necking to obtain stress-strain data beyond the point of onset of necking from a split Hopkinson bar. For this purpose, combined analytical and experimental techniques were considered. The analytical efforts were focused on validating the use of Bridgman solutions for high rate of deformation through a finite-element analysis of a tapered tensile specimen. The experimental technique involved the development of a photographic system using a light-emitting diode and a 35-mm rotating drum camera for the observation of necking during dynamic tensile tests conducted with a split Hopkinson tension bar. The developed new technique was successfully used to measure neck profiles of 6061-T6 aluminum, HY100 and 1020 steel tensile specimens. The measured profiles were used with the Bridgman analysis and stress-strain data were obtained to over 70-percent strain.     

The TSHB technique for material testing at high rates of strain

The material testing technique of Torsional Split Hopkinson Bar (TSHB) is investigated in this paper. It can solve nearly all the problems of Split Hopkinson Pressure Bar (SHPB). Furthermore, accurate experimental results can be obtained in large deformation condition. In this paper some dynamic stress-strain curves of some engineering materials are also given which are obtained from a TSHB apparatus made by ourselves.Projects Supported by the Science Fund of the Chinese Academia Sinica.