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.     

PP/PA共混高聚物在高应变率下的热粘弹性本构关系和时温等效性

采用Instron1342电液伺服试验机和改进的SHPB技术对以113材料为例的PP/PA共混高聚物进行了应变率在10-4~103 s-1宽广范围,温度为25、40、60、80 ℃下的一维应力力学性能试验。结果表明,这类共混高聚物的力学响应对温度和应变率都是敏感的。以朱-王-唐非线性粘弹性本构方程来描述这类PP/PA共混高聚物的力学响应,并拟合得到了其热粘弹性本构参数,理论预言与试验结果在应变小于7%时吻合良好。对113材料20~80 ℃温度范围内不同应变率下的试验结果进行分析,证明PP/PA共混高聚物存在率温等效关系,提高温度和增加作用时间（减小应变率）的效果相当,反之,降低温度与减少作用时间（提高应变率）的效果相当。通过引入量纲一参量Z,使应变率d/dt、温度T这2个参量归结为统一的Z参量,从而得到了体现时温等效性的统一曲线。     

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.     

NEPE推进剂低高应变率下改进的黏-超弹本构模型

为研究低高应变率条件下NEPE推进剂的力学特性,通过电子万能试验机和分离式霍普金森杆装置,对NEPE推进剂进行了准静态和冲击实验,得到了不同应变率下（1.667×10?4～4 500 s?1）的应力-应变曲线。实验结果表明NEPE推进剂具有明显的非线性弹性和应变率敏感性,随着应变率的增加,材料的强度、屈服应力和弹性模量显著增加,与低应变率相比,高应变率条件下材料的应变率敏感性更高。在高速冲击下材料内部瞬间产生大量热量无法及时散发出去,使得材料内部温度升高,导致材料出现软化效应,力学性能降低。本文建立了一个非线性黏超弹本构模型,其中采用Rivlin应变能函数来描述稳态超弹响应部分,采用积分型本构模型来描述材料的动态黏弹性响应部分,考虑到松弛时间具有应变率相关性,本文采用了一个率相关松弛函数来替代传统的Prony级数形式。使用极慢速压缩实验数据对本构模型中的超弹部分进行拟合获得超弹参数,然后用准静态和动态实验数据对本构模型进行拟合得出其他参数。不同应变率下的预测曲线与实验曲线具有较好的重合度,证明了该模型可以很好地描述低高应变率下NEPE推进剂的力学特性。     

双基推进剂的高应变率力学特性及其含损伤ZWT本构

为了解双基推进剂在冲击载荷下的力学特性及本构行为,利用材料试验机和分离式霍普金森压杆（SHPB）对双基推进剂进行了单轴压缩实验,并对实验数据的有效性进行了检验。用二波法对实验数据进行处理,得到了双基推进剂的应力应变曲线。实验结果表明：双基推进剂具有明显的应变率相关性,动态下屈服应力与静态下相比明显提高,且屈服应力表现为应变率对数的双线性关系;双基推进剂屈服应变表现为延脆转换特性,在低应变率下表现为延展性,高应变率下表现为冲击脆化特性。利用含损伤朱王唐（ZWT）本构模型对实验结果进行了拟合,得到了模型中的本构参数,并对损伤因子项进行了分析。通过模型预测曲线与实验曲线的对比,发现含损伤ZWT本构能较好地描述双基推进剂在0～0.14应变范围内的力学特性。     

A constitutive equation for filled rubber under cyclic loading

This paper describes experiments and the development of constitutive equations to predict the steady-state response of filled rubber under cyclic loading. An MTS servo-hydraulic machine was used to obtain the dynamic hysteresis curves for a filled rubber compound in uniaxial tension-compression. The material tests were performed with mean strains from −0.1 to 0.1, strain amplitudes ranging from 0.02 to 0.1, and strain rates between 0.01 and 10 s⁻¹. Temporary material set, the Payne effect and rate-dependence were observed from the experimental results. A hyper-viscoelastic constitutive model was developed to characterize the dynamic response of the rubber. A cornerstone of this constitutive modeling was to devise a scheme to evaluate material set and a finite strain, non-linear viscoelastic law from the test data. Predictions of the dynamic hysteresis curves using the proposed constitutive equation were found to be in good agreement with the uniaxial test results.     

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.     

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.     

Nanocrystalline aluminum and iron: Mechanical behavior at quasi-static and high strain rates,and constitutive modeling

The responses of nanocrystalline aluminum powder of different grain sizes, prepared by ball milling and consolidated into bulk specimens by hot pressing, were determined under quasi-static and dynamic compression. The experiments demonstrated that the reduction in grain size resulted in several-fold increase in hardness and strength; the responses of nanocrystalline aluminum was found to be strain-rate-dependent. Using these measurements, Khan, Huang and Liang (KHL) viscoplastic model was modified by including a bi-linear Hall–Petch type relation to correlate with the response of nanocrystalline aluminum, including the variation of work hardening with grain size. The modified constitutive equation gives results very close to the experimental observations on nanocrystalline aluminum. In addition, the response of nanocrystalline iron, previously published, was also correlated with proposed model. Both correlations of strain-rate-dependent responses for different grain sizes were in good agreement with the experimental results over a wide range of grain sizes (micrometer to nanometer) and strain rates.     

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.     

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.     

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...     

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.     

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.     

On the direct measurement of very large strain at high strain rates

When dynamic plastic strain exceeds 4-percent deformation in completely annealed polycrystalline aluminum, difficulties in the optical measurment of strain occur because of changes in the diffuse-ambient-background light arising from the growth of a mottled surface, or “organe peel.” This paper describes how the diffraction-grating technique may be modified to measure dynamic plastic strain for very large strain at high strain rates in the presence of changing light intensity. The experimental results obtained show that the strain-rate-independent finite-amplitude wave theory, governed by the present writer's generalized, linearly temperature-dependent parabolic stress-strain law, still applies.     

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。     

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.