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.     

Strain-rate and strain-rate-history effects in several metals in torsion

A machine for testing thin-walled tubes in torsion at shear-strain rates up to 25/sec is described. Results of constant and variable-strain-rate tests are presented for 1100-0 aluminum, AISI 1020 steel, and 50-A titanium. Results indicate that 1100-0 aluminum is very slightly strain-rate sensitive, but steel and titanium are noticeably sensitive to both strain rate and strain-rate history. Variable-rate tests show that subsequent dynamic loading on a statically prestrained specimen causes an increase in the flow stress in steel and a decrease in the flow stress in titanium.     

一种基于电磁霍普金森杆的材料动态包辛格效应测试装置及方法

金属材料在复杂载荷条件下的动态力学行为研究一直备受关注，但受限于实验设备，金属材料的动态包辛格效应响应一直都难以获得。为了探究金属材料的包辛格效应与应变率效应之间的关系，本文中提出一种基于电磁霍普金森杆(electromagnetic split Hopkinson bar，ESHB) 的非同步加载实验技术，为测试金属材料在高应变率加载下的包辛格效应提供了一种有效的实验方法。本文中，首先介绍了非同步加载装置的主要特点，即可以用两列由脉冲发生器产生的应力波对受载试样进行连续的一次动态拉-压循环加载，且加载过程保证了应力波的一致性。分析了应力波对试样加载过程中的波传播历程，确保了加载过程的连续性。随后介绍了动态加载过程，数据处理方法和波形分离手段，并对动态加载过程进行应力平衡性分析，论证了实验装置的可靠性。最后采用该方法测试了5%预应变下6061铝合金动态压缩-动态拉伸的包辛格效应，并与准静态下的实验结果进行对比。实验结果表明，该材料单轴压缩没有明显的应变率效应，但其包辛格效应具有应变率依赖性，高应变率下材料的包辛格应力影响因子由0.07增大至0.17，具有显著的提升，这对传统意义上铝合金材料应变率不敏感的结论提出了挑战。     

Design and evaluation of a testing machine for determining tensile properties of materials at moderate strain rates

A test fixture was designed and built to evaluate tensile properties at a specific rate of strain in the region from 0.01 to 25 in./in./sec. The specimen is of tubular section and loaded internally by fluid pressure. Details of the design and instrumentation are presented. Test results for annealed 1018 steel are given and compared with results of other investigators. This steel is shown to be strain-rate sensitive in the region tested.     

Elasto-visco-plastic modeling of mild steels for sheet forming applications over a large range of strain rates

A physically based elasto-visco-plastic constitutive model is presented and compared to experimental results for three different mild steels. The experiments consist of tensile tests ranging from quasi-static conditions up to strain rates of 10³ s^?1 as well as quasi-static simple and reverse shear tests at different amounts of pre-strain. Additional two-step sequential mechanical tests (Bauschinger and orthogonal effects) have been performed to further evaluate the ability of the model to describe strain-path changes at moderate/large strains. The model requires significantly fewer material parameters compared to other visco-plasticity models from the literature, while being able to describe some of the main features of the strain-rate sensitivity of mild steels. Accordingly, the parameter identification is simple and intuitive, requiring a relatively small set of experiments. The strain-rate sensitivity modeling is not restricted to a particular hardening law and thus provides a general framework in which advanced hardening equations can be adopted.     

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.     

Dynamic crushing of aluminum foams: Part I – Experiments

The two-part series of papers presents the results of a study of the crushing behavior of open-cell Al foams under impact. In Part I, direct and stationary impact tests are performed on cylindrical foam specimens at impacts speeds in the range of 20–160 m/s using a gas gun. The stress at one end is recorded using a pressure bar, while the deformation of the entire foam specimen is monitored with high-speed photography. Specimens impacted at velocities of 60 m/s and above developed nearly planar shocks that propagated at well-defined velocities crushing the specimen. The shock speed vs. impact speed, and the strain behind the shock vs. impact speed representations of the Hugoniot were both extracted directly from the high-speed images. The former follows a linear relationship and the latter asymptotically approaches a strain of about 90% at higher velocities. The Hugoniot enables calculation of all problem variables without resorting to an assumed constitutive model. The compaction energy dissipation across the shock is shown to increase with impact velocity and to be significantly greater than the corresponding quasi-static value. Specimens impacted at velocities lower than 40 m/s exhibited response and deformation patterns that are very similar to those observed under quasi-static crushing. Apparently, in this impact speed regime inertia increases the energy absorption capacity very modestly.     

Effects of strain rate and moisture content on the behaviour of sand under one-dimensional compression

The influence of strain rate and moisture content on the behaviour of a quartz sand was assessed using high-pressure quasi-static (10^?3 s^?1) and high-strain rate (10³ s^?1) experiments under uniaxial strain. Quasi-static compression to axial stresses of 800 MPa was carried out alongside split Hopkinson pressure bar (SHPB) experiments to 400 MPa, where in each case lateral deformation of the specimen was prevented using a steel test box or ring, and lateral stresses were recorded. A significant increase in constrained modulus was observed between strain rates of 10^?3s^?1 and 10³s^?1, however a consistently lower Poisson’s ratio in the dynamic tests minimised changes in bulk modulus. The reduction in Poissons ratio suggests that the stiffening of the sand in the SHPB tests is due to additional inertial confinement rather than an inherent strain-rate dependence. In the quasi-static tests the specimens behaved less stiffly with increasing moisture content, while in the dynamic tests the addition of water had little effect on the overall stiffness, causing the quasi-static and dynamic series to diverge with increasing moisture content.     

Photovisco-elasto-plastic analysis tested on polyester by the scattered-light method

A three-dimensional photovisco-elasto-plastic model considering the strain rate effect was investigated by the scattered-light method using polyester as a model material. To examine the mechanical and optical properties of the material, tension and torsion tests were carried out on cylindrical specimens under various strain rates at 30°C. The effects of strain rate on the stress-strain relation and scattered-light fringe appearance were evaluated. The equivalent shearing stress-strain relation can be approximated by the Ramberg-Osgood equation with rate-dependent modulus and yield stress. The fringe gradient, when normalized by a rate-dependent yield gradient, can be related to an equivalent strain in the same form regardless of the strain rate. The strain rate can be evaluated from the measurement of the rate of increase of the fringe gradient. Hence, the relation between the fringe gradient and its rate of increase was derived as a function of strain rate. Finally, a method is proposed for the estimation of the visco-elasto-plastic stress and strain in a three-dimensional specimen from the measurement of only the fringe gradient and its rate of increase. The method was successfully applied not only to uniaxial tension but also to pure torsion.     

损伤引起的反向应变率效应及其对本构关系和热粘塑性失稳的影响

对于材料在高应变率下的应变率无关和应变率负敏感现象,本文根据铸镁合金的宏观与微观相结合的试验结果,提出了一个基于损伤弱化的反向应变率效应机制,并建议了一个计及这一反向效应的热粘塑性本构方程。由此可以解释材料的表观应变率强化、表观应变率无关和表观应变率弱化三类基本情况。相应地,随损伤引起的反向应变率效应的增强,热粘塑性失稳也有三种基本情况:或在更高应变率或更大应变下发生绝热剪切,或由临界准则转化为临界应变准则,以及或在高应变率下不会发生绝热剪切。     

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.     

Dynamic stress-strain characteristics of metals at elevated temperatures

A method for measuring the load, strain and strain rate inside a high-temperature environment is described. Results of tests on specimens of high-purity copper are reported. Results indicate that copper is strain-rate dependent within the temperature range 78°–1000° F up to strains of 0.6 percent and strain rates of 10³ sec^–1.Paper was presented at 1969 SESA Spring Meeting held in Philadelphia, Pa., on May 13–16.This work was sponsored by the Army Research Office (Durham) under Contract No. DA 31-124-ARO-D229.     

Dynamic strain aging and related instabilities: experimental,theoretical and numerical aspects

Experimental data from uniaxial tensile tests on smooth and notched specimens of aluminium alloy 5083-H116 show that the material exhibits negative strain-rate sensitivity for strain rates within a certain range. The negative strain-rate dependence, which is attributed to dynamic strain aging, leads to serrated stress–strain curves, discontinuous plastic flow and propagating deformation bands during plastic straining (also denoted as the Portevin–Le Chatelier effect). Band analysis and linear perturbation analysis are performed using simple elastic-viscoplastic constitutive equations that include negative strain-rate sensitivity in a simplified manner. The negative strain-rate sensitivity allows for jumps in the plastic strain rate, which in turn permits the existence of localisation bands for the elastic-viscoplastic model. The simple elastic-viscoplastic constitutive model has been implemented in LS-DYNA, and non-linear finite element simulations of smooth and notched tensile test specimens are performed, allowing more detailed investigations into the effects of the negative strain-rate sensitivity on the material's behaviour.     

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.     

动载下韧性撕裂在三种管线钢材中传播阻力的研究

阐述了用实验确定在常温及静载和动载条件下韧性撕裂在三种管线钢材中传播时的断裂比能值。实验中采用了销钉加载双面开槽的双悬脊梁(DCB)试件。应用能量平衡法对实验结果进行了分析。考察了加载速率和试件厚度对撕裂韧性的影响。结果表明,管线钢材对韧性撕裂传播的阻力在动载条件下增大,对较薄的试件及应变率敏感性较高的材料其增大更为明显。对于纯剪切断裂的传播来说,撕裂韧性一般随试件厚度的增大而增加。     

碳布叠层/碳复合材料动态压缩性能测试研究

利用带有波形整形器的Split Hopkinson Pressure Bar(SHPB)技术测试了碳布叠层/碳复合材料在应变率为500、1 500 s-1时的动态压缩性能。研究结果表明:利用轧制紫铜作为整形器材料不仅可以有效地实现对碳布叠层/碳复合材料的常应变率压缩加载，而且有助于改善试样两端的应力平衡，从而保证测试数据的可靠性；此外，与准静态压缩相比较，在动态压缩载荷下，碳布叠层/碳复合材料的压缩强度有较强的应变率效应，且复合材料压缩强度的动态增加函数可以用Cowper-Symonds幂函数的形式来表示。     

Rate sensitivity of compressive strength of columnar-grained ice

Methods of selecting and preparing specimens and details of test procedures, including those for microstructural examination, are described for the investigation of uniaxial compressive strength of columnar-grained ice. It is shown that specimen strain rates are not constant for constant cross-head-displacement rate and that consequently the results are not representative of the constant strain-rate condition. Analysis shows that constant cross-head-displacement tests are more closely representative of the constant stress-rate condition. The paper also discusses failure strains, failure times, mode of failure and possible dependence of strength results on stiffness of the test system.     

Interrupted Test of Advanced High Strength Steel with Tensile Split Hopkinson Bar Method

The phase fraction evolution in a material during quasi-static and dynamic tests can be studied by interrupting the test at predetermined elongation values. While it is straightforward to interrupt quasi-static tests at a predetermined level of elongation, this interruption presents difficulties at high strain rate conditions. In the present paper, an interruption mechanism has been developed to control the elongation of specimens at high strain rate using a modified split Hopkinson tensile bar. This interruption mechanism is based on the interaction between the test specimen and the external interruption device. The influence of the designed external device on the stress waves and also the ability of the system to support the interruption of the deformation process were considered in the numerical analysis and verified by the experimental results. Finally, the influences of strain and strain rates on the volume fraction evolution of the retained austenite in quenched & partitioned steel were reported.     

Dynamic pre-strain and inertia effects on the fracture of metals

A combined experimental and theoretical study is described which examines the influence of strain-rate and dynamic pre-strain on the ductile fracture of thin cylinders. The thin-cylinder configuration is particularly important in this case because it allows inertia terms to be directly incorporated into the theory of plastic instability. A series of quasi-static and dynamic tests is conducted on three materials with differing degrees of strain-rate sensitivity and strain-hardening. The experimental observation that fracture is inhibited at high strain-rates is in accord with the theory when inertia can no longer be considered insignificant. It is also shown that dynamic pre-strain has little or no effect on the flow stress or the strain at fracture in materials which-are essentially strain-rate insensitive, but does reduce the fracture strain in the strain-rate sensitive materials.