Shear Failure of Inconel 718 under Dynamic Loads

Kinetics of deformation and fracture of nickel–iron alloy Inconel 718 under dynamic shear loading was measured using a split torsional Hopkinson bar facility and high-speed photography. Tubular specimens with a reduced gage length and a starter notch were sheared at strain rates up to 6 × 10³ s⁻¹. High-speed photographs of fiducial lines scribed on the specimen surface showed the development of local strains and cracking. This paper describes the experimental and analytical procedures, illustrates average and local plastic strain evolution, and presents shear crack initiation times and propagation speeds.     

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.     

动态拉伸试验中试样应变测试的有效性分析

为了评估将试样通过胶粘连接到加载杆的Hopkinson杆装置所获得试样应变的有效性,对四种强度刚度差异较大的纤维增强复合材料进行了动态拉伸试验。试验时,试样通过环氧胶和杆夹层粘接,试样的应变分别按照Hopkinson杆一维应力波理论计算和试样上应变计直接准确测量得到。结果证明：对小变形碳纤维复合材料,按一维应力波理论计算的应变与试样上直接所测应变值偏差超过100%;对较大变形的GFRP和KFRP层合板,两者偏差小于40%。说明采用Hopkinson杆一维应力波理论计算的试样应变不准确。为修正不准确性,一是通过大量数据分析建立按一维应力波理论计算值与直接测量应变之间的关系式,用此式可使此试验装置获得有效的试样应变;二是借助ABAQUS有限元模拟分析得出粘胶层以及试样过渡弧段的变形,用一维应力波理论计算的应变减去此变形,也可获得有效的试样应变。     

M-shaped Specimen for the High-strain Rate Tensile Testing Using a Split Hopkinson Pressure Bar Apparatus

An experimental technique is proposed to determine the tensile stress–strain curve of metals at high strain rates. An M-shaped specimen is designed which transforms a compressive loading at its boundaries into tensile loading of its gage section. The specimen can be used in a conventional split Hopkinson pressure bar apparatus, thereby circumventing experimental problems associated with the gripping of tensile specimens under dynamic loading. The M-specimen geometry provides plane strain conditions within its gage section. This feature retards necking and allows for very short gage sections. This new technique is validated both experimentally and numerically for true equivalent plastic strain rates of up to 4,250/s.     

Effects of pressure on small foil strain gages

This paper describes the behavior of small foil strain gages under high pressure. Effects of pressure were determined and calibration curves were established in prelininary experiments. The calibrations were then used for correcting measured strains in pressure vessels. Preliminary experiments at room temperature were conducted on small foil strain gages for pressures up to 35,000 psi. The effects of pressure on the gages bonded with a cynoacrylate contact cement, a room-temperature epoxy cement, a high-temperature epoxy cement and a filled epoxy resin were evaluated. Because the contact cement was least affected by pressure and was easiest to apply, it was chosen for use in successive experiments with different gage installations. Calibration curves were determined for strain gages of 0.031-, 0.062- and 0.125-in. gage lengths. The compensating gages were under atmospheric pressure. The calibrations included the pressure effects of gages bonded on both concave and convex surfaces, and the effect of tensile prestrains. Data could be duplicated for successive pressure tests and for several gage installations. The calibration curves proved to be an effective way for obtaining accurate readings from the foil strain gages bonded internally to a pressure vessel.     

On the use of electrical-resistance metallic foil strain gages for measuring large dynamic plastic deformation

The use of electrical-resistance metallic foil strain gages for measuring large plastic strain in dynamic experiments in studied. The maximum nominal strains obtained in this investigation are 35 percent in compression, 25 percent in tension. A linear variation of gage factor with strain is found in this range. The corrected maximum strains are in excellent agreement with permanent strains measured after the tests. Thus foil strain gages can be effectively used to measure the large dynamic plastic strains.     

Design of Inserts for Split-Hopkinson Pressure Bar Testing of Low Strain-to-Failure Materials

In the present study a new insert design is presented and validated to enable reliable dynamic mechanical characterization of low strain-to-failure materials using the Split-Hopkinson Pressure Bar (SHPB) apparatus. Finite element-based simulations are conducted to better understand the effects of stress concentrations on the dynamic behavior of LM-1, a Zr-based bulk metallic glass (BMG), using the conventional SHPB setup with cylindrical inserts, and two modified setups—one utilizing conical inserts and the other utilizing a “dogbone” shaped specimen. Based on the results of these computational experiments the ends of the dogbone specimen are replaced with high-strength maraging steel inserts. This new insert-specimen configuration is expected to prevent specimen failure outside the specimen gage section. Simulations are then performed to validate the new insert design. Moreover, high strain-rate uniaxial compression tests are conducted on LM-1 using the modified SHPB with the new inserts. An ultra-high-speed camera is employed to investigate the changes in failure behavior of the specimens. Additional experiments are conducted with strain gages directly attached to the gage section of the specimens to determine accurately their dynamic stress–strain behavior.     

基于Hopkinson压杆的M型试样动态拉伸实验方法研究

采用传统分离式Hopkinson压杆进行M型试样的动态拉伸实验,可避免试样与杆的连接问题,但该方法并未得到发展和验证。本文中,采用有限元数值分析和实验方法,对M型试样动态拉伸实验进行分析和改进。结果表明:（1）改进的封闭M型试样,可以增强试样整体刚度,有效减少试样畸变引起的附加弯矩对拉伸标段的影响,方便通过Hopkinson压杆加载实现一维拉伸变形;（2）采用试样刚度系数修正法,可消除M型试样整体结构的弹性变形对测试的影响,精确获得试样拉伸标段的塑性应变;（3）高加载率下,建议采用波形整器加载,可显著减少试样结构引起的载荷震荡现象、改善两端的应力平衡,获得准确的动态拉伸应力应变曲线,实现5 900 s?1甚至更高应变率下的动态拉伸实验。研究方法可为M型试样拉伸实验设计和应用提供参考。     

Small attachable interferometric strain gages

Laser-based interferometry from two tiny reflective indentations can be used to measure in-plane strain/displacement over a very short gage length (on the order of 100 μm). If the specimen material is not reflective, then some other means of generating the interference patterns must be found. This paper describes two kinds of attachable gages: plated acetate replicas of indentations and reflective foils that are indented after application. In either case, the gage is applied with the techniques used for foil-resistance gages and the gage itself is very small. The manufacturing procedures are described. The results of experiments comparing the strain to that measured with foil-resistance gages are presented. Finally, the small interferometric gage is used to measure strain on one of the metal strips in a foil-resistance gage.     

A shear-compression specimen for large strain testing

A new specimen geometry, the shear-compression specimen (SCS), has been developed for large strain testing of materials. The specimen consists of a cylinder in which two diametrically opposed slots are machined at 45° with respect to the longitudinal axis, thus forming the test gage section. The specimen was analyzed numerically for two representative material models, and various gage geometries. This study shows that the stress (strain) state in the gage, is three-dimensional rather than simple shear as would be commonly assumed. Yet, the dominant deformation mode in the gage section is shear, and the stresses and strains are rather uniform. Simple relations were developed and assessed to relate the equivalent true stress and equivalent true plastic strain to the applied loads and displacements. The specimen was further validated through experiments carried out on OFHC copper, by comparing results obtained with the SCS to those obtained with compression cylinders. The SCS allows to investigate a large range of strain rates, from the quasi-static regime, through intermediate strain rates (1–100 s⁻¹), up to very high strain rates (2×10⁴s⁻¹ in the present case).     

An experimental study of inhomogeneous cyclic plastic deformation of 1045 steel under multiaxial cyclic loading

An experimental study was conducted on the inhomogeneous cyclic plastic deformation of 1045 steel under multiaxial cyclic loading. Thin-walled tubular specimens were used and small strain gages were bonded on the specimen surface to characterize the local deformation. The controlled loading paths included cyclic tension–compression, cyclic torsion, proportional axial-torsion, 90°-out-of-phase axial-torsion, and fully reversed torsion with a constant axial stress. The maximum stress in each experiment was lower than the lower yield stress of the material. It was found that the cyclic plastic deformation within the gage section of the specimen under multiaxial stress state followed the three-stage process that was observed from uniaxial loading, namely, incubation, propagation, and saturation. The plastic deformation was significantly inhomogeneous during the propagation stage, and the inhomogeneity continued through the saturation stage. The duration of each stage and the saturated strains were dependent on the cyclic stress amplitude and the loading path. Multiaxial stress state reduced the incubation stage. With identical equivalent stress magnitude, the nonproportional loading path resulted in the shortest incubation and propagation stages, and the saturated equivalent plastic strain magnitude was the smallest. Although the deformation over the gage section was inhomogeneous, the plastic deformation in a given local area was found to be practically isotropic.     

A tension split Hopkinson bar for investigating the dynamic behavior of sheet metals

The dynamic response of sheet metals at high strain rate is investigated with a tensile split Hopkinson bar test using plate type specimens. The tension split Hopkinson bar inevitably causes some errors in the strain at grips with the plate type specimens, since the grip and specimens disturb the one-dimensional wave propagation in bars. To validate the experiment, the level of error induced from the grips is estimated by comparing the waves acquired from experiments with the Pochhammer-Chree solution. The optimum geometry of the specimen is determined to minimize the loading equilibrium error. High strain rate tensile tests are then performed with auto-body sheet metals in order to construct their appropriate constitutive models for use in crash-worthiness evaluation.     

High Strain Rate Torsion Properties of Ultrafine-Grained Aluminum

Mechanical properties of most metallic materials can be improved by reducing their grain size. One of the methods used to reduce the grain size even to the nanometer level is the severe plastic deformation processing. Equal Channel Angular Pressing (ECAP) is one of the most promising severe plastic deformation processes for the nanocrystallization of ductile metals. Nanocrystalline and ultrafine grained metals usually have significantly higher strength properties but lower tensile ductility compared to the coarse grained metals. In this work, the torsion properties of ECAP processed ultrafine grained pure 1070 aluminum were studied in a wide range of strain rates using both servohydraulic materials testing machines and Hopkinson Split Bar techniques. The material exhibits extremely high ductility in torsion and the specimens did not fail even after 300% of strain. Pronounced yield point behavior was observed at strain rates 500 s⁻¹ and higher, whereas at lower strain rates the yielding was continuous. The material showed slight strain softening at the strain rate of 10⁻⁴ s⁻¹, almost ideally plastic behavior at strain rates between 10⁻³ s⁻¹ and 500 s⁻¹, and slight but increasing strain hardening at strain rates higher than that. The tests were monitored using digital cameras, and the strain distributions on the surface of the specimens were calculated using digital image correlation. The strain in the specimen localized very rapidly after yielding at all strain rates, and the localization lead to the development of a shear band. At high strain rates the shear band developed faster than at low strain rates.     

基于超高速相机的数字图像相关性全场应变分析在SHTB实验中的应用

基于超高速相机和数字图像相关性全场应变分析方法对传统的分离式Hopkinson拉杆(SHTB)实验系统进行改进,获得尼龙和铝合金材料的动态拉伸应力应变曲线,验证了数字图像相关性全场应变分析在SHTB实验中的有效性。实验结果显示:该方法测量的平均应变与应变片测量结果一致性很好, 而传统的SHTB实验原理计算的应变结果则明显偏大,需要对试件原始标距进行修正后才能获得有效的试件应变,并且在试件的材料和几何尺寸不变的条件下标距修正不依赖于应变率。基于数字图像相关性全场应变测量,讨论了应变均匀性问题:脆性的尼龙试件在标距范围内应变均匀性良好,而韧性的铝合金试件表现出比较严重的应变不均匀性,归因于颈缩变形的影响。     

Temperature and rise-time effects on dynamic strain measurement

Strain pulses in a test specimen were measured over a temperature range of ?73 to +149°C with foil and semiconductor strain gages. These tests were performed to determine if the rise time and amplitude of the gage output change as a function of temperature. The existence of a constant that should be added to the theoretical rise times of resistance strain gages, as suggested by Koshiro Oi, was reexamined. ‘Long’ rise-time strain pulses were produced in the test specimen by an impacting steel ball. The rise times of these pulses were on the order of 7 μs and the amplitudes were approximately 65 μm/m. The results of these tests show that the rise time and amplitude of the gage do not change as a function of temperature. ‘Short’ rise-time strain pulses of approximately 500 μm/m with a rise time of 2 μs were produced in a test specimen by a short pendulum-type hammer apparatus. The results of these tests showed that the amplitude of the gage output was relatively independent of test temperatures but exhibited a slight hysteresis effect. The rise times for these tests remained constant up to a temperature of 93°C, then started to increase. The rise times at 149°C were approximately 100 percent longer than at room temperature. Under optimum conditions, a pulse with a measured rise time of 0.18 μs could be generated. The results of these tests indicated that the theoretical rise-time additive constant of resistance strain gages is 0.05 μs or less. This is one-half the value that Bickle arrived at by reevaluating Oi's data. However, since the real rise time of the pulse was unknown, this additive constant is not necessarily a property of the gage.     

Sensitivity of the shear gage to normal strains

This paper documents an experimental study that was conducted to demonstrate the sensitivity of the shear gage to the presence of normal strains. The shear gage is a specially designed strain gage rosette that measures the average shear strain in the test section of notched specimens such as the losipescu, Arcan and compact shear specimens. These specimens can have complicated stress states with high shear and normal strain gradients. To evaluate the sensitivity of the shear gage to normal strains, shear gages were tested on an Arcan specimen. The Arcan specimen is a notched specimen that can be loaded in pure shear (90 deg), pure tension (0 deg) and at intermediate 15- deg increments. The shear modulus for an aluminum specimen was determined at each of these loading angles. It was found that the gages display nearly zero sensitivity to normal strains ( _x, _y). Moiré interferometry was used to document the shear and normal strain distributions in the test section and to provide an independent method for determining the average shear strain. These results reinforce the robust nature of testing with the shear gage.     

应力平衡和接触状态在Hopkinson杆测试聚合物动态弹性模量中的影响研究

针对用Hopkinson杆试验能否准确测量聚合物动态弹性模量以及其中主要影响因素的问题,本文基于重构试样初始加载阶段的应力波反射透射过程,分别计算了6个特征时间内的前三次反射波和透射波,得到试样的应力平衡度和试样的应力应变曲线。对于所研究的聚合物材料,通过比较重构的应力应变曲线的弹性模量与输入的材料弹性模量,发现在4个特征时间后,误差仅在3%左右。因此试样变形过程中的应力平衡与否不是材料在Hopkinson杆试验中弹性模量测不准的原因。通过环氧树脂试样试验发现,根据Hopkinson杆理论计算的应变结果要大于试样上应变片实测的结果,误差在11%左右。相应的数值模拟研究发现:试样和杆子端面接触状态直接决定着试样弹性模量测量的精度。关于惯性效应和压痕效应的研究也证实它们的影响是可以忽略的。     

Strain-gage stability measurements for three years at 150°C in air

The zero shifts of nickel-chromium foil strain gages (modified Karma) were measured over a period of three years at a constant temperature of 150°C in air. Three gage lengths were included—1.585 mm (1/16 in.), 3.170 mm (1/8 in.), and 6.340 mm (1/4 in.). The strain gages were bonded to constant-stress cantilever beams which were subjected to nomial mechanical strain levels of 0, ±780 μm/m, and ± 1350 μm/m. Each strian gage was connected by threewire leads to a Wheatstone-bridge circuit for the test duration. The data support two general observations: (1) short gage lengths suffer larger zero shifts than longer gage lengths, and (2) gages in compression suffer large zero shifts than gages in tension. On the assumption that the major cause of the zero shifts is a combination of corrosion of the foil and creep of the gage/epoxy/beam system, the author suggests a possible way to correct for the zero shift by experimentally determining the combined corrosion/creep effect and substracting it from the strain-gage readings. Some of the data appear to be consistent with this assumption, but some of the data do not.     

Strain-field analysis acquired through correlation of X-ray radiographs of a fiber-reinforced composite laminate

The strain fields can be determined on the surface of fiber-reinforced composites by correlation analysis of X-ray radiographs of the specimen. One radiograph is taken of the specimen in an unloaded state and another radiograph of the same specimen is taken in a deformed state. Each radiograph is then imaged by a video camera and digitized using a Matrox digitization board. The displacement map is obtained from the two radiographs by dividing one image into subsets of 20 pixels by 20 pixels and using a correlation algorithm to identify the corresponding subsets in the second image. The correlation is completed between patterns of the grey-level intensities for each subset. The appropriate discrete derivatives can then be evaluated by first difference taken to form the in-plane strains. The X-ray radiographs correlation analysis strain-field method outlined above was applied to a uniaxially loaded [90, 0] _s Gl-Ep coupon. Simultaneously, an extensometer measured the average longitudinal strain over a 2.54-cm (1-in.) gage length. The error between the two methods was less than three percent of the applied strain of 1.3 percent. The same specimen was impacted and re-examined. A radical shift in the strain field was observed when the specimen was reloaded. Further investigation showed the method reliable down to 0.5-percent strain. Paper was presented at the 1986 SEM Spring Conference on Experimental Mechanics held in New Orleans, LA on June 8–13.