Mechanical Properties of Ballistic Gelatin at High Deformation Rates

The characterization of soft or low impedance materials is of increasing importance since these materials are commonly used in impact and energy absorbing applications. The increasing role of numerical modeling in understanding impact events requires high-rate material properties, where the mode of loading is predominantly compressive and large deformations may occur at high rates of deformation. The primary challenge in measuring the mechanical properties of soft materials is balancing the competing effects of material impedance, specimen size, and rate of loading. The traditional Split Hopkinson Pressure Bar approach has been enhanced through the implementation of polymeric bars to allow for improved signal to noise ratios and a longer pulse onset to ensure uniform specimen deformation. The Polymeric Split Hopkinson Pressure Bar approach, including the required viscoelastic bar analysis, has been validated using independent measurement techniques including bar-end displacement measurement and high speed video. High deformation rate characterization of 10% and 20% ballistic gelatin, commonly used as a soft tissue simulant, has been undertaken at nominal strain rates ranging from 1,000 to 4,000/s. The mechanical properties of both formulations of gelatin exhibited significant strain rate dependency. The results for 20% gelatin are in good agreement with previously reported values at lower strain rates, and provide important mechanical properties required for this material.     

软材料的SHPB实验设计

通过对SHPB实验中加载波波形进行控制设计 ,实现软材料试样在加载过程中的应力平衡和常应变率加载 ,从而保证SHPB实验的前提条件。采用这种方法研究了两种材料的高应变率本构 ,实验结果表明 :设计的方法是行之有效的。     

A quartz-crystal-embedded split Hopkinson pressure bar for soft materials

A dynamic experimental technique that is three orders of magnitude as sensitive in stress measurement as a conventional split Hopkinson pressure bar (SHPB) has been developed. Experimental results show that this new method is effective and reliable for determining the dynamic compressive stress-strain responses of materials with low mechanical impedance and low compressive strengths, such as elastomeric materials and foams at high strain rates. The technique is based on a conventional SHPB. Instead of a surface strain gage mounted on the transmission bar, a piezoelectric force transducer was embedded in the middle of the transmission bar of a high-strength aluminum alloy to directly measure the weakly transmitted force profile from a soft specimen. In addition, a pulse-shape technique was used for increasing the rise time of the incident pulse to ensure stress equilibrium and homogeneous deformation in the low-impedance and low-strength specimen.     

A split Hopkinson bar technique for low-impedance materials

An experimental technique that modifies the conventional split Hopkinson pressure bar has been developed for measuring the compressive stress-strain responses of materials with low mechanical impedance and low compressive strengths such as elastomers at high strain rates. A high-strength aluminum alloy was used for the bar materials instead of steel, and the transmission bar was hollow. The lower Young's modulus of the aluminum alloy and the smaller cross-sectional area of the hollow bar increased the amplitude of the transmitted strain signal by an order of magnitude as compared to a conventional steel bar. In addition, a pulse shaper lengthened the rise time of the incident pulse to ensure stress equilibrium and homogeneous deformation in the low-impedance specimen. Experimental results show that the high strain rate, compressive stress-strain behavior of an elastomeric material can be determined accurately and reliably using this technique.     

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.     

Micromechanical Modeling of Elastic-Viscoplastic Behavior of Armco-Fe at High Strain Rate

Heterogeneous dynamical stress-strain response of Armco-Fe was investigated at high strain rates through the Split Hopkinson Pressure Bar(SHPB) testing. It was found that the viscoplastic deformation in BCC ferrite grains is affected by the strain rate. Thermal softening and variation in crystal orientations under high-strain-rate loading were used in the elastic-viscoplastic modeling. The micromechanical analysis with self-consistent transition and homogenization was used for estimation of the global impact response of the material. The results from modeling were found in good agreement with the experimental data.     

用于高强度材料的SHPB实验添加垫块法

提出了用于高强度材料的改进的SHPB实验方法添加垫块法,运用数值模拟方法,利用有限元程序LS-DYNA3D分析了添加垫块实验方法的合理性和可行性。根据一维应力波理论,给出了数据处理的修正方法。作为应用实例,采用改进的实验方法对高强度的Al2O3陶瓷材料的动态力学性能进行了研究,得到了比常规方法较高的应变率及应力应变范围的动态应力应变曲线,表明Al2O3陶瓷为应变率相关的非线性弹脆性材料。结果表明,添加垫块实验方法可有效地防止实验中压杆端面的变形,提高试件的应力应变及应变率水平。添加垫块实验方法为在SHPB装置上实现高强度材料的动态实验提供了一种方便实用的途径。     

基于数字图像相关方法对冲击载荷下泡沫铝全场变形过程的测试

应用分离式霍普金森压杆(以下简称SHPB)和高速摄影装置研究了冲击载荷下泡沫铝试件全场变形的测量方法。使用SHPB对泡沫铝试件进行冲击压缩实验,同时用高速摄影装置对实验过程进行全程跟踪拍摄。将得到的高速摄影图像采用数字图像相关方法进行分析,由此可得到冲击压缩过程中泡沫铝试件全场应变的分布和变化规律。此研究揭示了冲击载荷下泡沫铝试件局部化变形的发展过程,为研究泡沫铝在不同冲击载荷下不同变形模式的内在机制提供了新的可靠的方法。     

冻土动态力学性能的实验研究

利用分离式霍布金森压杆(SHPB)对4种低温下的冻土进行了4种高应变 率的动态压缩实验. 实验结果表明：冻土不仅具有温度效应，还具有应变率效应，两种效应 反映出冻土材料的时温等效性. 另外这种时温等效性在分析冻土材料的破坏过程时还体现在 它的冻脆性和动脆性. 冻土材料动态应力应变曲线的汇聚现象和振荡现象均起源于这种冻脆 性和动脆性.     

子弹冲击下TiNi固支梁的结构动态响应特性研究

采用改装的霍普金森压杆装置结合数值模拟对伪弹性TiNi合金固支梁的结构动态响应特性进行了研究。结果表明,在子弹冲击下,撞击点和固定端附近首先发生相变,并随着载荷增加,进一步产生相变铰,梁演变为二杆铰接机构。由于轴力作用,此处相变铰为拉伸侧的单边铰。与传统塑性铰不同,卸载后相变铰完全消失,梁回复原状没有残余变形。此外,对固支边界条件的实现及其对实验结果的影响进行了专门研究。     

Modified Kolsky Formulas for an Increased Measurement Duration of SHPB Systems

The so-called incident, reflected and transmitted strain histories are typically recorded during standard Split Hopkinson Pressure Bar (SHPB) experiments. Subsequently, the stress-strain curve for the specimen material is determined based on these recordings. Unless wave deconvolution techniques are employed, the reliable measurement of the reflected wave requires an input bar which is at least twice as long as the striker bar (of equal impedance). The present brief technical note elucidates the advantages of a simple alternative configuration which has only been seldom used in the past. Based on the assumption of quasi-static equilibrium at the specimen level, we present a modification of Kolsky’s formulas such that the stress-strain curve for the specimen material can be obtained from the measurement of the incident and transmitted strain histories only. As a result, the measurement of the reflected wave may be omitted and a much shorter input bar can be chosen. Conversely, a much longer striker bar may be used for a given input bar length, thereby increasing the valid duration of standard SHPB experiments by up to 100 % through the use of the modified Kolky formulas. An example experiment is shown where the duration of valid measurements has been increased by more than 70 %.     

基于PVDF薄膜传感器的猪肝动态压缩力学性能测试

瞬态冲击载荷作用下肝脏的力学响应是损伤生物力学的重要研究内容。本文提出了一种可用于软组织动态压缩力学特性测试的改进SHPB(分离式霍普金森压杆,Split Hopkinson Pressure Bar)方法。该方法采用PVDF(聚偏氟乙烯,Polyvinylidene Fluor)压电薄膜传感器测量实验过程中试件两端面的受力,以此来计算试件的应力,从而无需测量透射杆上的微弱透射信号。猪肝试样前后端面的PVDF压电信号对比表明,加载过程中试样达到了动态应力平衡状态。试样动态压缩中的惯性效应主要在加载的初始阶段对透射应力信号造成较大影响,在大变形阶段惯性效应引起的轴向应力较小。利用此方法对猪肝组织进行三种高应变率(1800s^-1,2500s^-1,3500s^-1)的动态压缩实验,并采用基于真实应变的惯性效应公式对实验数据进行修正计算。结果表明:猪肝组织在准静态与高应变率时的应力应变曲线都呈现出凹向上的非线性特征,即曲线初始阶段应力增长较缓慢,当应变达到15%后应力值则迅速增大;猪肝组织也具有明显的应变率效应,即随着应变率的增加,应力应变曲线的整体应力值也随之增大。最后,采用黏超弹性本构模型描述了猪肝组织的动态应力应变曲线。     

Split Hopkinson Pressure Bar Graphical Analysis Tool

An open-source Split Hopkinson Pressure Bar graphical data analysis tool has been developed. Written in Matlab®, the code can be freely distributed either as an executable binary or editable Matlab files. Beginning with raw voltages from two strain gages along with the incident/transmitted bars’ mechanical and geometrical properties, the user can visually analyze forces and displacements at the bar faces and the stresses and strains in the specimen. Wave dispersion and modulus correction are available in this package. A modest documentation and video tutorials accompany the software.     

Dynamic characterization of compliant materials using an all-polymeric split Hopkinson bar

The split Hopkinson bar is a reliable experimental technique for measuring high strain rate properties of high-strength materials. Attempts to apply the split Hopkinson bar in measurement on more compliant materials, such as plastics, rubbers and foams, suffer from limitations on the maximum achievable strain and from high noise-to-signal ratios. The present work introduces and all-polymeric split Hopkinson bar (APSHB) experiment, which overcomes these limitations. The proposed method uses polymeric pressure bars to achieve a closer impedance match between the pressure bars and the specimen materials, thus providing both a low noise-to-signal ratio data and a longer input pulse for higher maximum strain. The APSHB requires very careful data reduction procedures because of the viscoelastic behavior of the incident and transmitter pressure bars. High-quality stress-strain data for a variety of compliant materials, such as polycarbonate, polyurethane foam and styrofoam, are presented.     

Estimating Measurement Uncertainty on Stress-Strain Curves from SHPB

Split Hopkinson Pressure Bar tests are commonly used to determine material stress-strain relationship at high deformation rates. Obtaining this relationship is dependant both on certain assumptions and substantial post-processing of the data recorded during the test. Measurement uncertainty rarely appears on the resulting curves. This article introduces a simple method of estimating the measurement uncertainty associated with SHPB tests.     

Loading and unloading split hopkinson pressure bar pulse-shaping techniques for dynamic hysteretic loops

Pulse-shaping techniques are developed for both the loading and unloading paths of a split Hopkinson pressure bar (SHPB) experiment to obtain valid dynamic stress-strain loops for engineering materials. Front and rear pulse-shapers, in association with a momentum trap, are used to precisely control the profiles of the loading and unloading portions of the incident pulse. The modifications, ensure that the specimen deforms at the same constant strain rate under dynamic stress equilibrium during both loading and unloading stages of an experiment so that dynamic stress-strain loops can be accurately determined. Dynamic stress-strain loops with a constant strain rate for a nickel-titanium shape memory alloy and polymethyl methacrylate are determined using the modified SHPB. The modified momentum trap prevents repeated loading on a specimen without affecting the amplitude of the desired loading pulse and without damaging the bar at high stress levels.     

SHPB实验中粘弹性试件内部应力波的传播

建立描述SHPB实验中线性粘弹性试件内部应力波传播的控制方程组,根据试件两端与入射杆及透射杆接触的应力波特征关系给出耦合边界条件.对方程组和定解条件进行Laplace变换,求得试件内部应力在变换域像函数的表达式.采用数值反变换技术进行反Laplace变换,获得试件两端的应力时程曲线.对现有的固定Tal-bot反变换算法进行改进:将入射波像函数分解为基本部分和延迟部分,利用固定Talbot算法对基本部分入射波作用下的波动问题求解,其他部分的解通过延迟定理得到,最终解为两部分的叠加.采用这种改进算法得到的不同入射波下粘弹性试件的内部应力解与传统的基于特征线数值模拟方法的结果吻合.在此基础上探讨了粘弹性试件的几何参数和材料本构参数对透射波波形的影响.     

一种用于软材料测试的改进SHPB装置

本文提出了一种新的、用于测试橡胶、高弹体及高聚物软泡沫材料动态力学性能的SHPB改进装置。该装置取消了常见的入射杆而采用长杆弹直接撞击试件从而实现了持续的长时间加载，使得在相当大的应变率范围内试件的最大应变在一个加载过程中即可达到。配合该装置采用了瞬态响应优良、分辨率良好的光电式位移测试系统来测量试件的变形；为记录微弱的应变信号，在透射杆中使用了半导体应变片。本方案克服了传统SHPB在测试软材料时由于子弹长度限制带来的加载幅度不足及由于阻抗失配导致的应变信号微弱的困难；与采用高聚物杆的SHPB改进方案相比，本方案的测试结果也更为可靠。在试验装置中还运用了加载整形技术以改善试件中的应力均匀性。从测试结果看，该装置能有效地实现大变形范围、近似恒应变率持续加载以及相应的微弱应变信号的测量。     

中高应变率下EPS泡沫的冲击压缩实验

用SHPB装置对三种密度的发泡聚苯乙烯(Expanded Polystyrene,EPS)材料进行了从300/s至1400/s共五个中高应变率下的冲击压缩实验。实验中采用波分离技术有效延长应力-应变曲线的测量范围,并简要介绍了其原理和具体实施办法。所有应变率下均获得了含有弹性段、平台屈服段和压实段完整三阶段的应力-应变曲线。曲线的重复性较好,应变率基本恒定。实验结果表明,相同密度EPS泡沫应力-应变曲线的屈服平台段长度随应变率的增加而增加,且趋于平缓。在相近应变率下,随EPS泡沫的密度增加,屈服应力增加,而变形及吸能能力减弱。     

Dynamic fiber debonding and frictional push-out in mode composite systems: Experimental observations

In the present work a modified Split Hopkinson Pressure Bar (SHPB) system is adopted to perform dynamic fiber push-out experiments on model single fiber composite systems. A tapered punch and a support connect a monofilament composite with the incident and transmitted bars of the SHPB. The tapered punch is used to apply compressive loading to a single fiber (either steel or aluminum) embedded in a surrounding matrix material (EPON 862). The SHPB allows real time measurement of relative fiber/matrix displacement and push-out force, as the debonding and push-out event progresses. Using this technique we have studied the effect of loading rate, material mismatch, fiber length, and surface roughness on the push-out event. It was seen that maximum push-out force increases with increasing loading rate. In addition dynamic interfacial strength and toughness is highly dependent on fiber surface roughness. Results from a finite element analysis incorporating a cohesive failure model were used to extract interface strength and toughness values. It was found that the particular aluminum/EPON interface used is characterized by a dynamic shear failure strength of 48±8 MPa, a mode II fracture toughness of 160±40 N/m, and a friction coefficient of 0.2 at a sliding rate of 6 m/s. For the rates tested here these quantities were found to be approximately constant.