Influence of Shock Pre‐Compression Stress and Tensile Strain Rate on the Spall Behaviour of Mild Steel

Abstract: A series of plate‐impact spall experiments were conducted to investigate the influence of shock pre‐compression stress and tensile strain rates on the dynamic tensile fracture (or spall) behaviour of shocked mild steel. The shock pre‐compression stress amplitude and tensile strain rate were controlled independently to ensure that only one single‐loading parameter varied for each experiment. A push–pull type velocity interferometer system for any reflector (VISAR) was used to measure the free surface velocity profiles of samples. It is observed from experimental results that the influence of shock pre‐compression stress amplitude on the spall strength is less significant in the range attained in these experiments, whereas with increasing tensile strain rate, an evident 65% increase of spall strength is determined in the present tensile strain rate range of 10⁴ to 10⁶ s^?1. VISAR data are compared with finite‐difference calculations employing a modified damage function model with a percolation–relaxation function, and a good agreement between the calculation and the experiments was obtained. Preliminary simulation results also revealed that a critical damage exists, which physically corresponds to the critical intervoid ligament distance for triggering the onset of void coalescence, and may be regarded as a material parameter for describing the dynamic tensile fracture and independent of the loading conditions.     

超高性能混凝土动态冲击拉伸性能研究

超高性能混凝土(Ultra-high performance concrete,UHPC)作为一种具有超高物理力学性能的新型建筑材料,能显著提高军事防护工程的抗爆炸冲击能力,对保障防护工程中人员的生命安全具有重要意义。为揭示爆炸冲击波在防护工程自由面引起的动态拉伸破坏行为,利用霍普金森压杆装置(Split Hopkinson pressure bar,SHPB)对UHPC进行动态冲击拉伸试验,系统研究了粗集料种类、钢纤维掺量以及应变率对UHPC动态冲击拉伸性能的影响规律。结果表明:粗集料种类对UHPC的动态冲击拉伸强度有较显著的影响,相比于花岗岩和铁矿石,玄武岩粗集料对动态冲击拉伸性能的提高更为明显;UHPC的动态冲击拉伸强度会随着钢纤维掺量的增加而显著提高,但钢纤维掺量对UHPC动态拉伸强度的贡献存在4%的临界值;此外,UHPC表现出明显的应变率效应,当应变率为7~50s-1时,其效应最为显著。     

Tensile failure of concrete at high loading rates: New test data on strength and fracture energy from instrumented spalling tests

For the numerical prediction of the response of concrete structures under extreme dynamic loading, like debris impact and explosions, reliable material data and material models are essential. TNO-PML and the Delft University of Technology collaborate in the field of impact dynamics and concrete modelling. Recently, TNO-PML developed an alternative Split Hopkinson Bar test methodology which is based on the old principle of spalling, but equipped with up-to-date diagnostic tools and to be combined with advanced numerical simulations. Data on dynamic tensile strength and, most important, on fracture energy at loading rates up to 1000 GPa/s are obtained. The paper describes the test and measurement set-up, presents the new test data and the analysis of the test results. In addition, a rate-dependent softening curve is given which is based on the integrated findings so far.     

轴向钢筋增强混凝土一维应力层裂实验研究

基于Φ74mmSHPB实验平台进行了混凝土及轴向钢筋增强混凝土(UDRC)杆的一维应力层裂实验,采用超高速相机拍摄实验中杆表面的实时变形情况,使用数字图像相关法(DIC)分析杆表面的位移场及应变场演化过程,探讨混凝土及增强混凝土在应力波加载过程中发生拉伸断裂(层裂)的规律,并进一步结合有限元分析了钢筋在层裂过程中的作用。结果表明:UDRC杆中应力波的传播满足一维应力假设;钢筋对UDRC发生拉伸层裂的影响可以忽略,而在混凝土基体断裂后将使结构保持完整;断裂试件中的裂纹在拉压应力波交替作用下反复张开闭合,随着应力波在杆中的衰减而趋于稳定;UDRC与混凝土的层裂强度基本相同,且具有相似的应变率增强效应;在实验加载范围内,光圆钢筋和螺纹钢筋的结构增强效果没有区别。     

An experimental method to study the dynamic tensile failure of brittle geologic materials

An experimental method was developed to study the tensile failure of brittle geologic materials at strain rates of approximately 10 to 20/s. In these experiments, a cylindrical rod specimen is first loaded in static triaxial compression, then the axial pressure is released from each end simultaneously and very rapidly. The resulting rarefaction waves interact in the center of the rod to produce a dynamic tensile stress equal in magnitude to the original static compression. The pressure acting on the radial surface is approximately constant during the experiment. As an application of this method, several experiments were performed on concrete. Transient measurements were made of the axial load at each end, the confining pressure, and axial and circumferential surface strains at several locations along the length of the rod. Usually a single fracture occurred near the midpoint of the rod. In some experiments multiple fractures occurred. Assuming the peak observed strains in these experiments to be elastic the unconfined tensile strength of the concrete at a strain rate of 10 to 20/s was, on average, approximately 40% higher than the static splitting tensile strength. At the same strain rate, the tensile strength with 10 MPa confining pressure averaged approximately 100% higher than the static splitting tensile strength and 40% higher than the unconfined tensile strength at 10 to 20/s. Nonlinear analyses indicate that these estimates are reasonable, but that in general the assumption of elastic response is not valid. To match the measured strain histories with calculations requires that the rod be modeled inelastically.     

Impact behaviour of concrete: a computational approach

The purpose of this study is to examine the numerical simulation of concrete specimens under high loading rates in tension. The data found in the literature are described: they show an increase in compressive and tensile strength as a function of the loading rate. To study this behaviour, we focused our attention on the assessment of the consistency model through the simulation of many experimental results related to a wide range of strain rates. In particular, the tests on unnotched and notched specimens performed at Delft University in recent years are examined. The proposed model is able to describe the increase in strength due to a high loading rate by an appropriate choice of the viscosity parameter.     

超高韧性水泥基复合材料的层裂试验研究

层裂是材料遭受冲击、爆炸等高速荷载时的一种常见破坏方式。该文利用直径80 mm的霍普金森杆实验装置,研究了超高韧性水泥基复合材料UHTCC(Ultra High Toughness Cementitious Composites)中应力波的传播特性和材料的层裂强度。通过在试件表面粘贴5组应变片,获得了在0.2 MPa、0.3 MPa、0.4 MPa、0.5 MPa打击气压下,UHTCC中应力波的传播曲线。利用高速摄影机记录层裂试验,观测了UHTCC的层裂破坏过程。由试件表面应变片测得的应力波曲线,计算了材料中的应力波波速、动态弹性模量,分析了应力波在该材料中传播的衰减规律,并计算出不同打击气压下材料的层裂强度及应变率。试验结果显示:UHTCC的层裂过程相比混凝土具有更多的韧性特征;UHTCC中的应力波峰值在0 mm～500 mm范围内衰减迅速;在同等应变率下,UHTCC与静态抗拉强度相近的混凝土相比,层裂强度高出10 MPa左右,且UHTCC的层裂强度具有明显的应变率敏感性。     

Plastic behavior of steel and iron in high strain rate regime

The shock response of anti-hydrogen steel (HR-2) and iron was studied in a series of laser-driven shock wave experiments. A line-imaging optical recording velocity interferometer system for any reflector was used to record the free surface velocity histories of shock loaded samples, 100–300 \(\upmu \hbox {m}\) thick and with an initial temperature ranging from 296 to 1073 K. Based on the recorded free surface velocity profiles, the elastic precursors, dynamic yield and tensile (spall) strengths of HR-2 and iron were calculated. The dependence of the measured HEL stresses on the propagation distance for HR-2 and polycrystalline iron is approximated by a power law relationship.But, that for the single crystal iron with orientation of (110) seems to be constant. Spall strengths \((\upsigma _{\mathrm{sp}})\) of HR-2 estimated from the magnitude of the pull-back signal show that the spall strength dependence on the strain rate \((\dot{\upvarepsilon })\) is approximated by a power law relationship \(\upsigma _{\mathrm{sp}} =0.24\left( \dot{\upvarepsilon } \right) ^{0.24}\,\left( {\hbox {GPa}} \right) \). The spall strength of HR-2 and single crystal iron at the initial temperatures of 296–1073 K decreases slightly with increasing temperature and that of poly crystal iron abnormally increases at a temperature of 873 K. The X-ray diffraction results on the recovered poly crystal samples indicate significant changes in the relative peak intensity and the change in the crystal orientation may be the reason for the abnormal increasing at 873 K. The spall fracture surfaces of HR-2 were observed using a 3D laser scanning confocal microscope. The spall surface contains many dimples, suggesting that the fracture mode is that of ductile fracture. At ambient temperatures, the dimples and crowns were evenly distributed at the fracture surface. At high temperatures, many large crowns appeared and were unevenly distributed at the fracture surface.     

Tensile properties and fracture behaviour of polypropylene-nickel-coated carbon-fibre composite

Polypropylene-based composites reinforced with nickel-coated carbon fibres have been prepared and the effect of filler content on tensile properties and fracture behaviour at different temperatures and strain rates was investigated. The elastic modulus of such composites is enhanced by two orders of magnitude while the tensile strength and strain-to-break are lowered. The fracture toughness parameters,G _c andK _c, are also enhanced with filler content. The yield stress of this composite showed strain rate and temperature dependence. Activation energy and volume of a single rate-activated yielding process, at relatively high strain rates, were determined. The variations of the measured physical quantities are discussed in terms of the observed composite morphology.On sabbatical leave from the Physics Department, University of Jordan, Amman, Jordan.     

岩石-混凝土界面拉伸断裂性能的率相关性研究EI北大核心CSCD

该文弯曲断裂试验获得了不同应变率下界面的抗拉强度、荷载-加载点位移曲线、荷载-裂缝口张开位移曲线、起裂荷载和峰值荷载,通过夹式引伸计法和DIC法获得了临界裂缝扩展长度。并计算了界面断裂能及双K断裂参数,分析了不同应变率下界面断裂过程区演化规律及特征长度的变化。结果表明:随应变率的增大,断裂能和起裂韧度增大,临界裂缝长度和失稳韧度先增加后减小,断裂过程区长度及特征长度随应变率的提高而减小。该文从裂缝发展路径、自由水粘性、惯性效应三方面探讨了岩石-混凝土界面断裂参数的率效应。     

Simulation of spall fracture of aluminum and magnesium over a wide range of load duration and temperature

Measurements of the dynamic strength of aluminum and magnesium have been carried out through investigations of spall phenomena. In experiments, free-surface velocity profiles were recorded with a VISAR. The initial temperature of samples was varied from room temperature to that close to the melting point. The peak pressure in shock waves was varied from 5 to 50 GPa for aluminum and from 2 to 10 GPa for magnesium. The load duration was varied by more than an order of magnitude. Measurements showed precipitous drop in the spall strength of preheated samples as temperatures approached the melting point. No significant influence of the peak pressure on the spall strength was observed until a residual temperature after unloading of shock-compressed matter approached the melting. The strain-rate dependencies of the spall strength can be represented as power functions with an exponent of 0.059 for aluminum and 0.072 for magnesium. An empirical constitutive relationship has been established to describe the fracture rate as a function of the tensile stress, ultimate tensile stress that has activated a damage in the point, the damage value, and the temperature. The constitutive relationshiop was constructed on a base of analysis of the wave dynamics at spalling. Computer simulations show reasonably good workability of the model over a wide range of the shock load parameters and the temperature of matter.     

Fracture energy of concrete at high loading rates in tension

The effect of high loading rates in tension on the failure energy and strength of concrete is reported in this paper. High loading rates exceeding 5000 GPa/s corresponding to strain rates higher than ∼120 s⁻¹ can be applied by use of Hopkinson bar set-up designed to produce spall. Tension tests were performed on cylindrical specimens made of micro-concrete. At high loading rates, or strain rates, the failure energy of micro-concrete, as well as the strength, was found to substantially increase.     

Impact Tensile Stress–strain Characteristics of Wrought Magnesium Alloys

Abstract:  Impact tensile properties of three different wrought magnesium alloys (AZ31B-F, AZ61A-F and ZK60A-T5) are evaluated using the split Hopkinson bar. Reliable tensile stress–strain data up to fracture in the extrusion direction at strain rates of nearly 1000 s⁻¹ are presented and compared with those at quasi-static and medium rates of strain obtained on an Instron testing machine. The effect of strain rate on the tensile strength, elongation at fracture and absorbed energy is examined in detail. It is demonstrated that the tensile strength increases with increasing strain rate, and the strain-rate dependence of elongation at fracture and absorbed energy varies, depending on the magnesium alloys tested. The limitations of the test technique are discussed.     

Numerical study of dynamic behavior of concrete by meso-scale particle element modeling

Based on the Particle Element Method, a meso-scale dynamic model is developed for numerical study of the dynamic failure behavior of three-phase concrete i.e., aggregate, mortar, and interface, under different strain rates. First, a pre-processing approach based on the background grid search method proposed in our previous work is applied to generate the three-phase concrete specimen in meso-scale; second, the meso-mechanical parameters of three phases of concrete are determined by inverse method; and third, using the meso-scale dynamic model, the complete force-deformation relationship and the corresponding dynamic increase factors (DIF) at different strain rates are obtained for dynamic splitting tensile and uniaxial compression tests of concrete. The results match satisfactorily with the preceding experiments in related literatures. Different fracture patterns, consumed energy curves and force chain distributions are discussed under different strain rates, explaining the mechanism of strain rate effects in concrete. The numerical simulations show that the higher the strain rates, the more reticular meso-cracks occur, the kinetic and frictional energies become more important, and the force chains in the specimen exhibit more bifurcation, implying that the fracture process at high strain rates requires more energy demand to reach failure.     

Dynamic tensile strength of organic fiber-reinforced epoxy micro-composites

Outer surfaces of spacecraft in orbit are exposed to hypervelocity impact originating from micro-meteoroids and space debris. The structural composite materials are integral parts of the spacecraft envelope. We studied the impact response of structural micro-composites containing Kevlar 29, spectra 1000 and oxygen RF (Radio Frequency) plasma surface-treated spectra 1000 fibers of 27-μm diameter, embedded in 100-μm epoxy resin films, in a series of planar impact experiments. The composites were loaded by 50-μm aluminum and polycarbonate impactors having velocities ranging from 400 to 550 m/s. The velocity of the free surface of the composite samples was continuously monitored by VISAR (Velocity Interferometer System for Any Reflector). The dynamic tensile (spall) strength of the micro-composites was calculated on the basis of the recorded free surface velocity profiles. Correlations were found between the spall strength and the separately measured: (i) fiber/matrix interfacial adhesion, (ii) tensile strengths of the fibers, of the matrix and of the micro-composites, and (iii) internal residual stresses. The spall strength of surface-treated spectra fibers micro-composites was found to be lower than that of both pristine spectra fibers micro-composites, and the pure epoxy film. The epoxy film reinforced by Kevlar fibers was found to have the highest spall strength.     

Spall fracture: methodological aspects, mechanisms and governing factors

The dynamic tensile strength of materials at load durations of a few microseconds or less is studied by analyzing the spall phenomena under shock pulse loading. The paper is devoted to discussing the methodology and capabilities of the technique to measure spall strength, its error sources, spall fracture of materials of different classes and the factors governing the high-rate fracture of metals and alloys under such conditions.     

A grain-scale study of spall in brittle materials

The evolution of spall for a brittle material is investigated under variance of anisotropy, grain boundary fracture energy, and loading. Because spall occurs in the interior of the specimen, fundamental studies of crack nucleation and growth are needed to better understand surface velocity measurements. Within a cohesive approach to fracture, we illustrate that for anisotropic materials, increases in the fracture energy cause a transition in crack nucleation from triple-points to entire grain boundary facets. Analysis of idealized flaws reveals that while crack initiation and acceleration are strong functions of the fracture energy, flaws soon reach speeds on the order of the Rayleigh wave speed. Finally, simulated surface velocities of spalled configurations are correlated with microstructural evolution. These fundamental studies of nucleation, growth, and spall attempt to link atomic separation to the macroscopic spall strength and provide a computational framework to examine the evolution of spall and the impact on the simulated surface velocity field.     

Comparison of hypervelocity fragmentation and spall experiments with Tuler–Butcher spall and fragment size criteria

The present investigation compares predictive theories of dynamic spall and fragmentation with previously reported experimental data. In the experimental tests, aluminum spheres normally impacted thin aluminum plates at over approximately 4.5–7.5 km/s. Scaling features of the impact breakup phenomenon were explored through selected variation in sphere size and plate thickness. The principal diagnostic was high-resolution flash radiography. Fragment-size features of resulting fragment clouds were determined through detailed analysis of the recorded radiographs. Other investigators have measured the spall strengths for aluminum at comparable ultra-high strain rates. Spall strength amplitude and the corresponding strain rate dependence are principal results of the study. Existing dynamic fracture criteria are specialized here to the sphere impact spall and fragmentation event, and compared with empirical data. Velocity and strain rate scaling relations are developed for fragmentation size in the sphere impact event.     

混凝土材料层裂强度的实验研究

利用Φ74大尺寸Hopkinson压杆和混凝土长杆试件研究了混凝土材料的层裂强度及其应变率效应.入射的压缩波通过压杆透入试件并反射成拉伸波而形成层裂.实验中采取在试件上多点贴应变片,讨论了应力波在混凝土试件中传播的波形弥散和幅值衰减,并在考虑了损伤演化影响的基础上确定了试件材料的层裂强度.对某种普通混凝土在不同应变率下的测试显示层裂强度受应变率影响明显.结果表明,本文提出了一种测定混凝土层裂强度的有效方法.