A meso-model of spalling with thermal coupling for hard metallic materials

Study and modeling of physical mechanisms of spalling observed via plate impact experiments for two industrial alloys are the subject of this paper. Because spalling is a specific kind of fracture, which is loading history dependent, the aspects of the initial microstructure and its evolution during plastic deformation are very important. In order to understand better the physical mechanisms of spall, numerous scanning electron microscopy pictures of the free surface created by spalling have been taken for two materials, a hard aluminum alloy and an armor steel. It has been confirmed that the microstructure has a direct influence on the mechanism of nucleation, growth and coalescence of micro-cavities or micro-cracks by means of distribution of nucleation sites and decohesion between the harder particles and the softer lattice. The results of measurements in the form of statistical distribution of horizontal micro-segments of fractured surfaces of targets, corresponding to quasi-brittle fracture, and vertical micro-segments, corresponding to ductile or adiabatic shear banding, all along the entire cross-section of a target, are reported for armor steel. As a result a new model has been proposed, based on the meso-scale approach. The model is in agreement with physical mechanisms which are present during spall fracture.     

The spall strength of silicon carbide and boron carbide ceramics processed by spark plasma sintering

The spall strength of silicon carbide (SiC) and boron carbide (B₄C) ceramics processed by Spark Plasma Sintering (SPS) has been studied as a function of the loading stress. In the course of the planar impact experiments, the velocity of either the sample free surface or of the sample–window interface was continuously monitored by a Velocity Interferometer System for Any Reflector (VISAR). With the increase of impact stress the spall strength of both ceramics, increases initially and then declines monotonously until it vanishes almost completely, as the impact stress approaches the respective Hugoniot Elasic Limit (HEL). The mechanisms that may account for that behavior and, in particular, the role of the compressive wing cracks in the onset of the spall strength decline are discussed.     

The computer simulation of an explosive test rig to determine the spall strength of metals

Spall fracture is produced by a tensile wave after reflection of a compressive shock wave at a free surface. The original shock wave may be initiated by the detonation of explosive in contact with the material or by the impact of a high velocity projectile. An explosive test rig has been devised where a shock wave produced by explosive detonation is attenuated by propagation along a bar. The degree of spall fracture in a sample on the other end of the bar depends on the bar length. A computer simulation, using the EPIC-2 code, has been made and compared to published values of the free surface velocities for various bar lengths. Good agreement was obtained by careful choice of input parameters used in the γ-law burn of the explosive, and when correction of the experimental values was made for the change in free surface velocity that occurs when the material has a finite spall strenght. The computer simulation enabled extrapolation of the pressure values to be made to longer bar lengths, to obtain the limit of incipient spall fracture. Also, information was obtained on the shock pulse shape and the pressure distribution across the bar. The spall strength of a 6061-T6 aluminium alloy was found to be 1400 MPa, in good agreement with published values for a similar pulse duration.     

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.     

对于层裂强度传统测定方法有效性的讨论

基于Gathers的工作,对试件靶背部贴有低阻抗材料的平面冲击波致层裂试验,导出了传统方法测定层裂强度的一般方程,在无低阻抗材料且作声学近似的条件下,即为Novikov的测定层裂强度的方程。研究指出,传统方法确定的层裂强度测定方程仅仅可能对采用瞬时层裂准则得到的数值模拟的层裂信号有效。数值模拟表明,层裂面上的由损伤演化引起的应力松弛严重影响层裂片中的应力剖面,因而影响靶板自由面速度历史或靶板-低阻抗材料界面应力历史。研究揭示,传统方法导出的估算层裂强度方程由于没有计及应力松弛,对于实测的靶板自由面速度历史或靶板-低阻抗材料界面应力历史并非有效。     

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。     

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.     

On the validity of the traditional measurement of spall strength

Basing on Gathers's work, a set of general equations for traditional determination of spall strength is given under some assumptions for the planar spall experiment with a low-impedance buffer placed behind the target. In the case of no buffer, the equations become the traditional expression given by Novikov within the acoustic approach. It is revealed that the propagation of wave profile in the spall scab is affected seriously by the damage evolution on the spall plane. Therefore, the free surface velocity profile of target or the stress profile of interface between target and low-impedance buffer depends critically on the damage evolution on the spall plane. It is concluded that the traditional determination of spall strength without taking into account the stress relaxation due to the damage evolution on the spall plane could be valid only for the numerically simulated ‘pullback’ by the simple spall cutoff criterion but not valid for the experimental ‘pullback’ in general.     

轴向钢筋增强混凝土一维应力层裂实验研究

基于φ74 mmSHPB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。     

Effect of Grain Size on the Spall Fracture Behaviour of Pure Copper under Plate‐Impact Loading

The effects of grain size on the spall response were investigated for high purity copper materials by plate‐impact experiments including real‐time measurements of the free surface velocity profiles as well as post‐impact fractography studies on the soft‐recovered samples. High purity copper plates were cold rolled and heat treated to produce recrystallized samples with average grain sizes of 78, 273 and 400 μm, respectively. The spall strength estimated from the free surface velocity profile is nearly constant with no significant effect on the grain size. However, differences are observed in the acceleration rate of velocity rebound beyond the minima. This may be attributed to the effect of grain size on the growth rate of damage. Metallographic analyses of the fracture surface show that the characteristic feature of the fracture surface clearly depends on the grain size. In the 78‐ and 273‐μm samples, the fracture surfaces are decorated with large, high‐density ductile dimples suggesting that the preferential failure mode is ductile intergranular fracture. In the 400‐μm samples, the fracture surfaces have a rock candy appearance with small, high density brittle dimples as well as large ductile dimples suggesting that the fracture mode is a mix of both brittle intergranular fracture and ductile transgranular fracture.     

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.     

Spall investigations for LY12 Al using triangular waves

Spall of LY12 Al was investigated using experimental techniques based on the dynamics of shock wave attenuation to produce decaying triangular shock pulse in the sample of plate-impact spall tests. Spall signals were measured by monitoring the time-resolved free surface velocity histories of the targets with VISAR techniques. Targets were soft recovered and two spall planes for the high-stress triangular wave experiment were observed. For triangular wave spall plane location is a variable and there can be several regions of relatively high tension. The void coalescence-based spall model presented by the authors is used in simulating the spall tests. Computed free surface velocity histories of targets and damage distributions through the thickness of the targets are compared with the VISAR data and the observed damages in soft recovered targets, respectively. It is noted that the modeling of spall process caused by triangular waves can be seriously influenced by the artificial viscosity, the constitutive equations of the sample and the spall fracture model.     

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.     

Critical stresses and strains at the spall edge of a case hardened bearing due to ball impact

Short spall propagation times of failing main shaft ball bearings of aircraft engines are a serious safety concern for single engine aircraft. Bearing designers would like to understand the impact of four variables namely (i) ball material density, (ii) subsurface residual stress, (iii) gradient in yield strength with depth (case hardening), and (iv) raceway surface hardness/yield strength that are thought to affect spall propagation. Extensive spall propagation experiments have been conducted at AFRL, Ohio in the past few years to address this issue. However, a detailed mechanistic analysis of these experiments has not been performed. This work presents an elastic–plastic finite element (FE) model that simulates a ball impacting a spall edge to determine the relative contributions of the four material variables on spall propagation. The magnitude and extent of damage of the spall edge material is determined based on critical stresses and plastic strains induced by the ball impact. The results indicate that the influence of ball density is greatest on inducing damage at the impacted spall edge when compared to the other three properties, which also agrees with the hybrid bearing spall propagation tests conducted at AFRL.     

Spall experiments for the measurement of the tensile strength and fracture energy of concrete at high strain rates

To study the behavior of concrete under dynamic loads, a Hopkinson-Bar was set up and used. Cylindrical concrete specimens were positioned at the end of the incident bar and the spall event was studied. The purpose of this contribution is to explain the measurement of the tensile strength and the specific fracture energy. To determine the tensile strength, the measured free surface velocity at the end of the specimen is used. The method is known from plate impact experiments and was adapted to Hopkinson-Bar experiments. The measurement of the specific fracture energy is more difficult in spall experiments. It cannot be measured directly as it can be done in direct tension tests. A method is proposed where the fracture energy is calculated from the change of the fragment velocities while cracking takes place.The experimental results of the investigation complete the data of the literature in regard to higher strain rates. In former investigations conducted by Weerheijm (PhD thesis. Delft University of Technology: Delft University Press; 1992), an increase of the specific fracture energy with the strain rate or the crack opening velocity was not seen. The experiments performed within this contribution consider the fracture behavior at higher strain rates. A sharp increase in the specific fracture energy at this strain rates was measured. The following paper describes the method and the experiments to measure the tensile strength and the specific fracture energy in spall experiments.     

Optimization of the Outer Laser-Induced Spalling

We develop an analytic model of the outer spalling fracture caused by pulsed laser loading and determine the optimal values of the pulse energy corresponding to the maximum thickness of spalling and the most efficient transformation of the pulse energy into the recoil momentum of the spall. These values can be used for the optimization of the outer laser spalling.     

Dynamic fracture of tungsten heavy alloys

Dynamic fracture of tungsten heavy alloys was induced by two different test techniques. The first was spall (e.g., 1-D strain fracture). The second was transverse impact, as occurs in a yawed penetrator. Spall failure is stress driven, and spall stress corresponds to the threshold for void formation, which is 2.6 GPa for a 91% WNiCo alloy and 2.1–2.5 GPa for a 95% WNiFe alloy. Yaw-induced fracture, on the other hand, is strain driven. Surface flaws can provide fracture sites. At the meso scale, grain cleavage is mainly responsible for transverse fracture. Grain fracture also appears to play a critical role in the initiation of spall fracture.     

A fracture mechanical treatment of free edge stress singularities applied to a brazed ceramic/metal compound

The theoretical fracture mechanical treatment of craek problems in regular stress fields is extended to account for singular stresses as occur in bi-material systems whenever a discontinuity in material properties and geometry exists. The singular stress fields are derived for arbitrary material combination and geometry and the global stress state as occurs in a real compound is obtained by Finite Element (FE) calculations. Then especially the mode I stress intensity factors are calculated for semi-elliptical surface cracks in the ceramic component of a brazed ceramic/metal joint. Critical crack sizes are determined for failure analysis of the compound.     

一种新的简化延性层裂模型

重新定义损伤、应用Cochran-Banner模型中的强度函数,提出了一种新的简化延性层裂模型。新模型抛弃了Cochran和Banner为计算他们所定义的损伤所作的基本假设:一旦微损伤形成,使微损伤演化远远易于使固体进一步发生体积应变。从而修正了差分微元中固体比容的计算。强调指出,选定重新定义的损伤以及强度函数或应力松弛方程提供了确定损伤的可能,排除了任何外加的损伤演化方程。在新的简化延性层裂模型中,一旦拉伸应力达到层裂强度,重新定义的损伤将由强度函数确定的应力松弛方程、计及损伤的能量守恒方程、状态方程以及本构方程等一系列封闭方程组确定。若干平板撞击致层裂实验的理论计算与实验结果已被比较。新模型中仅含两个参数:层裂强度及临界损伤度,它们的确定能使在一定初、边值条件下的层裂试验数值计算结果与实验测得的靶自由面速度历史或靶-低阻抗材料界面应力历史以及回收观测的层裂面上的损伤一致。     

High-rate deformation and spall fracture of hadfield steel under action of high-current nanosecond relativistic electron beam

Features of the plastic deformation and dynamic spall fracture of Hadfield steel under conditions of shock wave loading at a straining rate of ∼10⁶ s⁻¹ have been studied. The shock load (∼30 GPa, ∼0.2 μs) was produced by pulses of a SINUS-7 electron accelerator, which generated relativistic electron bunches with an electron energy of up to 1.35 MeV, a duration of 45 ns, and a peak power on the target of 3.4 × 10¹⁰ W/cm². It is established that the spalling proceeds via mixed viscous-brittle intergranular fracture, unlike the cases of quasi-static tensile and impact loading, where viscous transgranular fracture is typical. It is shown that the intergranular character of the spall fracture is caused by the localization of plastic deformation at grain boundaries containing precipitated carbide inclusions.