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.     

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.     

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.     

爆炸荷载作用下地下结构的震塌破坏模型研究

过去对地下结构震塌破坏的研究,往往是在假设地下结构为半无限厚的基础上进行的.基于层状介质中应力波的界面效应理论,提出了能考虑地下结构实际厚度的震塌破坏模型.通过实际算例,得到了应力波在地下结构中的传播规律,分析了岩石性质对地下结构局部震塌的影响.分析方法与结论对类似问题也有参考价值.     

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.     

The effect of temperature on the impact behaviour of glass/polycarbonate laminates

A systematic investigation has been performed into the mechanisms that lead to spall of bullet-proof glass/polycarbonate laminate constructions at low temperatures. A range of techniques were deployed including liquid jet impact, high speed photography, and a light gas gun. Spall formation was shown to take ca. ten times longer than a simple shock-wave overlap mechanism would imply. However, a number of experimental observations including the radii of fracture bands in the glass and fractographic examination of the edge of the polycarbonate spalls led us to consider a more complex elastic wave analysis: the reinforcement of Rayleigh surface waves by tensile elastic waves reflected from the various boundaries within the laminate. This predicted that the radius of the spall should be proportional to the thickness of the front glass layer. Comparison with the results of full-scale tests confirmed that this was indeed the case.     

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.     

冲击压缩下氧化铝陶瓷中的延迟破坏实验研究

利用轻气炮对不同厚度的氧化铝陶瓷试件进行了平板冲击实验,并借助激光速度干涉仪(VISAR)测试了试件的自由面速度历程。实验结果显示,自由面速度曲线上存在表征破坏波出现的二次压缩信号。根据实验结果计算获得了破坏波穿过试件的运动进程,并确定了试件中破坏波的运动轨迹近似为一条直线,得出在冲击压力为7.16GPa时试件内破坏波波速约为5.051km/s,破坏延迟时间约为0.105μs。最后简单分析了该现象产生的物理机制。     

Bubble-induced cavitation effect upon solid surfaces

The dynamic damage during cavitation erosion is of a spall nature and results from the interference of rarefaction waves. Spherical shock waves, which arise due to the collapse of cavitation bubbles, generate shock waves in the target. The rarefaction waves appear when the velocity of the contact boundary decreases below the sound velocity in the target material and the shock waves emerge at the free surface. The coordinate of the rarefaction wave formation site determines the zone of potential damage. The interference of rarefaction waves creates the spall channel crack, near which the coaxial cylindrical cracks are formed-as a rule, in the dynamic fatigue regime-in the course of subsequent loading.     

The Formation of Elastoplastic Fronts and Spall Fracture in AMg6 Alloy under Shock-Wave Loading

Full wave profiles were monitored by the laser interferometry method by means of a VISAR laser Doppler velocimeter under shock-wave loading of samples of AMg6 aluminum alloy. Analysis of these profiles was used to study the laws of elastic precursor formation and its amplitude variation during elastic–plastic transition front propagation in samples loaded by a shock wave of variable intensity. Critical stresses leading to the spall fracture of samples were determined as dependent on the strain rate under unloading.     

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。     

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.     

Cavitation erosion as a kind of dynamic damage

The purpose of this work is to show that the spherical shock waves arising in a liquid during cavitation bubble collapse can lead to formation of deep needle-like pits on the solid surface. The nature of dynamic damage during cavitation erosion is the spallation caused by interference of rarefaction waves. Rarefaction at spherical wave impact arises when the velocity of contact surface boundary becomes less than the speed of sound in a target. If the tension caused by the focused rarefaction wave exceeds the spall strength of material, channel spall cracks can arise. At low pulsed loading, spall cracks are formed in a dynamic fatigue mode. Needle-like damage arises upon focusing rarefaction waves. In terms of our model, a system of cylindrical spall cracks is consecutively formed around a deeper axial spall needle-like crack. Upon subsequent loading, each crack acts as a source of new rarefaction wave. Newly formed cylindrical spall cracks suppress the growth of the cracks of previous generation and give birth to the cracks of next generation. A distinctive feature is that the cracks are first formed at the periphery of damageability zone, subsequent cracks having a lower depth.     

A modified Cochran–Banner spall model

The original Cochran–Banner spall model was modified to suit the usual definition of damage and to abandon the simplifying approximation as unnecessary. The strength function given by Cochran–Banner was maintained using the redefined damage and the correction concerning the volume of the mesh cells was realized considering it unnecessary to expect that it is much easier to open microcracks once they are formed than to strain the solid further. In the case of abandoning the simplifying approximation made by Cochran–Banner to calculate the damage, the redefined damage also does not become a new independent variable for which new dynamic laws would need to be specified. Once the spall strength was reached, the damage would be only determined by a series of closed equations including the stress.relaxation relationship given by the strength function, the energy conservation equation, the equation of state and the constitutive equations for the damaged aggregate. The modified Cochran–Banner spall model also included only two parameters: the spall strength and the critical damage, which relate to material properties and specific loading conditions. Comparison of theoretical and experimental results for some spall tests was performed. It was found that the computed free surface velocity profile of target or stress profile of interface between target and soft buffer in plane spall tests was sensitive to the spall strength and the critical damage in the modified Cochran–Banner spall model.     

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.     

Spall in non-one-dimensional shock waves

Consideration is given to non-stationary shock wave on spallation. Spall strength can be written as (i) pressure — particle velocity diagram in a one-dimensional case, and (ii) pressure — angle of turn flow diagram in a two-dimensional case. Experimental procedure involves (i) loading of the explosive by sliding detonation and (ii) orthogonal flash X-raying. In this way, some metals in particular low-melting ones and plastics as well as liquids have been studied based on the present results and those of other researchers. The dependences of spall strength — deformation rate have been obtained for substances studied in the form of power or linear functions. Some aspects of spallation and of accompanying effects on the base relations obtained are discussed.     

Pulse Compression and Tension of Composites under Shock-Wave Impact

High Temperature - In this paper, we study the shock compressibility and spall strength of composites reinforced with carbon fibers and glass fibers using a VISAR laser interferometer. A two-wave...     

Dynamic fracture and spall in aluminum with helium bubbles

Investigation of the dynamic properties of aluminum targets with helium bubbles is presented. The targets were obtained by melting pure aluminum with 0.15% wt.¹⁰B powder. The solid targets were neutron irradiated to get homogeneous helium atoms inside the aluminum boron 10 matrix according to the reaction ¹⁰B + n → ⁷Li+⁴He. Helium atoms further accumulated into bubbles by diffusion in the bulk aluminum. Shock wave experiments were performed by accelerating the aluminum impactor into different targets: (1) pure aluminum, (2) Al-¹⁰B, and (3)Al-¹⁰B with different radii and concentrations of helium bubbles. The spall strength was calculated and analyzed from the free surface velocity measurements. It was found that the addition of ¹⁰B in pure aluminum reduces the spall strength of the material by 25–32%. However, irradiated sample with helium bubbles was found to have higher spall strength compared to samples without bubbles. This finding was reconstructed by numerical simulations. The impacted targets were collected after the impact experiments and examined by TEM. These targets were compared to TEM pictures before the impact. The number of helium atoms in the bubbles was calculated from the electron energy loss spectrum (EELS). TEM comparison between the pre-impacted and the impacted targets shows bubbles coalescence and EELS measurements demonstrate a reduction of the helium atoms concentration in the bubbles from ~10²⁸ m^?3 before the impact to ~10²⁷ m^?3 after the impact.     

Effect of an impact-generated gas cloud on entrained surface boulders and spall ejecta

The purpose of this investigation is to study the effect of an impact-generated gas cloud on the size-velocity distribution of large, solid ejecta fragments that become entrained in it, with particular reference to the possible Martian origin of the SNC meteorites. The entrainment both of loose surface boulders and of the early-time, large-size, high-velocity spall component of the crater ejecta is modeled numerically. Surface boulders from as far as 40 km from the center of impact can be accelerated by the high velocity leading edge of the gas cloud to velocities in excess of Martian escape velocity (5 km/s), but are generally crushed by the acceleration. Spall fragments become entrained later and nearer the center of the gas cloud, where gas velocities are much less. High velocity spalls are decelerated by the gas and low velocity spalls are accelerated by the gas, but no spalls ejected at < 5km/s are accelerated to velocities 5km/s. An impact-generated gas cloud is thus expected to scour the pre-existing surface of loose material and to change the size-velocity distribution of spall ejecta, but does not sufficiently enhance the velocities of crater ejecta to explain the Martian origin of SNC meteorites as large rocks.     

冲击压缩下A95陶瓷动态力学特性数值模拟

采用ANSYS/LS-DYNA数值模拟了平面冲击波压缩下A95陶瓷的自由面质点速度历程,将数值模拟结果与平板冲击压缩实验结果进行了对比分析.数值模拟结果表明采用JH-2材料模型能够较好地模拟陶瓷类材料在强动载荷作用下的物理力学性能.