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.     

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.     

Dynamic Tensile Fracture Behaviours of Selected Aluminum Alloys under Various Loading Conditions

Experiments investigating dynamic tensile fracture were performed on the extruded rods of 2024‐T4 and 7075‐T6 aluminum alloys under varying loading conditions. The initial yield stress and fracture strain of 7075‐T6 alloy obtained in spilt Hopkinson tension bar tests are higher than that of 2024‐T4 alloy. But the initiation fracture toughness and spall strength of 2024‐T4 alloy are higher than those of 7075‐T6 alloy in three‐point bending and plate impact experiments, which indicates that 2024‐T4 alloy has better crack initiation tolerance and stronger spall failure resistance. Based on metallurgical investigations by using optical and scanning electron microscopes, it is revealed that the microstructure has a profound effect on the dynamic tensile fracture mechanism of each aluminum alloy. The 2024‐T4 alloy is relatively brittle due to voids or cracks nucleated at many coherent CuMgAl₂ precipitate phases in the grain interiors, and the fracture mode is predominantly transgranular. The 7075‐T6 alloy exhibits relatively ductile fracture because voids or cracks growth is partly intergranular along the grain boundaries and partly transgranular by void formation around coarse intermetallic particles. The obvious differences of damage distribution and void coalescence mechanisms for 2024‐T4 and 7075‐T6 alloys under plate impact are also discussed.     

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.     

Fracture Parameters for Natural Rubber Under Dynamic Loading

Abstract: An experimental study was conducted to evaluate the tear energy of unfilled and 25 phr carbon black‐filled natural rubber with varying loading rates. The variation of the tear energy with far‐field sample strain rate between 0.01 to 10 s^?1 was found to be different from tensile strip and pure shear specimens. Above a sample strain rate of 10 s^?1, the tear energy calculated from either specimen was comparable. The differences in the tear energy derived from the tensile strip and pure shear specimens were attributed to differences in the local crack tip stress state and strengthening of the material due to strain‐induced crystallisation. Both of these factors resulted in crack speeds 3–4 times higher in the pure shear specimen as compared to the tensile strip specimen. Finite element analysis (FEA) indicated that fracture would initiate at the crack tip either when the strain energy density approached the material toughness or when the maximum principal stress and strain approached the material tensile strength and fracture strain, respectively. It was concluded that these parameters would be better than the tear energy in predicting fracture of natural rubber under dynamic loading.     

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.     

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.     

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.     

Dynamic fracture of bovine bone

True clinical fracture of bones in bovine, race horses or humans occur predominantly during impact loading (e.g. car accidents, falls or physical violence). Although static fracture tests provide an estimate of fracture toughness or R-curve behavior in bones, the static toughness values may be ill suited for predicting failure under dynamic loading conditions due to the visco-elastic response of bone (i.e. strain rate dependent properties). Despite decades of the study on deformation rate dependency of bone properties such as compression and fracture toughness, high-quality dynamic fracture data remain limited. Preliminary tests (compression and fracture toughness) have been conducted on dry and wet bovine bone under both static and dynamic loading conditions. While compression tests have been conducted with loading direction parallel and perpendicular to the bone axis (longitudinal and transverse, respectively), fracture tests were performed only in the transverse direction. The strain rate in compression tests varied between 10^− 3 and 10³ s^− 1, and the stress intensity rate varied between ∼10^− 3 and 10⁵ MPa√m/s. While low strain rate tests were conducted on conventional mechanical testing machines, high strain rate experiments were conducted on a split-Hopkinson bar under compression and a novel three-point bend configuration. The fracture morphology and the extent of damage of bone in each case were characterized using SEM, and an attempt is made to relate these to the rate dependent fracture toughness of the bone. It is believed that such understanding is crucial for mechanistic interpretation of bone fracture phenomenon and eventually for predicting bone failure reliably.     

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。     

Influence of hydrogen on microstructure and dynamic strength of lean duplex stainless steel

In this research dynamic strength is analyzed for the first time in a lean duplex stainless steel (LDS) uncharged and charged with hydrogen. In particular, the dynamic yield stress (Hugoniot elastic limit, HEL) and the dynamic tensile strength (spall strength) of LDS are studied. We also investigate the deformation mechanism of the LDS using metallurgical analysis. LDS was chosen since it has a mixed structure of ferrite (BCC, α) and austenite (FCC, γ), which allows an attractive combination of high strength and ductility. The dynamic loading was produced by accelerating an LDS impactor in a gas gun into an LDS target (uniaxial plate impact experiments). Data collection was performed by optical diagnostics through the velocity interferometer for any reflector device. The impact produces conditions of high pressure and high strain rate (~10⁵ s^?1), which can be comparable to explosions during extreme conditions of failure. In addition, investigations of hydrogen interaction with both crystal lattices were performed by means of X-ray diffraction (XRD) measurements. Several assessments can be made based on the results of this study. Using XRD analysis, it will be shown that even after hydrogen desorption some hydrogen remained trapped in the austenitic phase causing a small lattice expansion. After impact, a brittle spall was seen, which occurred through cavitation of cracks along both phases’ grain boundaries. Hydrogen increases the dynamic yield strength and when hydrogen content is sufficiently high it will also lead to higher spall strength. The relation between microstructure and dynamic strength of the LDS in the presence of hydrogen is discussed in detail.     

An investigation of the fatigue of CK45 steel in the as‐received state and after pre‐fatigue deformation

Fatigue failure, ratcheting behaviour and influence of pre‐fatigue on fatigue behaviour were investigated under uniaxial cyclic loading for CK45 steel at room temperature. The fatigue life was recorded for various stress ratios, and then, three mean stress models were considered. The Walker model showed an acceptable accuracy in comparison with Smith–Watson–Topper and Park et al. models. The ratcheting strains were measured for various loading conditions in order to evaluate the impact of mean stress, stress amplitude and stress ratio on ratcheting behaviour. The experimental results showed that the ratcheting strain increased with increasing mean stress, stress amplitude and stress ratio. In addition, the results of the post‐ratcheting‐fatigue tests showed that although the fatigue life decreased with increasing pre‐ratcheting strain (the ratcheting strain that is accumulated in pre‐fatigue), the loading condition that pre‐fatigue experiments were conducted has a significant effect on subsequent fatigue behaviour.     

Influence of Stress‐Aging Processing on Precipitates and Mechanical Properties of a 7075 Aluminum Alloy

Two‐step stress‐aging tests, as well as pre‐treatment plus stress‐aging experiments, are performed on a 7075 aluminum (Al–Zn–Mg–Cu) alloy. Influences of stress‐aging parameters on mechanical behavior and fracture mechanism are investigated through uniaxial tensile test and fracture morphology analysis. It is revealed that the stress‐aging dramatically influences the mechanical properties and fracture characteristics of the studied alloy, which is contributed to the sensitivity of microstructures to stress‐aging. When the alloy undergoes two‐step stress‐aging, the ultimate tensile strength and yield strength first increase and then decrease with the increased first step stress‐aging temperature, while the elongation first decreases and then increases. For the retrogression pre‐treated plus stress‐aged alloy, the yield strength first increases and then drops with the increased retrogression pre‐treatment time, while the ultimate tensile strength almost remains stable. Furthermore, the elongation continuously increases with the increased retrogression pre‐treatment time. The observation of fracture morphology indicates that the dimple‐type intergranular fracture is the main fracture mechanism for the two‐step stress‐aged and retrogression pre‐treated plus stress‐aged alloys.     

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.     

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。     

Limit velocity of fracture front and dynamic strength of brittle solids

The theories of propagation of brittle fracture fronts in solid materials are compared with experimental data. Instead of the well-known theory of the limit fracture stress the theory of limit velocity of fracture front is developed. Accordingly between the moving boundary at which the static strength is attained and the front of fracture the material can stand essential dynamic over-loadings. The experimental data on contained explosions in optically transparent intact blocks show that the limit velocity of brittle cracks front takes place immediately after the separation of the shock front and the front of brittle fracture. The hypothesis of the existence of limit front velocity leads to the conclusion that in the two-front structure of plane shock waves the amplitude of elastic precursors, known as “the Hugoniot elastic limit”, exceeds the value of ultimate static strength of a solid material and has to increase with increasing of a finite shock pressure. This effect is justified by a number of experiments with brittle materials. The analogue with the plane problem of a self-supporting brittle burst is shown. The explanation of exceeding of the ultimate static strength and of “the delay time” of fracture under the spall condition is given. The increasing of internal fractures, which is described by the dilatancy loosening of materials is discussed. The well-known laws of “the geometrical similarity” of contained explosions are in accordance with expression of the strength in terms of the ultimate stress but not in terms of Griffith's energy for creating of new cracks. The possibility of the regime of a limit front velocity of fracture at explosion motions in real rocks, for which the dilatancy has place, is discussed.     

An experimental investigation of rate-dependent deformation and failure of three titanium alloys

The response of three titanium alloys, Ti 6,4, Ti 550 and Ti 6,2,4,6, commonly used in aerospace applications, has been investigated at rates of strain between 10⁻⁴ and 10³ s⁻¹ in uniaxial tensile and compressive loading in ambient environment. This work identifies and discusses features of their behaviour that must be captured within material models developed for use in predictive modelling of response to in-service loading. That is, an increase in yield strength with increasing strain rate, a difference in yield strength between tensile and compressive loading regimes and, most importantly, the evolution of damage resulting in failure due to growth of voids in both tension and compression.     

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.     

Strain rate dependence of HPFRCC cylinders in monotonic tension

High-Performance Fiber-Reinforced Cementitious Composite (HPFRCC) materials exhibit strain hardening in uniaxial, monotonic tension accompanied by multiple cracking. The durability of HPFRCC materials under repeated loading makes them potentially suitable for seismic design applications. In this paper, the strain rate dependence of tensile properties of two HPFRCC materials in cylindrical specimens is reported from a larger study on strain rate effects in tension, compression and cyclic tension–compression loading. The cylindrical specimens were loaded in monotonic tension at strain rates ranging from quasi-static to 0.2 s⁻¹. To evaluate the impact of specimen geometry on tensile response, coupon specimens loaded in monotonic tension under a quasi-static strain rate were compared to corresponding cylindrical specimens made from the same batch of material. Tensile strength and ductility of the HPFRCC materials were significantly reduced with increasing strain rate. Multiple cracking, strain hardening, strain capacity, and the shape of the stress–strain response were found to be dependent on specimen geometry. SEM images taken of the fracture plane of several specimens indicated that pullout and fracture of the fibers occurred for both HPFRCC materials studied here.     

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.