Spall Strength Research Articles

Effect of stacking fault tetrahedron on spallation of irradiated Cu via molecular dynamics study

Stacking fault tetrahedron (SFT) is a common type of three-dimensional vacancy clustered defect in irradiated FCC metals and alloys, which has a great influence on the mechanical properties of the materials. Previous researches mostly concentrated on the effect of SFT on the mechanical response of material under quasi-static or constant strain rate loading condition, while very few studies focused on its influence on mechanical properties under the shock loading condition. Spallation is a typical failure mode of ductile metal material under shock loading, and the initial defects in the material have a great influence on the spallation behavior. In this study, molecular dynamics simulation is carried out to investigate the influence of SFT on spallation behavior of irradiated copper single crystal under different shock intensities. Copper single crystal with a perfect structural model is also investigated under the same simulation condition for comparison. The model is divided into two parts: the flyer and the target. The shock wave is generated by moving the flyer at a velocity in a range of 1.0–2.5 km/s along the [111] crystallographic orientation to achieve the desired shock-state particle velocity <i>U</i><sub>p</sub> in a range of 0.5–1.25 km/s. The time evolution of pressure, free surface velocity and corresponding microstructure, are analyzed in detail to illuminate the spallation behavior of the Cu with SFT. It is revealed that the SFT collapses during shock compression and induces the generation of dislocations and stacking faults in the material. Subsequently, spallation happens when the voids nucleate and grow in the region of dislocations and stacking faults. Moreover, the materials show different spallation behaviors at different shock intensities. When <i>U</i><sub>p</sub> ≤ 1.0 km/s, only elastic deformation occurs in perfect single crystal copper under shock compression, but in the copper with SFT, local defects appear and plastic deformation occurs due to the collapse of SFT under shock compression. The influence of SFT on spallation is most pronounced at a medium shock intensity. When <i>U</i><sub>p</sub> = 0.75 km/s, the local defects caused by the collapse of SFT provide a wider nucleation area for the voids and promote the heterogeneous nucleation of the voids, resulting in the decreasing of the spall strength. The void nucleation of single crystal copper with SFT is found to be much later than the perfect one and the rate of spall damage evolution also decreases due to energy dissipation during SFT’s collapse and plastic deformation. When <i>U</i><sub>p</sub> increases to 1.25 km/s, shock compression induces many defected atoms in both samples, so the SFT has little influence on the spall strength and spall damage of the materials.

Spall Strength of Shock-Heated Zirconium and Phase Diagram of Its High-Pressure Polymorphic Modification

Spall strength of zirconium heated by a strong shock wave to thousand-degree temperatures and that underwent transformations into denser polymorphic modifications was determined. Pressure profiles at the sample–soft barrier boundary were measured in spall experiments under flat one-dimensional loading. The equations of state of three polymorphic modifications of zirconium were constructed in the pressure range up to 50 GPa. Thermodynamic states of zirconium, which were calculated under conditions of experiments, in combination with results of measurements of pressure profiles, made it possible to determine the spall strength of zirconium heated in the shock compression–unloading cycle. The spall strength of zirconium was –2.8(7) GPa at 1027(70) K. Experimental pressure profiles were analyzed using the results of mathematical modeling of the performed experiments.

Incipient spallation of high purity copper under non-one-dimensional strain shock waves

A new spallation experimental method by using conical target is proposed. Based on the analysis of wave propagation, the basic principle of spallation experiment of conical target is discussed. Then incipient spallation of high purity (HP) copper under non-one-dimensional strain shock wave is studied experimentally by using a gas gun setup. The damage distribution characteristics and micro-mechanism of conical HP copper target are analyzed. The intrinsic relationship between the characteristics of free surface velocity profiles and damage evolution is explored. The results indicate that 1) continuous damage zones including different damage states appear in the conical HP copper target with initial spallation from the bottom of cone to the top of cone along the direction parallel to the cone surface, which is attributed to the spatial evolution of the amplitude and duration time of tensile stress in the conical target; 2) quantitative statistical analysis of damage inside conical HP copper target reveals that the nucleation and early growth of micro-voids are random, while the coalescence of micro-voids has significant localization characteristics; 3) the normal free surface particle velocity profiles with typical pull-back spallation signals at different locations of conical HP copper target are measured by multi-channel photon Doppler velocimetry. Comparing with the damage distribution characteristics, it is revealed that the spallation strength based on pull-back velocity is independent of damage, and is the critical nucleation stress of micro-voids. But the slope and amplitude of pull-back rebound velocity depend on damage evolution process, which relates to the change of damage evolution rate and stress relaxation caused by damage degree respectively.

Откольная прочность ударно-разогретого циркония и фазовая диаграмма в области существования его полиморфных модификаций высокого давления

Abstract Spall strength of zirconium heated by a strong shock wave to thousand-degree temperatures and that underwent transformations into denser polymorphic modifications was determined. Pressure profiles at the sample–soft barrier boundary were measured in spall experiments under flat one-dimensional loading. The equations of state of three polymorphic modifications of zirconium were constructed in the pressure range up to 50 GPa. Thermodynamic states of zirconium, which were calculated under conditions of experiments, in combination with results of measurements of pressure profiles, made it possible to determine the spall strength of zirconium heated in the shock compression–unloading cycle. The spall strength of zirconium was –2.8(7) GPa at 1027(70) K. Experimental pressure profiles were analyzed using the results of mathematical modeling of the performed experiments.

Spall strength of steel-fiber-reinforced concrete under one-dimensional stress state

A specially designed large-scale Hopkinson bar (φ100 mm) with hollow aluminum alloy bar as transmitted bar was used to measure the dynamic spall strength of steel-fiber-reinforced concrete (SFRC). The experimental results indicate that the steel fibers significantly enhance the spall strength of the SFRC. The enhancement of the spall strength from the steel fibers is linear with the product of the fiber influencing coefficient (α), the slenderness ratio (l/d), and the fiber volume fraction (Vf). Under dynamic loading, the value of α is higher than that observed under quasi-static loading, which is due to the enhancement of the dynamic bond strength between the fiber and the cement matrix. Furthermore, undulated fibers bring about a higher α than hooked fibers. Finally, an empirical formula is built to estimate the dynamic spall strength of SFRC under one-dimensional stress. The prediction was shown to be consistent with the experimental results. The steel fiber enhanced spall strength can be regarded as an important guideline in the design of high-performance concrete for improving the penetration resistance of protective structures.

Challenges to model the role of heterogeneities on the shock response and spall failure of metallic materials at the mesoscales

The predictive modeling of the experimentally observed behavior of metallic materials under shock loading conditions (wave structures, spall strengths) is a critical challenge toward the design of next-generation structural materials. This challenge is due to the lack of computational methods that can predict microstructural evolution at the mesoscales under dynamic loading conditions. While classical molecular dynamics simulations have been able to provide atomic-scale insights in the defect and damage nucleation/evolution mechanisms, the capability to have a direct comparison with experimental data at the same time and length scales is still a challenge. The current computational approaches require that several approximations be made either for the loading conditions or for the micromechanisms related to defect evolution and interaction at the mesoscales. This viewpoint discusses the insights obtained from molecular dynamics simulations of shock deformation and spall failure of heterogeneous metallic microstructures. An example Al–Ni microstructure is used to identify the critical atomic-scale phenomena that need to be addressed by the mesoscale methods when considering shock deformation and failure (spallation) at the mesoscales.

Shock and Spall in the Low-alloy Steel AF9628

The shock and spall behavior of tempered AF9628, an ultra-high strength (UHSS) martensitic low-alloy carbon steel, is investigated using gun-driven, symmetric, planar impacts. The study utilized laser velocimetry to obtain transmitted wave velocity histories that were analyzed to obtain the Hugoniot Elastic Limit (HEL), the shock Hugoniot, and the spall strength. The work was limited to the stress range below 13 GPa (below the e phase transition), and an HEL of 2.35 GPa and a spall strength of 6.8 GPa are reported. The HEL and spall strength of AF9628 are both above the typical values for inexpensive low-alloy steels, and only slightly below those for a much more expensive Aermet steel. The dynamic compressive yield strength (as calculated from the HEL) is only slightly higher than the quasi-static compressive yield strength when compared using a similar yield assignment convention, indicating a small, but positive, value of strain-rate sensitivity. The Hugoniot for AF9628, US = 0.67uP + 5.01 km/s, is in good agreement with other low-alloy martensitic steels for which data is available, and distinctly different than the Hugoniot for ferritic steels. The Hugoniot extrapolates to a bulk sound speed significantly higher than what is measured at ambient conditions, an incongruity that is unusual among metals and that the authors attribute to the unsteady nature of the shock waves generated in this work. Finally, it is suggested that there may be a relationship between dynamic compressive yield strength (calculated from the HEL) and dynamic tensile failure strength (the spall strength).

Shock deformation and spallation of Cu bicrystals with (1 1 1) twist grain boundaries

The shock deformation and spallation of Cu bicrystals with (111) twist grain boundary (GB) of different misorientation angles are investigated by using molecular dynamics simulations. The selected GBs include low angle (LAGB), near twin (NTGB) and intermediate angle (IAGB) twist GBs, and the shock direction is along the GB normal. It is demonstrated that the bicrystals are of lower Hugoniot elastic limit than single crystal, as the twist GBs provide dislocation sources for deformation. At the shock compression stage, GB plasticity at the LAGBs and NTGBs is initiated via reaction and dissociation of GB dislocations, and can be triggered by elastic shock wave more readily than that at the IAGBs, on which dislocation emission is homogeneous and irrelevant to initial GB dislocations. At the tension stage, the incipient spall for different twist GBs occurs at an identical shock strength, but is of different details in dislocation and void evolutions. With varying shock strength and misorientation angle, spall strength of the Cu bicrystals depends on whether GB plasticity is produced at the compression stage, and the values are consistent with that of Cu single crystal under similar shock loading conditions.

Numerical analysis of flyer plate experiments in granite via the combined finite–discrete element method

In this study, the combined finite–discrete element method (FDEM), which merges the finite element-based analysis of continua with discrete element-based transient dynamics, contact detection, and contact interaction solutions, is used to simulate the response of a flyer plate impact experiment in a Westerly granite sample that contains a randomized set of cracks. FDEM has demonstrated to be a strongly improved physical model as it can accurately reproduce the velocity interferometer system for any reflector plot and capture the spall region and spall strength obtained from flyer plate experiments in granite. The number and the distributions of preexisting fractures have also been studied to get better understanding of the effect of structural cracks on the mechanical behavior and the failure path of Westerly granite under high strain rate impact. These FDEM capabilities, in the context of rock mechanics, are very important for two main reasons. First, the FDEM can be further applied to many complex large-scale problems such as planetary impact, rock blasting, seismic wave propagation, characterization of material failure around explosive crater formations, and detection of hydrocarbon flow in petroleum industry. Second, it can be used to validate high strain rate impact experiments and essentially, via virtual experimentation, replace these high-cost experiments by very cost- and time-effective simulations.

Understanding and predicting damage and failure at grain boundaries in BCC Ta

Understanding the effect of grain boundaries (GBs) on the deformation and spall behavior is critical to designing materials with tailored failure responses under dynamic loading. This understanding is hampered by the lack of in situ imaging capability with the optimum spatial and temporal resolution during dynamic experiments, as well as by the scarcity of a systematic data set that correlates boundary structure to failure, especially in BCC metals. To fill in this gap in the current understanding, molecular dynamics simulations are performed on a set of 74 bi-crystals in Ta with a [110] symmetric tilt axis. Our results show a correlation between GB misorientation angle and spall strength and also highlight the importance of GB structure itself in determining the spall strength. Specifically, we find a direct correlation between the ability of the GB to plasticity deform through slip/twinning and its spall strength. Additionally, a change in the deformation mechanism from dislocation-meditated to twinning-dominated plasticity is observed as a function of misorientation angles, which results in lowered spall strengths for high-angle GBs.

Study on equation of state and spall strength of sintered Nd-Fe-B magnets

The experiments were carried out in a gas gun system to examine the equation of state (EOS) below or near the Hugoniot elastic limit (HEL) for the sintered Nd-Fe-B magnets. A laser velocity interferometer system for any reflector (VISAR) was used to measure the shock and particle velocity of the specimens. The obtained EOS data indicated that the EOS at high pressure could not be extrapolated to the lower pressure below or near the HEL for the Nd-Fe-B magnets. The spall strength of the Nd-Fe-B magnets was determined in the gas gun plane spall tests using the analysis of the free surface velocity profile of the specimens measured with the VISAR. It is found that the spall strength of the Nd-Fe-B magnets is dependent on the strain rates and larger than the tension strength of the magnets in the dynamic Brazilian tests.

The Dynamic Strength of ZrO2-Based Ceramic Materials Manufactured by Additive Technology

Some specimens of zirconia-based ceramic and ceramic composite materials were manufactured by additive technologies. The experimental studies of the manufactured specimens under shock-wave loading were performed. Using an analysis of the full wave profiles recorded for these specimens on a laser interferometer in the process of their shock compression with an amplitude of 6.8 and 13.8 GPa, the Hugoniot elastic limit and spallation strength of ceramics were determined.

Residual strength and microstructure of fiber reinforced self-compacting concrete exposed to high temperatures

One of the most important processes of physical deterioration in the concrete structures is the exposure to high temperatures that influences their durability and stability during service life. Hence, due to the importance of continuous service of the structure and safety of the residents, it is necessary to identify and evaluate properties of concrete materials after being exposed to high temperature conditions. This study implemented an experimental program to evaluate the effect of fly ash, steel fibers, and curing conditions on the mechanical properties, fracture energy, and microstructure of the self-compacting concrete at high temperatures. The study also evaluated physical-mechanical properties, including compressive strength, splitting tensile strength, flexural strength, fracture energy, ultrasonic plus velocity, weight loss, and images of SEM before and after exposure at 23, 110, 200, 400, and 600 °C. Experimental results showed that the loss of compressive strength of the specimens up to 200 °C is almost insignificance, but it will be 40% and 64% when the temperature increases by 400 °C and 600 °C, respectively. The steel fibers prevent the cracks expansion and contribute to the spalling and mechanical residual strength. However, as temperature increases, the slope of the ascending part (flexural hardness) of the load-deflection curves and fracture energy decrease. Moreover, microstructure analysis represents a close relationship between mechanical properties and different cracks and pores structure of the fibers-aggregates-cementitious matrix interface. Therefore, data obtained from the results of this experimental study were used to develop models, which predict mechanical strength of fiber reinforced self-compacting concrete and provide simplified relationships as a function of temperature.

Spall Fracture of a VNZh-90 Alloy Under a Shock Wave Load

Based on the results of experiments carried out using a gas gun, data are obtained on the fracture of a VNZh-90 alloy (90% W-7% Ni-3% Fe) under a shock wave load in a pressure range of 2.5–4.0 GPa. Spall strength, which is a function of the degree of fracture and varies in a range of 1.00 to 1.25 GPa, and the nature of fracture are determined. Metallographic analysis is used to determine the damage parameter values. It is revealed that, under these conditions, the fracture comprises several stages, occurs in a (Ni-Fe) bond, and the tungsten particles do not fracture. It is shown that experimental results are in good agreement with the results of numerical calculations.

Spallation of polycarbonate under plate impact loading

We investigate spallation of polycarbonate under plate impact loading. The Hugoniot equation of state up to ∼1.3GPa (corresponding to a peak particle velocity ∼380m/s) is obtained, and spall strength and corresponding strain rates are determined at peak shock stresses up to ∼2.4GPa (corresponding to a peak particle velocity ∼600m/s). With increasing shock strength, the transition from strain-hardening to softening at shock states occurs as a result of shock heating; spall strength remains approximately constant, followed by a rapid drop upon strain softening. Release/tensile melting occurs at higher impact velocities. Three-dimensional void configurations of the postmortem samples are obtained via X-ray computerized tomography. The small voids are flat and curved for low-speed shots but become ellipsoidal for high-speed shots, and their coalescence leads to different shapes likely due to different damage mechanisms.

Response of poly(methyl methacrylate) to shock-wave loading at elevated temperatures

The shock wave response of commercial poly(methyl methacrylate), PMMA, in the vicinity of its glass transition temperature (Tg = 110–120 °C) was studied in two series of impact experiments, the first of which was aimed at the variation of the PMMA spall strength with temperature. The purpose of the second series was the effect of temperature on the PMMA Hugoniot. It was found that the spall strength of PMMA experiences an abrupt twofold drop at ≈120 °C. The PMMA Hugoniot Us=C0+sup was found to be that of a virtually elastic solid with C0 close to the longitudinal speed of sound, cl, at room temperature and transformed above Tg into a viscous material with no shear strength and C0 close to the bulk speed of sound, cb.

Shock induced plasticity and phase transition in single crystal lead by molecular dynamics simulations

Shock-induced plasticity and phase transition in single crystal lead are investigated by nonequilibrium molecular dynamics simulations. Under dynamic shock loading, the appearance of plasticity in materials precedes that of phase transition. Plasticity mainly causes two effects: one is that plasticity has a significant relaxation effect on shear stress, and the other is that deformation twinning serves as important nucleation sites for the phase transition. This twinning is caused by mutual impediments among different cross-slips and {111} slips. There are three main stages in the dynamic phase transition process of lead: fcc → bcc-like phase transition, plasticity, and hcp phase formation and growth. Moreover, phase transition has a more significant relaxation effect on shear stress, which relaxes the shear stress to a minimum value. The spall strength of lead decreases as the shock intensity increases, but its rate of decrease under different shock intensities is different. Plasticity, especially phase transition, would obviously result in a lower rate of decrease in spall strength.

Cup-cone structure in spallation of bulk metallic glasses

A special spallation morphology in bulk metallic glass, named as the “cup-cone” structure, is of particular interest since it manifests a unique “ductile–brittle” transition. To gain insights into the underlying mechanism for the formation of a cup-cone structure, we conduct planar impact experiments at various impact velocities, as well as finite element method analysis. Spall strength increases with increasing impact velocity. Scanning electron microscopy and X-ray computed tomography are performed on postmortem samples to characterize cup-cone structures; their average size and spacing decrease as impact velocity increases, and they dominate fracture morphology at high impact velocities. Cups and cones are generally distributed on the side away from and on the side closer to the target free surface, respectively. The initial nucleation sites of voids become the conical vertices of cup-cones, and the subsequent nucleation sites form along the conical surface and coalesce into the cracks and fracture surfaces.

Spall Strength of Shock-Heated Hafnium and the Equation of State of Its Polymorphic Modifications

We determined the spall strength of hafnium heated by a loading shock wave to thousands of degrees and subjected to transformations into denser polymorphic modifications. To achieve this goal, the following tasks were solved. The pressure profiles at the interface between the sample and soft buffer material in the spall experiments with flat, one-dimensional loading are measured. The equations of state of three polymorphic modifications of hafnium are constructed in the pressure range up to 100 GPa. The thermodynamic states of hafnium were calculated under the conditions of the performed experiments, which, together with the results of measurements of pressure profiles, made it possible to determine the spall strength of hafnium heated in a cycle of shock compression–unloading. The spall strength of hafnium was –4(1) GPa at a temperature of 1680(380) K. The spall experiments were mathematically simulated in the framework of a one-dimensional hydrocode.

Estimation of spalling strength of sandstone under different pre-confining pressure by experiment and numerical simulation

Spalling failure is a common underground engineering disaster, particularly in deep environments with high geo-stress and strong stress disturbances. Therefore, the further investigation of the spalling behaviour of rock under different pre-confining pressures is of considerable importance. In the presented work, a modified split Hopkinson pressure bar (SHPB) system is modified with a pre-confining loading device that can apply pre-static loads to Φ50 mm × 300 mm specimens. The system is employed to study the spalling characteristics of rock specimens subjected to full pre-confining pressure. Spalling tests of Φ50 mm × 300 mm rock specimens under different pre-confining pressures were conducted. The experimental results indicated that spalling failure was influenced by pre-confining pressure. Furthermore, numerical simulations with the same loading conditions as the experiments were conducted using the finite element software, LS-DYNA, and the spalling strengths of the rock specimens under different pre-confining pressures were obtained based on the improved stress wave analysis method. The results indicated that the stress wave analysis method in view of numerical simulation can effectively be used for calculating the spalling strength of rock and rock-like material under pre-confining pressure. The spalling strength of the rock specimens increased first and then decreased as the pre-confining pressure increased.