Planar Shock Loading Research Articles

Experimental and theoretical investigation of failure mechanism in Al2O3/SiC composite under plane shock waves

The investigation of fracture and fragmentation is essential for evaluating the protection performance and structural design of ceramic armour. This paper focused on the dynamic failure and fracture mechanisms of the fine-grained Al2O3/SiC composite subjected to plane shock waves. The macroscopic shock response characteristic was determined through a series of plane impact tests, which included the Hugoniot curves of the composite. The results indicated that the fracture mechanism is significantly influenced by specific stress characteristics. The transgranular fracture in large grains and intergranular fracture in small grains exhibit obvious local plastic deformation characteristics. Moreover, the presence of second-phase SiC particles markedly influences both crack propagation and the microfracture mode of the composite. Lastly, a statistical analysis of the ceramic fragments was conducted after the soft recovery of specimens in impact experiments, and analytical models were developed and modified to predict the distribution of fragments under plane shock loading.

Shock response of single-crystal boron carbide along orientations with the highest and lowest elastic moduli

The response of monocrystalline boron carbide to planar shock loading has been investigated using molecular-dynamics simulations, along crystal orientations with the highest and lowest elastic moduli. While shocks of intensity lower than the Hugoniot elastic limit (HEL) generate quasilongitudinal and quasitransverse waves, an elastic precursor trailed by inelastic waves is observed when HEL is exceeded. Bond breakage, accompanied by temperature rise, is observed to be the primary mode of deformation under the inelastic waves. Higher shock intensities (particle velocity, ${U}_{p}>2.5\phantom{\rule{0.16em}{0ex}}\mathrm{km}/\mathrm{s}$) generate a deformation shock front, which induces loss of shear strength along with a considerable loss of crystalline order. Boron carbide is also revealed to exhibit two distinct deformation regimes. While shear strength increases with ${U}_{p}$ in the first regime $({U}_{p}\ensuremath{\le}2.5\phantom{\rule{0.16em}{0ex}}\mathrm{km}/\mathrm{s})$, a monotonic reduction is observed in the second $({U}_{p}>2.5\phantom{\rule{0.16em}{0ex}}\mathrm{km}/\mathrm{s})$. The latter regime is also characterized by a convergence in the shock Hugoniot curves obtained along the two loading directions, indicating that the Hugoniot state of boron carbide may be independent of crystal orientation for ${U}_{p}>2.5\phantom{\rule{0.16em}{0ex}}\mathrm{km}/\mathrm{s}$. Finally, it is shown that the simulation-derived hydrostat curve presented in this work is coherent with experimental data up to 140 GPa and provides an accurate basis for assessing residual strength of boron carbide under shock conditions.

Nonlinear thermomechanics for analysis of weak shock profile data in ductile polycrystals

Modeling of shock compression of isotropic, polycrystalline elastic-plastic solids that deform by dislocation glide is undertaken. Internal energy density of the material depends on a thermoelastic Eulerian strain tensor, entropy, and an internal state variable representative of dislocation density. Dislocation glide is incompressible, but inelastic volume changes arising from residual local strain fields and core effects of dislocations are captured. A semi-analytical method is advanced for extracting inelastic constitutive response information from particle velocity histories of polycrystalline samples under planar shock loading. The only parameters entering the procedure are fundamental thermoelastic properties and assumed bounds on the fraction of plastic work corresponding to energy storage of generated dislocations in the lattice. Densities of statistically stored and geometrically necessary dislocations, in addition to shear stress, plastic strain, plastic strain rate, and temperature, are outcomes of the analysis. The model is implemented for polycrystalline aluminum and copper. Certain results are compared with others in the literature obtained under different kinematic and thermodynamic assumptions. Effects of choices of nonlinear thermoelastic formulations and higher-order elastic constants on extracted deviatoric stress profiles can be substantial. Stored energy of dislocations and commensurate residual volume changes together can notably affect extracted shear stress. Stored energy significantly affects predicted entropy production and its contribution to temperature rise. The calculated density of geometrically necessary dislocations required to maintain compatibility of total strain across the structured steady plastic wave front is small relative to the line density of total dislocations.

Real-time distributed monitoring of pressure and shock velocity by ultrafast spectrometry with Chirped Fiber Bragg Gratings: Experimental vs calculated wavelength-to-pressure sensitivities in the range [0–4 GPa

Fiber Bragg Gratings (FBGs) are gaining acceptance as velocity/pressure gauges in the fields of detonation and shock physics on account of their sensitivity, small size, flexibility, electromagnetic immunity, and wavelength-encoded feature. Chirped FBGs (CFBGs) are investigated as wavelength-to-position discriminators with the purpose of monitoring pressure/velocity profiles over a distance range of typically 100 mm. The use of CFBGs simplifies both sensor deployment and data retrieval and finally improves the accuracy due to the increased number of measurement data. In this paper, the metrological performance of CFBGs used as in situ distributed shock pressure/velocity gauges is investigated both theoretically and experimentally in a planar shock loading configuration with an aluminum-based flyer and target. In the intermediate range for shock stress, i.e., less than the Hugoniot Elastic Limit (HEL) of silica, CFBGs provide simultaneous measurements of both shockwave velocity and stress within the target material. A Bragg wavelength-to-stress model is proposed that takes into account (i) the state-of-stress within the target material, (ii) the stress coupling coefficient due to imperfect impedance matching between the target material and the silica fiber, (iii) the conversion of the state-of-stress into a state-of-strain within the silica fiber, and (iv) the conversion of strain data into observable Bragg wavelength shifts. Finally, the model also takes into account the pressure dependence of constitutive parameters for silica and aluminum. Experiments were performed in planar shock loading using CFBGs as stress gauges, bonded along the target axis with Araldite glue. 6061-T6 aluminum flyers were launched at several velocities by a gas gun onto targets of the same material. A free-space Czerny-Turner (CT) spectrometer and an integrated-optics Arrayed-Waveguide Grating (AWG) were both used as dynamic spectrum analyzers. Experimental Bragg wavelength shifts agree well with theoretical predictions for both elastic and hydrodynamic planar shock loading of 6061-T6 aluminum, opening up large perspectives for shock physics experiments.

Shock-induced microstructural response of mono- and nanocrystalline SiC ceramics

The dynamic behavior of mono- and nanocrystalline SiC ceramics under plane shock loading is revealed using molecular-dynamics simulations. The generation of shock-induced elastic compression, plastic deformation, and structural phase transformation is characterized at different crystallographic directions as well as on a 5-nm grain size nanostructure at 10 K and 300 K. Shock profiles are calculated in a wide range of particle velocities 0.1–6.0 km/s. The predicted Hugoniot agree well with experimental data. Results indicate the generation of elastic waves for particle velocities below 0.8–1.9 km/s, depending on the crystallographic direction. In the intermediate range of particle velocities between 2 and 5 km/s, the shock wave splits into an elastic precursor and a zinc blende-to-rock salt structural transformation wave, which is triggered by shock pressure over the ∼90 GPa threshold value. A plastic wave, with a strong deformation twinning component, is generated ahead of the transformation wave for shocks in the velocity range between 1.5 and 3 km/s. For particle velocities greater than 5–6 km/s, a single overdriven transformation wave is generated. Surprisingly, shocks on the nanocrystalline sample reveal the absence of wave splitting, and elastic, plastic, and transformation wave components are seamlessly connected as the shock strength is continuously increased. The calculated strengths 15.2, 31.4, and 30.9 GPa for ⟨001⟩, ⟨111⟩, and ⟨110⟩ directions and 12.3 GPa for the nanocrystalline sample at the Hugoniot elastic limit are in excellent agreement with experimental data.

Spall strength of liquid copper and accuracy of the acoustic method

We investigate spallation in liquid copper at high strain rates induced by planar shock loading with classical molecular dynamics simulations. Spallation simulations are performed at different initial temperatures, shock durations, and shock strengths. Loading may have pronounced effects on spall strength. The acoustic method for deducing spall strength and strain rate from free surface velocity histories is discussed in detail and compared to direct simulations. The effects of temperature rise induced by shock wave, tension attenuation, sound speed, and density on the accuracy of the acoustic method are examined; the contributing factors to errors are identified; and the modifications to the choice of sound speed and density are proposed to improve the accuracy of the acoustic method.

The significance of grain morphology, moisture, and strain rate on the rapid compaction of silica sands

There is considerable interest in the high-rate compaction of brittle granular materials such as sand. However, the vast majority of studies focus on a single granular system, limiting our ability to make comparisons between materials to discern how granular structure manifests as bulk material response. Here, three different silica sands with similar grain size and shape are studied: we compare a rough quarry sand, a smoother-grained sand, and a sandy loam. Quasi-static compaction and planar shock loading responses are compared, and recovered samples analyzed. The combination provides information regarding the interplay between granular properties, loading conditions, and material response. We show that the fundamental grain-scale behaviour depends on loading conditions: At low strain rates compaction behaviour is dominated by grain morphology, and in particular, smoothness and particle size distribution. Under shock loading, grain rearrangement and force chain effects are suppressed, and the nature of inter-granular contact points, modified by the presence of moisture or fines, is most important. Furthermore, grain fracture under shock loading is substantially reduced with increasing moisture content.

Numerical study of mechanisms to minimize failure in a metal with soft backing under plane shock loading

In recent times, several experimental studies have reported improved ballistic penetration resistance and blast survivability of metallic structures to which an external coating of a soft elastomeric material has been applied. This work is aimed at understanding, through numerical simulations on a simple metal/elastomer flat plate geometry subjected to planar blast waves, the detailed mechanics of wave propagation, damage evolution and mitigation in a bilayer system. Void nucleation, growth and coalescence is assumed to be the damaging mechanism in the metal. A meshless technique based on smoothed particle hydrodynamics is used within the framework of large deformation elasto-viscoplasticity in the metal and nonlinear elasticity in the elastomer. We show that the thickness of the elastomer plays an important role in shielding void activity in the metal, by creating a sequence of closely spaced pulses that reflect from the interface and free surfaces to maintain non-tensile or weakly tensile states of stress. Moreover, a fictitious material that is capable of undergoing a transformation to a harder material under pressure is studied that proves to be an ideal candidate for damage mitigation.

Dynamic Properties of RHA Steel under Planar Shock Loading using Explosive Driven Plate Impact System

Planar shock loading of rolled homogeneous armour (RHA) steel has been studied at high pressures in the range of 20-100 GPa using an explosive-driven plate impact system. Shock velocities and flyer velocities are measured using time of arrival pins embedded in the target at known depths. The shock equation of state of RHA steel has been determined. α → e phase transition stress and hugoniot elastic limit (HEL) of RHA steel have been determined through manganin gauge and found to be 12.2 ±0.6 GPa and 4.1 ± 0.2 GPa, respectively. The experimental stress of phase transition has been compared with the stress calculated using ThermoCalc software. The shock properties have been incorporated in the Autodyn simulation package and simulations were performed to determine flyer velocity, pressures and the results are compared with that of experiments. Defence Science Journal, Vol. 65, No. 3, May 2015, pp.196-202, DOI: http://dx.doi.org/10.14429/dsj.65.7952

Mesoscale Modeling of Quartzite and Sandstone under Shock Loading: Influence of Porosity and Pressure-dependent Quartz Stiffness on Macroscopic Behavior

In this paper, quartzite and sandstone are numerically investigated under planar shock loading. Those geologic materials consist of cemented quartz grains. Quartzite has a compact structure whereas sandstone has a porosity of typically around 20%. A mesoscale (grain scale) model is developed in order to catch inter-granular interactions and porosity crushing under shock loading. For this purpose, quartz grains are explicitly resolved in a Finite-Element model such that their shape and orientation are represented. The quartz grains are modeled as elastic crystals with a pressure-dependent, anisotropic stiffness matrix. Using parameter variations, we study the effect of porosity and pressure-dependency of the quartz stiffness on the macroscopic behavior of quartzite and sandstone. Descriptors of the macroscopic behavior are macroscopic longitudinal stress and shock wave speed. These quantities are determined via a homogenization methodology.

Spallation caused by the diffusion and agglomeration of vacancies in ductile metals

In this paper, the spallation process for the ductile metals under plane shock loading is discussed in theory. By employing the phase transition theory and non-equilibrium theory, the spallation process may be understood as a result of the diffusion and agglomeration of the generated vacancies. Through the detailed theoretical analysis, the following important points are concluded: (1) the spalling temperature, a new concept, is proposed first and the appearance of spallation critical behavior is proved; (2) the quantitative grain size, tensile strain rate and temperature dependence of both the damage evolution rate and the void growth velocity is obtained; (3) the existence of a characteristic size for the voids and a characteristic stress at the void boundary is discovered first, and their magnitude depend on the vacancy excitation energy and the average volume of one vacancy; (4) the temperature of metal near the growing void is found to be high, possibly causing the metal to melt, and it decreases quickly with the distance away from the void; (5) the area of the plastic zone, surrounding one formed spherical void, is clarified; (6) the viewpoint is put forward that the void growth may arise from the agglomeration of vacancies rather than the emission of dislocations when the shocking temperature approaches spalling temperature. Most of the above theoretical results are novel and obtained first.

The Influence of Rolling Schedule on the Dynamic Properties of Accumulatively Roll Bonded Nano-Layered Cu-Nb

Cu-Nb nanolayered material was produced through an accumulative roll bonding (ARB) technique. Using this technique, two different rolling schedules were employed to produce a normal and transverse rolled material. This resulted in specimens with differing microstructures within the 135nm thick nanolayers and interface structures between the layers. The dynamic response of these bulk Cu-Nb nanocomposites was then investigated under planar shock loading. It was observed in dynamically fractured specimens that the characteristics of ductile failure features formed on the fracture surface after dynamic loading were dependent upon the processing route of the nanocomposite. Specifically, grain shape differences due to dissimilar rolling passes are linked with differences in the failure response, particularly kinetics of fracture. In addition, incipient failure immediately below the primary fracture surface was also observed. Numerous nanovoids were nucleated and aligned linearly in the middle of Cu layers within the shocked Cu-Nb nanocomposites. These observations indicate relative stability of Cu-Nb interfaces produced by the ARB methods utilized in this study under dynamic loading conditions.

An investigation of the dynamic separation of spot welds under plane tensile pulses

We performed ultra-high-speed tests for purely opening spot welds using plane tensile pulses. A gun system generated a parallel impact of a projectile plate onto a welded plate. Induced by the interactions of the release waves, the welded plate opened purely under the plane tensile pulses. We used the laser velocity interferometer system for any reflector to measure the velocity histories of the free surfaces of the free part and the spot weld of the welded plate. We then used a scanning electron microscope to investigate the recovered welded plates. We found that the interfacial failure mode was mainly a brittle fracture and the cracks propagated through the spot nugget, while the partial interfacial failure mode was a mixed fracture comprised ductile fracture and brittle fracture. We used the measured velocity histories to evaluate the tension stresses in the free part and the spot weld of the welded plate by applying the characteristic theory. We also discussed the different constitutive behaviors of the metals under plane shock loading and under uniaxial split Hopkinson pressure bar tests. We then compared the numerically simulated velocity histories of the free surfaces of the free part and the spot weld of the welded plate with the measured results. The numerical simulations made use of the fracture stress criteria, and then the computed fracture modes of the tests were compared with the recovered results.

Finite strain analysis of shock compression of brittle solids applied to titanium diboride

A finite strain theory is developed for polycrystalline brittle materials undergoing shock loading. Inelastic deformation arises principally from extension and opening or sliding of microcracks, and depends on pressure as well as deviatoric stress. In the general theory, internal energy depends on a logarithmic measure of finite elastic strain, entropy, and an internal variable associated with fracture. The theory is applied towards planar shock loading of an isotropic sample under possible static pre-stress. An exact analytical solution is derived when inelasticity is idealized as rate independent. The model and solution are applied to describe polycrystalline ceramic titanium diboride. Results provide new insight into experimental shock data, demonstrating importance of elastic nonlinearity and pressure dependent strength. The model describes shock pressure, mean stress, and shear stress in shocked titanium diboride, including the double yield point, with a minimal number of fitting parameters. The analysis predicts an increase in the Hugoniot elastic limit and suppression of inelasticity with increasing compressive pre-stress, in agreement with recent experiments.

Analysis of shock compression of strong single crystals with logarithmic thermoelastic-plastic theory

A finite strain theory is developed for anisotropic single crystals undergoing shock loading. Inelastic deformation may arise from dislocation slip, twinning, or fracture and crack sliding. Internal energy can generally depend on a logarithmic measure of finite elastic strain, entropy, and an internal variable associated with defect accumulation. A closed form analytical solution is derived for the planar shock response in the thermoelastic regime, at axial stresses up to the Hugoniot elastic limit. In the plastic regime, for highly symmetric orientations and rate independent shear strength, the Rankine–Hugoniot conditions and constitutive relations can be reduced to a set of algebraic equations that can be solved for the material response. The theory is applied towards planar shock loading of single crystals of sapphire, diamond, and quartz. Logarithmic elasticity is demonstrated to be more accurate (i.e., require fewer higher-order elastic constants) than Lagrangian or Eulerian theories for sapphire, diamond, and Z-cut quartz. Results provide new insight into criteria for initiation of twinning, slip, and/or fracture in these materials as well as their strength degradation when shocked at increasingly higher pressures above the Hugoniot elastic limit.

On shock response of nano-void closed/open cell copper material: Non-equilibrium molecular dynamic simulations

Non-equilibrium molecular-dynamic simulations were carried out on model three-dimensional nano-void copper material with different idealised pore structure and porosity to highlight differences in response behaviour between them when subjected to various piston velocities simulating planar shock loading of different intensities. This article demonstrates and explains from a mechanistic perspective the differences in response observed with respect to Hugoniot elastic limits, dislocation line and jet formation, void collapse mechanism and hot spot generation, specific volume, partial recrystallisation and temperature evolution in void collapsed regions, shock and particle velocity curves.

Molecular Dynamics Simulations of Plane Shock Loading in SiC

Large-scale molecular dynamics simulations are carried out to investigate 3C-SiC single crystals under plane shock loading. From the analysis of the shock profile and the evolution of the atomic structures, we demonstrate the interplay between the shock induced elastic compression, plastic deformation, and structural phase transformation (SPT). Particle velocity ranges from 0.4-6.0km/s. The predicted shock Hugoniot is divided into four regions. Below 2km/s, only elastic shock induced compaction exists. Plastic deformation appears between 2-3km/s, while the SPT emerges above 3km/s, when the induced pressure reaches over 90GPa. Plastic deformation in this cubic crystalline material is marked by extensive deformation twinning while at high pressure the original low pressure zinc blend structure is transformed into the more compact rocksalt structure. For particle velocity above 4.5km/s, a single overdriven transformation wave propagates in the system. These simulation results provide an atomistic view of the dynamic effects of shock impact on single crystal high-strength ceramics.

Deformation and failure of shocked bulk Cu–Nb nanolaminates

The deformation and failure of bulk Cu–Nb nanocomposites with a nominal layer thickness of 135nm was investigated under planar shock loading. It was observed that little substructural evolution was evident after shock compression to a peak stress of 7GPa, while specimens were fully spalled after loading to 7GPa under free surface conditions. In these fully spalled specimens, the characteristics of ductile failure that formed on the fracture surface were dependent upon the processing route of the nanocomposite. Specifically, process-induced grain-shape differences due to dissimilar rolling passes are linked with differences in the failure response. In addition, incipient failure was also observed. Numerous nanovoids, 20nm or less in size, nucleated and aligned in a row in the middle of Cu layers. Due to the reflection of the shock wave at the Cu–Nb interfaces, incipient voids tend to nucleate within the Cu phase, which has a higher impedance and lower spall strength than Nb. This occurs rather than nucleation along the Cu–Nb interfaces or in the Nb phase. This finding contradicts the general thinking of failure starting from interfaces, and indicates that the Cu–Nb interfaces are stable under dynamic loading. It is postulated that numerous voids nucleate in the Cu layers under shock loading, then lead to failure through their growth and coalescence.

Uncertainties in the shock devolatilization of hydrated minerals: A nontronite case study

Controlled recovery of hydrated minerals subjected to planar shock loading is challenging because of the large difference in shock impedance between the natural samples and the engineering materials used as the recovery capsules. Significant differences in recovery capsule design confound straightforward interpretation of existing data on shock modification of hydrated minerals. We present X‐ray diffraction and infrared spectroscopy results from new shock recovery experiments on nontronite (a smectite clay observed on Mars) and identify major issues in the interpretation of recovered samples. Previous work assumes that the first shock pressure step in a ring‐up configuration is the most important factor in the interpretation of shock modification. By comparing the X‐ray diffraction and infrared spectroscopy data from experiments with similar first shock steps but significantly different final shock states, we show that one cannot simply interpret the recovered samples based upon the first shock pressure step. This work demonstrates the need for a deeper understanding of the thermodynamics of ring‐up experiments in order to be able to interpret the results in terms of an equivalent single shock loading pressure for planetary applications. In this work, we also show that venting of the samples does not matter significantly at low pressures but may be important at high pressures. We have developed a recovery method and validation test that allows us to address the major issues and technical tradeoffs with shock recovery experiments on volatile materials.

Nanoscale Plasticity at Grain Boundaries in Face-centered Cubic Copper Under Shock Loading

We investigate the responses of four representative grain boundaries in face-centered cubic Cu bicrystals to shock compression as a function of the loading direction. Two loading directions are considered, either parallel or perpendicular to the grain boundary plane, representing the extremes that a polycrystalline sample will ordinarily experience under the uniaxial strain conditions of planar shock loading. Using molecular dynamics simulations, we demonstrate that the deformation processes during shock compression of the same boundary are altered measurably by changing the loading direction. The Majority of the differences in the nanoscale deformation processes were related to the activation of varying slip systems in the same boundary under the two loading conditions. This change in deformation processes, and hence the plastic response, might eventually affect the failure stress for a grain boundary.