Surface Velocity Histories Research Articles

Stress field measurements using quantitative schlieren

Quantitative schlieren analysis is extended here to optically transparent solids in quasi-static and dynamic experiments to measure stress distributions. The quasi-static experiments in polymethyl methacrylate (PMMA) compared refraction angles and stress gradients calculated from schlieren images to the analytical Flamant solution of a line load on a half-space. The quantitative schlieren measurements of the stress field in the thin sample with a load compared well to the analytical solution. The analysis method was then extended to explosive induced shock waves in PMMA. The explosive induced response of PMMA was experimentally studied using high-speed schlieren to visualize the shock propagation in conjunction with Photon Doppler Velocimetry (PDV) to record surface velocity histories. The stress state estimated from the schlieren images was compared to the stress calculated from the PDV measurements. High-speed imaging limitations caused the shock wave to not be fully resolved in the images, but was resolved in the PDV measurement. The stress state behind the shock calculated from the high-speed images followed a similar trend to the stress calculated from the PDV measurements.

Effects of microstructures on dynamic deformation and spallation damage of high-entropy alloy Al0.3CoCrFeNi under plate impact loading

Plate impact experiments are conducted on high-entropy alloy Al0.3CoCrFeNi with different microstructures to investigate the effects of grain size, precipitates and heterogeneous structure on dynamic response. Free surface velocity histories are obtained. All initial and postmortem samples are characterized with transmission electron microscopy and electron backscatter diffraction. Nanoscale L12 precipitates result in a considerable increase in dynamic yield stress. Spall strength is higher for the heterogeneous structure, the large grain size (200 μm) and small grain size (63 μm) with L12 precipitates by ∼4%, 19% and 10% than for the small grain size (77 μm) without precipitates. After shock compression, dislocation slip, stacking faults, the Lomer-Cottrell locks and nanotwins are found in the samples without the L12 precipitates. L12 precipitates increase the energy barrier and inhibit deformation twinning. Spall damage is ductile in Al0.3CoCrFeNi. For the homogeneous structures, intragranular voids are predominant. Voids are preferentially distributed in the fine-grain domains or at the fine-grain–coarse-grain domain boundaries of the heterogeneous structure.

Effect of grain size on spall fracture of CrCoNi medium-entropy alloy under Taylor-wave loading

The effect of grain size on spall properties of medium-entropy alloy CrCoNi under Taylor-wave loading is investigated. Three different grain sizes, 300 μm, 20 μm, and 3 μm, are explored. The free surface velocity histories are measured to obtain such quantities as dynamic yield strength and spall strength. With decreasing grain size, there is a slight decrease in spall strength, but a significant increase in damage rate. The shock-recovered samples are characterized with scanning electron microscopy and electron backscatter diffraction. In coarse-grained samples, voids tend to nucleate within grain interiors, while in fine-grained samples, voids nucleate preferentially at grain boundaries (GBs). Molecular dynamics simulations show that the nucleation of intergranular or intragranular voids is dominated by GB–slip and slip–slip intersections, respectively. The higher GB density results in more extensive GB–slip intersections, consistent with the experimental results.

Anisotropic dynamic response of AlSi10Mg fabricated via laser powder bed fusion under plate impact

The effects of structural anisotropy on dynamic yield and spallation damage of an AlSi10Mg alloy manufactured via laser powder bed fusion are investigated via plate impact experiments along the build direction (BD) and the transverse direction (TD). Free surface velocity histories are measured to deduce its dynamic mechanical properties. The as-received and postmortem samples are characterized with scanning electron microscopy, metallograpic microscopy, electron backscatter diffraction and synchrotron X-ray computed tomography. The Hugoniot elastic limit for loading along TD is about 40% higher than that along BD, given the initial 〈100〉∥BD texture. For spallation, voids prefer to nucleate at melt pool boundaries. Spall strength for loading along TD is about 18% higher than that along BD, as a result of higher critical stress for void nucleation and less nucleation sites due to the melt pool morphology. The damage evolution features are also correlated well with melt pool morphology and grain morphology within the pool interior, demonstrating the “ductile” interpool and “brittle” intrapool fracture modes for loading along BD and TD, respectively.

Examination of machine learning method for identification of material model parameters

In this work, we compare two methods of using artificial neural network (ANN) to determine the optimal parameters of material model by results of high-speed plate impact experiments. The first ANN is trained to determine the free surface velocity history based on the impact parameters and material model parameters; this ANN is used as a fast emulator of model to speed-up the statistical Bayesian calibration of the model parameters. The second ANN directly determines the material model parameters based on the impact parameters and the free surface velocity history, because this ANN is trained by inverse data set; this approach for inverse problem is proposed for the first time and can be more preferable for fast-track expert systems in engineering applications. Both approaches are successfully used to determine the optimal parameters of material model in the case of impact of copper and aluminum plates at different temperatures and impact velocities with experimental data from the literature. A simple relaxation plasticity model with a constant relaxation time is used in the present research as an example; more accurate coincidence with the experimental data and wider applicability of the ANN-based approach can be expected for a more realistic plasticity model.

Correlation between grain size and dynamic response of NiTi alloy during intense shock-induced multi-spallation

This work committed to performing non-equilibrium molecular dynamics simulations to explore the influence of grain size on multi-spall performance of nanocrystalline nickel-titanium (NiTi) alloy. By comparing the calculated Hugoniot relationship with present experimental results, the Finnis-Sinclair (FS) type potential used in this work was verified to be suited for reproducing the shock behavior of NiTi alloy at high strain rate. During shock wave evolution, a single plastic wave was clearly observed in the sample with grain size of 5 nm, while there was a more pronounced elastic-plastic double wave structure at larger grain size. According to the free surface velocity history, the predicted spall strength exhibited a decreasing tendency and subsequently increased when the grain size decreased from 50 to 5 nm, indicative of a critical grain size (10 nm). Correspondingly, there were multiple spall planes appearing in the sample, the grain size of which was not smaller than the critical one. Contrarily, a single spall plane was observed at 5 nm. By counting the void distribution statistic, we found that as the grain size increased, the void-nucleation behavior changed from the intergranular to intergranular/transgranular coexisting pattern. In consequence, more nucleation sites were provided to promote an increase in the number of voids. Interestingly, for intergranular, there were much more voids involved in spallation at smaller grain size, which was attributed to grain boundary effect. The results demonstrated that void evolutions rarely occurred at the grain boundaries parallel to the loading direction. Moreover, when the grain size was larger than 5 nm, the B19 phases were found to be produced around those potential void-nucleation sites. After void nucleation, these B19 phases decreased till disappearance, accompanied by the proliferation of a large number of [100] dislocations. Such dislocations accumulated in the region without voids could block the void growth in this region, which was expected to be the reason for the formation of multiple spall planes. On the contrary, the absence of dislocations at 5 nm was inclined to the fact that the space for dislocation emission and aggregation was preoccupied by nucleated voids.

Destruction of a magnesium alloy film in the condensed state by an ultrashort laser-driven shock wave

Laser-driven shock wave phenomena in a sub-micrometer Mg–4Al–2Zn alloy film are studied using spectral interferometry with spatial and temporal (1 ps) resolution. Upon irradiating the film through a glass substrate by 500 fs laser pulses, the ultrashort elastic compression pulses with the peak stress up to 4.6 GPa at a propagation distance of 0.5 μm were generated. Depending on the laser fluence, either spall fracture near the rear surface in the solid state or cavitation near the metal–glass interface in the liquid state was observed. The spall strength of the solid Mg alloy and the upper limit of the cavitation threshold in the melt at the strain rate of ∼109 s−1 were extracted from the free surface velocity history. The depth of fracture initiation was retrieved from the instant of the spall pulse exit, and the thickness of the molten layer was estimated to be 100–160 nm depending on laser fluence. The investigation of the residual morphology by scanning electron and atomic force microscopies revealed the presence of melting and nucleation within the irradiated area. The experimental findings are of interest for predicting the behavior of magnesium alloys in the condensed state at extremely high strain rates, for studying the physics of metastable states and for simulating the interaction of ultrashort laser pulses with thin film materials.

Unraveling Anisotropy in Crystalline Orientation under Shock-Induced Dynamic Responses in High-Entropy Alloy Co25Ni25Fe25Al7.5Cu17.5.

Shock-induced plastic deformation and spall damage in the single-crystalline FCC Co25Ni25Fe25Al7.5Cu17.5 high-entropy alloy (HEA) under varying shock intensities were systematically investigated using large-scale molecular dynamics simulations. The study reveals the significant influence of crystalline orientation on the deformation mechanism and spall damage. Specifically, the shock wave velocities in the [110] and [111] directions are significantly higher than that in the [001] direction, resulting in a two-zone elastic-plastic shock wave structure observed in the [110] and [111] samples, while only a single-wave structure is found in the [001] sample. The plastic deformation is dominated by the FCC to BCC transformation following the Bain path and a small amount of stacking faults during the compression stage in the [001] sample, whereas it depends on the stacking faults induced by Shockley dislocation motion in the [110] and [111] samples. The stacking faults and phase transformation in the [001] sample exhibit high reversibility under release effects, while extensive dislocations are present in the [110] and [111] samples after release. Interestingly, tension-strain-induced FCC to BCC phase transformation is observed in the [001] sample during the release stage, resulting in increased spall strength compared to the [110] and [111] samples. The spall strength estimated from both bulk and free surface velocity history shows reasonable consistency. Additionally, the spall strength remains stable with increasing shock intensities. The study discusses in detail the shock wave propagation, microstructure change, and spall damage evolution. Overall, our comprehensive studies provide deep insights into the deformation and fracture mechanisms of Co25Ni25Fe25Al7.5Cu17.5 HEA under shock loading, contributing to a better understanding of dynamic deformation under extreme environments.

A study of explosive-induced fracture in polymethyl methacrylate (PMMA)

The fracture response of geologic materials is of interest for applications, including geothermal energy harnessing and containment of underground explosions. To better understand the explosively induced fracture response of geomaterials, polymethyl methacrylate (PMMA) was used as a transparent rock surrogate to allow imaging of internal shock propagation and fracture growth processes. Experiments were conducted using high-speed shadowgraphy and photon Doppler velocimetry (PDV), which were compared to numerical simulations. Experiments measured fractures produced in 304.8mm×304.8mm×304.8mm PMMA cubes with two simultaneously initiated detonators. The cubes were subjected to varying amounts and directions of externally applied uniaxial stresses, including no stress, 2 MPa stress, and 20 MPa stress. The fracture radius as a function of time was extracted from the high-speed videos. Post-test images of the PMMA cubes aided in the determination of three-dimensional effects not directly imaged by the cameras. The surface velocity history and the shock response captured in PDV and the high-speed videos were compared to the simulated explosive-induced shock response. The simulation results indicate that the shock drives the fracture for the first 20 μs corresponding to a fracture radius of approximately 15 mm in the experiments. The gas-driven fracture extent was estimated analytically using an equilibrium stress distribution calculated after the shock wave propagation through the sample. Reduction in the gas pressure due to the leakage of the explosive products through the crack as a function of time was accounted for. The estimated fracture lengths were in agreement with the experimentally observed fracture lengths.

Effect of minor elements Al and Ti on dynamic deformation and fracture of CoCrNi-based medium-entropy alloys

Three texture-free CoCrNi-based medium-entropy alloys (MEAs) with similar grain sizes, CoCrNi, (CoCrNi)94Al3Ti3 and (CoCrNi)90Al5Ti5, are investigated under plate impact loading. Free surface velocity histories are obtained along with microstructure characterizations of postmortem samples. The influences of the addition of minor elements Al and Ti on the microstructures, dynamic mechanical properties and underlying deformation and damage mechanisms of MEAs are elucidated. Compared to the single-phase CoCrNi MEA, spherical nanosized L12 precipitates and micron sized body-centered-cubic phase are found in (CoCrNi)94Al3Ti3 and (CoCrNi)90Al5Ti5, respectively. The addition of minor elements Al and Ti leads to an increase in the dynamic yield stress approximately by 70% (to 1.0 GPa) and 130% (to 1.4 GPa) for (CoCrNi)94Al3Ti3 and (CoCrNi)90Al5Ti5, respectively, due to the solid solution strengthening and precipitate strengthening. Multiple deformation mechanisms are observed. Planar dislocation glide and stacking faults are the dominant deformation mechanisms for all the MEAs. However, deformation twinning is deactivated in (CoCrNi)94Al3Ti3 and (CoCrNi)90Al5Ti5 with small additions of Al and Ti. For spallation, damage is ductile in nature for CoCrNi and (CoCrNi)94Al3Ti3, but brittle for (CoCrNi)90Al5Ti5. Under similar shock stress, the spall strength of (CoCrNi)94Al3Ti3 is comparable to that of CoCrNi, ∼ 150% higher than that of (CoCrNi)90Al5Ti5 because intergranular brittle fracture activation does not require substantial plastic deformation. The minor addition of Al and Ti in medium-entropy alloys significantly affects their dynamic mechanical properties, deformation and damage mechanisms.

Impact response of metastable dual-phase high-entropy alloy Cr10Mn30Fe50Co10

Plate impact experiments are conducted on a metastable dual-phase high-entropy alloy (HEA) Cr10Mn30Fe50Co10 with different matrix grain sizes and phase fractions. Free surface velocity histories are obtained along with microstructure characterizations. Postmortem samples are characterized with transmission electron microscopy and electron backscatter diffraction. Multiple deformation mechanisms are observed, including dislocation slip and stacking fault in the face-center cubic (FCC) phase, dislocation slip and deformation twinning in the hexagonal close-packed (HCP) phase, and the FCC to HCP transformation. For spallation, damage is ductile in nature. Despite different microstructures, micro-voids prefer to nucleate at high-angle grain boundaries within the FCC phase, leading to similar spall strength. Upon shock loading, a dynamic plastic deformation partitioning behavior among the two phases is observed; at high shock stress, denser dislocations in the HCP phase result in increased fractions of voids around the FCC/HCP phase interface and within the HCP phase during spallation damage.

Exploding wire method for the characterization of dynamic tensile strength of composite materials

In the presented study a wire electric explosion method is adopted for the shock loading test of wound T700/LY113 carbon/epoxy composite. The advantage of the proposed test method is a possibility to reach strain rate ∼104 s−1, exceeding upper limit of split Hopkinson pressure bar, but matching lower limits of plate impact test. Compared to the latter test method, a promising feature is a capability to measure in-plane tensile strength of the laminated composite. To implement the proposed method, test samples were fabricated by winding of carbon fiber layers over a polymethyl methacrylate (PMMA) cylinder. Electric explosion of wire inserted in the channel inside the cylinder generates a shock wave, which propagates towards the outer composite shell, and free surface velocity history is recorded using a laser interferometer. It allows estimation of failure strain and tensile strength of the composite in circumferential direction. However, incident shock wave and reverberations are also critical for out-of-plane strength, including delamination, so finite element analysis is used to elaborate what type of failure mode is critical.

Shock compression and spall damage of dendritic high-entropy alloy CoCrFeNiCu

Plate impact experiments are conducted on a dendritic dual face-center cubic phase high-entropy alloy (HEA) CoCrFeNiCu, consisting of Cu-lean dendritic (DR) and Cu-rich interdendritic regions (ID). Free surface velocity histories are obtained along with microstructure characterizations. The Hugoniot equation of state and spall strength at different shock stresses are determined. Dislocation slip is the main deformation mode for CoCrFeNiCu HEA, and the dislocation density of the Cu-rich interdendritic regions increases more significantly during shock compression. Both ductile and brittle damage modes are observed. With increasing impact velocity, the Cu-rich interdendritic regions with severe strain localizations and more defects provide more damage nucleation sites. The spall strength increases firstly, reaches its maximum at a peak shock stress of 5.8 GPa, and then decreases. Molecular dynamics simulations reveal that the abnormal dependence of spall strength on peak shock stress is a result of strain localization and thermal softening in the Cu-rich regions.

Deformation and damage of heterogeneous-structured high-entropy alloy CrMnFeCoNi under plate impact

Plate impact experiments are conducted on a hot-rolled, heterogeneous-structured, high-entropy alloy CrMnFeCoNi consisting of two types of domains: the UR domains containing unrecrystallized stretched grains and the FR domains containing fine recrystallized grains. Free surface velocity histories are obtained along with microstructure characterizations. Shock-induced deformation twinning is activated firstly in the UR domains, and the dislocation density of the FR domains increases more significantly during shock compression. Under similar shock stress, spall strength is the highest for loading along the rolling direction as a result of the texture-induced highest longitudinal sound velocity. Voids prefer to nucleate at the triple junctions of high angle grain boundaries in the FR domains or around the UR–FR domain boundaries. Compared to the homogeneous (annealed) structure, the heterogeneous structure leads to a negligible increase in spall strengths because of grain refinement in the FR domains and relatively severe plastic deformation around the UR–FR domain boundaries.

Molecular dynamics study on the shock induced spallation of polyethylene

Macroscopic experimental results of the plate impact tests of polymers are generally interpreted using the free surface approximation and the acoustic approximation. However, their validity over a range of shock pressures has not been thoroughly investigated yet. We conducted molecular dynamics simulations of plate impact tests of polyethylene to obtain molecular-level insights on those two common approximations associated with the interpretation of shock pressure and spall strength. Our results revealed that the free surface approximation could slightly underpredict the shock pressure in the polymer. The spall strength computed from the free surface velocity history can be significantly smaller than the actual tensile stress in the region of spallation.

Dependence of spallstrength on temperature, grain size and strain rate in pure ductile metals

When a shockwave, which can be generated by high velocity impact or explosive detonation, reflects from the free surface of a metal, it usually creates tensile stress inside the metal. While the tensile stress is large enough, voids nucleation, growth and coalescence happen inside the metal, causing the metal to spall. As one of the main contents of the spallation damage research, the spallation strength, which is often characterized by features of the free surface velocity history measured in spallation experiments, represents the maximum tensile stress that the material can withstand, and is actually a complex interaction among several competing mechanisms. Optimizing the spallation strengths of metals is important for their applications in the aerospace, automotive, and defense industries, and can be achieved by using the advanced manufacturing strategies, if we can know better the meaning and present analytic model of the spallation strength of metal. A large number of experiments show that the spallation strength of ductile metal is strongly dependent on the tensile strain rate, grain size and temperature of material. Based on the analysis of early spallation evolution and influence of grain size and temperature on the material, a simple analytic model of spallation strength is presented in this paper, which takes into account the effects of strain rate, grain size and temperature in materials. The applicability of this model is verified by comparing the calculated results from the model with the experimental results of spall strength of typical ductile metals such as high purity aluminum, copper, and tantalum.

Shear Reaction of Explosives and Propellants

When loaded by weak impact, both explosives and propellants undergo shear reaction. Out shear reaction hydro-reactive model (TDSR) is similar to our old surface burn hydro-reactive model (TDRR), except for the reaction rate equation. We perform tests and computer simulations of shear reaction in both explosives and propellants. For explosives we use the well-known Steven test but with different diagnostics (back surface velocity histories). For propellants we use a new test configuration. In both cases we run our TDSR simulations and are able to get a reasonable reproduction of test results.

Effects of shock-induced phase transition on spallation of a mild carbon steel

Effects of shock-induced phase transition (PT) on spallation of a mild carbon steel are investigated via plate impact experiments at impact velocities of 0.433–1.163 kms−1. The free surface velocity history is recorded to deduce spall strength and wave propagation/interaction within the sample. Postmortem samples are characterized with scanning electron microscopy and electron backscatter diffraction. Detailed wave analysis indicates that the PT affects wave propagation and interaction. Such wave propagation and interaction finally lead to the change of spall strength and spall plane position for different stress ranges. In the peak shock stress range of 13–17 GPa (slightly above the PT stress), the release fan of the PT wave accelerates the free surface but is not involved in the major spallation, giving rise to an overestimation of spall strength by the conventional acoustic method. However, at higher shock stress above PT (>17 GPa), the release fans of the PT wave interact with each other and induce secondary spallation, and the acoustic method is applicable in such cases; the major spall plane moves to the sample central region, and multiple secondary spall planes appear. In addition, the reverse PT upon release facilitates nucleation and growth of deformation twins which subsequently act as nucleation sits of voids during spallation. With increasing shock stress, the spall damage exhibits mode transitions from brittle damage (transgranular cleavage cracks), to mixed brittle and ductile damage, and to ductile damage (void nucleation and growth).

Molecular Dynamics Simulations of Shock Propagation and Spallation in Amorphous Polymers

Abstract We conducted large-scale molecular dynamics (MD) simulations of shock wave propagation and spallation in amorphous polyurethane and polyurea. First, we computed the shock Hugoniot of the polymers using the multiscale shock technique and compared them with available experimental data to establish the upper limit of the shock pressure that can be accurately modeled using a non-reactive interatomic force field. Subsequently, we simulated shock wave propagation in the polymers, varying the shock particle velocity from 0.125 km/s to 2 km/s. A remarkable similarity in the shock behavior of polyurethane and polyurea was observed. The spall strength of each sample was computed by two methods: (a) the indirect method (based on the free surface velocity history)—accessible in experiments and (b) a direct method (based on the atomic stresses in the region of spallation)—accessible only through MD. The results reveal that the tensile strength computed from the indirect method is consistently smaller than the value obtained from the direct method. Moreover, the strength computed from the indirect method shows a noticeable agreement with the fracture nucleation stress. Our results provide novel molecular-level insights into the spallation mechanisms of amorphous polymers, which could facilitate the design of polymers for structural barrier applications.

Impact-induced twinning and phase transition in a medium carbon steel

Deformation twinning in a medium carbon steel containing ferrite and pearlite under shock compression is investigated below and above the α–ε phase transition stress (σT), within a peak stress range of 10–20 GPa. Free surface velocity histories are measured to obtain the Hugoniot elastic limit (2.7 GPa), σT (13.3 GPa) and bulk plastic strain. Postmortem samples are characterized with electron backscatter diffraction and transmission electron microscopy. Below σT, all the {112}〈111〉 twinning activation in ferrite and pearlite follows the Schmid law, while above σT, approximately 1/6 of the activation deviates from the law. Propagation of the {112}〈111〉 twins in pearlite depends on the orientation of the activated twinning plane relative to cementite lamellae. With increasing peak stress, the {112}〈111〉 twin area fraction in ferrite/pearlite increases greatly/slightly; the {112}〈111〉 twin area fraction in ferrite is about 7 times that of pearlite. The {332}〈113〉 twins can only form above σT, favoring ferrite over pearlite, and are likely to be the secondary twins originated at the {112}〈111〉 twin boundaries.