Free Surface Velocity Histories Research Articles

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.

Bayesian calibration of a physics-based crystal plasticity and damage model

In this work, we present a model parameter calibration procedure for a physics-based crystal plasticity model. The calibration process utilizes a powerful statistics-based Bayesian calibration method. Calibration of the crystal plasticity parameters makes use of experimentally-measured data, i.e. compressive stress–strain response, from 〈100〉 and 〈123〉 single crystal copper dynamically loaded via Kolsky bar tests. The calibration of damage parameters is achieved using experimentally-measured free-surface velocity history data from plate impact test on 〈100〉 and 〈110〉 single crystal copper, which generates shock compression followed by dynamic tensile failure. A validation assessment is then carried out by comparing the calibrated model predictions and experimental measurements of the dynamic tensile damage generated in an impacted bicrystal copper plate. Lastly, a model-informed rationale for the experimentally-observed dependence of the spatial distribution of ductile damage (porosity) on crystallography is provided.

Effects of temperature and strain on the resistance to high-rate deformation of copper in shock waves

Elastic–plastic shock compression, unloading, and the stepwise shock compression of copper were investigated at room temperature, 710 °C, and 850 °C to expand the measurement range of high-rate deformations. The dependences of the dynamic yield stress on the temperature and pressure of shock compression were determined from an analysis of the free-surface velocity histories. Although the initial resistance to high-rate deformation increases anomalously with increasing temperature, even a small strain in the shock wave can change the sign of the temperature dependence of the flow stress. Using these data, the dependence of the plastic strain rate on the shear stress in shock waves and temperature was obtained in the range 105–107 s−1. It was found that at room temperature, the ratio between the shear stress and the plastic shear strain rate in a shock wave practically does not depend on the loading history, whereas at 850 °C, the parameters of the plastic flow in the second shock wave deviates significantly from the initial dependence for lower stresses and higher strain rates.

Anisotropic spall behavior of CNT/2024Al composites under plate impact

Plate impact experiments are conducted on the carbon nanotube (CNT) reinforced 2024Al composite fabricated by flake powder metallurgy and hot extrusion, to investigate the effects of microstructural anisotropy on its dynamic deformation and damage, as well as the role of CNTs. Three loading directions are explored with the loading axis being parallel to the extrusion, transverse or normal direction. Free-surface velocity histories are measured to evaluate the mechanical properties and damage processes, including the Hugoniot elastic limit (HEL; ∼0.8 GPa) and dynamic spall strengths (1.4−1.9 GPa). Postmortem samples are characterized with synchrotron X-ray computed tomography and scanning electron microscopy. The microstructural anisotropy of the composite (in terms of the orientation of lamellar microstructures) has a negligible effect on HEL but induces an anisotropy in spall strengths; spall strength is the highest for loading along the extrusion direction, the long axis of the lamellar microstructures. CNTs appear to increase the spall strengths of the 2024Al matrix, in contrast to other reinforcing fibers/particles. The crack propagation direction and damage features can be correlated with collinear propagation of microcracks following the lamellar microstructures.

High-Rate Deformation and Fracture of 15Kh2NMFA Steel under Impact Loading at Normal and Elevated Temperatures

In this study, we present the results of the recording of shock-wave phenomena in 15Kh2NMFA steel at room temperature and 504 ± 5°C. Based on measurements of the free surface velocity histories, the dependences of the material resistance to deformation and fracture on the strain rate are determined. 15Kh2NMFA steel was found to be characterized by a twice higher dynamic tensile strength than iron, with almost equal values of the Hugoniot elastic limit. At increasing temperature, the Hugoniot elastic limit of steel decreases faster than that of iron while the dynamic tensile strength varies slightly.

Dynamic Strength of AZ31B-4E and AMX602 Magnesium Alloys Under Shock Loading

Free surface velocity histories for two magnesium (Mg) alloys are obtained from planar shock compression experiments. Symmetric plate impacts at velocities of approximately 400, 600, 800, and 1000 m/s are reported, where axisymmetric cylindrical specimens (flat-faced discs) are launched in single stage light gas guns. The studied specimens have been produced from an equal channel angular extrusion process for Mg AZ31B-4E and from a hot extrusion of consolidated powder prepared via a spinning water atomization process for Mg AMX602. The present studies focus on the region of the velocity profiles spanning the Hugoniot elastic limit through the plastic rise up to the Hugoniot state, as opposed to wave reflection, release and spall studied previously in these materials. A semi-analytical method is invoked to extract inelastic constitutive response information from particle velocity histories. The only parameters entering the procedure are fundamental thermoelastic properties—notably including elastic constants up to order three—and the ratio of plastic work to energy storage of defects generated in the crystal lattice. Plastic shock velocities are not available from the present data; these are estimated from the initial bulk modulus, its pressure derivative, and known shock velocities in conventional Mg AZ31B. Shear stress, plastic strain, plastic strain rate, temperature, and dislocation density are computed outcomes. Results demonstrate similar trends in extracted behaviors for the two alloys, whereby maximum strength in the plastic shock front increases with increasing impact velocity in each material. Strain rate sensitivity appears to be greater in AZ31B-4E than AMX602. Flow stress on the Hugoniot is calculated as 295 to 336 MPa for AZ31B-4E and 163 to 293 MPa for AMX602. Maximum flow stress in the plastic rise, as extracted from tests with maximum impact velocity, is on the order of 700 MPa for each alloy.

Grain Size Effects on Static and Dynamic Strength of Ultrafine-Grained Al-Mg-Mn Alloy Produced by High-Pressure Torsion

In the paper, the structure and static and dynamic mechanical properties of ultrafine-grained A5083 alloy (Al-Mg-Mn) produced by high-pressure torsion (HPT) are reported. The static yield stress and tensile strength were determined in tensile tests at a strain rate of ~ 10−3 s−1, and the dynamic yield stress and spall strength were calculated from free-surface velocity histories obtained during shock-wave loading at a strain rate of 105 s−1. The HPT technique provides strong grain refinement. The average grain size of the alloy after HPT is 100-180 nm and depends on the accumulated true strain. HPT significantly improves the static strength properties of the alloy. The static yield stress is increased by 360-390% and the static ultimate tensile strength by 166-182%. It is shown that the dynamic yield stress improved by 168-181%, while the dynamic spall strength was not improved by HPT. Moreover, the nanostructured alloy with a grain size of ~ 100 nm demonstrates the lowest spall strength.

Evaluation of the Yield Stress of Solids upon Unloading from a Shock-Compressed State

A simple method for evaluating the yield stress of shock-compressed material from the measured unit free-surface velocity history is proposed, verified, and approbated. For the first time, the dynamic yield stress of shock-compressed metal (aluminum) is experimentally evaluated at an elevated temperature. It is found that its value is lower than that at the room temperature and lower than the initial value of the dynamic yield stress at high temperatures.

Molecular dynamics simulations on shock response and spalling behaviors of semi-coherent {111} Cu-Al multilayers

Shock response and spalling behaviors of semi-coherent {111} Cu-Al multilayer are investigated by molecular dynamics simulations. Firstly, the influences of interfaces on shock wave propagation are studied. The simulations show that reflection-unloading happens when the shock wave propagates from Cu to Al and reflection-loading occurs when the shock wave propagates from Al to Cu. Strong discontinuities of stress components at the interfaces are revealed as well, the discontinuities are correlated to mismatches of Hugoniot curves and elastic-plastic properties of the two materials adjacent to the interfaces. Secondly, shock induced dislocation activities are studied. It is found that the stress barrier offered by the interface Cu-Al is smaller than that offered by Al-Cu. In fact, the resistance for dislocations to transmit through interfaces is determined by the coherency stresses, Koehler stresses and misfit dislocations at the interface. In addition, spalling fracture of Cu-Al multilayers after stress wave reflection at the free surface is studied. It is observed that ductile damage only nucleates in Al layer, rather than in Cu layers. This observation agrees well with the experimental results of Han (Acta Mater., 2014 (63) 150–161). Due to complex reflection and transmission of the stress waves at the interfaces, the profile of the free surface velocity histories of the multilayer target is quite different from that of the single-crystalline counterpart. In order to study thermal dissipation process during cavitation, analysis on thermal dissipation in the spalling damage zones is also provided in this paper. Moreover, contour plots and profiles of stress are illustrated to understand the spallation process of the multilayer target deeply. Tensile stress emerges in Al1 layer first, causing voids to nucleate; then the tensile stress wave attenuates rapidly and propagates to Cu1 and Cu2 layers. With the dissipation effect of damage and plastic deformation in the target, the tensile stress wave dissipates ultimately.

Shock-induced twinning and texture in a mild carbon steel

Deformation twinning is investigated in a polycrystalline mild steel under shock compression to about 12 GPa. The free surface velocity history is measured to calculate twinning stress. The postmortem sample is characterized with electron backscatter diffraction (EBSD). We provide a method to calculate the activated twinning systems in all twinned grains from EBSD data. Twinning is completely activated and suppressed for grain size above 36μm and below 4μm, respectively. For intermediate grain sizes (14–30μm), twinning tends to occur in the grain orientations near 〈101〉, consistent with the Schmid factor analysis. Almost all the twins nucleate on the twinning systems with the largest or second largest Schmid factors. The twinning stress is 1.16 GPa, and critical resolved shear stress for twinning is 0.47 GPa. Twinning in weakly textured sample can induce a strong 〈001〉 fiber texture, as a result of its following the Schmid’s law.

Dynamic fragmentation of boron carbide using laser-driven flyers

Laser-driven micro-flyer plates exhibit high planarity within the first 500 µm of travel, but deform into curved impactors due to loss of flight-driving plasma at the edges of the plate and interaction of the plate with the atmosphere [1, 2]. This time-of-flight based tunability of impactor geometry offers adjustable loading conditions in stress space. Here we explore the dynamic fracture of Boron Carbide under loading at 1100–1200 m/s impact velocities (strain rates up to 107 s−1) from two impactor geometries: (1) a nominally flat aluminum micro-flyer and (2) an Al micro-flyer with a radius of curvature. We compare these results to prior ballistic experiments with a spherical projectile impacting at 930 m/s. In-situ high-speed imaging at 10 million frames-per-second enables characterization of the flyer geometry and identification of active failure mechanisms in the target. Photon Doppler velocimetry provides the target free surface velocity history and allows estimates of the internal stress state during failure. Optical microscopy of the as-received microstructure and generated fragments suggests a link between the microstructure and fragmentation behavior. Statistics from laser-driven fragmentation are similar to ballistic fragmentation experiments, demonstrating the utility of the laser-driven apparatus in fragmentation studies.

Effects of alloying element segregation bands on impact response of a 304 stainless steel

The influence of segregation bands of alloying elements Cr and Ni on impact response of a 304 stainless steel is investigated under high strain rate impact loading with a single-stage gas gun. Free-surface velocity histories are measured to evaluate the mechanical properties. The Hugoniot elastic limits are 1.0–1.1 GPa, and the spall strengths are 2.1–2.4 GPa for the impact velocities explored. Oriented segregation bands induce negligible anisotropy in the Hugoniot elastic limit (dynamic yield stress) and spall strength. Scanning electron microscopy analyses show that microvoids tend to coalesce along the segregation bands, regardless of the loading direction, indicating segregation bands or the interfaces between segregation bands and matrix are the weakest nucleation sites. The fracture strength is dominated by the segregation bands, and thus independent of strain rate and peak stress. However, the damage degree is related to both peak stress and segregation band orientation. When the peak stress is lower than 5 GPa, damage degree is independent of the loading direction. At higher peak stresses, the damage degree is larger for impact direction aligned along segregation bands.

Deformation twinning in a mild steel: Loading dependence and strengthening

Deformation twinning in a mild steel is investigated under quasi-isentropic compression (IC) and shock compression (SC) to about 12 GPa, as regards the effects of pulse duration (plateau width) and strain rate (rising edge slope), and associated twin strengthening. The pulse duration ranges from 80 ns to 790 ns; and two rise times are explored, approximately 30 ns for SC and 300 ns for IC. Free-surface velocity histories are measured to obtain strain and strain rate. The postmortem samples are characterized with electron backscatter diffraction, and the yield strengths of the samples pre-deformed by impact are examined with a materials testing system. For SC, twin density and size increase with pulse duration up to 580 ns. At longer pulse durations, the increase in twin density is stagnated as a result of deviatoric stress relaxation, while twin size continues growing. For IC (410 ns), twin density and size are much larger than the SC counterpart, as a result of shallower rising edge. Increased deformation time can compensate the effects of reduced strain rate or applied stress for deformation twinning. Twin strengthening effect is strong in postmortem samples, depends on twin density instead of area fraction, and follows the empirical Hall–Petch relationship.

Dynamic Spallation in Uranium under Laser Shock Loading**Supported by the Science Foundation of China Academy of Engineering Physics under Grant No A090504.

The spall behavior of uranium is investigated using direct laser ablation loading experiments. The uranium targets are cut and ground to 0.05 mm, 0.1 mm, and 0.15 mm in thickness. Laser energies are varied to yield a constant peak pressure. This results in different strain rates and varying degrees of damage to the uranium targets. The spall strength is calculated and analyzed from the free surface velocity histories recorded using a line velocity interferometer for any reflections system. The spall strength increases from 4.3 GPa to 9.4 GPa with strain rates ranging from 4.0 × 106 s−1 to 1.7 × 107 s−1. Post-mortem analysis is performed on the recovered samples, revealing the twin-matrix interfaces together with the inclusions to be the primary factor governing the spall fracture of uranium.

Compressive and tensile strength of steel fibrous reinforced concrete under explosive loading

In order to determine the compressive and tensile strength of concrete under conditions of explosive loading, and to develop a methodological framework in this regard, three types of concrete have been investigated: concrete with fine-grained granite in the form of crushed stone having a static compressive strength of 47 MPa, the same concrete with the addition of steel fibers and also the same concrete reinforced by steel bars. The samples were rods of 50 and 100 mm diameter and five to ten diameters in length. The compressive fracture occurs at a relatively small distance of propagation of the load pulse along the rod and is accompanied by fast decay. The measurements of parameters of the compression pulse at the end of the fracture zone allowed us to determine the values of the dynamic compressive strength of the concrete while measurements of the free-surface velocity history at long distances were used for determining the dynamic tensile strength or spall strength values. The values of the dynamic compressive strength were found to be 2.5 times higher than the static strength. The steel fibers increased the dynamic compressive strength by about 10%. The obtained values of the dynamic tensile strength are 3–8 times higher than the values of the static tensile strength. The steel fibers increase the tensile strength by 20–50%. The reinforced sample has shown an increase of dynamic tensile strength by a factor of about 30.

Anisotropic deformation and damage of dual-phase Ti-6Al-4V under high strain rate loading

Plate impact experiments are conducted on a rolled titanium alloy Ti-6Al-4V to investigate the effects of structural anisotropy on dynamic deformation and damage, with the loading axis being parallel to the normal direction or transverse direction, referred to as LA∥ND and LA∥TD, respectively. Free-surface velocity histories are measured to evaluate the mechanical properties; the Hugoniot elastic limits for the LA∥ND and LA∥TD loading are 3.38 GPa and 3.75 GPa, respectively; the spall strengths are 4.54–4.71 GPa for the LA∥ND loading, and 4.69–4.91 GPa for the LA∥TD loading, for the impact velocities explored. The postmortem samples are characterized with scanning electron microscopy, electron backscatter diffraction and synchrotron X-ray computed tomography. The {101¯2} extension twins are activated near spall cracks and their number increases with increasing impact velocity. Microvoids nucleate at both grain (in the matrix) and phase boundaries, and grain boundary nucleation is more likely to occur given the small volume fraction of the β-phase. Cracks for the LA∥ND loading are generally perpendicular to the shock direction, while they are serrated and distributed more discretely for the LA∥TD loading. The damage degree for the LA∥ND loading is larger than for the LA∥TD loading, consistent with the corresponding spall strengths. At incipient spall, the average size of voids/cracks is larger for the LA∥ND loading than for the LA∥TD loading. Compared with the LA∥ND loading, small voids/cracks are more isotropic and large voids are more anisotropic for the LA∥TD loading.

Intragranular void formation in shock-spalled tantalum: Mechanisms and governing factors

Intragranular void formation in polycrystalline tantalum is investigated with plate impact experiments and molecular dynamics simulations, as regards its mechanisms and governing factors: grain boundary (GB) misorientation, grain orientation, grain size and shock pressure. Free-surface velocity history measurements are performed to obtain spall strength. Electron backscatter diffraction characterizations are used to obtain spatial distribution of voids, GB misorientation, and grain orientation associated with twins and intragranular voids. Intragranular voids are smaller in size but larger in number than intergranular voids, and nucleate in the GB vicinities. Smaller grains are favorable for the formation of intergranular and intragranular voids. At higher shock pressure, intragranular voids increase in fraction and tend to distribute at grain centers. Deformation twinning depends on grain orientation and prefers to form at high-angle GBs. However, intragranular voids have negligible dependence on grain orientation and favor medium-angle GBs, and the preference is enhanced slightly with increasing impact velocity and decreasing grain size. The simulations show GB-induced multiple-slip, slip-slip intersections and strain localizations act as the prerequisites to intragranular void formation.

Characterization of a signal recording system for accurate velocity estimation using a VISAR

The linearity of a signal recording system (SRS) in time as well as in amplitude are important for the accurate estimation of the free surface velocity history of a moving target during shock loading and unloading when measured using optical interferometers such as a velocity interferometer system for any reflector (VISAR). Signal recording being the first step in a long sequence of signal processes, the incorporation of errors due to nonlinearity, and low signal-to-noise ratio (SNR) affects the overall accuracy and precision of the estimation of velocity history. In shock experiments the small duration (a few µs) of loading/unloading, the reflectivity of moving target surface, and the properties of optical components, control the amount of input of light to the SRS of a VISAR and this in turn affects the linearity and SNR of the overall measurement. These factors make it essential to develop in situ procedures for (i) minimizing the effect of signal induced noise and (ii) determine the linear region of operation for the SRS. Here we report on a procedure for the optimization of SRS parameters such as photodetector gain, optical power, aperture etc, so as to achieve a linear region of operation with a high SNR. The linear region of operation so determined has been utilized successfully to estimate the temporal history of the free surface velocity of the moving target in shock experiments.

Deformation and damage of sintered low-porosity aluminum under planar impact: microstructures and mechanisms

Plate impact experiments are conducted to study compaction and spallation of 5% porosity aluminum. Free surface velocity histories, the Hugoniot elastic limit (HEL), and spall strengths are obtained at different peak stresses and pulse durations. Scanning electron microscopy, electron backscatter diffraction, and X-ray computed tomography are used to characterize 2D and 3D microstructures. 3D void topology analyses yield rich information on size distribution, shape, orientation, and connectivity of voids. HEL decreases/increases with sample thickness/impact velocity and approaches saturation. Its tensile strength increases with increasing peak stress and shock-induced densification. With the enhanced compaction under increasing impact velocities, spall damage modes change from growth of original voids to inter-particle crack propagation and to “random” nucleation of new voids. Such a change in damage mechanism also gives rise to a distinct decrease in damage extent at high impact velocities. Compaction induces strain localizations around the original voids, while subsequent tension results in grain refinement, and shear deformation zones between staggered cracks.

VISAR signal analysis with an emphasis on ellipse fitting.

A method based on ellipse fitting for analysis of VISAR (Velocity Interferometer System for Any Reflector) signals has been described. The errors introduced on the free surface velocity history due to common measurement imperfections in the amplitude and phase angle of the VISAR signal has been investigated and a remedy to mitigate this using a proper ellipse fitting technique has been presented. Performance comparison among various ellipse fitting techniques based on empirical evidence is carried out, and the geometric fitting technique of the Gauss Newton algorithm with initial conditions from the Bookstein algebraic fitting method is proposed. The new method provides better result in terms of accuracy than existing techniques. The method is especially useful when a fractional fringe signal is present which is quite common in VISAR based measurements. The applicability of the ellipse fitting technique is first theoretically justified, and then numerical simulation of ellipse fitting is carried out. Finally, the proposed method is validated by applying it for the analysis of VISAR signals recorded in the shock wave experiment conducted on the Al-2024T4 target material. The results of present analysis display a good agreement with the data available from other sources.