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Dynamic Behavior of Materials, Volume 1 of the Proceedings of the 2018 SEM Annual Conference & Exposition on Experimental and Applied Mechanics, the first volume of eight from the Conference, brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Experimental Mechanics, including papers on:

Synchrotron Applications/Advanced Dynamic Imaging

Quantitative Visualization of Dynamic Events

Novel Experimental Techniques

Dynamic Behavior of Geomaterials

Dynamic Failure & Fragmentation

Dynamic Response of Low Impedance Materials

Hybrid Experimental/Computational Studies

Shock and Blast Loading

Advances in Material Modeling

Industrial Applications

Inhaltsverzeichnis

Frontmatter

Chapter 1. Error Analysis for Shock Equation of State Measurements in Polymers Using Manganin Gauges

Piezoresistive manganin gauges undergo a change in resistance as a function of applied stress and have been used in shock experiments to measure both longitudinal and transverse stress. Careful studies are required to calibrate the gauges where the experimental conditions are well-known. In this paper, a series of shock experiments on PMMA, where manganin gauges are used as input, propagated, and transverse gauges to measure shock velocity and stress will be analyzed to understand the sources and magnitude of error. Discussion of error propagation through the experiment will be provided.

Jennifer L. Jordan, Daniel Casem

Chapter 2. Ballistic Impact Experiments and Quantitative Assessments of Mesoscale Damage Modes in a Single-Layer Woven Composite

In this work, we investigated the mesoscale impact and perforation damage of a single layer, woven composite target transversely impacted below and above the ballistic limit by a rigid projectile sized on the order of a tow width. To visualize mesoscale impact damage in woven composites, a thin translucent composite target was used, which provided access to both impact and back-face surfaces. High-resolution photography was used to visualize mesoscale damage, and impact and residual velocity data relative to the location of projectile impact on weaving architecture were quantified. It was found that impact on a tow-tow crossover requires more energy to perforate than impact on a matrix-rich interstitial site or on adjacent, parallel tows. Mesoscale damage in thin, woven composites was characterized for impact velocities below and above the ballistic limit. Four mesoscale damage modes were identified: transverse tow cracks, tow-tow delamination, 45° matrix cracks, and punch- shear. These damage modes were observed both on the surface and inside the composites. High-resolution images of these damage modes were quantified in digital damage maps whereby the output of color intensity correlated with the quantity and type of material damage. Digital maps generated for select specimens revealed characteristic damage patterns in woven fabric composites including a diamond pattern in matrix cracking and a cross pattern in tow–tow delamination. It was found that the greatest extent and quantity of mesoscale damage occurs for impact velocity just below the ballistic limit.

Christopher S. Meyer, Enock Bonyi, Bazle Z. Haque, Daniel J. O’Brien, Kadir Aslan, John W. Gillespie

Chapter 3. A Novel Approach for Plate Impact Experiments to Obtain Properties of Materials Under Extreme Conditions

In this paper we present a novel approach to conduct normal plate impact experiments at elevated temperatures up to 1000 °C. To enable this approach, custom adaptations are made to the breech-end of the single-stage gas-gun at Case Western Reserve University. These adaptations include a precision-machined steel extension piece, which is strategically designed to mate the existing gun-barrel by providing a high tolerance match to the bore and keyway. The extension piece contains a vertical cylindrical heater-well, which houses a resistive coil heater attached to a vertical stem with axial/rotational degrees of freedom. The assembly enables thin metal specimens held at the front-end of a heat-resistant sabot to be heated uniformly across the diameter to the desired test temperatures. Using the configuration, symmetric normal plate impact experiments are conducted on 99.6% tungsten carbide (no binder) using a heated (room temperature to 650 °C) WC flyer plate and a room temperature WC target plate at impact velocities ranging from 233 to 248 m/s. The measured free-surface particle velocity profiles are used to obtain the elastic/plastic behavior of the impacting WC plates as well as the temperature-dependent shock impedance of the flyer. The results indicate a dynamic strength of approximately 6 GPa for the WC used in the present study (strain-rates of about 105), and a decreasing flyer plate longitudinal impedance with increasing temperatures up to 650 °C.

Bryan Zuanetti, Tianxue Wang, Vikas Prakash

Chapter 4. Effect of the Ratio of Charge Mass to Target Mass on Measured Impulse

A common way to measure the loading on a target above the explosion of a charge buried in soil is to measure the total vertical impulse applied to the target. The impulse is often calculated by multiplying the mass of the target by its maximum velocity. While this seems a reasonable approach, in actuality, the impulse so calculated, depends not only on the actual load applied to the target but also on the ratio of the mass of the target to the mass of the explosive. This paper shows that, if the other conditions of an explosive event are the same, i.e., depth of burial of the charge, height of the target, soil properties, etc., there is a consistent, power law, relationship between the charge to target mass ratio and the measured impulse. In this paper, this relationship is developed to provide a heuristic tool to estimate the impulse that would be measured if the charge or target mass is changed.

L. C. Taylor, W. G. Szymczak, H. U. Leiste, W. L. Fourney

Chapter 5. Fracture and Failure Characterization of Transparent Acrylic Based Graft Interpenetrating Polymer Networks (Graft-IPNs)

IPNs are made of two or more polymer networks, each polymerized in the presence of the other/s. They can be suitable alternatives to traditional polymers made from single monomer as desirable characteristics of the constituent polymers can be engineered into IPNs. In this study, an acrylic-based transparent graft Interpenetrating Polymer Networks or simply graft-IPNs were processed and their mechanical properties in general and fracture/failure behaviors in particular were characterized. Good optical transparency, high fracture toughness, and high stiffness were among the attributes targeted in the graft-IPNs for potential transparent armor applications. The graft-IPNs were synthesized by sequential polymerization of compliant elastomeric polyurethane (PU) phase and a stiff acrylate-based copolymer (CoP) phase to generate crosslinks (or, ‘grafts’) between the two networks. A series of such graft-IPNs were synthesized by varying the ratios of CoP:PU. Uniaxial tension tests were performed on the resulting IPNs to measure the elastic modulus and strength whereas mode-I fracture toughness was measured under both quasi-static and dynamic loading conditions. A Hopkinson pressure bar was used in conjunction with an optical technique called Digital Gradient Sensing (DGS) and ultrahigh-speed photography to measure the fracture behavior during stress wave loading. The results show significant enhancements in the crack initiation toughness for some of the graft-IPN compositions relative to the constituents as well as commercially procured PMMA and polycarbonate (PC) sheet stocks. Besides the optical transparency, the increase in fracture toughness is attributed to the grafts or crosslinks generated between the PU and CoP networks.

Balamurugan M. Sundaram, Ricardo B. Mendez, Hareesh V. Tippur, Maria L. Auad

Chapter 6. Dynamic Crack Branching in Soda-Lime Glass: An Optical Investigation Using Digital Gradient Sensing

Transparent brittle materials such as soda-lime glass (SLG) with relatively low fracture toughness and high stiffness pose unique challenges for performing full-field optical measurement of deformations and stresses to characterize their fracture behavior. The current work builds on authors’ previous report wherein the feasibility of Digital Gradient Sensing (DGS) was demonstrated for measuring stress wave induced crack-tip deformations in SLG. In this study, ultrahigh-speed photography (>1 million frames per sec) was used in conjunction with DGS and a Hopkinson pressure bar to load V-notched SLG plates to investigate the crack branching phenomenon. The experimental parameters were controlled such that a single mode-I crack that initiated at the V-notch tip propagated through the glass plate before branching into two prominent mixed-mode daughter cracks. The optical measurements of angular deflection fields that represent stress gradients in two orthogonal in-plane directions were obtained. Using higher order finite-difference based least-squares integration (HFLI) scheme, stress invariant fields (σ xx + σ yy) were evaluated near dynamically propagating crack-tip throughout the branching process.

Balamurugan M. Sundaram, Hareesh V. Tippur

Chapter 7. A Hybrid Experimental-Numerical Study of Crack Initiation and Growth in Transparent Bilayers Across a Weak Interface

Transparent layered structures are of importance to both the military and civilian communities. Their applications include but not limited to lightweight transparent armor, automotive windshields and canopies, personnel shields and visors as well as electronic displays. The introduction of adhesive interlayers is a low-cost approach for developing mechanically resilient multilayered lightweight structures. However, a rigorous mechanics based design of such architectures requires tailoring interfaces (layer thickness, adhesive properties, number of layers, interface location, etc.). Among the multitude of issues involved in this regard, grasping the mechanics of dynamic crack growth across interfaces is of paramount importance. In this context, this work builds on optical investigations of Sundaram and Tippur (J Mech Phys Solids 96:312–332, 2016) who reported dynamic crack-interface interactions related to crack penetration vs. crack branching at a weak interface when the interface was oriented perpendicular to the incoming mode-I crack in an otherwise homogeneous bilayer. A major finding of this work was that a slowly growing crack with a lower stress intensity factor penetrated the interface and grew into the next layer without branching. On the contrary, a fast growing crack with a higher stress intensity factor debonded the interface ahead of its arrival at the interface and hence branched into the interface and subsequently into the next layer as (two) mixed-mode daughter cracks creating higher fracture surface area. In order to exploit this observation and gain further insight into crack growth in multilayered structures, a hybrid experimental-numerical approach that mimics the complexities observed in the bilayer experiments is attempted. This includes optical measurement of the force histories imposed on the bilayer during impact loading of a V-notched PMMA sample impacted by a long-rod with wedge shaped tip matching the notch. Digital Gradient Sensing (DGS) method has been utilized in conjunction with ultrahigh-speed photography followed by optical data analysis to visualize and quantify the force histories. The measured force histories along with other previously determined interface and PMMA characteristics are used as input parameters into a finite element model that includes cohesive elements to benchmark the experiments. Thus validated computational model will be used to investigate a variety of parameters far too complex to emulate experimentally in multilayer architectures.

Sivareddy Dondeti, Hareesh V. Tippur

Chapter 8. Inelastic Behavior of Tungsten-Carbide in Pressure-Shear Impact Shock Experiments Beyond 20 GPa

Pressure-shear plate impact (PSPI) tests commonly use Tungsten-Carbide (WC) as anvil plates, sandwiching the tested material. The common use of WC in these tests is due to its high impedance and high strength, allowing to reach high pressures, with an elastic response, enabling a straightforward analysis of the tested material. Recent modifications of a powder gun facility at Caltech have enabled pressure-shear plate impact experiments (PSPI) to reach higher velocities with corresponding higher pressures and strain rates. Entering this regime, the inelastic behavior of WC has to be taken into account to extract the response of the tested material. In this work we examine the inelastic behavior of WC in the pressure-shear set-up via numerical simulations and PSPI experiments. The 3D numerical simulations enabled to study effects of friction, slip and tilt on the measured signals and so their sensitivity to the material strength and failure behavior. A material model was calibrated in relation to the experimental results.

Z. Lovinger, C. Kettenbeil, M. Mello, G. Ravichandran

Chapter 9. Mechanical Response and Damage Evolution of High-Strength Concrete Under Triaxial Loading

Current weapons effects modeling efforts rely heavily on quasi-static triaxial data sets. However, there are fundamental knowledge gaps in the current continuum modeling approach due to limited experimental data in the areas of dynamic effects and damage evolution. Arbitrary scalar values used for damage parameters have experimentally unverified mathematical forms that often do not scale to different geometries, stress states, or strain rates. Although some preliminary tests have been performed through dynamic triaxial compression experiments, the results are difficult to interpret due to changes in specimen diameter and length-to-diameter ratio. In this study, a high-strength concrete (f’c ∼130 MPa) was investigated under triaxial loading conditions at confining pressures up to 300 MPa. Three cylindrical specimen sizes were used to determine size effects, including 50 × 114 mm, 25 × 50 mm, and 25 × 13 mm. For a limited number of specimens, X-Ray Computed Microtomography (XCMT) scans were conducted. It was noted that size and length-to-diameter ratio have substantial effects on the experimental results that must be understood to determine dynamic effects based on specimen geometries used in dynamic triaxial compression experiments. Additionally, by quantifying pore crushing and crack development under a variety of triaxial loading conditions, future multi-scale modeling efforts will be able to incorporate systematically defined damage parameters that are founded on experimental results.

Brett Williams, William Heard, Steven Graham, Bradley Martin, Colin Loeffler, Xu Nie

Chapter 10. Heterodyne Diffracted Beam Photonic Doppler Velocimeter (DPDV) for Pressure-Shear Shock Experiments

We present details on the design and validation of a heterodyne diffracted beam photonic Doppler velocimeter (DPDV) for pressure-shear plate impact (PSPI) shock experiments. The fiber optic interferometer collects symmetrically diffracted 1st order beams produced by a thin, specular, metallic grating deposited on the rear surface of the impacted target plate and separately interferes each of these beams with a reference beam of a slightly increased wavelength. The resulting interference signals contain an upshifted carrier signal with a constant frequency at zero particle velocity. Signal frequency content in recorded waveforms from PSPI experiments is extracted using a moving-window DFT algorithm and then linearly combined in a post- processing step to decouple and extract the normal and transverse velocity history of the rear target surface. The 0th order (normally reflected) beam can also be interfered in a separate heterodyne PDV configuration to obtain an additional, independent measurement of the normal particle velocity. An overview of the DPDV configuration is presented along with a discussion of the interferometer sensitivities to transverse and normal particle velocities. Results from a normal impact experiment conducted on Y-cut quartz are presented as experimental validation of the technique.

M. Mello, C. Kettenbeil, M. Bischann, Z. Lovinger, G. Ravichandran

Chapter 11. An Optimization-Based Approach to Design a Complex Loading Pattern Using a Modified Split Hopkinson Pressure Bar

The split Hopkinson pressure bar (SHPB) technique is used to characterize the mechanical response of a material during impact loading when a single stress wave pulse passes through that material [1]. The SHPB setup consists of two long bars: an incident bar and a transmission bar. The specimen, which needs to be characterized, is placed between these two bars. A striker propelled from a gas gun hits the incident bar generating a stress wave that propagates through the incident bar. A part of this wave is transmitted to the specimen and the transmission bar while the remaining part of the wave reflects back into the incident bar. By measuring the incident, transmitted, and reflected waves, the mechanical properties of the specimen are determined for high-strain-rate deformations.

Suhas Vidhate, Atacan Yucesoy, Thomas J. Pence, Adam M. Willis, Ricardo Mejia-Alvarez

Chapter 12. Development of “Dropkinson” Bar for Intermediate Strain-Rate Testing

A new apparatus – “Dropkinson Bar” – has been successfully developed for material property characterization at intermediate strain rates. This Dropkinson bar combines a drop table and a Hopkinson bar. The drop table was used to generate a relatively long and stable low-speed impact to the specimen, whereas the Hopkinson bar principle was applied to measure the load history with accounting for inertia effect in the system. Pulse shaping technique was also applied to the Dropkinson bar to facilitate uniform stress and strain as well as constant strain rate in the specimen. The Dropkinson bar was then used to characterize 304L stainless steel and 6061-T6 aluminum at a strain rate of ∼600 s−1. The experimental data obtained from the Dropkinson bar tests were compared with the data obtained from conventional Kolsky tensile bar tests of the same material at similar strain rates. Both sets of experimental results were consistent, showing the newly developed Dropkinson bar apparatus is reliable and repeatable.

Bo Song, Brett Sanborn, Jack Heister, Randy Everett, Thomas Martinez, Gary Groves, Evan Johnson, Dennis Kenney, Marlene Knight, Matthew Spletzer

Chapter 13. Radial Inertia Effect on Dynamic Compressive Response of Polymeric Foam Materials

Polymeric foams have been extensively used in shock isolation applications because of their superior shock or impact energy absorption capability. In order to meet the shock isolation requirements, the polymeric foams need to be experimentally characterized and numerically modeled in terms of material response under shock/impact loading and then evaluated with experimental, analytical, and/or numerical efforts. Measurement of the dynamic compressive stress-strain response of polymeric foams has become fundamental to the shock isolation performance. However, radial inertia has become a severe issue when characterizing soft materials. It is even much more complicated and difficult to address the radial inertia effect in soft polymeric foams. In this study, we developed an analytical method to calculate the additional stress induced by radial inertia in a polymeric foam specimen. The effect of changing profile of Poisson’s ratio during deformation on radial inertia was investigated. The analytical results were also compared with experimental results obtained from Kolsky compression bar tests on a silicone foam.

Bo Song, Brett Sanborn, Wei-Yang Lu

Chapter 14. Examining Material Response Using X-Ray Phase Contrast Imaging

Propagation based X-ray phase contrast imaging (PCI) offers unique opportunities for ultrafast, high-resolution measurements to examine dynamic materials response at extreme conditions. Within the past decade, efforts on the IMPULSE system at the Advanced Photon Source included the development of a novel Multi-frame X-ray PCI (MPCI) system that was used to obtain the first shock-movies to examine material deformation with micron spatial resolution on nanosecond timescale. The MPCI system has been systematically developed over the years to improve optical efficiencies, spatial resolution, obtain more images per experiment, and to develop a dual-imaging, dual-zoom feature useful for many applications. With the MPCI system, X-ray PCI has been successfully used to study a wide range of phenomena including jet-formation in metals, crack nucleation and propagation, response of additively manufactured materials, and detonator dynamics to name a few. In this paper, a brief overview of the MPCI system development is provided along with its application to study shock propagation in materials.

B. J. Jensen, B. Branch, F. J. Cherne, A. Mandal, D. S. Montgomery, A. J. Iverson, C. Carlson

Chapter 15. History Note: Machining, Strain Gages, and a Pulse-Heated Kolsky Bar

A special Kolsky bar apparatus with the capability to pulse heat the sample was built at the National Institute of Standards and Technology (NIST). This Kolsky bar laboratory’s initial purpose was to measure dynamic material properties in support of machining analysis research. Machining is a high-strain, high-strain-rate, high-temperature, high-heating-rate process. Developing mathematical models to analyze machining processes presents unique challenges, including appropriate material stress-strain relationships. The NIST system can heat a sample to over 1000 C in less than a second immediately prior to a Kolsky bar impact test. Although there are many traditional Kolsky bars in operation, the ability to achieve a very rapid temperature increase by electrical resistive heating is unique. The development and construction of this laboratory involved cooperative effort of several researchers from different NIST divisions. The work benefitted from a rich history of strain measuring research at the National Bureau of Standards (NBS), now named NIST, as well as drawing on a long history of interaction with the Society for Experimental Mechanics (SEM). .

R. Rhorer, S. Mates, E. Whitenton, T. Burns

Chapter 16. Improved Richtmyer-Meshkov Instability Experiments for Very-High-Rate Strength and Application to Tantalum

Recently, Richtmyer-Meshkov instabilities (RMI) have been used for studying metal strength at strain rates up to at least 10^7/s. RMI experiments involve shocking a metal interface with geometrical perturbations that invert, grow, and possibly arrest subsequent to the shock. In experiments one measures the growth and arrest velocities to study the specimen’s flow (deviatoric) strength. In this paper, we describe experiments on tantalum at three shock pressure from 20 to 34 GPa, with six different perturbation sizes at each pressure, making this the most comprehensive set of RMI experiments on any material. In addition, these experiments were fielded using impact loading, as compared to high explosive loading in previous experiments, allowing for more precise modeling and more extensive interpretation of the data. Preliminary results are presented.

Michael B. Prime, William T. Buttler, Saryu J. Fensin, David R. Jones, Ruben Manzanares, Daniel T. Martinez, John I. Martinez, Derek W. Schmidt, Carl P. Trujillo

Chapter 17. Mechanical Characterization and Numerical Material Modeling of Polyurea

The mechanical behavior of four unique blends of polyurea materials has been investigated through a combined experimental and computational study. Mechanical characterization of each material was evaluated under both tensile and compressive loading at strain rates ranging from 0.01 to 100 strains per second (1/s). Planar blast wave experiments utilizing a 40 mm light gas gun were also conducted which imparted strain rates up to 104 strains per second (1/s). The material testing results showed that stress-strain response is a function of loading, strain level, and strain rate. These results were utilized to define a non-linear rubber material model in Ls-Dyna which was validated against the test data through a series of “block” type simulations for each material. Each material model was shown to replicate both the tensile and compressive behavior as well as the strain rate dependence. The material models were subsequently extended to the simulations of the blast wave experiments. The blast wave simulations were shown to accurately capture wave propagation resulting from a shock type pressure loading as well as the stress magnitudes of the transmitted waves after passing through the respective polyurea materials. The current study has resulted in the mechanical characterization of four polyurea materials under tensile/compressive loading at increasing strain rates, a suitably validated numerical material model, and suitable correlations between experimental and simulation results.

James LeBlanc, Susan Bartyczak, Lauren Edgerton

Chapter 18. Full-Scale Testing and Numerical Modeling of Adhesively Bonded Hot Stamped Ultra-High Strength Steel Hat Sections

The implementation of structural adhesives to join multi-material lightweight vehicle structures requires advanced computer aided engineering (CAE) and therefore thorough material characterization and model validation at the component level. Hot stamped, 1.2 and 1.8 mm thick ultra-high strength steel hat section channels were joined to form closed tubular structures using a two-part toughened epoxy adhesive applied to the flanges, with a bondline thickness of 0.007″ (0.178 mm). The joined tubes were tested under quasi-static loading in two configurations: three-point bending to load the adhesive in shear (Mode II) and axial crush resulting primarily in Mode I loading. Finite element models of the tests were developed using previously measured material properties for the adhesive implemented using cohesive zone elements. The three-point bending response included a linear loading regime followed by localized plastic deformation of the tube and finally abrupt failure of the adhesive joint between the hat sections at an average load of 34.0 kN for the 1.2 mm tubes and 78.8 kN for the 1.8 mm tubes. The axial crush response included an initial average peak force of 260 kN followed by a local folding or global deformation mode, leading to progressive separation of the adhesive joint and an average energy absorption of 8.45 kJ. Finite element models based on published adhesive and metal properties demonstrated good correlation with experimental results in predicted peak force and overall loading response.

Y. B. Liu, D. Cronin, M. Worswick

Chapter 19. Mechanical Characterization of ZrO2 Rich Glass Ceramic

Glass-Ceramics (GCs) find wide applications in electronic packaging, kitchenwares, optics, acoustic systems, aerospace industry, as armor materials, and as aesthetic material for dental restoration due to their simple processing, easy machinability, low porosity and high strength.. However, they are inevitably subjected to tensile load resulting in catastrophic failure due to their sometimes low fracture toughness and high brittleness. In this context, a zirconia containing lithium disilicate glass ceramic is developed and mechanically characterized. Its fracture toughness and hardness are measured using Chevron Notch Short Bar (CNSB) method and Vickers indent respectively.. Further, the material was subjected to single edge notched bar (SENB) loading in 3-point bend configuration. The non-linearity in the load-deflection curve suggested the presence of R-curve behavior which was subsequently measured. The results of this technique are compared with those of Corning Ultra Low Expansion (ULE) glass, which was used as a standard for the measurement. In the glass-ceramic material a rising R-curve, a desirable attribute as it suppresses subcritical crack growth, was evident. With higher fracture toughness, rising R-curve and improved brittleness index, this GC has advantaged mechanical attributes. Further, the fracture surface exhibited significant roughness as compared to ULE glass. With multiple potential factors contributing to the improved fracture toughness, each of their contributions is yet to be fully understood.

Balamurugan M. Sundaram, Jamie T. Westbrook, Charlene M. Smith, John P. Finkeldey

Chapter 20. Microstructure Characterization of Electrodeposited Nickel Tested at High Strain Rates

A newly developed micro-kolsy bar system at the Army Research Laboratory has made it possible to test materials in compression at strain rates greater than 104 s−1. Opening up a new realm for testing of materials at high strain rates. In order to reach these high strain rates, sample diameters must be on the order of tens to hundreds of microns. Fabrication of these micro-samples is done using a femtosecond laser, since the ultrashort pulse width of this laser does not produce any appreciable damage layer. The high strain rate (103–105 s−1) behavior and resulting microstructure of electrodeposited nickel was investigated using this micro-kolsy bar system. The microstructure of the as-deposited and tested samples was examined with electron backscatter diffraction and transmission electron microscopy. Tested samples show evidence of dynamic recrystallization and formation of a large number fraction of high angle, Σ3 boundaries.

Jonathan P. Ligda, Daniel Casem, Heather Murdoch

Chapter 21. The Flow Stress of AM IN 625 under Conditions of High Strain and Strain Rate

Additively manufactured (AM) nickel superalloy (In 625) with known processing history and quasi-static properties has been investigated under extreme strains up to about 100% and strain rate up to about 104/s by machining. A model for the calculation of the component of force that is due to indentation by the tool cutting edge was utilized to correct the measured shear force and material flow stress. The results are compared to flow stress measurements produced by Kolsky compression testing under strains of about 25% and strain rate of about 103/s. The highly instrumented setups utilized for the machining testing made possible an accurate description of the strain and strain rate at the primary shear zone (PSZ), and the temperature at the tool rake face that prevailed throughout the machining. The strain and strain rate were determined by digital image correlation. The temperature was determined by through-the-tool thermography. Differences observable during the cutting and dynamic compression of additive and wrought In 625 are outlined.

Rajesh K. Ananda-Kumar, Homar Lopez-Hawa, Wilfredo Moscoso-Kingsley, Viswanathan Madhavan

Chapter 22. Proton Radiography of Reverse Ballistic Impacts

Ceramics are important materials due to their high strength and hardness, particularly in armor systems such as personnel body armor where they are used extensively. Understanding the failure process for these types of systems is key to improving their performance. To better understand the process of failure in ceramic materials subjected to ballistic impacts, we planned and executed reverse ballistic experiments to study material failure during impact on a silicon carbide target. The primary diagnostic tool we used was proton radiography conducted at Los Alamos National Laboratory Neutron Science Center (LANSCE) using their 800 mega-electron-volt (MeV) linear accelerator. Proton radiography at this facility is capable of excellent spatial and temporal resolution with up to 31 frames of data captured with variable frame spacing and gate time. We report and discuss some of the results of these experiments.

Brady Aydelotte, Michael Golt, Brian Schuster, Jason Allison, Frank Cherne, Matthew Freeman, Johnny Goett III, Brian Hollander, Brian Jensen, Julian Lopez, Fesseha Mariam, Michael Martinez, Jason Medina, Christopher Morris, Levi Neukirch, Adam Pacheco, Mary Sandstrom, Alexander Andy Saunders, Tamsen Schurmann, Amy Tainter, Zhaowen Tang, Dale Tupa, Joshua Tybo, Wendy Vogan-McNeil, Carl Wilde, John Wright

Chapter 23. The Effect of ECAE on the Ballistic Response of AZ31

The equal channel angular extrusion (ECAE) process that refines the grains by severe plastic deformation has been noted to increase the high strain rate compressive strength of metals, such as magnesium alloy, AZ31. However it is not known if the improvement in the properties translates to improvement in the ballistic properties. In this study, ballistic experiments were performed on magnesium AZ31B that were ECAE processed by the 4Bc route. The targets were cut from orientations that exhibit disparate mechanical responses. The complex failure process was characterized by photonic Doppler velocimetry.

Tomoko Sano, Phillip Jannotti

Chapter 24. Development of an Interferometer and Schlieren Based Measurement Technique for Resolving Cavitation Pressure Fields

The existence of cavitation in soft matter introduces challenging problems as it exhibits unique deformation and failure mechanisms. The motivation of our study was to develop an understanding of cavitation and resulting bubble dynamics in and near soft materials, with applications in the study of biological tissues, polymeric coatings, biofouling, composites and other synthetic materials. In this work, we describe a new experimental technique to measure the internal pressure of quasi-statically induced bubbles within compressible time-dependent hydrogels. A Michelson interferometric technique and background-oriented schlieren (BOS) were paired with digital image correlation (DIC) to resolve spatiotemporal pressure fields during cavitation in the bubble and surrounding material. These measurements are meant to inform existing cavitation models and gain new insight into the highly localized deformation mechanism of cavitating bubbles.

Selda Buyukozturk, Alexander K. Landauer, Christian Franck

Chapter 25. Quasi-Static and Dynamic Poisson’s Ratio Evolution of Hyperelastic Foams

Poisson’s ratio of soft, hyperelastic foam materials such as silicone foam is typically assumed to be both a constant and a small number near zero. However, when the silicone foam is subjected to large deformation into densification, the Poisson’s ratio may significantly change, which warrants careful and appropriate consideration in modeling and simulation of impact/shock mitigation scenarios. The evolution of the Poisson’s ratio of foam materials has not yet been characterized. In this study, radial and axial measurements of specimen strain are made simultaneously during quasi-static and dynamic compression test on a silicone foam. The Poisson’s ratio was found to exhibit a transition from compressible to nearly incompressible based on strain level and reached different values at quasi-static and dynamic rates.

Brett Sanborn, Bo Song

Chapter 26. Revisit of Dynamic Brazilian Tests of Geomaterials

Understanding the dynamic behavior of geomaterials is critical for refining modeling and simulation of applications that involve impacts or explosions. Obtaining material properties of geomaterials is challenging, particularly in tension, due to the brittle and low-strength nature of such materials. Dynamic split tension technique (also called dynamic Brazilian test) has been employed in recent decades to determine the dynamic tensile strength of geomaterials. This is primarily because the split tension method is relatively straightforward to implement in a Kolsky compression bar. Typically, investigators use the peak load reached by the specimen to calculate the tensile strength of the specimen material, which is valid when the specimen is compressed at quasi-static strain rate. However, the same assumption cannot be safely made at dynamic strain rates due to wave propagation effects. In this study, the dynamic split tension (or Brazilian) test technique is revisited. High-speed cameras and digital image correlation (DIC) were used to image the failure of the Brazilian-disk specimen to discover when the first crack occurred relative to the measured peak load during the experiment. Differences of first crack location and time on either side of the sample were compared. The strain rate when the first crack is initiated was also compared to the traditional estimation method of strain rate using the specimen stress history.

Brett Sanborn, Elizabeth Jones, Matthew Hudspeth, Bo Song, Scott Broome

Chapter 27. Interface Chemistry Dependent Mechanical Properties in Energetic Materials Using Nano-Scale Impact Experiment

Energetic materials are sensitive to mechanical shock and defects caused by a high velocity impact, which may result in unwanted detonation due to hot-spot formation. In order to understand the underlying mechanism, characterization of high strain rate mechanical properties needs to be studied. One of the key factors that can contribute to this type of defect is the failure initiated at the interfaces such as those between Hydroxyl-terminated polybutadiene (HTPB)-HMX (or HTPB-Ammonium Perchlorate (AP)). In this work, interface mechanical properties of HTPB-HMX (and HTPB-AP) interfaces are characterized using nano-scale impact experiments at strain rates up to 100 s−1. The experiments were conducted with impactor of radius 1 μm on the interfaces with varying amount of binding agent. For HTPB-AP samples, Tepanol is used as the binding agent. The impact response is determined in the bulk HTPB, HMX, and AP as well as at the HTPB-HMX and HTPB-AP interfaces. A power law viscoplastic constitutive model is fitted to experimental stress-strain-strain rate data which can be used in Finite Element Model simulation to predict the shock behavior of energetic materials. An in-situ mechanical Raman spectroscopy (MRS) setup was used to analyze the effect of interface chemistry on interface level stress variation. The stress distribution near the interface captures the effect of interface chemistry variation.

Ayotomi Olokun, Chandra Prakash, I. Emre Gunduz, Vikas Tomar

Chapter 28. Optimization of an Image-Based Experimental Setup for the Dynamic Behaviour Characterization of Materials

The present work aims at identifying an elastic-viscoplastic material constitutive model over a wide strain and strain-rate range (up to 0.1 and 1000 s−1 respectively), using the so-called Virtual Fields Method. To define the experimental campaign, a design process has been set. It relies on the numerical optimization of the setup – notably the specimen shape, the impact conditions and the measurement resolution (time and space) – with respects to user-defined criteria. Finally, the selected configuration ensures an accurate and robust identification.

Pascal Bouda, Delphine Notta-Cuvier, Bertrand Langrand, Eric Markiewicz, Fabrice Pierron

Chapter 29. High Strain Rate Response of Adhesively Bonded Fiber-Reinforced Composite Joints: A Computational Study to Guide Experimental Design

Adhesively bonded carbon fiber-reinforced epoxy composite laminates are widely used in aerospace applications. During a high energy impact event, these laminates are often subjected to high strain rate loading. However, the influence of high strain rate loading on the response of these composite joints is not well understood. Computational finite element (FE) modeling and simulations are conducted to guide the design of high strain rate experiments. Two different experimental designs based on split Hopkinson bar were numerically modeled to simulate Mode I and Mode II types loading in the composite. In addition, the computational approach adopted in this study helps in understanding the high strain rate response of adhesively bonded composite joints subjected to nominally Mode I and Mode II loading. The modeling approach consists of a ply-level 3D FE model, a progressive damage constitutive model for the composite material behavior and a cohesive tie-break contact element for interlaminar delamination.

Suraj Ravindran, Subramani Sockalingam, Addis Kidane, Michael Sutton, Brian Justusson, Jenna Pang

Chapter 30. Pressure-Shear Plate Impact Experiments on Soda-Lime Glass at Pressures Beyond 20 GPa

Recent modifications of a powder gun facility at Caltech have enabled pressure-shear plate impact (PSPI) experiments in a regime of pressures and strain rates that were previously inaccessible. A novel heterodyne diffracted beam photonic Doppler velocimeter (DPDV) has also been developed for simultaneous measurement of the normal and transverse particle velocity histories using the ±first order diffracted beams produced by a 400 lines/mm diffraction grating deposited onto the polished rear surface of the impacted target plate. We present and interpret the results of PSPI experiments conducted on 5 μm thick soda-lime glass samples subjected to normal stresses beyond 20 GPa and shear strain rates approaching 108 s−1. Transverse particle velocity measurements are used to infer the shearing resistance of soda-lime glass under these extreme conditions.

C. Kettenbeil, M. Mello, T. Jiao, R. J. Clifton, G. Ravichandran

Chapter 31. Dynamic Mechanical Response of T800/F3900 Composite Under Tensile and Compressive Loading

The effect of strain rate on the mechanical response of T800/F3900, a strengthened epoxy carbon-fiber reinforced polymer, is studied by conducting compression and tensile tests at different strain rates. Low strain rate tests (0.001 s−1 and 1 s−1) are done using a hydraulic frame and high strain rate tests (300 s−1–600 s−1) are done with the SHB technique. Digital Image Correlation is used in all tests to obtain full-field strain measurements. Tension tests have been done on unidirectional laminates in the 90 ° direction. Compression tests have been done on unidirectional laminates in the 90 ° and through the thickness directions. No or small strain rate effect is observed between the low strain rate tests. The results from the high strain rate tests show significant strain rate effects.

Yogesh Deshpande, Peiyu Yang, Jeremy Seidt, Amos Gilat

Chapter 32. Experimental Investigation of Rate Sensitive Mechanical Response of Pure Polyurea

The application of layered composite structural systems to protect the main structure during vehicle collisions, blast loading and other high impact applications has been a major focus of interest in the automobile industry over the last few decades. Enhancing the energy absorption, improving blast resistance and improving the dynamic fracture resistance of metallic plate structures has been the main challenges in these studies. Polyurea is a good candidate which has excellent mechanical as well as chemical properties. In the present work, a detailed study has been made on the rate sensitive response of pure form of polyurea. The experiments were carried out by Split Hopkinson Pressure Bar(SHPB) over a wide range of strain rates(1000–4500 s−1) to measure the stress-strain response of the material. A brief analysis has been made on the stiffness calculation & to see how stress is varying with respect to strain rate at different strains.

K. Srinivas, C. Lakshmana Rao, Venkitanarayanan Parameswaran

Chapter 33. Experimental Study on Dynamic Fracture Response of Al6063-T6 Under High Rates of Loading

The focus of the current article is to investigate the dynamic fracture toughness of aluminum alloy Al6063-T6 under three-point transient loading conditions. Prior to the dynamic evaluation, three-point bend experiment were also conducted under the quasi-static conditions to evaluate the static fracture toughness using standard formulations available in the literature. Modified Hopkinson pressure bar and ultra-high speed 3D-Digital image correlation (DIC) procedure was utilized to identify the crack initiation time and the crack mouth opening displacement (CMOD) of the specimen under transient loading conditions. To develop the better understanding of the failure mechanism of the specimen, fracture toughness at different strain rates were evaluated. A good agreement between the both Strain gauge measurements and DIC results was observed.

Anoop Kumar Pandouria, Purnashis Chakraborty, Sanjay Kumar, Vikrant Tiwari

Chapter 34. Ballistic and Material Tests and Simulations on Ultra-High Performance Concrete

Ultra-high performance concretes (UHPC), meaning concretes with compressive strengths above 150 MPa (B-150), introduce improved properties such as stiffness, compressive strength, and post-failure compliance as compared to standard concretes. Advantages are shown in standard applications of construction, yet, a large potential exists in applications of protective structures to withstand impulsive loadings of blast or direct impact. In this work an UHPC with a compression strength of 200 MPa was used to test and develop a material model to enable predictions for impact and penetration. The material was first tested to characterize the material behavior under quasistatic loading in torsion, compression and triaxial compression, up to confinement pressures of 500 MPa. Moreover, the UHPC was characterized under dynamic loading, using a Kolsky bar (Split Hopkinson Pressure Bar). Based on these lab-scale tests, a Johnson-Holmquist material model was calibrated for the numerical simulations. Finally, ballistic tests were performed with two projectile geometries, using two configurations: a standalone UHPC panel to obtain the ballistic limit, and depth of penetration (DOP) measurements, with aluminum backing, to better relate to the concrete strength during penetration conditions. Preliminary ballistic computations with the UHPC model, calibrated from the lab-scale tests for LS-DYNA, provided good predictions when compared to most of the tests.

Sidney Chocron, Alexander Carpenter, Nikki Scott, Oren Spector, Alon Malka-Markovitz, Zev Lovinger, Doron Havazelet

Chapter 35. Mechanical Behavior of Ta at Extreme Strain-Rates

The compressive stress-strain response of a commercially pure (99.98%) Ta was investigated at strain-rates ranging from 0.001/s to 500 k/s. Strain-rates up to 20 k/s were obtained using conventional load frames and Kolsky bar methods. The higher strain-rates were obtained using optically instrumented miniature Kolsky bars. Because these experiments require sample sizes as small as ∼30 um, a fine grain structure was desired. To achieve this, we study a Ta billet that was processed by ECAE to produce an ultrafine grain structure. The billets were subsequently annealed at 1203 K under high vacuum for 2 h to coarsen the grain size to approximately 2 um. The as-worked and annealed microstructures were investigated by electron backscatter diffraction to verify the grain structure. A strong rate dependence is observed over this range of strain-rates, although there is a discrepancy between data at similar strain-rates using different sample sizes. This discrepancy is the subject of on-going investigation.

Daniel Casem, Daniel Magagnosc, Jonathan Ligda, Brian Schuster, Timothy Walter

Chapter 36. Constitutive Modeling of Polyamide Split Hopkinson Pressure Bars for the Design of a Pre-stretched Apparatus

This paper aims to model the constitutive behavior of polyamide material used in the Split Hopkinson Pressure bars (SHPB). The Hopkinson bars apparatus is employed for the mechanical characterization of many materials under high strain rates at large strains. Nevertheless, testing soft materials is a challenging task regarding their low impedance properties and the difficulty to achieve a dynamic equilibrium. To address that issue, polyamide (nylon) SHPB are employed. However, the application of the pre-stretched technique to tensile apparatus using polyamide bars may provide a flexible mechanical characterization device reaching moderate to high strain rates at large strains. It requires bars of several meters where wave attenuation and dispersion are dominant. Moreover, the design of such apparatus is extremely complex with respect to the sample shape and rigidity as well as connectors. While analytical techniques are proposed in the literature, they are not sufficient to provide guidance in the design and the optimization of a pre-stretched apparatus.Therefore, the aim of the present study is to develop a finite element model of polyamide SHPB. Various experimental tests are conducted using compressive polyamide SHPB. These tests are computationally modeled using the Radioss explicit FE code through an axisymmetric analysis. The generalized Maxwell model is chosen to consider the viscoelastic material properties. An optimization procedure by inverse method is applied using both experimental and numerical strain signals to identify the material coefficients.Experimental tests are repeatable for each test configuration. The viscoelastic model parameters of the bars are identified through one configuration and validated against three others. This model gives very satisfactory results and presents interesting predictive abilities.

A. Bracq, G. Haugou, H. Morvan

Chapter 37. Investigating the Mechanical and Thermal Relationship for Epoxy Blends

The mechanical response of epoxy networks was investigated under uniaxial compression at low, intermediate, and high strain rates. These epoxy blends are tailored to achieve a broad range of glass transition temperatures. Previous studies have shown a correlation of the epoxies’ Tg in relationship to its ballistic performance as well as its mechanical properties at quasi-static rates. To better understand these phenomena, a MWIR camera was used to directly measure the transient surface temperature and determine temperature change. The extent and rate of deformation highly influences the flow stress behavior which coincides with the rise in the adiabatic temperatures, hence the thermal softening response. One intriguing aspect for results at rates 0.01/s – 0.1/s and higher reveals that the surface temperature continues to increase despite pressure ceasing. This would indicate the core temperatures are still gradually transferring to the surface. The experimental setup and results are discussed.

Michael Harr, Paul Moy, Timothy Walter, Kevin Masser

Chapter 38. A Novel Auxetic Structure with Enhanced Impact Performance by Means of Periodic Tessellation with Variable Poisson’s Ratio

This study proposes a new approach to designing impact resistant elastomeric structures using innovative bi-dimensional patterns composed of a combination of circular and elliptical voids with variable aspect ratios. Key to the design are discrete sections each with different effective Poisson’s ratios ranging from negative to positive. Cubic samples 80 × 80 × 80 cm in size with different void geometry and effective Poisson’s ratios were fabricated and successively tested under compressive and low-velocity impact loads as a proof-of-concept, showing good agreement with finite element simulations.The numerical comparisons for different porosity levels demonstrated that the variable Poisson’s ratio materials resulted in better impact responses compared to those characterized by a positive (constant) value of the effective Poisson’s ratio. The promising results also show that the variable shape of the voids can lead to a modular trigger of overall effective auxetic behavior, opening up new ways design and use auxetic macro-structures with variable porosity and variable Poisson’s ratio for a wide range of applications and, in particular, for impact and protecting devices.

M. Taylor, L. Francesconi, A. Baldi, X. Liang, F. Aymerich

Chapter 39. On the Response of Polymer Bonded Explosives at Different Impact Velocities

Multiscale experiments are performed to understand the deformation mechanisms in polymer bonded explosives at a range of impact velocities. The experiments are conducted in a direct impact configuration, where a polycarbonate projectile is directly shot onto polymer bonded sugar samples at different impact velocities. During the deformation process, the images are captured at five million frames/second using an ultrahigh speed camera. For the macro scale experiment, the images are captured at a resolution of 75 μm/pixel and for the mesoscale experiments, the magnification factor is 10 μm/pixel. The deformation field is obtained using digital image correlation technique. From the macroscale displacement field, the spatial stress distribution is calculated using a nonparametric method. The meso-scale experiments are used to explain the deformation mechanisms observed at the macroscale.

Suraj Ravindran, Addis Tessema, Addis Kidane

Chapter 40. Localized Microstructural Deformation Behavior of Dynamically Deformed Pure Magnesium

Dynamic grain boundary region deformation of pure magnesium was investigated and verified by utilizing in-situ full field strain measurements obtained from Digital Image Correlation (DIC) techniques. This method was confirmed to effectively characterize the microstructural response of an area of interest in the vicinity of multiple grain boundaries and triple junctions. The highly heterogeneous evolution of the material strain patterns was quantified, and the highest concentrations of the localized response were seen to occur primarily at the interfaces between grains, while the amount of in-grain deformation, specifically in the larger grains was minimal by comparison. Locations of suspected active slip and twinning regions were identified and conclusions about other possible modes of deformation are discussed.

Peter Malchow, Suraj Ravindran, Addis Kidane

Chapter 41. Energy Absorption Characteristics of Graded Foams Subjected to High Velocity Loading

In this study the effect of layer stacking arrangement on the energy absorption characteristics of density-graded cellular polymers subjected to high velocity impact is investigated experimentally. Dynamic loading is performed using Split Hopkinson Pressure Bar (SHPB) which is also modified for a direct impact experiment. Different bulk density polymeric foam layers are bonded together in different stacking arrangements and subjected to impact loading. Ultra-high speed imaging is implemented to measure the deformation and observe the formation and propagation of compaction waves during direct impact. The effect of the orientation of the discrete layers on the dynamic stress-strain response is analyzed using digital image correlation (DIC). The effects of material compressibility are implemented to the analysis. The approach uses DIC to calculate the full-field acceleration and material density, later used to determine the stress gradients developed in the material. The best arrangement of layer structure is chosen by the highest energy absorption characteristics measured. Failure mechanisms associated with energy dissipation in graded materials are discussed.

Abigail Wohlford, Suraj Ravindran, Addis Kidane

Chapter 42. Residual Structural Capacity of a High-Performance Concrete

In this study, the residual unconfined compressive strength of a high-performance concrete (f’c ∼ 140 MPa) was investigated using samples that were pre-loaded to specific states of triaxial confinement. The residual unconfined compressive strengths of the samples were then compared to the unconfined compressive strength of pristine samples not subjected to the pre-load triaxial conditions. To accomplish the pre-load triaxial conditions, the samples were first subjected to specified stress-strain paths corresponding to pure hydrostatic compression and uniaxial strain in compression. Both the hydrostatic compression and uniaxial strain (in compression) tests were performed at low- and high-pressure levels under controlled conditions to prevent reaching the material failure limit. Once the samples were tested through either hydrostatic compression or uniaxial strain, they were recovered and subjected to unconfined compression until failure. Data from these samples were compared to the unconfined compressive strength of pristine samples from the same concrete batch. Residual structural capacity was determined through a comparison of these values and as a means to quantify damage induced (both with and without shear) by the specified stress-strain paths. Applications of these data are discussed for future improvements to concrete constitutive models commonly used at the U.S. Army Engineer Research and Development Center to simulate dynamic events.

George Vankirk, William Heard, Andreas Frank, Mike Hammons, Jason Roth

Chapter 43. Dynamic Mode II Fracture Response of PMMA Within an Aquatic Environment

Sheets of Poly Methyl Methacrylate (PMMA) 3 mm thick are lasercut into rectangles, and then subjected to a high-energy impact while submerged in distilled water, to investigate the effect that submersion may have on mode II fracture. The experiment has been carried out using a compressed air gun, which launches a delrin projectile towards the PMMA test specimen. A unique apparatus was constructed, which contains and allows the test specimen to be suspended in distilled water, while the projectile impacts a buffer adhered to the test specimen. The buffer transfers the impact onto the edge of the test specimen. Transparent walls in the apparatus allow the use of ultra-high-speed photography (up to 10Mfps), and digital image correlation (DIC) to measure dynamic response within the specimen throughout fracture. Data collected was used to calculate critical stress intensity factor. Results are compared to those from experiments in which test samples are not submerged.

Vivianna Gomez, Ian Delaney, Rodrigo Chavez, Veronica Eliasson

Chapter 44. An Image-Based Inertial Impact Test for the High Strain Rate Properties of Brittle Materials

Testing ceramics at high strain rates presents many experimental difficulties due to the brittle nature of the material being tested. When using a split Hopkinson pressure bar (SHPB) for high strain rate testing, adequate time is required for stress wave effects to damp out. For brittle materials, with small strains to failure, it is difficult to satisfy this constraint. Thus, most available high strain rate data for ceramics focuses on using the SHPB for strength testing in compression. Due to the limitations of the SHPB technique, there is minimal data on the stiffness and tensile strength of ceramics at high strain rates. Recently, a new image-based inertial impact (IBII) test method has shown promise for analysing the high strain rate behaviour of brittle materials. This test method uses a reflected compressive stress wave to generate tensile stress and failure in an impacted specimen. Throughout the propagation of the stress wave, full-field displacement measurements are taken. Strain fields and acceleration fields are derived from the displacement fields. The acceleration fields are then used to reconstruct stress information and identify the material properties. The aim of this study is to apply IBII test methodology to analyse the stiffness and strength of ceramics at high strain rates. Preliminary results have shown that it was possible to use the IBII test method to identify the elastic modulus and strength of tungsten carbide at strain rates on the order of 1000/s. For a tungsten carbide with 13% cobalt binder the elastic modulus was identified as 520 GPa and the tensile strength was 1400 MPa at nominal strain rate of 1000/s. Further tests are planned on several different grades of tungsten carbide and other ceramics including boron carbide and sapphire.

Lloyd Fletcher, Fabrice Pierron

Chapter 45. An Image-Based Approach for Measuring Dynamic Fracture Toughness

In order to model the dynamic failure of engineering structures it is necessary to have a thorough understanding of dynamic fracture processes. Dynamic fracture toughness has been experimentally analysed by fitting the K-dominant solution to the displacement field measured with a local or full-field technique, such as caustics, photoelasticity or digital image correlation. For highly dynamic crack propagation the stress state at the crack tip is influenced by stress waves. A dynamic propagating crack emits stress waves which can be reflected and/or scattered away. These waves are felt by the evolving crack front, as well as through the sample configuration, and hence material inertia may lead to effects more subtle (yet still present) than those associated with load transfer. The K-dominant solution only indirectly accounts for these inertial effects by including the crack velocity as an input or by using higher order terms in the series expansion. The aim of this work is to develop a new image-based method for measuring dynamic fracture toughness. This method uses full-field measurements to perform an energy balance on a fracture specimen and calculate the energy consumed by crack growth. Using full-field data the impact energy, strain energy and kinetic energy can be measured. When the material cracks the fracture energy is the difference between the impact energy and the sum of the strain and kinetic energy. Explicit dynamics simulations using cohesive elements were used to validate the methodology. The finite element data was used for simulated image deformation experiments. These virtual experiments were used to analyse measurement error propagation from camera spatial and temporal resolution. Future work will include additional image deformation simulations and a first experimental validation of the test method.

Lloyd Fletcher, Leslie Lamberson, Fabrice Pierron

Chapter 46. The Effect of in-Plane Properties on the Ballistic Response of Polyethylene Composites

Using developed experimental and analytical methods for in-plane shear characterization of quasi-statically loaded polyethylene laminates, this work seeks to evaluate the effect the in-plane shear behavior has on ballistic performance (resistance to penetration and back face deflection). In-plane shear is a matrix-dominated phenomena and processing pressure is known to influence noticeable changes in the shear properties of polyethylene composites, so by varying matrix materials and processing conditions it is possible to probe an array of configurations. Quasi-static tensile tests of laminates with [±45°] orientation are performed to obtain the in-plane shear properties. To evaluate the ballistic response, a high pressure helium laboratory gas gun is used to accelerate 0.22 caliber spherical steel projectiles toward specimen panels to characterize the V50 ballistic limit velocity and back-face deflection.

Julia Cline

Chapter 47. Storage and Loss Moduli of Low-Impedance Materials at kHz Frequencies

Standard Dynamic Mechanical Analysis (DMA) is generally used to measure the mechanical properties of polymers at frequencies around and below 100 Hz. Ultrasonic (US) techniques measure wave speeds and impedances at higher frequencies. However, both approaches run into issues between the two regimes. DMA systems become less reliable due to the dynamic response of the frames and load path as one tries increasing the frequency. On the other hand, the internal multiple reflections in the wave propagation techniques introduce challenges in clean measurements and require careful analysis. In this presentation, we introduce a robust procedure for determining the storage and loss moduli of low-impedance materials, where a cylindrical sample is placed between two long metal bars, similar to SHPB technique. However, unlike SHPB, the incidence signal is created by a very light impact, to ensure that the sample does not experience permanent or large deformation. Furthermore, due to the length of the specimen, dynamic equilibrium is neither guaranteed nor intended. The reflected and transmitted pulses are measured using semi-conductor strain gages. The wave speed may be determined using a phase spectral analysis of the time-resolved signals. Determination of the material loss requires a more thorough transfer matrix analysis. The method was applied to a soft polyurea elastomer that was tested in a temperature-control chamber and results were compared with DMA and US data using time-temperature superposition (TTS). While the predictions of the storage modulus using DMA and TTS matched very well with the direct measurements, the DMA/TTS predictions generally underestimate the material loss at higher frequencies. We expect that this method may be applied successfully to other low impedance materials including foams and metamaterials.

Wiroj Nantasetphong, Zhanzhan Jia, M. Arif Hasan, Alireza V. Amirkhizi, Sia Nmeat-Nasser

Chapter 48. Effects of Pressure and Strain Rate on the Mechanical Behavior of Glassy Polymers

In this study the mechanical response of transparent polymers under varying strain rates and hydrostatic pressures is investigated. Quasi-static and dynamic tests are performed under uniaxial and multi-axial loadings and the effect of hydrostatic pressure on the response of the material is explored. In both quasi-static and dynamic experiments, the confinement pressure was increased to a predetermined level and kept constant during the test. This test subjects specimens to confining pressure (up to 200 MPa) prior to loading. Loading was either applied quasi-statically using a servo-hydraulic load frame or at dynamic rates using a modified SHPB. The strain rate dependency of the Polycarbonate material is studied using an Instron UTM and split Hopkinson pressure bar (SHPB) technique. Digital image correlation is used to record full field deformation and calculate the strain. Ultra-high strain rate tests are also performed using a micro-Kolsky bar and small (50–100 um length) specimens. The confinement experiments show that the yield stress is linearly proportional to the confinement pressure but the elastic modulus is insensitive to confinement pressure. Significant rate sensitivity is observed at moderate strain rates and becomes insensitive to strain rate at the highest strain rates measured.

Abigail Wohlford, Timothy Walter, Daniel Casem, Paul Moy, Addis Kidane

Chapter 49. The Role of Texture on the Strain-Rate Sensitivity of Mg and Mg Alloy AZ31B

In this study, the role of texture on the quasi-static and dynamic response of pure magnesium and magnesium alloy AZ31B is investigated. Texture is imparted through thermo-mechanical processes of hot-rolling or equal channel angular extrusion. Constant strain-rate, both dynamic and quasi-static, and strain-rate jump experiments, dynamic-quasi-static, quasi-static-dynamic and dynamic-dynamic, are used to examine plastic flow anisotropy and strain hardening response. Observations of the macroscopic material behavior, specifically the stress-trajectory, are supported by electron back-scatter diffraction analysis to gain insights of texture evolution and predominant deformation processes taking place during deformation increments.

Nathan Briggs, Moriah Bischann, Owen T. Kingstedt

Chapter 50. Shock Compaction of Al Powder Examined by X-Ray Phase Contrast Imaging

Shock compaction response of ∼50% porous aluminum powder, encapsulated in PMMA cylinders and impacted at 0.3–1.7 km/s using 6061-T6 Al impactors, was examined in situ and in real time using a propagation-based X-ray phase contract imaging (PCI) technique capable of providing micron spatial resolution at the Advanced Photon Source. Numerical simulations of the PCI data accurately captured the propagating compaction shock wave in the powder and the deformation of the powder column.

A. Mandal, M. Hudspeth, B. J. Jensen, S. Root

Chapter 51. Shock Compression Response of Model Polymer/Metal Composites

Heterogeneous materials do not respond mechanically to an impulse in the manner of homogeneous metals and alloys. Wave propagation in a microstructure with chemically distinct identities, that are only in incidental contact with each other, is a complex process and not well understood. Here we report on a series of plate-impact experiments on a polymer-metal composite, where the volume fraction of the metallic phase was systematically varied from 0% to 40%, while other parameters like the sample thickness were kept constant. The velocity histories at the sample/window interfaces were measured to examine the continuum response corresponding to the internal materials processes. The unfilled polymer demonstrated a steady shock wave response; whereas the wave profiles obtained from mixture samples showed structured waves that depended on the volume fraction of the fill. The shock wave profiles were quantified using parameters strongly correlated to the material composition. The likely physical basis of these correlations is discussed.

David Bober, Yoshi Toyoda, Brian Maddox, Eric Herbold, Yogendra Gupta, Mukul Kumar

Chapter 52. High-Strain Rate Interlaminar Shear Testing of Fibre-Reinforced Composites Using an Image-Based Inertial Impact Test

In this work a novel image-based inertial impact test is proposed to measure the interlaminar shear modulus of fibre-reinforced polymer composite materials at high strain rates. The principle is to combine ultra-high-speed imaging and full-field measurements to capture the dynamic kinematic fields, exploiting the inertial effects generated under high strain rate loading. The kinematic fields are processed using the virtual fields method to reconstruct stress averages from maps of acceleration. In this way, the specimen acts like a dynamic load cell, with no gripping or external force measurement required. This paper focusses on validation of the test principle using explicit dynamic simulations in ABAQUS. Simulations demonstrate the potential for the proposed method to identify the shear modulus at strain rates where current test methods become unreliable (500 s−1 on average, and on the order of 2000 s−1 locally). Access to spatial maps of stress averages provides opportunity to estimate the shear strength in the future. Further design work is required to amplify shear stress and strain in the specimen, after which the test will be validated experimentally. Eventually, the objective is to tailor the test to begin populating regions of a tension-shear failure envelope.

J. Van Blitterswyk, L. Fletcher, F. Pierron

Chapter 53. Mechanical Behavior and Deformation Mechanisms of Mg-based Alloys in Shear Using In-Situ Synchrotron Radiation X-Ray Diffraction

A fundamental understanding of magnesium-based alloys during high rate, large deformation processes that occur during impact and penetration are not well-known. This metal possesses a limited number of deformation mechanisms, each with their own disparate strengths, strain hardening rates, and strain rate sensitivities. Consequently, these alloys exhibit severe tension-compression asymmetry and anisotropy dictated by their processing history and the applied deformation. Thus, an understanding of material behavior undergoing large shears at dynamic rates is required. Experiments have been performed on a specimen geometry that induces shear localization in “pure” simple shear, called the compact forced simple shear (CFSS) specimen. The deformation occurs on a 2D plane in the specimen, which is oriented with respect to directional aspects of the material’s microstructure and deformation modes. Experiments at dynamic strain rates have been performed to determine how the mechanical behavior in shear evolves and correlates to the microstructural deformation mechanisms. The experiments were performed at the Dynamic Compression Sector of the Advanced Photon Source at Argonne National Laboratories using in-situ synchrotron x-ray diffraction aimed to probe the microstructural evolution during shear-induced localization. By correlating the propensity for shear localization to occur with the mechanical response of various orientations, we have built a data set to compare existing models to identify key deformation mechanisms responsible for localization.

Christopher S. Meredith, Zachary Herl, Marcus L. Young

Chapter 54. Developing an Alternative to Roma Plastilina #1 as a Ballistic Backing Material for the Ballistic Testing of Body Armor

Ballistic clay (Roma Plastilina #1; RP1) is currently used as a backing material that is meant to simulate the penetration resistance of the human body during the ballistic testing of body armor. RP1 is a modeling clay with a primary market in the artistic community. Over time, RP1’s formulation and performance have changed to meet the demands of the artistic community. As a result, RP1 must now be heated to 100 °F to obtain the desired response and exhibits a strong temperature-dependent performance such that the backing material is considered out of calibration after 45 min. This presentation will focus on our efforts to develop a replacement for RP1 that exhibits the desired backing material response at room temperature with minimal temperature-dependence. Specifically, the challenges of designing a viscoplastic material with a controlled response that exhibits dimensional stability while providing minimal elastic recovery from deformation even at high strain rates and linking the quasistatic mechanical response with the ballistic performance.

Randy Mrozek, Tara Edwards, Erich Bain, Shawn Cole, Eugene Napadensky, Reygan Freeney

Chapter 55. IBII Test for High Strain Rate Tensile Testing of Adhesives

This paper presents the application of the new Image-Based Inertial Impact (IBII) test methodology to study the high strain rate response of adhesives. It relies on an inertial impact (spalling-like) test configuration and the use of ultra-high speed imaging to record the deformation of the test specimen in the MHz range. The underlying novelty is to use the acceleration obtained from the time-resolved displacement maps to derive stress information leading to the identification of the material constitutive parameters. Here, an epoxy adhesive is tested at strain rates up to 1000 s−1 and its modulus and tensile strength are successfully derived from just the deformed images.

A. Guigue, L. Fletcher, R. Seghir, F. Pierron

Chapter 56. Two Modified Digital Gradient Sensing with Higher Measurement Sensitivity for Evaluating Stress Gradients in Transparent Solids

Two modified full-field Digital Gradient Sensing (DGS) methods with higher measurement sensitivity are presented for quantifying small angular deflections of light rays caused by a non-uniform state-of-stress in a transparent solid. These methods are devised by combining or altering previously proposed methods, reflection-mode DGS (r-DGS) (Periasamy and Tippur, Meas Sci Technol 24:025202, 2013) and transmission-mode DGS (t-DGS) (Periasamy and Tippur, Appl Opt 51:2088–2097, 2012). In this presentation, the working principles of r-DGS and t-DGS are introduced first. Then, the so-called t2-DGS method is proposed with the aid of a separate reflective planar surface located behind the transparent solid. The sensitivity of t2-DGS is shown to be twice that of t-DGS. Next, an even higher sensitivity method called the transmission-reflection DGS or simply tr-DGS is developed by making the back surface of a transparent planar solid specularly reflective. The governing equations of tr-DGS are proposed followed by a comparative demonstration of t2-DGS and tr-DGS methods by measuring stress gradients in the crack tip region during a dynamic fracture experiment. The tr-DGS is ∼1.5 times more sensitive than t2-DGS, and at least three times more sensitive than t-DGS approach.

Chengyun Miao, Hareesh V. Tippur

Chapter 57. Quantitative Visualization of Sub-Micron Deformations and Stresses at Sub-Microsecond Intervals in Soda-Lime Glass Plates

Full-field optical measurement of deformations and stresses on transparent brittle ceramics such as soda-lime glass is rather challenging due to the low toughness and high stiffness characteristics. Particularly, the surface topography and stress field evaluation from measured orthogonal surface slopes and stress gradients could be of considerable significance for visualizing and quantifying deformation of glass plates under dynamic impact loading. In this work, two full-field optical techniques, reflection Digital Gradient Sensing (or r-DGS) and a new DGS method, called transmission-reflection Digital Gradient Sensing (or tr-DGS) are employed to quantify surface slopes and stress gradients, respectively, as glass specimens are subjected dynamic impact loading using a modified Hopkinson pressure bar. These two methods can measure extremely small angular deflections of light rays caused by surface deformations and local stresses in specimens. The tr-DGS methodology is especially more sensitive than r-DGS. Using such optical methods, sub-micron surface deflections and the corresponding stress field, (σxx + σyy), can be quantified using a Higher-order Finite-difference-based Least-squares Integration (HFLI) scheme. When used in conjunction with ultrahigh-speed photography, microsecond or sub-microsecond temporal resolution is possible.

Chengyun Miao, Hareesh V. Tippur

Chapter 58. Microstructural Effects in the High Strain Rate Ring Fragmentation of Copper

Understanding the failure of rings and shells at high strain rates is a longstanding challenge (Mott, N.F. (1947), Fragmentation of rings and shells, Proc. Royal Soc., A189, 300--308, January.). Predicting the distribution of fragment sizes, shapes and velocities has been an important objective for the many modelling techniques applied to the problem; a detailed history of this research can be found in the work of Grady (Grady, Fragmentation of rings and shells. Springer, Berlin Heidelberg, 2006). Physical testing is particularly important for model development and validation. More recently, ring fragmentation has been used to study the relationship between material microstructure and dynamic fracture.A series of explosively loaded fragmentation experiments were conducted to investigate microstructural effects in the dynamic tensile behaviour of high purity copper. Rings of high purity copper were expanded at strain rates of approximately 104 s−1. Diagnostics include PDV, high speed photography and soft capture. The fracture mechanism is studied through the detailed analysis of fracture surfaces and fragments using scanning electron microscopy. Microstructural changes induced by the plastic deformation developed during the applied loading are also examined.

Sarah Ward, Christopher Braithwaite, Andrew Jardine

Chapter 59. Uncertainties in Low-Pressure Shock Experiments on Heterogeneous Materials

Understanding and quantifying the uncertainties in experimental results are crucial to properly interpreting simulations based on those results. While methods are reasonably well established for estimating those uncertainties in high-pressure shock experiments on homogeneous materials, it is much more difficult to treat relatively low-pressure experiments where shock rise times are significant and material strength is not negligible. Sample heterogeneity further complicates the issue, especially when that heterogeneity is not characterized in each sample. Here, we extend the Monte Carlo impedance matching approach used in high-pressure Z experiments to low-pressure experiments on heterogeneous porous materials. The approach incorporates uncertainties not only in the equation of state of the impedance matching standard but also those associated with its strength. In addition, we also examine approaches for determining material heterogeneity and evaluate its effect on the experimental results.

Tracy J. Vogler, Matthew Hudspeth, Seth Root

Chapter 60. Effects of Fluid Viscosity on Wave Propagation Through Submerged Granular Media

Wave propagation through dry granular media has been extensively studied both numerically and experimentally in the past, however, wave dynamics of wet granular materials have not received adequate attention. The cohesion at inter-particle contacts, largely ignored in dry macroscopic granular materials, plays a major role in mechanics of wet granular materials. In this study, a drop-tower based experimental setup was developed to investigate wave propagation through the 2D assembly of cylindrical particles immersed in optically transparent fluids. These granular assemblies, consisting of polyurethane cylinders arranged into two different configurations – cubic and hexagonal, can be subjected to low-speed impact loading up to a projectile velocity of about 6 m/s. The deformation of individual particles in the granular assemblies can be recorded using a high-speed camera and the kinematics and the strain fields on each speckle-patterned particle can be calculated by digital image correlation (DIC). Moreover, an electrodynamic shaker can also be coupled with the aforementioned fixture and the influence of liquid viscosity on the low-amplitude vibrational response of the immersed granular crystals can be quantified using a scanning vibrometer. The wave dynamics of granular crystals immersed in fluids with varying levels of viscosity were investigated using the impact loading using the drop-tower setup and the scanning vibrometer based vibrational measurements. In order to quantify the effect of single or multiple defects on wave propagation, the impact response of dry and immersed granular crystals with different types of defects (size, stiffness or both) was also investigated.

Hrachya Kocharyan, Nikhil Karanjgaokar

Chapter 61. Numerical Study of the Failure Mechanism of Ceramics during Low Velocity Impact Used in Protective Systems

The rapid advancement of computing power and recent advances in numerical techniques and material models have resulted in accurate simulation of ballistic impacts into multi-layer armor configurations. For both transparent and opaque protective systems, low velocity impact damage can also compromise structural integrity (Fig. 61.1). Drop-tower experimentation is used to assess the damage of low velocity impact of ceramics. Modeling and simulation of material impact by various threat types has proven to be a significant analysis tool in the identification of damage mechanisms and the failure process. Impact can be numerically studied by various available commercial packages. However, each package has its own limitations and the accuracy of result duplication differs. The commercial software packages AUTODYN (ANSYS/AUTODYN Vol 14.5 October 2012, Manual) and ANSYS/WORKBENCH ( https://www.ansys.com/about-ansys/news-center/01-27-16-ansys-unveils-release-17-0 ) were used for the numerical analysis of the low velocity impact during the drop-tower experimentation. AUTODYN has been successfully implemented for the modeling of the medium to high velocity impact. ANSYS/WORKBENCH has been used successfully to model systems of complex geometry. Both software packages showed similar simulated damage results in alumina targets caused by an indenter dropped at various heights. However, ANSYS/WORKBENCH due its superior preprocessing capabilities can be a valuable tool for fast assessment of the failure prediction of ceramics at low impact velocity.

Constantine (Costas) Fountzoulas, Raymond E. Brennan

Chapter 62. Influence of High Strain Rate Transverse Compression on the Tensile Strength of Polyethylene Ballistic Single Fibers

Ballistic impact onto fiber-based armor systems induce high strain rate (HSR) multiaxial loading including axial tension, axial compression, transverse compression and transverse shear. Fiber failure during impact is expected to occur under multiaxial loading conditions. The transverse compressive deformation induced in the fibers during impact is significant enough to cause permanent deformation (shear cutting and compressive fibrillation) at the sub-micron length scales. However, the influence of high strain rate transverse damage from compression and/or shear on the tensile strength of fibers is not well understood. In this study, ultrahigh molecular weight polyethyelene (UHMWPE) Dyneema SK76 single fibers are compressed at HSR loading conditions in a unique small (283 μm) diameter Kolsky bar. Subsequently, the compressed fibers are subjected to axial tension at quasi-static and HSR loading to understand the influence of transverse compression.

Frank David Thomas, Daniel Casem, Tusit Weerasooriya, Subramani Sockalingam, John W. Gillespie

Chapter 63. The Utility of 3D Digital Image Correlation for Characterizing High-Rate Deformation

Digital image correlation has become a popular technique for making full-field measurements during high-rate mechanical testing, blast experiments, and shock loading; however, limited work to date has been done to evaluate the fidelity of this diagnostic tool. The aim of this work is to understand the underlying elements of uncertainty that affect the collected data. A methodology is presented for characterizing imaging system resolution and quantifying error when measuring out-of-plane displacements. High-velocity impact experiments were then performed on 6.35 mm thick aluminum disks to demonstrate the efficacy of digital image correlation when characterizing a ballistic impact.

Phillip Jannotti

Chapter 64. Characterization of Dynamic Deformation and Failure of Novel Light Weight Steel Alloy

The need for new weight-saving high-strength materials has been increasing in recent years. The demand for fuel efficiency in the auto industry has driven research in the development of lightweight materials and structures while maintaining crash worthiness and safety. The constraints on vehicle weight is also felt in the defense industry. The need to maintain or reduce weight while enhancing protection and durability is a critical goal for the DoD. Fe-Mn-Al is a family of alloys which have been identified as a potential replacement for high strength structural steel such as RHA. Fe-Mn-Al has shown similar properties and performance with 10–15% reduction in weight when compared to RHA (Howell, Microstructural Influence on Dynamic Properties of Age Hardenable FeMnAl Alloys, 2009).This study will examine the high strain rate properties of a lightweight Fe-Mn-Al alloys using the split Hopkinson pressure bar. Tension and compression tests will be performed to examine flow stress and strain to failure as a function of loading rate. High rate digital image correlation will be performed using a pair of Kirana high speed cameras capable of 5 M fps. A combination of SEM techniques (e.g. EDS and EBSD) and micro-XCT will help identify damage and deformation of tested specimens.

T. R. Walter, P. Moy, T. Sano, K. Limmer

Chapter 65. Dynamic Fragmentation of MAX Phase Ti3SiC2 from Edge-On Impact Experiments

MAX phases are an emerging class of nanolayered ternary carbides or nitrides with hexagonal crystallographic structures where only basal slip is available for plastic deformation under ambient conditions. At the same time, these materials also exhibit potentially advantageous energy-absorbing micromechanisms of kink banding and delamination, stemming from nonlinear buckling on the atomistic plane; thus presenting a unique material for next-generation protection and shielding applications. In the present study two EOI (edge-on impact) testing configurations have been used with MAX phase Ti3SiC2 tiles (60 × 30 × 4 mm), in order to investigate the damage modes generated under highly inertial conditions. The samples are made using the hot isostatic pressing technique, producing nominally isotropic needle-like grain structures with an average size of approximately 10 μm. Small cylindrical projectiles are launched at impact speeds from 190 to 250 m/s onto the edge of the MAX tiles, and a fragmentation process is developed in less than 20 μs, captured with an ultra-high-speed camera at 2 million frames per second. The two configurations differ depending on the use or not of a dynamic confinement system. In the configuration without dynamic confinement, comminution and erosion occurred significantly around the impact site, and only a few dominant cracks radiated from the damage zone; a few with characteristic branching. Conversely, fragmentation composed of radial cracks is observed when the dynamic confinement prevents excessive damage near the impact side. The resulting fragments are analyzed under the scanning electron microscope (SEM), and these results are discussed within the context of the DFH (Denoual-Forquin-Hild) anisotropic damage model, comparing cracking density and velocity of the damage front.

P. Forquin, N. Savino, L. Lamberson, M. Barsoum, M. Morais

Chapter 66. Application of High-Speed DIC to Study Damage of Thin Membranes Under Blast

High-intensity impulsive sounds caused by high-amplitude blast pressures (e.g., explosion or large caliber military ordnance, etc.) may damage the human eardrum and produce conductive hearing loss. But little is known about sound-matter interaction during rupture of the eardrum. In this study, thin membranes (Teflon sheets) with orthotropic material properties resembling the human eardrum are ruptured by air pressure loading produced with a custom-made apparatus. The orthotropicity of the membrane was verified and measured with scanning electron microscopy and micro-tensile tests. Two calibrated high-speed cameras in a stereo configuration measured 3D surface displacements of the membranes during rupture using a digital image correlation (DIC) method at framerates as high as 1.2 million fps. DIC results show the mechanics of rupture can be divided into three stages that require different temporal resolutions to describe them, these include: global expansion (∼3 ms), bulging (∼300 μs), and crack initiation and propagation (∼40 μs). The average strain rate in the global expansion is estimated to be around 100 microstrain/μs. The strain rates of bulging, crack initiation and crack propagation are difficult to determine with speckle pattern decorrelation. High-speed photography shows the crack first propagates along one direction, followed by opening in a perpendicular direction. The former has a velocity estimated at ∼0.73 Mach while the latter has an estimated opening velocity of ∼1.05 Mach. This study indicates the potential utility of high-speed DIC for the study of hearing mechanics, and highlights the need for the development of miniaturized imaging tools to perform high strain rate measurements in confined volumes.

P. Razavi, H. Tang, K. Pooladvand, M. E. Ravicz, A. Remenschneider, J. J. Rosowski, J. T. Cheng, C. Furlong

Correction to: High Strain Rate Response of Adhesively Bonded Fiber-Reinforced Composite Joints: A Computational Study to Guide Experimental Design

There was a spelling mistake in the name of “Brian Justusson”. This has been corrected.

Suraj Ravindran, Subramani Sockalingam, Addis Kidane, Michael Sutton, Brian Justusson, Jenna Pang
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