River Rapids Conference Proceedings of the Society for Experimental Mechanics Series Dynamic Behavior of Materials, Volume 1 Bo Song Dan Casem Jamie Kimberley Proceedings of the 2013 Annual Conference on Experimental and Applied Mechanics River Publishers
Conference Proceedings of the Society for Experimental Mechanics Series Series Editor Tom Proulx Society for Experimental Mechanics, Inc., Bethel, CT, USA
River Publishers Bo Song • Dan Casem • Jamie Kimberley Editors Dynamic Behavior of Materials, Volume 1 Proceedings of the 2013 Annual Conference on Experimental and Applied Mechanics
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Preface Dynamic Behavior of Materials, Volume 1: Proceedings of the 2013 Annual Conference on Experimental and Applied Mechanics represents one of eight volumes of technical papers presented at the SEM 2013 Annual Conference & Exposition on Experimental and Applied Mechanics organized by the Society for Experimental Mechanics and held in Lombard, IL, June 3–5, 2013. The complete Proceedings also includes volumes on: Challenges in Mechanics of Time-Dependent Materials and Processes in Conventional and Multifunctional Materials; Advancement of Optical Methods in Experimental Mechanics; Mechanics of Biological Systems and Materials; MEMS and Nanotechnology; Experimental Mechanics of Composite, Hybrid, and Multifunctional Materials; Fracture and Fatigue; Residual Stress, Thermomechanics & Infrared Imaging, Hybrid Techniques and Inverse Problems. Each collection presents early findings from experimental and computational investigations on an important area within Experimental Mechanics, Dynamic Behavior of Materials being one of these areas. The Dynamic Behavior of Materials track was initiated in 2005 and reflects our efforts to bring together researchers interested in the dynamic behavior of materials and structures and provide a forum to facilitate technical interaction and exchange. In the past years, this track has represented an ever-growing area of broad interest to the SEM community, as evidenced by the increased number of papers and attendance. The contributed papers span numerous technical divisions within SEM, which may be of interest not only to the dynamic behavior of materials community but also to the traditional mechanics of materials community. The track organizers thank the authors, presenters, organizers, and session chairs for their participation, support, and contribution to this track. We are grateful to the SEM Technical Division chairs who cosponsored and/or co-organized the sessions in this track. We would also like to acknowledge the SEM support staff for their devoted efforts in accommodating the large number of paper submissions this year, making the 2013 Dynamic Behavior of Materials track successful. Livermore, CA, USA Bo Song Aberdeen, MD, USA DanCasem Socorro, NM, USA Jamie Kimberley v
Contents 1 Dynamic Deformation Behavior of AA2099-T8 Under Compression and Torsion Loads...................... 1 Daniel O. Odoh, Gbadebo M. Owolabi, and Akindele G. Odeshi 2 High Strain Rate Performance of Pressureless Sintered Boron Carbide....................................... 13 Tomoko Sano, Matthew Shaeffer, Lionel Vargas-Gonzalez, and Joshua Pomerantz 3 Interpretation of Strain Rate Effect of Metals.................................................................... 21 Kun Qin, L.M. Yang, and Shi-sheng Hu 4 High Strain Rate Friction Response of Porcine Molar Teeth and Temporary Braces ........................ 29 S.J. Chen, Y.H. Chen, and Liren Tsai 5 Dynamics of Interfaces with Static Initial Loading............................................................... 37 Jacob C. Dodson, Ryan D. Lowe, Jason R. Foley, Christopher Mougeotte, David Geissler, and Jennifer Cordes 6 Loading Rate Effects on Mode I Delamination of Z-Pinned Composite Laminates ........................... 51 Andrew Schlueter, Niranjan D. Parab, and Weinong Chen 7 Multi-scale Testing Techniques for Carbon Nanotube Augmented Kevlar................................... 59 E.D. LaBarre, M.T. Shanaman, J.E. Tiffany, J.A. Thomas, X. Calderon-Colon, M. Morris, E.D. Wetzel, A.C. Merkle, and M.M. Trexler 8 Single Fiber Tensile Properties Measured by the Kolsky Bar Using a Direct Fiber Clamping Method........................................................................... 69 J.H. Kim, N.A. Heckert, W.G. McDonough, K.D. Rice, and G.A. Holmes 9 A Testing Technique for Characterizing Composite at Strain Rates up to 100/s .............................. 73 Guojing Li and Dahsin Liu 10 A New Technique of Dynamic Spherical Indentation Based on SHPB......................................... 81 Song Li and Liang Haozhe 11 Analysis and Simulations of Quasi-static Torsion Tests on Nearly Incompressible Soft Materials.......................................................................... 89 Adam Sokolow and Mike Scheidler 12 Damage of Rubber Foams During Large Cyclic Compression................................................. 101 Jevan Furmanski, Carl M. Cady, Andrea Labouriau, Brian M. Patterson, Kevin Henderson, and Eric N. Brown 13 Extreme Tensile Damage and Failure in Glassy Polymers via Dynamic-Tensile-Extrusion.................................................................................... 107 Jevan Furmanski, Eric N. Brown, George T. Gray III, Carl Trujillo, Daniel T. Martinez, Stephan Bilyk, and Richard Becker vii
14 Strain Rate and Temperature Dependence in PVC............................................................. 113 M.J. Kendall and C.R. Siviour 15 Strain Rate Dependence of Yield Condition of Polyamide 11 .................................................. 121 Masahiro Nishida, Rie Natsume, and Masayuki Hayashi 16 Effect of Strain Rate on Mechanical Response of PBX Simulants ............................................. 129 Chunghee Park, Hoon Huh, and Jungsu Park 17 Effect of Loading Rate on Dynamic Fracture Toughness of Polycarbonate................................... 139 Anshul Faye, Sumit Basu, and Venkitanarayanan Parameswaran 18 Mixed Mode Fracture Behavior of Layered Plates.............................................................. 147 Arun Jose Jacob, Servesh Kumar Agnihotri, and Venkitanarayanan Parameswaran 19 Failure Analysis of Micron Scaled Silicon Under High Rate Tensile Loading................................ 157 Steven Dubelman, Nithin Raghunathan, Dimitrios Peroulis, and Weinong Chen 20 Dynamic Fracture Analysis of Semi-circular Bending (SCB) Specimen by the Optical Method of Caustics................................................................................ 159 Guiyun Gao, Jie Zhou, and Zheng Li 21 Effect of Loading Rate on Dynamic Fracture Behavior of Glass and Carbon Fiber Modified Epoxy ............................................................................... 169 Vinod Kushvaha, Austin Branch, and Hareesh Tippur 22 Application of Element Free Galerkin Method to high Speed crack Propagation Analysis............................................................................................... 177 A. Agarwal, N.N. Kishore, and V. Parameswaran 23 Improving Ballistic Fiber Strength: Insights from Experiment and Simulation.............................. 187 C.W. Lomicka, J.A. Thomas, E.D. LaBarre, M.M. Trexler, and A.C. Merkle 24 Simulating Wave Propagation in SHPB with Peridynamics.................................................... 195 Tao Jia and Dahsin Liu 25 Investigation of Dynamic Failure of Metallic Adhesion: A Space-Technology Related Case of Study.............................................................................................. 201 D. Bortoluzzi, M. Benedetti, C. Zanoni, J.W. Conklin, and S. Vitale 26 Shock Wave Profile Effects on Dynamic Failure of Tungsten Heavy Alloy ................................... 209 E.N. Brown, J.P. Escobedo, C.P. Trujillo, E.K. Cerreta, and G.T. Gray III 27 Adhesively Joined Crush Tube Structures Subjected to Impact Loading..................................... 217 Luis F. Trimin˜o and Duane S. Cronin 28 Dynamic Buckling of Submerged Tubes due to Impulsive External Pressure ................................ 225 Neal P. Bitter and Joseph E. Shepherd 29 High Strain Rate Response of Layered Micro Balloon Filled Aluminum..................................... 237 Venkitanarayanan Parameswaran, Jim Sorensen, and Manish Bajpai 30 Dynamic Triaxial Compression Experiments on Cor-Tuf Specimens ......................................... 245 Alex B. Mondal, Wayne Chen, Brad Martin, and William Heard 31 Deceleration-Displacement Response for Projectiles That Penetrate Concrete Targets...................... 251 M.J. Forrestal, T.L. Warren, and P.W. Randles 32 Dynamic Fracture and Impact Energy Absorption Characteristics of PMMA-PU Transparent Interpenetrating Polymer Networks (IPNs) ...................................... 277 K.C. Jajam, H.V. Tippur, S.A. Bird, and M.L. Auad viii Contents
33 Estimating Statistically-Distributed Grain-Scale Material Properties from Bulk-Scale Experiments ..................................................................................... 285 William L. Cooper 34 Spall Behavior of Cast Iron with Varying Microstructures .................................................... 291 Gifford W. Plume IV and Carl-Ernst Rousseau 35 A Scaling Law for APM2 Bullets and Aluminum Armor....................................................... 297 M.J. Forrestal, T.L. Warren, and T. Børvik 36 A Novel Torsional Kolsky Bar for Testing Materials at Constant-Shear-Strain Rates....................... 301 Jason R. York, John T. Foster, Erik E. Nishida, and Bo Song 37 A New Method for Dynamic Fracture Toughness Determination Using Torsion Hopkinson Pressure Bar .......................................................................... 307 Addis Kidane and Jy-An John Wang 38 Characterization of Sheet Metals in Shear over a Wide Range of Strain Rates .............................. 313 Kevin A. Gardner, Jeremy D. Seidt, Matti Isakov, and Amos Gilat 39 Material Identification of Blast Loaded Aluminum Plates Through Inverse Modeling ...................... 319 K. Spranghers, D. Lecompte, H. Sol, and J. Vantomme 40 Implosion of a Tube Within a Closed Tube: Experiments and Computational Simulations................. 327 Sachin Gupta, James M. LeBlanc, and Arun Shukla 41 Testing Techniques for Shock Accelerometers below 10,000 g................................................. 333 Waterloo Tsutsui, Nithin Raghunathan, Weinong Chen, and Dimitrios Peroulis 42 ONR MURI Project on Soil Blast Modeling and Simulation................................................... 341 Richard Regueiro, Ronald Pak, John McCartney, Stein Sture, Beichuan Yan, Zheng Duan, Jenna Svoboda, WoongJu Mun, Oleg Vasilyev, Nurlybek Kasimov, Eric Brown-Dymkoski, Curt Hansen, Shaofan Li, Bo Ren, Khalid Alshibli, Andrew Druckrey, Hongbing Lu, Huiyang Luo, Rebecca Brannon, Carlos Bonifasi-Lista, Asghar Yarahmadi, Emad Ghodrati, and James Colovos 43 Dynamic Behavior of Saturated Soil Under Buried Explosive Loading ....................................... 355 A. Yarahmadi and R. Brannon 44 Sand Penetration: A Near Nose Investigation of a Sand Penetration Event................................... 363 John Borg, Andrew Van Vooren, Harold Sandusky, and Joshua Felts 45 Poncelet Coefficients of Granular Media......................................................................... 373 Stephan Bless, Bobby Peden, Ivan Guzman, Mehdi Omidvar, and Magued Iskander 46 Effect of Moisture on the Compressive Behavior of Dense Eglin Sand Under Confinement at High Strain Rates ........................................................................ 381 Huiyang Luo, William L. Cooper, and Hongbing Lu 47 Shearing Rate Effects on Dense Sand and Compacted Clay.................................................... 389 Jenna S. Svoboda and John S. McCartney 48 High-Energy Diffraction Microscopy Characterization of Spall Damage ..................................... 397 John F. Bingert, Robert M. Suter, Jonathan Lind, Shiu Fai Li, Reeju Pokharel, and Carl P. Trujillo 49 Quantitative Visualization of High-Rate Material Response with Dynamic Proton Radiography............................................................................... 405 E.N. Brown, R.T. Olson, G.T. Gray III, W.T. Buttler, D.M. Oro, M.B. Zellner, D.P. Dandekar, N.S.P. King, K.K. Kwiatkowski, F.G. Mariam, M. Marr-Lyon, F.E. Merrill, C. Morris, D. Tupa, A. Saunders, and W. Vogan Contents ix
50 Investigation of Dynamic Material Cracking with In Situ Synchrotron-Based Measurements.............. 413 K.J. Ramos, B.J. Jensen, J.D. Yeager, C.A. Bolme, A.J. Iverson, C.A. Carlson, and K. Fezzaa 51 Impact Bend Tests Using Hopkinson Pressure Bars............................................................. 421 R.A. Govender, G.S. Langdon, and G.N. Nurick 52 A Methodology for In-Situ FIB/SEM Tension Testing of Metals............................................... 427 J.P. Ligda, Q. Wei, W.N. Sharpe, and B.E. Schuster 53 Characterization of Damage Evolution in Ti2AlCandTi3SiC2 Under Compressive Loading............... 435 R. Bhattacharya and N.C. Goulbourne 54 Viscoelastic Behaviour of Maturating Green Poplar Wood .................................................... 445 Guillaume Pot, Evelyne Toussaint, Catherine Coutand, and Jean-Benoˆıt Le Cam 55 Permeability and Microcracking of Geomaterials Subjected to Dynamic Loads ............................. 451 Wen Chen, Christian La Borderie, Olivier Maurel, Thierry Reess, Gilles Pijaudier-Cabot, and Franck Rey Betbeder 56 Vibration Analysis and Design of a Monumental Stair ......................................................... 461 Mehdi Setareh 57 Improvement of Safety Engineering Design in Rotating Structures by Detection of Resonance Frequency Signals ................................................................... 469 Hisham A.H. Al-Khazali and Mohamad R. Askari 58 Dynamic Compressive Response of Unsaturated Clay Under Confinements.................................. 479 Y.Q. Ding, W.H. Tang, X. Xu, and X.W. Ran 59 Dynamic Tensile Testing of Based and Welded Automotive Steel ............................................. 489 J.G. Qin, Y.L. Lin, F.Y. Lu, R. Chen, and M.Z. Liang x Contents
Chapter 1 Dynamic Deformation Behavior of AA2099-T8 Under Compression and Torsion Loads Daniel O. Odoh, Gbadebo M. Owolabi, and Akindele G. Odeshi Abstract The suitability of aluminum alloys in a vast majority of engineering applications forms the basis for the need to understand the mechanisms responsible for their deformation and failure under various loading conditions. Aluminum AA2099 alloy finds application in fuselage structures that are statically and dynamically loaded, stiffness dominated designs, and in lower wing structures. The fuselage structures and wings of aircraft experience huge damage due to foreign object impacts. AA2099 aluminum alloy has an advantage of high specific strength compared with other alloys in the AA2000, 6000, and 7000 series; this characteristic makes it the material of choice in high performance aerospace structures. In this paper, the dynamic high strain rate impact deformation of AA2099 aluminum alloy under compression and torsion loading conditions using the split Hopkinson pressure and Kolsky torsion bars was performed. Digital image photogrammetric evolution of localized strain in aluminum samples during deformation process using high speed digital camera is reported. Microstructural analysis of deformed aluminum samples was performed using high resolution electron microscopes in order to determine the influence of impact strain rate on localized strain along narrow adiabatic shear bands in the AA2099 aluminum alloys. Results obtained indicate that peak flow stress in the deformed aluminum sample depends on the strain rate at which the deformation test was performed. An increase in impact strain rate results into an increase in the peak flow stress observed in the impacted aluminum sample. The type of adiabatic shear band localized in the aluminum sample also depends on the strain rate at which material was impacted. Keywords High strain rate impact • Digital image photogrammetric evolution • Microstructural analysis • Adiabatic shear bands • Dynamic deformation 1.1 Introduction Aluminum alloys exhibit an attractive combination of mechanical and physical properties such as high stiffness, good fracture toughness, and a high strength to weight ratio making them materials of choice in the automobile [1] and defense industry [2]. The low density of aluminum makes it find greater application than steel in situations where fuel efficiency and economy are of great concern. Aluminum AA2099 alloy has a high specific strength when compared with other aluminum alloys and is usually used in structures that are dynamically or statically loaded such as fuselage structures of aircrafts and other low wing structural components[3]. The dynamic deformation of materials at strain rates in the region of 103 s 1 are characterized by intense strain localization [4]. The dynamic loading of materials results into a phenomenon referred to as an adiabatic shear band. Adiabatic shear bands (ASBs) are regions of narrow deformation with intense strain localization [5]. These narrow bands are planar or two dimensional microstructural features characterized by large shear [6]. Adiabatic shear bands are known to be characterized by intense strain localization, an elevated temperature, intense shearing and an elongation of micro-pores within the shear band preceding failure. D.O. Odoh (*) • G.M. Owolabi Department of Mechanical Engineering, Howard University, 2300 Sixth Street NW, Washington, DC 20059, USA e-mail: daniel.odoh@bison.howard.edu A.G. Odeshi Department of Mechanical Engineering, University of Saskatchewan, 57 Campus Drive, Saskatoon, SK S7N 5A9, Canada B. Song et al. (eds.), Dynamic Behavior of Materials, Volume 1: Proceedings of the 2013 Annual Conference on Experimental and Applied Mechanics, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-00771-7_1, #The Society for Experimental Mechanics, Inc. 2014 1
Localized strain as a major characteristic of adiabatic shear band located in the transverse section of impacted monolithic aluminum sample is shown in Fig. 1.1. During high strain rate loading of materials, three mechanisms are usually in place. These include work hardening, strain hardening and thermal softening [6]. Work hardening and strain hardening tend to increase the isothermal flow stress within the material while thermal softening tends to decrease it. This results into a ‘war’ of mechanisms, thermal softening tend to win over the other mechanisms during the deformation process and it is responsible for the continued deformation of the material under high strain rate loads instead of it experiencing fracture. Thermal (otherwise referred to as work) softening is an extremely important process that determines the onset of adiabatic shear band formation. As the plastic shearing of the sample occurs during the plastic deformation process, most of the kinetic energy of the hitting projectile is converted to heat. Based on the fact that the deformation process is so rapid, there is not enough time for the heat energy to be conducted away from the surface of the specimen and this results into tensile stresses been generated and concentrated in narrow bands referred to as adiabatic shear bands. Adiabatic shear bands are microstructural defects that can trigger premature failure in materials under high strain rate loading. Once an ASB develops in a material under high strain rate loading, the performance of the material becomes compromised. The fragmentation of steel encasements after explosion has been observed to occur after strain localization which results into the formation of an adiabatic shear band [8]. Figure 1.2 shows the initiation and propagation of crack in impacted AISI 4340 steel samples, the adiabatic shear band formed serves as preferential site for the initiation of cracks; the material is to be changed or reprocessed since it will experience unexpected failure. Therefore, failure of materials under high strain rate loads are usually preceded by the formation of adiabatic shear bands. The tensile stresses generated inside an adiabatic shear band become sufficiently high enough to open up micro-pores inside these bands. Due to the coalescence of the micro-pores, voids are formed which elongate and rotate to elliptical shapes. These voids are finally connected, initiating micro cracks which propagate along the shear band leading ultimately to fracture. The need to explain failure of materials under high strain rate loading conditions has been the main reason for more research into the concept of adiabatic shear bands. In this research work, the dynamic high strain rate loading of aluminum AA2099-T8 alloy is performed in compression and torsion using the split Hopkinson pressure and torsion Kolsky bars respectively in order to determine the influence of impact strain rate on the formation adiabatic shear band. Digital image photogrammetric evolution of localized strain in Fig. 1.1 Macroscopic view of transverse section of impacted monolithic aluminum showing adiabatic shear band region characterized by intense localization [7] Fig. 1.2 (a) Adiabatic shear band in impacted steel sample. (b) Crack initiation and propagation within the adiabatic shear band [9] 2 D.O. Odoh et al.
aluminum samples during deformation process using high speed digital camera is determined. Microstructural analysis of deformed aluminum samples is performed using high resolution electron microscopes in order to determine the influence of impact strain rate on localized strain along narrow adiabatic shear bands in the AA2099 aluminum alloys. 1.2 Material and Experimental Procedure The properties exhibited by AA2099-T8 aluminum alloy under various loading conditions can be traced to its elemental composition. Aluminum AA2099-T8 alloy can contain as high as 92 % of aluminum by weight and other elements in trace quantity. The chemical composition of the other elements in trace quantity in AA2099-T8 from ALCOA data sheet is given in Table 1.1. The compression and torsion specimens with dimension are shown in Fig. 1.3a, b respectively. The operation and working principle of the split Hopkinson pressure bar and torsion Kolsky bar that were used in this research work are described in details elsewhere [10]. The elastic waves obtained from the split Hopkinson and torsion Kolsky barsin voltage- time form are converted into stress–strain relationship by using a calibration factor obtained from the initial calibration of the bars. The processes involved in calibrating the bars and also converting the voltage-time data to stress–strain relationship are outlined elsewhere [11]. Figure 1.4 shows a typical voltage-time graph obtained during the compression of the cylindrical aluminum specimen. The elastic wave technique is based on the assumption of a homogenous stress–strain relationship during material deformation. However, it has been observed that this usually does not hold true for all cases during high strain rate deformation of materials [4]. Therefore, there exists a need to determine localized strain in the aluminum sample by using a technique that is not based on a homogenous stress–strain assumption. The digital image correlation (DIC) technique used is a non-contact measuring technique used for determining the deformation which occurs on the surface of an object. It has several advantages among which include: Non-altering of the behavior of the specimen during testing, No recourse to analytical model, Measurement of large strain by correlation of series of images recorded during mechanical testing, Measurement of strain at local region of interest as well as a good strain accuracy. The 3D digital image correlation technique uses two high resolution photron cameras (shown in Fig. 1.5) that provide synchronized images of the deformation process in time steps. The high resolution photron cameras make use of the principle of pattern matching on the specimen in the determination of localized strain. This is achieved by applying a random dot pattern on the surface of the AA2099-T8 specimen with black and white spray paints to provide a gray scale distribution. This ensures sufficient contrast between the un-deformed and the deformed images. Figure 1.6 shows a typical dot pattern made on the cylindrical compression specimen prior to testing. Table 1.1 Chemical composition of AA2099-T8 aluminum alloy Chemical composition (Wt. %) Cu Li Zn Mg Mn Zr Ti Fe 2.4–3.0 1.6–2.0 0.4–1.0 0.10–0.50 0.10–0.50 0.05–0.12 0.10 0.07 Fig. 1.3 (a) Compression specimen. (b) Torsion specimen 1 Dynamic Deformation Behavior of AA2099-T8 Under Compression and Torsion Loads 3
The compression experiment was captured by the digital cameras at an array of 192 216 pixels resolution and 124,000 frames per second (FPS) while the torsion test was performed at a pixel resolution of 320 128 and 140,000 FPS. Images of the deformation process captured by the high resolution camera are saved as tiff files and uploaded into a digital image software package for post processing to obtain full field strain versus time data. The software package referred to as Aramis is used to analyze the images captured during the deformation process. Strain calculation was performed in the correlation software using a 3 3 minimum facet point. This allows for a wide coverage of points on the deformed sample. The correlation technique used keeps track of the movement of the grayscale random pattern distribution within each facet relative to its centre point from image to image in order to obtain a displacement from which the strain is obtained. The compression test was performed at strain rates ranging between 1,000 and 3,000 s 1 in order to determine the influence of strain rate on the deformation behavior of the aluminum sample as well as formation of adiabatic shear band within the specimen. The strain rate and corresponding impact velocity at which the compression tests were performed are reported in Table 1.2. Fig. 1.4 Typical voltage-time graph obtained during compression test Fig. 1.5 Digital image correlation set-up showing high resolution digital cameras Fig. 1.6 Random dot pattern on cylindrical sample prior to torsion test 4 D.O. Odoh et al.
During the torsion test, a torque equivalent to the desired strain rate was applied resulting into torsion waves being generated on the incident bar of the torsion Kolsky bars. The impact strain rate at which test was performed and corresponding applied torque is recorded in Table 1.3. 1.3 Result and Discussion The stress–strain results obtained from the compression and torsion loading of aluminum AA6061-T6 sample during dynamic impact test are reported. The effect of impact velocity and hence strain rate on the dynamic stress–strain relationship during impact of the compression specimen is discussed. Also the effect of applied torque (which is a function of strain rate) on the deformation of the torsion sample is also reported. The influence of strain rate on the adiabatic shear band behavior of the specimen is also outlined. A typical stress–strain relationship obtained during the dynamic loading of the aluminum AA2099-T8 specimen is shown in Fig. 1.7. As shown in Fig. 1.7, the deformation which occurs in the aluminum sample subjected to dynamic load is elastic up until the yield point. This means that the material will return to its initial condition if load was removed just before the yield point. However beyond the yield point, plastic deformation sets in and the material is permanently deformed from its initial condition. During the plastic deformation which occurs beyond the yield point, strain hardening and thermal softening are two mechanisms that occur simultaneously. These phenomena can be attributed to the heat generated inside the material due to the kinetic energy of the projectile being converted into heat energy. The strain hardening phenomenon dominates the deformation process up until a point when the material’s maximum flow stress is reached. Once the maximum flow stress is reached, thermal softening dominates the deformation process and it is said to have ‘won’ the war over strain hardening. The domination of thermal softening is usually characterized by a stress collapse due to mechanical instability resulting from intense adiabatic heating along narrow paths leading to strain localization. During the thermal softening process, an increase in strain usually results into a decrease in the flow stress. The point when a drop in the material flow stress is observed is referred to as the critical strain and it is designated εcrit. Figure 1.8 shows the true stress versus true strain graph obtained at different impact velocities during the compression test. A peak flow stress of about 412 MPa was recorded for the test performed at 9.6 m/s; this increased to about 456 MPa for impact test performed at 19.8 m/s. The critical strain and time during which thermo-mechanical instability occur increases as the impact velocity is increased. This can be attributed to an increase in the plastic strain and thermal softening in the specimen as the impact velocity increases. The increased thermal softening behavior of the specimen as impact velocity increases usually results into an increase in the plastic nature of the deformation process. An increase in the impact velocity has been observed to increase the temperature inside the shear band significantly, hence leading into significant effect in plasticity and material yielding. Beyond the critical strain, the peak stress recorded at each impact velocity experienced a drop due to stress collapse from mechanical instability as a consequence of intense adiabatic heating resulting in localization of strain. The time history of the localization of strain along the compression specimen was determined via the digital image correlation technique and the conventional elastic wave techniques in order to compare both techniques. The strain-time history plot shows the path of strain localization in the specimen as a function of time in Fig. 1.9. Table 1.2 Impact strain rate and corresponding velocity during compression test Strain rate (/s) Impact velocity (m/s) 1,000 9.60 1,500 12.10 2,000 18.64 3,000 19.80 Table 1.3 Impact strain rate and corresponding torque Strain rate (/s) Applied torque (Nm) 750 144.95 1,000 168.90 1,500 216.53 1 Dynamic Deformation Behavior of AA2099-T8 Under Compression and Torsion Loads 5
It is observed from Fig. 1.9 that the elastic waves strain gauging technique gives a slightly higher result compared with the non-contact image correlation technique. During test conducted at 9.6 m/s, the strain determined via the digital image correlation system was 5.34 % lower than that recorded via the conventional strain gauging technique. Also, the strain obtained via the DIC method during tests conducted at 19.8 m/s was 7.8 % lower than that determined via the elastic wave technique. This decrease can be traced to the absence of an assumed homogenous stress- strain relationship in the digital image correlation technique. The homogenous stress- strain relationship is a situation which is assumed to hold true in the conventional elastic wave strain gauging technique; however, this assumption does not hold true in the DIC technique based on the fact that the DIC technique can be used to measure localized strain at region of interest. A linear relationship is Fig. 1.8 Dynamic impact stress–strain relationship for AA2099-T8 aluminum alloy specimen as a function of impact velocity Fig. 1.9 Strain – time history obtained using 3D DIC system and elastic wave as a function of the impact velocity Fig. 1.7 Typical stress–strain curve for aluminum sample subjected to dynamic impact loading. 6 D.O. Odoh et al.
observed between the time over which the deformation process occurs and the localization of strain. This signifies that the localized strain in the aluminum material increases linearly with time as the time of deformation increases, reaching a peak at the end of the deformation process. Figure 1.9 shows that the rate at which strain localization occurs increases as the impact velocity and hence strain rate increases. This is due to the fact that an increase in strain rate results into a higher possibility for occurrence of thermal softening and hence adiabatic heating. Therefore, at higher impact velocity, localized strain results from a quicker thermal softening process followed by adiabatic heating. The pattern distribution of strain along compression samples deformed at different strain rates is obtained via the digital image correlation system. From this color map (shown in Fig. 1.10), the localized strain and average of strain at certain locations on the specimen can be determined. Figure 1.10 indicates the strain localization within the aluminum sample deformed at 9.6 m/s. Images A, B, C, and, D indicate the strain map distribution at time 0, 35, 60, and 105 μs respectively during the deformation process. Figure 1.10a indicates that no strain was localized in material at the start of the test corresponding to time 0 μs. As deformation progresses, the strain localized within material increases with time; At time t ¼35μs, the average localized strain within the material (region colored red in map) was about 2 %, this increased to about 6 % at deformation time corresponding to 60 μs. The average localized strain within the compression specimen at time t ¼105 μs was about 12 %. From the image plot shown in Fig. 1.10, it is observed that the strain localized within the specimen increases with time. The strain prediction as time increases observed via the color map in Fig. 1.10 agrees with the trend observed using elastic wave technique. Fig. 1.10 Digital image correlation map of strain localization in compression specimen as a function of time at a velocity of 9.6 m/s (color figure in online) 1 Dynamic Deformation Behavior of AA2099-T8 Under Compression and Torsion Loads 7
The torsion test of the aluminum sample was performed at strain rates ranging between 750 and 1,500 s 1 (see Table 1.3); Fig. 1.11 shows the dynamic stress- strain behavior of the aluminum alloy under torsional loads. The peak flow stress observed during test conducted at 210 Nm was 121 MPa and this increased to about 142 MPa at 168.9 Nm, the peak flow stress experienced at 216.53 Nm was 137 MPa. During the test conducted at 1,000 s 1, the material became shattered into pieces and this indicates that the material cannot withstand torsional loading at strain rates beyond 1,000 s 1 and this explains why a lower peak flow stress is observed in the aluminum material loaded at 216.53 Nm compared with that loaded at 168.9 Nm. Figure 1.12 shows the digital image correlation map of the aluminum sample when it is under a torsion load of 168.9 Nm. Figure 1.12a corresponds to the start of the test and indicates that no strain is localized within the aluminum material. Fig. 1.11 Dynamic impact stress–strain relationship for AA2099-T8 aluminum alloy specimen as a function of impact velocity Fig. 1.12 Digital image correlation map of strain localization in compression specimen as a function of time at a velocity of 168.9 Nm 8 D.O. Odoh et al.
Figure 1.12b indicates that the average strain localized within the material was about 3 % at time t ¼35 μs during the test, this value increased to about 6 % when the deformation time increased to 60 μs and 11 % at a deformation time of 105 μs. The increase in localized strain as deformation time increases during the torsion test is similar to that observed in the compression test and further confirms that as the deformation time progresses; the localized strain within the material also increases. The microstructural examination of the deformed AA2099-T8 samples was performed in order to determine the effect impact velocity on formation of adiabatic shear bands within the aluminum sample. The pre-impact optical examination of AA6061-T6 aluminum alloy reveals very fine second phase particles. These second phase particles are usually irregular in shape and size and are uniformly dispersed within the material microstructure. Figure 1.13a, b show the optical and SEM images of the elongated second phase particles within the aluminum specimen before impact. The examination of the aluminum samples impacted at 9.60 m/s indicate that no obvious adiabatic shear band was initiated during the deformation process. The micrograph of samples deformed at 12.10 m/s is shown in Fig. 1.14, this indicates a fairly deformed adiabatic shear band that has not fully developed. During tests conducted at 18.64 m/s, very faint transformed adiabatic shear bands and cracks were observed to propagate at certain regions of the deformed aluminum specimen. Figure 1.15 shows optical micrographs of the aluminum sample impacted at 18.64 m/s, faint transformed shear bands are observed and crack can be visualized within the microstructure at higher microscope resolution In samples impacted at 19.8 m/s, a fully formed transformed adiabatic shear band is observed within the aluminum material. These shear bands shown in Fig. 1.16 are heavily distorted grain structures with propagated crack along their path. Table 1.4 shows the impact velocity, corresponding impact pressure, the strain rate, and the type of adiabatic shear band which initializes in the deformed aluminum alloy. Fig. 1.13 Microstructural composition of the pre-impact aluminum alloy. (a) Optical. (b) SEM micrograph revealing elongated second phase structures 1 Dynamic Deformation Behavior of AA2099-T8 Under Compression and Torsion Loads 9
Fig. 1.15 Faint transformed adiabatic shear band in AA2099-T8 aluminum impacted at 18.64 m/s Fig. 1.14 Slightly deformed adiabatic shear band observed in AA2099-T8 alloy impacted at 12.10 m/s 10 D.O. Odoh et al.
1.4 Conclusion The high strain rate behavior of AA 2099-T8 aluminum alloy has been studied under compression and torsion load configurations. It is observed that the intensity of plastic deformation is a function of the strain rate at which the aluminum sample is impacted, intense strain localization is experienced as the impact velocity increases. During the compression test, an increase in impact velocity results into an increase in the peak flow stress within the material; no drop in peak flow stress was observed at the impact velocities at which test was performed. During the torsion test, the maximum stress observed in the hollow torsion specimen increased as the applied torque increased from 144.95 to 168.9 Nm; however a drop in peak stress was observed in the test performed at an applied torque of 216.53 Nm. The drop in peak flow stress can be attributed to the fact that heavily distorted transformed band already initiated in the aluminum sample and hence the internal strength of the material to resist impact had reduced. It is observed that during dynamic loading of the AA2099-T8 aluminum in compression and torsion, intense shear localization along narrow adiabatic shear bands initiates failure in the aluminum Fig. 1.16 Heavily distorted transformed shear bands observed in AA2099-T8 aluminum impacted at 19.8 m/s Table 1.4 Data sheet for impact test performed on AA2099-T8 aluminum alloy Impact velocity (m/s) Impact pressure (kPa) Strain rate (/s) Type of adiabatic shear band 9.6 61.64 1,000 No obvious band 12.10 90.66 1,500 Slightly deformed band 18.64 126.72 2,000 Faint transformed band 19.80 215.67 3,000 Heavily distorted transformed band characterized by cracks 1 Dynamic Deformation Behavior of AA2099-T8 Under Compression and Torsion Loads 11
sample. The type of shear band that initiates in the aluminum sample depends on the impact velocity or strain rate at which the impact is performed. The stress–strain behavior of the deformed aluminum sample determined via the conventional elastic wave strain gauging technique and the non-contact digital image correlation method are similar. The slight difference is due to the fact that non-homogenous stress–strain behavior is assumed in the DIC technique while a homogenous stress–strain relationship is assumed in conventional elastic wave technique. It is also observed that the localized strain within the impacted aluminum sample increases as the deformation time increases. Acknowledgement The authors are grateful for the support provided by the Department of Defense (DoD) through the research and educational program for HBCU/MSI (contract # W911NF-12-1-061) monitored by Dr. Larry Russell (Program Manager, ARO) References 1. Burger GB, Jeffrey PW, Lloyd DJ (1995) Microstructural control of aluminum sheet used in automotive applications. Mater Charact 35(1):23–39 2. Feng H, Bassim MN (1999) Finite element modeling of the formation of adiabatic shear bands in AISI 4340 steel. J Mater Sci Eng A266:255–260 3. Alloy 2099-T83 and 2099-T8E67 extrusion ALCOA aerospace technical fact sheet 4. Odoh DO (2012) Full-field measurement of AA-6061 T6 aluminum alloy under high strain rate compression and torsion loads. M.Sc. thesis, Howard University 5. Kuriyama S, Meyers MA (1985) Numerical analysis of adiabatic shear band in an early stage of its propagation. In: IUTAM symposium on MMMHVDF, Tokyo, 12–15 Aug 1985 6. Wright TW (2002) The physics and mathematics of adiabatic shear bands. Cambridge University Press, Cambridge 7. Owolabi GM, Odeshi AG, Singh MNK, Bassim MN (2007) Dynamic shear band formation in aluminum 6061-T6 and aluminum 6061-T6/ Al2O3 composites. Mater Sci Eng A 457(1–2):114–119 8. Schoenfeld SE, Wright TW (2003) A failure criterion based on material instability. Int J Solids Struct 40(12):3021–3037 9. Odeshi AG, Al-ameeri S, Bassim MN (2005) Effect of high strain rate on plastic deformation of low alloy steel subjected to ballistic impact. J Mater Process Technol 162–163:385–391 10. Owolabi GM, Odoh DO, Odeshi AG, Whitworth H (2012) Full field measurements of the dynamic response of AA6061 T-6 aluminum alloy under high strain rate loads. In: Proceedings of the ASME 2012 International Mechanical Engineering Congress and Exposition (IMECE 2012), Houston, 9–15 Nov 2012 11. Gray GT (2000) Classic split-Hopkinson pressure bar testing. In: ASM handbook, vol 8, Mechanical testing and evaluation. ASM International, Materials Park, pp 462–476 12 D.O. Odoh et al.
Chapter 2 High Strain Rate Performance of Pressureless Sintered Boron Carbide Tomoko Sano, Matthew Shaeffer, Lionel Vargas-Gonzalez, and Joshua Pomerantz Abstract The processing technique used to consolidate ceramics powders can have a large effect on the microstructure, and hence the performance of the material. In this research, microstructure, mechanical properties, and the high strain rate compressive behavior of pressureless sintered boron carbide (B4C) samples were examined and compared to those of conventional hot pressed B4C. Penetration velocity tests were conducted on identical targets made with the pressureless sinteredB4C samples and hot pressed B4C. Microstructural and post mortem characterization showed that test results of the pressureless sintered B4C were affected by significant porosity in the samples. The effects of the processing technique on the microstructure, properties, and the high rate behavior of the pressureless sintered B4C will be discussed. Keywords Boron carbide • Pressureless sintering • Microstructure • High rate behavior 2.1 Introduction Boron Carbide (B4C) is used widely in abrasive, wear resistant components, and armor applications due to its high hardness and low density properties. Hot pressing B4C powder is the typical commercial technique used to form personnel armor plates and components for various applications. B4C components can reach nearly full theoretical density by the hot pressing technique, which requires vacuum or inert atmosphere, sintering temperatures near 2,300 K, and pressures up to 40 MPa [1]. The hot pressing technique using additives allows densification at lower temperatures, improves oxidation and thermal shock resistance, and increases mechanical properties by inhibiting grain growth. The limitation of the hot pressing technique is the high operation cost per batch and only plates or cylindrical shapes of a limited size can be produced. Also, in addition to a larger die, to achieve the same pressure applied to a smaller specimen, a much larger hot press equipment size is required for larger specimens. Another technique, pressureless sintering, is also used to consolidate and densify B4C powders [2–4]. The pressureless sintering technique is a less expensive method, but requires fine grained starting power (<3 μm), higher temperatures (roughly 2,500 K) and amorphous carbon additions to achieve greater than 95 % theoretical density [5]. In both techniques, the additives could form precipitates or secondary phases at the grain boundaries that are detrimental to the mechanical performance. In addition to quasi-static behavior, high rate compressive behavior is often tested using the Kolsky bar to evaluate the failure of structural ceramic materials [6, 7]. The high strain rate compressive behavior of B4C has been studied by Paliwal and Ramesh [8]. In their experiment using the Kolsky bar, they determined at strain rates between 102 and 104/s, the peak compressive strength of a hot pressed B4C sample reached 3.8 GPa. A similar study [9] on high strain rate compression testing also using the Kolsky bar comparing the baseline hot pressed B4C results from Paliwal and Ramesh to two types of pressureless sintered B4C, one hot isostatically pressed (HIPed) and the other sintered. All three B4C types showed T. Sano (*) • L. Vargas-Gonzalez • J. Pomerantz U.S. Army Research Laboratory, 4600 Deer Creek Loop, Aberdeen Proving Ground, MD 21005, USA e-mail: tomoko.sano.civ@mail.mil M. Shaeffer Johns Hopkins University, Center for Advanced Metallic and Ceramic Systems, 028 Latrobe Hall, 3400 N. Charles St., Baltimore, MD 21218, USA B. Song et al. (eds.), Dynamic Behavior of Materials, Volume 1: Proceedings of the 2013 Annual Conference on Experimental and Applied Mechanics, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-00771-7_2, #The Society for Experimental Mechanics, Inc. 2014 13
comparable compressive strengths. The HIPed samples’ compressive strength distribution ranged from 3.4 to 4.0 GPa, falling within the 3.1–4 GPa range of the hot pressed samples, and the sintered samples ranged from just over 3.0–3.7 GPa. An often applied technique to evaluate the penetration resistance of armor materials is by the V50 test [10]. Several B4C samples have been tested in the past, with various target assembly. One such impact test [11] which compared the V50 technique to depth of penetration measurements, tested 6 in. B4C tiles (presumed to be hot pressed) with thicknesses of 1.0, 1.5, and 2.0 in. The B4C was observed to have performed better compared to similarly tested silicon carbide (SiC) and 90 % alumina (Al2O3). A recent work by Dateraksa et al. [12] determined the V50 values of 100 100mm2 Al 2O3, SiC and hot pressedB4C tiles with S2 – glass composite backing plates. The V50 of the hot pressed B4C was determined to be 829 m/s, or 2,720 ft/s and had the lowest V50 value of the materials tested. 2.2 Experimental Pressureless sintered square B4C tiles with the nominal dimensions of 50 50 8 mm, and hexagonal tiles with the nominal dimensions of 35 mm flat to flat and 20 mm thick were obtained. Density was measured by the Archimedes principle for both tile morphologies. For microstructural characterization and hardness measurements, samples from each tile morphology were cut, mounted with a Buehler cold mount epoxy, and polished on the Struers Rotopol-31 with decreasing diamond suspension sizes starting with 45 μm and ending with 0.25 μm. Microstructural and elemental characterizations were conducted on the FEI Nova NanoSEM600 (FEI Company, Hillsboro, OR) scanning electron microscope (SEM), and EDAX Pegasis XM4 (EDAX Inc. Mahwah, NJ) energy dispersive spectroscopy (EDS), respectively. X-ray diffraction spectra were obtained with the Siemens 05005 diffractometer for phase analysis. The polished samples were subjected to Knoop microindentation (Wilson Tukon 2100, Wilson Hardness, Norwood, MA) at 1.0, 2.9, 4.9, 9.8, and 24.5 Newton loads. From the square tiles, flexural specimens according to the ASTM C1161 type B standard [13], and high strain rate compression samples with cuboidal dimensions 3.5 4.0 5.3 mm were machined by Bomas Machine Specialties Inc., Somerville, MA. Two sets of samples were machined such that for one set of samples, the loading surface (3.5 4.0mm) was parallel to the square surface (referred to as “horizontal samples”) and the other set of samples, the loading surface was perpendicular to the square surface (referred to as “vertical samples”). A set of horizontal and a set of vertical compression samples were also machined from the hexagonal tile with the same dimensions. Flexural strength experiments were conducted on the Instron 5500R load frame (Instron, Norwood, MA) with a lower support span of L ¼40 mm and an upper support span of U¼20 mm. The width and thickness of the flexural specimens were recorded and loaded at 0.5 mm/ min. Tests were conducted according to ASTM C1161. High strain rate compression testing on the Kolsky bar with the same test setup as Paliwal and Ramesh [8] was conducted on five compression specimens from each sample set (square plate horizontal, vertical, hexagonal plate horizontal and vertical). Before testing, each specimen was measured for variance in the angle of the corners and the parallelism. A high speed camera was used to capture the specimen failure at 2.4 microsecond intervals with exposure times ranging from 230 nanoseconds to 1 microsecond, and the post mortem fragments were collected in a plexiglass box surrounding the specimen for SEM characterization. To assess the penetration resistance of the pressureless sintered B4C material, ceramic/ultra-high molecular weight polyethylene (UHMWPE) composite specimens were manufactured. Ten 50.8 50.8 07.4 mm samples were supplied for testing. A commercially available hot-pressed B4C material (PAD – B4C, CoorsTek, Inc. Vista, Vista, CA) was also procured at the same size to serve as the performance baseline. The composite backings were manufactured using Spectra Shield II®SR-3136 (Honeywell Specialty Materials, Morristown, NJ), a UHMWPE fiber and thermoplastic matrix sheet product. Each tile was bonded to the center of each composite backing using Sikaflex-252, a moisture-cure polyurethanebased sealant. Small strips of a 0.5 mm nylon line were used to control the adhesive thickness. The composite specimens were placed underneath a vacuum bag and cured under vacuum for 1 week at ambient room temperature. The penetration resistance of the composite panels was evaluated through tests which are used to experimentally determine the probabilistic limit velocity (V50) and derive a probabilistic curve. The probabilistic V50 value corresponds to the velocity at which the probability of the projectile being stopped or the projectile penetrating through the panel is at 50 %. The testing and the determination of the V50 value was conducted as specified in the MIL-STD-662F standard [10]. Each panel was impacted in the center of the ceramic strike face with a test projectile fired from a universal receiver. Impact velocities are varied until there are several partial and complete penetration values within a specified range of velocities. The values within the range of velocities are average to determine the V50 result. If a mixed mode of values within the specified range is obtained, then the entire range of tests can be input into a calculation algorithm to generate a logistic regression 14 T. Sano et al.
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