Dynamic Behavior of Materials, Volume 1: Proceedings of the 2020 Annual Conference on Experimental and Applied Mechanics (Conference Proceedings of the Society for Experimental Mechanics Series) 3030599469, 9783030599461

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Conference Proceedings of the Society for Experimental Mechanics Series

Leslie Lamberson · Steven Mates Veronica Eliasson  Editors

Dynamic Behavior of Materials, Volume 1 Proceedings of the 2020 Annual Conference on Experimental and Applied Mechanics

Conference Proceedings of the Society for Experimental Mechanics Series Series Editor Kristin B. Zimmerman, Ph.D. Society for Experimental Mechanics, Inc., Bethel, CT, USA

The Conference Proceedings of the Society for Experimental Mechanics Series presents early findings and case studies from a wide range of fundamental and applied work across the broad range of fields that comprise Experimental Mechanics. Series volumes follow the principle tracks or focus topics featured in each of the Society’s two annual conferences: IMAC, A Conference and Exposition on Structural Dynamics, and the Society’s Annual Conference & Exposition and will address critical areas of interest to researchers and design engineers working in all areas of Structural Dynamics, Solid Mechanics and Materials Research. More information about this series at http://www.springer.com/series/8922

Leslie Lamberson • Steven Mates •  Veronica Eliasson Editors

Dynamic Behavior of Materials, Volume 1 Proceedings of the 2020 Annual Conference on Experimental and Applied Mechanics

Editors Leslie Lamberson Colorado School of Mines Golden, CO, USA

Steven Mates National Institute of Standards and Tech Gaithersburg, MD, USA

Veronica Eliasson Department of Mechanical Engineering Colorado School of Mines Golden, CO, USA

ISSN 2191-5644     ISSN 2191-5652 (electronic) Conference Proceedings of the Society for Experimental Mechanics Series ISBN 978-3-030-59946-1    ISBN 978-3-030-59947-8 (eBook) https://doi.org/10.1007/978-3-030-59947-8 © The Society for Experimental Mechanics, Inc. 2021 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface

Dynamic Behavior of Materials represents one of seven volumes of technical papers to be presented at the 2020 SEM Annual Conference & Exposition on Experimental and Applied Mechanics organized by the Society for Experimental Mechanics scheduled to be held in Orlando, FL, September 14–17, 2020. The complete proceedings also include volumes on: Challenges in Mechanics of Time-Dependent Materials; Fracture, Fatigue, Failure and Damage Evolution; Advancement of Optical Methods & Digital Image Correlation in Experimental Mechanics; Mechanics of Biological Systems and Materials, Microand Nanomechanics & Research Applications; Mechanics of Composite, Hybrid & Multifunctional Materials; and Thermomechanics & Infrared Imaging, Inverse Problem Methodologies and Mechanics of Additive & Advanced Manufactured Materials. Each collection presents early findings from experimental and computational investigations on an important area within Experimental Mechanics. Dynamic Behavior of Materials is 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 to provide a forum to facilitate technical interaction and exchange. Over the years, this track has been representing the ever-growing interests in dynamic behavior to the SEM community, working toward expanding synergy with other tracks and topics, and improving diversity and inclusivity, as evidenced by the increasing number and diversity of papers and attendance. The contributed papers span numerous technical divisions within SEM, demonstrating its relevance not only in the dynamic behavior of materials community but also in the mechanics of materials community as a whole. The track organizers thank the authors, presenters, organizers, and session chairs for their participation, support, and contribution to this track. The SEM support staff is also acknowledged for their devoted efforts in accommodating the large number of paper submissions this year, making the 2020 Dynamic Behavior of Materials Track a success. Golden, CO Gaithersburg, MD  Golden, CO 

Leslie Lamberson Steven Mates Veronica Eliasson

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Contents

1 Mechanical Characterization of 304L-­VAR Stainless Steel in Tension with a Full Coverage from Low, Intermediate, to High Strain Rates����������������������������������������������������������������������������������������������������������������������������� 1 Bo Song, Helena Jin, Brett Sanborn, and Wei-Yang Lu 2 Expanding Inertial Microcavitation Rheometry to Cover Large Material Stretches in Soft Materials��������������� 7 Selda Buyukozturk and Christian Franck 3 Development of a Kolsky Bar Shaft-­Loaded Blister Test to Evaluate Dynamic Behavior of Adhesives���������������11 Shane Paulson, Chelsea Davis, and Wayne Chen 4 Constitutive Behavior of AA7475-T7351 at High Strain Rate and Elevated Temperatures ���������������������������������15 Purnashis Chakraborty, Anoop Kumar Pandouria, M. K. Singha, and Vikrant Tiwari 5 Experimental Investigation of the Failure Rate Dependency of Composite Materials Using Off-Axis Tensile Tests���������������������������������������������������������������������������������������������������������������������������������������������������25 Thomas Fourest and Julien Berthe 6 Observations of Velocity-Dependent Drag and Bearing Stress in Sand Penetration���������������������������������������������29 B. Kenneally, M. Omidvar, S. Bless, and M. Iskander 7 Ultra-Fast and Tunable Liquid Nanofoam Load Limiter�����������������������������������������������������������������������������������������37 Mingzhe Li, Robert McCoy, Dean Jaradi, and Weiyi Lu 8 Dynamic Rugae Strain Localizations and Instabilities in Soft Viscoelastic Materials During Inertial Microcavitation�������������������������������������������������������������������������������������������������������������������������������������������������������������45 Jin Yang, Harry C. Cramer III, and Christian Franck 9 Spall Response of Electroplated Gold Samples���������������������������������������������������������������������������������������������������������51 Anirban Mandal, William W. Anderson, Brian J. Jensen, Frank J. Cherne, and Daniel E. Hooks 10 Simulated Construction of FeMnAlC Alloy System Phase Diagram and Study of Its Dynamic Characterization���������������������������������������������������������������������������������������������������������������������������������55 Constantine (Costas) G. Fountzoulas 11 Developing a Methodology for Testing of Hearing Protection Systems�������������������������������������������������������������������59 S. de Oliveira, C. Mullins, J. Purutyan, L. Reiniger, B. Reymann, J. J. Rosowski, J. T. Cheng, and C. Furlong 12 An Innovative Experimental Approach for the Assessment of Composite Panel Ballistic Limit �������������������������65 G. Portemont, R. De Coninck, and R. Ortiz 13 Development of a Micro Tensile Kolsky Bar �������������������������������������������������������������������������������������������������������������69 Daniel T. Casem 14 Analysis of the Explosively Driven Expanding Ring Tension Test���������������������������������������������������������������������������73 Brady Aydelotte

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15 Static and Dynamic Mechanical Characterization of a Spark Plasma Sintered B6O–B4C Composite�����������������79 Kimia Ghaffari, Salil Bavdekar, and Ghatu Subhash 16 The Development of Split Hopkinson Tension-Torsion Bar for the Understanding of Complex Stress States at High Rate�������������������������������������������������������������������������������������������������������������������������������������������������������89 Yuan Xu, Lukasz Farbaniec, Clive Siviour, Daniel Eakins, and Antonio Pellegrino 17 High Strain Rate Characterization and Impact Analysis of Fiber Reinforced Composites ���������������������������������95 Karthik Ram Ramakrishnan, Gustavo Quino, Justus Hoffmann, and Nik Petrinic

Chapter 1

Mechanical Characterization of 304L-­VAR Stainless Steel in Tension with a Full Coverage from Low, Intermediate, to High Strain Rates Bo Song, Helena Jin, Brett Sanborn, and Wei-Yang Lu

Abstract  A 304L-VAR stainless steel was mechanically characterized in tension over a full range of strain rates from low, intermediate, to high using a variety of apparatus. While low- and high-strain-rate tests were conducted with a conventional Instron and a Kolsky tension bar, the tensile tests at intermediate strain rates were conducted with a fast MTS and a DropHopkinson bar. The fast MTS used in this study was able to obtain reliable tensile response at the strain rates up to 150 s−1, whereas the lower limit for the Drop-Hopkinson bar was determined to be 100 s−1. Combining the fast MTS and the DropHopkinson bar fully closed the gap within the intermediate strain rate regime. Using these four apparatus, the tensile stress-­ strain curves of the 304L-VAR stainless steel were obtained at various strain rates on each order in magnitude ranging from 0.0001 to 2580 s−1. All tensile stress-­strain curves exhibited linear elasticity followed by a significant work hardening prior to necking. After necking occurred, the specimen load decreased and the deformation became highly localized until fracture. The tensile stress-strain response the 304L-VAR stainless steel was also strain rate dependent. The flow stress increased with increasing strain rate. The strain-rate sensitivity was also observed to be strain-dependent, possibly due to thermosoftening caused by adiabatic heating at high strain rates. The 304L-VAR stainless steel also showed a significant ductility (or elongation to failure). The true failure strain was determined with the minimum diameter of the posttest specimen. The results showed that the true failure strains were approximately 210% at low strain rates, but were significantly lower (~110%) at high strain rates. The transition of true failure strain occurred within the intermediate strain rate range between 10−2 and 102 s−1. Keywords  Intermediate strain rate · Tensile property · 304L-VAR · Strain rate effect

1.1  Introduction Stainless steels have been of great interest to and extensively utilized in the architecture, food, medical, civil, energy, automotive, aerospace, and defense industries due to their notable corrosion resistance, recyclability, and reusability. The largest group and the most widely used among stainless steels is 300 series, with Type 304 as the best-known grade favored for its machinability, weldability, and formability in addition to corrosion resistance. Strain-rate-dependent mechanical response of 304 stainless steel is an important parameter in applications where the material is subjected to accidental drop, low-speed collision, high-speed perforation, or even ultra-high-speed blast or shock loading. The investigation of mechanical properties of 304 stainless steel with different mechanical loading conditions started in the 1970s [1, 2] and has been extensively conducted since the 1990s. In the past decades, 304 stainless steel has been mostly characterized within the quasi-static strain rate regime with little work within intermediate- and high-strain-rate regimes, particularly for tensile tests. Recently, Cadoni et al. [3] employed a universal electromechanical testing machine, a hydro-­pneumatic apparatus, and a split Hopkinson tension bar to characterize an AISI 304 stainless steel from low, intermediate to high strain rates. Both yield and ultimate tensile B. Song (*) · B. Sanborn Sandia National Laboratories, Albuquerque, NM, USA e-mail: [email protected]; [email protected] H. Jin · W.-Y. Lu Sandia National Laboratories, Livermore, CA, USA e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 L. Lamberson et al. (eds.), Dynamic Behavior of Materials, Volume 1, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-59947-8_1

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stresses increased with increasing strain rate. More extensive mechanical characterization of stainless steels is still needed to broaden the application space, particularly in the intermediate- and high-strain-rate tension regime. The primary barrier to precise characterization in those regimes has been experimental technique development. In this study, we used a 304L-VAR stainless steel to investigate the upper limit of a fast MTS high-rate servo-hydraulic machine and the lower limit of the Drop-Hopkinson bar to close the gap at intermediate strain rates. With on conventional Instron machine and a split Hopkinson tension bar, the 304L-­VAR stainless steel was characterized in tension at every order of magnitude of strain rate from 0.0001 to ~3500 s−1. The strain rate effect on the tensile stress-strain response of the 304LVAR stainless steel was determined.

1.2  Material and Specimens The material investigated in this study was 304L-VAR stainless steel. Two designs were used for the tensile specimens for quasi-static and dynamic tests, respectively, as shown in Fig. 1.1. The quasi-static tensile specimens (Fig. 1.1a) followed an ASTM standard E8/E8M-09 with a diameter of 3.18 mm and a gage length of 15.88 mm, making an aspect (length to diameter) ratio of ~5 [4]. Relatively short tensile specimens are needed to achieve stress equilibrium in dynamic tensile tests. Therefore, the dynamic tensile specimens were designed with the same diameter but a shorter gage length of 6.35 mm, resulting in an aspect ratio of 2. Both quasi-static and dynamic tensile specimens had the same ½ in.-20 threads at both ends and transitional portion from the gage section to the threaded ends. The only difference between the two specimen geometries was the gage length. Preliminary test results showed that the specimen size effect was negligible prior to necking. The nominal stress-strain response for the necked specimens with different gage lengths deviated due to highly localized deformation in the necking region.

1.3  Mechanical Tests at Low, Intermediate, and High Strain Rates In this study, low-strain-rate tensile tests were conducted with an Instron material test frame under displacement control. Long tensile specimens shown in Fig. 1.1a were used for all low-strain-rate tests up to 0.1 s−1. The force was measured with a load cell on the top of the test frame to calculate the specimen stress. A laser extensometer was used to measure the deformation of the specimen over the gage section. The engineering stress-strain curve was therefore obtained. Two experimental apparatus—a fast MTS and a Drop-­Hopkinson bar [5]—were employed to cover the intermediate strain rates. Since specimen size effect is negligible, particularly prior to necking, long specimens (Fig. 1.1a) were used for fast

Fig. 1.1  Tensile specimen design (unit in mm). (a) Long specimen and (b) short specimen

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MTS tests and short specimens (Fig. 1.1b) were used for Drop-Hopkinson bar tests in this study. The fast MTS was used to cover the lower portion of the intermediate strain rate regime and the higher portion was covered with a Drop-Hopkinson bar. A Phantom camera system was synchronized with the fast MTS for in situ specimen d­ eformation measurement over the gage section. A dynamic load washer was used to measure the force during the fast MTS tests. The procedure of the DropHopkinson bar tests was presented in [5]. A high-speed laser extensometer was employed to accurately track the in situ motion of the incident and transmission bar ends independently with a split beam of a line laser into two separate high-speed photodetectors [6]. It is noted that the specimen deformation over the gage section was corrected from the high-speed laser extensometer measurement [7]. High-strain-rate tensile tests were conducted with a Kolsky tension bar. The stress history of the sample is therefore obtained using the transmitted strain signal [8]. The same high-speed laser extensometer and posttest correction method were applied to calculate specimen strain over the gage section. Following the procedure presented previously, the 304L-­VAR stainless steel was characterized in tension at various strain rates ranging from 0.0001 to ~2580 s−1 with full coverage in the intermediate strain rate regime. At each condition, 3–5 tests were repeated, and the mean curves were calculated and are shown in Fig. 1.2. As shown in Fig. 1.2, the 304L-­VAR stainless steel clearly possessed a typical elastic-­hardening tensile response, until the onset of necking, with significant strain-rate effect. At certain engineering strains, the flow stresses increased with increasing strain rates, as shown in Fig. 1.3. Since the specimen failed within a highly localized region, it is erroneous to use the engineering measurement over the entire gage section to calculate the failure strain. In this study, the minimum neck diameter was measured for all posttest tensile specimens to calculate true failure strains [9]. Figure 1.4 shows the strain rate effect on true failure strain. The true failure strain decreased with increasing strain rate, although the data was scattered. The true failure strains were around 210% at low strain rates but dropped to around 110% at high strain rates on the order of 103 s−1. The true failure strains were not observed to be significantly dependent on strain rate within the low (below 10−2 s−1) or high (above 102 s−1) strain rate regime. However, a significant strain rate effect on true failure strain was observed when the strain rate fell into the intermediate strain-rate regime between 10−2 and 102 s−1.

Fig. 1.2  Tensile stress-strain curves at various strain rates

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Fig. 1.3  Strain rate effect on flow stress

Fig. 1.4  Strain rate effect on true failure strain

1.4  Conclusion 304L-VAR stainless steel was characterized in tension with a full coverage from low, intermediate to high strain rates, particularly with a significant focus on intermediate strain rates between 100 and 102 s−1. The 304L-VAR stainless steel possessed a significant work-hardening response with a significant strain rate effect. The strain rate sensitivity of the flow stress was observed to depend on strain. The material showed a high ductility with approximately 50% strain prior to the onset of necking. The true failure strain was calculated based on the final necked diameter of the sample. The true failure strains were

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observed to be ~210% at low strain rates up to 0.01 s−1 and reduced to ~110% at high strain rates above 100 s−1, leaving a drastic change within the intermediate strain rate range. Acknowledgments  Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. The views expressed in this chapter do not necessarily represent the views of the U.S. Department of Energy or the United States Government.

References 1. Korbonski, J.A., Murr, L.E.: Effects of plastic strain and strain rates on the mechanical properties and thermal recovery of type 304 stainless steel. Metals Eng. Quart. 11, 47–48 (1971) 2. Steichen, J.M.: Effect of irradiation on the strain rate dependence of type 304 stainless-steel mechanical properties. Nucl. Technol. 16, 308–315 (1972) 3. Cadoni, E., Fenu, L., Forni, D.: Strain rate behavior in tension of austenitic stainless steel used for reinforcing bars. Constr. Build. Mater. 35, 399–407 (2012) 4. ASTM: Standard Test Methods for Tension Testing of Metallic Materials. ASTM Standard E8/E8M-09 (2009) 5. Song, B., Sanborn, B., Heister, J., Everett, R., Martinez, T., Groves, G., Johnson, E., Kenney, D., Knight, M., Spletzer, M., Haulenbeek, K., McConnell, C.: An apparatus for tensile characterization of materials within the upper intermediate strain rate regime. Exp. Mech. 59, 941–951 (2019) 6. Nie, X., Song, B., Loeffler, C.M.: A novel splitting-beam laser extensometer technique for Kolsky tension bar experiment. J. Dyn. Behav. Mater. 1, 70–74 (2015) 7. Song, B., Sanborn, B., Susan, D., Johnson, K., Dabling, J., Carroll, J., Brink, A., Grutzik, S., Kustas, A.: Correction of specimen strain measurement in Kolsky tension bar experiments on work-hardening materials. Int. J. Impact Eng. 132, 103328 (2019) 8. Song, B., Antoun, B.R., Jin, H.: Dynamic tensile characterization of a 4330-V steel. Exp. Mech. 53, 1519–1529 (2013) 9. Sanborn, B., Song, B., Thompson, A., Reece, B., Attaway, S.: High strain rate tensile response of A572 and 4140 steel. Proc. Eng. 197, 33–41 (2017)

Chapter 2

Expanding Inertial Microcavitation Rheometry to Cover Large Material Stretches in Soft Materials Selda Buyukozturk and Christian Franck

Abstract  The existence of cavitation in soft materials introduces challenging problems as it exhibits unique deformation and failure mechanisms. Soft materials behave differently under high strain-rates than under quasi-static loading conditions. Particularly, the effects of strain-rates in the ballistic and blast ranges are unknown. Laser-induced cavitation (LIC) is a thermally driven inertial process for generating large deformations at high to ultra-high strain-­rates in optically transparent materials by way of cavitation. This study focuses on LIC as a reliable and robust experimental method for characterizing the constitutive response of materials across an order of magnitude in material stretches. Through the integration of an appropriate theoretical framework, material stresses and strains during cavitation can be estimated for homogeneous, isotropic materials with Inertial Microcavitation Rheometry (IMR), a tool developed to characterize the nonlinear viscoelastic properties of soft materials at high strain-rates. The long-time bubble radius at mechanical equilibrium and maximum bubble radius, defined as the material stretch in the hydrogel, determine the initial gas pressure in the bubble to initialize the simulation. However, the current theoretical framework was developed with limited experimental modulation of bubble amplitude, limiting the regime of accessible material deformations. Furthermore, the model neglects to address inelastic material behavior at large material stretches. In this work, an extensive library of material stretches due to bubble oscillation are experimentally achieved to identify critical material stretches during the transition from viscoelastic to inelastic behavior by systematically controlling bubble amplitude and material deformations over a large stretch range. This library of material stretches defined by the bubble dynamics are used in the simulation to test the robustness of IMR, and identify new avenues for future theoretical and numerical developments. In sum, this critical experimental data will lay the foundation for incorporating damage and failure mechanisms of inelastic behavior of soft materials undergoing high strain-rate deformations. Keywords  Laser-induced cavitation (LIC) · Inertial microcavitation rheometry (IMR) · Ultra-high strain-rate · Bubble amplitude · Material stretch

2.1  Introduction The recent recognition and use of cavitation in biological and other soft material systems has motivated the development of understanding bubble dynamics in and near soft materials. Specific applications include the study of biological tissues, polymeric coatings, biofouling, composites, and other synthetic materials. Laser-induced cavitation (LIC) is a thermally driven inertial process with the ability to characterize material behavior at high strain-rate (103–108 s−1) deformations. Through the integration of an appropriate theoretical framework, material stresses and strains during cavitation can be estimated for homogeneous, isotropic materials through Inertial Microcavitation Rheometry (IMR), a tool we recently developed to characterize the nonlinear viscoelastic properties of soft materials at high strain-rates [1].

S. Buyukozturk (*) School of Engineering, Brown University, Providence, RI, USA Department of Mechanical Engineering, University of Wisconsin–Madison, Madison, WI, USA e-mail: [email protected] C. Franck Department of Mechanical Engineering, University of Wisconsin–Madison, Madison, WI, USA e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 L. Lamberson et al. (eds.), Dynamic Behavior of Materials, Volume 1, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-59947-8_2

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The previous development of IMR has considered only a limited material stretch ratio regime, neglecting to incorporate inelastic material behavior. This study aims to identify the critical material stretches exhibited at the transition from viscoelastic to inelastic material behavior and develop new experimentation for the modulation of LIC bubble amplitudes. Experimental methods to achieve these aims include varying cavitation laser energy and using micron-sized heat sink particles to drive bubble nucleation. This characterization will pave the way for future work in the development and incorporation of damage and failure mechanisms into the theoretical framework.

2.2  Background Generally, cavitation is the process in which a void emerges in a liquid or solid medium due to localized pressure changes [2]. LIC is an experimental method for generating spatially controlled cavitation bubbles in soft materials and has proven to be reliable and robust. A high-energy laser pulse focused within a soft material results in the ionization and formation of a bubble consisting of an approximate two-phase vapor and gas mixture. The resulting oscillating bubble interacts with the surrounding material and is modeled to determine constitutive behavior to predict material stresses and strains at high strain-rates. IMR uses the experimentally obtained high-speed time-­lapse data of bubble oscillations within the given material of interest, and for spherically symmetric bubbles computes the temporal evolution of the bubble radius, R(t) [1]. The normalized value R(t)/Req is also defined to be the material stretch, λ(t). Assuming spherical bubble symmetry and near-­field material incompressibility, the 1D momentum balance and conservation of mass equations, with the incorporation of traction and kinematic boundary conditions of the bubble, present the Keller-Miksis equation, 



æ R ö ¨ 3 æ 2g 2g R ö 2 1 æ R ö æ ö 1 Ræ ö + S - p¥ ÷ + ç 1 - ÷ R R + ç 1 - ÷ R = ç 1 + ÷ ç pb ç pb - R + S ÷ c r r C 2 3 c c R è ø è ø è ø è ø è ø

(2.1)

R is bubble radius, c is material wave speed, ρ is mass density, pb is bubble pressure, γ is surface tension, and p∞ is far-field pressure. S describes the constitutive material behavior as a function of hoop and radial stress. IMR employs the least squares method to best fit material parameters across several constitutive models to determine the best material fit. However, the model may fail to capture the complete bubble dynamics due to unaccounted inelastic material behavior. Experimentally, this can be reflected by loss of bubble amplitude, as well as bubble asphericity. As schematically depicted in Fig. 2.1, experimental bubble radius vs. time is compared to its simulated IMR curve. The first peak consistently fits well, but there is a discrepancy for subsequent peaks unaccounted for by the current IMR nonlinear viscoelastic model. In order to improve this discrepancy, there is an experimental need to explore the critical material stretches in which elasticity breaks down and incorporate the dominating inelastic material behavior into IMR.

Experimental R(t) IMR simulation

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Fig. 2.2 (a) LIC experimental setup on a Ti2 Nikon Microscope. (b) LIC bubble time-lapse (2–3 μs per frame) video in a soft polyacrylamide hydrogel (G∞,soft = 461 Pa)

2.3  Experimental Approach A Q-switched 532 nm Nd:YAG laser (Amplitude) with 6 ns pulse is aligned into the back port of a Ti2 Nikon Microscope. The laser is expanded to five times the original beam size, enough to fill the back aperture of a microscope objective and focused within a volume of a hydrogel to initiate cavitation. High-speed imaging is used to capture the bubble kinematics by aligning a high-speed camera to the focal plane of the microscope side port. With appropriate lighting conditions, a timeseries of the bubble evolution is captured, an example of which is shown in Fig. 2.2b. The laser energy is adjusted to achieve a high enough energy output to form a bubble large enough to fill the field of view of the high-speed camera. Laser energy attenuation is then controlled using neutral density (ND) filters along the optical pathway of the laser prior to its entrance into the microscope. To measure laser energy output into the material for cavitation, an EnergyMax Sensor (Coherent) is placed within the sample holder of the microscope stage. Isotropic homogeneous “soft” polyacrylamide hydrogels are used for cavitation with quasi-static shear moduli, G∞,soft = 461 Pa. Additionally, separate polyacrylamide samples are made with heat sink particles, to lower the bubble nucleation threshold in the gels. Polyethylene particles with a conductive paramagnetic coating (Cospheric) are treated with 2% w/v of Tween 80  in water. The solution is then used to make polyacrylamide hydrogels, resulting in heat sink particles embedded within its volume.

2.4  Analysis Polyacrylamide hydrogels undergoing large finite deformations at high strain-rates have been measured and fitted to nonlinear Kelvin-Voigt model, which extends the traditional quasi-static Neo-Hookean description of polyacrylamide to include dynamic shear viscosities [1]. In this study, it is found that at different cavitation laser output energies, the maximum bubble radius, Rmax, scales with the cavitation laser energy; this trend is in line with other cavitation energetics studies performed in the literature [3]. However, the normalized radius vs. time curves for all experiments show a reasonable overlap between energy experiments. Particularly, the curves collapse on top of each other regardless of cavitation laser energy used for nucleation. In fact, it is found that the maximum material stretch is relatively unchanged with respect to the measured cavitation laser energy. Since Rmax and Req scale with laser energy and it is found that maximum material stretch is relatively constant per material, heat sink particles in polyacrylamide gels are used to extend the finite deformation regime in which IMR is tested. By focusing the cavitation laser at a singular iron-­based particle, dynamic bubble events are initiated through a direct phase change rather than dielectric breakdown and plasma formation. In Fig. 2.3a, a series of experiments in soft polyacrylamide hydrogels at a laser energy of 133 μJ were nucleated. It is shown that bubbles initiated with a 45 μm heat sink particle exhibited the largest bubble amplitude, while a gel with no heat sink particle resulted in the lowest amplitude; the equilibrium radius of the bubbles followed the same trend. In the normalized bubble radius vs. time plot, there is reasonable convergence of the curves at the first peak, but a divergence in subsequent peaks. However, when plotting material stretch with respect to equilibrium radius, it is shown that the maximum material stretch is experimentally varied. Bubbles initiated with 20 μm particles exhibit a maximum material stretch of approximately 5, while bubbles initiated with 45 μm particles exhibit a maximum material stretch of approximately 3–4. Preliminary results demonstrate an experimental technique to vary material stretch in LIC

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S. Buyukozturk and C. Franck 350 “Soft” 45µm particle “Soft” 20µm particle “Soft”

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Fig. 2.3 (a) Radius vs. time curves of bubbles nucleated at 133 μJ laser energy in “soft” polyacrylamide with and without particles. (b) Normalized radius vs. time curve. (c) Time-dependent material stretch

bubbles deforming under high strain-rates. In this work, we will evaluate IMR for a complete finite deformation range and analyze its performance in polyacrylamide.

2.5  Conclusion This study will test the limitations of our current IMR model to identify critical stretches at the transition from viscoelastic to inelastic material behavior, as well as provide new experimental methods for controlled bubble amplitude modulation. The experimental acquisition of a full finite deformation regime will lay the foundation for the incorporation of inelastic material into the theoretical framework. Studies such as energy loss through the material, asphericity, rupture, wrinkling, and more may be included ultimately improving our fundamental understanding of the high-rate deformation behavior of soft materials and improve our ability to predict constitutive material properties and material performance. Acknowledgments  We gratefully acknowledge support from the Office of Naval Research (Dr. Timothy Bentley) under grant N000141712058.

References 1. Estrada, J.B., et al.: High strain-rate soft material characterization via inertial cavitation. J. Mech. Phys. Solids. 112, 291–317 (2018) 2. Brennen, C.E.: Cavitation Bubble Dynamics. Cambridge University Press, Cambridge (2013) 3. Quinto-Su, P.A., Suzuki, M., Ohl, C.-D.: Fast temperature measurement following single laser-induced cavitation inside a microfluidic gap. Sci. Rep. 4, 5445 (2014)

Chapter 3

Development of a Kolsky Bar Shaft-­Loaded Blister Test to Evaluate Dynamic Behavior of Adhesives Shane Paulson, Chelsea Davis, and Wayne Chen

Abstract  Adhesive joints are used in a wide variety of applications, ranging from epoxy-set structural anchors in concrete buildings to providing the interface in layered armor plates in military vehicles. With this wide range of applications, adhesive joints experience the full range of strain rates as well, from long-duration creep conditions to high-­velocity impact. While research into the delamination behavior of layered materials is common at high strain rates, very little has been done to link this research to the strength of adhesion and interfacial toughness of the constituent adhesive. Adhesion research is common as well; however, few methods have been adapted to evaluate adhesion strength at high strain rates. In this study, a traditional Kolsky bar was modified to employ the shaft-­loaded blister technique to increase strain rates. Blister samples were fabricated with an aluminum 6061 substrate and three different polymer coatings: Sylgard® 184, SC-15 epoxy, and a TGDDM epoxy cured with Jeffamine® D230. For each case, sample failure was induced at a quasi-static strain rate before using the Kolsky bar apparatus to examine the failure behavior with an initial shaft velocity of ~5 m/s. The growth of the blister was observed using a high-speed camera for the radial growth, and the height of the blister was determined by the crosshead displacement at the quasi-static load rate and using the strain signals obtained using the Kolsky bar. This technique was successful in observing the adhesive fracture of three different polymers and comparing the failure behavior for the quasi-static load case with that observed at a high strain rate. Keywords  Dynamic behavior · Adhesive · Interface · Fracture

3.1  Introduction The use of adhesives has continually seen growth across a wide variety of industries from office supplies and home products to high-performance materials in construction and composite manufacturing. With the continuing development of high-performance adhesives, layered material systems have also seen increased use in conventional sandwich panel construction as well as laminated impact-resistant materials. Previous studies have shown that the delamination of these layered materials leads to reduced structural integrity. This delamination behavior is well-studied in the quasi-static regime; however, this problem is difficult to evaluate at increased loading rates. As most adhesives are composed of polymeric materials, they will each have a degree of viscoelastic behavior. This viscoelastic effect will not only affect the strength of the adhesive itself but also how an applied load will travel to and across an interface. For composite sandwich panels, this is a critical topic to study, as blast loads have been shown to induce layer delamination [1, 2]. In addition, those panels which have suffered delamination show reduced strength under typical loading

S. Paulson (*) Department of Aeronautics and Astronautics Engineering, College of Engineering, Purdue University, West Lafayette, IN, USA e-mail: [email protected] C. Davis Department of Materials Engineering, College of Engineering, Purdue University, West Lafayette, IN, USA e-mail: [email protected] W. Chen Department of Aeronautics and Astronautics Engineering, College of Engineering, Purdue University, West Lafayette, IN, USA Department of Materials Engineering, College of Engineering, Purdue University, West Lafayette, IN, USA e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 L. Lamberson et al. (eds.), Dynamic Behavior of Materials, Volume 1, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-59947-8_3

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conditions [3]. In order to obtain a better understanding of this delamination phenomenon, the authors here seek to develop a technique that will isolate those behaviors that contribute to delamination in layered materials. An ideal method for the study of this behavior is the shaft-­loaded blister test, used commonly in the field of adhesion science. This method has been used at quasi-static load rates to measure the properties of thin adhesive films [4] as well as the adhesion of epoxy coatings [5]. Due to the mechanical application of the applied load, the shaft-loaded blister test is an attractive option to be modified for dynamic load conditions. This chapter discusses preliminary work to apply this experimental method to study the dynamic behavior of an adhesive interface.

3.2  Methodology For this study, experiments were performed on three different polymer coatings applied to a 6061-T6 aluminum substrate. The substrates were 61 mm × 61 mm × 1.5 mm, with a 12.7 mm diameter hole punched through the center. These center holes were sealed with press-fit PTFE discs before applying the adhesive material. For the adhesive materials, we selected Sylgard® 184 elastomer, SC-15 epoxy, and TGDDM epoxy cured with Jeffamine® D230. After curing the adhesive at 90 °C for 12 h, the PTFE discs were carefully removed such that the adhesive coating was not damaged. Initial experiments were conducted at a quasi-static strain rate using an MTS-810 testing machine, and a schematic of this setup is provided in Fig. 3.1. The stationary shaft shown in Fig. 3.1 was manufactured from 316 stainless steel with a tip radius of 6.35 mm. The shaft had an overall length of 50.8 mm. At the load cell or incident bar end, the shaft has a circular cross-section with a diameter of 12.7 mm and length 25.4 mm. At the radius end, the shaft was milled to a hexagonal cross-section with an edgeto-edge distance of 9.1 mm. Samples were loaded with a shaft displacement rate of 1.0 mm/min, and images were captured using a Dino-Lite Edge digital microscope at a frame rate of 10 Hz.

Fig. 3.1  Shaft-loaded blister test setup for quasi-static load condition

3  Development of a Kolsky Bar Shaft-Loaded Blister Test to Evaluate Dynamic Behavior of Adhesives

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Fig. 3.2  Schematic of Hopkinson bar setup for shaft-loaded blister experiments

In order to observe the behavior of these materials at an increased loading rate, the shaft shown in Fig. 3.1 was fixed to the end of a Split-Hopkinson Pressure Bar, specifically the incident bar. For these preliminary experiments, the system was composed of a striker bar (12.7 mm diameter, 305 mm length) and an incident bar (12.7 mm diameter, 1372 mm length), both composed of Vascomax 300 maraging steel. Images of these experiments were captured using a Shimadzu HPV-X2 camera at a frame rate of 1.0 MHz. A schematic for this setup is provided in Fig. 3.2.

3.3  Results For the quasi-static load condition, each adhesive exhibited clear delamination behavior with very little applied load. In addition, the two epoxy materials exhibited significant delamination growth before fracture of the adhesive material. The two epoxy materials exhibited high rigidity with little blister height growth for a high applied load, while Sylgard® 184 delaminated easily with very little applied load for a large blister height. The load in Newtons was plotted versus shaft displacement for these experiments, and the results are presented in Fig. 3.3. For the samples loaded with the dynamic setup, each adhesive showed little delamination failure with the high input loads applied. Each sample was impacted with a shaft end velocity of approximately 5.5 m/s. Assuming an equal contact area between the shaft and the adhesive, this corresponds to an approximate input load of 37, 1460, and 1550 N for Sylgard® 184, SC-15, and TGDDM, respectively. For the Sylgard® 184 adhesive, samples showed some delamination postmortem, but this behavior was not observed in the captured images. This implies that much of the input load was absorbed or dampened by the material. For both the SC-15 and TGDDM epoxy samples, fracture of the adhesive was observed at the boundary of the hole in the substrate with no apparent delamination. In this case, there appears to be a threshold at which the dominating failure mechanism changes from delamination to adhesive fracture. Images from SC-15 samples are provided in Fig. 3.3 to note these clear differences in fracture behavior.

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Fig. 3.3 (a) Load-displacement data for quasi-static blister experiments. (b) Image from final failure of sample SC15-1 under quasi-static loading. Point (1) denotes the boundary of the growing delamination and (2) marks the location of fracture of the adhesive. (c) Image of SC15 adhesive failure under dynamic loading. (1) Marks the location of the ring fracture at the substrate boundary and (2) marks the location of a tensile fracture at the location of the shaft

3.4  Conclusion This preliminary study observed the difference in failure modes in a layered adhesive-substrate system under the same geometric conditions. Samples exhibited clear delamination behavior under quasi-static load conditions. Under these conditions, Sylgard® 184 showed large displacements and significant delamination with very low applied loads. In contrast, epoxy materials, SC-15 and TGDDM, produced higher shaft loads for a low displacement. These materials also exhibited delamination behavior before a final fracture of the adhesive. To observe the dynamic load condition, samples were loaded with a shaft velocity of 5  m/s, producing higher input loads than those measured under quasi-static conditions. For this condition, Sylgard® 184 showed significant resistance to delamination, and no fracture was observed. Both epoxy materials showed no apparent delamination behavior, instead of failing due to fracture at the boundary of the substrate. These results show some significant differences in the behavior of adhesives at different loading rates. With further improvements to sample design and measurement systems, this is a promising technique to study these behaviors in more detail. Acknowledgments  The authors would like to thank their colleagues from the Impact Science Laboratory at Purdue University for their assistance and support in understanding and improving this work.

References 1. Rolfe, E., Kelly, M., Arora, H., Hooper, P.A., Dear, J.P.: X-ray CT analysis after blast of composite sandwich panels. Proc. Eng. 167, 176–181 (2016) 2. Dear, J.P., Rolfe, E., Kelly, M., Arora, H., Hooper, P.A.: Blast performance of composite sandwich structures. Proc. Eng. 173, 471–478 (2017) 3. Daniel, I.M., Abot, J.L., Schubel, P.M., Luo, J.J.: Response and damage tolerance of composite sandwich structures under low velocity impact. Exp. Mech. 52, 37–47 (2012) 4. Wan, K., Liao, K.: Measuring mechanical properties of thin flexible films by a shaft-loaded blister test. Thin Solid Films. 352, 167–172 (1999) 5. O’Brien, E.P., Case, S.L., Ward, T.C.: Critical and subcritical adhesion measurements of a model epoxy coating exposed to moisture using the shaft-loaded blister test. J. Adhes. 81, 41–58 (2005)

Chapter 4

Constitutive Behavior of AA7475-T7351 at High Strain Rate and Elevated Temperatures Purnashis Chakraborty, Anoop Kumar Pandouria, M. K. Singha, and Vikrant Tiwari

Abstract  The use of Aluminum alloys in the aerospace and defence industries has been rapidly increasing in the last few decades, due to their high strength-to-weight ratio and high fracture toughness. Mechanical behavior of aluminum alloys at high temperature and under high strain rate need to be investigated thoroughly to predict the response of structural members under extreme types of loading conditions like crash, impact, etc. In this chapter, the mechanical behavior of AA7475-T7351 alloy is investigated at elevated temperatures under quasi-static and high strain rate conditions. The present work is carried out using two distinct setups for loading the specimens quasi-­statically and dynamically at a wide range of temperatures. Cylindrical tensile specimens made of AA7475-T7351 were evaluated under a quasi-static (tensile loading) condition on an electromechanical universal testing machine (10−4–10−1  s−1) subjected to a temperature range 25–250  °C.  While Split Hopkinson Tensile Pressure Bar technique is utilized to obtain the mechanical behavior in the high strain rate range of 500–1500 s−1 at room temperature. Johnson-Cook constitutive model parameters were evaluated from the experimentally obtained stress-strain data. The flow stress prediction ability of this phenomenological model is compared with the experimental result in terms of average absolute error and correlation coefficient. Keywords  Constitutive modeling · JC model · AA7475-T7351 · Tensile SHPB

4.1  Introduction The 7XXX series aluminum alloys are extensively used as structural material in defense, automobile, and aerospace industry because of their high strength-to-weight ratio, good machinability, and excellent corrosion resistance [1–3]. The use of aluminum alloys in these industries improve the efficiency and performance without any compromise in survivability. AA7475-T7351 processes highest fracture toughness, low fatigue crack growth, and high strength, which makes it ideal for use in airframe, fuselage, and wings [4]. Strain rate sensitive dynamic behavior of aluminum alloys is an ongoing hot topic for several decades. The serviceability of structural component made of high-valued material subjected to high temperature and rapid loading condition largely depends upon the precision of material characterization. The effects of composition, temperature, microstructure, and strain rate on the mechanical behavior of aluminum alloys were studied by Higashi et al. [5]. The mechanical response of aluminum under different strain rate and temperature are reported by number of investigators [6–10]. Oosterkamp et al. [6] studied the response of AA6872-T6 and AA7108-T79 under compressive loading condition at strain rate ranging from 0.1 to 2000 s−1. The authors found very small strain rate sensitivity for yield and flow stress at room temperature. Reyes et al. [7] did tension test on AA7003-T79 and AA7108-T6 at strain rate level 0.1−3–103. They also observed a moderate increase in flow stress with the increase of strain rate. Børvik et al. [8] reported strong positive strain-rate sensitivity of AA6006-T6 in a wide range of strain rate (0.00078–1200 s−1) and temperature (293–573 K). Singh et al. [9, 10] investigated the tensile and compression behavior of AA6063-T6 in the strain rate range 0.1−3–850 s−1. Chen et al. [11] studied the dynamic response of series of extruded aluminum alloys AA6082-T6, AA6060-T6, AA7108-T6, and AA7003-T6 at a wide range of strain rate. They observed that AA6082-T6 and AA6060-T6 are almost strain rate insensitive, whereas AA7108-T6 and AA7003-T6 poses a strong strain rate sensitivity. In order to predict the flow stress at high temperature and strain rate, researchers propose various types of constitutive laws. These constitutive models can be broadly divided

P. Chakraborty (*) · A. K. Pandouria · M. K. Singha · V. Tiwari Department of Applied Mechanics, Indian Institute of Technology Delhi, New Delhi, India e-mail: [email protected]; [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 L. Lamberson et al. (eds.), Dynamic Behavior of Materials, Volume 1, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-59947-8_4

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into three categories (1) phenomenological model, (2) artificial neural network models, and (3) physics-based models. Due to the convenience of lesser material constant Johnson-­Cook [12] model is widely used to predict the stress-strain response of material at dynamic condition. The first objective of this experimental investigation is to quantify the effect of the strain rate and the temperature on mechanical properties (yield, ultimate and flow tensile stresses) of AA7475-T7351. Secondly, to evaluate the parameter for Johnson-Cook constitutive material parameter form the experimentally obtained stress-strain data at different strain rate and temperature. Deviation of model predictions from experimental results is also estimated through error calculation. The structure of this chapter is given as follows. In Sect. 4.2, chemical composition of the material is reported. In Sect. 4.3, the experimental procedure is explained. Experimental results are demonstrated in Sect. 4.4. In Sect. 4.5, material parameters of Johnson-Cook c­ onstitutive modeling are evaluated. The effectiveness of this model is checked through error analysis in Sect. 4.6.

4.2  Material The 7475-aluminum alloy used in the present study was procured from Falcon Aerospace (USA) in the form of rolled plate of 12.75 mm thick and as T7351 temper condition. This is basically Al-Zn-Mg-based alloy, with high yield, high fracture toughness and it also provides good ballistic performance. The chemical composition of the alloy is shown in Table 4.1.

4.3  Experimental Program The mechanical behavior of AA7475-T7351 is studied over a wide range of strains, strain rate, and temperature under static and dynamic condition.

4.3.1  Quasi-Static Experiment The quasi-static experiments were performed using electromechanical universal testing machine Zwickroll/Z50, having maximum load capacity of 50 kN. Cylindrical dog-bone specimens having gauge diameter of 6 mm (±0.01) and gauge length of 25 mm (±0.01) as per ASTM E8 were directly extracted from the sheet along the rolling direction. These specimens were tested at different strain rate (10−4–10−1 s−1) and temperature (25–250 °C). The specimens were heated to required temperature at a heating rate 1 °C/s and were held for 20 min by thermocouple-feedback-controlled AC current to maintain a uniform temperature. A high precision video extensometer VideoXtens1-120 with a resolution of 0.6 μm was used to conduct higher temperature experiments.

4.3.2  Dynamic Experiment High strain rate experiments were performed by using Split Hopkinson Tensile Bar (SHTB) [13] installed at Impact Mechanics Laboratory at Indian Institute of Technology, Delhi. SHTB consists of two high strength Ti-6Al-4V bars having a diameter of 20 mm, length 3 and 2 m, respectively, for the input and output bar. Aluminum tensile specimens were screwed between the incident and the transmission bar. High precision strain gauges were placed on the input and output bar to measure the incident transmission and reflected signal in the specimen. The diameter of the bar is small in comparison to the generated pulse length and also time taken by the pulse to travel through the specimen is very small. These conditions allow uniform stress and strain throughout the specimen. As the bar is elastically loaded and satisfying the above two conditions, Table 4.1  Chemical composition of aluminium alloy 7475-T7351 Elements W (%)

Al 90.85

Zn 5.2203

Mg 2.12

Cu 1.4216

Fe 0.074

Si 0.0506

Ni 0.0023

Mn 0.005

Cr 0.1944

Ti 0.0379

V 0.0097

Sn