River Rapids Conference Proceedings of the Society for Experimental Mechanics Series Fracture, Fatigue, Failure and Damage Evolution, Volume 8 Allison M. Beese Alan T. Zehnder Shuman Xia Proceedings of the 2015 Annual Conference on Experimental and Applied Mechanics River Publishers
Conference Proceedings of the Society for Experimental Mechanics Series Series Editor Kristin B. Zimmerman, Ph.D. Society for Experimental Mechanics, Inc., Bethel, CT, USA
River Publishers Allison M. Beese • Alan T. Zehnder • Shuman Xia Editors Fracture, Fatigue, Failure and Damage Evolution, Volume 8 Proceedings of the 2015 Annual Conference on Experimental and Applied Mechanics
Published, sold and distributed by: River Publishers Broagervej 10 9260 Gistrup Denmark www.riverpublishers.com ISBN 978-87-7004-922-1 (eBook) Conference Proceedings of the Society for Experimental Mechanics An imprint of River Publishers © The Society for Experimental Mechanics, Inc. 2016 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, or reproduction 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.
Preface Fracture, Fatigue, Failure, and Damage Evolution represents one of nine volumes of technical papers presented at the SEM 2015 SEM Annual Conference & Exposition on Experimental and Applied Mechanics organized by the Society for Experimental Mechanics and held in Costa Mesa, CA, June 8–11, 2015. The complete Proceedings also include volumes on: Dynamic Behavior of Materials; Challenges in Mechanics of Time-Dependent Materials; Advancement of Optical Methods in Experimental Mechanics; Experimental and Applied Mechanics; MEMS and Nanotechnology; Mechanics of Biological Systems and Materials; Mechanics of Composite & Multifunctional Materials and 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, Fracture and Fatigue being one of these areas. Fatigue and fracture are two of the most critical considerations in engineering design. Understanding and characterizing fatigue and fracture has remained as one of the primary focus areas of experimental mechanics for several decades. Advances in experimental techniques, such as digital image correlation, acoustic emissions, and electron microscopy, have allowed for deeper study of phenomena related to fatigue and fracture. This volume contains the results of investigations of several aspects of fatigue and fracture such as microstructural effects, the behavior of interfaces, the behavior of different and/or complex materials such as composites, and environmental and loading effects. The collection of experimental mechanics research included here represents another step toward solving the long-term challenges associated with fatigue and fracture. Pennsylvania, PA Allison M. Beese Ithaca, NY Alan T. Zehnder Atlanta, GA ShumanXia v
Contents 1 Reflection-Mode Digital Gradient Sensing Technique for Experimental Fracture Mechanics ................. 1 Amith S. Jain and Hareesh V. Tippur 2 Experimental and Computational Investigation of Out-of-Plane Low Velocity Impact Behavior of CFRP Composite Plates.............................................................................................. 9 O.T. Topac, B. Tasdemir, B. Gozluklu, E. Gurses, and D. Coker 3 Prediction of Incipient Nano-Scale Rupture for Thermosets in Plane Stress ..................................... 17 J.C. Moller, S.A. Barr, T.D. Breitzman, G.S. Kedziora, A.M. Ecker, R.J. Berry, and D. Nepal 4 Effect of Degree of Cure on Damage Development in FRP......................................................... 27 Takahiro Ozaki, Tatsuro Kosaka, and Kazuhiro Kusukawa 5 Stochastic Discrete Damage Simulations of Laminate Composites ................................................ 35 Gunjin Yun and Li Zhao 6 Development of a Specimen for In-Situ Diffraction Planar Biaxial Experiments ................................ 45 G.M. Hommer and A.P. Stebner 7 V-Notched Rail Test for Shear-Dominated Deformation of Ti-6Al-4V............................................ 51 Sharlotte Kramer, John Laing, Thomas Bosiljevec, Jhana Gearhart, and Brad Boyce 8 A Statistical/Computational/Experimental Approach to Study the Microstructural Morphology ofDamage ................................................................................................................ 61 J.P.M. Hoefnagels, C. Du, T.W.J. de Geus, R.H.J. Peerlings, and M.G.D. Geers 9 Prediction of Ductile Fracture Through Small-Size Notched Tensile Specimens................................. 67 L. Farbaniec, H. Couque, and G. Dirras 10 Development of a Generalized Entropic Framework for Damage Assessment ................................... 73 Anahita Imanian and Mohammad Modarres 11 Modelling of Experimental Observations of Electrical Response of CNT Composites .......................... 83 K. Shkolnik and V.B. Chalivendra 12 Effect of Micro-Cracks on the Thermal Conductivity of Particulate Nanocomposite ........................... 89 Addis Tessema, Dan Zhao, Addis Kidane, and Sanat K. Kumar 13 Fatigue Tests on Fiber Coated Titanium Implant–Bone Cement Interfaces...................................... 95 M. Khandaker, Y. Li, P. Snow, S. Riahinezhad, and K. Foran 14 Fatigue Behavior of Carburized Steel at Long Lives ................................................................ 105 D.V. Nelson and Z. Long 15 Fatigue Behavior of Fluid End Crossbore Using a Coupon-Based Approach .................................... 115 Mahdi Kiani, Rayford Forest, Steven Tipton, and Michael W. Keller vii
viii Contents 16 Notch Strain Analysis of Crossbore Geometry....................................................................... 125 Mahdi Kiani, Steven Tipton, and Michael W. Keller 17 Opto-acoustic and Neutron Emissions from Fracture and Earthquakes.......................................... 135 Alberto Carpinteri 18 Field Theoretical Description of Shear Bands........................................................................ 141 Sanichiro Yoshida and Tomohiro Sasaki 19 Measuring the Effective Fracture Toughness of Heterogeneous Materials ....................................... 151 Chun-Jen Hsueh, Guruswami Ravichandran, and Kaushik Bhattacharya 20 Local Strain Analysis of Nitinol During Cyclic Loading............................................................ 157 Kenneth Perry, Alex Teiche, and Izak McGieson 21 Environmental Protection by the Opto-acoustic and Neutron Emission Seismic Precursors ................... 165 O. Borla, G. Lacidogna, E. Di Battista, M. Costantino, and A. Carpinteri 22 Neutron Emissions from Hydrodynamic Cavitation................................................................. 175 A. Manuello, R. Malvano, O. Borla, A. Palumbo, and A. Carpinteri 23 From Dark Matter to Brittle Fracture ................................................................................ 183 P.C.F. Di Stefano, C. Bouard, S. Ciliberto, S. Deschanel, O. Ramos, S. Santucci, A. Tantot, L. Vanel, andN. Zaïm 24 Compositional Variations in Palladium Electrodes Exposed to Electrolysis...................................... 187 A. Carpinteri, O. Borla, A. Goi, S. Guastella, A. Manuello, R. Sesana, and D. Veneziano 25 Strain-Rate-Dependent Yield Criteria for Composite Laminates.................................................. 197 Joseph D. Schaefer and Isaac M. Daniel 26 Experimental Fatigue Specimen and Finite Element Analysis for Characterization of Dental Composites .. 209 Dhyaa Kafagy and Michael Keller 27 Fracture Toughness and Impact Damage Resistance of Nanoreinforced Carbon/Epoxy Composites ......... 213 Joel S. Fenner and Isaac M. Daniel 28 Compression Testing of Micro-Scale Unidirectional Polymer Matrix Composites............................... 225 Torin Quick, Sirina Safriet, David Mollenhauer, Chad Ryther, and Robert Wheeler 29 Crack Analysis of Wood Under Climate Variations ................................................................. 235 Nicolas Angellier, Rostand Moutou Pitti, and Frédéric Dubois 30 Numerical Fracture Analysis Under Temperature Variation by Energetic Method............................. 243 Rostand Moutou Pitti, Seif Eddine Hamdi, Frédéric Dubois, Hassen Riahi, and Nicolas Angelier 31 Use of a Multiplexed Photonic Doppler Velocimetry (MPDV) System to Study Plastic Deformation of Metallic Steel Plates in High Velocity Impact...................................................... 253 Shawoon K. Roy, Michael Peña, Robert S. Hixson, Mohamed Trabia, Brendan O’Toole, Steven Becker, Edward Daykin, Richard Jennings, Melissa Matthes, and Michael Walling 32 In-service Preload Monitoring of Bolted Joints Subjected to Fatigue Loading Using a Novel ‘MoniTorque’ Bolt....................................................................................................... 261 Anton Khomenko, Ermias G. Koricho, Mahmoodul Haq, and Gary L. Cloud 33 Fatigue Behavior of Novel Hybrid Fastening System with Adhesive Inserts...................................... 269 Ermias G. Koricho, Anton Khomenko, Mahmoodul Haq, and Gary L. Cloud
Chapter 1 Reflection-Mode Digital Gradient Sensing Technique for Experimental Fracture Mechanics Amith S. Jain and Hareesh V. Tippur Abstract In this work, the reflection-mode Digital Gradient Sensing (r-DGS) method is extended for visualizing and quantifying crack-tip deformations in solids under quasi-static and dynamic loading conditions. The r-DGS technique employs digital image correlation principles to quantify two orthogonal surface slopes simultaneously in specularly reflective solids by quantifying small deflections of light rays. For the first time, r-DGS has been implemented here to study both mode-I and mixed-mode (I/II) problems and quantify fracture parameters. Under dynamic loading conditions, r-DGS is implemented in conjunction with high-speed digital photography to map surface slopes in edge cracked plates subjected to one-point impact. The measured surface slopes have been used to successfully evaluate stress intensity factor histories by pairing measurements with the corresponding asymptotic crack tip field descriptions using overdeterministic least-squares analyses. Keywords Optical metrology • Surface slopes • Stress wave propagation • High-speed photography • Fracture mechanics 1.1 Introduction Measurement of stresses, strains, and deformations is at the heart of experimental mechanics studies. Over the years, experimental mechanics community has developed numerous measurement techniques to study stress concentration problems. In this spirit, a new technique called Digital Gradient Sensing (DGS) based on 2-D digital image correlation, has been recently introduced for studying transparent [1, 2] and reflective [3] solids by quantifying small angular deflections of light rays caused by defects or deformation of solids. In the former works, the method has been successfully demonstrated by measuring two orthogonal stress gradients near stress concentrations in solids whereas the latter has been demonstrated via full-field orthogonal surface slope fields in flexural problems. The purpose of the current work is to extend the reflection-mode DGS (or, simply r-DGS) method to quasi-static and dynamic fracture mechanics. Visualization of time-resolved deformations near mode-I and mixed-mode (mode I/II) cracks for quantifying fracture parameters are among the goals of this work. 1.2 Optical Setup and Working Principle The schematic of the optical setup used for reflection-mode DGS (or, r-DGS) is shown in Fig. 1.1. It consists of a specularly reflective planar object (cracked specimen), a beam splitter, a randomly speckled/textured planar target and a digital camera. The speckle pattern on the target is prepared by decorating a planar surface with alternative black/white mists of paint. The optical arrangement is such that the digital camera is used to record speckles on the target plane via the reflective specimen and the beam splitter. In the undeformed or the reference state of the specimen, a generic point P on the target is photographed through a point O on the specimen surface. When the specimen deforms, O moves to O0 on the target due to an out-of-plane displacement win the z-direction (the optical axis). This results in the camera photographing a neighboring point Q on the target in the deformed state of the specimen. By correlating these two images corresponding to the reference and deformed states, the local displacement components ıx and ıy in the x- and y-directions, respectively, can be evaluated A.S. Jain • H.V. Tippur ( ) Department of Mechanical Engineering, Auburn University, Auburn, AL 36849, USA e-mail: tippuhv@auburn.edu © The Society for Experimental Mechanics, Inc. 2016 A.M. Beese et al. (eds.), Fracture, Fatigue, Failure and Damage Evolution, Volume 8, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-21611-9_1 1
2 A.S. Jain and H.V. Tippur Fig. 1.1 Schematic depicting the experimental setup and working principle of reflection-mode DGS (r-DGS) method in the whole field. Using this information, the surface slope components in, say, the x–z and y–z planes can be evaluated as [3], xIy tan xIy D2 @w @xI y D ıxIy (1.1) where x;y represent angular deflections of light rays. Here denotes the distance between the specimen and target planes and controls the sensitivity of the method. 1.3 Quasi-Static Mixed-Mode Experiments Quasi-static 3-point bend experiments were performed on edge notched PMMA specimens using r-DGS. A130 60 8.9mm3 specimen was used. An initial crack of length 12 mm cut at 45ı to the edge as shown in Fig. 1.2. The specimen resting on two anvils (120 mm span) was loaded in a displacement control mode (cross-head speedD0.005 mm/s). One of the two 130 mm 60 mm faces of the specimen was deposited with a thin aluminum film to make the surface specularly reflective. A beam splitter was positioned between the specimen and the camera at an angle of 45ı to the optical axis of the camera. A speckle target plate was placed at 45ı to the beam splitter. The normal distance between the specimen surface and the speckle plane was . D/65mm. A digital SLR camera fitted with 28–300 mm focal length macro lens was placed in front of the specimen at a distance (L) of 1150 mm. A reference image was recorded with a camera resolution of 1504 1000 pixels in no-load/reference state. During the experiment, speckle images were recorded at different load levels. Due to deformations in the crack-tip vicinity, the reflected light rays carry surface slope information relative to the reference state. Using 2-D DIC, the angular deflection fields x and y were obtained by correlating images corresponding to the deformed state with the one from the reference state. The images were divided into 15 15 pixel sub-images and correlated with a 5 pixel overlap during image correlation. Figure 1.3 shows the resulting surface slopes near the crack-tip at a select load level. The contours represent surface slopes .@w=@x/ and .@w=@y/ where wis the displacement in the out-of-plane (in the z-) direction. These contours show qualitative similarities with the reflection-mode coherent gradient sensing counterparts where the same field quantities are measured but one component at a time. The availability of two orthogonal fields offers flexibility to evaluate slopes in a rotated coordinate system aligned with the crack orientation, denoted by the coordinates x0 and y0 in Fig. 1.2. Accordingly, in this research, the orthogonal angular
1 Reflection-Mode Digital Gradient Sensing Technique for Experimental Fracture Mechanics 3 Fig. 1.2 Specimen geometry for crack tip deformation measurement for mixed-mode-I/II loading Fig. 1.3 Contours representing surface slopes in the mixed-mode crack tip vicinity. Contour incrementsD15 10 5 rad x 10-3 1.5 1 0.5 0 −0.5 −1 −1.5 deflections of light rays and hence the respective surface slopes in the local x0 and y0 directions were evaluated using transformations, ( 0 x 2 0 y 2 ) D( @w @x0 @w @y0 ) D cos˛ sin˛ sin˛ cos˛ ( @w @x @w @y ) (1.2) where ˛ (D45ı in this case) is the crack orientation angle. The asymptotic expansion for in-plane surface slopes for mixed-mode loading condition is obtained by superposing the mode-I and mode-II fields [4], 0 x 2 D @w @x0 D B 2E 2 66 66 4 ( 1 XND1 AN N 2 1 r .. N 2 / 2/ cos N 2 2 0 ) C ( 1 XND1 BN N 2 1 r .. N 2 / 2/ sin N 2 2 0 ) 3 77 77 5 0 y 2 D @w @y0 D B 2E 2 66 66 4 ( 1 XND1 AN N 2 1 r .. N 2 / 2/ sin N 2 2 0 ) C ( 1 XND1 BN N 2 1 r .. N 2 / 2/ cos N 2 2 0 ) 3 77 77 5 (1.3) where (r, ’) are polar coordinates centered at the crack-tip in the local coordinates x0 and y0 with 0 D C˛, Ethe elastic modulus, the Poisson’s ratio, B the nominal specimen thickness, A1I B1 Dp2= .KII KII/ with KI and KII being the mode-I and mode-II stress intensity factors, respectively. Solutions based onNup to 3 were used to extract the stress intensity
4 A.S. Jain and H.V. Tippur Fig. 1.4 Comparison of mixed-mode stress intensity factors from r-DGS and finite element simulation 1 0.8 0.6 0.4 0.2 –0.2 –0.4 –0.6 0 0 KI and KII (MPa√m) 200 400 600 800 1000 1200 1400 Load (N) KI from fx KII from fx KI from fy KII from fy KI from FEA KII from FEA factors. The results thus obtained are plotted in Fig. 1.4 for different load levels. A finite element analysis for the problem was carried out using ABAQUS™ software package to complement mixed-mode stress intensity factors obtained experimentally and details of the same are suppressed here for brevity. Figure 1.4 shows the variation of these computations overlaid on the experimental results. A good match between the two is evident from the plot, suggesting the feasibility of r-DGS for studying mixed-mode fracture problems. 1.4 Dynamic Mixed-Mode Experiments The crack-tip deformation measurements under mixed-mode (I/II) conditions for an edge notched PMMA specimen (130 60 8.9mm3) during stress wave propagation were performed using a long-bar impactor used in conjunction with high-speed photography and r-DGS method. The schematic of the experimental setup is as shown in Fig. 1.5. The loading device consisted of an aluminum 7075-T6 long-bar (25.4 mm diameter and 2 m long) with a cylindrical impacting head, a gas-gun and a high-speed digital camera. The long-bar was aligned co-axially with the barrel of the gas-gun housing a 305 mm long, 25.4 mm diameter aluminum striker. The crack-tip deformations were photographed using a Cordin 550 high-speed digital camera equipped with 32 CCD sensors and two high-energy flash lamps to illuminate the target plate. A beam splitter positioned between the lens and the specimen at 45ı angle was used to view the speckle pattern on the target via the reflective face of the specimen. The cylindrical tip of the long-bar was registered against the notch-free edge of the specimen. To achieve mixed-mode loading an eccentricity of 20 mm with respect to the crack line and the axis of the long-bar (see, Fig. 1.6) was used. As in the quasi-static experiments, one of the faces of the specimen (130 mm 60mm) was made specularly reflective by sputter coating it with aluminum. In these experiments, the distance between the target plate and specimen was ( D) 102 mm (and the distance between the camera lens and the specimen was 715mm). A set of 32 reference images (one image from each CCD sensor of the high-speed camera) prior to loading was captured by operating the camera at 150,000 frames per second. Next the camera was triggered as the striker contacted the long-bar. A second set of 32 speckle images was captured at the same framing rate while the specimen was experiencing transient loading. The deformed and reference image pairs recorded by the same sensor of the high-speed camera were paired and correlated to obtain orthogonal displacements ıx andıy on the target plane (see, Fig. 1.1). These were subsequently converted into surface slopes .@w=@x/ and.@w=@y/ on the specimen plane. Figures 1.7 show r-DGS contours near a dynamically loaded mixed-mode crack-tip for a time instant just before crack initiation. The contour plots of surfaces slopes in Fig. 1.8 represent the ones for the post-initiation regime following crack kinking from its initial orientation. The stress intensity factors in the pre-crack initiation phase was performed in the global coordinate system (x and y) defined at the crack-tip aligned with the loading direction and the specimen edges (Fig. 1.2). The stress intensity factors for a
1 Reflection-Mode Digital Gradient Sensing Technique for Experimental Fracture Mechanics 5 Fig. 1.5 Schematic of the experimental setup used in the dynamic mode-I fracture study. Inset is the photograph showing the close-up view of the optical arrangement in front of the sample gas gun striker image acquisition system strain gage delay generator flash lamp high speed camera long-bar oscilloscope signal conditioner specimen beam splitter speckle target Fig. 1.6 Specimen loading configuration and crack tip coordinate system used in dynamic fracture experiments. Global and local coordinates for mixed-mode (mode-I/II) crack propagation. Specimen sizeD130mm 60mm 20 mm Load x a x' y' y (r,q) . stationary but dynamically loaded crack were evaluated using the mixed-mode asymptotic equations [4] given in (1.3). The details of the analysis are suppressed here for brevity. In the post-crack initiation regime, the data analysis utilized crack tip field equations for a steadily growing mixed-mode crack that takes into account the instantaneous crack speed. The results from the analysis are shown in Fig. 1.9. Initially both mode-I and -II stress intensity factors are negative. Though unintuitive, the former is caused when the notch (initially 300 m wide) closes due to eccentric loading above the crack line (relative to the initial notch direction) as shown in Fig. 1.6. With the passage of time, upon reflection of compressive stress waves as tensile waves from the free edges (particularly from the cracked edge) of the sample, the crack
6 A.S. Jain and H.V. Tippur Fig. 1.7 Experimental x (left) and (right) y contours near the crack-tip before crack initiation. Contours are plotted every 20 10 5 rad Fig. 1.8 Experimental x (left) and y (right) contours near the crack-tip in global x, y coordinates. Contours incrementsD20 10 5 rad 1.5 1 2 x 10-3 0.5 -0.5 -1 -1.5 -2 0 Chart Area flanks open (and slide simultaneously) causing mode-I stress intensity factor to turn positive. Mode-II stress intensity factor continue to be negative, consistent with the loading configuration used. Further, its magnitude increases monotonically until crack initiation. After initiation, however, the magnitude of mode-II stress intensity factors decreases to zero as the crack kinks and re-orients to propagate in an increasingly dominant mode-I condition. 1.5 Conclusions In this work, the reflection-mode digital gradient sensing (r-DGS) method has been successfully extended to study static and dynamic fracture mechanics problems. First, the method has been demonstrated here for mixed-mode (I/II) problems using edge cracked PMMA samples. Three-point bend configurations with inclined edge cracks in otherwise symmetric loading are used. The measurements based on an overdetermininistic least-squares analysis of optical data in conjunction with crack tip field descriptions have produced reliable fracture parameter estimates. Next, the r-DGS method has been extended to study mixed-mode dynamic fracture problems under impact loading conditions. The orthogonal deformations near the tip of dynamically loaded stationary cracks as well as transiently propagating cracks have been mapped by coupling r-DGS method with high-speed digital photography. The results presented include kinked crack growth relative to the initial crack orientation. The evolution of both mode-I and mixed-mode (I/II) stress intensity factor histories have been analyzed using measured data in conjunction with plane stress elasto-dynamic steady-state crack tip field descriptions. Acknowledgments The partial support for this research through grants from the National Science Foundation (grant #1232821) and Department of Defense (grant # W31P4Q-14-C-0049) are gratefully acknowledged.
1 Reflection-Mode Digital Gradient Sensing Technique for Experimental Fracture Mechanics 7 Fig. 1.9 Dynamic mixed-mode stress intensity factor histories from regression analysis of surface slope data (symbols) 0 1 2 3 4 0 −1 10 20 30 40 50 60 70 KI from fx KII from fx post-crack initiation Time (μs) KI and KII (MPa√m) References 1. Periasamy, C., Tippur, H.V.: A full-field digital gradient sensing method for evaluating stress gradients in transparent solids. Appl. Optics. 51(12), 2088–2097 (2012) 2. Periasamy, C., Tippur, H.V.: Measurement of orthogonal stress gradients due to impact load on a transparent sheet using digital gradient sensing method. Exp. Mech. 53(1), 97–111 (2013) 3. Periasamy, C., Tippur, H.V.: A full-field reflection-mode digital gradient sensing method for measuring orthogonal slopes and curvatures of thin structures. Meas. Sci. Technol. 24, 025202 (2013) 4. Kirugulige, M.S., Tippur, H.V.: Mixed-mode dynamic crack growth in functionally graded glass-filled epoxy. Exp. Mech. 46(2), 269–281 (2006)
Chapter 2 Experimental and Computational Investigation of Out-of-Plane Low Velocity Impact Behavior of CFRP Composite Plates O.T. Topac, B. Tasdemir, B. Gozluklu, E. Gurses, and D. Coker Abstract Strength of composite materials under transverse loading has remained a major weakness despite numerous advancements in composite technologies. Most frequent and critical result of this characteristic is internal delamination damage, which is undetectable and lead to major strength reduction in the structure. This condition is usually encountered in low-velocity impact situations which frequently occur during the maintenance of aircraft. Past studies have successfully developed experimental and analysis methods for accurately predicting impact force history and damage footprint based on the comparison with post-impact results. However, there is almost no experimental work on the progression sequence of damage during impact in the literature. This paper focuses on experimental and computational investigation of the damage initiation and growth process during low-velocity impact of [07/904]s and [907/04]s cross-ply CFRP laminates. In the experiments, through-the-thickness direction is tracked using ultra-high speed camera and DIC technique to record damage progression and dynamic strain fields. In the numerical part of the study 3-D explicit, finite element analysis is conducted to model matrix crack initiation and propagation. The finite element results are then compared with experiments in terms of failure modes and sequence. Keywords Delamination • Matrix cracking • Transverse impact • High-speed camera • Experimental validation 2.1 Introduction Due to the advances in composite technologies, carbon-fiber reinforced polymer (CFRP) composite laminates are widely used in a large variety of engineering applications. Specifically, in aerospace industry, composite material application has increased up to 500 % in the past 20 years [1]. In spite of greater strength of composites, they are much weaker under loading in through-the-thickness (transverse) direction. This results in a sudden and catastrophic brittle failure. This kind of loading is encountered in impact situations, which frequently occur during ground operations and maintenance of aircraft. Among impact conditions with different velocities, low-velocity impact (LVI) has a special importance since it creates insidious delamination damage inside the laminate. It occurs frequently and usually without any visible damage from the outside of structure. Hence, they can stay unrepaired for the remaining life of the aircraft. In aerospace industry, this phenomenon is considered as one of the most critical weaknesses of composite materials. For damage tolerant design, element level LVI tests are generally relied upon, which usually requires hundreds of specimens for different test and specimen configurations. However, it is impossible to conduct impact tests for each condition. Due to the abundant requirement of tests and uncertainty of the process, the designed damage tolerant structures are generally thicker and heavier than required. O.T. Topac Department of Aerospace Engineering, Middle East Technical University, Ankara 06800, Turkey Helicopter Group, Turkish Aerospace Industries, Ankara 06980, Turkey e-mail: tanaytopac@gmail.com B. Tasdemir • E. Gurses Department of Aerospace Engineering, Middle East Technical University, Ankara 06800, Turkey B. Gozluklu Helicopter Group, Turkish Aerospace Industries, Ankara 06980, Turkey D. Coker ( ) Department of Aerospace Engineering, Middle East Technical University, Ankara 06800, Turkey METU Center for Wind Energy, Middle East Technical University, Ankara 06800, Turkey e-mail: coker@metu.edu.tr © The Society for Experimental Mechanics, Inc. 2016 A.M. Beese et al. (eds.), Fracture, Fatigue, Failure and Damage Evolution, Volume 8, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-21611-9_2 9
10 O.T. Topac et al. In the literature, low-velocity impact response of composite laminates is investigated in terms of load and displacement histories of the laminate and resulting damages. One of the pioneering low velocity impact experiments on laminated composites was conducted by Cantwell et al. where the mass was dropped from a simple drop-weight tower and resulting damage was successfully observed by non-destructive inspections [2]. In their experimental and numerical study, Choi et al. investigated impact-induced damage mechanisms [3]. Beam-like 2D composite plates with several cross-ply stacking sequences were impacted by 2D impactors to achieve a damage scheme uniform in width direction. Resulting damages obtained for [0n/90m/0n] and [0n/90m/0n/90m/0n] laminates showed coupled matrix cracking and delamination, the characteristic impact-induced damage. In a computational effort, a finite element analysis of a simple 2D [0/90/0] beam done where matrix cracking and delamination damage interaction were simulated [4]. More recently, effects of dispersed stacking sequence were investigated in a combined experimental and numerical study, in which element level impact experiments were conducted on composite laminates according to ASTM D7136 standards. In numerical side, finite element analyses were conducted with matrix, fiber and delamination damage considerations to completely simulate experiments [5, 6]. A good agreement was obtained for post-impact results of experiments and analyses in terms of resulting damage, force, displacement and energy histories. However, to this date, almost no effort has been made to get a complete understanding and computational analysis of matrix and delamination damage progression sequence under impact conditions. This study aims to observe damage progression sequence in carbon-epoxy composite laminated plates and verify the damage modeling of finite element analyses (FEA). Low velocity impact experiments are conducted on two types of [0/90] cross-ply specimens. Resulting matrix cracking and delamination process is captured by a high speed camera (1M fps). In computations, the experiment conditions are simulated in ABAQUS/Explicit and matrix damage evolution is investigated. In those, intralaminar matrix cracking damage is modeled via continuum damage mechanics (CDM) based failure approach proposed by Christensen [7] and compared with real-time results from high-speed camera. 2.2 Experimental Method 2.2.1 Experimental Setup The experimental setup consists of an external structure for drop weight-tower, a base fixture to clamp the composite specimen and a guiding rail to provide an aimed drop of the impactor. CAD drawing and photograph of the setup with high speed camera and lighting are shown in Fig. 2.1. At the base fixture, both ends of the test specimen are fixed between two thick aluminum plates. In order to prevent possible sliding, the specimen is drilled and bolted from its ends to the base structure. Guiding rail is provided by a hollow aluminum tube with a rectangular cross-section vertically fixed above the center of the specimen. Impact specimens, are made of Cytec T300/895 CFRP material with individual ply thickness of 0.16 mm. The size of the specimen is 85 mm 15 mm which provides plane strain condition. Two different stacking sequences of [07/904]s and [907/04]s are manufactured where the thickness of the specimens are equal to 3.5 mm. The impactor, seen in Fig. 2.2a, is made of SAE 304 stainless steel material and designed to have variable mass of 0.365, 0.788 and 1.21 kg. It is designed with semi-cylindrical cross section to create line load impact conditions in the width direction of the specimen. The progression of damage during impact event is captured by Photron SA5 high speed camera, capable of capturing images at rates up to one million frame per second (fps). Fig. 2.1 Experimental set-up for line load impact testing; (a) CAD drawing and (b) photograph of setup with high speed camera and lighting
2 Experimental and Computational Investigation of Out-of-Plane Low Velocity Impact Behavior of CFRP Composite Plates 11 Fig. 2.2 (a) Close-up side-view of the specimen with the impactor and grips, (b) micrograph images of two stacking sequences used in this paper: [07/904]s and [907/04]s 2.2.2 Experimental Procedure Firstly, side sections of composite specimens are polished by Minitech-233 polishing machine in order to achieve clear visualization of their side section. Before conducting the tests, polished specimens were scanned with Huvitz HDS-5800 Digital Microscope from the edge section to reveal manufacturing flaws which were in the acceptable limits. Images are captured with lens having zoom rate of 50 . The experiments are conducted as drop-weight impact events. Two sets of specimens with different stacking sequences are tested, each set having four individual composite beams. The high-speed camera is focused on at the edge section of the composite with frame rates from 15,000 to 210,000 fps are used to provide adequate compromise between capture rate of crack progression and picture resolution. Steel impactor of 0.365 kg is symmetrically placed inside the guiding rail and dropped from 1 m height resulting in 3.58 J kinetic energy at the instant of impact. A free fall of impactor is assumed and friction between impactor and guiding rail is neglected in analyses and evaluation of tests. Image acquisition module of high-speed camera is triggered just before impact and the whole impact event is successfully captured. After first impact, bounce-back of the impactor is prevented to avoid any further damage after the first contact. An illustrative picture just before impact is given in Fig. 2.2a. After the experiments, resulting damage scheme is optically examined with microscope. 2.3 Computational Method In the computational part of this study, simplified experimental impact case is modeled as seen in Fig. 2.3 and simulated in ABAQUS/Explicit finite element software. For the geometrical model, only the region of laminate between gripping tabs is modeled which results in a 45 15 mm plate. Rest of the plate beyond the tabs is lumped in the clamped boundary conditions. Material properties of T300/985 carbon/epoxy composite are obtained from manufacturer specification sheet and previous studies [8, 9] which are provided in Table 2.1. The impactor is modeled as an analytical rigid body with lumped mass of 0.365 kg at its centroid. An initial vertical velocity of 4.3 m/s that corresponds to a free fall from 1 m is defined for the impactor. In computational analysis, only matrix cracking damage is considered and compared with experiments. The composite laminate is meshed with solid C3D8R (Reduced integration, eight noded hexagonal) elements as in Fig. 2.3 where each layer is modeled with one element in thickness direction, and in longer side of the beam, elements are biased to have a finer mesh near the impacting region. The total number of elements is 580,800. Contact condition between impactor and composite laminate is defined with general contact algorithm of ABAQUS. Normal behavior is defined as hard contact with penalty algorithm and tangential Coulomb friction between impactor and composite is defined with a friction coefficient of D0:3 based on the study of [6, 10].
12 O.T. Topac et al. Fig. 2.3 Finite element model and mesh of the impact analysis Table 2.1 Cytec T300/985 ply properties Density 1600kg/m3 Elastic properties E1 D106 GPa; E2 DE3 D7:8 GPa; 12 D 13 D0:30; 23 D0:44; G12 DG13 D10:5 GPa; G23 D2:7 GPa Strength properties SC 22 D50 MPaI S 22 D170 MPaI S12 D170 MPaI S13 DS23 D95 MPa In computational analysis, only matrix cracking damage is considered and compared with experiments. Intraply damage in composite materials is commonly studied by continuum damage mechanics (CDM), where several load interaction criteria exist to predict initiation of crack under normal and shear loading of the plies. In this study, Christensen CDM criterion with only matrix cracking consideration is applied using Autodesk Simulation Composite Analysis 2015 plugin. Christensen failure criterion is chosen due to its high order transverse stress terms ( m 33, m 13, m 23) in crack prediction, which are dominant in transverse impact situations. Christensen criterion considers tensile and compressive failure strengths of a ply in normal orthotropic directions SC11;S 11;SC22;S 22 and absolute values of longitudinal and transverse shear strengths (S12, S23). It assumes that matrix crack initiates when the interaction equation becomes equal to or greater than one: 1 SC22 1 S 22!. 22 C 33/ C 1 SC22S 22 . 22 C 33/ 2 C 1 S2 23 2 23 C 22 33 C 1 S2 12 2 12 C 2 13 1 2.4 Results 2.4.1 Experimental Results 2.4.1.1 Impact Testing of [07 / 904]s Unidirectional CFRP Laminates Series of photographs are taken with high speed camera from the side of the specimen. While observable damage occurred at the side section, no visible damage is produced on the contact region between impactor and the specimen. In the results, 0 s represents the impact instant. In Fig. 2.4, series of high speed camera images taken at 15,000 fps, 66.7 s interframe time are presented. The photograph in Fig. 2.4a shows the impactor and specimen just before impact and Fig. 2.4b, taken 133 s later, shows loading of the composite plate with no visible sign of damage. One frame later, shown in Fig. 2.4c complete composite failure is observed. Resulting damage scheme closely resembles the results of Choi et al. on a similar composite laminate [3]. Delaminations between the 0ı and 90ı plies are observed consisting of a delamination of the upper interface under the impactor and a delamination of the lower interface away from the impact region. Matrix cracks appear in the 90ı plies connecting the two delaminations. However, damage progression and its sequence are not captured at this camera speed. The micrograph images of the front and mirrored back faces of the laminate after the experiment are shown in Fig. 2.5a and b, respectively. The delamination and the matrix cracking patterns are observed to be the same throughout the width of the specimen.
2 Experimental and Computational Investigation of Out-of-Plane Low Velocity Impact Behavior of CFRP Composite Plates 13 Fig. 2.4 High speed camera images of [07/904]s specimen taken at 15,000 fps. (a) Just before the impact and (b) after impact subjected to loading with no damage, (c) after damage initiation Fig. 2.5 Micrograph images of two faces of damaged specimen showing uniformity of damage Fig. 2.6 High speed camera images of [07/904]s specimen taken at 210,000 fps showing progression of matrix cracking and delamination Fig. 2.7 Micrograph of laminate after the impact experiment showing the final failure pattern and the location of the field of view of the high speed camera To look at the failure sequence at a higher time resolution, an impact test was conducted under the same conditions and the results were captured with the high speed camera at 210,000 fps, 4.76 s interframe time. In the first frame the composite is loaded and initial delamination in the bottom 0/90 interface can be seen. 38 s later a matrix crack starts from the lower interface and is followed by a delamination at the upper interface growing towards the impact point. Five microseconds 5 s later, a second matrix crack initiates at the right hand side from the bottom interface and propagates towards the upper interface. In the last picture, 24 s later, upper delamination grows from the matrix crack towards the impact point and joins with the upper left delamination front. This illustrates the failure sequence of [07/904]s laminates under low velocity impact (Fig. 2.6). In order to observe the strain fields at the crack front during impact, DIC analysis is performed on the high speed camera images captured at 20,000 fps. The post-impact micrograph is shown in Fig. 2.7 with the final failure pattern similar to the previous cases. Because of the resolution, framing rate and shutter speed limitations, the field of view of the high speed camera is limited to the area just under the impact site, highlighted with red frame in Fig. 2.7. The high speed camera pictures and the Tresca strain fields using DIC method during the impact event are shown in Fig. 2.8a and b, respectively. At 100 s, initial delamination fronts are observed at upper interface from both sides and lower interface from only the left side. One frame (50 s) later, the delaminations at the upper interface propagate towards the center from both sides, however the lower delamination is found to have arrested. In the final frame, the upper delaminations from both sides combine to form a single
14 O.T. Topac et al. Fig. 2.8 Close-up of the middle section of [07/904]s specimen showing stress fields at lower and upper delamination regions. (a) High speed camera images, (b) Tresca strain contours from Digital Image Correlation (DIC) analysis program ARAMIS upper delamination. An interesting observation is that between 150 and 250 s, the delaminations seem to arrest and even show closure of delamination front. However, upon closer examination, the crack surfaces, which have coalesced at 150 s, are observed to close due to compressive waves from the impactor. At 300 s, the tensile waves arrive and the delamination opens up. 2.4.1.2 Impact Testing of Unidirectional OE [907 / 04]s CFRP Laminates Second set of impact tests are conducted on [907 / 04]s unidirectional CFRP laminates. The images during the impact event were captured at 20,000 fps for DIC analysis; however due to shutter speed limitations blurry images were obtained and could not be processed for DIC. The images of the plate at 0, 200, 300 and 700 s after impact are shown in Fig. 2.9. At 200 s crack is initiated from the middle lower layer because of normal tensile stresses on matrix material caused by bending of the beam. Two frames later, at 300 s, four additional matrix cracks are observed next to other cracks with an average of 3.8 mm distance from each other. At 700 s, all of the initial matrix cracks are propagated to delamination at lower interface. 2.4.2 Computational Results Finite element analyses are conducted with Christensen failure criterion to correlate crack location and sequence with experiments. Resulting matrix crack initiation and propagation schemes of [07/904]and[907/04]s configurations are presented in Fig. 2.10a and b respectively. In [07/904]s stacking sequence, represented in Fig. 2.10a, local matrix damage is predicted at the impact location, unlike experimental results that produced no visible surface damage. However at the side section, a similar crack pattern is obtained. Initially, a matrix crack is initiated at bottom close to the center and after 8 s, it propagated towards the center diagonally reaching to the upper interface. Afterwards, matrix cracking propagated just below and above interfaces resembling a
2 Experimental and Computational Investigation of Out-of-Plane Low Velocity Impact Behavior of CFRP Composite Plates 15 Fig. 2.9 High speed camera images of [907/04]s specimen taken in 20,000 fps showing matrix cracking initiation and propagation to delamination Fig. 2.10 Matrix crack initiation and progression scheme predicted by Christensen criterion for (a) [07/904]s and (b) [907/04]s stacking sequences delamination pattern. While the crack angle of 45ı is very close to the experiment results, the distance between two matrix cracks were about two times shorter than experimental results. In [907/04]s stacking sequence, represented in Fig. 2.10b, several matrix cracks are initiated in a region of 2 mm at bottom layer progressing perpendicular towards the bottom 0/90 interface. Upon reaching interface at 157 s, additional matrix cracks are obtained due to lack of delamination damage in the computational model.
16 O.T. Topac et al. 2.5 Conclusions Experimental and computational studies are conducted on [07/904]s and [907/04]s 2-D beam-like unidirectional CFRP laminates to evaluate the failure progression of composites under out-of-plane impact loading. The line load impact tests on a composite plate was carried out to observe the impact failure phenomena from the edge using a high-speed camera and DIC system. Two different failure modes were captured depending on the stacking sequence. For [07/904]s lay-up, the damage initiates as delamination in the bottom interface followed by matrix cracking towards the impact point causing delamination in the upper layer. For [907/04]s lay-up, vertical matrix cracks initiate at the lower 90 layers in the line of impact, leading to delamination of the lower interface. Finite element simulations using Christensen matrix failure model was able to capture the general trend of matrix failure initiation and propagation observed in the experiments for both layups. A further study is being carried out to implement Cohesive Zone Method to model subsequent delamination observed in the experiments. Acknowledgements The authors would like to acknowledge the contributions of METU Center for Wind Energy for allowing access to the experimental facilities. The authors would also like thank to Ayse Begum Erdem, Ali Gezer, and Miray Aydan Arca for their contributions. References 1. Roeseler, B., Sarh, B., Kismarton, M.: Composite structures-the first 100 years. In: 16th International Conference on Composite Materials, Kyoto, 8–13 July 2007 2. Cantwell, W.J., Curtis, P.T., Morton, J.: An assessment of the impact performance of CFRP reinforced with high-strain carbon fibres. Compos. Sci. Technol. 25, 133–148 (1986) 3. Choi, H.Y., Downs, R.J., Chang, F.-K.: A new approach toward understanding damage mechanisms and mechanics of laminated composites due to low-velocity impact: Part I—experiments. J. Compos. Mater. 25, 992–1011 (1991) 4. Geubelle, P.H., Baylor, J.S.: Impact-induced delamination of composites: a 2D simulation. Compos. Part B29(5), 589–602 (1998) 5. Lopes, C.S., Seresta, O., Coquet, Y., Gürdal, Z., Camanho, P.P., Thuis, B.: Low-velocity impact damage on dispersed stacking sequence laminates. Part I: experiments. Compos. Sci. Technol. 69(7–8), 926–936 (2009) 6. Lopes, C.S., Camanho, P.P., Gürdal, Z., Maimí, P., González, E.V.: Low-velocity impact damage on dispersed stacking sequence laminates. Part II: numerical simulations. Compos. Sci. Technol. 69(7–8), 937–947 (2009) 7. Christensen, R.M.: The numbers of elastic properties and failure parameters for fiber composites. J. Eng. Mater. Technol. 120(2), 110–113 (1998) 8. Hiel, C.C., Sumich, M., Chappell, D.P.: A curved beam test specimen for determining the interlaminar tensile strength of a laminated composite. J. Compos. Mater. 25, 854–868 (1991) 9. Cheremisinoff, N.P. (ed.): Handbook of Ceramics and Composites: Mechanical Properties and Specialty Applications, p. 528. CRC Press, New York (1991) 10. Shi, Y., Pinna, C., Soutis, C.: Modelling impact damage in composite laminates: a simulation of intra- and inter-laminar cracking. Compos. Struct. 114, 10–19 (2014)
Chapter 3 Prediction of Incipient Nano-Scale Rupture for Thermosets in Plane Stress J.C. Moller, S.A. Barr, T.D. Breitzman, G.S. Kedziora, A.M. Ecker, R.J. Berry, and D. Nepal Abstract There is limited experimental evidence that fracture nucleation in polymers includes a small number of covalent bond scissions followed by rapid void growth by chemo-mechanical processes. Generalized criteria for predicting such bond scission, then, would help anticipate fracture in polymer matrix composites. Strain states at incipient bond scission for thermoset resins in plane stress are here predicted by atomistic simulation. Several cured epoxy systems were examined, each having a different chain length. For biaxial extension and a portion of the shearing regime, scission occurs at a critical value of the larger principal strain. This value increases with increasing chain length. The corresponding dilatation is largest for biaxial extension and decreases to nearly zero for pure shear. Results are compared with strain invariants at fracture measured from experiments in which polymer matrix composites having various ply stacking sequences were loaded to rupture. Keywords Plane stress • Strain invariant • Atomistic • Thermoset 3.1 Introduction Owing to steep gradients in displacement and non-linear material behavior, stress states in the vicinity of a crack tip can be highly varied. It is also well-known that fracture depends upon whether the bulk of the test sample places the crack tip zone in plane strain or plane stress. Unlike an equiaxed multigranular metal, a uniaxial tensile test of a polymer does not necessarily provide results which can be reliably applied to anticipate material response in other loading states. Published work has shown the results of atomistic simulations of polymer systems in one-directional tensile deformation with simplified boundary conditions and deformation methods. More investigation is therefore necessary to develop a generalized nano-scale characterization of mechanical properties including yield and rupture thresholds. Generalized descriptions are important for informing larger-scale models and for anticipating fracture nucleation in the wide variety J.C. Moller ( ) Miami University, Oxford, OH 45056, USA Universal Technology Corporation, Dayton, OH 45432, USA Air Force Research Laboratory, WPAFB, Dayton, OH 45433, USA e-mail: mollerjc@miamioh.edu S.A. Barr • D. Nepal Universal Technology Corporation, Dayton, OH 45432, USA Air Force Research Laboratory, WPAFB, Dayton, OH 45433, USA R.J. Berry Air Force Research Laboratory, WPAFB, Dayton, OH 45433, USA T.D. Breitzman Exploratory Research Section, Air Force Research Laboratory, WPAFB, Dayton, OH 45433, USA G.S. Kedziora Air Force Research Laboratory, WPAFB, Dayton, OH 45433, USA Engility Corporation, Franklin, OH 45005, USA A.M. Ecker Air Force Research Laboratory, WPAFB, Dayton, OH 45433, USA University of Dayton, Dayton, OH 45469, USA © The Society for Experimental Mechanics, Inc. 2016 A.M. Beese et al. (eds.), Fracture, Fatigue, Failure and Damage Evolution, Volume 8, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-21611-9_3 17
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