Thermomechanics and Infra-Red Imaging, Volume 7

Conference Proceedings of the Society for Experimental Mechanics Series

For other titles published in this series, go to www.springer.com/series/8922

Tom Proulx

Thermomechanics and Infra-Red Imaging, Volume 7 Proceedings of the 2011 Annual Conference on Experimental and Applied Mechanics

Tom Proulx Society for Experimental Mechanics, Inc. 7 School Street Bethel, CT 06801-1405 USA [email protected]

ISSN 2191- 5644 e- ISSN 2191- 5652 ISBN 978-1-4614-0206-0 e-ISBN 978-1-4614-0207-7 DOI 10.1007/978-1-4614-0207-7 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2011929341 ¤ The Society for Experimental Mechanics, Inc. 2011 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid- free paper Springer is part of Springer Science+Business Media (www.springer.com)

Preface

Thermomechanics and Infra-Red Imaging represents one of eight volumes of technical papers presented at the Society for Experimental Mechanics Annual Conference & Exposition on Experimental and Applied Mechanics, held at Uncasville, Connecticut, June 13-16, 2011. The full set of proceedings also includes volumes on Dynamic Behavior of Materials, Mechanics of Biological Systems and Materials, Mechanics of Time-Dependent Materials and Processes in Conventional and Multifunctional Materials, MEMS and Nanotechnology; Optical Measurements, Modeling and, Metrology; Experimental and Applied Mechanics, and Engineering Applications of Residual Stress. Each collection presents early findings from experimental and computational investigations on an important area within Experimental Mechanics. The Thermomechanics and Infra-Red Imaging conference track was organized by: Janice Dulieu-Barton*, University of Southampton, UK, Fabrice Pierron, Arts et Métiers ParisTech, France, Rachel Tomlinson, University of Sheffield, UK and David Backman, National Research Council Canada and sponsored by the Thermomechanics and Infra-Red Imaging Division In recent years the applications of infra-red imaging techniques to the mechanics of materials and structures has grown considerably. The expansion is marked by the increased spatial and temporal resolution of the infra-red detectors, faster processing times and much greater temperature resolution. The improved sensitivity and more reliable temperature calibrations of the devices have meant that more accurate data can be obtained than were previously available. The purpose of the track is to bring together novel work on all aspects of thermomechanics with the focus on the application of infra-red imaging approaches. The main thrust of the session will be on the analysis of thermomechanical behavior of materials and using this behavior to elicit information on material characteristics, stresses and failure. Of particular interest are strong thermomechanical

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couplings that result in nonlinear behavior such as viscoelasticity, diffusivity and material phase changes. An objective is to share experience on how data-rich experimental mechanics can help scientists and engineers to better understand and simulate the behavior of materials and structures. It is also envisaged that papers utilizing other imaging techniques in conjunction with infra-red approaches will be a key part of the track program enabling cross-fertilization over disciplines and applications. The following general technical research areas are included: High speed thermography Multiscale thermodynamic couplings Thermography in fatigue and damage assessment Application to composite materials Thermoelastic stress analysis The track organizers thank the authors, presenters, organizers and session chairs for their participation and contribution to this track. The opinions expressed herein are those of the individual authors and not necessarily those of the Society for Experimental Mechanics, Inc. Bethel, Connecticut

Dr. Thomas Proulx Society for Experimental Mechanics, Inc

Contents

1. Challenges in Synchronising High Speed Full-field Temperature and Strain Measurement D.A. Crump, J.M. Dulieu-Barton, R.K. Fruehmann, University of Southampton

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2. The use of Infrared Thermography at High Frame Rates R.K. Fruehmann, D.A. Crump, J.M. Dulieu-Barton, University of Southampton

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3. In Situ Heat Generation and Strain Localization of Polycrystalline and Nanocrystalline Nickel T. Chan, University of Toronto; D. Backman, R. Bos, T. Sears, Institute for Aerospace Research, National Research Council; I. Brooks, Integran Technologies Inc.; U. Erb, University of Toronto

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4. Dissipative and Coupling Effects Accompanying the Natural Rubber Elongation B. Wattrisse, R. Caborgan, J.-M. Muracciole, L. Sabatier, A. Chrysochoos, Montpellier University

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5. Experimental Estimation of the Inelastic Heat Fraction From Thermomechanical Observations and Inverse Analysis T. Pottier, F. Toussaint, Université de Savoie; H. Louche, Université Montpellier 2; P. Vacher, Université de Savoie 6. Energy Balance Properties of Steels Subjected to High Cycle Fatigue A. Chrysochoos, A. Blanche, Montpellier University; B. Berthel, École Centrale de Lyon; B. Wattrisse, Montpellier University 7. Contribution of Kinematical and Thermal Full-field Measurements for Identification of High Cycle Fatigue Properties of Steels R. Munier, C. Doudard, S. Calloch, ENSIETA - LBMS; B. Weber, ArcelorMittal Maizières Research & Development

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8. Dissipative Energy: Monitoring Microstructural Evolutions During Mechanical Tests N. Connesson, F. Maquin, F. Pierron, Arts et Metiers ParisTech

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9. Bidirectional Thermo-mechanical Properties of Foam Core Materials Using DIC S.T. Taher, O.T. Thomsen, Aalborg University; J.M. Dulieu-Barton, University of Southampton

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10. Optimization of Transient Thermography Inspection of Carbon Fiber Reinforced Plastics Panels B.G. Bainbridge, Southern Illinois University Carbondale; Y. Pan, University of Akron; T. Chu, Southern Illinois University Carbondale

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11. Experimental Investigation of Thermal Effects in Foam Cored Sandwich Beams R.K. Fruehmann, J.M. Dulieu-Barton, University of Southampton; O.T. Thomsen, Aalborg University; S. Zhang, University of Southampton 12. Intelligent Non-destructive Evaluation Expert System for Carbon Fiber Reinforced Plastics Panel Using Infrared Thermography Y. Pan, University of Akron; T. Chu, Southern Illinois University Carbondale 13. Successful Application of Thermoelasticity to Remote Inspection of Fatigue Cracks T. Sakagami, Kobe University; Y. Izumi, S. Kubo, Osaka University 14. Investigation of Residual Stress Around Cold Expanded Hole Using Thermoelastic Stress Analysis A.F. Robinson, J.M. Dulieu-Barton, S. Quinn, University of Southampton; R.L. Burguete, Airbus Operations Ltd.

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15. TSA Analysis of Vertically- and Incline-loaded Plates Containing Neighboring Holes A.A. Khaja, R.E. Rowlands, University of Wisconsin-Madison

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16. Examination of Crack Tip Plasticity Using Thermoelastic Stress Analysis R.A. Tomlinson, University of Sheffield; E.A. Patterson, Michigan State University

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Challenges in synchronising high speed full-field temperature and strain measurement

Author: D.A. Crump, School of Engineering Sciences, University of Southampton, Highfield, Southampton, SO17 1BJ, UK, [email protected] Co-Author: J.M. Dulieu-Barton, R.K. Fruehmann, University of Southampton ABSTRACT The overall motivation for the research described in the paper is an enhanced understanding of the behaviour of fibre reinforced polymer composites subjected to high velocity loading. In particular, the work described here considers a method that allows the collection of synchronised high speed full-field temperature and strain data to investigate the complex viscoelastic behaviour of fibre reinforced polymer composites material that occurs at high strain rates. The experimental approach uses infra-red thermography (IRT) and digital image correlation (DIC). Because high strain rate events occur rapidly it is necessary to capture the images at high speeds. The paper concentrates on the challenges of the use of IRT and DIC at high speeds to obtain temperature and strain fields from composite materials, and in particular using them in a synchronised manner. In the future such data-rich techniques provide the opportunity for detailed investigation into the viscoelastic behaviour and allow in-depth material characterisation for input to future finite element or numerical models. INTRODUCTION Increasing use of polymer reinforced polymer composites in high performance applications, e.g. military structures, is leading to an increased risk of impact or blast events imparting high velocity loading. Whilst the behaviour of such materials subjected to quasi-static elastic loading is reasonably well understood, the response to high strain rate requires further investigation. To reduce and mitigate the risk of failure it is essential that knowledge of the behaviour of these materials under high velocity deformation is established. Hence the subsequent effects of damage on structural performance can be defined. Therefore the motivation for this work is the need to map the effect of high velocity loading on the overall structural performance. High velocity/strain rate deformations are usually accompanied by a temperature evolution. Therefore the material behaviour is a function of time, strain and temperature, so to fully understand the material structural performance the thermomechanical material constitutive behaviour is required. The overarching aim of the current research is to provide thermomechanical characterisations of glass and carbon fibre polymer composite over a range of strain rates, with the ultimate goal of inputting the constitutive behaviour into a finite element (FE) modelling approach. Hamouda [1] and Sierakowski [2] discuss the range of approaches for high strain rate testing. The preferred technique is the split Hopkinson bar that allows strain rates up to 104 s-1. However in this work a specialised conventional servo-hydraulic test machine (Instron VHS) is used, which allows moderate strain rates up to 102 s-1. Whilst this machine cannot match the strain rates of the split Hopkinson bar, it allows specimens of approximately 25 mm wide by 100 mm long to be used, unlike the much smaller coupons that must be used in conjunction with the split Hopkinson bar. These specimens are of a similar size, and aspect ratio, to those recommended for quasi-static characterisation by testing standards and therefore provides a larger surface for the application of optical measurements techniques. The complex behaviour of fibre reinforced composite materials lends itself to the use of full-field optical measurement techniques, as information from the entire specimen is obtained that allows the identification of failure zones, loading paths etc. Digital image correlation (DIC) is used to measure strain, and infra-red thermography (IRT) to obtain the temperature evolution. One of the primary advantages of techniques such as DIC and IRT is that they are non-contacting, so the measurand does not affect the measurement by, for example, localised reinforcement or heating. However, it is essential that the images are synchronised temporally with any independent load or strain data collected from other sensors used in the experiment. Therefore the relative image capture rates, time delays and thresholding are important considerations. The aim of the current paper is to discuss the application of DIC and IRT to high velocity testing and the corresponding challenges. DIC and IRT are initially applied separately to both metallic and composite specimens, and some initial results are presented demonstrating the approach. The metallic specimens were expected to undergo higher strains and temperature changes, and were therefore chosen as a good starting point for assessing the abilities of DIC and IRT applied to such tests. This is

T. Proulx, Thermomechanics and Infra-Red Imaging, Volume 7, Conference Proceedings of the Society for Experimental Mechanics Series 9999999, DOI 10.1007/978-1-4614-0207-7_1, © The Society for Experimental Mechanics, Inc. 2011

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2 followed by a discussion of approaches to synchronise data capture from the two optical systems and an independent load measure. DIGITAL IMAGE CORRELATION (DIC) Digital image correlation is a full-field, optical method to measure the deformations and strains in a material or structure. DIC tracks the movement of a random surface pattern to monitor deformation or displacement. The random pattern is usually achieved by covering the surface of a component with a painted speckle pattern. Images of the deformation process are recorded using either one (2D DIC) or two (3D DIC) charge coupled device (CCD) cameras. The images are divided into discrete interrogation windows (or cells) and the displacement is obtained by tracking features within each cell [3]. Strain values are obtained by taking the measured displacement and dividing by the size of the undeformed cell. Strain resolutions are quoted as being as low as 40 µstrain [4], although this is highly dependent upon application and test conditions, such as lighting and alignment. The DIC technique has been successfully used to analyse the strains in heterogeneous engineering materials such as composites [5] and there is some reported work on the use of high speed cameras to collect images for DIC [6, 7]. Tiwari et al [6] described the use of high speed cameras for DIC, and the inherent limitations of such an approach. To apply DIC to high velocity testing, commercially available high speed digital cameras are used to record the images. In this work the images are then imported into the DaVis 7.4 (LaVision) software for analysis. The application of DIC to high speed imaging uses the same speckle analysis algorithm as that applied at quasi-static test speeds. The accuracy of the algorithm is the same as quoted above, but additional sources of error are likely due to the acquisition of images using high speed cameras. To obtain images at the highest possible frame rates it is necessary to reduce the resolution of the sensor, therefore the user must accept a coarse strain map or use smaller cell sizes which give greater uncertainty in the strain result. Secondly it is more difficult to obtain well illuminated images with high contrast at high speed as the integration time must be reduced. Therefore it is important to increase the lighting intensity which may have adverse effects such as specimen heating, or heat haze in the images. Three different high speed cameras are used to capture the images for this work, Photron’s SA-1 and 3 cameras, and Redlake’s MotionPro X3 details of each are described in Table 1. The three cameras have similar maximum resolutions (~ 1 MP), and the X3 and SA-3 are capable of recording this resolution up to 2 kHz whilst the SA-1 extends this to 5.4 kHz. The advantage of the use of the SA-1 to collect images for DIC is clear, allowing full-size images to be used at higher strain rates. The X3 only uses vertical sub-windowing to increase the frame rate, leading to an image with high aspect ratio that lends itself to recording test on tensile strips. The SA-1 and SA-3 sub-window in both directions, producing squarer images. In both cases the compromise is always between spatial and temporal resolution. Table 1 Specification of high speed cameras used in this work Parameter MotionPro X3+ Photron SA-3 Max resolution (pixels) 1280 x 1024 1024 x 1024 Max frame rate at max resolution (kHz) 2 2 Sub-windowing (pixels) Vertical only to 16 Both to 128 x 16 Max frame rate (kHz) 128 120 Storage size (Gb/~full size images) 8/5500 2-8/1500-5500

Photron SA-1 1024 x 1024 5.4 Both to 64 x 16 675 8-32/5500-21500

Steel and unidirectional (UD) GFRP tensile specimens were loaded at both quasi static speed (0.12 m/s, i.e. 2 mm/min), using a standard Instron electro-mechanical test machine, and then at 1 m/s, on a specialised Instron VHS 1000 test machine capable of testing specimens at speeds up to 20 m/s. Steel dog bone specimens with a cross-sectional area in the gauge length of 14.5 mm by 1 mm were used as proof of concept, three specimens at the QS speed and three at 1 m/s. Followed by GFRP specimens manufactured from ACG, MTM28-1\E-glass-200 prepreg with dimensions 200 mm by 20 mm and were 0.4 mm thick. During the tests the load was recorded by the load cell attached to the machine; in the case of the VHS this is a piezoelectric Kistler load cell. For comparison, the strain was separately recorded using Vishay’s CEA-06-240UZ-120 attached to Vishay’s Strainsmart system with a maximum sampling rate of 10 kHz. In addition, Photron’s SA-1 high speed camera was used to capture images during the 1 m/s tests. The specimens were prepared by spraying with black, grey and white paint to provide a speckle pattern. The cameras were recording at 30 kHz with an image size 512 x 256 pixels. The DIC was performed on each image using a cell size of 64 pixels and 50 % cell overlap, therefore providing a strain map with 16 x 8 data points. Figure 1 presents the evolving strain map for a steel specimen tested at 1 m/s, alongside a plot of the average longitudinal and transverse strains across the specimen. The plot highlights the advantages of using DIC. Where the strain gauge has debonded early the DIC measures up to 30 % strain, and allows longitudinal and transverse strain to be measured simultaneously.

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t = 0 ms

2.7 ms 17.2 ms Fig. 1 Full-field strain evolution and average longitudinal and transverse strain for steel at 1 m/s

The load and strain data from each of the three specimens tested at both quasi static and 1 m/s is used to calculate the average Young’s modulus shown in Table 2. There is a distinct difference between the value of Young’s modulus at 1 m/s measured by the strain gauge and DIC. For the steel specimens, the strain gauge data provides a reduction in material stiffness with test speed. The DIC data shows little difference between the quasi static and 1 m/s test. This is expected, as it is likely that 1 m/s is not fast enough to encounter the well-documented stiffening effect. The opposite is true of the data for GFRP specimens. Whilst both strain gauge and DIC show a stiffening effect, the strain gauge has measured almost twice the stiffening to that from DIC. At higher test speeds the strain gauge appears to be providing erroneous results; this can be attributed to sampling rate. Sampling at 10 kHz is not fast enough to accurately measure the strain progression. Further tests are required to increase the confidence in the DIC results, and to ensure all errors from test fixtures, specimen preparation and the processing algorithm are accounted for. This will be the subjected of a future paper. It should also be noted that the Young’s modulus values for the material tested at 1 m/s all have a scatter of around 10 % except for the steel strain gauge value. Further tests are required to assess the sources of this scatter and improve confidence in the results.

Steel GFRP

Table 2 Young’s modulus of steel and GFRP specimens E: Quasi-static (GPa) E: 1 m/s (GPa) strain gauge strain gauge 192.1 ± 2.3 171.0 ± 5.7 42.2 ± 1.4 69.3 ± 5.8

E: 1 m/s (GPa) DIC 192.9 ± 19.5 55.6 ± 6.7

INFRA-RED THERMOGRAPHY (IRT) Infra-red thermography uses an IR detector to monitor the emissions from the surface of a structure, from which the surface temperature is derived. IRT is therefore a full-field non-contacting technique for temperature measurement that has a sensitivity determined by the thermal resolution of the IR detector, and spatial resolution by the number of elements in the detector array. IRT has a large range of commercial uses for non-contact temperature measurement, but has also been used to detect hot-spots in structures that may identify sub-surface damage in non-destructive testing [8]. Commercially available IR detectors, such as those from FLIR systems, are capable of 100s Hz with detector array sizes upwards of 320 x 256. Using these detectors to capture data at higher frame rates has the same limitations as white light high speed cameras used for DIC. The internal electronics that control data transfer from the detector elements into digitised values force a limit on the total number of samples from all elements per second. Therefore to improve the frame rate the number of detector elements utilised must be reduced. As for the white light camera the image is sub-windowed sacrificing spatial for temporal resolution. The necessary reduction in detector integration time is a special case for IR imaging. For white light cameras it is possible to counter the effects of lower integration times by increasing illumination and therefore maintaining an adequate amount of photons striking the CCD array. However IR is dependent on the finite amount of energy emitted from the materials surface due to its temperature. The amount of photons and the sensitivity of the detector elements therefore limit the minimum integration time and hence the maximum frame rate given that the integration time must be equal or less than the reciprocal of the frame rate.

4 There is little research reported in the literature on the use of high speed IR; however the few examples found used specifically designed systems. Noble [9] described the use of a thermal scanning camera to measure the temperature change occurring during high strain rate test on ductile iron at a rate of 1600 s-1 in a split Hopkinson bar rig. The scanner was an AGEMA 880LWB that used a liquid-nitrogen cooled CdHgTe detector with an accuracy of ± 2 K. The camera was only capable of scanning at 2500 Hz, and therefore was not fast enough to record temperature evolution during the test. Instead the camera recorded the temperature change approximately 0.5 ms after specimen fracture. The nature of the material tested, and the high speed applied, produced temperatures up to 573 K at the necking site. Three possible error sources were identified that could account for uncertainty of ~ 100 K; movement of the specimen with respect to the camera, change of specimen orientation and changing emissivity during deformation. Improvements in electronics allowed Zehnder [10, 11], to produce a system capable of 1 MHz with 64 HgCdTe detector elements in an 8 x 8 plane array. Studies of the temperature rise near the tip of a notch in high strength steel sample subjected to an impact showed the system was capable of a temperature resolution of approximately ± 2 K. Finally, more recently, Ranc [12] used a bar of 32 InSb infrared detectors to measure a line of temperature points on a high strain torsion test on titanium. This also sampled at 1 MHz, but was measuring temperatures of the order of 100s K. In the current work infrared data was recorded using a Silver 480M (FLIR systems) detector. The Silver 480M uses a dual layer InSb sensor with 320 x 256 pixels. At maximum resolution it is possible to capture data at 383 Hz, and by windowing down to 48 x 4 pixels it is possible to achieve 20 kHz. It was decided to operate the detector at 15 kHz with a window of 64 x 12 and an integration time of 60 µs as a compromise between spatial, temporal and temperature resolution. When operating the detector outside of its standard configuration it is necessary to perform calibration and non-uniformity correction procedures different to those provided by the manufacturers. These processes set-up the detector and the internal electronics for use at higher speeds, and altered window size to allow calibrated temperatures to be measured. Full details of the calibration and non-uniformity techniques, and their requirement, are discussed in a separate paper [13]. Tests were performed on the Instron VHS machine at an actuator speed of 10 m/s initially on a steel specimen and then a glass fibre chopped strand mat (CSM) specimen. The tests were performed as described in the DIC section, but the surface of the specimen was sprayed only with matt black paint to provide a constant emissivity. Figure 2 is a full window image of the steel specimen before and after the test to demonstrate the location of the subwindowed data, shown by the red box. By varying the stand-off distance it was possible to view the entire gauge length of the specimen, and it is clear from the post test image that the failure section was captured. The temperature evolution with time is plotted in Figure 3 at the six points displayed on the final image from the series show next to the graph. The data is displayed in its raw format as the number of digital levels measured. For reference the load signal from the Kistler load cell on the VHS machine is included shown by the blue line. While it is noisy there is a definite change in signal as the specimen fails at approximately 3 ms into the test time. The temperature at all six points increases steadily at a similar rate as the load is initially applied to the specimen, but towards the end of the test the temperature of the point at the failure location diverges from the rest as it rises rapidly. Therefore there are two distinct stages in the temperature evolution during the high speed test. The first represents temperature change as the specimen is stressed, whilst the second demonstrates large temperature increase due to damage at failure. The apparent cyclic temperature change at point six after failure has been identified as outof-plane movement of the specimen. The temperature evolution during the test on a CSM specimen is plotted in Figure 4. The data is plotted from the same points used for the steel specimen. It should be noted that the timescale of the temperature evolution is far shorter than for the steel specimen. The temperature rise is much sharper, approximately 0.1 ms, whilst the rise for steel was spread across 2 ms. Secondly the data from the composite is a couple of orders of magnitude less than the steel. It is evident that the shorter timescale and lower data values produce noisier IRT. Point six is near to the failure zone, and as for the steel specimen, there is a sudden temperature rise as the specimen fractures. However, point one on the CSM plot also shows a temperature increase lagging slightly behind point six. From the images taken during the test, and from the remains of the specimen post test, it became clear that two failure sites were present. The failure at point six was first to initiate, shortly followed by a fracture at point one. This highlights the more complex nature of tests involving composite materials. CSM specimens are particularly weak, and therefore during failure there is less energy and consequently lower temperature evolutions. It is expected that applying IRT to stronger composites, e.g. UD glass fibre specimens, will provide higher energy failures and higher temperatures.

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Fig. 2 Full window images of steel specimen before and after test

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Fig. 3 Plot of the temperature evolution of the specimen at six points during the test 530 525

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Fig. 4 Plot of the temperature evolution of the specimen at six points during the test

6 SYNCHRONISED DATA CAPTURE The overall goal of the research is to obtain full-field temperature and strain information from composite materials subjected to high velocity loading. Initial tests on the separate use of DIC and IRT at high speeds have shown promise in the two techniques although further work is required to improve consistency and obtain a better understanding of the error sources. The next step is to develop an approach that will allow both systems to capture data concurrently. In the literature there is little mention of the use of white light imaging and IRT together, particularly at high speed. Noble [14], used the IR system mentioned above in the IRT section and a white light high speed camera during a test on iron in a split Hopkinson bar rig. The white light camera was used to obtain deformation information by monitoring the change in shape of the specimen, and did not provide full-field strain. The IR system did not operate at a high enough sampling rate to capture temperature evolution during the test. Instead it was triggered shortly after the specimen failure to measure the maximum temperature at the fracture site. These systems were still effectively used separately to obtain information at different stages of the test. To fully characterise the viscoelastic behaviour of the composite material subjected to high velocity loading it is necessary to measure load, temperature and strain at the same temporal location. Therefore an approach is required to synchronise the three data types together. The first challenge to overcome is to ensure all data capture systems are initiated at the same time; this is achieved using specifically designed LabView code for operation on National Instruments Compact Rio hardware. The Compact Rio monitors the voltage signal from the Kistler load cell and at a user defined threshold triggers the capture of load data and generates a logic signal that is sent to the two camera systems. The white light cameras and IR detector can be triggered from a digital pulse with a known jitter of the order of 100 ns. With a known frame rate it is a simple matter to find a corresponding load value for each white light and IR image. The second challenge is an artefact of the different performances of the white light and IR systems. Whilst the white light cameras can achieve frame rates over 100 kHz (although with much reduced spatial resolution), it has been shown that detector sensitivity will limit the IR system to approximately 15 kHz. Both systems are to be initiated at the same time, but with different frame rates they will quickly lose phase. It is envisaged that using the white light system at a frame rate that is a multiple of the sampling rate of the IR detector would ensure that for each IR image there is also a DIC strain image. It is advantageous to operate the white light camera at higher frame rates to assist the DIC algorithm in obtaining accurate strain information. The final perceived challenge is in the physical collection of the white light and IR images. DIC requires the specimen surface to be sprayed with a speckle pattern, whilst, to obtain the best results, IR requires a surface preparation of matt black paint. Further tests are required to investigate the effect of using a painted speckle pattern on the collection of IR data. The illumination required for DIC will also have an effect on IR data, particularly with specimen heating. ‘Cold’ light LEDs are being investigated to illuminate the white light images. It may also be possible to obtain DIC data from the front of specimen, and IRT data from the rear. Consideration must be taken though that any localised effects from damage may affect the relevance of the two data sets. CONCLUSIONS It has been shown that DIC and IRT with commercially available cameras, detectors and software are feasible techniques to obtain full-field strain and temperature information from high strain rate testing on composite materials. Further work is required to improve consistency and fully understand the errors involved. A system is in place that allows the data capture to be synchronised, even accounting for differences in sampling rates of the DIC and IRT. Consideration is required of the physical aspects of collecting data simultaneously from two techniques that have some conflicting requirements. ACKNOWLEDGEMENTS The work was supported by the UK Engineering and Physical Sciences Research Council (EPSRC) grant number EPG042403/1 and the UK Defence Science and Technology Laboratories (DSTL). The SA3 cameras were provided by Airbus and the SA1 from the UK STFC Equipment Loan Pool. REFERENCES 1. 2. 3. 4.

Hamouda, A.M.S., and Hashmi, M.S.J. Testing of composite materials at high rates of strain: advances and challenges. Journal of Materials Processing Technology, 77, 327-336, 1998. Sierakowski, R.L. Strain rate effects in composites. ASME, 1997. Brillaud, J. and Lagattu, F. Limits and possibilities of laser speckle and white-light image correlation methods: theory and experiments. Applied Optics, 41, 6603-6613, 2002. Anon, Optical deformation and strain field imaging, L. Vision, Editor.

7 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.

Godara, A. and Raabe, D. Influence of fiber orientation on global mechanical behavior and mesoscale strain localization in a short glass-fiber-reinforced epoxy polymer composite during tensile deformation investigated using digital image correlation. Composites Science and Technology, 67, 2417-2427, 2007. Tiwari, V., Sutton, M., and McNeil, S. Assessment of high speed imaging systems for 2D and 3D deformation measurements: Methodology development and validation. Experimental mechanics, 47, 561-579, 2007. Koerber, H., Xavier, J. And Camanho, P.P. High strain rate characterisation of unidirectional carbon-epoxy IM78552 in transverse compression and in-plane shear using digital image correlation. Mechanics of Materials, 42, 1004-1019, 2010. Maldague, X.P.V. Theory and practice of infrared technology for non-destructive testing. John Wiley and Sons, ed. Chang, K., 2001. Noble, J. P. and J. Harding. Temperature measurement in the tensile Hopkinson bar test. Measurement Science and Technology, 5, 1163-1171, 1994. Zehnder, A.T., Guduru, P.R., et al. Million frames per second infrared imaging system. Review of Scientific Instruments, 71, 3762-3768, 2000. Guduru, P.R., Rosakis, A.J., and Ravichandran, G. Dynamic shear bands: an investigation using high speed optical and infrared diagnostics. Mechanics of Materials, 33, 371-402, 2001. Ranc, N., L. Taravella, et al. Temperature field measurement in titanium alloy during high strain rate loading: Adiabatic shear bands phenomenon. Mechanics of Materials, 40, 255-270, 2008. Fruehmann, R.K., Crump, D.A., and Dulieu-Barton, J.M. The use of infrared thermography at high frame rates. In: International Congress of the Society for Experimental Mechanics (SEM), Uncasville, USA, 2011. Noble, J. P., Goldthorpe, B.D., et al. The use of the Hopkinson bar to validate constitutive relations at high rates of strain. Journal of the Mechanics and Physics of Solids, 47, 1187-1206, 1999.

The use of infrared thermography at high frame rates

R K Fruehmann1, D A Crump1, J M Dulieu-Barton1 1

Faculty of Engineering and the Environment, University of Southampton, University Road, SO17 1BJ, Southampton, UK

ABSTRACT Composite materials are finding increased use in applications where impact and high strain rate loading form a significant part of a component’s service loads. It is therefore imperative to fully characterise the thermomechanical response of composite materials at high strain rates. The work described in the paper forms part of a project investigating the thermomechanical response of composite materials at high strain rates. To obtain the temperature evolutions during the high strain rate event (thermoelastic, viscoelastic and fracture energy), full-field infrared thermography is used. In contrast to visible light photography, the measurand in thermography is the intensity of the emitted radiation from the specimen surface, as opposed to reflected radiation. At increasing recording rates, the emittance available for measurement reduces proportional to the exposure time; the faster the data capture the less the exposure time. Hence, signal noise and detector calibration present a major challenge. This is accompanied by challenges arising from controlling an infrared detector that has not been optimised for the purpose of high speed data acquisition. The present paper investigates the possibility of applying infra-red thermography to high strain rate events and discusses the challenges in obtaining reliable values of the temperature changes that occur over very short time scales during high strain rate events. KEYWORDS: Infrared, thermography, calibration, high speed testing INTRODUCTION High strain rate events, such as those that occur during a collision or impact, are known to invoke a different material response compared with that observed in quasi-static conditions [1]. One of the challenges associated with high strain rate testing is the short duration of the test and the required high data recording frequency. Here an infrared (IR) detector is used to obtain the temperature evolution of a specimen during high strain rate loading. The overall goal is to include the temperature data in constitutive laws that characterise the material behaviour. The present paper describes initial work on the implementation of high speed IR thermography in high strain rate tests using a commercially available system. The paper discusses in detail the challenges associated with obtaining temperature values from an IR detector output at high recording rates. IR detectors are used in a wide variety of applications to measure temperature; the basic physics is described by Planck’s law [2]. At ambient temperature, the radiation band with the strongest emission is the middle IR band (1.5 – 20 μm). In this range two types of detector can be used: bolometers where the detector experiences a rise in temperature due to incident radiation and a temperature sensitive material property (e.g. resistance) is measured or photon detectors where a

T. Proulx, Thermomechanics and Infra-Red Imaging, Volume 7, Conference Proceedings of the Society for Experimental, Mechanics Series 9999999, DOI 10.1007/978-1-4614-0207-7_2, © The Society for Experimental Mechanics, Inc. 2011

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10 semiconductor is excited by an incident photon and releases a charge that is collected in a capacitor. Of the two, photon detectors have a greater sensitivity and faster response rates and are therefore most suited to high speed data capture. To obtain a quantitative temperature measurement it is necessary to characterise the detector response. Calibration procedures are well established in industry and detectors that can be used to obtain quantitative measures of temperature are supplied with a manufacturer calibration. However, no commercial off-the-shelf system is available with a suitable calibration to obtain measurements at the recording frequencies required for high strain rate testing. The equipment used in the this work is a Cedip Silver 480M IR camera with a 320 x 256 element indium / antimonide (InSb) detector array. This is a photon detector, sensitive to radiation with wavelengths from 3 to 5 μm. In standard operation, the detector has a sensitivity of 4.2 mK at 25°C, with a maximum frame rate of 383 Hz at full frame. To capture the temperature evolutions during a high strain rate test however, acquisition frequencies in excess of 10 kHz are required. Therefore the paper describes in detail the characterisation and calibration of an off-the-shelf detector for high speed thermography. DETECTOR CHARACTERISATION Fig. 1 shows a schematic of the data capture for a photon detector such as that used in the 480M system. The photons are focused on the detector array. The electronic shutter controls the exposure time, known as integration time (IT), by controlling the time the switches are left open. To achieve the highest possible frame rate and sensitivity, the system comprises two sets of capacitors in the read out circuit, enabling almost continuous data capture; while data is being read from one bank of capacitors, the second bank is recording. The output from the capacitors is converted in to a 14 bit logic signal using analogue to digital convertors built into the detector device. The digital output is then sent directly to the computer for further processing.

Fig. 1 Schematic of data acquisition Selecting a suitable frame rate is a compromise between three main parameters: the duration of the test, the required thermal sensitivity and the number of detector elements used to collect the data. The frame rate is limited by the (IT), which controls the detector thermal sensitivity and the data handling capacity of the read out circuit which dictates the maximum window size for the image (i.e. number of detector elements) that can be recorded at a given frame rate. Fig. 2 illustrates how the three parameters are related for the system used in this work and shows that a practical limit is reached around 16 kHz above which the sensitivity and image window size fall below a useable threshold.

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Fig. 2 Relationship between a) integration and frame rate and b) window size and frame rate Each detector element has a slightly different sensitivity and similarly each capacitor has its individual characteristics. To obtain quantitative measurements, the first step is to identify this variation so as to be able to correct for it. This process is called the non-uniformity correction (NUC), which comprises exposing the detector to a uniform diffuse emission source (generally a flat plat with a high emissivity coating) and recording several images. The average signal from the whole image (spatial average) is compared with the average signal of each detector element (temporal average). This is done at two different temperatures within the range of temperatures to be measured, as shown in Fig. 3. A linear fit is then assumed between the two points, providing a gain and an offset value for each detector element from which the correction factor can be calculated, to bring it in line with the mean response of the whole array. This linear fit is however only an approximation of the detector response curve. In a typical test setup, the IT is selected to maximise the use of the full range of the detector (typically from 25 to 75% of the detector saturation). The two points for the NUC are chosen at 30 and 70% of the detector saturation to minimise the average error across the full range. The NUC is stored in two tables (one for each array of capacitors) which are loaded directly into the flash memory onboard the camera so that the data output by the camera is already corrected. In the current work however, the IT time is selected to enable a particular frame rate to be achieved. At this IT the detector will only operate between 2 and 10% saturation for room temperature measurements, so the NUC was performed at 30 and 70% of the desired temperature range (i.e. 28 and 51°C for the range 10 to 70°C). Over such a small range, the linear fit assumed in the NUC should be a relatively good approximation.

Fig. 3 Linear fit for NUC

12 CALIBRATION As the necessary IT is so small, the calibration data produced by the manufacturer does not cover this range since it is well outside the usual operating conditions for the IR system. It was therefore necessary to devise a methodology to establish a calibration at small IT. The methodology followed that of the manufacturers approach by taking the detector output in digital level from a high emissivity body with a known temperature. In this work a cavity black body was used [3] with a platinum type thermocouple inserted. The cavity walls were maintained at a uniform temperature by water circulated from a temperature controlled bath with a temperature range from 4 to 75°C. The calibration was conducted twice; the first time a series of videos (20 images each) was collected over a temperature range from 8 – 50°C using an IT of 60 μs and a frame rate of 15 kHz and an image size of 64 x 12 pixels. A NUC was conducted at 10 and 30°C. A calibration curve of detector response against black body temperature was obtained for odd and even numbered frames separately to compare differences that might occur due to the two capacitor arrays. The results showed an almost identical response. It was also possible to obtain the noise in each detector element, calculated as the standard deviation from 10 readings at nominally identical temperature. A standard deviation between 1.5 and 2.5 DL was obtained for most detector elements, with a few pixels having a standard deviation up to a maximum of 3.5 DL at 50°C. This represents a measurement precision of 0.35 to 0.2°C over the range from 15 to 50°C. The calibration procedure was then repeated over the range from 5 to 70°C, this time taking only single images at each temperature to reduce the data processing. A second NUC was performed, this time at 28 and 51°C to account for the extended temperature range. From this data the standard deviation across the image was obtained. This showed a nearly Gaussian distribution at temperatures up to 30°C. Fig. 4 shows that at 50°C, the pixel value distribution across the image shows two spikes, and a greatly increasing spread. Viewed as a percentage standard deviation the noise appears to be quite small, as shown in Fig. 5, but the change in the image noise characteristics seems to display a systematic pattern in the detector response and must therefore be considered significant. This is attributed to an error with the NUC as the pattern in the output has been shown to match the noise pattern of an image obtained with no NUC. The outcome is counter intuitive as the lowest error associated with the NUC process would be expected at the two points at which the NUC was conducted, i.e. at 28 and 51°C. However, it is at 50°C where two spikes start to appear in the image histogram as shown in Fig. 4. The signal noise from an individual pixel, however, remains fairly constant across the temperature rage, increasing from 1.5 to 2.5 DL between 15 and 70°C. Hence, the increase in noise is not a function of the detector elements themselves but of how the NUC process is integrated into the onboard hardware.

Fig. 4 Histogram of image noise at different temperatures

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Fig. 5 Change in image standard deviation with temperature The error with the standard NUC procedure can be avoided by obtaining raw detector data and performing the NUC in a postprocessing stage off-line. The strategy in this work is to conduct a calibration on a pixel-by-pixel basis. This takes into account the responsivity of each individual detector element. The calibration has to be conducted separately for odd and even frames to account for the two arrays of capacitors in the data acquisition hardware. By conducting the calibration directly on the individual pixel response, the two steps are combined. This enables the measurement precision to be assessed for each pixel individually in the resulting image. This calibration was conducted with 2°C intervals across the calibration range from 10 to 70°C. The plot shown in Fig. 6 shows the image average for odd and even frames. The error associated with each measurement is less than 4 DL. Table 1 shows the aggregate detector sensitivity (temperature increment per DL) and precision (detector noise calibrated into °C) over the measurement range.

Fig. 6 Calibration curve (image average for odd and even frames)

14 Table 1 Detector Precision Temperature (°C) 15 20 30 50

Sensitivity (°C) 0.14 0.11 0.10 0.07

Precision (°C) 0.35 0.27 0.25 0.20

The final step in obtaining accurate measurements is to evaluate the emissivity of the surface of the test specimen. For this, material coupons were placed in a thermal chamber with a temperature range up to 80°C and a small hole cut into one side to provide optical access to the IR detector. Thermocouples were mounted to the rear of the coupons while the forward facing side was prepared in the same way as for a mechanical test. Images were then collected over a range of temperatures from 15 to 55°C to assess the emissivity of the specimen surfaces over the full range of temperatures expected to occur during the high rate testing. Because the specimen surface is not a perfect emitter, background radiation will be partly reflected from the surface, leading to a measurement error. To assess the effect of a background radiation source, the specimens were also placed at a slight angle to the detector (approximately 20°) and a diffuse emission source (a flat plate with a high emissivity coating) was placed in the reflection path. The emissivity of lightly abraided E-glass / epoxy composite was measured to lie in the range 0.90 – 0.92. This uncertainty is due to some inherent noise in the detectors and variability in the surface preparation. TEST RESULTS Preliminary tensile tests were performed on an E-glass / epoxy specimen made from 4 layers of chopped strand mat to assess the range of temperatures to be expected from a composite specimen in the approach to failure and evaluate the calibration and NUC procedure described above. The specimen was waisted to provide a gauge length that fitted entirely within the field of view of the detector (approximately 10 x 50 mm). The mechanical load was applied using an Instron VHS servo-hydraulic test machine at an actuator velocity of 10 ms-1 and a maximum load capacity of approximately 30 kN. The load was measured using a Kistler piezo electric load cell. However the load data was extremely noisy and could therefore not be used. As a strain gauge was not attached to the specimen directly, the strain rate was estimated using the gauge length, actuator velocity and the assumptions of no slip in the grips and was considered to be between 50 – 100 s-1. The image in Fig. 7 shows the temperature on the specimen surface at the time of fracture. The fracture location is clearly visible on the right hand side of the specimen as a region of significant heating. Temperature measurements taken at five locations on the specimen surface (as marked in Fig. 7) are plotted over time in Fig. 8 a) and b) from 1 ms before fracture to 1 ms after. Fig. 8 b) shows a zoomed in portion of the graph in Fig. 8 a) enabling two distinct regions to be identified: an elastic strain region where there is a uniform decrease in the temperature across the whole specimen due to the thermoelastic effect [4] and a region where the specimen temperature increases all across the specimen surface as the failure strain is reached. The final failure propagates from one location on the specimen (point 5). Here heat is generated by the formation of new surfaces. Post failure inspection indicated manifold failure modes, including fibre pull-out, fibre failure and matrix cracking at the fracture site.

Fig. 7 Image of specimen surface temperature at time of fracture

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Fig. 8 Surface temperature evolution at 5 points on the specimen, a) full range b) zoomed in CONCLUSIONS It has been demonstrated that an off-shelf IR detector can be used to obtain temperature measurements at high speed. In doing so it is necessary to carefully investigate how the detector behaviour changes. Manufacturers’ calibration processes are often integrated into the detector hardware in a manner that may not be transparent and possibly even a trade secret. Apparently straight forward processes such as the NUC may therefore not perform as expected when operating outside the detectors normal range. The work in this paper has highlighted the procedures necessary to obtain quantitative temperature measurements as well as some of the potential pitfalls to be aware of. It is demonstrated that data can be obtained with sufficient precision to make a meaningful addition load and strain measurements during high speed testing. REFERENCES [1]

Hamouda, A.M.S. and Hashmi, M.S.J., “Testing of composite materials at high rates of strain: advances and challenges”, Journal of Materials Processing Technology, vol. 77, pp. 327-336, (1998)

[2]

Bramson, M.A., “Infrared Radiation: A Handbook for applications”, Plenum Press, (1968)

[3]

Irani, K., “Theory and construction of blackbody calibration sources”, Thermosense XXIII - Proceedings of SPIE, vol. 4360, pp. 347-362, (2001)

[4]

Dulieu-Barton, J.M. and Stanley, P., “Development and applications of thermoelastic stress analysis”, Journal of Strain Analysis, vol. 33, pp. 93-104, (1998)

In Situ Heat Generation and Strain Localization of Polycrystalline and Nanocrystalline Nickel

T. Chan1,a, D. Backman2,b, R. Bos2,c, T. Sears2,d, I. Brooks3,e and U. Erb1,f 1

Department of Materials Science and Engineering, University of Toronto, Wallberg Building, 184 College Street, Suite 177, Toronto, ON, Canada M5S 3E4 2

3 a

Institute for Aerospace Research, National Research Council, M-14, 1200 Montreal Road, Ottawa, ON, Canada K1A 0R6

Integran Technologies Inc, 1 Meridian Road, Toronto, ON, Canada M9W 4Z6

[email protected], [email protected], [email protected] d [email protected], [email protected] [email protected]

ABSTRACT Commercially available polycrystalline nickel (Ni200; grain size: 30 µm) and electrodeposited nanocrystalline nickel (grain size: 30 nm) were analyzed for the phenomena of in-situ heat generation and strain localization during plastic deformation at room temperature. Tensile specimens according to ASTM E8 standard dimensions were tested at a strain rate of 10-2/s to record the amount of heat dissipated and the change of localized strain using a high resolution infrared detector and digital image correlation (DIC) camera, respectively. For deformation close to ultimate tensile strength, data recorded for the maximum temperature increase and localized strain for nanocrystalline were 110C and 4.5%, whereas polycrystalline nickel showed 170C and 60%, respectively. The amount of heat generated locally by strain is related by the heat conversion factor (i.e. Taylor Quinney coefficient). Polycrystalline nickel showed a decreasing trend of heat conversion due to lattice distortions or defect formation during deformation. In contrast, nanocrystalline nickel showed an increasing trend, likely due to differences in deformation mechanisms. INTRODUCTION Over the past three decades, major research efforts have been concerned with the study of the mechanical properties of nanocrystalline materials, in particular nanocrystalline metals [e.g.1,2]. For nanocrystalline metals produced by the electrodeposition methods, significant improvements in their yield strength and hardness are observed which are due to HallPetch grain size hardening [3]. The influence of grain size on other mechanical properties such as the Young’s modulus, abrasive and adhesive wear resistance, and coefficient of friction are also well documented [3,4]. However, many issues regarding deformation mechanisms, intrinsic ductility or strain hardening capacity of these materials still require further study. One aspect issue that needs to be addressed is the phenomenon of in-situ heat generation and strain localization during deformation, which could have a considerable effect on the mechanical properties. Temperature increases during deformation could lead to thermal softening, which in turn could affect the failure process. It is well known [5,6] that most of the energy of plastic deformation is dissipated as heat and the remaining balance stored in the material as strain energy (e.g. lattice

T. Proulx, Thermomechanics and Infra-Red Imaging, Volume 7, Conference Proceedings of the Society for Experimental, Mechanics Series 9999999, DOI 10.1007/978-1-4614-0207-7_3, © The Society for Experimental Mechanics, Inc. 2011

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distortions, defect formation). For example, this subject is of interest in the study of stored energy and its effects on the process of recrystallization during deformation. In recent years, infrared imaging technology [7] combined with digital image correlation (DIC) strain measurement [8] during tensile testing have been widely used. Examples include studies on the effect of cold expansion of holes using thermoelasticity and digital correlation [9,10] and the analysis of stress distributions on turbine blades [11]. Effects of heat generation and strain localization on mechanical properties are also well documented. For example, the infrared technique has been applied successfully to study heat generation due to plastic deformation in tensile testing of TRIP steels during deformation at strain rates up to 10-1/s [12]. Results showed a maximum temperature increase of 350C within the strain hardening regime; 580C near the necking regime and 900C just before sample fracture. One particular study on strain localization using DIC acquired full-field necking behaviour of mild steel deformed at a strain rate of 10-3/s [13]. Localized strain gradually developed and built up during the deformation process. The results showed that the highest localized strain was located at the necking zone beyond ultimate tensile strength and the position of highest localized strain corresponded to the area of fracture. In another study, the rapid evolution of shear banding close to the necking region was captured with the DIC method on fully dense nanocrystalline nickel at a strain rate of 10-4/s [14]. The purpose of this study is to correlate the phenomena of in-situ heat dissipation and strain localization for both polycrystalline and nanocrystalline nickel and to analyze the coupling effect to the thermomechanical properties during plastic deformation. EXPERIMENTAL PROCEDURE Tensile coupons of electrodeposited nanocrystalline nickel (grain size: 30 nm) of dimensions according to ASTM E8 standard (12 cm X 2 cm X 0.1 cm) were provided by Integran Technologies Inc, Toronto. Polycrystalline nickel samples with the same size were machined from commercially available Ni 200 (grain size: 30 µm). Prior to tensile testing, tensile samples were spray painted black on one side to equalize emissivity for better infrared detection. On the other side, samples were lightly abraded using 320 grit sandpaper for the measurement of localized strains. The high resolution infrared camera was calibrated before each experiment. Tensile samples were loaded on a MTS servo-hydraulic tensile testing machine. All samples were tested at a strain rate of 10-2/s. Temperature changes and localized tensile strain were measured simultaneously during tensile testing using a high resolution infrared camera (Deltatherm 1410) and a high resolution Digital Image Correlation Camera (Allied Vision Technologies), respectively. Temperature and strain were continuously recorded to sample fracture. However, in this paper the thermomechanical response was only analyzed up to ultimate tensile strength for each material. RESULTS AND DISCUSSION Polycrystalline and nanocrystalline nickel exhibit very distinct engineering stress-strain curves as shown in Fig. 1. Polycrystalline nickel has a yield strength of 208 MPa, ultimate tensile strength of 442 MPa and 50% elongation-to-fracture. On the other hand, nanocrystalline nickel shows a yield strength of 950 MPa, ultimate tensile strength of 1504 MPa and 8% elongation-to-fracture. These results illustrate that yield strength (σy) and ultimate tensile strength (σUTS) improve significantly when the grain size is refined to 30 µm to 30 nm. This can be explained on the basis of the Hall-Petch grain size strengthening mechanism. Both polycrystalline and nanocrystalline show considerable amounts of necking beyond UTS. However, polycrystalline nickel shows much higher ductility compared to nanocrystalline nickel due to the extended region of uniform plastic deformation, which can be attributed to the high intrinsic ductility of fcc materials with large grain size. Localized strain and heat distribution were measured by the DIC camera and the infrared detector, respectively, and the results of strain and heat recorded up to UTS for both polycrystalline and nanocrystalline nickel were also quite distinct (Fig. 2). Polycrystalline nickel with relatively high ductility showed noticeable changes in localized strain along the sample gauge when deformed to 25% and 45% engineering strain. The increase of localized tensile strain is highlighted by the gradual change in colour scale from dark purple and blue to bright green and yellow. At the 45% engineering strain level (i.e. just before UTS), polycrystalline nickel exhibits two regions of highly localized strain (i.e. yellow regions). One of the two regions with the highest strain levels corresponds to the position of final fracture, indicated by the dashed line in Fig. 2. On the other hand, for nanocrystalline nickel with relative high σy and σUTS, and low ductility only one high localized strain region was observed at 5.5% engineering strain (i.e. just before UTS). Such distinct behaviour of polycrystalline and nanocrystalline nickel regarding localized strain distribution is likely due to the nature of plastic flow within the uniform deformation regime. Localized strain of polycrystalline nickel (Fig. 3) showed a transition from homogeneous to inhomogeneous flow from ~ 20% engineering strain onwards. Within the region of inhomogeneous flow, the detected localized strain is higher than the engineering strain. For example, deformation at 40% engineering strain yielded 47% localized tensile strain in the region shown by the dashed line.

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Fig. 1 Engineering stress-strain curves for polycrystalline and nanocrystalline nickel

Fig. 2 Localized tensile strain (top) and heat distribution (bottom) of polycrystalline (left) and nanocrystalline nickel (right) at various engineering strain levels. The dashed lines indicate the position of the final fracture planes

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In contrast, nanocrystalline nickel (Fig. 4) shows that localized tensile strain is consistently lower than the engineering strain within the region of uniform deformation. For example, the deformation at 3% engineering strain in nanocrystalline nickel only yields 2% maximum localized tensile strain. This results in a relative homogeneous strain distribution observed in nanocrystalline nickel and low localized strain hardening capacity. In addition to the localized strain, the heat distribution (Fig. 2) during deformation was also recorded by the infrared camera. Similar to the result in strain localization, polycrystalline nickel also shows noticeable changes in temperature at different engineering strain levels. With the increase of engineering strain to 25% and 45%, an increasing amount of heat is dissipated and a considerable increase of temperature is detected at the center of the gauge (dashed line). The temperature increase reached its highest point of 170C at 45% engineering strain (Fig. 3). On the other hand, nanocrystalline nickel dissipates less heat and heat distribution along the sample gauge is more uniform. At 5.5% engineering strain, the maximum temperature increase reached 110C which is lower than for polycrystalline nickel (Fig. 4). The observed temperature increase correlates with the localized strain. In other words, increasing of localized tensile strain during deformation in both polycrystalline and nanocrystalline nickel induces heat dissipation. The difference in heat dissipation for the two materials could be explained by the heat conversion factor of polycrystalline and nanocrystalline nickel. According to the laws of thermodynamics, plastic work is converted to either stored energy (i.e. lattice distortions, defect formation) or to heat dissipation when metals undergo deformation process [15,16]. The fraction of heat converted from plastic work is known as the Taylor Quinney coefficient (β). 



C p T 



where is the material density; the heat capacity; the heat rate; represents the plastic stress and is the strain rate. In both cases of polycrystalline and nanocrystalline nickel, the heat capacity and density are constant at 480 J/mol K and 8.3g/cm3, respectively [3,17]. Different heat conversion trends were observed for polycrystalline and nanocrystalline nickel. Polycrystalline nickel shows that a decreasing amount of energy is converted to heat for increasing plastic strain to 40% (Fig. 5). In contrast, for nanocrystalline nickel the amount of plastic strain energy converted to heat increases with increasing strain (Fig. 6). The main deformation mechanism during room temperature deformation of polycrystalline nickel is dislocation slip. On the other hand, for nanocrystalline nickel a number of potential mechanisms have been proposed, including diffusional creep, grain boundary sliding and grain rotation [1-3]. We are currently assessing the correlation between heat dissipation/defect formation for the various deformation mechanisms in these materials. 20

Maximum temperature increase Maximum localized tensile strain

80 70

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Fig. 3 The maximum temperature increase and localized tensile strain of polycrystalline nickel

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Fig. 4 Maximum temperature increase and localized tensile strain of nanocrystalline nickel

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Fig. 5 Taylor Quinney coefficient of polycrystalline nickel

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Engineering plastic strain, % Fig. 6 Taylor Quinney coefficient of nanocrystalline nickel CONCLUSIONS In situ heat generation and strain localization during plastic deformation of polycrystalline and nanocrystalline nickel are interdependent. It was shown that localized strain induced localized heat dissipation in both materials. At 45% engineering strain (at UTS) in polycrystalline nickel, 60% localized strain induced a maximum temperature increase of 170C. On the other hand, nanocrystalline nickel at 5.5% engineering strain (at UTS) yielded 4.5% localized strain which induced a maximum temperature increase of 110C. The fractions of energy converted from plastic work to heat during deformation in polycrystalline nickel decreased with increasing deformation, which resulted in 80% of plastic work contributing to lattice distortions or defect formation at UTS. On the other hand, most of the plastic work in nanocrystalline nickel at UTS is converted to heat. ACKNOWLEDGEMENTS The authors would like to acknowledge the financial support by the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Ontario Research Fund (ORF). REFERENCES [1] Weertman J.R. in: Nanostructured Materials, 2nd ed., edited by C.C. Koch William Andrew Publishing, Norwich, NY, 2007 [2] Koch C.C., Structural nanocrystalline materials: an overview, Journal of the Materials Science, vol 42, p. 1403-1414, 2007 [3] Erb U., Aust K.T., Palumbo G. in: Nanostructured Materials, 2nd ed., edited by C.C. Koch William Andrew Publishing, Norwich, NY, 2007 [4] Erb U., Size effects in electroformed nanomaterials, Key Engineering Materials, vol 444, p. 163-188, 2010

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[5] Bever M.B., Holt, D.L. Titchener A.L., The stored energy of cold work, Progress in Materials Science, vol 17, p.190, 1973 [6] Taylor G.I., Quinney M.A., The latent energy remaining in a metal after cold working, Proceedings of the Royal Society of London. Series A, vol 143, p. 307-326, 1934 [7] Rogalski A., Infrared detectors: an overview, Infrared Physics & Technology, vol. 43, issue 3-5, p. 187-210, 2002 [8] Chu T.C., Ranson W.F., Sutton M.A., Applications of digital-image-correlation techniques to experimental mechanics, Experimental Mechanics, vol. 25, issue 3, p. 232-244, 1985 [9] Backman D., Liao M., Crichlow L., Yanishevsky M., Patterson E.A., The use of digital image correlation in a parametric study on the effect of edge distance and thickness on residual strains after hole cold expansion, The Journal of Strain Analysis for Engineering Design, vol. 43, issue 8, p. 781-789, 2008 [10] Backman D., Cowal C., Patterson E.A., Analysis of the effects of cold expansion of holes using thermoelasticity and image correlation, Fatigue & Fracture of Engineering Materials & Structures, vol. 33, issue 12, p. 859-870, 2010 [11] Backman D., Greene R.J., Gas turbine blade stress analysis and mode shape determination using thermoelastic methods, Applied Mechanics and Materials, vol. 13-14, p. 281-287, 2008 [12] Rusinek A., Klepaczko J.R., Experiments on heat generated during plastic deformation and stored energy for TRIP steels, Journal of Materials & Design, vol. 30, issue 1, p. 35-48, 2009 [13] Coppieters S., Cooreman S., Sol H., Houtte P.V. and Debruyne D., Identification of the post-necking hardening behaviour of sheet metal by comparison of the internal and external work in the necking zone, Journal of Materials Processing Technology, vol. 211, issue 3, p. 545-552, 2011 [14] Zhu R., Zhou J. Jiang H. Lui Y. Ling X., Multi-scale modeling of shear banding in fully dense nanocrystalline Ni sheet, Materials Science and Engineering: A, vol. 527, issue 7-8, p. 1751-1760, 2010 [15] Zehnder A.T., A model for the heating due to plastic work, Mechanics Research Communications, vol. 18, p. 23-28, 1991 [16] Zehnder A.T., Babinsky E., Palmer T., Hybrid method for determining the fraction of plastic work converted to heat, J. Experimental Mechanics, vol. 38, issue 4, p. 295-302, 1998 [17] Turi T., Erb U., Thermal expansion and heat capacity of porosity-free nanocrystalline materials, Materials Science and Engineering A, vol. 204, issue 1-2, p. 34-38, 1995

Dissipative and coupling effects accompanying the natural rubber elongation

B. Wattrisse, R. Caborgan, J.-M. Muracciole, L. Sabatier, A. Chrysochoos LMGC UMR CNRS5508 Montpellier University, CC048, Place E. Bataillon, 34095 Montpellier, France

ABSTRACT Rubber-like materials can undergo very large strains in a quasi-reversible way. This remarkable behavior is often called hyper (or entropic) elasticity. However, the presence of mechanical loops during a load-unload cycle is not consistent with a purely elastic behavior modeling. Using Digital Image Correlation and Infra-Red Thermography, the present study aims at observing and quantifying dissipative and coupling effects during the deformation of natural rubber at different elongation ratios. For elongation ratios less than 2, the famous thermo-elastic inversion is revisited within the framework of the irreversible processes thermodynamics, and interpreted as a competition between two coupling mechanisms. For elongation of about 3 or 4, the predominance of entropic elasticity is shown and the relevance of the analogy with perfect gases, at the root of its definition, is energetically verified. For very large elongation ratios (about 5), the energy effects associated with stress-induced crystallization-fusion mechanisms are underlined. The current experiments, performed at relatively slow strain rate, did not exhibit any significant dissipation.

Introduction In the literature, the first experimental studies on natural rubber were performed by Gough in the early 19th century [1]. They evidenced the coupled nature of its thermo-mechanical behavior. The experiments were resumed later by Joule [2] who observed that the straining of a vulcanized rubber generated a cooling of the specimen for small elongations, followed by a warming for higher elongations. He also noticed that the thermal expansion coefficient changes its sign – from positive to negative – with the increasing applied stress. This change of sign has since been associated with the so-called thermo-elastic inversion mechanism. This inversion phenomenon has been thoroughly studied by numerous authors (e.g. [3, 4]), and modeled within the framework of finite non-linear thermo-elasticity (e.g. [5,6]). We have recently proposed to override the hypothesis of pure thermo-elasticity to interpret this inversion phenomenon as the result of the competition between two concurrent coupling effects: a standard thermo-elastic effect (associated with the classical thermo-dilatation of materials), and a rubber effect (similar to perfect gas effect). At the micro scale, the macromolecular approach indeed highlights the very high mobility of the rubber molecular chains. Various experiments [2, 7] showed that the elasticity of this material was due to the entropy variation of the molecular chains network. They also suggested that the coupling mechanism was associated with the unfolding of the chains. The macromolecular approach is classically integrated within the statistical thermodynamics framework, and more specifically within the kinetic theory of gases. Using this analogy, which is the basis of “entropic elasticity” or “rubber elasticity”, one can demonstrate that the stress is proportional to the temperature, and that the internal energy depends only of the temperature (as a perfect gas) [4]. These results imply that the deformation energy developed by the material is totally transformed into heat [8, 9]. Numerous models were proposed in order to predict the mechanical behavior of rubber

T. Proulx, Thermomechanics and Infra-Red Imaging, Volume 7, Conference Proceedings of the Society for Experimental, Mechanics Series 9999999, DOI 10.1007/978-1-4614-0207-7_4, © The Society for Experimental Mechanics, Inc. 2011

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26 materials, but very few were able to also take possible dissipative effects (inducing self-heating) and thermo-mechanical coupling (associated with the material thermo-sensitivity) into account. This study aims at observing, understanding and modeling the dissipative and thermo-mechanical coupling effects involved in the deformation of natural rubber during small amplitude cyclic loading around different given elongations. The material behavior analysis is achieved through energy balances performed using complementary imaging techniques, namely InfraRed Thermography (IRT) and Digital Image Correlation (DIC), giving simultaneously temperature and strain fields on the sample surface. The present paper describes the experimental procedure in a first part. The obtained results are shown and discussed in a second part. A heuristic thermo-mechanical model that account for the main characteristics of the observed energy balance is finally proposed.

Experimental setup and tests The experimental setup is presented in Fig.1.a. It involves a testing machine and two cameras set perpendicularly to the sample surface. An infrared “Titanium” camera (Cedip) provides thermal images of the surface, while a “Camelia 8M” camera (Atmel) gives images in the visible spectrum of the sample during the test. The sample is a classical dog bone shaped specimen, as illustrated in Fig.1.b. The dimensions of the gauge part of the sample are the following: initial length L0 (35 mm), width w0 (6 mm), and thickness t0 (2.1 mm).



λ




 






(a)

(b) Fig.1: (a) experimental setup, (b) sample geometry

The in-plane deformation is measured using a mark tracking technique. The initial gauge length between the vertical marks L0GP is 6 mm and the axial elongation λGP is computed as the ratio of the current gauge length LGP obtained by the marks tracking algorithm and the initial one. A specific calibration allows converting the thermal radiation digitized by the infrared camera into temperature. This calibration involves a black body with a uniform high emissivity coating, and guaranteed temperature homogeneity. As the sample undergoes very large deformations (more than 500%), it is not possible to paint or cover it in order to homogenize and increase its emissivity. Un-stretched natural rubber have a high emissivity (>0.9), and we have checked that it does not significantly change with the material elongation. The temperature variations are very small (less than 0.5 K), and it is necessary to take account of the environment thermal fluctuations that modify the heat exchanges with the surroundings.

27 These fluctuations are determined by placing a reference sample (of same material, and same geometry) in the immediate vicinity of the loaded sample. The thermal variations of this sample are used to estimate the thermal fluctuations of the sample environment. The heat sources, responsible for the temperature variations, are deduced from the in-plane thermal measurements, using the integrated form of the heat equation given in Eq. 1 [10]: dθ

ρ 

dt

θ

+ =  ⋅ τ

(1)

where  ⋅ represents the overall heat sources developed within the material, ρ the mass density of the material, C the specific heat, τ a time constant characterizing the linearized heat exchanges by diffusion, convection, and radiation. The particular time derivative of the temperature variation θ in (Eq. 1) is computed using the kinematic and thermal data given by the two cameras. The geometric transformation between the frames of reference of the two cameras is determined using a calibrated target. The whole experimental procedure is described in [11]. Furthermore, the “time constant” τ, characterizing the overall heat losses, depends on the geometry of the sample that changes significantly during the test. A classical heat fin model allowed us to take the evolution of τ with the measured axial elongation λGP into account. Two types of tests were performed. The first ones aimed at characterizing the thermo-elastic inversion phenomenon. The sample was submitted to a constant load (masses varying from 0 g to 730 g), and it was then heated of 25 K. Its deformation was recorded during the thermal return at room temperature. This test is the “dual” of the one performed by Anthony [12] where the stress evolution was measured at constant elongation during the temperature change. The thermal expansion coefficient can be derived by plotting strain vs. temperature. The second type of tests consists in a velocity-controlled ramp (v = 10 mm.s-1) up to a given maximum elongation (λGPM), followed by several loading cycles performed at a given elongation amplitude (∆λGP) with a given loading frequency (fL). Cycles were designed to separate the coupling from the dissipative mechanisms.

Results Fig.2.a illustrates the results obtained on the thermo-elastic inversion test. It represents the evolution of the axial Hencky strain εxx with the temperature variation θ – the initial temperature being higher than the room temperature – for different imposed loads (here the axial Cauchy creep stress σxx). The existence of thermo-mechanical couplings is here obvious as the material deforms when its temperature varies. We can clearly distinguish the manifestations of two opposite couplings since the material tends to contract when temperature decreases for small applied loads, and to expand for higher loads. The inversion stress σinv corresponds to the case where these opposite couplings annihilate one another. Fig.2.b shows the mechanical response of the natural rubber during a cyclic test at λGPM ≈ 1.5, ∆λGP ≈ 0.2 and fL = 0.2Hz. We can observe the quasi-linear response and the non-hysteretic character of the material behavior in this range of elongation. The thermal response is plotted in Fig.2.c that represents the imposed axial strain and the sample temperature with respect to time t. The temperature variations remain small throughout the test (less than 0.05 K), and the existence of a small thermal drift (amplitude smaller than 0.02 K), uncorrected by the experimental protocol described earlier can be noticed. Nevertheless, the coupled nature of the material behavior can be clearly observed as the temperature evolves in phase with the applied load. 

Fig.2.d represents the time course of the deformation energy   =  :  d – D representing the eulerian strain 

rate tensor –, and of the heat   =   ⋅  d. The deformation energy is, in good approximation, equal to the heat

during all the cycles. This experimental result confirms the existence of a thermo-mechanical coupling, and its entropic nature (i.e. similar to perfect gases). Furthermore, the amplitude of the possible dissipative effects seems to be negligible when compared with the amplitude of the thermo-mechanical coupling sources.

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(a)

(b)

(c) (d) Fig.2: Experimental results for small elongations (λ < 1.5), (a) thermo-elastic inversion test: thermal dilatation response, (b) cyclic test: mechanical response, (c) cyclic test: thermal response, (d) cyclic test: calorimetric response Discussion The preceding results led us to propose a heuristic constitutive model involving two competing coupling mechanism (a classical thermo-elasticity and a rubber elasticity) in series, with no intrinsic dissipation. In a simple one-dimensional approach, three state variables are chosen: the temperature T, the logarithmic strain ε and a rubber strain εr, which play the role of internal state variable. The potentials defining the behavior model are the free energy Ψ,ε,εr , and the dissipation potential !"#, ε$ , %$& . They are defined in Eq. 2 and Eq. 3. The free energy is the combination of a classical thermo-elastic free energy, and the free energy of an affine 1D model. '

(

ρ.

Ψ,ε,εr  = )% * %& * αth  *  - *  (

/0

!"#, ε$ , %$&  =

+ 1α2th :;#⋅:;#

(