Young Stress Analyst

Competition Final

2018

Held at the BSSM 13th International Conference on

Experimental Mechanics. Grand Harbour Hotel, Southampton,

UK.

sponsored by:

Young Stress Analyst 2018The final round of the YSA2018 competition, sponsored by Airbus, will take

place as a plenary session on Thursday 30th August. To get to this stage theentrants submitted a 1000 word summary of their work. The summaries werethen sent to an expert review panel where they were marked on technical contentand clarity. The top four entrants were then selected and invited to present theirwork during the session. So congratulations to all the finalists for getting thisfar!

The finalists are asked to provide a 10 minute presentation of their work,leaving 5 minutes for questions. During the session a wider panel of judges areinvited to mark the presentations and responses to questions. All delegates areencouraged to attend the YSA competition session and all audience membersare invited to ask questions to the presenters. After the session the marks willbe collated and the results and awards will be presented during the conferencedinner.

ContentsDavid Brigido-Gonzalez - Switchable-stiffness morphing aerostructures usinggranular jamming

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Jared Van Blitterswyk - Image-based inertial impact tests for compositeinterlaminar tensile properties.

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Marissa Linne - Deformation mechanism interaction in high-purity columnarAl.

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Marta Pena-Fernandez - Preservation of bone tissue mechanics with tem-perature control for in situ SR-microCT experiments.

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Switchable-Stiffness Morphing Aerostructures using Granular Jamming

J.D. Brigido-González1a, S.G. Burrow2, and B.K.S Woods1

1,2Departament of Aerospace Engineering, University of Bristol, Senate House, Bristol, BS8 1TH, UK.

adavid.brigido@bristol.ac.uk

Abstract. One of the persistent challenges facing the development of morphing aerostructures is the need to have material and structural solutions which provide a compromise to the competing design drivers of low actuation-energy and high resistance to deformation under load. This work proposes a solution to this using a novel switchable stiffness morphing structural concept based on the principle of granular jamming. Granular jamming is a well-known phenomenon in which particulate matter will transition from a liquid-like, smoothly flowing state to a locked, rigid state upon the application of external pressure which ‘jams’ the granular particles together. This work applies this physical principle for the first time to the design of morphing aerostructures in a manner which allows the structure to have ‘switchable stiffness’ through the application of a net pressure field to the granular core of a morphing structure or skin panel. Experiments into the flexural properties of various granular media with jamming induced by applied vacuum pressure are then presented. Four-Point bending tests are used to obtain the flexural rigidity and bending stiffness of different type of grains. Following this, non-linear Finite Element Analysis simulations are presented using non-linear stress-strain curves of these materials in order to properly capture their global bending behaviour. Finally, a novel morphing aerostructure is designed, incorporating the non-linear flexural properties of the granular material, and the structure tested in bending and compared with results from non-linear Finite Element Analysis.

Introduction

Granular jamming has been applied successfully in soft robotic applications for variable stiffness mechanism, most of those applications have been designed using only the bulk behaviour of the granular material. Morphing structures can use jammed systems not only to vary stiffness but also for changing shape, this kind of properties are quite dependent of the flexural properties of the jamming behaviour. The mechanical behaviour of granular jamming materials has been studied using different kind of tests, most of those tests are based in the analyse of the bulk behaviour. Triaxial compression and shear tests are the most common. Analytic models for granular matter are well understood only for specific applications like soil mechanics (compression analysis), but the flexural properties of structure employing granular jamming are very complex to model and except for very simple cases, it is not possible to develop closed form analytical expression. Based on the granular matter as a main contributor for the understandable of the mechanics of jammed system; non-linear FEA methods are a promising option to analyse those properties in a numerical way. This material characterization work will then naturally lead into the design, construction and manufacture of an initial prototype demonstrator of a morphing airfoil employing the switchable stiffness material.

Material Characterization and Non-linear FEA

For the four-point bending test, a beam with a rectangular cross-section shape was designed using an elastic membrane and granular material as the core. The dimensions were selected based on ASTM C880/C880M21. The pressure level applied to the beam is measured by an analog sensor connected to the ball valve closure of the vacuum pump. The bending load was applied with a material test frame (Shimadzu) supplied with a 1kN load cell. To measure the displacement of the beam as well as the strains, a video extensometer (iMETRUM) was used, which works by capturing continuous images that measures the pixel distance of targets (speckle pattern). Fig. 1, shows the four-point bending test setup. The objective of the tests is to measure the flexural rigidity of the beam filled with each type of core material with the aim of obtaining the fundamental underlying non-linear stress vs -strain behavior of the granular media at different jamming pressures.

Figure 1. Four-point bending test and flexural stiffness of granular matter.

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The non-linear FEA analysis was implemented in ABAQUS. The material properties for the numerical simulation were defined assuming a Von Mises plastic material and it uses as input the non-linear strain curves taken from the four-point bending test. The results from Fig. 2, shows a good agreement between the experimental data and FEA simulations.

Figure 2. Non-linear FEA

Morphing Demonstrator

The use of different deployable control surfaces like ailerons, elevators, slats, and flaps, etc. allows for adaptation and control of aircraft in different flight environments, but increases drag aerodynamic resistance (more power required, more energy consumption and noise) due to the discontinuities of the control surface and the wing. Morphing wings can combine different control surfaces into one single surface (single shape-shifting surfaces) allowing to reduce the weight and improving the lift-to-drag relation. It highlights the redundancy and robustness to account for actuator breakdown. The FishBAC morphing wing designed by Woods [1], can integrate several control surfaces into a continuous control surface, since there are no discontinuities, the wing can be controlled by the number of cells (spines and stringers) along the span. Inspired by the example mentioned above, a new morphing concept was developed. The main objective is to increase the skills of the FishBAC concept to eliminate the discontinuities of the airfoil, and from that concept the spine and stringers were taken to create a Unit-cell (upper and lower cells). The Unit-cell was manufactured on nylon using a 3d printing. To control and vary the level of rigidity, the granular jamming stiffness mechanism is used. Fig. 3, displays the new morphing mechanism, where the upper and lower cells are full of coffee grains.

Figure 3. FishBAC Mechanism and Unit-cell design

This new morphing concept has two great characteristics. First, it has the ability to increase and vary its rigidity as a function of the vacuum (see Fig. 4), and its other feature is based on controlling the deflections of the spine using a pressure difference between the upper cell and the lower cell (see Fig. 5).

Figure 4. Variable stiffness mechanism in the Unit-cell

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Figure 5. Actuation through differential pressure and control for spine deflection. Image a) No spine deflection. Image b) Upwards deflections on the spine. c) Downwards deflections on the spine.

Finally, the Unit-cell was tested in bending tests and compared with non-linear FEA analysis (the material properties were taken from the non-linear stress-strain curves) and Euler beam theory. The results are shown in Fig. 6.

Figure 6. Non-linear FEA of the Unit-cell

Conclusion

It was demonstrated how to perform the four-point bending tests to obtain the flexural rigidity of different granular materials and thereby obtain the non-linear stress-strain curves. These curves are essential for the development of a numerical solution in FEA for a Von Mises plastic material. The results of the simulations in FEA showed a convergence with respect to the experimental values. The design of the Unit-cell based on the FishBAC as a discontinuity eliminator to reduce drag and noise uses the properties of granular jamming to show that is capable of changing shape (spine deflection) and changing rigidity up to more than 2.4 times. Finally, the experimental bending tests were compared using non-linear FEA with the same model that was used to describe the flexural behaviour of granular jamming, obtaining results in agreement between both tests.

References

[1] B.K. Woods, O. Bilgen and M.I. Friswell, Journal of Intelligent Material Systems and Structures, 2014, 25, 772-785.

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Image-Based Inertial Impact Tests for Composite Interlaminar Tensile Properties J. Van Blitterswyk1a, L. Fletcher1 and F. Pierron1

1Faculty of Engineering and the Environment, University of Southampton, UK aj.van-blitterswyk@soton.ac.uk

Abstract. In this work a novel image-based inertial impact test is proposed to measure the interlaminar tensile modulus and strength of fibre-reinforced polymer composite materials at high strain rates. Ultra-high-speed imaging is combined with full-field measurements to capture the dynamic kinematic fields and exploit the inertial effects generated under high strain rate loading. The kinematic fields are processed using the virtual fields method to reconstruct stress averages from maps of acceleration. Interlaminar stiffness and tensile strength are successfully identified at average, peak strain rates on the order 4,000 s-1. Results show an increase in stiffness of 30%, and an increase in strength of at least 100% compared to quasi-static values.

Introduction

Many composite structures are subjected to high rates of deformation (crash, blast, etc.). Under these conditions, the interlaminar properties drive the mechanical response. Unfortunately, the effect of strain rate on the interlaminar properties of fibre-reinforced polymer (FRP) composites is not currently well understood. This can be primarily attributed to limitations of existing experimental techniques, such as the Kolsky bar system. Under high strain rate loading, inertial effects induce heterogeneous kinematic fields, which violates the assumption of quasi-static equilibrium required to infer the response of the material. For low wave speed materials, this restricts achievable strain rates to below 200-300 s-1 in tension [1]. This work presents the design and experimental validation of a novel, image-based inertial impact (IBII) test. Ultra-high-speed imaging is combined with the grid method [2] and the virtual fields method (VFM) to measure interlaminar stiffness and tensile strength at strain rates not achievable with current techniques (> 1,000 s-1).

Methodology

The material used in this study is a unidirectional carbon/epoxy pre-preg (AS4-145/MTM45-1). A plate having a nominal thickness of 18 mm was used to provide a long enough specimen in the through-thickness direction for the tests to be successful. The specimen height was fixed at 12 mm to maximise the camera spatial resolution (Shimadzu HPV-X, 400 x 250 pixels). The proposed test configuration (Figure 1) is designed to indirectly load the specimen in tension through the application of a compressive pulse from a projectile traveling at speed, . The specimen is bonded to the end of a ‘waveguide’, to reduce effects from slight misalignments at impact.

(a)

(b)

Figure 1: (a) Schematic of the simulated experiment (1-3 plane specimen), and (b) experimental setup.

The waveguide length, , projectile length, , and impact speed, , were optimised using parametric simulation sweeps in ABAQUS/Explicit. Parameters were chosen such that impact induced at least 100 MPa of tensile stress and the geometry maximised the reflected stress ratio. Separate design sweeps were performed for each laminate orientation with the following experimental parameters selected for both cases:

= 10 mm, = 50 m·s-1, and = 50 mm. From equilibrium, the average axial stress, , at any position, , and time, , can be expressed as a function of the measured surface accelerations (`stress-gauge approach’ Eq. 1) [3]. (1) In Eq. 1, is the material density, the superscripts and , coupled with the overline, respectively denote the line average at , and the average surface acceleration between the free edge and . This equation was

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used to estimate the failure strength and reconstruct stress-strain curves along the length of the specimen. The average over the middle 50 % of the specimen was used to estimate for the test. Figure 2 shows the map of acceleration at failure (17 μs) and stress-strain curve at = 7.9 mm (fracture plane), for a 1-3 plane specimen.

(a)

(b)

Figure 2: (a) Map of acceleration (m·s-2) at 17 μs (failure), and (b) stress-strain curve at = 7.9 mm.

Special optimised virtual fields have also been adopted for direct stiffness identification, as developed in [4]. Simulated displacement maps were used to generate a set of deformed synthetic images. These images were processed with the same procedure as experimental images to investigate the effect of spatial and temporal smoothing on the identification of interlaminar stiffness parameters. A cost function was constructed to select the optimal smoothing parameters that minimise total error on the identifications [5].

Results and Discussion

To validate the proposed test, ten specimens were cut such that the fibres were perpendicular to the direction of impact (1-3 plane), and ten with the fibres pointing out of the image plane (2-3 plane). Measured interlaminar stiffness and tensile strength are listed in Table 1.

Table 1: Summary of measured interlaminar strength and stiffness from image-based inertial impact test Specimen Stress-Gauge Optimised VFM Quasi-Static [6] [GPa] [MPa] [GPa] [GPa] [MPa] 1-3 plane 10.4 ± 0.3 97.6 ± 16.5 10.9 ± 0.4 - 7.9 ± 0.3 28.9 - 50.3 2-3 plane 10.2 ± 0.6 107.3 ± 23.6 10.4 ± 0.6 0.45 ± 0.03

The results show good consistency in the measurement of strength and stiffness. Assigning a single strain rate value to the measured properties is challenging as the inertial effects create highly heterogeneous strain and strain rate maps. However, when axial strain is high, so too is strain rate and therefore, the peak, width-average strain rate can be considered as the limiting case for an `effective' strain rate for these measurements (on the order of 4,000 s-1). Reliable measurement of stiffness and strength at these strain rates is not possible using existing test methods. Relative to quasi-static values, the stiffness increases by approximately 30 %, and strength by at least 97 %.

Conclusions and Future Work

A novel image-based inertial impact test has been successfully designed and validated. By combining ultra-high speed, full-field measurements with the virtual fields method, the proposed approach removes many limitations associated with existing techniques and opens the way for the next generation of high strain rate tests. Simultaneous measurements on the front and back of the specimen will be the used to further develop the technique. Attempts will be made to quantify the strain rate sensitivity of stiffness by parameterisation with the virtual fields method. Moreover, the IBII test concept will be extended to combined tension and shear loading to populate a failure envelope at strain rates not achievable with current techniques.

References 1. Van Blitterswyk J., Fletcher L., Pierron P., Adv. Exp. Mech., 2:3-28, 2017. 2. Grédiac M., Sur F., Blaysat B., Strain, 52:205-243, 2016. 3. Pierron F., Zhu H., Siviour C. R., Philos. T. R. Soc. A, 372: 20130195, 2014. 4. Avril S., Grédiac M., Pierron F., Comput. Mech., 34:439-452, 2004. 5. Rossi M., Pierron F., Int. J. Solids Struct., 49:420-435, 2012. 6. ACG Inc. Materials and Process, MTM45-1/AS4-145-32%RW Laboratory Report, http://www.niar.wichita.edu/coe/NCAMP_Documents/Cytec5320-1/, Accessed: 15 Nov. 2017.

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Fig.1: In-SEM tensile stage with mounted columnar

aluminum specimen.

Deformation Mechanism Interaction in High-Purity Columnar Al

M. Linne1a

, A. Venkataraman2, M. Sangid

2, S. Daly

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1Department of Materials Science and Engineering, University of Michigan, Ann Arbor, MI 48109

2Department of Aeronautics and Astronautics, Purdue University, West Lafayette, IN 47907

3Department of Mechanical Engineering, UCSB, Santa Barbara, CA 93106

aContact: marlinne@umich.edu

Abstract.This experimental work is aimed at improving our understanding of deformation mechanism relationships, specifically those between slip transmission and grain boundary sliding, by examining mechanism-mechanism interactions in high purity oligocrystalline aluminum. Using SEM-DIC and EBSD, high-resolution displacement fields and grain orientation information are obtained. These data are analyzed using a statistical approach to identify trends in slip transmission-grain boundary sliding interactions with respect to microstructural features. In addition, experimental results are integrated with a tandem crystal plasticity model to improve simulations of damage-inducing strain localization.

Introduction

Dislocation slip and grain boundary sliding (GBS) are centrally important to the behavior of polycrystalline metallic materials, but little is known about the interactions between these mechanisms during plastic deformation, limiting our ability to accurately model and predict deformation behavior. This research is aimed towards understanding the relationship between GBS and dislocation slip in oligocrystalline aluminum. It is hypothesized that a synergistic relationship exists between these mechanisms. This claim is supported by the fact that increasing shear stress on a grain boundary (GB) simultaneously enables GBS and decreases the energy barrier for slip transmission through the boundary [1]. However, current research and modeling of polycrystalline plasticity largely treats deformation mechanisms as separate events. Thus, the relationships between them – whether collaborative or competitive, simultaneous or sequential – remain unclear and supported by limited experimental data. These ambiguities lead to inaccuracies in material modeling, and consequently a failure to optimize material design. This experimental investigation is aimed towards improving predictions of damage-inducing stress localization, and ultimately towards improving the capability to develop materials with greater resistance to failure.

The specific aims of this research are to (1) quantitatively characterize deformation behavior across grain boundaries across large (mm-scale) fields of view, with very high spatial resolution, providing local detail around the boundary as well as information on long-range interactions in the material; (2) explore the temperature dependence of these mechanisms to further probe mechanism interaction for high temperature applications; (3) achieve the above aims with the development of new experimental methodologies for mechanical testing and acquiring full-field deformation and microstructure data; (4) use full-field deformation and microstructure data to inform a parallel crystal plasticity model (Sangid Group) and to provide statistical insight for improving predictions of damage-inducing strain localizations.

Experimental Approach

The two main experimental steps in this approach are (1) Grain Orientation Maps: acquire full gage grain orientation maps using electron backscatter diffraction (EBSD), (2) Strain Fields: acquire high resolution full-gage strain fields from tensile loading using in-SEM digital image correlation (SEM-DIC). Columnar, high-purity (99.999%) aluminum was chosen as a model material because, in addition to its significance in structural light-weighting applications, it has a fcc crystal structure and a high stacking fault energy, reducing deformation complexity with only 12 slip systems and minimal twinning. High-purity (5N) Al was used to examine grain boundary-dislocation interactions without impurities affecting these deformation mechanisms. Because the specimen are oligocrystalline, the full specimen microstructure can be characterized with EBSD without subsurface ambiguity. Due to their high purity, oligocrystalline microstructure and 1 x 5 mm gage size, these samples are extremely delicate but allow collection of a very modelable and unique full-gage data set.

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Fig.2: Example of full-field strain data measured experimentally using in-SEM digital image correlation: (a) full gage εxx strain field

measured from a columnar Al specimen at 5.0 % strain, (b) subset shows the high resolution of the strain data, with individual slip traces

resolved, (c) displacement tangent to the grain boundary highlights relative displacement between grains and magnitude of grain

boundary sliding. This high resolution DIC data set enables measurement of relative contributions of grain boundary sliding and

dislocation slip and how these contributions change with microstructural neighborhood.

Specimen Preparation and EBSD. Specimen were cut from high purity sheets with thicknesses of either 0.25 or 0.5 mm, by wire electro-discharge machining. To achieve a through-thickness grain structure, all specimens were annealed at 550°C in an argon atmosphere for 6 hours. Both sides of the aluminum specimen were polished to a mirror finish using mechanical polishing and full-gage grain orientation maps were acquired from the front and back gage surfaces using EBSD. One side of the specimen was patterned for SEM-DIC with 300 nm diameter gold nanoparticles (Sigma-Aldrich), using a surface silanization technique similar to that described by Kammers et. al. [2].

SEM-DIC. Uniaxial tensile tests were performed at both room (24°C) and elevated (190°C) temperatures. It is expected that at this elevated temperature, enhanced diffusion increases the relative contribution of GBS to the sample deformation, compared to the room temperature case. Comparing deformation behavior between these two cases provides insight into GBS-slip mechanisms dependencies. In both tests, specimen straining is performed using a tension-compression module (Kammrath and Weiss), seen in Fig. 1, and SEM-DIC images are collected in an array that encompasses the entire specimen gage at progressive strain increments using a Teneo field-emission SEM (FEI). At room temperature, images were captured in-situ. In the elevated temperature case, the specimen is heated and strained in atmosphere and SEM-DIC images were collected ex-situ after unloading and cooling. The room temperature strain fields reflect the combined elastic and plastic deformation, and the elevated temperature test strain fields reflect the plastic deformation. SEM distortions were corrected and strain/displacement fields were stitched using custom-developed MATLAB codes.

Results and Future Work The resulting strain fields and grain orientation maps comprise an information-rich data set. Each strain field has ~ 10

6 data points, each point associated with several hundred points of local microstructure and

deformation information, all of which evolve in time. An example of a full-gage strain field, obtained from room temperature in-situ straining, overlaid with EBSD-identified grain boundaries, is seen in Fig.2. Inset (b) of Fig.2 (lower-left) highlights the high spatial resolution of the strain data; individual slip traces and slip transmission events are resolved. With grain orientation data, the slip systems involved in slip transmission events can be identified. A statistical analysis using a custom-developed MATLAB code was used to identify instances of slip transmission and GBS and correlate to underlying microstructure characteristics. In addition to statistical analysis, these experimental data are used to inform a GBS-sensitive CPFE model in collaboration with the Sangid Group (Purdue). Deformation trends discerned with these experimental and computational approaches will provide insight into the currently limited understanding of plastic deformation and deformation mechanisms relationships. This information will help to improve capabilities to model and predict damage-inducing strain localization and

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design materials structural components with greater resistance to failure.

References

[1] M.D.Sangid, private correspondence, [2015]. [2] Kammers, A. Daly, S. Self-Assembled Nanoparticles Surface Patterning for Improved Digital Image Correlation in Scanning Electron

Microscope. Exp Mech 53 (8) [2013].

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Preservation of bone tissue mechanics with temperature control for in situ SR-microCT experiments

Marta Peña Fernández1a, Alexander Kao1, Katerina Karali1, Andrew J Bodey2, Enrico Dall’Ara3, Gordon

Blunn1, Asa H Barber1 and Gianluca Tozzi1

1. University of Portsmouth, UK; 2. Diamond Light Source, UK; 3. University of Sheffield, UK;

amarta.pena-fernandez@port.ac.uk

Introduction

Digital volume correlation (DVC) combined with in situ synchrotron micro-computed tomography (SR-microCT)

is increasingly gaining popularity for quantification of full-field strain distribution in bone , notably enhancing

the understanding of bone failure mechanisms [1]. Nevertheless, it was reported how long exposures to SR X-

ray radiation leads to deterioration of the mechanical properties of bone as a consequence of collagen matrix

degradation [2]. In fact, radiation produces reactive free radicals by the radiolysis of water, causing the

destruction of collagen alpha chains. Also, whether temperature gradients play a role in the tissue degradation

process is still unclear. Lowering temperature is beneficial as reduces the mobility of water molecules and

therefore, it decreases the production of free radicals, protecting the mechanical properties of bone tissue [3].

However, to date experimental protocols for in situ SR-microCT mechanics able to preserve tissue properties

are still missing and, although recent progress has been made [4]. The aim of this study is to propose a proof-

of-concept methodology to retain bone tissue integrity based on residual strain determination via DVC as a

result of decreasing the environmental temperature during in situ SR-microCT testing.

Experimental procedure

Cylindrical samples of compact bone (D=4mm, L=8mm, N=2) and trabecular bone (D=6mm, L=12mm, N=2) were cored from bovine proximal femur. Specimens were immersed in saline solution during image acquisition within a loading stage (CT5000, Deben, UK) equipped with an environmental chamber and temperature control. SR-microCT images were acquired at the beamline I13-2 at Diamond Light Source (DLS), UK, using a filtered polychromatic pink beam and a pco.edge 5.5 detector. The effective voxel size was 0.81 µm, with a field of view of 2.1 x 1.8 mm. Tomographic datasets were obtained using an exposure time of 512 ms per projection, and 1801 projections were taken over 180 degrees, resulting in an absorbed radiation dose of ~35 kGy per scan [4]. Image reconstruction was performed at DLS, using the in-house reconstruction pipeline Savu [5]. The reconstructed 3D images were filtered and masked (Fig. 1) prior to DVC analysis.

Half of the samples were imaged at room temperature (21-23°C), and the other half at 0°C, to assess the influence of the environmental temperature on the tissue damage. Temperature readings were processed via thermocouples immersed in the saline solution attached to the surface of to the bone sample and were used to investigate possible temperature gradients during image acquisition (i.e. opening/closing of the shutter). Each specimen underwent five full consecutive tomographies (zero-strain) after applying a small preload (~5N) to minimize movement artefacts. DVC (DaVis 10, LaVision, Germany) was carried out to evaluate the residual strain in the tissue due to progressive damage induced by X-ray exposure during SR-microCT imaging at different temperatures.

Figure 1. Three-dimensional (3D) SR-microCT reconstruction of trabecular (a) and cortical (b) bone and corresponding two-dimensional (2D) slices through the middle of the volume in trabecular (c) and cortical (d) bone specimens.

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Results

A visual inspection of the reconstructed tomograms showed the presence of several microcracks after five tomograms, corresponding to ~80 min of total exposure to SR radiation, in the trabecular bone tissue at room temperature (Fig. 2-I-a,b). However, decreasing the temperature to 0°C facilitated tissue preservation, as microcracks were not observed (Fig. 2-II-a,b). Furthermore, DVC successfully correlated visual microdamage on the bone with important levels of residual strain (Fig. 2-I-d).

Figure 2. SR-microCT cross-sections (top row) through the trabecular bone specimens imaged at room temperature (I) and 0°C (II) for the second (a) and fifth (b) acquired tomograms. Maximum principal strian (εp1) in the bone tissue (bottom row) computed using DVC indicated higher residual strains after five tomograms (d) compared to after two tomograms (c).

Microcracks (white arrows) were correlated to high levels of strain (I-d).

The full-field strain distributions (maximum principal strain) for the trabecular bone specimens at room temperature and 0°C are reported in Figure 3. An increase of the residual strains was observed when increasing the total exposure to SR radiation from 30 min (two full tomograms, Fig. 3-I) to 75 min (five full tomograms, Fig. 3-II). This effect was more pronounced for the specimen imaged at room temperature. The histograms for the principal strain (Fig. 3-III) captured the residual strain evolution during the five acquired

tomograms. Peak strain values increased from ~ 1500 µε to ~3000 µε after two and five consecutive scans in

the specimen at room temperature. However, imaging the specimens at 0°C kept peak strain values below

1000 µε.

Figure 3. 3D maximum principal strains (εp1) in trabecular bone tissue imaged at room temperature (top) and 0°C (bottom) for the second (I) and fifth (II) acquired tomograms. Histograms of the residual strain distribution (III) in the bone tissue after each acquired tomogram are shown. 16

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No damage was visually detected in cortical bone tissue after five tomograms, either at room temperature or 0°C. Additionnaly, the residual strain distribution (Fig. 4) did not show notable changes after two (Fig. 4-I) and five (Fig. 4-II) acquired tomograns, with some localised areas of higher residual strains in the specimen imaged at room temperature. The histograms of the maximum principal strian showed peak strain values below 1000 µε for both specimens, and no relationships were observed between exposure time and peak strian values.

Figure 4. 3D maximum principal strains (εp1) in cortcial bone tissue imaged at room temperature (top) and 0°C (bottom) for the second (I) and fifth (II) acquired tomograms. Histograms of the residual strain distribution (III) in the bone tissue after each acquired tomogram are shown.

Temperature readings from thermocouple attached to the surface of a cortical bone sample seems to suggest

a consistent increase of temperature (ΔT=~0.4°C) at each exposure period (Fig. 5) corresponding to the

opening (rise in temperature) and closing (drop in temperature) of the shutter. Small fluctuations in the

temperature were recorded once the X-ray shutter was open, more evident once the loading stage was rotating

compared to a steady position. However, those fluctuations were far less important.

Figure 5. Temperature reading from thermocouple attached to the surface of bone sample. Saline solution surrounding the sample was at room temperature. Shutter open and thermocouple in the FOV during ~15min (blue) and one tomographic acquisition (orange) after closing/opening the shutter.

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Discussion

This proof-of-concept experiment enables important understanding on the damage induced by SR X-ray exposure and the effect of heat generation on the bone tissue. This, reducing the temperature seemed to importantly reduce the microdamage and residual strains in trabecular bone specimens (Fig. 3). However, minimal effect was observed for the cortical bone samples (Fig. 4). Despite the overall change of temperature during image acquisition was minimal, the prolonged effect in time may be sufficient to induce localized collagen dehydration and subsequent damage [6]. Several studies [3], [7], [8] have reported the possibility that the temperature during irradiation plays a critical role in protection against SR-radiation damage, translating the approach to clinical practice when sterilizing bone grafts in order to preserve the osteoinductive capacity and mechanical properties.

This study showed that lowering the environmental temperature to only 0°C has a positive effect on tissue preservation, although specimens were maintained far below the physiological temperature. It could be argued that the mechanical properties of the bone tissue could be altered, although freeze-thaw cycles have been shown not to alter its biomechanical properties [9], [10]. Future work is mandatory to establish protocols for the application of SR-microCT to in situ mechanics of bone and potentially extend the knowledge to other biological tissues in order to minimise SR-induced damage.

References

[1] R. Voide et al., “Time-lapsed assessment of microcrack initiation and propagation in murine cortical bone at submicrometer resolution,” Bone, vol. 45, no. 2, pp. 164–173, 2009.

[2] H. D. Barth, M. E. Launey, A. A. MacDowell, J. W. Ager, and R. O. Ritchie, “On the effect of X-ray irradiation on the deformation and fracture behavior of human cortical bone,” Bone, vol. 46, no. 6, pp. 1475–1485, 2010.

[3] A. J. Hamer, I. Stockley, and R. A. Elson, “Changes in allograft bone irradiated at different temperatures,” J Bone Jt. Surg, vol. 81, pp. 342–4, 1999.

[4] M. Peña-Fernández et al., “Effect of SR-microCT exposure time on the mechanical integrity of trabecular bone using in situ mechanical testing and digital volume correlation,” J. Mech. Behav. Biomed. Mater., Under review.

[5] R. C. Atwood, A. J. Bodey, S. W. T. Price, M. Basham, and M. Drakopoulos, “A high-throughput system for high-quality tomographic reconstruction of large datasets at Diamond Light Source,” Philos. Trans. R. Soc. A Math. Phys. Eng. Sci., vol. 373, no. 2043, 2015.

[6] O. S. Rabotyagova, P. Cebe, and D. L. Kaplan, “Collagen structural hierarchy and susceptibility to degradation by ultraviolet radiation,” Mater. Sci. Eng. C, vol. 28, no. 8, pp. 1420–1429, 2008.

[7] A. Dziedzic-Goclawska, K. Ostrowski, W. Stachowicz, J. Michalik, and W. Grzesik, “Effect of radiation sterilization on the osteoinductive properties and the rate of remodeling of bone implants preserved by lyophilization and deep-freezing,” Clin. Orthop. Relat. Res., no. 272, p. 30—37, Nov. 1991.

[8] U. Antebi, M. B. Mathor, A. F. da Silva, R. P. Guimarães, and E. K. Honda, “Effects of ionizing radiation on proteins in lyophilized or frozen demineralized human bone,” Rev. Bras. Ortop. (English Ed., vol. 51, no. 2, pp. 224–230, 2016.

[9] H.-J. Jung et al., “The effects of multiple freeze-thaw cycles on the biomechanical properties of the human bone-patellar tendon-bone allograft,” J. Orthop. Res., vol. 29, no. 8, pp. 1193–1198, 2011.

[10] F. Linde and H. C. F. Sørensen, “The effect of different storage methods on the mechanical properties of trabecular bone,” J. Biomech., vol. 26, no. 10, pp. 1249–1252, 1993.

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