ImageBased Inertial Impact Test for Composite Interlaminar Tensile Properties
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Abstract
In this work an imagebased inertial impact test is proposed to measure the interlaminar tensile stiffness and strength of fibrereinforced polymer composite materials at high strain rates. The principle is to combine ultrahighspeed imaging and fullfield 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. In this way, the specimen acts like a dynamic load cell, with no gripping or external force measurement required. Stress averages are combined with strain measurements to construct stress–strain curves and identify the interlaminar stiffness and tensile strength. Special optimised virtual fields are also implemented to identify interlaminar stiffness parameters from complete maps of strain and acceleration. Interlaminar stiffness and tensile strength are successfully identified at average, peak strain rates on the order 3500 s\(^{1}\) and 5000 s\(^{1}\), respectively. Results show an increase in stiffness between 30 and 35%, and an increase in strength of 125% compared to quasistatic values.
Keywords
High strain rate Interlaminar tension Fibrereinforced polymer composites Dynamic test methods Ultrahigh speed imaging Virtual Fields MethodIntroduction
There are many engineering applications where fibrereinforced polymer (FRP) composite structures are subjected to dynamic loading (e.g., impact, blast, crash, etc.). In order to develop useful numerical simulations for composite structures subjected to these loading cases, a thorough understanding of the constitutive behaviour over a wide range of strain rates must first be established. Since interlaminar properties are matrixdominated, literature suggests that the interlaminar stiffness and strength should exhibit a strain rate dependency [1, 2]. However, the number of studies attempting to measure high strain rate properties in the interlaminar direction are relatively scarce and inconsistent [2].
Studies on the strain rate dependency of interlaminar tensile properties are comparatively fewer compared to compression and shear. The effect of strain rate is not well understood, as exemplified by highly scattered measurements in available studies [2]. For example, measured changes in stiffness for glass/epoxy woven composites range from + 10% at 125 s\(^{1}\) [3], to + 500% at 400 s\(^{1}\) [4], and − 15% at 950 s\(^{1}\) [5], compared to quasistatic values. A similar situation exists for tensile strength measurements at high strain rates. Most studies report moderate increases in strength of around 30% compared to quasistatic values [3, 5], while others report much more significant increases of up to several hundred percent [6, 7, 8]. Therefore, much ambiguity remains regarding the effect of strain rate on interlaminar stiffness and tensile strength. Some of the inconsistency in the literature stems from variations in material composition (fibre and matrix materials, fibre volume fraction, reinforcement architecture). Additionally, scatter is likely amplified by other factors complicating tensile tests, such as gripping, alignment and geometry (stress concentrations).
Limitations of the SplitHopkinson pressure bar (SHPB) technique are thought to be the primary source of inconsistency in measurements above 200–300 s\(^{1}\). At such strain rates, inertial effects violate the necessary assumption that the specimen is in a state of quasistatic equilibrium. As a result, measurements of strain on the input and output bars cannot be used to directly infer the stress–state in the material until specimen acceleration dampens out. The low wave speed and small ultimate strain typical of composite materials in the throughthickness direction means that a state of quasistatic equilibrium may not be achieved before failure occurs. The lower wave speed also tends to reduce the signaltonoise ratio of the material response transmitted to the output bar [1, 9]. Even if inertial effects dampen out prior to failure, it is generally agreed that the SHPB cannot produce reliable measures of the material stiffness [10, 11, 12, 13].
More recently, fullfield measurement techniques, combined with ultrahighspeed imaging, have shown to be a promising alternative for high strain rate testing. Ultrahighspeed imaging refers to framing rates upwards of 1 Mfps, according to [14]. Having access to dynamic fullfield measurements of displacement alleviates some of the fundamental assumptions attached to test methods such as the SHPB. Specifically, the Virtual Fields Method (VFM) can be used to process dynamic maps of acceleration to exploit the inertial, heterogeneous deformation and reconstruct stressaverages in the material. Moulart et al. [15] showed that acceleration could be used in practice to identify stiffness parameters at high strain rates. The ‘ImageBased Inertial Impact’ (IBII) test first emerged from the study by Pierron and Forquin [16], and was later formalised in [17]. The concept of using acceleration to reconstruct stressaverages and identify constitutive material properties has since been successfully demonstrated in a number of experimental studies [16, 17, 18, 19, 20, 21, 22, 23, 24, 25].
This work presents an extension of the IBII test method to measure the interlaminar stiffness and tensile strength of a unidirectional, carbon/epoxy composite. Both interlaminar material planes are considered (1–3 and 2–3). The IBII test is advantageous as it eliminates the need to grip the specimen or measure force externally; both of which are particularly problematic for testing interlaminar specimens in tension. This paper will begin by describing the test concept and design approach in Sect. 2. A parametric finite element model is used to design the experimental parameters (e.g., projectile length and impact velocity) in Sect. 3. In Sect. 4 the displacement fields from the finite element model are used to synthetically deform images. These images are used to systematically optimise the postprocessing parameters and estimate the error on identified stiffness parameters. A description of the experimental setup is presented in Sect. 5. Experimental results are presented and discussed in Sect. 6. Finally, the limitations of the proposed test, and future developments for the work are discussed in Sect. 7.
ImageBased Inertial Impact (IBII) Test Concept and Design
The Virtual Fields Method (VFM)
The VFM is used to directly identify constitutive properties from fullfield measurements of strain and acceleration. The specific application of the VFM to the IBII test is outlined in [20] and therefore, only the specific aspects that apply to the interlaminar test are included here. The reader is referred to [26] for a comprehensive description of the VFM.
Stiffness Identification
Special Optimised Virtual Fields An infinite number of virtual kinematic fields can be selected to use Eqs. (2) and (3). If strain and acceleration fields are exact, all virtual fields will provide the same identification. In practice, measurements inevitably contain noise and therefore, each set of virtual fields will provide different identifications. If one selects the virtual fields intuitively, it is impossible to ensure that the chosen ones are optimal. Special optimised virtual fields are adopted here, as developed in [27]. This procedure automates the selection of virtual fields for direct identification of stiffness parameters, such that the sensitivity to strain noise is minimised. For the 1–3 plane, the uniaxial virtual displacement field results in the direct identification of \(E_{33}\). For the 2–3 plane, the isotropic, special optimised virtual field procedure is used to directly identify \(Q_{33}\) and \(Q_{23}\) [17]. From the identified stiffness parameters, one can calculate \(\nu _{23}\) (\(\nu _{23} = Q_{23}/Q_{33}\)) and \(E_{33}\) (\(E_{33} = Q_{33}(1\nu _{23}^{2})\)). This is performed at each time step over the whole field. Full details on the implementation of special optimised virtual fields are described in [26].
Strength Identification
An additional, posthoc way to reconstruct stress is to use the identified stiffness parameters to convert strain maps to stress maps. Divergence of the different stress measures (from acceleration and from strain) provides information about the damage process, indicating when the assumptions of the constitutive law break down (i.e., plasticity, damage, failure, etc.). This can also be used to validate the constant and linear approximations for the stress field as reconstructed with the stressgauge equations.
Numerical Design and Optimisation
The following section describes the implementation of the numerical simulations and parametric design sweeps to select test parameters.
Model Configuration and Parametric Design Sweep
There are some important differences between the test design for interlaminar and inplane properties. For direct imaging of the specimen, the geometry of an interlaminar test specimen is dependent on the thickness of the laminate. In this work, a thicker laminate (18 mm) is considered for practical reasons. Specifically, this enables platelike specimen to be machined and accurate grids to be deposited for fullfield measurement purposes. To maximise measurement spatial resolution, a smaller grid pitch is required (on the order of 0.3 mm compared to 0.9 mm in [20]). With a smaller length compared to the transverse tension specimens, the wave transit time is also shortened. This requires a higher framing rate to ensure sufficient temporal resolution of the kinematic fields (the Shimadzu HPVX camera allows for frame rates up to 5 Mfps at full resolution).
Separate design sweeps were performed for each interlaminar plane. The length of specimens from both material planes was fixed at the nominal plate thickness of 18 mm. A height of 12 mm was selected to maximise the spatial resolution of the camera (Shimadzu HPVX, 400 \(\times\) 250 pixels), including approximately 2 mm at the free edge of the specimen to account for rigid body motion. The material used in this study is a unidirectional carbon/epoxy composite, AS4145/MTM451. The properties of this material were characterised by the National Center for Advanced Material Performance (NCAMP) as summarised in [28]. Unfortunately, only quasistatic interlaminar tensile strength was measured in that campaign (\(\sigma _{T}^{ult}\) = 50.4 MPa). Therefore, for test design it was assumed that reported values for the inplane transverse Young’s modulus, shear modulus, and Poisson’s ratio were representative of that for the interlaminar planes. The quasistatic, inplane transverse compressive strength (\(\sigma _{C}^{ult} \approx\) 290 MPa) was assumed as a conservative limit for allowable compressive stress. To the authors’ knowledge, the high strain rate properties for this material have not been measured. Therefore, it was also assumed that the material strength will exhibit a similar strain rate sensitivity to that reported in [20] measured using the same IBII test (+ 57% increase in strength at strain rates on the order of 2000 s\(^{1}\)). Even though reference [20] focussed on the inplane transverse properties, the reported strain rate sensitivity was expected to be reasonably representative of the interlaminar behaviour as a matrix dominated property. Therefore, the interlaminar tensile strength at high strain rates is estimated to be 80 MPa. For the IBII interlaminar test the design space is defined by the tensile and compressive strengths as: − 290 MPa \(< \overline{\sigma _{xx}}^{y}<\) 80 MPa.
Summary of simulated values used in parametric sweep for test design
Parameter  Min  Max  Increment 

Projectile length, \(L_P\) (mm)  2.5  20  2.5 (\(L_P \le\) 5) 5 (\(L_P \ge\) 5) 
Impact speed, \(V_P\) (\({\text{m}}\,{\text{s}}^{1}\))  20  50  10 
The sabot length was variable such that the total length of projectilesabot assembly was a constant 50 mm. A maximum projectile length of 20 mm was set to avoid creating an input pulse length that exceeds the specimen length. This would result in a superposition of the input and reflected waves, reducing the maximum tensile stress in the specimen. Since the waveguide and projectile are made of the same material, the waveguide length must be at least twice the length of the projectile to avoid clipping the pulse. Therefore, the waveguide length, \(L_{WG}\), is fixed at 50 mm.
Finite Element Implementation
Simulation parameters and material properties for the interlaminar tension IBII test
Specimen (AS4145/MTM451)  
\(E_{11}\) (GPa)  129\(^{\mathrm{{a}}*}\) 
\(E_{22}\) (GPa)  7.9\(^{\mathrm{{a}}*}\) 
\(E_{33}\) (GPa)  7.9\(^{\mathrm{{a}}*}\) 
\(G_{13}\) (GPa)  3.65\(^{\mathrm{{a}}**}\) 
\(G_{23}\) (GPa)  3.65\(^{\mathrm{{a}}**}\) 
\(\nu _{13}\)  0.015\(^{\mathrm{{a}}}\) 
\(\nu _{23}\)  0.225\(^{\mathrm{{a}}}\) 
Specimen length (mm)  18 
Specimen height (mm)  12 
\(\rho\) (\({\text{kg}}\,{\text{m}}^{3}\))  1605\(^{\mathrm{{b}}}\) 
Mesh size (mm)  0.1 
Waveguide and projectile (aluminium 6061T6)  
E (GPa)  70 
\(\nu\)  0.3 
\(\rho\) (\({\text{kg}}\,{\text{m}}^{3}\))  2700 
Waveguide length (mm)  50 
Waveguide height (mm)  25 
Projectile height (mm)  25 
Mesh size (mm)  0.2 
Sabot (nylon 6–6)  
E (GPa)  3.45 
\(\nu\)  0.4 
\(\rho\) (\({\text{kg}}\,{\text{m}}^{3}\))  1140 
Sabot length (mm)  50 
Sabot height (mm)  25 
Mesh size (mm)  0.2 
Parametric Sweep Results
Material and Experimental Setup
Specimen Manufacturing
Material properties of AS4145/MTM451 are provided in Table 2. The density of the plate was measured using a micro balance and water immersion to be 1605 ± 20 \({\text{kg}}\,{\text{m}}^{3}\). The plate had an average measured cured thickness of 17.9 mm (est. 128 layers, 0.14 mm cured ply thickness [28]). Twenty interlaminar specimens were cut (10 \(\times\) 1–3 material plane and 10 \(\times\) 2–3 material plane). The specimens were first rough cut from the plate using a large tile saw with a diamond cutting wheel. The specimen faces were then cut using a Streurs E0D15 diamond saw. The automated stage was set to a low feed rate of 0.1 m\({\text{m}}\,{\text{s}}^{1}\) to reduce the likelihood of inducing machining defects. For the 1–3 plane, specimen dimensions (L \(\times\) H \(\times\) e) were measured to be 17.9 mm \(\times\) 12.1 mm \(\times\) 2.6 mm (SD ±0.2 mm, ±0.2 mm, ±0.6 mm). Similarly, 2–3 plane specimen dimensions were measured to be 18.2 mm \(\times\) 12.0 mm \(\times\) 2.6 mm (SD ±0.1 mm, ±0.3 mm, ±0.4 mm). Note that reported thickness measurements include the grid deposited on the surface.
Grid Deposition Techniques
Grids with a pitch p of 0.3 mm were bonded to ten specimens (5 for each interlaminar plane), using the process outlined in [29]. The epoxy layer had a typical thickness of approximately 225 \(\upmu\)m. While this deposition procedure worked quite well in [20] for inplane specimens, the smaller specimens in this study were more susceptible to grid defects from air bubbles in the underlying resin layer. Since grid defects are detrimental to the inverse identification procedures, a second grid deposition process was explored for the remaining ten specimens (5 for each interlaminar plane). A thin coat of white rubber paint (RustOleum Peel Coat) was first applied to the specimen. The paint layer had a typical thickness of approximately 20 \(\upmu\)m. A series of black squares were then printed onto the painted surface with a Canon Océ Arizona 1260 XT flat bed printer. This formed a white grid with an average pitch of 0.337 mm. Trial prints of uniform grids were found to contain periodic defects every 80 mm in the horizontal direction. This was used to define the true print resolution and adjust the grid pitch when printing on specimens. As grids were defined according to a constant ‘pointsperpitch’ ratio (6:7 (x:y) closely matches that of the true resolution), the actual pitch in the vertical and horizontal directions is 0.338 mm and 0.336 mm, respectively. More information is available online [30, 31]. This required processing of the grid images using the iterative procedure described in [32]. The limited printer resolution reduces the spatial resolution compared to the bonded grids. However, this was a manageable compromise given the simplicity of the deposition process and significant reduction in grid defects.
Specimen Naming Convention
Specimens will be referred here by specimen number followed by a dash and a letter specifying the grid type; ‘P’ denotes a printed grid (p = 0.337 mm), and ‘B’ denotes a bonded grid (p = 0.3 mm), respectively. The interlaminar plane is specified in square brackets. For example, specimen #1 from the 1–3 plane with a 0.337 mm printed grid pitch is referred to as: ‘#1P[1–3]’.
Experimental Setup
Imaging and measurement performance for the IBII tests with the grid method
Optical setup  
Camera  Shimadzu HPVX 
Pixel array size  400 \(\times\) 250 
Sensor  FTCMOS 
Interframe time  0.2 \(\upmu\)s 
Integration (shutter) time  110 ns 
Number of images  128 
Lens  Sigma 105 mm 
Flash  Bowens Gemini 1000 Pro 
Grid method  
Grid pitch (mm)  0.3, 0.337 
Sampling (pixels/period)  6, 7 
Field of view (mm)  20 \(\times\) 12.5, 19.25 \(\times\) 12.04 
Displacement computation  Iterative [32] 
Image Processing and Identification of Material Properties
Obtaining Displacement Fields from Deformed Grid Images
The Shimadzu HPVX camera is used to collect a set of deformed grid images. These grid images are processed using the grid method to obtain phase maps, using a windowed discrete Fourier transform. For the bonded grids only, the phase maps were corrected for air bubble defects using a threestep procedure. (1) Each \(\phi _{x}\) phase map was fitted with a mesh of linear finite elements (8 \(\times\) 5 elements (x,y)) to capture gradients in the phase fields. The phase values at the nodal positions were determined using a leastsquares regression fit and linear shape functions were used to interpolate the phase within each element. The regression plane fit was then subtracted from the raw phase field to obtain a map of residuals. Grid defects were first characterised by regions with phases values exceeding a 2\(\sigma\) threshold on the residual. (2) A second linear regression plane fitting was performed to the phase maps, with the defects identified in (1) removed. The full extent of the defect was characterised by again using a 2\(\sigma\) threshold. These defect maps were then used to remove defects in the \(\phi _{y}\) maps. (3) A sliding square window of seven pitches in length was used to linearly interpolate the phase information over the defective regions identified in (2). The displacement fields were then computed from the ‘corrected’ phase maps using the iterative approach described in [32]. The iterative approach accounts for initial phase modulations in the grid (e.g., remaining small grid defects, slight grid spacing irregularities). The phase maps contain discontinuous jumps when the grid displaces more than one pitch. These jumps were corrected using spatial and temporal unwrapping. Spatial unwrapping was performed using the procedure described in [34]. Temporal unwrapping was performed using an inhouse MATLAB routine. In this procedure, the spatial mean of the unwrapped phase is plotted against time and the 2\(\pi\) mean phase jumps in time are corrected to obtain a monotonic increase of the longitudinal displacement representative of the rigid body translation in the impact direction.
Obtaining Strain and Acceleration Fields
One pitch of information is corrupted on the border of the phase maps due to edge effects from the windowed Fourier transform. Rather than discarding this data, previous studies have shown that identifications using the virtual fields method were drastically improved when this data was recovered using some sort of extrapolation [35, 36]. In this work, the corrupted displacement data was replaced using a linear regression fitting based on the data over one pitch (6 pixels (0.3 mm grids) or 7 pixels (0.337 mm grids)) inwards from the corrupted region. The extrapolation was performed independently for each row of pixels (\(u_{x}\) fields), or column of pixels (\(u_{y}\) fields). This approach was found to be better at rejecting noise compared to the approach in [20], where data was recovered using a linear extrapolation based on two points inward from the corrupted region. The displacement maps were then processed in two ways to obtain acceleration and strain fields (Fig. 5). Displacement maps were smoothed temporally using a third order Savitsky–Golay filter, and then differentiated twice in time to obtain acceleration maps. Displacement fields were padded in time by one half of the kernel size (in frames) to minimise edge effects from the filter. Raw displacement maps were also smoothed spatially, using a Gaussian filter, before differentiating to obtain strain maps. Both temporal and spatial differentiations were computed using a central difference. Strain rate maps were computed from the smoothed strain maps using a central difference, except for computing strain rate at fracture, which was performed using a backward difference based on the raw strain maps to avoid temporal leakage from unrealistic strains computed after crack initiation. To reduce edge effects from spatial smoothing, the displacement fields were first padded out by 3 smoothing kernels using a linear extrapolation. The fields were smoothed and then cropped back to the original size. The details of the corrections and smoothing can be consulted in the Matlab program provided as supplementary material with this article.
Identifying Material Properties from Kinematic Fields
The special optimised virtual fields methods presented in Sect. 2.1 were used to process acceleration and strain fields to identify stiffness parameters. Material properties were identified from acceleration and strain maps using two VFM approaches: (1) using special optimised virtual fields, and (2) using reconstructed stress averages to compute stress–strain curves at each position along the specimen length.
Special Optimised Virtual Fields The special optimised virtual fields approach provides an identification of each stiffness parameter for each time step. For 1–3 plane specimens, the reduced approach was used to process \(a_{x}\) and \(\epsilon _{xx}\) fields to directly identify \(E_{33}\). For 2–3 plane specimens, the \(a_{y}\), \(\epsilon _{yy}\) and \(\epsilon _{xy}\) fields were also included in the general isotropic formulation of the special optimised virtual fields approach. In this case, \(Q_{33}\) and \(Q_{23}\) were identified, from which \(E_{33}\) and \(\nu _{23}\) were determined. The value of each identified stiffness parameter for the test was taken as the average over all time steps where the identification is stable. The identification is generally poor during the first few frames of the test due to low strains as the wave enters the specimen. Stability is also challenged as the wave reflects from the freeedge, as the incoming and reflected waves superimpose, resulting in temporary low strain and acceleration signal. When the material cracks in tension, nonphysical strains corrupt the identification. Therefore, optimal conditions for identification (high strain and acceleration signal) generally occurs during the first compressive loading after the stress wave has entered the specimen, but before it reflects at the free edge. The optimized virtual fields were expanded using a basis of piecewise functions (finite elements), as proposed initially in [37]. A virtual mesh refinement study was performed on the image deformation data (described in Sect. 5) and the results showed that the identification converged at a virtual mesh of 5 \(\times\) 1 elements (x,y) and 5 \(\times\) 4 elements (x,y) for the reduced and isotropic special optimised routines, respectively. Data is discarded within one pitch plus one spatial smoothing kernel at the impact edge to reduce smoothing filter edge effects on the identification.
Reconstructed Stress–Strain Curves Here, the stressgauge equation (Eq. 4) was used to calculate stress averages (\(\overline{\sigma _{xx}}^{y}\)) from \(a_{x}\) fields for all specimens. Using these stress averages, combined with axial strain (\(\overline{\epsilon _{xx}}^{y}\) for 1–3 plane specimens, and \(\overline{\epsilon _{xx}+\nu _{23}\epsilon _{yy}}^{y}\) for 2–3 plane specimens), stress–strain curves were generated along the length of the specimen. For the case of 2–3 plane specimens, the identified value of \(\nu _{23}\) from the special optimised virtual fields procedure was used. The interlaminar stiffness (\(E_{33}\) for 1–3 plane specimens, and \(Q_{33}\) for 2–3 plane specimens) was identified using a linear regression fit to the stress–strain curve up to the maximum compressive stress. This is henceforth referred to as the ‘stress–strain curve’ approach. \(E_{33}\) was calculated for 2–3 plane specimens using the identified value of \(\nu _{23}\) from the special optimised virtual fields approach. The identification of \(E_{33}\) tends to be poor near the free and impact edges due to extrapolated data at the edges of the specimen, and edge effects from spatial smoothing. Therefore, the value of \(E_{33}\) for the test was taken as the average of identified values over the middle 50% of the specimen. The stressaverage reconstructed at the first crack location using linearstress gauge equation was used to estimate the interlaminar tensile strength.
Clearly, the selection of spatial and temporal smoothing parameters will influence the identification procedures. The smoothing parameters were selected using an image deformation simulation procedure similar to [36, 38, 39], as described in the following section.
Smoothing Parameter Selection and Error Quantification
Generating Synthetic Images
Summary of parameters used to generate synthetic images for processing parameter optimisation
Image parameter  Printed grids  Bonded grids 

Grid pitch (mm)  0.3  0.337 
Mean grey level (% dyn. range)  50  40 
Grid contrast amp. (% dyn. range)  20  25 
Noise amplitude (% dyn. range)  0.4  0.25 
Pixel sampling (pixels/period)  7  6 
The deformed synthetic images were then processed using the same procedure as the experimental images (Sect. 4.5). Different combinations of spatial and temporal smoothing were used to quantify the effect of processing parameters on the identification of stiffness parameters.
Identification Sensitivity to Smoothing Parameters
Selected smoothing parameters for processing experimental images and corresponding measurement performance
Grid Pitch (mm)  

1–3 Plane  2–3 Plane  
Parameter  0.3  0.337  0.3  0.337 
Spatial Kernel (pixels)  31  41  41  41 
Temporal Kernel (frames)  11  11  11  11 
Error \(Q_{33}\) (%)  0.4  0.2  0.5  0.5 
Error \(Q_{23}\) (%)  –  –  2.8  2.1 
Measurement resolution  
Displacement (\(\upmu\)m)  0.3  0.4  0.3  0.4 
(Pixel)  0.006  0.008  0.006  0.008 
(Pitch)  p/1000  p/850  p/1000  p/850 
Strain (\(\upmu \hbox {m} \, \hbox {m}^{1}\))  46  56  46  56 
Acceleration (\(\times 10^{5}\) m s\(^{2}\))  8.4  5.1  8.4  5.1 
Experimental Results and Discussion
FullField Measurement Results
In this section typical experimental kinematic fields are presented for two time steps for a 1–3 plane and 2–3 plane interlaminar specimen. Since it is difficult to get a true appreciation for the dynamic nature of an impact test through still images, videos of all kinematic field for all specimens, as well as the raw grey level images can be found in the data repository detailed at the end of the manuscript.
The \(\epsilon _{xx}\), \(\epsilon _{yy}\) and \(\epsilon _{xy}\) strain maps for the two specimens, at the same two time steps, are shown in Figs. 16 and 17. The experimental strain maps for the 1–3 interlaminar specimen confirm that the \(\epsilon _{yy}\) strains are much lower than for the \(\epsilon _{xx}\) strains. Significant \(\epsilon _{yy}\) strains are measured in the case of the 2–3 plane interlaminar specimen, however, the signaltonoise ratio remains less favourable than the \(\epsilon _{xx}\) strains. As a result, the edge data extrapolation procedure does not perform as well, creating some localised regions of high artificial strain. As mentioned previously, despite having high signal in the \(\epsilon _{xx}\) fields, the lower signal in the \(\epsilon _{yy}\) and \(\epsilon _{xy}\) fields will act to reduce the identification stability since these strains are used to simultaneously identify \(Q_{33}\) and \(Q_{23}\). Strain rate maps (\(\dot{\epsilon _{xx}}\)) are shown in Figs. 18 and 19 for specimen #2P[1–3] and specimen #6B[2–3], respectively. Local \(\dot{\epsilon _{xx}}\) strain rates are on the order of 4000 s\(^{1}\) to 7000 s\(^{1}\). For specimen #6B[2–3], \(\dot{\epsilon _{yy}}\) were measured on the order of 3000 s\(^{1}\). Strain rates in the experiments are slightly lower than that predicted from processed synthetic images based on simulated fields (peak compressive strain rates on the order of 14,000 s\(^{1}\) and peak tensile strain rates on the order of 10,000 s\(^{1}\)). As previously explained, this is expected since the simulation assumes perfect, hard contact at waveguide interfaces between the projectile and specimen. Some ‘pulseshaping’ is expected in the experiments from the thin layer of tape on the front face of the waveguide for the camera trigger, and the thin layer of glue between the waveguide and specimen.
Interlaminar properties were identified from the acceleration and strain fields using the methods presented in Sect. 2 and Sect. 4.5.3. The identification of interlaminar stiffness parameters are presented in Sect. 6.2 and the identification of interlaminar tensile strength are presented in Sect. 6.3.
Stiffness Identification
Experimental measurements of interlaminar stiffness parameters are presented separately for each of the identification techniques. The identifications using the special optimised virtual fields methods are presented first in Sect. 6.2.1 followed by the stiffness identifications with the stress–strain curve approach in Sect. 6.2.2.
Special Optimised Virtual Fields Approach
The random error associated with identifications for 2–3 plane specimens is higher compared to the 1–3 plane. A possible explanation for this is the inclusion of \(a_y\), \(\epsilon _{yy}\) and \(\epsilon _{xy}\) fields in the identification procedure, which have a lowertonoise ratio. The optimised virtual fields method is formulated such that each set of virtual fields results in the direct identification of each stiffness parameter. Since these parameters are identified simultaneously, the identification of a weakly activated material parameter will influence the identification of the other parameters.
Measured high strain rate interlaminar elastic modulus for AS4145/MTM451 (1–3 plane specimens)
Specimen  1–3 plane  

\(E_{33}\) (SS) (GPa)  \(E_{33}\) (VFM) (GPa)  
1P  10.3  11.0 
2P  10.3  10.8 
3P  10.5  11.7 
4P  10.5  11.0 
5P  10.8  11.1 
6B\(^{r}\)  10.3  10.3 
7B\(^{r}\)  10.3  10.7 
8B  9.8  10.3 
9B  9.9  10.9 
10B  10.9  11.3 
Mean  10.4  10.9 
SD  0.34  0.35 
COV (%)  3.3  3.5 
Diff. to Q–S (%)  + 31  + 38 
Measured high strain rate interlaminar stiffness for AS4145/MTM451 (2–3 plane specimens)
Specimen  2–3 plane  

\(Q_{33}\) (SS) (GPa)  \(Q_{33}\) (VFM) (GPa)  \(\nu _{23}\) (VFM)  \(E_{33}\) (SS) (GPa)  \(E_{33}\) (VFM) (GPa)  
1P  12.6  12.5  0.41  10.4  10.5 
2P\(^{r}\)  14.1  14.1  0.45  11.3  11.3 
3P\(^{r}\)  13.1  13.9  0.50  9.9  10.4 
4P  13.1  13.1  0.43  10.7  10.7 
55\(^{r}\)  13.7  13.7  0.49  10.4  10.4 
6B  12.1  13.9  0.44  9.8  11.2 
7B  13.0  13.1  0.43  10.7  10.7 
8B  11.7  12.2  0.44  9.4  9.9 
9B  13.3  11.9  0.46  10.5  9.4 
10B\(^{r}\)  11.8  12.15  0.44  9.4  9.5 
Mean  12.8  13.0  0.45  10.2  10.4 
SD  0.83  0.87  0.03  0.61  0.64 
COV (%)  6.5  6.7  6.4  6.0  6.1 
Diff. to Q–S (%)  –  –  –  + 30  + 32 
Peak compressive widthaverage strain rate (\(\overline{\dot{\epsilon _{xx}}}^{y}\))
Specimen  1–3 plane  2–3 plane 

\(\overline{\dot{\epsilon _{xx}}}^{y} ({\mathrm{{s}}}^{1})\)  \(\overline{\dot{\epsilon _{xx}}}^{y} ({\mathrm{{s}}}^{1})\)  
1P  \(\) 3000  \(\) 2200 
2P  \(\) 3100  \(\) 4400 
3P  \(\) 3700  \(\) 3800 
4P  \(\) 3200  \(\) 2800 
5P  \(\) 3700  \(\) 1700 
6B  \(\) 4800  \(\) 4500 
7B  \(\) 3900  \(\) 5100 
8B  \(\) 3300  \(\) 2900 
9B  \(\) 3300  \(\) 5400 
10B  \(\) 2000  \(\) 3000 
The average value for \(E_{33}\)[1–3] was 10.9 GPa with a coefficient of variation (COV) of 3.5 %. This level of scatter is quite low and comparable to that for quasistatic testing of this material (COV = 3.6 %) [28]. \(E_{33}\) [2–3] is identified from \(Q_{33}\) and \(\nu _{23}\) with an average value of 10.4 GPa, and a COV of 6.1%. The slightly higher scatter in \(E_{33}\) [2–3] is likely caused by the inclusion of fields with low signaltonoise ratios into the identification routine as described previously. Therefore, the stiffness measured on the 1–3 plane specimens is thought to be more reliable. The measured interlaminar modulus of 10.9 GPa represents an increase of 38% compared to quasistatic values [28].
Overall, the measurements are quite promising considering this is the first implementation of the IBII test to obtain interlaminar properties at such high strain rates. Regarding strain rate, it is difficult to assign a single strain rate value to the measurements due to the heterogeneity of the fields. However, when axial strain is high, so too is strain rate (see Figs. 16, 17, 18, 19). Therefore, the peak, widthaverage strain rate (\(\overline{\dot{\epsilon _{xx}}}^{y}\)) achieved during the compressive loading sequence can be considered as the limiting case for an ‘effective’ strain rate for these measurements (Table 8). It is part of future work to derive an effective strain rate using the virtual fields and the virtual strain rate fields to be able to quote a welldefined value. However, the strain rate sensitivity of this material is low enough so that this is not a critical issue and a mean or peak value is a good estimate. For most specimens, the peak compressive strain rate is on the order of 3500 s\(^{1}\). Obtaining stiffness measurements at such strain rates with the SHPB test is challenging and generally unreliable. Identifications using reconstructed stress–strain curves are presented next.
Stress–Strain Curve Approach
In general, the identifications from reconstructed stress–strain curves are quite consistent and stable over the middle portion of the specimen. A slightly lower stiffness is measured near the free edge on some samples with bonded 0.3 mm grids, particularly specimens #6B[1–3], #8B[1–3], and #9B[1–3]. Since this is not observed on specimens with printed, 0.337 mm grids, this is thought to be a result of a slight rotation of the grid with respect to the specimen. This could also be a result of some missing data at the edge from trimming the overflow epoxy during the grid debonding process. Both have the effect of increasing the amount of missing data at the free edge, and thus the error on reconstructed stress. This highlights another key advantage of using printed grids, as alignment is easily and consistently controlled, and no additional steps are required to clean up the edges of the specimen following grid application. The identification of \(E_{33}\) [1–3] and \(E_{33}\) [2–3] was measured to have an average value of 10.4 GPa, and 10.2 GPa, respectively. The coefficient of variation for both types of specimens is low ranging between 3 and 6%. Between 1–3 and 2–3 plane specimens, this represents a 30% increase in stiffness compared to quasistatic transverse stiffness measurements (\(E_{33}\) = 7.9 GPa) [28].
Figures 24 and 25 show that the identifications of \(E_{33}\) and \(Q_{33}\) fluctuate periodically along the length of the specimen by approximately 0.5 GPa from the mean. This pattern was also observed in the identifications from synthetic images, although with a lower magnitude (0.2 GPa). Image deformation simulations suggest that this oscillation is primarily attributed to fluctuating error on reconstructed acceleration and strain as the pulse moves through the extrapolation region at the free edge (one pitch). Extrapolation errors are highest as the high signal information within the pulse travels through the extrapolated region. It is thought that the experimental images are more sensitive to this since the pulse is smoother compared to the simulated pulse (i.e., extrapolation errors affect high signal information for a longer period of time). The effect is more pronounced on the 0.337 mm grids due to lower measurement resolution and a larger extrapolation region at the free edge.
To the authors’ knowledge, no interlaminar high strain rate data are available for AS4145/MTM451. Furthermore, existing studies are limited to reporting an ‘apparent’ modulus, and scatter is so large that strain rate effects cannot be reliably extracted [2]. Therefore, it is difficult to make direct comparisons with other studies. This preliminary study shows that a consistent measurement of \(E_{33}\) can be obtained by processing measured strain and acceleration fields in two different ways. Both approaches are suitable for identifying a global stiffness value in this study since material properties do not vary in space or time. Therefore, a comparison of the two methods provides a kind of validation of the measured values. The use of image deformation also shows that both routines can identify the reference \(E_{33}\) within 1% when smoothing parameters are chosen appropriately. However, when material properties vary in space and time preference might be given to a single identification method depending on the information desired. For example, the stress–strain curve method might be preferred in cases where a spatial variation in stiffness is of interest, since it provides a stiffness measurement for each transverse slice along the length of the specimen. Alternatively, the special optimised virtual fields might be more useful if one was interested in resolving timedependent behaviours, as it gives a single stiffness value for each point in time. This level of information and versatility is not available with existing test methods and highlights the potential of imagebased test methods for high strain rate testing.
Strength Identification
The linear stressgauge equation (Eq. 5) is used to estimate the tensile strength of the material, as in [20]. A comparison of the stress fields reconstructed using the identified constitutive model and the linear stressgauge equation are shown at a frame before fracture (t = 15.0 \(\upmu\)s) in Fig. 26a and b, respectively. The agreement is excellent apart from the region close to the impact, demonstrating that for such a test, the linear representation in Eq. 6 provides a reasonable actual approximation of the stress field. Fracture initiation is identified using the raw, unsmoothed maps of \(\epsilon _{xx}\). A crack becomes clearly visible in the \(\epsilon _{xx}\) field as a concentrated region of high (artificial) strain, as shown in Fig. 26c. The temporal variations of local stress, computed with the linear stressgauge equation, was extracted from a 2 pitch \(\times\) 4 pitch (2p \(\times\) 4p) virtual gauge region centred on the identified crack initiation site (as shown in Fig. 26c). The corresponding stress maps, and stress–strain curve over the virtual gauge region are shown in sub figures d, e and f. While not clearly shown in the strain map in Fig. 26d a second crack had started to form at x = 9.5 mm, but did not crack the paint. The crack clearly appears three frames later. At the fracture frame shown, the acceleration fields are strongly influenced by these two cracks, explaining the discrepancy between the stress field in Fig. 26d and the reconstructed field using the linear stressgauge shown in Fig. 26e.
Measured high strain rate interlaminar tensile strength for AS4145/MTM451 and peak tensile strain rate (\(\overline{\dot{\epsilon _{xx}}}^{VG}\)) within virtual gauge at fracture location
Specimen  1–3 plane  2–3 plane  

\(\overline{\sigma _{xx}}^{VG}\) (SG) (MPa)  \(\overline{\sigma _{xx}}^{VG}\) (LSG) (MPa)  \(\overline{\dot{\epsilon _{xx}}}^{VG}\) (s\(^{1}\))  \(\overline{\sigma _{xx}}^{VG}\) (SG) (MPa)  \(\overline{\sigma _{xx}}^{VG}\) (LSG) (MPa)  \(\overline{\dot{\epsilon _{xx}}}^{VG}\) (s\(^{1}\))  
1P  94.3  95.0  3100  72.6\(^{x}\)  83.9\(^{x}\)  4300\(^{+}\) 
2P  83.2  95.7  4600  107.2  109.7  4600 
3P  90.3  94.9  5300  112.0  115.6  4100 
4P  86.1  121.3  3500  74.5  81.5  6300 
5P  107.7  135.6  4900  54.4\(^{x}\)  71.5\(^{x}\)  6800\(^{+}\) 
6B  130.5  157.6  5300  116.4  122.9  3900 
7B  91.1  106.6  6200  136.9  143.5  4900 
8B  92.1\(^{x}\)  98.8\(^{x}\)  6000\(^{+}\)  77.4  79.9  4700 
9B  82.4\(^{x}\)  83.7\(^{x}\)  6000\(^{+}\)  126.7  130.8  5800 
10B  44.6\(^{x}\)  50.7\(^{x}\)  4000\(^{+}\)  88.1\(^{x}\)  134.1\(^{x}\)  5300\(^{+}\) 
Mean  97.6  115.2  4700  107.3  112.0  4900 
SD  16.5  24.2  1100  23.6  24.0  900 
COV (%)  16.9  21.0  22.8  22.0  21.4  17.6 
Diff. to Q–S (%)  + 96  + 135  –  + 113  + 122  – 
The results in Table 9 suggest that strain rate has a significant influence on the interlaminar tensile strength. The interlaminar strength with the linear stressgauge equation was measured to be 115 MPa (COV = 21%) for the [1–3] specimens and 112 MPa (COV = 21%) for the [2–3] specimens. Combining the two interlaminar planes results in an average strength of 114 MPa, with a COV = 20%. This represents an increase in strength of 125% compared to the quasistatic value of 50.4 MPa (COV = 13%) in [28]. Since the strain rate is generally high when the strain is high, the peak widthaveraged strain rate at the plane of fracture offers an ‘effective’ strain rate for the measurements. This is generally on the order of 5000 s\(^{1}\). It is worth noting that comparisons to quasistatic values need to be interpreted with some caution because quasistatic interlaminar tensile tests are quite sensitive to experimental factors such as misalignment, gripping and volume effect. Typical scatter in the literature for quasistatic strength measurements ranges from 10 to 50% [6, 7, 40, 41]. Therefore, the reported coefficient of variation for quasistatic interlaminar strength of this material is comparatively low. The level of scatter in the current measurements at high strain rates is promising, with scatter comparable to well controlled quasistatic tests.
The time histories of stress averages at the fracture location are shown in Fig. 27 for four specimens (2 from each interlaminar plane). Also shown for comparison is the average stress in the gauge region as reconstructed using the stressgauge equation (Eq. 4) and the constitutive model. In the latter, the interlaminar stiffness is taken as the average values identified from stress–strain curves and the special optimised virtual fields routine. However, this stress is not used as a measure of strength due to the uncertainty in determining when strains become nonphysical and contamination from grid defects as explained later. Figure 27 shows the initial compressive loading, where all three stress measures agree well. Two of the presented specimens (Fig. 27a, b) show good agreement during the unloading, until a marked drop in average stress (stressgauge and linear stressgauge equations) is observed between t = 15.5–19 \(\upmu\)s. Specimen #2P[1–3] shows a small offset and lowamplitude oscillation in stress averages at the start of the unloading phase. It is suspected that some throughthickness wave dispersion may have occurred as the wave reflects due to a nonsquare free edge cut. This effect is observed over a very short duration, and is unlikely to influence strength measurements.
As previously mentioned, no high strain rate studies have been reported on AS4145/MTM451, thus, no direct comparisons can be made. However, indirect comparisons can be made with studies on the high strain rate throughthickness properties of other composite systems. Comparison of the current measurements to those in other studies shows the robustness of the IBII test for measuring interlaminar strength. For example, a similar strain rate sensitivity was measured by Nakai & Yokoyama (+ 77%) [6, 7]. However, the scatter on measured strength was significantly higher (39% COV), and measurements were made at much lower strain rates (50 s\(^{1}\)). This amount of scatter is typical of most studies reporting tensile strength measurements using a SHPB at high strain rate such as [4, 8, 42]. Govender et al. [43] used pulse timeshifting to avoid the assumption of quasistatic equilibrium, and produced strength measurements of similar consistency to the current study. However, their approach relied on predicted stresses based on 1D wave theory and no quasistatic values were provided to quantify the strain rate sensitivity. By using ultrahigh speed imaging and fullfield measurements, many of the assumptions tied to existing techniques are removed. The measurements reported here exemplify the potential for such techniques to be applied to obtain remarkably consistent strength measurements.
Future Work and Limitations
While further work is still required to refine the IBII test, the preliminary results are promising. This study exemplifies the potential of test methods developed around fullfield imaging to expand the range of strain rates where composite interlaminar properties can be reliably characterised. Based on this initial study, the following points describe some limitations of the test method. This is followed by a summary of possible future investigations to better understand the preliminary results proposed here, improve the test method, and possible extensions for more comprehensive material characterisation.
Assumptions for Processing the Data with the Virtual Fields Method Since only surface deformations are measured, the following assumptions are required here: (1) the specimen is in a state of plane stress, and (2) the mechanical fields need to be uniform through the thickness. Compared to the inplane specimens in the study by Fletcher et al. [20], the specimen dimensions are less favourable here for ensuring a state of plane stress is achieved. Based on the current specimen manufacturing technique, the smallest thickness that could be achieved, while maintaining good dimensional consistency, was approximately 2 mm. Nonuniformity through the thickness may arise following wave reflection from an angled free edge, which would violate assumption (2). Further work is required to better understand the effect of specimen geometry (e.g., thickness variation and free edge perpendicularity) on the identifications of stiffness and strength. This will be explored as part of future work using threedimensional finite element simulations and simultaneous imaging on the front and back surfaces of the specimens during experiments. Image deformation simulations will be required to quantify the effect of these geometric ‘defects’ and other experimental factors not accounted for in the current simulation. This will assist in identifying the source of discrepancies between identifications from simulated and experimental images and establish tolerances for specimen geometry and the experimental setup.
Reconstruction of Edge Data Oscillations in the stiffness identified from the stress–strain curves was primarily attributed to reconstruction errors as the pulse moves through the extrapolated data region at the free edge. This occurs since data is inferred for a temporal phenomenon, based solely on spatial information. This effect is amplified for the 0.337 mm printed grids compared to the 0.3 mm grids due to a larger reconstructed data region. A simple way to reduce extrapolation errors is to reduce the grid pitch to enable a lower grid sampling to be used (5 pixels per pitch). It is thought that the effect of reconstructed data on stiffness identifications may also depend on the pulse. A simple way to study this is to use image deformation simulations by systematically varying the pulse characteristics (e.g., rise time, duration and amplitude). The necessity to reconstruct edge data with the grid method will unavoidably introduce errors. Fortunately, this issue will become less problematic as the spatial resolution of ultrahighspeed cameras improves.
Grid Defects The results from this study suggest that grid defects have a significant influence on the identification of stiffness parameters using the isotropic special optimised virtual fields routine. Artificial signal with high signaltonoise ratio is thought to cause bias in the optimisation of the virtual fields, due to the low signal associated with the underlying material response. The effect is amplified when defects occur near the edges of the specimen and interact with the data extrapolation procedures. Identifications of \(Q_{33}\) and \(Q_{23}\) have higher scatter and are less stable compared to the image deformation simulations, which do not take into account grid defects. There are several other factors that are also not considered in the simulations and therefore, future work is required to isolate and quantify the effect of defects on the identifications. Image deformation simulations serve as a useful tool for conducting such investigations. Systematic studies on defect position, size and density can be performed by corrupting greylevels of synthetic images based on defect profiles from real grid images. The corrupted synthetic images may then be processed using the same procedure as experimental images to quantify the influence on identified stiffness parameters.
Considering these limitations, the following summarises possible directions of future work to develop the interlaminar IBII test.
Identification of a Strain Rate Sensitive Constitutive Law Assigning a single strain rate to the measured properties is difficult due to the heterogeneous nature of the fields. This is unavoidable when testing at high strain rates in the wave regime. While this is also problematic for existing techniques, fullfield measurements create the potential to exploit the heterogeneity in strain rate fields. One approach is to formulate the unknown stiffness parameters as a function of strain rate in the optimised virtual fields routine. Provided the material is subjected to a range of strain rates, the coefficients of the model could be identified from each set of kinematic fields. The potential of this approach could be explored using a userdefined material subroutine in ABAQUS combined with the synthetic image deformation methodology. Another approach is to use the virtual fields and the virtual strain rate fields to identify a welldefined value for the effective strain rate. This will be investigated in the future.
Extension to Thinner Specimens The drawback with the current configuration is that thick plates are required, which are expensive and may not be representative of thinner panels. It will be of particular interest in the future to see how small in length we could go, and beyond this, whether a thinner specimen sandwiched between two tabs would be feasible.
Error Quantification for Interlaminar Tensile Strength This work has demonstrated the usefulness of image deformation simulations for selecting optimal smoothing parameters and estimating the total error on stiffness identifications. The ideal extension of this is an image deformation routine that provides an estimate on the error for interlaminar tensile strength. This requires finite element modelling with cohesive elements to simulate the formation of the crack. Displacements from these simulations can then be used to generate a set of deformed images. This will provide valuable insights into the effect of temporal and spatial smoothing on the current strength identification procedures. This could also extend the work to crack propagation and toughness measurements.
Combined Tension–Shear Testing Work is currently under way to explore the extension of the IBII concept to develop a test for obtaining interlaminar shear, and combined tension–shear properties. This would enable more complete failure envelopes to be populated at high strain rates. This information is not currently available and would be invaluable for improved high strain rate modelling of composite materials.
Conclusions

Despite limited spatial resolution, the current study demonstrates that measurement quality of current ultrahigh speed cameras is sufficient to identify interlaminar stiffness and tensile strength from the same test.

Stiffness and strength were found to exhibit a substantial sensitivity to strain rate. An average interlaminar elastic modulus of 10.3 GPa was identified across all 1–3 plane specimens using reconstructed stress–strain curves. For the same specimens, the reduced special optimised virtual fields approach identified an average modulus of 10.7 GPa. Stiffness measurements were made at peak average strain rates on the order 3500 s\(^{1}\). This represents an increase between 30 and 35% compared to quasistatic values.

Tensile strength was found to have a higher strain rate sensitivity than stiffness. The average tensile strength over all specimens was measured to be 114 MPa at peak average strain rates on the order 4500 s\(^{1}\). This corresponds to an increase of approximately 125%, compared to quasistatic values.

Image deformation simulations are a powerful diagnostic tool for characterising the errors arising from measurement resolution and noise. This enables one to robustly select optimal smoothing parameters. It is also a useful diagnostic tool for studying the effect of postprocessing operations (e.g., effect of data extrapolation at the edges) and experimental factors (e.g., grid size, specimen geometry, grid contrast) on the identification of stiffness parameters.

The use of printed grids has proven to be effective for significantly reducing the number of grid defects. Therefore, this approach is recommended for interlaminar testing where higher magnification is required. However, the current technology is limited to grid periods on the order of 0.3 mm, which will not be enough either for higher spatial resolution cameras or for higher magnification (smaller specimens). Other deposition routes like the one recently proposed by Brodnik et al. [44] could be pursued.
Notes
Acknowledgements
This material is based on research sponsored by the Air Force Research Laboratory, under Agreement Number FA95501710133. The authors are grateful to the grant programme manager, Dr. David Garner from EOARD/AFOSR. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the Air Force Research Laboratory or the U.S. Government. The authors kindly acknowledge Dr. Devlin Hayduke from Material Sciences Corporation, USA for supplying the material tested in this work. The authors would also like to thank Mr. Ian Wilcox from the University of Southampton Print Centre and Dr. Yves Surrel for developing the method for printing grids directly onto samples. Dr. Lloyd Fletcher and Prof. Fabrice Pierron acknowledge support from EPSRC through Grant EP/L026910/1. Jared Van Blitterswyk acknowledges Ph.D. funding support from EPSRC.
Compliance with Ethical Standards
Data Provision
All data supporting this study are openly available from the University of Southampton repository at: https://doi.org/10.5258/SOTON/D0561.
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