. Novel experimental procedure and determination of full displacement fields of delaminating composite layer interfaces for evaluation of the mode II cohesive law. Engineering Fracture Mechanics, 149, 326-337.

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Introduction
Cohesive crack models are one of the classical approaches for predicting and modelling delamination in layered structures such as adhesively bonded joints [1][2][3][4] and composite laminates [5][6][7][8][9][10][11][12][13][14][15][16][17][18].The modelling technique was initially developed and implemented in FE codes for isotropic materials such as concrete and metals [19][20][21][22], but spread quickly to composites.The main advantage of this approach over alternative analysis techniques e.g. the virtual crack closure technique (VCCT) is that it includes a nonlinear constitutive material model (cohesive law) that combines crack initiation [23] and propagation [24] criteria and as a result, it can be applied for problems with a variety of loading modes.Cohesive interface elements normally have zero thickness and the interlaminar stress components are coupled to the displacement discontinuities (jumps) across the faces of the deformed element through the cohesive law.
Different types of cohesive laws with different shapes e.g.bilinear [10], parabolic [25], exponential [26], trapezoidal [27], etc. were proposed for different materials and validated against experiments.The structures' modelled responses were mostly in good agreement with the test results, and it seems that cohesive laws with different shapes can give similar structural response [25,28] especially if the crack is much longer than the damage process zone.Most of the modellers therefore use the simplest bilinear shape for the cohesive law and pay attention only to the interfacial shear strength and the fracture toughness.Although, it has been shown that in some problems, the shape of the cohesive law can affect the structural response significantly [29][30][31], the actual shape for composite layer interfaces was not investigated extensively to date due to difficulties in measuring the very small displacements around the crack tip.
Some researchers studied the cohesive law experimentally with less assumptions.This section aims at giving a short overview of the most important test configurations applied.Sørensen et al. [32,33] investigated the effect of fibre-bridging during mixed mode delamination propagation.They derived mixed mode cohesive laws from J-integral values experimentally measured on special specimens.Their experimental setup consists of a cantilever beam (supported with rollers against rotation) incorporating an interlaminar notch at one end, where both layers are loaded with pure but different bending moments.The displacements at the initial notch tip were measured with linear variable differential transformers (LVDT).This complicated but mechanically sound setup is activated by a cable and several rollers.De Moura et al. [34] proposed a method for determination of cohesive laws of adhesives experimentally using simple double cantilever beam (DCB) specimens but it can only be applied for mode I loading.The crack opening displacements (COD) were monitored with optical sensors.Fernandes et al. [35] used end notched flexure (ENF) specimens under three point bending to determine the mode II cohesive laws of composite bonded joints.The applied external load and displacement were measured and the J-integral was worked out.Then, the cohesive law was obtained based on derivation of the variation of J-integral versus the measured displacement jump at the crack tip.The displacements of the initial crack tip were monitored with a digital image correlation (DIC) system.Dourado et al. [36] also executed ENF tests on carbon/epoxy composite samples and determined the mode II cohesive law of the interface inversely by fitting FE data (generated with different piecewise linear cohesive law parameters) to their test graphs.Cui et al. [37] applied the advanced but complicated mixed mode bending (MMB) test alignment to evaluate the mixed mode constitutive laws of a 280 lm thick epoxy adhesive layer between woven carbon/epoxy composite plates.The constitutive laws were calculated using a J-integral approach, and DIC monitoring of the crack opening displacements at the initial position of the pre-crack in the specimen.
The short review of the literature shows that no simple test setup was applied for determination of mode II cohesive laws, and the deformations of the damage process zone were not analysed in detail.Although DIC has been applied in some of the most recent studies [35,37], this was only on the macroscopic scale to record displacements at the initial crack tip and therefore the full displacement fields of the interfaces were not reported.Most of the previous papers presented investigations of ductile adhesives using a J-integral approach.The stress components were worked out based on estimated or measured displacements at one point close to the initial tip of the crack and the estimated J-integrals.
Micro-scale optical analysis of damage in composites became available recently due to developments of suitable in-situ test apparatuses for simple loading scenarios such as tension, compression and bending.Although in-situ testing was first adapted for the assessment of transverse cracking of unidirectional composite layers [38][39][40][41], this technique offers scope for an in-depth analysis of mode II damage process zones as well.González and LLorca [38] investigated the damage mechanisms in a transversely compressed unidirectional (UD) composite in-situ in a scanning electron microscope (SEM) and identified the key parameters for failure modelling.Canal et al. [39] analysed the progression of a tensile transverse crack in a three point bending (3PB) UD composite specimen by executing the tests in-situ in a SEM.Test results were correlated with the outcomes of an embedded cell modelling study and showed good agreement.Canal et al. [40] successfully applied DIC on single SEM images in another study to analyse the micro-scale deformations during transverse compression cracking of a UD composite specimen.
The idea behind the present research based on the indications of the literature survey is the following: High resolution micrographs of delaminating composite layer interfaces can be obtained in-situ in a SEM if a simple loading scenario is found.The SEM images of the deformed specimen can be post-processed with DIC to establish the full displacement fields, which can be used in the next phase for calculating the mode II cohesive law of the interface.
The wider scope of the research is to investigate the delamination initiation and propagation phenomena in detail and propose a procedure by which, the displacement field of adjacent layers of a composite plate made with a brittle epoxy matrix with a very thin interfacial layer can be captured at subsequent stress levels.The displacement fields can then be used for analysis of the displacement jumps as well as the traction (i.e.shear stress) across the interface and finally to evaluate the mode II cohesive law.This methodology provides a deep insight into the deformations of a mode II damage process zone and valuable information such as variation of displacement jump values all along the interface.A novel aspect of the proposed approach is that the tractions and the displacement jumps can be evaluated independently and more directly from the same high resolution displacement field than with other reported techniques.
The overall research aims at exploring the actual shape of the mode II cohesive law of composite layer interfaces.The specific aim of this paper is to present the first step towards the overall goal by the development of a novel experimental procedure to obtain the full displacement field of delaminating interfaces.The approach is to capture the displacements directly on the surface of a progressively delaminating UD composite specimen in a simple loading scenario and analyse the deformations on the micro-scale.

Experimental
This section gives a detailed description of the development of a novel test setup and design of matching specimen geometry, which is suitable for in-depth analysis of the deformations around a mode II interlaminar crack in a UD composite.The chosen mechanical testing, image acquisition, post-processing and correlation procedures are discussed as well.

Development of the novel experimental setup
In order to study the longitudinal displacement field of delaminating composite layers under load with high spatial resolution, the following conditions are necessary: (i) A digital image acquisition device with appropriate magnification and resolution to provide high quality images for deformation analysis, (ii) a simple loading device, which can be suitably positioned for image acquisition, (iii) the mode II crack propagation during the mechanical test must be stable and allow time for image acquisition at subsequent load steps, (iv) the specimen surface of interest showing interlaminar damage and crack propagation must be visible through the imaging system, (v) the observed specimen surface must have features suitable for tracking by an image correlation software, to allow post-processing.
All these requirements can be fulfilled and the displacements of delaminating composite layer interfaces can be captured if a simple tensile test is executed in-situ in the vacuum chamber of a SEM on a specially designed UD composite specimen showing stable mode II crack propagation due to the presence of well positioned ply cuts (see Fig. 1a).The SEM images can be processed with DIC to generate the full displacement field of the delaminating layers (see Section 2.8 for more details).The SEM is more suitable than an optical microscope for image acquisition, because it has higher resolution and is able to tolerate small misalignment of the surface of interest.The SEM utilised for the experiments is a Zeiss EVO MA 15 with a relatively large (365 mm (Ø) Â 275 mm length) cylindrical vacuum chamber which is able to accommodate a wide range of mechanical testing modules.The simple tensile test was preferred over more complicated bending-based techniques, because it requires less space and it is free of large displacements, therefore more suitable for in-situ SEM testing.

Specimen design
UD tensile specimens made with cut central plies have been studied experimentally and numerically by Cui et al. [42] to analyse delamination, a key failure mode in layered composites.It was shown that when the specimen is under tension, the interlaminar normal stresses are small, compressive and restricted to the vicinity of the initial cut.Jalalvand et al. [43] analysed a similar problem and reported, that the required stress for driving delamination is independent of the interlaminar crack length.The mentioned analysis results indicate that the cut central layer UD specimen design allows for unique interlaminar fracture conditions very close to pure mode II.The discontinuous central layer UD specimens with continuous outer layers which can take the full load after delamination initiation furthermore assures stable propagation of mode II interlaminar cracks, allowing for image acquisition.Similar cut central layer but glass/carbon interlayer hybrid specimens, which show stable central layer pull-out, were used earlier by Czél et al. [44] to study the mode II fracture toughness of hybrid composite interfaces.This layer-by-layer hybrid specimen type with a cut central carbon/epoxy and continuous outer glass/epoxy layers was a good starting point for the development of similar architecture but different size specimens suitable for in-situ testing in a SEM chamber.In order to make the delamination of the specimen visible, the 1 mm thick cross-ply glass/epoxy end tabs had to be bonded on the surfaces showing the glass and carbon layers (edges of a specimen cut from a laminated plate).This was necessary because the in-situ tensile module can accommodate specimens only one way round.The specimens were made by curing a 1.5 mm thick laminated hybrid composite plate in an autoclave, and cutting it up into 1.5 mm wide sticks with a diamond wheel to give them 1.5 Â 1.5 mm square nominal cross sections.The end-tabs were bonded on the cut edges of the sticks to let the interesting surfaces, showing the three layer hybrid structure with a cut in the centre of the carbon layer, face towards the electron beam (EB) source when mounted in the SEM tensile module.A schematic of the specimen design and a photograph is shown in Fig. 1.The specimen length was also reduced to make the specimens fit in the available in-situ tensile module.
After the geometric design, preliminary tests were executed to confirm that the layers of the specimens delaminate stably.Fig. 2 shows the stress-strain graphs of various specimen types with different glass/carbon ratios (controlled by the number of carbon plies in the lay-up sequence) tested in a Shimadzu AGS-X type electro-mechanic test machine with a 10 kN load cell, at 2 mm/min crosshead speed.Properties of the constituent materials can be found in Tables 1 and 2. Please note that the carbon prepreg was a special thin type only 0.03 mm thick, compared with the  All specimens failed in a favourable way, showing progressive failure at the layer interfaces in the form of stable mode II crack propagation.Earlier delamination initiation strains were observed in specimen types with thicker carbon layers because of their higher mode II energy release rates.The crack propagation plateaus of the thickest specimen configuration with 10 plies of carbon were the most stable, suitable for step-by-step acquisition of the displacement field on the edge of the specimen at subsequent load levels.Therefore this specimen configuration with stacking sequence: [E-glass 4 /Carbon 10 /E-glass 4 ] was selected for the in-situ SEM tests.

Specimen surface preparation
The cut surfaces of the fabricated specimens were not suitable for high quality SEM imaging and did not have suitable texture for DIC and therefore it was necessary to prepare them.The cured composite plates were cut roughly to the specimen size and one edge of each specimen (i.e. one showing the layered hybrid structure) was wet polished using SiC papers down to P2500 grit size followed by diamond suspension polishing down to 1 lm particle size.A speckle pattern was then created on this surface by depositing submicron alumina particles from a suspension containing 1 mass% Al 2 O 3 in propanol.The agglomerated particles were broken up to smaller pieces in an ultrasound bath before application.The particle coated specimen surfaces were sputtered with gold to avoid charging due to the electron beam in the SEM chamber.Fig. 3 shows a typical micrograph of the particle coated surface of the specimens.

Materials
The materials considered for specimen design, and applied for the experiments were selected to be consistent with the authors' previous studies [18,[43][44][45][46] and because of high mismatch between the stiffness of the carbon and glass layers, which is useful for stabilising the stress in the plateau region of the stress-strain curve.Furthermore glass/carbon hybrid composites are widespread and their delamination behaviour is of high interest to the scientific community.In particular they have been used in our recent work on pseudo-ductile composites which produce gradual failure by stable fragmentation of the thin carbon plies [45].Please note that this study primarily focuses on the damage and fracture of the interface between unidirectional composite layers, the specific materials were selected because of their suitability to approve the novel experimental concept.Therefore the test setup may be suitable for other material combinations as well if stable delamination is assured.The materials applied in this study were E-glass/913 epoxy prepreg supplied by Hexcel, and Sky Flex USN 020A carbon/epoxy prepregs from SK Chemicals made with high strength Pyrofil TR30 carbon fibres produced by Mitsubishi Rayon.Both resin systems in the hybrid laminates were 120 °C cure epoxies, which were found to be compatible, although no details were provided by the suppliers on the chemical formulation of the resins.Good integrity of the hybrid laminates was confirmed during composite processing, specimen fabrication and testing and no phase separation was observed on micrographs.Material properties of the applied fibres and prepreg systems can be found in Tables 1 and 2.

In-situ tensile testing procedure
A Kammrath&Weiss tensile-compression module equipped with a 10 kN load cell was applied for the in-situ tensile tests at crosshead speeds from 0.05 to 0.5 mm/min (higher speeds in the initial elastic regime, lower speeds towards interlaminar crack initiation and propagation).The module shown in Fig. 4 was designed to move both grips aside with the same speed to keep the centre of the specimen in the same position during the tensile test, making the image acquisition easier.
Fig. 5 shows typical load-time and load-extension graphs of the in-situ tensile tests.Significant stress relaxation was observed after the crosshead was stopped for image acquisition and therefore sufficient relaxation time ($10 min) was left at each load step before scanning the specimen surface in a quasi-steady state (see Fig. 5a).The load-steps were designed to highlight the fracture behaviour around the expected plateau, so early steps were set to be bigger and then they were reduced towards the plateau.

SEM image acquisition
Multiple images (tiles) covering the central part ($7 mm) of the specimen were recorded at subsequent nearly constant stress levels from zero up to the interlaminar crack propagation stress.The individual images were recorded with 10% overlaps suitable for later stitching of the tiles as shown in Fig. 6.Special care has been taken to keep the centre of image no. 1. at the same position for each load step to make the post-processing easier.The SEM images only covered around 65% of the specimen thickness including one full glass layer and the full central carbon layer (see Fig. 6).This restriction of the region of interest was necessary in order to optimise the spatial resolution of the images, which were recorded at the full resolution (3072 ⁄ 2304 pixels) of the Zeiss EVO MA15 microscope at moderate (Â300) magnification.Fig. 3 shows an individual SEM image with 0.3262 lm/pixel resolution saved in an uncompressed file format (8-bit grayscale.tiff)and the level of detail it offers for post-processing.The combination of the highest available resolution and a moderate magnification resulted in the maximum area captured with a high level of detail and the minimum number of stitching zones generated during the post-processing steps.The most important post-processing step on the images taken by the microscope was the stitching of the individual images (tiles) into one single high resolution mosaic image without any loss of quality.This was done in Image J v 2.0.software with a plugin called Mosaic J.The tiles were pre-aligned manually, and then the built-in algorithm performed the fine adjustment of the overlapping images allowing only for translations (rotation was blocked).The overlapping areas were ''blended'' by the software to create an even smoother transition between the tiles.It was observed, that the tiles had lower quality (became blurred) towards the corners so these parts of the stitching regions were considered as possible weak spots for image correlation.

Grips Specimen
After stitching the tiles the mosaic images corresponding to subsequent stress levels were cropped to the same pixel size in the general purpose image processing software Gimp 2 as this is required for image correlation.

Correlation of the mosaic SEM images
Dantec Dynamic's Istra 4D v 4.3 software was applied for correlating the mosaic images with a spatial resolution of 0.3262 lm/pixel to work out the displacement fields of the tensile specimens.The key parameters of the image correlation, the subset or facet size, (which is the size of the sub-areas the correlation algorithm tracks) and grid spacing (which defines the points where output is generated) were set to 17 pixels (5.55 lm) and 12 pixels (3.91 lm) respectively based on parametric studies to maximise the number of correlated facets and improve the spatial resolution.The optimum facet size was controlled by the particle size and distribution on the specimen surface and the grid spacing was kept as low as possible to ensure the highest possible spatial resolution.As a result a significant overlap was set between the adjacent subsets, which did not compromise the independence of results for each subset [50].

Results and discussion
This section presents and explains the results of SEM image acquisition and DIC post-processing.The stresses were calculated based on the original measured full cross-sectional area of the specimen.

High resolution mosaic images of the delaminating interfaces
Since it is a unique opportunity to observe micrographs of delaminating composite interfaces at subsequent stress levels it worth discussing some of the observations.Fig. 7 shows the mosaic image of one half of the scanned area of the specimen at two different stress levels at the early stage of crack propagation.First of all the opening of the initial through thickness cut in the carbon layer and the progress of the visible interlaminar crack tip can be seen.It is also worth noting, that the mode II crack appears to be sharp at a given stress level (Section 1 on Fig. 7), but the newly formed section (Section 2 on Fig. 7) of the same crack shows a completely different appearance (i.e.shear hackles) at the next load step.This interesting behaviour suggests that the properties of an interface may not be identical along the length therefore one single crack may show different appearances along specific sections.variation of the geometry or material properties of the interfaces can let one of the four mode II cracks propagate a little further than the others, redistributing the loads in the whole specimen.The advantage of the specimen design is, that the analysis of the deformations and stresses can be executed for all four interfaces and suitable compensation techniques (e.g.averaging) can be found to minimise the effect of asymmetry.

Full displacement fields
The full displacement field data is suitable for analysis of the displacement jumps across the interface in the adjacent UD composite layers, which is one of the two required parameters for generating the cohesive law experimentally.Fig. 10 shows the displacement plots along lines at various y distances from the initial cut in the carbon layer.The plots show the high quality, low scatter and the sub-micron (less than 0.1 lm) displacement resolution of the full field data which makes it suitable for future quantification of the cohesive law.
The displacement jumps can be analysed by assigning a straight line for a given interface and recording the y coordinates of its intersections with tangents fitted to the displacement plots from the carbon and glass sides as shown in Fig. 10 with dashed lines.The corresponding plot of Fig. 10 shows that there is almost zero displacement jump at the interface À1100 lm away from the cut and therefore no more plots were added to the figure.Fig. 11 shows example displacement jump plots for the interface analysed on Figs. 7 and 10 (lower left).The nearly linear sections of the plots of Fig. 11 close to the initial cut in the carbon layer indicate the movement of an unloaded carbon ply block relative to its position before separation from the glass which is loaded at approximately constant strain.This suggests that there is little or no stress transfer through this part of the interface, therefore it can be interpreted as an open interlaminar crack.On the other hand, the asymptotically horizontal ends of the curves indicate that the layers are moving together there, therefore the interface is intact.The non-linear sections between the linear and flat parts indicate the damage process zones.The plots of Fig. 11 suggest that the length of the damage process zone for the specific specimen configuration and materials is in the order of 0.5-1 mm.The calculation of the shear stresses (i.e.traction) is more challenging because it is not as direct as the displacement jump (i.e.separation) assessment and needs suitable numerical procedures, therefore it will be reported in a separate paper.

Conclusions
The following conclusions were drawn from the study of delaminating unidirectional carbon/glass fibre reinforced epoxy interlayer hybrid composites: A novel stable mode II fracture test setup based on a simple tensile loading scenario was proposed which allows high resolution in-situ SEM image acquisition of delaminating composite layer interfaces.A matching discontinuous interlayer hybrid composite specimen type was developed which is capable of being tested in tension in-situ in an SEM and shows stable mode II interlaminar crack propagation suitable for imaging at subsequent load steps.A suitable surface preparation procedure including submicron alumina particle deposition was found which makes digital image correlation possible on the acquired SEM images.An optimised imaging methodology was developed which consists of recording the area of interest with overlapped, high resolution SEM images at moderate magnification and stitching them afterwards into mosaic images.This technique ensures the highest level of detail and maximum covered area with minimum number of stitch lines.The deformations of the composite layer interfaces were successfully captured at subsequent stress levels during the in-situ tensile tests in a SEM.The full displacement fields of 1 Â 7 mm areas of the tested specimen were correlated on a 4 lm grid with better than 0.1 lm displacement resolution.
The generated full displacement fields of composite layer interfaces undergoing damage allowed for unique observations e.g. of the appearance of the mode II cracks, approximate damage process zone length and direct quantitative analysis of the displacement jumps across the interfaces.The displacement data can be extensively post-processed and exploited to help understand the mode II interfacial behaviour of composite laminates.Further research is planned to develop suitable procedures for the analysis of the shear stresses at the interfaces which can yield an experimentally determined mode II cohesive law.

Fig. 1 .
Fig. 1.(a) Schematic and (b) photo of the specimen type developed for in-situ SEM tensile tests.

Fig. 2 .
Fig. 2. Tensile test results summary of 1.5 Â 1.5 Â 30 mm 3 nominal size UD glass/carbon-epoxy hybrid specimens with a single cut through the central carbon/epoxy layer.

Fig. 3 .
Fig. 3. Typical scanning electron micrograph showing the alumina particle coated surface of the tensile specimens.(Light grey bands are individual glass fibres, bright white spots are the alumina particles.)

Fig. 4 .
Fig. 4. Photograph of the Kammrath&Weiss tensile module for in-situ testing in SEM (the separation between the grips is $30 mm).

Fig. 5 .Fig. 6 .
Fig. 5. Typical (a) load-time and (b) load-extension graphs of an in-situ SEM tensile test.(Test speeds: 0.5 mm/min up to the first step, 0.1 mm/min up to the fourth step and 0.05 mm/min up to the last step.)

Fig. 8 Fig. 7 .Fig. 9 .Fig. 8 .
Fig.8shows the full displacement fields at three different stress levels obtained by the image correlation of mosaic scanning electron micrographs.The palette used is not suitable for quantitative representation of the data (this is the reason for no colour scale), but very useful to show the overall shape and correlation quality (degree of continuity, missing data, etc.) of the displacement fields over a relatively large area ($1 Â 7 mm) of the specimen.The black spots in the correlated fields indicate missing data due to unsuccessful correlation of the corresponding subset.It is obvious that the opening central crack in the carbon layer resulted in a growing uncorrelated patch because the new surfaces were not coated with gold and started to

Fig. 10 .Fig. 11 .
Fig. 10.Plots of y displacements across the thickness (x direction) of the hybrid layers at 428 MPa stress level with a schematic showing the positions of the un-deformed lines at various y coordinates.

Table 1
Fibre properties of the applied UD prepregs (based on manufacturer's data).

Table 2
Cured ply properties of the applied UD prepregs.
a Coefficient of variation.b Based on manufacturer's data.c Measured on different specimen types in tension.