Modelling the effects of patch-plug configuration on the impact performance of patch-repaired composite laminates

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Introduction
Composite materials based upon carbon-fibre reinforced-plastics (CFRPs) have been increasingly employed in aircraft structures over recent years. However, such materials may suffer a significant loss of performance when subjected to an impact loading [1][2][3][4][5][6][7][8][9][10][11][12][13]. Of particular concern is that an impact may lead to damage, such as intralaminar and interlaminar, i.e. delamination, damage, which then reduces the cyclic-fatigue properties of the composite component or structure. Thus, the initial impact performance of the pristine CFRP is of interest because there are many ways that an impact may arise. For example, from an impact via dropped tools, bird strikes, hail stones, runway debris, airport equipment striking the fuselage and hard landings. These impact events may lead to damage, which will require repairs to be undertaken to recover the mechanical performance of the composite material.
Naturally, the impact performance of the repaired CFRP is also of interest.
There are two main types of repair techniques for composite materials, namely patch and scarf repairs. Both the patch and scarf repairs have been extensively employed in industrial practice. Airbus and Boeing both have well defined protocols for composite repairs. EDF also have procedures for wind turbine blades, which can be found in Ref. [14]. Generally, patch repairs are recommended for secondary structural components, as they are more straightforward and sufficiently effective. Scarf repairs are often preferred for composite structures requiring aerodynamic performance. Scarf repairs give lower stress concentration and better aerodynamic efficiency. To evaluate the effectiveness of repair techniques, tensile, compressive, flexural and impact testing can be employed to characterise the recovered stiffness and strength [15][16][17][18]. In the case of secondary and non-critical structure repair, the adhesively-bonded patch repair has been widely used, in which the material is typically bonded to the parent composites as a patch via the use of adhesive-bonding techniques. There have been many papers which have considered the adhesively-bonded patch repair of damaged CFRP panels [15][16][17][18][19][20][21][22][23][24]. For example, Soutis et al. [19,20] have shown that using a relatively simple patch consisting of an adhesively-bonded external patch bonded to a CFRP panel, to repair a hole in the panel, led to a recovery of nearly 80% of the initial compressive strength. They also found that the thickness of the patch influenced the effectiveness of the patch repair. Tie et al. [23,24] have studied the impact behaviour of single-sided, CFRP patch repairs which had been adhesively-bonded to a CFRP parent panel. Using an impact velocity of 3.25 m s − 1 and an impact energy of 13.2 J, they examined various designs of patches and reported that the shape of the patch also influenced the effectiveness of the patch repair. The design of the patches included circular, square, hexagonal and octagonal shaped patches, which all had the same nominal area. They found that the use of the circular-shaped patch gave the best recovery percentage for the patch-repaired CFRP panel.
Now, several researchers [25][26][27][28][29], have recently modelled the impact damage in composites and derived the relationships between the different types of observable damage and the permanent indentation and matrix cracking that have been shown to be a precursor to delamination. However, these models were not always able to capture the unstable delamination growth and sudden drop in load at the delamination threshold, and were not applied to repaired CFRP composites. With these limitations in mind, a previously proposed computational finite-element analysis (FEA) model [30] is employed in the present research. This novel model incorporates elastic-plastic (E-P) behaviour, through a power-law relation, to predict the permanent indentation damage and to also capture the transverse through-thickness intralaminar matrix cracking, as well as interlaminar, i.e. delamination, damage. Compared to commercially-available three-dimensional (3-D) FEA damage models, which do not incorporate accurate non-linear models, this E-P 3-D FEA composite model is found to be very useful for studying the impact of composite repair geometries, which exhibit relatively complex mechanical behaviour and damage modes.
In the present work, single-sided CFRP patch repairs, which are adhesively-bonded to the damaged CFRP parent panel, are subjected to a low-velocity impact at an energy of 7.5 J. For the repair panels, a hole, which represents the removal of the impact damage, is cut-out from the centre of a pristine panel to creat the parent panel. A single-sided, circular CFRP patch is then bonded to the parent panel over the hole generated. Furthermore, in some designs, a CFRP plug is used to fill the hole generated in the parent panel. The effects of the design of the patch, for example its diameter and thickness and the presence, or not, of a plug, are studied. The E-P 3-D FEA model detailed in Ref. [30] has been employed to predict the impact behaviour of the pristine panel and the various designs of patch-repaired CFRP panels. For the composite repair designs, this FEA model has had to be significantly extended to include an adhesive layer, which bonds the patch to the parent panel, and to include the plug for the plugged repairs. The novel aspect of the present research is that, for the first time, the effects of the design of the patch and plug on the impact behaviour of repaired composite panels are thoroughly studied using a combined experimental and numerical methodology. Detailed experimental measurements and numerical predictions, including the load response, the permanent indentation caused by the impactor and impact-associated damage, e.g. matrix cracking and delamination, are presented for the repaired CFRP composites using the various patch-repair designs.

Materials and panels
The CFRP flat panels had a quasi-isotropic lay-up of [45 2 /-45 2 /0 2 / 90 2 ] s and were made using a unidirectional carbon-fibre, epoxy-matrix prepreg ('MTC510-UD300-HS-33%RW', SHD Composite Materials Ltd, UK). An autoclave was employed and the panels were cured at 110 • C for 120 min. The glass transition temperature of the cured epoxy matrix was 133 • C. In the CFRP panels the 0 • plies were aligned with the longer edge of the panels and the panel had a nominal thickness of 4.6 mm, see Fig. 1. The rectangular panels were 150 mm × 100 mm in size.
The patch-repaired CFRP panels were manufactured by removing a 40 mm diameter disk from the centre of a pristine CFRP panel to represent the impact-damaged area of a pristine CFRP panel, which now became the 'damaged', parent, CFRP panel. The repair patch was a disc of CFRP which was either 55 mm or 65 mm in diameter. In addition, two different thicknesses of patch were used: the thinner patch had a nominal thickness of 2.3 mm, with a lay-up of [45/-45/0/90] s whilst the thicker patch had a thickness of 4.6 mm with the same lay-up, i.e. [45 2 /-45 2 /0 2 /90 2 ] s , as that of the parent CFRP. (Note: when the patch repair approach is employed to repair the aerodynamic surface, thinner patches are often considered to be more appropriate than thicker patches and where possible the patch should have minimal protrusion and ideally be scarfed into the surface, so as not to adversely affect the aerodynamic behaviour.) The size tolerances for the hole that was cutout from the pristine panel and for the patch was ±0.1 mm. The patch repair was positioned with a fibre-orientation in the same direction as that of the parent panel and was then bonded to the parent CFRP using a single-layer of a toughened epoxy-film adhesive ('MTFA-500', SHD Composite Materials Ltd, UK). The film adhesive had a nominal thickness of 0.25 mm. The surfaces of the parent and the patch were prepared prior to bonding using 50 grit sanding-discs and were then cleaned with acetone. In some cases, the patch-repaired panels were made using a push-fit plug of the CFRP parent composite to fill the 40 mm hole, which was again orientated in the same direction as the parent panel. For other designs of patch repairs the hole was left unfilled, i.e. non-plugged. The adhesive layer was cured at 130 • C for 90 min to complete the manufacture of the patch-repaired panels.

Compressive strength testing
To assess the compressive strength of patch-repaired composite laminates, compressive strength testing has been conducted on both pristine and patch-repaired composite panels as shown in Fig. 2. This is with the composite panels being supported by the test rig, which was originally designed for the compression-after-impact experiments. Such a test rig inhibits global buckling behaviour through effective support of the edges of composite panels. Speckle strain mapping was also employed to make sure the applied load was uniform along the top edge of the specimen. Displacement control was adopted in this compressive strength testing, with an applied loading rate of 0.5 mm/min to minimise dynamic effects. Experimental data were directly recorded on a PC and the accompanying software (Instron, USA) gave both the reaction load and resulting displacement of the composite panels for this compression event. Three composite specimens were tested for each case.

Drop-weight impact testing
The drop-weight impact testing scheme described in ASTM 7136 [31] was employed to investigate the impact behaviour of the pristine and patch-repaired panels, as shown schematically in Fig. 3. In these experiments, the pristine and the patch-repaired panels were clamped in place on a steel picture-frame platform, which had a 125 mm х 75 mm cut-out window. A hemispherical steel impactor, with a diameter of 16 mm and a mass of 5.26 kg, was used to strike the pristine and the patch-repaired panels with an impact energy level of 7.5 J. The impact force was instantaneously measured by a dynamic load-sensor located in the impactor. A catching system was used to prevent further impact events from occurring after the initial impact and no software filtering was applied to the load versus time data. These data were directly recorded on a PC and the accompanying software (CEAST, Italy) gave both the impact load and resulting displacement of the composite panels as a function of time for the impact event. Two duplicate specimens were tested for each panel design.

C-scan and optical microscopy inspections
All the post-impacted pristine and the patch repaired composite specimens were examined using a portable C-scan device ('Prisma 16:64 TOFD', Sonatest Ltd, UK) which was fitted with a 5 MHz probe. The results were presented as the time-of-flight C-scan maps, which showed the extent of any delaminations as a function of the depth through the thickness of the panel. The areas of the delamination footprints were then calculated. An optical microscope was also employed to inspect the damage in the pristine and the patch-repaired panels, whereby postimpacted panels were first sectioned using a diamond saw to obtain the initial cross-sections, which were then polished in water using silicon carbide grinding papers, using a series of grades from P180 to P4000, and then finely polished using a polishing cloth with a diamond suspension fluid.

Overview
A finite-element analysis (FEA) numerical model, integrating an elastic-plastic (E-P) user-defined sub-routine [30] and cohesive surface models, has been employed to predict the impact behaviour of composite repairs with different patch and plug designs. The FEA model was implemented in 'Abaqus 2020' (Dassault Systemes, France) and the overall flowchart is shown in Fig. 4 (Note that the basic model in Ref. [30] was implemented in 'Abaqus 2018' but the later version of 'Abaqus 2020' was used in the present research. A check confirmed that no differences in the results were recorded using these two versions of 'Abaqus'.). All the methodologies and equations that are used in the numerical model, as given in this figure, are derived and presented in Ref. [30] where the equations are numbered as in Fig. 4. In Ref. [30] the reader can follow the logical development of this numerical model, including the novel E-P model that has been developed, the failure criteria used and how crack initiation and propagation for the intralaminar and interlaminar damage regions are defined and quantitatively modelled. In the present extended FEA model an adhesive layer has been added between the patch and the parent panel, which can deform and transmit stress across the interface, and the presence of a CFRP plug has been included when appropriate. In the FEA model, the basic mechanical properties of the composite plies and the adhesive layer, including strength, modulus, Poisson's ratio and fracture toughness, etc., that are required for the simulation were obtained from the manufacturer's data sheets and from the literature [30,[32][33][34][35][36][37]and are given in Table 1.
The novel E-P in-house user-defined sub-routine which has been embedded into the FEA computational model to capture the E-P material response prior to the damage initiation enables an accurate prediction of the impact behaviour of the composite panels and allows the modelling of any permanent indentation arising from the impact to be simulated. The constitutive relation for the E-P model was obtained by combining the classical elastic model with a plastic model. To address the complex stress state, the effective stress and effective strain were defined in the extended E-P model and the relationship between them was defined via a power-law function. The interlaminar damage involves the initiation and growth of delaminations between the plies that make up the composite laminate and was captured using the 'Abaqus' built-in surfacebased cohesive surface solution, in which the traction is a function of the displacement using a bilinear cohesive law for a linear-softening material model. The energy under the bilinear cohesive law was equivalent to the interlaminar fracture energy, G c . Before the initiation of any delamination, the cohesive law possessed linear-elastic behaviour with a stiffness of k i . Once the interlaminar damage criterion was satisfied the cohesive stiffness was degraded linearly until separation of the interface occurred, i.e. interlaminar cracking occurred, when the traction tended to zero and the maximum failure displacement was now attained. It should be noted that the initiation and growth of any intralaminar damage significantly influenced the extent of interlaminar damage and hence these two damage modes were modelled to be interactive in the 'Abaqus' simulation. In the intralaminar damage model, the 3-D damage criteria derived by Daniel et al. [30,[38][39][40] were employed to capture the onset of the initiation of intralaminar damage such as matrix cracking, etc. These criteria are partially interactive, which means that more than one stress component was employed and different types of intralaminar damage may be introduced into a composite ply via various stresses, including the longitudinal tensile and compressive stresses, transverse tensile and compressive stresses, through-thickness tensile and compressive stresses, transverse and through-thickness shear stresses. Eight corresponding damage variables were defined [30] to indicate the propagation of intralaminar damage in a composite ply. These damage parameters have the value of 0 when the element is undamaged and 1 when fully damaged and they were used to degrade the elasticity matrix to form the damaged elasticity matrix for describing the behaviour of impact-damaged material. Again, all the relevant details and equations that were used are presented in Ref. [30].

The finite-element analysis (FEA) model
To simulate the impact events on the pristine and the patch-repaired composite panels, FEA models were run on the 'Abaqus 2020' platform. Created models for the pristine and patch-repaired panels are shown in Both the parent panel and the patch were meshed using C3D8R solid elements where 3 mm × 3 mm elements were employed for the parent panel and 1.5 mm × 1.5 mm elements were employed for the patch. The adhesive layer in the patch-repaired specimen was modelled using 1.5 mm × 1.5 mm C3D8R elements and an exuded spew fillet of adhesive was modelled at the edge, as shown in Fig. 5. Cohesive surfaces were employed to model the contacts between the composite plies with different fibre directions to capture the interlaminar failure as well as the adhesive film/patch and the adhesive film/panel contacts to capture adhesive bonding failure if it should occur. The general contact algorithm was used to govern the global contact. The composite damage model described above was also employed to simulate the impact of the patch-repaired panels with a plug, where the plug had the same thickness and lay-up as the parent panel. For the plug/adhesive film interface the same cohesive surface contact, as for the patch/adhesive film interface, was again employed. It was assumed that no relative movement occurred between the parent panel and the pushed-in plug, so a tiecontact mode was implemented in 'Abaqus' to define this contact. The hemispherical steel impactor and the steel picture-frame platform were modelled as an analytical rigid surface and a discrete rigid body, respectively. Friction coefficients were defined as 0.25 and 0.2 for the composite/composite interfaces and the composite/steel interfaces, respectively. In the simulation, composite panels were located on a 100 mm × 150 mm rigid platform with a 75 mm × 125 mm cut-out window. The rigid impactor was given an initial velocity to strike the composite laminates. Four clamps were employed to constrain the vertical movement and also provide the friction which can inhibit the in-plane slip of composite laminates during impact. The simulations of the impact on the pristine and patch-repaired composite panels were undertaken using

Compressive strength
The load-carrying capability of the non-plugged patch-repaired CFRP panels was characterised through the quasi-static in-plane compression tests. The compressive loading response measured from these non-plugged patch-repaired CFRP panels have been presented and compared with the loading response of pristine panels in Fig. 6. To be noted is that the stiffness of the patch-repaired panel is comparable with the pristine panel. The average maximum compressive load achieved by the pristine and the 55 mm thin patch repaired panels are 136.5 kN and 84.7 kN respectively, which give average compressive strengths of 297 MPa and 184 MPa respectively. The comparison between the average compressive strengths obtained the pristine and the 55 mm thin patchrepaired panels shows that about 62% of the original compressive strength has been restored by using this patch repair approach, which for the main model and for the elastic-plastic (E-P) user-defined sub-routine are shown. This FEA modelling simulation of the impact event would be run typically over a time-scale, t, of 0 to ca. 8 ms, with ca. 100 time-steps being employed. The simulation runs were stopped when the defined total computation time for the impact simulation event had expired. (All the methodologies and equations that are used in the above FEA model are derived and presented in [30], where they are numbered as above, and see also the summary in Appendix A.) demonstrates reasonable effectiveness for the patch repair. This is with the benefit of removing delamination, if it were to occur from impact, before a patch (and/or a plug) is attached.

Experimental results for impact loading responses and overall interlaminar damage
The loading responses for the pristine panels and the different designs of non-plugged patch-repaired CFRP panels were measured from the drop-weight impact tests and are compared in Fig. 7. Several interesting observations may be made. Firstly, the results from the duplicate tests for a given type of test panel are in excellent agreement which indicates very good repeatability of the experimental test data. Secondly, in all cases there are relatively small amplitude, sinusoidal oscillations on the rising part of the load versus time, and the load versus displacement, experimental curves which are especially pronounced for the pristine CFRP panel. Such oscillations have previously been discussed in detail [30,[41][42][43][44][45][46][47] and are indicative of mass-spring oscillations. Thirdly, the patch-repaired panels using relatively thin repair patches, i.e. with a thickness of 2.3 mm, gave an impact response with a lower maximum load and reduced stiffness, as seen in the load versus displacement curves, when compared to that of the pristine panel. Fourthly, increasing the diameter of the patch, for a given patch thickness of 2.3 mm, only changes the impact response very slightly, as shown in Fig. 7, where, for example, the difference between the maximum loads obtained the 55 mm and 65 mm diameter (thin) patch-repaired panels is less than 5%. This result is supported from the C-scans shown in Fig. 8, where providing the patch diameter is appreciably larger than the hole, then the delamination, i.e. interlaminar, damage tends to be almost completely confined to the patch directly above the hole. Finally, to assess the effect of having a thicker patch, which had the same thickness as that of the parent CFRP, a patch of 4.6 mm thickness with the larger diameter of 65 mm was evaluated. It is evident for a panel with a 65 mm diameter patch of thickness 4.6 mm, the bending stiffness was slightly greater than for the pristine panel, see the load versus displacement curves in Fig. 7b. The area where the patch overlaps with the parent material gives an annulus or ring of overlapping composite laminate of thickness 9.2 mm, which includes both patch and parent panel. It is this 9.2 mm thick overlap area which leads to a significantly higher bending stiffness for the 65 mm thick patch repaired composite panel, compared to the pristine panel. The stiffness for the studied panels follows the sequence from high to low: 65 mm thick patch > pristine >65 mm thin patch >55 mm thin patch, which is as to be expected. The stiffness of the panel is one of main factors that can considerably influence the critical load in the loading response curves, which is mainly associated with the localised deformation due to matrix compressive damage and subsequent delamination near the contact zone. For the thick composite panels, the localised deformation in the contact zone tends to be more constrained due to the panel with the thicker patch having higher bending stiffness. As a result, higher loads are required to cause localised deformation, which can give a more substantial load drop in the loading response curves. For this reason, the critical load drop and the magnitude of the loads drop follow the sequence from high to low: 65 mm thick patch > pristine >65 mm thin patch >55 mm thin patch.
Typical C-scan maps and average damage areas obtained from the pristine and patch-repaired composite panels are presented in Fig. 8 for a range of patch designs. Naturally, there was no hole cut-out from the pristine panel but a white-dashed line is included here to indicate that the damage from the impact was all contained with a 40 mm diameter, justifying the dimensions of the removed area for the patch-repaired panels. For the patch-repaired panels, the white-dashed line represents the 40 mm diameter hole that was cut-out. In the interlaminar damage maps, such as Fig. 8a, the right-hand side scale in these figures indicates the location of the delaminations as a function of the depth through the thickness of the panel, where the dark-red colour represents the front (impacted) face and the dark-blue colour represents the rear (nonimpacted) face of the composite panel. The 0 o fibre direction is also indicated. The areal footprint of the damage, i.e. the damage area (labelled 'DA'), is given at the bottom left in each case and this was Table 1 The properties, as defined in Ref. [30], of the unidirectional CFRP and the rubber-toughened adhesive used in the FEA modelling studies [30,[32][33][34][35][36][37].  determined by counting the number of pixels which had a colour that was not dark blue, since the rear surface simply reflects the ultrasound and appears as being dark blue in colour. These damage areas arise from interlaminar damage, i.e. delaminations, in the panels resulting from the impact event. Delaminations initiate and grow at interfaces where the fibre direction is different in the plies below and above the interface. This is with the delamination propagation dominated by the fibre direction of the ply which is furthest from the impact surface. Localised deformation drives the initiation of matrix cracking and subsequent delamination. Due to the changes in stiffness across the interface between composite plies in different directions, the interfacial shear stresses can drive the crack growth mainly in Mode II (or shear loading) to form a larger delamination area. These delamination processes occur in the pristine specimens as well as the patches of the repaired composite specimens subjected to impact loading. There are several noteworthy observations. Firstly, the results shown in Fig. 8b reveal that the measured damage areas from the duplicate tests for a given type of panel give a relatively low scatter in the data. Secondly, all the interlaminar damage in the patch-repaired panels is contained within the patch. Indeed, no such damage was ever found in the parent CFRP to which the patch was adhesively-bonded, or within the adhesive layer or at the adhesive/CFRP interfaces either. Thirdly, all the patch-repaired panels possess larger damage areas than the pristine panels. However, a comparison between the C-scan maps obtained from the different designs of repair patches shows that the design can significantly influence the profile and extent of damage due to impact loading. For example, the difference between the average damage areas in the 55 mm and 65 mm diameter thin patch-repaired composite panels is not statistically significant, which reveals that the diameter of the patch has a relatively minor effect on the extent of impact damage. On the other hand, a comparison between the average damage areas obtained for the thin (e.g. DA = 1252 mm 2 ) and thick (e.g. DA = 923 mm 2 ) 65 mm diameter patches shows that the difference is about 25%, which demonstrates the significant effects that the thickness of the patch has upon the extent of damage. These observations from Fig. 8 agree with the results shown in Fig. 7, where only the use of the 65 mm diameter thick patch (4.6 mm) gave a stiffness, and other measured impact parameters, which were comparable to those of the pristine panel. The thinner patch deforms more during an impact, leading to higher levels of delamination. However, as seen in Fig. 8, the extent of the delamination is confined to the region above the hole and, for this reason, the thinner patch is still a reasonably effective repair.   Fig. 9 presents the experimental and predicted loading versus time curves obtained from the pristine and patch-repaired composite panels.

The overall loading response
As may be seen, there is a very good agreement between the measured experimental results with those predicted using the numerical model. Fig. 10 shows that there is also a very good agreement between the load versus displacement responses obtained from the experiments and from the predictive numerical simulations of the pristine and patch-repaired composites. The experimental impact results for all the composite panels indicate a linear response at the start of loading, followed by a drop in load, or change in gradient, which is associated with damage initiating and propagating. In addition, the magnitude of the maximum loads and displacements, and the displacement at failure, have also been accurately predicted by the numerical model. The level of agreement between the experimental and numerical loading responses demonstrates that the present computational model is capable of accurately predicting the impact behaviour of both the pristine and repaired composite panels. In particular, load drops and changes of stiffness which are indicative of the onset of damage are captured in the modelling. Fig. 11 shows the experimental and predicted interlaminar damage footprints obtained from the pristine and patch-repaired composite panels. The first noteworthy point from these results is that the various designs of repair patch give a widespread in the measured values of the interlaminar, i.e. delamination, damage footprint. Such values range from 923 mm 2 to 1365 mm 2 , with the pristine CFRP panel having suffered 681 mm 2 of interlaminar damage, see also Table 2. Furthermore, for the patch-repaired panels, all of this interlaminar damage was found to be contained only in the CFRP patch repair material, just above the hole beneath the patch. Secondly, the numerical model predicts the extent of the interlaminar damage relatively accurately, with the largest difference compared to the experimental results being only about 15% for the patch-repaired panel using the 65 mm diameter patch with a thickness of 4.6 mm. As noted above, the colour coding of the delaminations shows their depth through the thickness with a scale bar for the depth on the right of Fig. 11. This scale bar is consistent for both the experimental and predicted damage plots and it can clearly be seen that the delaminations for both the experiments and predictions occur at the ply interfaces, where there is a change of fibre direction, and exhibit a similar shape and extent through the thickness. This is a powerful feature of the model which is discussed further below.

Interlaminar damage
To further demonstrate the predictive capability of the numerical damage model, results are shown in Fig. 12 from the numerically predictive simulations of an exploded view for the interlaminar damage at different interfaces in the multi-axial lay-up of the CFRP patch. The patch-repaired panel with a patch of 55 mm diameter and a thickness of 2.3 mm was chosen for this exercise. As may be seen, the extent of the predicted areal numerical damage areas is near a maximum at a depth of 0.9 mm, i.e. at the ply interface just above the central-blocking 90 • plies. This peanut-shaped delamination is orientated across the width of the specimen, in the direction of the 90 • ply. At the ply interface at a depth of about 1.5 mm, just below the central-blocking 90 • plies, the predicted peanut-shaped delamination is large and elliptic in shape and orientated along the length of the panel in the direction of the 0 • ply. It should be noted that due to the large delamination on the 90 • /0 • interface, the predicted delaminations below this interface cannot be observed in the overlapped view of the numerical, or experimentally-measured, simple damage footprint maps. Thus, the exploded view in Fig. 12 can be employed to show the details of the delaminations on these interfaces which are obscured by the larger damage footprint areas. These exploded views clearly show that delaminations occur on the interfaces at different depths of the CFRP patch and develop as to be expected from the physics and micromechanics of the impact event demonstrating the capability of the model. For example, the delamination has a characteristic peanut shape with the orientation of the maximum extent of the delamination being aligned in the ply direction beneath the ply interface. The delamination tends to grow in the direction of the ply beneath the ply interface, as this ply can deflect in that direction. Also, delaminations increase in extent as you move away from the impactor face, as they are initiated by localised indentation and associated matrix cracking that occurs under the impactor. The delamination is largest in extent at a depth of about 1.5 mm, as this is just below the neutral axis where the shear stresses reach their maximum. The tendency for a delamination to occur at the 90 o /90 o interface is low, as the relative bending stiffness of the plies is similar due to the relative fibre orientation of the plies. Finally, there were no indications of any adhesive cracking or adhesive/CFRP interfacial debonding in the patch-repaired specimens at all. These experimental observations are in agreement with the results from the FEA studies, which indeed predicted that no such adhesive cracking or debonding would occur in the impacted patch-repaired specimens. Thus, the film adhesive used in these applications is very effective at providing a good level of intrinsic adhesion such that the composite is found to fail rather than the film adhesive, as is typically the case in engineering applications.

Intralaminar damage
Some of the post-impacted patch-repaired panels were examined using optical microscopy to study the formation of any intralaminar cracking in the patch. Fig. 13 shows two cross-sections comparing the experimentally-observed and numerically-predicted intralaminar matrix cracking damage in a patch from a post-impacted thin (i.e. 2.3 mm thickness) 55 mm diameter patch-repaired panel, where the red rectangle represents the region that has been inspected. There is relatively extensive intralaminar matrix cracking through the thickness of the patch. This has been accurately captured by the numerical model, which predicts a very similar distribution of intralaminar damage to the experimental observations. Interestingly, the cross-sectional damage map from the numerical simulation reveals a significant and continuous intralaminar matrix crack just above the central blocking 90 • plies, which is in agreement with the optical micrograph. This was undoubtedly a precursor to the initiation and propagation of the major delaminations that occurred at the ply interfaces below and above the central-blocking 90 • plies, as shown Fig. 12.

Permanent indentation damage
Many experimental studies [30,45,48] have reported that a permanent indentation can be induced on the impacted surface of composite laminates when subjected to a low-velocity impact using a hard impactor. Fig. 14 presents the numerically-predicted indentation depths for the pristine and patch-repaired panels and Table 3   patch and so variations in indentation depth and extent are observed. A problem for aircraft structures subject to impact is that the delamination damage is frequently hidden, or barely visible, and can often only be seen by C-scan inspection. This tell-tale indentation mark could therefore be a useful diagnostic tool.

Introduction
When repairing damaged composite laminates, the hole left after the damage has been cut-out is often filled, i.e. plugged, to further support the repair patch and to prevent fluids, e.g. water, fuel, etc., from accumulating in the empty space. Therefore, the effects of using a closefitting plug on the impact behaviour of patch-repaired composites panels has been studied.

Experimental results for impact loading responses and overall interlaminar damage
The load versus time and load versus displacement curves measured for the pristine panel and a patch-repaired panel using a thin (i.e. 2.3 mm thickness) patch with a 55 mm diameter are shown in Fig. 15, with values from these data also presented in Table 4. Again, the very good repeatability of the experimental data is noteworthy. The comparisons shown in Fig. 15 demonstrate that, when a plug is introduced, the bending stiffness of the patch-repaired composite panel significantly increased from about 2 kN/mm to about 5 kN/mm, which is also higher than the about 3 kN/mm of the pristine composite panel. The duration time, maximum load and maximum displacement associated with this increase in the bending stiffness of the plugged panels also exhibit obvious changes compared to the pristine and non-plugged composite panels, as shown in Table 4. Based on these results it would appear that the presence of a plug in the hole, which replaces the cut-out damaged composite region, can benefit the repaired panel by increasing the stiffness and reducing the deformation due to external impact loading. However, a consequence of this is that there is a more abrupt load drop for the load response, from about 7.8 kN to just over 6 kN with accompanying oscillations in load, for the plugged composite panels. This load drop is believed to be caused by matrix cracking and subsequent delaminations [49,50]. The higher stiffness and higher maximum load, storing more strain energy, for the plugged composite panels, results in a more marked load drop, when compared with pristine and non-plugged composite panels.
Considering the overall delamination damage that was measured, the damage maps experimentally-measured from the C-scan inspection technique from the top and the bottom surfaces of the pristine and patch-repaired composite panels are presented in Fig. 16. (It should be noted that, due to the presence of the hole cut-out in the parent CFRP under the non-plugged repair patch, no C-scan maps could be obtained from the bottom surface inspection on the non-plugged panels.) A comparison of these damage maps shows that the plugged panel clearly exhibits the smallest damage footprint among these three panel designs. This confirms that the introduction of the CFRP plug significantly contributes to obtaining a very good impact performance of a patchrepaired composite panel, as shown in Fig. 15 and Table 4. The reason is that the presence of a plug increases the bending stiffness of the patchrepaired composite panel and so decreases the out-of-plane Table 2 Comparison between the areas of the damage footprints for interlaminar damage obtained from the experimental studies and the numerical predictions for the pristine and patch-repaired panels using various designs of non-plugged repair patch.  displacement due to an impact load. As a result, this will constrain the growth of delaminations within the panel, which is reflected by the superior structural integrity of the plugged patch-repaired panel. Fig. 17 presents the loading responses obtained from experiment and numerical modelling simulations undertaken using the thin patchrepaired panels, with a 55 mm diameter patch and a plug. The experimentally-measured and numerically-predicted impact responses  shown in Fig. 17 indicate that the numerical model can accurately capture the key features in the overall loading versus time curves, including the peak load and duration as well as the notable load drop, etc. Fig. 18 shows the experimentally-measured and numericallypredicted interlaminar damage footprint contours obtained from patch-repaired panels with thin (i.e. 2.3 mm thickness) 55 mm diameter patches with plugs as seen from (a) the top surface and (b) the bottom surface. The agreement between the experimental and numerical results is again good.

Intralaminar damage
Before considering a comparison between the experimentallyobserved and numerically-predicted intralaminar damage in the thin (i.e. 2.3 mm thickness) 55 mm diameter patch-repaired panels with a CFRP plug, it is of interest to compare the experimental results for the thin (i.e. 2.3 mm thickness) 55 mm diameter patch-repaired panels with and without a plug present. Fig. 19 shows optical micrographs obtained from cross-sections of the (a) non-plugged and (b) the plugged thin (i.e. 2.3 mm thickness) 55 mm diameter patch-repaired panels, where the red rectangle represents the region that has been inspected. The micrographs of the non-plugged and plugged panels show that the interlaminar cracks, i.e. delaminations, at the interfaces near to the bottom surface were found to be linked with each other through 45 • aligned intralaminar matrix cracks, which are formed due to the tensile stresses acting on the bottom plies. In the plugged panel, no detectable cracking is observed at the interfaces between the adhesive layer and the CFRP patch and the CFRP plug, as was indeed predicted from the modelling studies. However, obvious and continuous interlaminar cracking can be observed on the third interface (counting from top to bottom) which agrees with the C-scan results. The lengths of the interlaminar cracks in the patch-repaired panels containing a CFRP plug are considerably shorter than those seen in the non-plugged panels, which is reflected by the significantly smaller damage area in the C-scan maps, see Fig. 17. The good predictive capability of the proposed model is confirmed in Fig. 20, by comparing the experimentally-observed and numericallypredicted intralaminar damage in the thin (i.e. 2.3 mm thickness) 55 mm diameter patch-repaired panels containing a plug. Fig. 21 shows the indentation of the impacted surface of the thin (i.e. 2.3 mm thickness) 55 mm diameter patch-repaired panels containing a CFRP plug, for both: (a) the numerically-predicted indentation and (b) a comparison between the measured and predicted indentations. Fig. 21b shows that there is good agreement between the measured and predicted values of the permanent indentation. From Table 3 the measured permanent indentation of the corresponding non-plugged panel was 160 ± 20 μm, compared with 65 ± 15 μm for the corresponding panel containing a plug. Thus, the plug significantly decreases the depth of permanent indentation that results from the impactor striking the patch. This arises from the plug giving support to the repair and hence the plastic deformation in the patch is reduced, which leads to a reduction in the intralaminar and interlaminar damage by virtue of the presence of the supporting plug.

Post-impact status of the adhesive layer
The damage maps of the adhesive layers in the non-plugged and plugged repaired panels were extracted from the numerical simulation and compared in Fig. 22. The comparison shows that minor damage in Table 3 Comparison between indentation depths obtained from experimental measurements and numerical predictions for the pristine and patch-repaired composite panels.      the adhesive layer was observed in the region near to the edge of the hole for the non-plugged repaired panel, whilst damage in the adhesive layer of the plugged repaired panel was only observed in the central area. Clearly, adding a plug alters the stress distribution in the repair structure. These results showed that the introduction of the plug can provide for protection of the adhesive bonding between the patch and the parent panel in the overlap region by providing more support. However, for the plugged case, some damage in the adhesive layer now occurs under the impact site.

Conclusions
In this paper, the compressive strength and impact resistance of both the pristine and patch-repaired composite laminates are experimentally evaluated. Subsequently, a three-dimensional elastic-plastic computational model from Ref. [30] has been extended and employed to predict the impact behaviour of both pristine CFRP panels and various designs of patch-repaired CFRP panels. The key findings in this research are presented below.
• The 3-D FEA model is capable of replicating the load versus time and load versus displacement behaviour from drop-weight impact tests very well and accurately captures the damage initiation associated with load drops or changes in stiffness. • Delaminations predicted using the 3-D FEA model exhibit a very similar shape and extent through the thickness of the panels as observed by C-scan inspection. Permanent indentations associated with the matrix plasticity and cracking are also accurately predicted. • Comparison between the results of laminates repaired with different patches shows that a relatively thick patch can reduce the deformation and delamination of repaired laminates. However, an increase in the diameter of the patch has little effect once an adequate bonded-overlap is achieved.  • The presence of a plug in the hole, to replace the cut-out damaged region, can benefit the patch-repaired panel by increasing the stiffness of the patch-repaired region and so reducing the deformation and damage due to external impact loading.
In all cases, the 3-D FEA model is able to reasonably capture the overall deformation and damage of pristine and repaired composite laminates subjected to impact loading. Future research will focus on the effectiveness of different repair techniques for composite materials, so that the developed model can serve as a powerful design tool for composite repair.

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability
Data will be made available on request.

The material response prior to the initiation of intralaminar damage
An extended elastic-plastic (E-P) constitutive model has been developed from previous research [30,51,52] to capture the material response prior to the initiation of matrix cracking and other failure processes and is given by: where dε ij and dγ ij (i, j = 1, 2, 3) are the incremental total strains and dσ ij and dτ ij (i, j = 1, 2, 3) are the incremental stresses. The terms be set as having a value of two and the coefficient a 55 , associated with τ 2 13 , is equal in value to the coefficient a 66 , associated with τ 2 12 . Now, the coefficient a 66 can be readily determined from off-axis tensile and compression experiments, relative to the fibre direction, using a unidirectional composite, The relationship between the effective stress, σ eff , and the effective plastic strain, ε p eff , can be expressed as a power-law function, given by: where A and n are the nonlinear coefficients, which can be determined by fitting to the σ eff versus ε p eff data, again as obtained from the off-axis experiments are employed using a unidirectional composite e.g. Refs. [53][54][55]. Based on the determined single parameter, a 66 , and the nonlinear coefficients, A and n, the incremental plastic strain tensors, dε p ij (i, j = 1, 2, 3), can be calculated as:

A.1.2 The initiation of intralaminar damage
The Northwestern University (NU) damage criteria were employed to capture the initiation of intralaminar damage in the CFRP laminates, such as matrix cracking, etc. The NU criteria were proposed by Daniel et al. [38,56]. These 3-D criteria are partially interactive failure criteria, in which more than one stress component has been used to evaluate the different failure modes. The mathematical details of the damage initiation model for a composite ply are given in Table A-1, where σ ij and τ ij are the normal and shear stresses and F iT (i = 1, 2, 3), F iC (i = 1, 2, 3) and F iS (i = 2, 3) are the tensile, compressive and shear damage criteria in the three material directions, respectively, and the initiation of damage is predicted to occur when F ≥ 1. The terms S it (i = 1, 2, 3) are the tensile strengths in the three material directions and S ic (i = 1, 2, 3) are the compressive strengths in the three material directions. Finally, S 12 , S 13 and S 23 represent the shear strengths in the corresponding material directions. The use of these criteria for the initiation of intralaminar damage are included in the flow chart for the FEA model.

A.1.3 The propagation of intralaminar damage
The damage evolution law, based on the energy dissipated during the damage process and assuming linear material softening, was used to predict the evolution of the intralaminar damage in the composite skins. Corresponding to the damage initiation mechanisms defined in the NU damage criteria, eight damage parameters are defined in the damage evolution model. A general form of the damage variable for a particular damage initiation mechanism is given by Ref. [57]: where: when d = d 1t this represents longitudinal tensile-dominated failure, when d = d 1c this represents longitudinal compression-dominated failure, when d = d 2t this represents transverse tensile-dominated failure, when d = d 2c this represents transverse compression-dominated failure and when d = d 2s this refers to transverse shear-dominated failure. Similarly, when d = d 3t this represents through-thickness tensile-dominated failure, and when d = d 3c and d = d 3s these refer to the through-thickness compression-dominated failure and through-thickness shear-dominated failure, respectively. The strains, ε and ε p , are the combined total strain and the combined plastic strain respectively in the composite ply. The strain values, ε 0 and ε f , are the combined strains corresponding to initial failure and final failure, respectively. For longitudinal tension or compression failure, the strains ε, ε 0 and ε f would be assigned to be ε = ε 11 , ε 0 = ε 0 11 and ε f = ε f 11 , respectively. For transverse tension or compression failure, the strains ε, ε 0 and ε f would be assigned to be ε = where the respective values of G c | ij are the tensile, G Ic | ft , and compressive, G Ic | fc , intralaminar ply fracture energies in the longitudinal fibre-direction, and for the transverse direction are the tensile, G Ic | mt , compressive, G Ic | mc , and shear, G IIc | ms , intralaminar ply fracture energies. The term σ 0 ij is the stress corresponding to damage initiation and l c is the characteristic length which can be determined based on the volume of the elements.

A.2.1 Initiation of interlaminar damage
Interlaminar damage typically involves the initiation and growth of delaminations, i.e. interlaminar cracking, between the plies that make up the composite skins and this was captured using the 'Abaqus/Explicit' built-in cohesive law (i.e. interface) element, having a zero thickness, using a fracture-mechanics approach. The interface element was described via a cohesive (i.e. damage) surface law [59][60][61][62][63] where a traction, t, is a function of the displacement, δ, and is in the form of a bilinear cohesive law for a linear-softening material model with a stiffness, k, and an initial stiffness of k i . Interface elements were inserted between each ply of composite material in the CFRP laminates, using the properties shown in Table 1 for the CFRP. For the interlaminar failure, a quadratic-traction criterion was employed to capture the damage initiation in the interface, as given by Ref. [64]: where t i (i = 33, 31, 32) represent the current normal and shear tractions and t 0 i (i = 33, 31, 32) represent the normal and shear cohesive strengths. The corresponding displacements are denoted by δ 33 , δ 31 and δ 32 , and by δ 0 33 , δ 0 31 and δ 0 32 , respectively. The value of the cohesive strength, t 0 33 , was determined from the theory proposed in Refs. [65,66], which maintains computation accuracy whilst avoiding a very fine mesh and a commensurate increase in computational cost, and for the shear cohesive strengths then t 0 31 = t 0 32 . Thus, the onset of damage initiation at δ 0 which may be defined at a value of the combined displacement in the cohesive law when: ̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ ̅ 〈δ 33

A.2.2 Evolution of interlaminar damage
The energy-based Benzeggagh-Kenane (B-K) [67,68] criterion for Mixed-mode propagation was used to derive a total value G c for the growth of the delamination and is given by: where G Ic is the Mode I (opening tensile),G IIc is the Mode II (in-plane shear) interlaminar facture energy, and η is the B-K Mixed-mode interaction exponent. The values of G Ic , G IIc and η may all be experimentally measured [69,70] and so inputted into the FEA model. The parameters G I , G II and G III are the current Mode I (opening tensile), Mode II (in-plane shear) and Mode III (anti-plane shear) energy-release rates, respectively, as calculated from the FEA code. For the node at the interlaminar crack tip, an interlaminar damage parameter, d inter , may be defined from degrading the initial cohesive stiffness, k i (i = 33, 31, 32) as the interlaminar damage after initiation, when δ = δ o , now evolves to the point when separation, i.e. interlaminar cracking, occurs at δ = δ f . Now, this interlaminar damage parameter, d inter , starts with a value of 0 when δ = δ o and finishes with a value of 1 when δ = δ f according to the relationship: where the term δ = ̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ ̅ 〈δ 33 2 〉 + δ 31 2 + δ 32