Experimental and numerical assessment of aerospace grade composites based on high-velocity impact experiments

Accepted Manuscript Experimental and numerical assessment of aerospace grade composites based on high-velocity impact experiments. Tim Wagner, Sebastian Heimbs, Florian Franke, Uli Burger, Peter Middendorf PII: DOI: Reference:

S0263-8223(18)30677-9 https://doi.org/10.1016/j.compstruct.2018.07.019 COST 9936

To appear in:

Composite Structures

Please cite this article as: Wagner, T., Heimbs, S., Franke, F., Burger, U., Middendorf, P., Experimental and numerical assessment of aerospace grade composites based on high-velocity impact experiments., Composite Structures (2018), doi: https://doi.org/10.1016/j.compstruct.2018.07.019

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Experimental and numerical assessment of aerospace grade composites based on high-velocity impact experiments. Tim Wagnera,∗, Sebastian Heimbsb , Florian Frankec , Uli Burgerc , Peter Middendorfd a Airbus

Central R&T, 81663 Munich, Germany Operations, 21129 Hamburg, Germany c Technische Hochschule Ingolstadt , 85049 Ingolstadt, Germany d University of Stuttgart, 70569 Stuttgart, Germany b Airbus

Abstract The experimental and numerical assessment of different aerospace grade composite materials under high-velocity impact is treated in this study. Characterisation of the materials, including thermosets (epoxy) and thermoplastics (PEEK) with carbon (unidirectional and woven fabric) and glass fibres, was conducted using high-velocity impact experiments. The test results indicate the glass fibre composites’ superiority in the domain of classical composites in terms of weight-specific impact performance. The different carbon fibre composites have very similar ballistic limits but differ in terms of delamination behaviour. Subsequently, materials models are developed which reproduce interlaminar failure through the usage of surface-based cohesive contact formulations. By these means efficient and reliable simulation methods for impact events are developed. Keywords: High-velocity impact, Impact simulation, S-2 glass fibre, HTS carbon fibre, HTA carbon fibre, Abaqus/Explicit

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1. Introduction Fibre-reinforced plastics’ (FRPs) usage in recent aerospace developments is still growing. Within the domain of composite materials, glass fibre (GF) and carbon fibre (CF) materials are most widely used. Due to their advantage of weight-specific strength and stiffness they are replacing traditional metals in more and more areas. Especially in areas that are prone to foreign object impact damage, the use of composite materials requires special attention. Compared to classical metal materials, FRPs show a much broader range of potential failure modes. Due to their anisotropy and the compound of matrix and fibre material, failure of the matrix, fibre or the interfaces between different plies can occur. This interface failure, called delamination, can play an important role in the failure of composite structures [1]. Assessment of structures through numerical methods is desirable to reduce costs for physical testing and enable fast development cycles. The finite element method (FEM) can be seen as the standard for numerical analysis. Barely visible impact damage (BVID) can be introduced through low-velocity impacts as they might occur during manufacturing and maintenance (e.g. tool drop). The numerical description of these low-velocity impacts is a large research area (e.g. [2–8]), but often requires fine meshing. This results in either high computational cost or requires special procedures, such as submodelling or multiscale methods [9] to assess large structures. Highly-dynamic impact loads often occur through objects with high weight and therefore high energies. Examples for such loads include bird strike, which is even specifically mentioned in most aviation regulations (e.g. [10] §25.631), hail impact [11] or foreign object impact damages such as runway debris, tyre debris or rim failure. These impact scenarios affect a larger area when compared to typical low-velocity impact scenarios. For such analysis the usage of a fine mesh would require unreasonably long computations. Explicit simulations of such low and high-velocity impacts often utilise cohesive element formulations to capture the interlaminar behaviour (e.g. in [12, 13]). These cohesive elements are computationally ∗ Corresponding

author Email address: [email protected] (Tim Wagner)

Preprint submitted to Composite Structures

June 27, 2018

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expensive as they often are a main driver in the critical time step calculation. Surface-based cohesive contact formulations are promising a less severe effect on the total computational effort of a simulation [14]. To develop numerical methods which capture the effects in high-velocity impact with the help of surface-based cohesive formulations was the goal of this research. As mentioned, carbon and glass fibres are the most important representatives of composite materials in aerospace applications. As matrix materials, either epoxy based thermosets or thermoplastics are deployed. To assess the capabilities of these materials and to develop efficient simulation methods for large numerical applications, an extensive test campaign is necessary. Following a building bock approach which unifies physical testing and simulation from an early stage on, leads to reliable simulation models. Utilising this approach is capable of achieving certification through simulation as presented by Heimbs et al. [15]. Figure 1 illustrates the building block approach deployed in this study. On the coupon level, material characterisations for in-plane and out-of-plane behaviour were conducted. Tensile, compressive and shear tests according to DIN EN ISO 527-4, DIN EN ISO 527-5, ISO 14126 and ISO 14129 were performed. The shear tests used ±45◦ tensile specimens. To assess the out-of-plane behaviour, and in this context the aforementioned delamination behaviour, double cantilever beam (DCB) and end-notched flexure (ENF) tests based on DIN EN 6033 and DIN EN 6034 were conducted. A high-velocity impact test campaign was conducted in the context of this research to cover the element level of the building block approach and is the experimental focus of this publication. A spherical impactor was accelerated using a gas gun and hit a 300 mm x 200 mm large, flat composite panel with a thickness of approximately 2 mm. Velocities ranged from 38 m/s – 102 m/s to assess the ballistic limit as well as damage evolution with increasing velocities. Four different FRPs were tested. S-2 glass R fabric with epoxy resin (EP), unidirectional (UD) HTS carbon fibres, available through SAERTEX R as a non-crimp-fabric (NCF), with epoxy resin, HTA carbon fibre fabric with epoxy resin and a unidirectional HTS carbon fibre with a thermoplastic PEEK matrix. The component level of the test pyramid is usually covered through simultaneous testing and numerical simulation of small but critical parts of the final structure (e.g. [16]). The aim of this building block approach is the fully numerical assessment of the top level of the test pyramid. Through continuous correlation at the different levels, expensive physical testing can be reduced and design changes can be incorporated in an early stage of the design process [17].

Structure level

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Figure 1: Building block approach used in this study which unifies physical testing and simulation to derive reliable models for structure level applications.

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2. Material characterisation The following section describes the selected composite materials and their characterisations in terms of the highvelocity impact test campaign. 2

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2.1. Materials

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To obtain comparable test results, the thickness of all 4 materials was selected at around 2 mm. Due to the different thicknesses of a single ply of each material and to achieve a quasi-isotropic layup in all plates, the final plate thickness varied slightly among the tested materials. Width and height of each plate was 300 mm x 200 mm. The S-2 glass R fabric with epoxy resin (S-2 fabric/EP), was composed of an 8H satin weave material from Hexcel (HexForce R 6781) and Hexcel HexFlow R RTM6 resin. The manufacturing was done using a vacuum assisted process (VAP R ) resin transfer moulding and curing of the resin at 180◦C. The symmetric 8 ply stacking sequence of the laminate was [±45/0 − 90]2S . This resulted in a cured thickness of the plates of 2.14 mm and a fibre volume fraction of 45%. The density was measured at 1.73 g/cm3 . The HTS unidirectional carbon fibre material was a Tenax HTS 12K fibre with RTM6 epoxy resin (CF UD/EP). The process was the same as described for the S-2 glass R fabric. The 8 ply layup of [−45/ + 45/0/90]S lead to a 2.16 mm thick plate. The fibre volume fraction was 56% and the density was 1.50 g/cm3 . The carbon fibre fabric consisted of Tenax HTA40 E13 carbon fibre with RTM6 resin (CF fabric/EP). The fabric material was a plain weave fabric from C. Cramer & Co (CCC) Style 450. The manufacturing process of the 11 plies plates resulted in a fibre volume fraction of 48 % and a laminate density of 1.44 g/cm3 . The stacking sequence was [±45/0 − 90/ ± 45/0 − 90/ ± 45/0 − 90]S with a cured thickness of 2.57 mm. The last representative of the composite materials was manufactured from a Tenax E HTS45 12K carbon fibre and a high-performance PEEK thermoplastic matrix (CF UD/PEEK). The thickness of the 16 ply laminate with stacking sequence [+45/90/ − 45/0]2S was 2.20 mm with a fibre volume fraction of 56% and a density of 1.55 g/cm3 .

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2.2. Test set-up

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The impact test set-up consisted of a gas gun. The impactor, a glass sphere with a mass of 55 g and a diameter of 35 mm, was accelerated along a 5 m long pipe by releasing pressurised air from a pressure tank. Due to the lower density of glass compared to steel, higher velocities could be achieved before the ballistic limit was reached. Failure of the glass sphere did not occur throughout the study. The velocity of the impactor was measured via a light barrier right after separation from the sabot. Between six and nine plates were impact for each material combination. Due to scatter and measurement inaccuracies achieving the exact same velocity multiple times is difficult. A dense velocity range was tested in close proximity to the ballistic limit. The impact target was clamped in a steel frame purely based on friction. No bolts were used to fixate the specimen. However, possible slippage of the specimen was afterwards excluded as no scratches on the specimen surfaces were found by microscopy. An overview of the test facility is shown in Figure 2. Further details on the high-velocity experimental test set-up can be found in [18]. High-speed camera

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Pressure tank Figure 2: Test set-up for the high-velocity impact test campaign. 80 81 82 83 84 85

Ultrasonics C-Scans of all manufactured plates were conducted prior to testing to exclude preexisting damage and after impact testing to assess internal damage due to delamination and matrix cracking. A water immersion shockwave transducer for high-resolution applications was used for each test specimen. The ultrasonic scans were performed with a single, spherically focused element with a centre frequency of 5 MHz and a bandwidth of 2.5 MHz — 7.5 MHz. The auxiliary reflector echo was analysed to determine damaged areas of the plate. Darker areas in the C-Scan images denote a lower amplitude of the auxiliary echo which is caused by scatter at fracture surfaces.

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2.3. Experimental results The impact velocities for the S-2 glass R fibre fabric specimens ranged from 43.37 m/s to 100.30 m/s, corresponding to kinetic energies between 51.37 J and 276.65 J. At the lowest energy levels, damage is only externally visible on the backside of the specimen. C-Scans revealed very localised damage in the area of the externally visible damage. This damage increased linearly with the impact energy up to the ballistic limit, which was found at 216.17 J or 88.60 m/s, respectively. To account for variations in density and thickness of the tested materials alike, this value was divided by the specimen’s weight to obtain a weight-specific impact energy at perforation. All plates had the same width and height which justifies the usage of this denominator to obtain a comparable measurement unit. In case of the S-2 glass R fibre this yielded a value of 973 J/kg. At slightly higher energies of 219.30 J and 220.18 J no penetration occurred in the test programme, which can be explained with scatter effects in the specimens and measurement of the impactor velocity. Furthermore, the concept of a velocity V50 , at which 50% of the specimens are penetrated [19] supports this variance. Figure 3 shows an overview of the test results. 51.37 J 43.37 m/s Top view:

77.69 J 53.15 m/s

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The unidirectional HTS carbon with RTM6 epoxy resin (CF UD/EP) showed considerably lower impact performance in terms of the impact energies at perforation. From low energies on, internal damage was larger than in the S-2 fabric. Starting from 72.63 J, the bottom −45◦ ply of the laminate separated, which is visible in the C-scans in Figure 4 as a diagonal line. Penetration occurred at 127.38 J, yielding a weight-specific ballistic limit of 655 J/kg. It was noticeable in the test campaign, that even though no damage was visible at the lowest energy levels from the outside. a considerable amount of damage was revealed in the ultrasonic scans. The HTA carbon fibre fabric with epoxy resin (CF fabric/EP) showed a similar ballistic limit like the previous mentioned CF UD/EP material (Figure 5). However, the damage was more localised in the impact area, similar to the S-2 glass fibre’s behaviour. Furthermore, the damage pattern, a cross-shaped fibre rupture at the back of the impact point, was also comparable. The ballistic limit, at 113.59 J or 511 J/kg, was almost half of that of the glass fibre’s one. Among all CFRP tested in this study, this material showed the least impact resistance. 4

51.32 J 43.20 m/s Top view:

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72.63 J 51.39 m/s

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90.35 J 57.32 m/s

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Figure 4: Impact test results of unidirectional HTS carbon fibres with epoxy resin.

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The thermoplastic PEEK matrix in the unidirectional HTS carbon fibre material, did not influence the ballistic limit, as is visible from Figure 6. The energy at which penetration first occurred in the test programme was 123.01 J, or 601 J/kg, respectively. Damage behaviour was localised to the area of the impact and damage increased linearly with increasing impact energy. The impact test results indicated the glass fibre composites’ superiority in terms of impact performance. Figure 7 summarises the impact energies at perforation and weight-specific impact energies of the tested materials. All three carbon fibre materials yielded comparable impact performance, with the CF UD/EP material being best. The usage of a thermoplastic matrix or of a woven fabric did not improve impact performance in this study. Other experimentally obtained material properties which were necessary for modelling and simulation of impact events are summarised in Table 1. Tensile, compressive and shear moduli were obtained through quasi-static testing according to DIN EN ISO 527-4 (tensile, fabric), DIN EN ISO 527-5 (tensile, UD), ISO 14126 (compressive) and ISO 14129 (±45◦ shear). Interlaminar energy release rates under mode I and mode II were obtained by quasi-static DCB and ENF experiments according to DIN EN 6033 and DIN EN 6034, respectively.

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3. Numerical implementation

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As expensive physical testing should be reduced, efficient numerical methods to replace them are necessary. Through a building block approach as presented in Figure 1, such methods can be developed which are acceptable for certification in aerospace applications. In this study, numerical models to replicate the impact behaviour from the experimental campaign in an efficient way were developed. For these simulations, the commercial software code Abaqus/Explicit 2016 was used. First, the in-plane constitutive material behaviour was implemented and validated with one element and coupon level simulations. The constitutive behaviour for the out-of-plane direction with the help of a cohesive traction-separation law was developed through DCB and ENF simulations. With these cohesive formulations, simulations of the high-velocity impact experiments were conducted. 5

53.22 J 49.99 m/s Top view:

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Figure 5: Impact test results of HTA carbon fibre fabric with epoxy resin.

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3.1. Model development For the implementation of the constitutive behaviour of the studied materials, the available methods within Abaqus were used. Hexahedral continuum shell elements (SC8R) were used to discretise the three-dimensional structure. They provide better contact detection when compared to conventional shell elements but still rely on plane-stress formulations. Second-order accuracy to prevent simulation termination due to single, quickly rotating elements (occurring after impact which penetrates the specimen) was enabled. Enhanced hourglass controls as well as the default element deletion criterion were used. For a structural level simulation, typical element sizes are 5 mm. The critical time step size and by such the size of the computational problem is directly related to the element size. All simulations in this study were performed with element sizes in this range. The material behaviour is defined based on the fibre’s dry conditions. For UD materials (CF UD/EP and CF UD/PEEK), the elastic response is defined in terms of orthotropic moduli. It was assumed that tensile and compressive moduli are identical. In-plane damage initiation is defined based on the Hashin failure criteria in its form from [20]. For fabric materials (S-2 fabric/EP and CF fabric/EP) the implemented Virtual User Material (VUMAT) ABQ PLY FABRIC was employed. It is based on the Ladeveze continuum damage model [21]. Elastic moduli were defined for tensile and compressive loads, respectively. The implemented properties are as presented in Table 1. For modelling the cohesive behaviour in the resin layer between two laminae, cohesive element (COH3D8) or surface-based cohesive contact formulations are available in Abaqus/Explicit. In reality the thickness of the resin interface is small [22] or not even clearly distinguishable. Figure 8 illustrates a micrograph of CF UD/PEEK where the thickness of the resin at the ply interface is not distinguishable. For such applications, cohesive elements with zero thickness [23] or a surface-based interaction [14] can be used to model the resin behaviour. However, cohesive elements, also those with zero thickness, often require a fine mesh and by such negatively influence the critical time step. Cohesive contacts are node to surface based interactions and follow a similar constitutive behaviour as cohesive elements. They promise better performance and are more versatile for modelling of complex geometries. While the process to define cohesive elements requires creation of an orphan 6

39.32 J 37.77 m/s Top view:

41.31 J 38.76 m/s

67.93 J 49.70 m/s

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Figure 6: Impact test results of unidirectional HTS carbon fibres with PEEK matrix.

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mesh, which needs to be recreated if there is a minor design change, surface-based definitions allow for quicker and less error prone adaption. Following the presented building block approach, the cohesive behaviour was implemented in DCB and ENF simulations. Besides the experimental and numerical assessment of DCB and ENF specimens, analytical expressions have been presented by Diehl [24] and Fiolka [25] for DCB and ENF respectively. The parameters for the tractionseparation law are the stiffness in normal (Knn ) and shear directions (K ss and Ktt ) and a damage initiation and evolution criterion. In the present study, the maximum nominal stress criterion was selected to define damage initiation. Damage evolution was defined based on the measured energy release rates from the DCB and ENF experiments (G Ic and G IIc ). Softening was assumed to be linear while the mixed mode behaviour was selected according to Benzeggagh and Kenane [26], with an exponent of 2.58. Several authors presented approaches for calculating the parameters of the traction-separation law [24, 27–29]. However, in surface-based cohesive contacts, the stiffness and damage initiation values in these approaches do not lead to meaningful results for explicit simulations. Due to the high stiffness in the order of several GPa large vibrations were introduced into the simulations. High damage initiation values can lead to unstable failure. Therefore, these values were fitted to replicate the coupon level experiments. The energy release rates are seen as physically sound parameters and were implemented as given in Table 1. It should be noted that the in-plane and out-of-plane parameters of the cohesive behaviour influence each other. Figure 9 and Figure 10 summarise the results of these simulations and compare them to the experiments and analytical solutions. Good agreement was found in all cases, following the presented approach. An exception was the DCB experiment for CF UD/PEEK. The observed initial stiffness deviates from the analytical expression and could not be properly reproduced in simulations. Mesh sensitivity was found to be low and good results were achieved with 5 mm meshes. The derived cohesive parameters are summarised in Table 2 The high-velocity experiments were modelled using the developed delamination model for each material. The test set-up was modelled in accordance with the conditions from the physical experiment. It has become obvious that accurate boundary conditions are essential in reliable simulations [30]. Simplified boundary conditions, such 7

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Tensile modulus 1-direction E1 Tensile modulus 2-direction E2 Shear modulus 1,2-direction G12 Tensile strength 1-direction X t Tensile strength 2-direction Y t Compressive strength 1-direction X c Compressive strength 2-direction Y c Mode I energy release rate G Ic Mode II energy release rate G IIc

[GPa] [GPa] [GPa] [MPa] [MPa] [MPa] [MPa] [J/m2 ] [J/m2 ]

S-2 fabric / EP 23.5 22.0 2.67 549 504 472 433 1460 1943

CF UD / EP 120.0 8.5 4.50 1970 67 990 240 365 1990

CF fabric / EP 64.6 64.4 3.75 852 860 639 645 453 1866

CF UD / PEEK 130.0 8.5 2.67 2450 88 1578 240 1517 2530

Table 1: Material properties of the tested materials which were used in the numerical implementations.

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as assuming a fully fixed plate border, has lead to preliminary material failure due to overprediction of the stiffness. The model set-up is illustrated in Figure 11. The stacking sequences, as presented in subsection 2.1, were split into two parts. A delamination interface was introduced in the symmetry layer. Element sizes of 5 mm in-plane and approximately 1 mm out-of-plane (corresponding to 1 element over the thickness of half a plate) were used. A time period of 3 ms was simulated. It should be noted that the delamination interfaces in the simulation were located in between 0◦ or 90◦ plies. Research [31] indicates that energy release rates between differently oriented plies might differ from the values obtained by classical DCB and ENF experiments, where usually a precrack is introduced in between two 0◦ plies. Therefore, introduction of delamination interfaces at other positions requires special attention.

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3.2. Numerical results

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Numerical simulations of the high-velocity impact test campaign were conducted. With the presented numerical model and 5 mm meshing, the total problem size was approximately 28 000 elements which took roughly 5 minutes of calculations on 16 CPUs. These calculation times are reasonable for transfer of the methods into larger application as will be presented by the end of this section. 8

Figure 8: Micrograph of a CF UD/PEEK specimen. The resin thickness between plies is hardly distinguishable.

Stiffness normal direction Knn Stiffness shear direction K ss = Ktt Maximum normal stress Maximum shear stress Mode I energy release rate G Ic Mode II energy release rate G IIc

[GPa] [GPa] [MPa] [MPa] [J/m2 ] [J/m2 ]

S-2 fabric / EP 0.583 1.00 1.17 155.40 1460 1943

CF UD / EP 0.583 0.583 6.16 36.464 365 1990

CF fabric / EP 0.583 0.583 11.68 15.54 453 1866

CF UD / PEEK 0.383 0.648 2.00 40.48 1517 2530

Table 2: Parameters of the cohesive traction-separation law of the tested materials.

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The simulation models were able to properly reproduce the impact behaviour. Through the introduction of a delamination model, the ballistic limit was correctly reflected in the simulations. Without such a model, simulations were too conservative. The additional energy absorption due to separation of cohesive surfaces was responsible for this increase in ballistic performance. Figure 12 shows the correct representation of the ballistic limit for S-2 fabric/EP. The simulation for the S-2 fabric/EP material, shown in Figure 13, indicated that delamination was slightly overpredicted. At low energy levels, hardly any damage was present in either simulation or experiment. It should be noted that the damaged area at these low energy levels has a diameter of roughly 5 mm, about the same size as the simulation’s elements. At higher energies, delamination shape and size were in good agreement and can be interpreted as slightly conservative. The results were seen as a good agreement and basis for application in structure level simulations. The simulations underpredicted the expected delamination for the CF UD / EP material. At low energy levels as shown in Figure 14 (a), the difference was acceptable. However for the higher energy level, as shown in Figure 14 (b), the model was not able to properly reproduce the delaminated area. In the present simulation approach, only one delamination interface was incorporated. Delamination does however not solely occur in the symmetry layer in physical testing. As can be seen from Figure 15 (a), the outer parts of the cross-shaped damaged area did not lead to the same reduction in amplitude in the ultrasonic c-scan and it can be concluded that less damage was present in these areas. It should also be noted that the diagonal line from the top left corner to the bottom right corner of the image is due to spalling of the backmost −45◦ layer and is not covered in the simulation model. This would require modelling of every individual ply. If only the area of lowest amplitude (dark areas), corresponding to the largest damage, is considered, the underprediction of delamination is less severe, as can be seen in Figure 15 (b). This indicates that the current model for the CF UD / EP material is generally capable of predicting the areas of large damage but should be improved for an industrial application case where conservatism is required. This can be achieved through the introduction of further delamination interfaces but which lead to a higher computational effort. 9

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Application of the numerical methods to larger structure level simulations is illustrated in Figure 16. The impact of a wheel fragment onto an aircraft wing structure is shown. Dark areas indicate delamination. In such a simulation with approximately 250 000 elements and a simulated time period of 20 ms, the approach allows for turn-around times in the order of 5 hours, which is seen as efficient for a risk assessment in the design phase.

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4. Discussion & Conclusions

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The impact test campaign demonstrated the S-2 glass R fibre’s superiority in terms of impact performance compared to carbon fibre composites. These carbon fibre materials showed very similar ballistic limits but differ in delamination behaviour. CF UD / EP showed the best performance among these carbon fibre materials, but also showed the most severe delamination behaviour. At low impact energies, large internal damage became obvious through ultrasonic scans. CF UD / PEEK, the thermoset representative in this study, should be in contemplation for future applications as similar structural performance is present while the delamination behaviour is beneficial. The development of efficient numerical models along a building block approach lead to reliable simulations. The application of DCB and ENF experiments to derive cohesive contact delamination models is promising. Even though the stiffness and damage initiation parameters can not directly be linked to physically sound expressions, correlation between test and simulation lead to good results. The application of these methods to impact simulations showed a good overall agreement with experiments and gave an overview of expected damage behaviour. However for materials where delamination is prevalent even at 10

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low energy levels (CF UD / EP), the described methods underestimate the actual damage. Before application in an industrial set-up, these methods should gain conservatism. Cohesive element formulations might be able to reproduce failure more detailed, especially if fine meshes for the impact area are used, but the computational effort is much higher and might require submodelling or multiscale approaches. If such additional effort is not desired the presented approach provides a good comprehensive view. In future research the implementation of more advanced composite failure theories than the Hashin theory could provide ground for improvements for modelling of UD materials. In the present study no interaction between intraand interlaminar failure has been implemented. The commercially implemented methods do not directly allow for such an interaction. Future studies to further improve the simulation methods while maintaining the computational efficiency could also include the development of Virtual User Material (VUMAT) models which can cover this interaction (e.g. presented in [13]). For the preliminary and early design phase, the presented methods provide an efficient approach for numerical predictions of high-velocity impact responses.

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5. Declaration of competing interests

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The authors declare no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

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Figure 11: Experimental set-up (a) and numerical implementation (b).

(a) 178.21 J (80.50 m/s)

(b) 216.17 J (88.66 m/s)

Figure 12: Simulations of the S-2 fabric / EP experiments. Penetration of the specimen is correctly rejected or allowed. (a) no penetration, (b) penetration.

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6. Acknowledgments Part of this study was performed within the framework of the project MAI Impact, funded by the Federal Ministry of Education and Research of Germany (BMBF) under grant agreement no. 03MAI40B. The financial support is gratefully acknowledged.

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Figure 13: Simulation of the S-2 fabric / EP experiments. Delamination was reasonably represented. (a) Delamination at low energies was hardly present in experiment and simulation. (b) Delamination was conservative in the simulation compared to the experiment.

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Figure 14: Simulation of the CF UD / EP experiments. Delamination is underpredicted at low (a) and high (b) energy levels.

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Figure 15: If only the area of lowest amplitude in the C-Scan is considered (dark blue areas), the underprediction of delamination is less severe.

Figure 16: Possible application of the developed numerical methods. Wheel fragment impacting an aircraft wing structure. Dark areas indicate delamination.

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