# Parametric experimental-numerical investigation of the impact behavior of Carbon/Epoxy composites

Ayoub Soufri, Christophe Bouvet, Ameur Chettah

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Ayoub Soufri, Christophe Bouvet, Ameur Chettah. Parametric experimental-numerical investigation of the impact behavior of Carbon/Epoxy composites. Journal of Composite Materials, 2025, 10.1177/00219983251366218. hal-05224686

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Parametric experimental-numerical investigation of the
impact behavior of Carbon/Epoxy composites

<table><tr><td>Journal:</td><td>Journal of Composite Materials</td></tr><tr><td>Manuscript ID</td><td>JCM-25-0038.R2</td></tr><tr><td>Manuscript Type:</td><td>Original Manuscript</td></tr><tr><td>Date Submitted by the Author:</td><td>n/a</td></tr><tr><td>Complete List of Authors:</td><td>Soufri, Ayoub; Université de Bourgogne, ISAT bouvet, christophe; ISAE-SUPAERO, ; Clement Ader Institute, Chettah, Ameur; Université de Bourgogne, ISAT;</td></tr><tr><td>Keywords:</td><td>impact, Composite structures, finite element model, Discrete ply model</td></tr><tr><td>Abstract:</td><td>This article provides test/model dialogue of impact on composite laminates at low and medium impact velocity. An experimental setup featuring a compressed air cannon launches projectiles at composite laminates, while high-speed imaging, load measurement, and infrared thermography enable in-situ damage monitoring. Numerical simulations employ the Discrete Ply Model (DPM) to analyze the impact events and damage evolution. The study examines various impact parameters, such as projectile energy, velocity, and impact location, to assess their effects on structural response and damage mechanisms. Experimental results highlight the effectiveness of these techniques in capturing the dynamic behavior and quantifying damage from impacts. Numerical simulations offer insights into damage mechanisms, including delamination, matrix cracking, and fiber breakage, as well as their interactions. The findings elucidate damage formation during single impact and emphasize the significance of spatial impact distribution and local bending stiffness in understanding damage patterns. Validation of the numerical model against experimental results confirms its predictive capabilities, showcasing its potential for virtual testing and parametric studies. By integrating the strengths of both approaches, this article enhances understanding of the single impact behavior of composite structures, providing a valuable experimental and numerical database for researchers to test and validate their models, ultimately paving the way for improved design and performance in engineering applications.</td></tr></table>
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# Parametric experimental-numerical investigation of the impact behavior of Carbon/Epoxy composites

Ayoub Soufri<fnref n="1" />, Christophe Bouvet<fnref n="2" />, Ameur Chettah<fnref n="1" />

## Abstract

This article provides test/model dialogue of impact on composite laminates at low and medium impact velocity. An experimental setup featuring a compressed air cannon launches projectiles at composite laminates, while high-speed imaging, load measurement, and infrared thermography enable in-situ damage monitoring. Numerical simulations employ the Discrete Ply Model (DPM) to analyze the impact events and damage evolution. The study examines various impact parameters, such as projectile energy, velocity, and impact location, to assess their effects on structural response and damage mechanisms. Experimental results highlight the effectiveness of these techniques in capturing the dynamic behavior and quantifying damage from impacts. Numerical simulations offer insights into damage mechanisms, including delamination, matrix cracking, and fiber breakage, as well as their interactions. The findings elucidate damage formation during single impact and emphasize the significance of spatial impact distribution and local bending stiffness in understanding damage patterns. Validation of the numerical model against experimental results confirms its predictive capabilities, showcasing its potential for virtual testing and parametric studies. By integrating the strengths of both approaches, this article enhances understanding of the single impact behavior of composite structures, providing a valuable experimental and numerical database for researchers to test and validate their models, ultimately paving the way for improved design and performance in engineering applications.

## Keywords

Impact, composite structures, discrete ply model.

## 1 Introduction

Composite materials are frequently exposed to impact loadings by foreign objects during manufacturing, service and maintenance operations (1). Understanding the response of carbon/epoxy composites to single impact events is essential for ensuring their structural integrity, reliability, and safety under dynamic loading conditions. This article presents a comprehensive investigation into the impact behavior of carbon/epoxy composites, combining experimental and numerical approaches to gain deeper insights into the underlying mechanisms and enhance predictive capabilities.

The existing body of literature extensively [(2)-(14)] covers the single impact behavior of composite structures, primarily focusing on experimental investigations and numerical simulations. Experimental studies have employed diverse techniques, such as high-speed imaging (15) to track the projectile and verify the consistency of energy between experimental and numerical, load measurements (16), and non-destructive evaluation methods (17), to characterize the damage mechanisms and failure modes induced by impact events. These studies have revealed the complex interplay of various factors, including impact energy, velocity, projectile properties, and laminate configuration, in determining the structural response and damage progression.

The modeling of impact on composite laminates has been extensively studied in the literature [(18)-(38)] but mainly due to low velocity impacts, using various approaches to model the initiation and evolution of inter- and intra-laminar impact damage modes (continuum damage

mechanics, discrete methods, or a combination of both). This article provides the composite scientific community with experimental results of impacts on composite laminate with medium impact velocity and different boundary conditions and to explain the obtained results thanks to a test/model dialogue.

Despite all advancements, challenges persist in accurately capturing the intricate damage mechanisms and interaction between damage mechanisms. The heterogeneous nature of composites, coupled with the dynamic and often high-rate loading conditions, pose significant difficulties (39). For example, high loading rates during impacts can significantly alter mechanical properties (e.g., elastic modulus, strength) before strain softening and influence failure characteristics within localized zones (e.g., failure mechanisms, fracture energy) (40).

The influence of various parameters, including stacking sequence, impact energy, and boundary conditions, has been studied by authors such as Olsson (41) and Caprino et al. (42). Additionally, the use of high-speed imaging and

## Corresponding author:

Christophe Bouvet, Université de Toulouse, Institut Clément Ader, ISAE-SUPAERO – UPS – IMT Mines Albi – INSA – CNRS, Toulouse, 31000, France

Email: christophe.bouvet@isae-supaero.fr

<footnote n="1">¹Laboratoire DRIVE, Université de Bourgogne, Nevers, 58000, France</footnote>

<footnote n="2">²Université de Toulouse, Institut Clément Ader, ISAE-SUPAERO – UPS – IMT Mines Albi – INSA – CNRS, Toulouse, 31000, France</footnote>
infrared thermography to monitor damage during impact events has been explored by researchers including Berthe et al. (43), Emery et al. (44), and Johnston et al. (45). Berthe et al. (43) specifically explored the use of high-speed infrared (IR) thermography to monitor the evolution of damage in composite materials in real time during impact tests. Focusing on Carbon/Epoxy quasi-isotropic laminates, the tests were performed at different energy levels to demonstrate the contribution of this measurement technique to the understanding and quantification of impact damage for damage scenarios of increasing complexity. While traditional post-mortem methods like C-Scan and CT-Scan are useful, they do not provide real-time data, making it challenging to understand the progression of damage. The study demonstrated that IR thermography effectively captures damage initiation and propagation during impacts (specifically transverse and delamination crack during impact), although it tends to overestimate the extent of damage compared to other methods. Nevertheless, the real-time insights provided by IR thermography offer significant potential to enhance the understanding and prediction of damage in composite materials, making it a valuable complement to traditional post-mortem techniques. This article details the methods and tools employed in this research, including material selection, manufacturing processes, and in-situ and post-mortem impact monitoring techniques. It also introduces the Discrete Ply Model (DPM) (46) and discusses the modifications implemented to adapt it for this study.

The aim of this article is to provide the composite materials scientific community with experimental results of impact tests on composite laminates at medium impact velocities, considering various energy levels, impactor diameters, and boundary conditions, along with detailed explanations of the associated damage scenarios. Each test is repeated three times to estimate the standard deviation, particularly in relation to the delamination area, which can offer valuable insights for researchers looking to assess the reliability and variability of their models. Furthermore, the purpose of the proposed model is to facilitate a thorough dialogue between experiments and simulations, enabling a deeper understanding of the damage mechanisms. The model also helps support the experimental results obtained through the extensive instrumentation employed during the testing campaign, particularly the infrared (IR) measurements.

A summary of the studied effects and the logical sequence of the work is provided in Table 1. The reference case is first analyzed in detail to illustrate the typical damage mechanisms. Then, the capability of the Discrete Ply Model (DPM) is demonstrated. The relevance of infrared (IR) measurements is highlighted, before investigating the influence of different impact conditions.

## 2 Materials & Methods

### 2.1 Material

Composite laminates were manufactured using a draping method followed by press molding of unidirectional carbon fiber/epoxy prepreg (Gurit (49)) with a resin content of 37%. The resulting cured plates measured 380 mm × 380 mm.

<table><caption>**Table 1.** Summary of configurations, figure references, and studied effects.</caption><thead><tr><th>Configuration</th><th>Figures and descriptions</th><th>Studied effect</th></tr></thead><tbody><tr><td>Ø20/15J/A</td><td>4: Exp. & num. Cscan and curves comparison<br>5: Num. damage scenario<br>6: Num. Cscan scenario<br>7: Num. energy sorting<br>8: Cscan, IR and num. delamination<br>9–10: IR and microscopic observation, IR monitoring</td><td>Reference case (§ 3)</td></tr><tr><td>Ø20/15J/B</td><td>11: Exp. & num. Cscan</td><td>Impact position (§ 4.1)</td></tr><tr><td>Ø20/15J/C</td><td>12: Exp. & num. Cscan</td><td></td></tr><tr><td>Ø20/30J/A</td><td>13–15: Num. perforation, Exp. perforation by IR</td><td>Impact energy (§ 4.2)</td></tr><tr><td>Ø10/15J/A</td><td>16: Exp. & num. Cscan</td><td>Projectile diameter (§ 4.3)</td></tr></tbody></table>

The epoxy resin (SE 84LV) was cured using a heating rate of 2C/min, reaching a minimum viscosity temperature of 99C and achieving a dry glass transition temperature of 115C. The cure dwell time was 1 hour at 80C, followed by polymerization under 3.5 bar pressure.

High Elongation Carbon (HEC) fibers, with a reinforcement area weight of 150 $g/m^2$ per ply and a cured ply thickness of 0.175 mm, were used. The stacking sequence was [0/-45/90/45]$_s$, resulting in a quasi-isotropic laminate.

After curing, specimens with final dimensions of 350 mm × 350 mm × 1.4 mm were cut from the center region of the plates using a circular saw equipped with a diamond blade. This method ensured clean edges and minimized thermal or mechanical damage to the composite material. Following the cutting process, the plate thickness is measured for verification. The specimens are then inspected for potential manufacturing defects using ultrasonic immersion testing (C-scan). A 25 MHz transducer (NDT Automation IU25X1-1.5) in combination with the UltraPAC Immersion Systems device is employed for this purpose. For data analysis, the experimentally obtained C-scan results are compared with numerically simulated C-scans (delamination elements).

For the numerical part, the average material properties used are provided by the manufacturer (Gurit). Any missing material data were supplemented with standard values or values found in the literature ((50), (51), (52)). Table 2 summarizes the mechanical properties of the material used, where *l*, *t*, and *z* represent, respectively, the longitudinal transverse and out-of-plane direction. The primary aim of the numerical part is to understand physical phenomena
that are difficult to observe experimentally, such as wave propagation and interactions, or to investigate the effects of changing impact parameters without the need for time-consuming and costly experimental campaigns.

<table><caption>**Table 2.** Material properties.</caption><thead><tr><th>Property</th><th>Value</th><th>Description</th></tr></thead><tbody><tr><td>ρ<sub>V</sub></td><td>1600 kg/m<sup>3</sup></td><td>Mass density</td></tr><tr><td>E<sub>lt</sub></td><td>134000 MPa</td><td>Longitudinal Young's modulus in traction</td></tr><tr><td>E<sub>lc</sub></td><td>121000 MPa</td><td>Longitudinal Young's modulus in compression</td></tr><tr><td>E<sub>t</sub></td><td>8300 MPa</td><td>Transverse Young's modulus</td></tr><tr><td>ν</td><td>0.3</td><td>Poisson's ratio</td></tr><tr><td>G<sub>lt</sub></td><td>5200 MPa</td><td>Shear modulus in the plane</td></tr><tr><td>G<sub>tz</sub></td><td>E<sub>t</sub> / (2(1+ν))</td><td>Shear modulus through thickness</td></tr><tr><td>σ<sub>t</sub><sup>f</sup></td><td>40 MPa</td><td>Transverse tensile strength</td></tr><tr><td>τ<sub>lt</sub><sup>f</sup></td><td>90 MPa</td><td>Shear failure stress</td></tr><tr><td>σ<sub>0</sub></td><td>200 MPa</td><td>Crushing stress</td></tr><tr><td>ε<sub>0t</sub></td><td>0.0185</td><td>Tensile fiber failure strain</td></tr><tr><td>ε<sub>0c</sub></td><td>-0.0112</td><td>Compressive fiber failure strain</td></tr><tr><td>G<sub>Ic</sub></td><td>0.25 N/mm</td><td>Delamination mode I fracture toughness</td></tr><tr><td>G<sub>IIc</sub></td><td>1 N/mm</td><td>Delamination mode II fracture toughness</td></tr><tr><td>λ<sub>comp</sub></td><td>0.05 MPa<sup>-1</sup></td><td>Compression reinforcement coefficient</td></tr><tr><td>G<sub>ft</sub></td><td>60 N/mm</td><td>Tensile fiber fracture toughness</td></tr><tr><td>G<sub>fc</sub></td><td>10 N/mm</td><td>Compressive fiber fracture toughness</td></tr><tr><td>k<sub>mat</sub></td><td>1.10<sup>6</sup> MPa/mm</td><td>Matrix cracking interface stiffness</td></tr><tr><td>k<sub>del</sub></td><td>5.10<sup>5</sup> MPa/mm</td><td>Delamination interface stiffness</td></tr></tbody></table>

## 2.2 Methods

### 2.2.1 Experimental Setup

Figure 1 shows the experimental test bench, which is composed of five compressed air cannons, one of which is used in this study. Each cannon is equipped with an automatically controlled triggering system, which is configured based on the selected shooting parameters using a LabVIEW program. For this study, only one launcher is utilized. The setup is instrumented with four displacement sensors (Keyence LK-H082), operating at 100 kHz each, and positioned at the rear of the plate to measure displacement during impacts. A high-speed thermal camera (FLIR X6800sc) is also employed to capture and analyze thermal signatures during impacts, enabling the reconstruction of damage scenarios and their correlation with the structural response of the plate and numerical simulations. This setup allows both in-situ and post-mortem observation of impact damage in the studied material.

The velocity of the projectiles exiting the cannons is measured using chronographs (Acetech Airsoft Gun AC6000 BT), while velocities before and after impact are captured using a high-speed camera (MotionBLITZ EoSens-mini2). These measurements enable the determination of velocity vectors and the calculation of energy absorbed during

impact. Following the impacts, the plates are analyzed using immersion ultrasonic testing (C-scan). Impacts are conducted using steel balls with diameters of 20 mm and 10 mm, having respective masses of 32.7 g and 4.0 g.

A comprehensive test matrix is designed to investigate the influence of various impact parameters on the impact behavior of carbon/epoxy composite laminates. The parameters considered include:

* Effect of impact location (§4.1): Impacts are performed at three distinct locations on the plate to evaluate the sensitivity of the results to the impact position relative to the plate edges. The choice of these positions is associated with a larger test campaign using this cannon to study multi-impact on the same composite plates. The slight differences between impact positions in configurations A and B enable an assessment of the numerical model's predictive accuracy.

* Effect of impact energy (§4.2): Impact energy is varied by adjusting the air pressure in the compressed air cannon, allowing the investigation of the relationship between impact energy and damage severity up to 30 J.

* Effect of projectile diameter (§4.3): Steel projectiles with diameters of 10 mm and 20 mm are employed to study the effect of impactor size on damage patterns and failure modes.

### 2.2.2 Numerical Model Setup

A discrete ply model (DPM) has been utilized (Figure 2), initially developed for simulating impacts on composite structures, various types of damage, including delamination, matrix cracks, and fiber breaks, are observed using this model.

Figure 2 shows the Discrete Ply Model (DPM), developed by Bouvet et al. (46), designed at the mesoscale level (ply scale). Plies are divided into strips of volume elements, and cohesive interface elements with zero thickness are placed between plies to account for delamination. Additional interface elements are used along the ply length to represent matrix cracking. The coupling of inter- and intra-laminar damage is automatically handled by the model. Coupling is also ensured between inter- and intra-ply damage through the exchange of information between delamination and volume elements for fiber breakage, and between matrix cracking and volume elements for matrix cracks. Discontinuities caused by shear matrix cracks are considered, primarily induced by three stress components (the mesh of each layer represents the material's orthotropic properties to facilitate crack formation). To ensure proper representation of crack directions (despite inclined directions not being fully represented to maintain simplicity), plies are divided into small strips along the longitudinal direction, with one volume element in width and thickness. Given that the ply thickness (0.175 mm) is small compared to the total laminate thickness (1.4 mm), this approximation is deemed reasonable, justifying the use of a single finite element in the ply thickness. These strips are connected using interface elements with zero thickness. Moreover it can be shown that for the DPM the mesh size is physical, indeed it represents the physical distance between two consecutive matrix cracks (47). This distance classically equals between 1.5 and 3 times
the ply thickness; then ratio between the element size in the transverse direction (0.5 mm) and the ply thickness (0.175 mm) was chosen equal to 2.875 (and 1.4375 for the double central ply) which respects this condition. An additional work could be done in order to show that decreasing this ration up to 1.5 doesn't change significatively the results. In fact, this distance between two consecutive matrix cracking interface elements can be seen as a internal length scale (or more precisely as a stacking length scale because it is linked to the ply thickness) and it has been shown that it makes possible to account for size effect, as this one observed for the open hole tension failure (48).

The constitutive equations of the DPM have been described in detail in previous articles ((23),(32),(36),(46)), then the objective here is only to remind the main characteristics. In fact, the DPM was almost not modified for the present case of impact, and in spite of the relatively important impact velocity, no strain rate effect has been taken into account, the objective was to use the DPM to better understand the test. Nevertheless, this strain rate effect could be necessary, in particular to take into account the delamination developing near the impact perforation.

### Fiber failure model

Fiber failure is modelled using a linear softening law between the longitudinal stress and strain ($\sigma_l$ and $\varepsilon_l$), parametrized by failure initiation tensile or compressive strains ($\varepsilon_{0t}$ and $\varepsilon_{0c}$ in Table 1), and by the tensile or compressive critical strain energy release rate in mode I ($G_{ft}$ and $G_{fc}$ in Table 2):

$$ \int_V \int_0^{\varepsilon_l} \sigma_l d\varepsilon_l \cdot dV = S \cdot G_f \quad (1) $$

with $l$ being the longitudinal direction, $\varepsilon_l$ the strain of full deformation damage, $S$ and $V$ being the element section and volume, and $G_f$ the critical strain energy release rate of fibre failure.

The evaluation of the fiber fracture toughness in tension, and even more in compression, are known as very tricky, and for this study, these values are taken based on experience of previous studies ((23),(32),(36)). Moreover, these values do not seem to have a too much importance in this study, probably due to the fact that the main damage is driven by the delamination propagation. Nevertheless, recent studies shows that this value can be better evaluated thanks to compact tension test (53). Moreover, in compression, we take into consideration a plastic behavior and a crushing stress $\sigma_0$ (54), corresponding to the plateau stress obtained during a crash test.

In order to avoid mesh dependency issues, the size of the element in the longitudinal direction, $L_c$, which also represents the characteristic length of the element, should be taken into account in the computation. At each step of the simulation, the damage is evaluated and aggregated into a single damage variable $d$ for the 8 Gauss points of the element, and is assumed to be the same for longitudinal tension and compression; this approach allows the consideration of alternating loading and bending ((32),(36)).

Moreover, once a volume element is damaged by fibre failure, the neighbouring delamination elements are

damaged, considering the explosive character of the fibre fracture.

### Delamination/matrix crack modelling

Matrix cracking and delamination are both modelled using a cohesive zone model in interface elements of null thickness. Regarding the model of matrix cracking, a Hashin criterion is computed for the 8 integration points surrounding the cohesive element:

$$ \left( \frac{\sigma_t^+}{\sigma_t^-} \right)^2 + \frac{\tau_{lt}^2 + \tau_{tz}^2}{(\tau_{lt}^f \cdot (1 - \lambda_{\text{comp}} \sigma_t^-))^2} \le 1 \quad (2) $$

Where $l, t, z$ are respectively the longitudinal, transverse, and out-of-plane directions, $\langle \sigma_t \rangle^{(+/-)}$ represents the positive/negative value of $\sigma_t$, and $\sigma_t^f, \tau_{lt}^f$ are respectively the shear and transverse strengths defined in Table 1. $\lambda_{\text{comp}}$ enables to take into account the reinforcement effect of the shear failure due to compressive stress. This effect can be relatively important in impact solicitation, in particular under the projectile. The stiffness of the delamination interfaces is classically taken equal to $5 \times 10^5$ MPa/mm and the stiffness of the matrix cracking interfaces is taken equal to $1 \times 10^6$ MPa/mm, which is high enough in order not to reduce the structure stiffness too much, and at the same time not to destabilize the explicit calculation process (Table 2). In fact, the interface stiffness of matrix cracking can be taken higher than the delamination ones, because it doesn't need to dissipate the fracture toughness (they are driven using Hashin criterium, cf. equation 2), contrary to the delamination ones which are classical cohesive zone model driven using fracture mechanics (cf. equation 3). Moreover, the interface stiffness of matrix cracking is taken higher than that of delamination because it is not driven by energy, contrary to the delamination one, and it is most of the time the first to be reached, so at a time when the delamination prevents large crack opening.

Regarding the cohesive zone model interfaces of delamination, a traction-separation linear softening law is implemented, with respect to the initiation stresses and critical strain energy release rate in mode I, II, and III. For mixed-modes failure, a linear combination coupling criterion is considered, and the modes II and III are supposed equivalent:

$$ \frac{G_I}{G_{Ic}} + \frac{G_{II} + G_{III}}{G_{IIc}(1 - \lambda_{\text{comp}}\sigma_z^-)} = 1 \quad (3) $$

$\lambda_{\text{comp}}$ enables to take into account the reinforcement effect of the shear fracture toughness due to compressive stress, $\langle \sigma_z \rangle^-$. In first approximation, and in the absence of precise experimental data on this phenomenon, it is assumed equal to this one of matrix cracking (Table 2). This effect can be relatively important in impact solicitation, in particular under the projectile.

The execution of explicit calculation code of Abaqus involves a mesh generator coded in Fortran used to create the set of nodes and elements for the simulation. Then, the mesh is inserted into an input file for Abaqus (input file), which contains material data, boundary conditions, and the definition of different calculation steps. Finally, a user-defined material law in Abaqus (VUMAT) is coded in Fortran to incorporate behavior laws for each damage
phenomenon. The calculation is then launched from the CALMIP platform (www.calmip.univ-toulouse.fr), which provides excellent computing resources, 180 cores on 5 nodes were used to perform these calculations.

## 3 Reference case

The single impact behavior of composite structures was investigated through a combination of experimental and numerical approaches. This section presents the key findings, analyses, and discussions of the results obtained. The test matrix includes multiple replicates for each combination of impact parameters to ensure statistical significance and account for variability in the impact response. Each configuration is repeated three times to ensure reproducibility.

Impact locations for each configuration are detailed in Figure 3, providing experimental and numerical results on delaminated surface area, energy dissipation, and damage mechanisms. Validation of the model is performed using experimental data. In-situ monitoring is conducted with a high-speed infrared camera, while Singular Value Decomposition (SVD) is used to analyze damage evolution in real time. The plate's boundary conditions are fully clamped.

The configuration name reflects the changes. For example, Ø20/30J/A indicates an impact with a Ø20 mm steel ball at Position A, delivered with an energy of 30 J.

### 3.1 Position A

In Configuration Ø20/15J/A, the impact is performed using a 20 mm diameter ball with an energy of 15 J (velocity of 30 m/s) at position A. An average dissipated energy of 12.92 J with a standard deviation of 0.06 J is recorded, resulting in an average maximum displacement of the impactor of 8.79 mm (with a standard deviation of 0.84 mm), as shown in Figure 4a. The average impact time across the three trials is approximately one millisecond. However, the contact time is highly dependent on the acquisition frequency of the high-speed camera, and a question mark is placed on the figure to indicate the uncertainty of this value. A similar limitation applies to the displacement measured with the high-speed camera. These values are determined by tracking the ball's trajectory using the high-speed camera. In this case, an average delaminated surface area of 653 mm² is measured with a standard deviation of 32 mm, using the C-scan method. The different interfaces and orientations of the delamination through the thickness can be distinguished. It can be observed that the load-displacement curves obtained numerically and experimentally are very similar (see Figure 4c). It should be recalled that the experimental curve was derived by twice differentiating the ball displacement curve obtained from high-speed camera recordings. As a result, sudden events—especially dynamic phenomena caused by the back-and-forth propagation of elastic waves, particularly those with very high frequencies through the thickness of the plate—were not captured. Greater detail regarding the ball-plate contact was provided by the numerical model, with the various force drops corresponding to different damage

events. Additional numerically obtained curves can then be examined to better understand the mechanisms of energy dissipation. In Figure 4c, the area hatched in yellow represents the ball's initial kinetic energy at impact. At the point of maximum displacement, the ball's velocity passed through zero, marking the beginning of the rebound. From that point on, part of the energy was returned to the ball—represented by the green hatched area in the Figure 4c. The difference between these two areas (i.e., the area under the load-displacement curve) primarily corresponds to the energy dissipated through plate damage, friction, and viscous effects, as well as the kinetic and strain energy stored in the plate at the end of the contact—indicated by the blue hatching. It was verified that the sum of the rebound energy and the so-called "dissipated energy" (in quotation marks because strain and kinetic energy are not technically dissipated) is equal to the ball's initial kinetic energy. At the end of the impact event, it was observed that, in this configuration, less than one-tenth of the initial kinetic energy was recovered during the ball's rebound.

It is evident that the area beneath the impactor is subjected to compression, and the delaminated surface is caused by the separation of the inferior ply (ply on the non-impacted side of the plate) in the direction of the impact. The direction of delamination is determined by the orientation of the inferior ply. This principle is repeated across the different interfaces. Figure 4a illustrates the first interface between the 0 and -45 plies, followed by the second interface between the -45 and 90 plies, and so forth. No delaminated surface is observed between the two 45 plies, and these two plies can even be considered as a single ply (as represented in the numerical model). A total of six well-defined interfaces are identified. Closer to the impacted side, the elements exhibit more damage, making it increasingly difficult for the sound wave to penetrate the plate, thereby complicating the identification of delaminated surfaces under the impactor. In order to easily compare the C-scan experimentally obtained (Figure 4a) with the numerical model, the damaged delamination interfaces ($d > 0.5$) are colored with the color corresponding to the interface color experimentally obtained by ultrasonic investigation (Figure 4b). The same procedure has been used for all the comparisons.

Figure 5 presents a numerical multi-cut view of the creation of delamination in Configuration Ø20/15J/A, uncertainty arises regarding interface 6, as it is possible that the visualized feature on the C-scan is merely signal noise from the impacted surface. It is unlikely for a larger delaminated surface to be present beneath the impactor than at interface 1 (since this region is under compression and therefore not prone to delamination; instead, matrix cracking and fiber breaks may occur, further hindering delamination propagation). Further details on the shape and projected surface of delamination can be found for Configuration B.

From a numerical perspective, the energy dissipated by the ball is calculated as 12.02 J, with a maximum displacement of the impactor determined to be 9.31 mm and an impact time of 0.95 ms. The projected delaminated surface area is estimated to be 687 mm² (Figure 4b). The average error in the delaminated surface area between the numerical model and experiments is found to be approximately 6%. A
compression zone is observed between the last ply and the
penultimate ply beneath the impactor, along with a tension
zone between these plies away from the impactor (Figure 5). This explains why the largest delaminated surface
area is located between the last and penultimate ply. The
same interfaces and orientations of delamination within the
thickness as those obtained experimentally are observed.

Subsequently, this numerical model was used to refine the
method for determining impact times by reprocessing the
videos from the high-speed camera with greater accuracy.
The model also indicated that the displacement sensors
should have been placed directly behind the point of impact
to track the displacement of each impactor. This placement is
critical for accurately assessing the displacement of the plate
in the impact zone, particularly in cases of multiple impacts,
where interactions between impacts far from the point of
impact become increasingly complex. Measurements taken
far from the points of impact are challenging to interpret,
as they are influenced by multiple impactors rather than a
single one. Consequently, measurements of impact times,
maximum plate displacement, or applied forces are likely to
be inaccurate at points distant from the impact, as the wave
arrival is delayed.

The model also facilitated the accurate tracking of
damage formation. Figure 6 illustrates the formation of
delamination over time. Delamination is initiated as a result
of matrix cracking in a ply located closer to the impact
site (specifically, ply 2 from the non-impacted side). The
delamination is subsequently propagated by the ply on the
non-impacted side, as it is subjected to tensile stresses. The
direction of delamination propagation is naturally governed
by the lower ply, as delamination is driven by its damage
evolution. Matrix cracking occurring within one ply leads
to delamination in the adjacent lower ply (with respect to
the impact direction). In the direction perpendicular to the
fibers of ply 1 at 0°, the propagation of delamination is not
controlled by the same ply, since matrix cracking within
it prevents further propagation. Instead, the ply closest to
the impacted surface governs the delamination process, due
to the tensile stresses acting along its fiber direction. This
ply also controls the propagation direction of delamination
across the neighboring interface closest to the impacted face,
and the process continues iteratively between plies. Although
the final delaminated ply is not necessarily the outermost one
—particularly in cases involving a large number of plies—
the initiation is generally driven by the first significant
matrix crack occurring farthest from the impactor or by the
maximum out-of-plane shear stress at mid-thickness.

Figure 7 describes the variation of different forms of
energy during impact, numerically obtained, it is observed
that most of the energy transferred to the plate is in the form
of strain and kinetic energy (ranging from 60% to 90%, with
an average of 80%), while a smaller portion is attributed to
damage and frictional energy. The kinetic energy of the ball
rebound is found to correspond to approximately 20% of
the initial impact energy, which is slightly higher than that
observed experimentally. Viscous energy remains low but is
not zero. Finally, the energy balance is verified by ensuring
that the sum of the energies remains almost constant.

To gain a comprehensive experimental understanding
of damage formation mechanisms, a high-speed infrared
thermography for in-situ damage monitoring during impact
test was used. Traditional approaches, such as post-
mortem analysis using C-scans, provide only a retrospective
perspective on the damage. In order to overcome this
limitation, the implementation of an in-situ monitoring
technique is deemed imperative. By utilizing real-time
observation and data acquisition during the damage process,
the dynamic evolution and intricate details of the damage
mechanisms as they unfold can be captured. This enables
valuable insights to be gathered that would otherwise be
missed with post-mortem analysis alone. A more holistic
and accurate assessment of the damage formation is offered
by in-situ monitoring, facilitating a deeper understanding of
the underlying mechanisms and leading to more effective
mitigation strategies.

The in-situ damage mechanisms of impacts were not being
monitored, and the experimental perspective was limited
to post-mortem analysis only. To overcome this problem,
high-speed infrared camera monitoring was introduced, and
used the SVD (Singular Value Decomposition) method
to process these results. Figure 8 demonstrates a perfect
correlation between the C-scan and the SVD method. The
main advantage of the SVD method lies in the fact that
the result is instantaneous and does not require the plate
to be dismantled and placed in water for the C-scan. In
the future, the benefits of using thermal monitoring to track
impact damage in-situ will be further explored. In equivalent
configurations in terms of the energy involved, images from
the digital videos captured by the IR camera will be used to
illustrate the size of the delaminated surfaces.

Then, the images obtained need to be analyzed in order
to highlight the physical character. Figure 9 shows the result
of this analysis, where the projected delaminated surface is
directly recognized. Later, vertical fiber breakage at 90 and
matrix cracking at -45 are also recognized (it is important
to constantly point out that the camera is positioned behind
the plate, on the non-impacted face, and thus a symmetry
of the image versus the 0 direction is obtained, as shown
in Figure 9). By analyzing the images taken directly from
the digital videos captured by the IR camera, the damage
within the material can be identified. Matrix cracking and
delamination occur first, followed by fiber breakage at the
center of the impact and at 90 ply direction. To ensure that
fiber fracture, and not just matrix cracking, is occurring,
microscopic observation has been carried out, as shown in
Figure 9. In this way, fiber breakage at direction -45 (in the 90
ply) and direction 0 (in the -45 ply) emerging at the surface
was recognized.

In Figure 10, the thermo-signature is used to confirm that
the break at 90 is indeed a fiber break in the volume of the
material. From this same figure, the diffusion time through
one ply can be estimated; since fiber breakage crosses three
plies in about 16 ms, the diffusion time per ply is expected to
be strictly less than 5.3 ms (since fiber breakage obviously
did not occur at t = 0 ms). It should be noted that this
fiber break does not occur on the outer surface (the surface
observed by the thermal camera), but rather in the volume
of the plate, which explains the reduction of the thermal
signature of the fiber breakage. Finally, in Figure 9, a 0 fiber
breakage in the -45 ply, a -45 fiber breakage in the 90 ply, and a 90 fiber breakage in the 45 ply are shown; following the same reasoning, a fiber break at -45 in the 0 ply is expected. It is observed that the thermal camera images capture the damage with a delay, due to thermal diffusion; the second image in the Figure 10 is recorded well after the impact time.

Matrix cracking in the last ply is also easily recognized through thermal images and microscopic observation. It should be noted that, during the measurements, an emissivity of 0.92 was considered in line with the values from the literature ((55),(56)). The camera was slightly non-perpendicular to the composite panel. Experiments were recorded with up to 2000 Hz, depending on the required recording window. Finally, the temperature evolution corresponding to each damage type can also be deduced. These measurements are specific to the tests in this work, and the thermal signatures obviously depend on the breaking energies involved and their position in relation to the thickness, etc. In particular, because heat conduction is greater in the *l*-direction (the direction of the fibers, which are more conductive than other elements):

* $\Delta T$ Fiber breakage [8C - 31.6C]

* $\Delta T$ Matrix cracking (≈ 5C)

* $\Delta T$ Delamination (≈ 3C)

# 4 Effect of impact conditions

## 4.1 Effect of impact position

### 4.1.1 Position B

In Configuration ◦20/15J/B, the average dissipated energy per ball is calculated to be 12.66 J, with a standard deviation of 0.95 J, resulting in an average maximum displacement of the impactor measured at 7.52 mm (with a standard deviation of 0.73 mm). An average delaminated surface area of 731 mm² is recorded, with a standard deviation of 48 mm² (Figure 11a). The different interfaces and orientations of the delamination within the thickness are distinguishable. Interface 6 is not reached due to the extensive damage beneath the impactor, which causes the sound wave to struggle to penetrate these areas, resulting in negligible signal return.

From a numerical perspective, the energy dissipated by the ball is determined to be 10.56 J, with a maximum displacement of the impactor recorded at 7.54 mm and an impact time of 0.9 ms. The projected delaminated surface area is calculated to be 385 mm², as shown in Figure 11b. Fiber breakage occurs prematurely, which slows the propagation of delamination. This behavior is suspected to result from the exclusion of dynamic effects (such as strain rate) and the extrapolation of fiber strain failure criteria in the thickness direction. In this case, classical extrapolation coefficients of 1.366 and 0.366 are used (corresponding to Gauss points positioned at a distance of $\frac{1}{\sqrt{3}}$). These coefficients imply that for opposite strain values (e.g., in pure bending deformation), the extrapolated strain value would be 1.732 times greater. Consequently, fiber failure in a pure bending scenario is expected to occur 1.73 times earlier in the extrapolated case than in the non-extrapolated scenario. In the future, a more detailed investigation into the

extrapolation methodology is required.

### 4.1.2 Position C

In Configuration ◦20/15J/C, the average dissipated energy per ball is 12.58 J with a standard deviation of 0.54 J, resulting in an average maximum displacement of the impactor of 9.76 mm (with a standard deviation of 0.14 mm). An average delaminated surface area of 724 mm² with a standard deviation of 45 mm² is measured (Figure 12a). The different interfaces and orientations of the delamination within the thickness can be distinguished. Interface 6 is not reached because of the large amount of damage under the impactor; the sound wave struggles to penetrate these areas, and signal return is negligible. From these first three configurations, it can be observed that the closer the impact is to the center of the plate, the smaller the delaminated area. This is attributed to the fact that the plate is large and flexible enough to store energy in elastic form, which is not the case when the impact is close to the edges, where more energy is dissipated in the plate.

From a numerical perspective, Figure 12b, the energy dissipated by the ball is 11.49 J, with a maximum displacement of the impactor of 7.59 mm and an impact time of 0.9 ms. The projected delaminated surface area is 438 mm². As for configuration B (the impact point is slightly displaced), it appears that the fibers are broken prematurely, thus stopping the delamination propagation.

Finally, the impact angle was varied on the numerical model between 0 and 7, as was done experimentally. It was found that the difference is small and may be neglected.

By comparing the delaminated areas in the three different positions tested, it is noticed that as the minimum distance between the ball's position and the nearest edge of the plate decreases, the delaminated surface becomes smaller. However, the variation in the delaminated area remains small compared to the variation in the minimum distance to the edges.

## 4.2 Effect of impact energy

In Configuration ◦20/30J/A, which is compared to Configuration ◦20/15J/A, the 20 mm diameter projectiles are launched with a kinetic energy of impact of 30 J (velocity of 43 m/s). The plates have been perforated, so it is difficult to judge the amount dissipated in the plate experimentally. The impact time is 1.6 ms (compared with 1 ms for the 15 J configurations). An average delaminated surface area of 4222 mm² with a standard deviation of 48 mm² was measured (Figure 13a). An average displacement of 16.53 mm with a standard deviation of 0.92 mm was measured. The different interfaces and orientations of the delamination within the thickness can be distinguished. All delaminated surfaces are larger compared to the 15 J configurations, especially interface 1, which reaches the edges of the plate. It is important to note that the loss of signal return is related to the chosen synchronization threshold (12%). However, for the same C-scan parameters used in the 15 J configurations, a total loss of signal was observed here due to the breakage of these surfaces, which become too inclined, and the signal return is subsequently very weak. It should be borne in mind that the
plate is perforated rapidly during impact and then resealed afterwards, thanks to the plies that do not come detached because of matrix cracking, which occurs earlier than fiber breakages. This point of view will be explained in more detail later in this configuration.

From a numerical perspective, as shown in Figure 13b, the maximum displacement of the impactor is 18.7 mm, and the impact time is 1.9 ms. The projected delaminated surface area is 1384 mm². The energy dissipated by the ball is 30 J, which means that the ball is completely stopped by the plate, and a quasi-perforation of the plate is predicted by the model, unlike the experiments. Additionally, the main difference is that interface 1 does not delaminate as it would under real-life conditions. This appears to be due to premature fiber breakage, which halts the propagation of delamination.

Precise mechanical characterization is required to examine this problem in detail. It should also be reminded that, to make this numerical calculation converge, the broken delamination elements are removed from the model. This abrupt removal of the elements concentrates the stress applied to the fibers and also contributes to their premature destruction. Figure 14 describes the difference between the driving damage mechanisms: in numerical modeling (a&c), it is mainly fiber breakage, whereas in experiment (b), it is mainly matrix cracking of the last ply that directly generates the important delaminated surface of interface 1.

By analyzing the digital images captured by the IR camera (Figure 15), it is once again confirmed that matrix cracking comes first. More importantly, this figure shows the important role of cracking in driving impact damage scenarios in composite materials. Indeed, the matrix cracking observed at t = 1.905 ms directly causes the delamination of interface 1, and it is this same matrix cracking that seals the plate after perforation by the ball (After matrix cracking, a visual closure of the cracks was observed; essentially, after the perforation by the ball, no open hole was found but rather a closed interface), making it dangerous from an industrial point of view. In fact, if the plate is only checked with a post-mortem inspection process (visually, with a C-scan or other), it will not be realized that the plate is completely perforated in its center. On the other hand, with in-situ thermal analysis, it can be clearly seen that, in terms of mechanical characteristics, the plate is completely perforated at its center, as shown in Figure 15 at (t = 1.905 ms). Interestingly, the delamination process at interface 1 is different from the conventional one (with matrix cracking in the lower ply): here, it is directly caused by contact with the ball, which detaches the last ply. The matrix crack at 0 to the center of the impact splits the latter ply in two, allowing the ball to close the surface again. Compared to the 15 J configurations, the damage here is more significant, which is expected. The plate is unable to dissipate all the energy from the 30 J projectiles, resulting in perforation.

## 4.3 Effect of projectile diameter

In Configuration Ø10/15J/A (which is compared to Configuration Ø20/15J/A), the 10 mm diameter projectiles are launched with a kinetic energy of 15 J at a velocity of 87 m/s at the moment of impact. The plates have been perforated. The impact time is 0.6 ms (compared with 1 ms

for the 15 J-Ø20 mm configurations). The plate is rapidly perforated, and the energy supplied is concentrated locally, given the small size of the ball, which leads to rapid fiber breakage due to the ball's velocity. As a result, the impact contact is also reduced to 0.6 ms. An average delaminated surface area of 1424 mm² with a standard deviation of 26 mm² is measured (Figure 16). An average maximum displacement of 10.14 mm with a standard deviation of 0.76 mm is measured.

No complete perforation was observed in the model, whereas it was observed in the experimental tests. To improve the model, further work is needed on the energy dissipated by fiber breakage, which has obviously become an important factor in simulating perforation. The severity of the damage is greater for the 10 mm diameter balls compared to the 20 mm diameter balls (where no perforation occurred). This is also due to the higher speed of the smaller diameter balls, which results in equivalent energy between the two experiments.

The results of the studied configurations are summarized in Table 3. This table presents the average values and standard deviations of the dissipated energy, delaminated area, and maximum displacement obtained from both experimental and numerical analyses. While the previous sections described one case for each configuration, this table instead provides the averaged results per configuration. It is shown that the energy dissipated can vary depending on the impact position under the same loading, that the maximum displacement is not necessarily correlated with the amount of energy dissipated. The most critical case remains, of course, the one where the dissipated energy is maximal, but also the one with the smallest diameter of the impactor. The comparison between experimental and numerical results reveals a generally good agreement in terms of dissipated energy and maximum displacement across all configurations. However, notable discrepancies are observed in the delamination area, with numerical predictions consistently underestimating the experimental values, especially in higher energy and velocity impact scenarios (e.g., Ø20/30J/A and Ø10/15J/A). These differences may be attributed to simplifications in the numerical model. Overall, the numerical model shows promising predictive capabilities but requires refinement to more accurately capture delamination behavior.
<table><caption>**Table 3.** Comparison of Experimental and Numerical Results</caption><thead><tr><th rowspan="2">Configuration</th><th colspan="3">Experimental results</th><th colspan="3">Numerical results</th></tr><tr><th>Dissipated energy (J)</th><th>Delamination area (mm²)</th><th>Maximum displacement (mm)</th><th>Dissipated energy (J)</th><th>Delamination area (mm²)</th><th>Maximum displacement (mm)</th></tr></thead><tbody><tr><td>Ø20/15J/A</td><td>12.92 0.06</td><td>653 32</td><td>8.79 0.84</td><td>12.02</td><td>687</td><td>9.31</td></tr><tr><td>Ø20/15J/B</td><td>12.66 0.95</td><td>731 48</td><td>7.52 0.73</td><td>10.56</td><td>385</td><td>7.54</td></tr><tr><td>Ø20/15J/C</td><td>12.58 0.54</td><td>724 45</td><td>9.76 0.14</td><td>11.49</td><td>438</td><td>7.59</td></tr><tr><td>Ø20/30J/A</td><td>30.00</td><td>4222 48</td><td>16.53 0.92</td><td>30.00</td><td>1384</td><td>18.70</td></tr><tr><td>Ø10/15J/A</td><td>15.00</td><td>1424 26</td><td>10.14 0.76</td><td>12.57</td><td>437</td><td>11.63</td></tr></tbody></table>
# 5 Conclusion

It was demonstrated that the different techniques used to study the impact on composite structures are consistent with each other. C-scans and the SVD method provide a post-mortem perspective on delamination, due to couplings between the different involved damage mechanisms (transverse cracks, delamination, fibre failure), the determination of the damage scenarios is still very challenging considering only post-mortem controls. Infrared thermal camera analysis and numerical modeling enable an understanding of the phenomena during the impact time. Overall, except in some cases where the accuracy of the numerical model failed to capture the experimental findings under certain high strain rate loading scenarios, the different methods are complementary and reliable for in-situ and post-mortem monitoring of impacts on composite structures. The use of these methods can be considered for studying the multi-impact behavior of laminated composite structures. This article also serves as an experimental and numerical database for validating the models of researchers in this field.

By combining both experimental and numerical findings, a comprehensive understanding of the single impact behavior of composite structures has been gained, shedding light on several key aspects of their response to impact. The results have highlighted the significant influence of various factors, such as the impact location, the diameter of the projectiles, and the impact energy and velocity, on the behavior of composite materials during impact events. These parameters are shown to directly affect the extent of damage and the mechanisms behind it, including the initiation and propagation of different types of damage, such as matrix cracking, fiber breakage, and delamination. It was demonstrated that the dissipated energy can vary depending on the impact position, even under identical loading conditions. Moreover, the impact time is not necessarily correlated with the amount of dissipated energy, nor is the maximum displacement. Consequently, it is more appropriate to assess each of these parameters individually relative to their respective admissible limits. Furthermore, as a given parameter approaches its admissible limit, its criticality increases.

Furthermore, valuable insights into the complex interplay between these damage mechanisms have been provided, revealing how they evolve in different layers and interfaces within the composite material. This deeper understanding is considered crucial for the development of more accurate models of composite behavior under impact loading, contributing to the optimization of composite structures for impact resistance.

Looking ahead, the next logical step is to investigate whether these observed phenomena are consistent in the case of multiple impacts. Specifically, it will be necessary to determine if the impact parameters—such as impact energy, velocity, and location—continue to play the same role in multi-impact scenarios, or if other factors come into play when multiple impacts occur over time. Further experimental studies and numerical simulations will be required to explore the cumulative effects of repeated impacts and their influence on the long-term performance of composite materials.

In addition, the scope of the investigation will need to be expanded to include different types of composite materials and configurations, as well as the potential influence of environmental factors such as temperature, humidity, and aging on impact behavior. By extending the research in these directions, a more holistic understanding of composite impact behavior can be gained, leading to improvements in the design and durability of composite structures in real-world applications.

## 5.1 Copyright

Copyright © 2025 SAGE Publications Ltd, 1 Oliver's Yard, 55 City Road, London, EC1Y 1SP, UK. All rights reserved.

## Acknowledgements

The authors would like to duly thank CALMIP High Performance Computing platform (https://www.calmip.univ-toulouse.fr/) for providing the computational means required to conduct the numerical simulations under the project reference p1026.

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<figure><img src="image_3.png" /><figcaption>**Figure 1.** Compressed air cannon test bench : (1) Infrared camera (2) Displacement sensors, (3) High-speed camera, (4) Clamping system, (5) Composite panel, (6) Setting up TV, (7) Chronographs, (8) Laser rangefinder, (9) Laser sight, (10) Pressure sensors, (11) Electrical enclosure, (12) Triggering system, (13) Guiding tubes, (14) Compressed air reservoirs, (15) Control room.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>**Figure 2.** DPM principle and the 4 mesh types of 0, 90, 45, and -45 plies (46).</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>**Figure 3.** Single impact positions: A, B, and C.</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>(a) C-scan of Configuration Ø20/15J/A.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>(b) DPM C-scan of Configuration Ø20/15J/A.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>(c) Experimental vs. Numerical Load-Displacement curve.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>**Figure 5.** Multi-cut view, creation of delamination (DPM, Configuration Ø20/15J/A) at 9.03 mm displacement.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>**Figure 6.** Formation and propagation of delamination (DPM, Configuration Ø20/15J/A).</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>**Figure 7.** Variation of different forms of energy during impact (DPM, Configuration Ø20/15J/A).</figcaption></figure>
<figure><img src="image_12.png" /><figcaption>**Figure 8.** Comparison of delaminated surface after impact obtained experimentally, by SVD analysis and numerically, Ø20/15J/A.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>**Figure 10.** Thermographic monitoring of impact damage (Configuration Ø20/15J/A).</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>**Figure 9.** Cross-analysis between thermography and microscopic observation (Configuration Ø20/15J/A).</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>(a) C-scan of Configuration Ø20/15J/B.</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>(b) DPM C-scan of Configuration Ø20/15J/B.</figcaption></figure>

<caption>**Figure 11.** Comparison between experimental and DPM C-scan for Configuration Ø20/15J/B.</caption>
<figure><img src="image_17.png" /><figcaption>(a) C-scan of Configuration Ø20/15J/C.</figcaption></figure>

<figure><img src="image_18.png" /><figcaption>(b) DPM C-scan of Configuration Ø20/15J/C.</figcaption></figure>

<figure><img src="image_19.png" /><figcaption>(a) C-scan of Configuration Ø20/30J/A.</figcaption></figure>

<figure><img src="image_20.png" /><figcaption>(b) DPM C-scan of Configuration Ø20/30J/A.</figcaption></figure>

<figure><img src="image_21.png" /><figcaption>**Figure 14.** (a,c) Driving damage mechanisms : DPM, (b) experiments (Configuration Ø20/30J/A).</figcaption></figure>

<figure><img src="image_22.png" /><figcaption>**Figure 15.** Digital images captured by the IR camera from behind the plate and a schematic of the load-time curve (Configuration Ø20/30J/A).</figcaption></figure>

<figure><img src="image_23.png" /><figcaption>**Figure 16.** C-scan of delaminated surface : DPM vs. Experiments (Configuration Ø10/15J/A).</figcaption></figure>
<figure><img src="image_24.png" /></figure>