# Impact of coatings on the performance of resonant electromechanical de-icing systems

G. Gastaldo, G. Hernández-Rodríguez, V. Pommier-Budinger, M. Budinger, J. Pothin, A.M. Coclite

► To cite this version:

G. Gastaldo, G. Hernández-Rodríguez, V. Pommier-Budinger, M. Budinger, J. Pothin, et al. Impact of coatings on the performance of resonant electromechanical de-icing systems. Results in engineering, 2025, 27, pp.106636. 10.1016/j.rineng.2025.106636. hal-05497740

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Submitted on 6 Feb 2026

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Research paper

# Impact of coatings on the performance of resonant electromechanical de-icing systems

<figure><img src="image_2.png" /></figure>

G. Gastaldo<sup>a, ID</sup>, G. Hernández-Rodríguez<sup>c</sup>, V. Pommier-Budinger<sup>a, ID, *</sup>, M. Budinger<sup>b</sup>, J. Pothin<sup>b, ID</sup>, A.M. Coclite<sup>d</sup>

## ARTICLE INFO

### Keywords:

* Hybrid ice protection systems
* Electromechanical resonant de-icing
* Anti-icing coatings
* Ice fracture

## ABSTRACT

Efficient ice protection systems are essential to ensure the operational capability and reliability of aircraft and energy infrastructures operating in cold environments. Hybrid ice protection systems, which integrate active mechanisms (such as thermal or mechanical systems) with passive solutions (such as icephobic coatings), offer promising potential to improve the performance of active systems while reducing overall energy requirements. This paper examines the impact of coatings on ice fracture mechanisms, as these coatings can significantly alter interfacial properties by reducing shear strength or toughness, thereby enhancing fracture propagation and ice shedding. This paper aims to provide coating manufacturers with guidelines for the efficient design of coatings for resonant ice protection systems. The study focuses on two coatings: a low-toughness coating applied via iCVD and a commercial low-shear-strength coating. The results show that low-toughness coatings are more effective than low-shear-strength coatings in improving the performance of resonant electromechanical de-icing systems.

## 1. Introduction

Ice accretion negatively affects wind turbines [11,14], energy infrastructures such as electrical power lines [27], and aircraft structures [16], leading to performance losses and compromising the reliability and safety of these systems. Ice accretion on wind turbines leads to significant challenges, including measurement inaccuracies during wind assessment and reductions in power output [39]. For aircraft, ice accumulation deteriorates the aerodynamic characteristics of the wings [29,10,6]. Furthermore, ice formation on air intake protection grids contributes to higher fuel consumption and power losses [52]. Consequently, ice protection systems are used to ensure both safety and operational efficiency.

Thermal systems, which apply heat to exposed surfaces, are widely used for ice protection in wind turbines, aircraft, and electrical power lines. These systems use methods such as hot air blowing or electrical heating to create a water film at the ice/substrate interface, facilitating ice shedding [39,32,55]. These systems can either prevent ice formation or provide a solution when ice has already accumulated on the

structure. However, as Palanque et al. highlighted in the case of aircraft ice protection systems, the required power is significant [38].

Mechanical de-icing systems provide energy-efficient alternatives, with electromechanical resonant systems standing out for their potential benefits in terms of energy efficiency and reduced onboard weight. These systems use electromechanical transducers integrated into the aircraft skin to generate high stresses and facilitate energy release in the ice, causing it to crack and delaminate from the surface [38,41,15].

Another solution that has been extensively studied is the use of anti-icing coatings [49,36,48]. These coatings can be divided into two categories [2]: icephobic coatings, which lower ice adhesion, reduce ice nucleation temperature, and delay freezing, and water-repellent surfaces, particularly superhydrophobic surfaces [45,26]. There is no universal correlation between the adhesion forces of ice and water on a surface. Superhydrophobic surfaces can exhibit low ice adhesion [50,5,44,33,25,34], but most studies do not display a clear trend [22,35,23,9,56,1,57,30]. Various coatings have demonstrated effectiveness under certain icing conditions, but the effectiveness is not universal [51,12,24,43].

<footnote><sup>a</sup> Fédération ENAC ISAE-SUPAERO ONERA, University of Toulouse, 10 Avenue Marc Pêlegrin, Toulouse, 31400, France</footnote>

<footnote><sup>b</sup> Institut Clement Ader, University of Toulouse, INSA, ISAE-SUPAERO, MINES ALBI, UPS, CNRS, 3 Avenue C. Aigle, Toulouse, 31400, France</footnote>

<footnote><sup>c</sup> Institute of Solid State Physics, NAWI Graz, Graz University of Technology, Petersgasse 16, Graz, 8010, Austria</footnote>

<footnote><sup>d</sup> University of Bari, Via Orabona 4, Bari, 70125, Italy</footnote>

<footnote>* Corresponding author.
E-mail address: valerie.budinger@isae-supaero.fr (V. Pommier-Budinger).</footnote>
## Nomenclature

<table><tr><td>iCVD</td><td>Initiated Chemical Vapor Deposition</td><td>MAC</td><td>Modal Assurance Criterion</td></tr><tr><td>IWT</td><td>Icing Wind Tunnel</td><td>VCCT</td><td>Virtual Crack Closure Technique</td></tr><tr><td>LWC</td><td>Liquid Water Content</td><td>PFDA</td><td>1H,1H,2H,2H-perfluorodecylacrylate</td></tr><tr><td>MVD</td><td>Median Volumetric Diameter</td><td>V<sub>4</sub>D<sub>4</sub></td><td>1,3,5,7-tetravinyl-1,3,5,7-tetramethylcyclotetrasiloxane</td></tr></table>

<figure><img src="image_3.png" /><figcaption>Fig. 1. Type of resonant modes in free boundary conditions.</figcaption></figure>

Although current coatings are not sufficient to fully address icing challenges, their application on aerodynamic and structural surfaces can improve the performance of anti-icing and de-icing systems. Additionally, they can help lower the energy demands of existing systems.

Recent studies have explored the potential of hybrid solutions. In [21], the application of a superhydrophobic coating to a surface equipped with an electrothermal ice protection system resulted in approximately 50% energy savings.

Other experimental studies on hybrid anti-icing systems, combining thermoelectric technology with hydrophobic coatings, demonstrated significant energy savings. Tests in an icing wind tunnel revealed that superhydrophobic coatings reduced energy consumption by approximately 33% for glaze ice and 13% for rime ice, while hydrophobic coatings saved around 8% and 13%, respectively [13]. Antonini et al. [3] found that superhydrophobic coatings on airfoils could lower the heating power requirements of an electrothermal anti-icing system by up to 80% and reduce runback ice formation.

A study on a hybrid anti-icing system combining heating elements, piezoelectric actuators, and a hydrophobic coating demonstrated significant energy savings in an icing wind tunnel. The system achieved a power density of 2.74 kW/m², far lower than the 16.4 – 62 kW/m² required for purely thermal systems [47]. However, the specific role of the hydrophobic coating in reducing power density was not analyzed.

The integration of hybrid ice protection systems combining anti-icing coatings with electromechanical resonant de-icing systems, has been investigated in only a few studies at a general level [42,20]. The interaction between these systems remains largely unexplored, highlighting a significant gap in current research. This paper proposes to address this gap by evaluating the impact of coatings on fracture mechanisms in resonant electromechanical de-icing systems. Following a theoretical study summarizing the principles of resonant electromechanical de-icing systems and the method of predicting ice fracture mechanisms, the paper presents three configurations with different resonant modes, which are used to analyze the impact of coatings on the de-icing mechanism. Two types of coating are used in this study: a low-toughness coating and a low-shear strength coating. The coatings are not assessed in terms of durability, but important considerations regarding the interfacial properties of coatings that enhance ice fracture and shedding are provided.

# 2. Theoretical background

## 2.1. Working principle of electromechanical resonant de-icing systems

Electromechanical resonant de-icing systems use actuators to vibrate iced surfaces at one of their natural frequencies, maximizing vibration

amplitude. This creates high stresses in the ice and facilitates the release of energy, causing the ice to break and detach from the surface [4,53].

Three different types of resonant modes can be used: out-of-plane flexural modes, extensional modes, and in-plane flexural modes. Out-of-plane flexural modes involve significant bending perpendicular to the surface (Fig. 1(a)) and typically occur at relatively low frequencies (a few hundred Hz).

Extensional modes involve in-plane stretching vibrations (Fig. 1(b)) and are generally observed at higher frequencies, greater than 10 kHz. A comparative study of these two modes was conducted by Budinger et al. [7], [8], highlighting that while extensional modes require more energy than out-of-plane flexural modes, they facilitate ice removal over larger areas.

In-plane flexural modes involve bending within the surface plane (Fig. 1(c)) and start to appear in the range of a few kilohertz (approximately 5-7 kHz).

## 2.2. Fracture mechanics

Two different types of fracture can appear when an electromechanical resonant de-icing system is used: cohesive and adhesive fractures. Cohesive fractures occur within the ice bulk, while adhesive fractures occur at the interface between the ice and the substrate. Cohesive fractures alone are insufficient to ensure ice removal. Without the occurrence of adhesive fractures, the ice remains bonded to the surface, preventing its complete detachment. Adhesive fractures are therefore crucial for shedding ice.

Fracture initiation within the ice and at its interface with the substrate can be analyzed using Leguillon's coupled criterion [28,31]. This approach requires both stress and energy conditions to be satisfied. Assuming negligible effects from kinetic energy and external forces, a fracture over a surface $\Delta S$, smaller than the total surface $S$, can occur if the following two conditions are met:

$$ \tau (\text{or } \sigma) > \tau_c (\text{or } \sigma_c), \quad \forall \Delta S \in S \qquad (1) $$

$$ G = -\frac{\Delta E_p}{\Delta S} \geq G_c \qquad (2) $$

where $\Delta E_p = E_p(0) - E_p(i)$ represents the change in potential strain energy between the undamaged state and the damaged state $i$ for a cracked surface $\Delta S$.

Once a crack is initiated, creating a sharp fracture within the system, the resulting stress concentration at the crack tip ensures that the stress condition is automatically met. Consequently, the propagation of the fracture can be governed exclusively by the energy release rate criterion, which is expressed as:
<figure><img src="image_4.png" /><figcaption>Fig. 2. Example of two consecutive steps in the propagation of an adhesive crack from the center.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 3. Studied resonant modes.</figcaption></figure>

$$-\frac{\Delta E_{pi}}{\Delta S} \geq G_c \qquad (3)$$

where $\Delta E_{pi} = E_p(i) - E_p(i + 1)$ represents the difference in potential strain energy between two consecutive propagation steps $i$ and $i + 1$. A schematic of the propagation steps is illustrated in Fig. 2 for an adhesive crack propagating from the center.

This criterion emphasizes that propagation is primarily influenced by toughness, $G_c$. This is consistent with the results of Golovin et al. [17], later confirmed by [46], which demonstrate that, for large ice/substrate interfaces, ice detachment is governed by the condition $G \geq G_c$. Therefore, if fracture propagation is desired, attention must be paid to the toughness of the interface, as it plays a more critical role than the shear strength in this context. For relatively small interfaces, the fracture mechanism would be stress-dominated [17].

A method is developed to evaluate these fracture criteria, applicable to both the initiation and propagation of fractures. This approach relies on the critical mechanical properties of bulk ice and of the ice-substrate interface, combined with modal parameters derived from Finite Element Analysis. It consists of determining the vibratory amplitudes necessary to initiate or propagate a fracture by exceeding the tensile and shear strengths and those required to exceed the toughness of the ice/substrate interface. Based on the methodology previously introduced in [8,37], the amplitudes that are representative of the $\sigma$, $\tau$ and $G$ criteria respectively can be expressed as follows:

$$x_{\sigma} = \frac{\sigma_c}{\sigma_{\text{mod}}} x_{\text{mod}}, \quad x_{\tau} = \frac{\tau_c}{\tau_{\text{mod}}} x_{\text{mod}}, \quad x_G = \sqrt{\frac{G_c}{G_{\text{mod}}}} x_{\text{mod}}$$

where $\sigma_c$, $\tau_c$ and $G_c$ are the critical properties (tensile strength, shear strength and toughness), $\sigma_{\text{mod}}$ and $\tau_{\text{mod}}$ are the modal tensile and shear stresses, and $x_{\text{mod}}$ the maximum modal displacement of the system. If an out-of-plane flexural mode is considered, $x_{\text{mod}}$ is an out-of-plane displacement, while, for the extensional mode, $x_{\text{mod}}$ is the lateral in-plane displacement.

For fracture initiation, the amplitudes are used to quantify the initiation fracture length. This is determined when the amplitudes associated with the stress-based and energy-based mechanisms are equal.

# 3. Selected resonant modes and sample configurations

## 3.1. Selected resonant modes

The objective of this study is to assess the effectiveness of coatings when using different resonant modes, as these modes may activate

distinct fracture mechanisms, and their effectiveness could vary based on the loading mode. Fractures can occur under three distinct loading modes: Mode I (opening), Mode II (sliding), and Mode III (tearing). To fully understand the system's behavior, it is essential to identify the specific fracture mode generated by the resonant mode being tested or to assess whether the resonant mode induces mixed-mode loading.

In this study, three modes will be examined: the first out-of-plane flexural mode under free boundary conditions, the second in-plane flexural mode under clamped boundary conditions, and the second extensional mode under clamped boundary conditions. The three modes are reported in Fig. 3. Two different sample dimensions are used. The plate tested under free boundary conditions is 130 x 50 x 1 mm³, while the plate under clamped boundary conditions is 200 x 70 x 1 mm³. Both are modeled with a uniform 3-mm-thick ice layer on top, potentially with different lengths.

Equivalent Virtual Crack Closure Technique static models are used to understand the contribution of the three loading modes to the energy release rate $G$, but it is first necessary to assess whether these static models can accurately represent the dynamic ones. This is done by evaluating the respective displacement fields and calculating the Modal Assurance Criterion (MAC) [40]. The MAC serves as an indicator to quantify the similarity between two modes. It is calculated using the following expression:

$$MAC(\phi_1, \phi_2) = \frac{|\phi_1^T \phi_2|^2}{(\phi_1^T \phi_1)(\phi_2^T \phi_2)} \qquad (4)$$

where $\phi_1$ and $\phi_2$ are the modal and the static deflection vectors, respectively. For $\phi_1$, the displacement vector is chosen based on the dominant motion of each mode. For the first out-of-plane flexural mode, it corresponds to the vertical displacement. For the second in-plane flexural mode and the second extensional mode, it corresponds to the in-plane displacement. Values of this indicator close to 1 indicate a high degree of similarity between the two configurations.

In the static analyzes, an equivalent distributed load is applied to replicate the maximum displacement observed in the modal analysis. For the modal analyzes, the entire plates are modeled, whereas the static analyzes use only half of the plate for in-plane and out-of-plane flexural modes, and a quarter for the extensional mode. This approach ensures consistency with the subsequent VCCT analyzes.

The results for the three different modes are summarized in Table 1, demonstrating that the static models accurately capture the dynamic behavior.
<figure><img src="image_6.png" /><figcaption>(a) Model of the central adhesive crack.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>(b) Model of the side adhesive crack.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>(c) G-curve for the central adhesive crack model.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>(d) G-curve for the side adhesive crack model.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>(a) Model's schematic.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>(b) Crack length = 5 mm.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>(c) Crack length = 45 mm.</figcaption></figure>

<caption>Fig. 5. Equivalent 3D VCCT study of the second in-plane flexural mode - propagation on the short side.</caption>

<table><caption>**Table 1**
MAC indicators for the three studied modes.</caption><thead><tr><th></th><th>Out-of-plane flexion</th><th>In-plane flexion</th><th>Extension</th></tr></thead><tbody><tr><td>MAC</td><td>0.9998</td><td>0.9997</td><td>0.9907</td></tr></tbody></table>

### 3.1.1. First out-of-plane flexural mode under free boundary conditions

2D VCCT is employed to characterize two distinct fracture scenarios. In the first scenario, a cohesive crack has already formed at the center of the ice layer and an adhesive fracture propagates from the crack towards the external edges of the plate. In the second scenario, an adhesive crack propagates from the edges of the plate in the absence of any cohesive crack. These two configurations are illustrated in Fig. 4(a) and Fig. 4(b). As observed in Figs. 4(c) and 4(d), where the $G/X^2$ curves are plotted (with G being the energy release rate and X the maximum modal displacement), the $G_I$ curve closely aligns with the $G_{tot}$ curve in both cases, indicating that the contribution of $G_{II}$ is negligible. This suggests that the entire fracture propagation process predominantly follows a pure opening mode.

### 3.1.2. Second in-plane flexural mode under clamped boundary conditions

For this mode, an initial cohesive fracture is assumed at the center of the ice layer, cutting the ice block in two parts, and only half of the plate is modeled, with an antisymmetry in the middle of the plate. Two fracture propagation configurations are considered: the first (Fig. 5(a)), for which the fracture propagation occurs along the shorter side of the plate,

and the second (Fig. 6(a)), for which the propagation occurs along the longer side of the plate. This allows the analysis of both possible mechanisms, as the in-plane fracture mechanism has never been observed before.

The indicator $G/(E/S)$, corresponding to the energy release rate normalized by the potential strain energy inside the ice divided by the interfacial ice/substrate surface, is then plotted. The propagation along the 70-mm-long side is reported in Fig. 5 for different fracture propagation steps. It is possible to notice that, throughout the propagation, the fracture mechanism is mixed, with mode I and mode II being the dominant ones. On the other hand, it can be seen in Fig. 6 that the propagation on the longer side would be dominated by a Mode III mechanism.

### 3.1.3. Second extensional mode under clamped boundary conditions

For the extension, half of the plate is modeled. A central cohesive crack is introduced, and the adhesive propagation is modeled only along the long side of the plate (Fig. 7(a)), as the fracture mechanism is known. In Fig. 7(b) and 7(c), the first two VCCT plots for propagation are reported (for a fracture length of 5 mm and 30 mm). It can be seen that the mode of fracture is mixed, mode II and mode III contributions being predominant.

## 3.2. Samples

For the first out-of-plane flexural mode, the tests are performed on the plate described in Fig. 8(a) and tested in the freezer with a 3-mm-
<figure><img src="image_13.png" /><figcaption>Fig. 6. Equivalent 3D VCCT study of the second in-plane flexural mode - propagation on the long side.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>Fig. 7. Equivalent 3D VCCT study of the second extensional mode - propagation on the long side.</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>Fig. 8. Aluminum plates dimensions.</figcaption></figure>
thick ice layer. For these samples measuring 130 x 50 x 1 mm³ and equipped with soft piezoceramics (PIC 255) measuring 50 x 22 x 0.5 mm³, the numerical simulation identified the first resonant frequency at approximately 696 Hz (with a calculated force factor N = 0.04 N/V).

For the second in-plane flexural mode and the second extensional mode, the study uses the plate with the actuator configuration described in Fig. 8(b). Both these modes were tested in the icing wind tunnel (IWT). The dimensions of the plate were adjusted to fit the IWT test section (200 x 200 mm²). The plate measures 300 x 70 x 1 mm³, but the additional length of the samples is used to clamp them at the sides. Each plate is equipped with five 1 mm-thick, soft piezoceramics (PIC 255), with dimensions as shown in Fig. 8(b). This specific configuration is designed to facilitate the excitation of the targeted resonant modes. The plate is assumed to be covered with a 3-mm layer of ice. The simulation identified the second in-plane flexural mode at 7.3 kHz and the second extensional mode at a frequency of 15.8 kHz. The force factors N are computed and equal 0.27 N/V for the second in-plane flexural mode and 0.45 N/V for the second extensional mode. These frequencies (especially that of the extensional mode) are higher than those observed experimentally because of the discrepancy in ice properties and experimental conditions, which differ slightly from the ideal boundary conditions considered in the simulation.

The experiments were conducted in the IWT, where a 3-mm-thick ice layer was accreted on the samples to replicate the conditions used in the numerical analyzes. The accretion process was performed under the following parameters: T = -5 °C, v = 18 m/s, MVD = 50 µm, and LWC ranging from 1 to 10 g/m³. The de-icing tests followed a consistent procedure: first, a low-voltage sweep (20 Vpk) was applied to identify the resonant mode. Subsequently, all five transducers were actuated using multiple chirp signals centered around the detected resonant frequency, operating at higher voltages for a total duration of 10 s.

## 4. Low-toughness coating

The present study focuses on the investigation of a gradient polymer coating deposited via initiated Chemical Vapor Deposition (iCVD), as described in [19] and [18]. The gradient polymer coating consists of poly-1,3,5,7-tetravinyl-1,3,5,7-tetramethylcyclotetrasiloxane (pV₄D₄) and poly-1H,1H,2H,2H-perfluorodecyl acrylate (pPFDA). According to the referenced studies, the V₄D₄ polymer is initially deposited to improve adhesion between the coating and the substrate. Subsequently, the PFDA monomer is gradually introduced until the desired copolymer thickness is achieved. In the upper section, deposition of the V₄D₄ polymer ceases, resulting in a layer composed solely of pPFDA, which alters the surface wettability. The overall thickness of these coatings remains within the nanometric scale. The studied coating, referred here as Grad300 coating, is a gradient polymer with a 300 nm top pPFDA section.

### 4.1. Interfacial properties

In [19], adhesion tests were performed on bare or Grad300-coated aluminum samples, polished or unpolished. In [18], the fracture mechanism was found to be toughness-dominated. The adhesion reduction factor for the Grad300 coating was evaluated using a horizontal shear test setup which allows measurements for a mixed-mode fracture mechanism [46]. It was observed that the adhesion reduction factor for an unpolished sample with the Grad300 coating varies depending on the brushing direction. When the brushing is parallel to the crack propagation direction, which is the same case as that tested in the present paper, the adhesion reduction factor is approximately 4.5.

Since 0.5 J/m² is a typical G_c value for the bare aluminum substrate, based on the adhesion reduction factor mentioned above, a G_c value of 0.11 J/m² will be adopted for further studies with the Grad300-coated plate.

### 4.2. Experimental results

In this section, the three modes are studied experimentally and the difference in behavior between bare and coated samples is evaluated.

#### 4.2.1. First out-of-plane flexural mode

In this study, the fracture mechanism is analyzed to determine if it is affected by the presence of the Grad300 coating for various lengths of the ice layer. Two competing coupled criteria are considered: one to initiate a cohesive fracture in the ice bulk, and one to initiate adhesive fracture at the interface between the ice layer and the substrate. The critical properties considered for the ice bulk are σ_c = 3 MPa, G_c = 1 J/m². At the interface, the tensile strength is assumed to be the same for the bare and coated substrates (σ_c = 500 kPa), while the toughness G_c varies depending on the interface. For the bare substrate, G_c = 0.5 J/m², while for the Grad300-coated substrate, G_c = 0.11 J/m².

3D numerical calculations are used to determine the amplitudes necessary to initiate a fracture when exciting the first out-of-plane flexural mode. Fig. 9 shows the cohesive and adhesive initiation curves for 100% ice coverage. It is possible to notice that the coupled criterion is met exclusively in the case of cohesive initiation (Fig. 9(c)). For this reason, cohesive initiation is expected, regardless of variations in interfacial properties. The initiation curves for 80% ice coverage are reported in Fig. 10. In this case, the coupled criterion is satisfied for both cohesive and adhesive fractures. For the bare specimen (G_c = 0.5 J/m²), the amplitude required to obtain a cohesive fracture is 52 µm, while it is 87 µm to obtain an adhesive fracture. The first fracture is therefore expected to be cohesive. For the Grad300-coated sample (G_c = 0.11 J/m²), the amplitude required to initiate an adhesive fracture is less than that required to initiate a cohesive fracture (40 µm versus 52 µm). Thus, adhesive initiation becomes the favored mechanism. Finally, in Fig. 11, the same initiation curves are reported for the 60% ice coverage. In this case, adhesive initiation is expected for both bare and coated substrates.

The numerical analyzes suggest a transition in the fracture mechanism as ice coverage approaches 80%, with adhesive initiation becoming more favorable as ice coverage decreases. These results are experimentally evaluated to confirm the transition in fracture mechanisms when the Grad300 coating is applied and to assess whether the coating enhances the de-icing capability. The tests are performed on bare and Grad300-coated samples with 100%, 80% and 60% ice coverage, each with a 3 mm ice thickness. Each test is repeated at least twice. Both bare and coated plates (Figs. 12(a) and 13(a) respectively) exhibit a cohesive fracture at the antinode when fully covered with ice. However, with 80% ice coverage, two different fracture mechanisms are observed. The bare sample continues to display cohesive fracture at the center of the ice layer (Fig. 12(b)), whereas the Grad300 sample shows adhesive propagation from the external edge of the ice layer towards the center (Fig. 13(b)). With 60% ice coverage, the fracture mechanism shifts from cohesive to adhesive in both samples (Figs. 12(c) and 13(c)). The variation in the fracture mechanism observed at 80% ice coverage is attributed to differences in interfacial properties, specifically the lower toughness at the interface of the Grad300 sample compared to the bare sample.

However, although the Grad300 coating alters the fracture mechanism, it does not achieve complete ice detachment. While the interfacial properties are modified, there is no significant improvement in de-icing efficiency. This is a limitation of out-of-plane flexural modes for which the energy release rate decreases significantly as the fracture propagates, as shown in Fig. 4. So, even if a coating modifies the interfacial properties, there may not be enough energy to completely detach the ice. It may be advantageous to use other resonance modes in which the energy release rate remains more constant with fracture propagation to analyze whether the coating contribution is more prominent [8,15].
<figure><img src="image_16.png" /></figure>

<figure><img src="image_17.png" /></figure>

<figure><img src="image_18.png" /><figcaption>(c) Cohesive initiation amplitudes.</figcaption></figure>

<figure><img src="image_19.png" /><figcaption>(d) Adhesive initiation amplitudes.</figcaption></figure>

<figure><img src="image_20.png" /><figcaption>Fig. 9. Amplitudes required to initiate fracture with 100% ice coverage.</figcaption></figure>

<figure><img src="image_21.png" /></figure>

<figure><img src="image_22.png" /><figcaption>(c) Cohesive initiation amplitudes.</figcaption></figure>

<figure><img src="image_23.png" /><figcaption>(d) Adhesive initiation amplitudes.</figcaption></figure>

<caption>Fig. 10. Amplitudes required to initiate fracture with 80% ice coverage.</caption>

### 4.2.2. Second in-plane flexural mode and second extensional mode

Further tests were performed to evaluate the performance of the Grad300 coating when used with resonant de-icing systems based on mode II or mode III fracture mechanisms and on in-plane flexural and extensional modes, for which the energy release is lower than for flexural modes but more constant as the fracture propagates. Bare and coated samples were tested in the icing wind tunnel using the second extensional mode and the second in-plane flexural mode. This time, two polished aluminum samples were prepared: a half-coated Grad300 plate and a fully-coated Grad300 plate.

The half-coated plate was tested using the second extensional mode. A mixed ice layer was formed. As illustrated in Fig. 14(a), the results indicate that the coated side of the plate (left) was completely free of ice after 4 s of excitation. In contrast, the uncoated side (right) presented some ice adhering to its surface even after 10 s of excitation. The experiment was repeated under the same conditions; however, due to the

thermal inertia present in the system, caused by the prolonged operation of the IWT, the accreted ice was more rime-like. As shown in Fig. 14(b), de-icing proved more challenging due to the lower density of the ice layer. However, the majority of the ice was shed from the coated side, with only a small portion remaining attached to the lower edge of the plate. Conversely, the uncoated side did not experience any ice shedding. These results highlighted the beneficial effect of the application of a Grad300 coating on the de-icing process with the second extensional mode.

The half-coated plate was subsequently tested using the second in-plane flexural mode. Two separate ice blocks, each 3 mm thick, were formed to further evaluate the de-icing performance of the Grad300 coating compared to the bare plate. Given the lower force factor of this mode (N = 0.27 N/V) compared to that of the second extensional mode (N = 0.45 N/V), a slightly higher de-icing voltage was selected (250 Vpk). As seen in Fig. 15(a), upon activation, the ice detached almost
<figure><img src="image_24.png" /><figcaption>Fig. 11. Amplitudes required to initiate fracture with 60% ice coverage.</figcaption></figure>

<figure><img src="image_25.png" /><figcaption>Fig. 12. Bare plate - Fracture mechanism depending on the ice length for the first out-of-plane flexural mode (200 Vpk de-icing).</figcaption></figure>

immediately from the coated side, with only a minor cohesive fracture observed at the top left of the plate. The detachment was predominantly adhesive. On the uncoated side, the ice block remained firmly adhered to the substrate, with no evidence of cohesive or adhesive failure. A second test was conducted (Fig. 15(b)), resulting in the immediate detachment of the ice block from the coated side, while the ice block remained attached to the uncoated side.

Experiments on the second in-plane flexural mode were also performed on a fully-coated plate completely covered by ice to assess whether the de-icing performance would be affected by a larger iced surface. Fig. 16(a) illustrates that, apart from a minor adhesive propagation observed in the bottom left corner of the plate, all the ice was rapidly shed from the surface in less than half a second following activation. A second test was conducted to ensure the repeatability of the de-icing process, as shown in Fig. 16(b). Due to the thermal inertia of the system, the ice formed was more rime-like in nature. Approximately 6 s after the activation of the actuators, the ice was completely shed from the surface.

Overall, these tests have demonstrated the very good performance of the Grad300 coating when combined with resonant de-icing systems based on mode II or mode III fracture mechanisms present in in-plane flexural and extensional modes. The coating largely favors adhesive fracture propagation and ice shedding.

## 5. Low-shear-strength coating

This section examines the properties and performances of a commercial low-shear coating from Wearlon, known as Super F-6M. This coating is a water-based silicone-epoxy formulation primarily designed for maritime applications.

### 5.1. Interfacial properties

While the manufacturer does not specify any icephobic characteristics, experimental studies have demonstrated its potential in this regard. Vincent et al. [54] reported that the Super F-6M coating exhibited low ice adhesion in their experiments. The results indicated that the ice
<figure><img src="image_26.png" /><figcaption>Fig. 13. Grad300 plate - Fracture mechanism depending on the ice length for the first out-of-plane flexural mode (200 Vpk de-icing).</figcaption></figure>

<figure><img src="image_27.png" /><figcaption>Fig. 14. Half-coated plate - Second extensional mode de-icing (200 Vpk, 10 s). The right-most picture coincides with the final configuration at $t = 10$ s.</figcaption></figure>

<figure><img src="image_28.png" /><figcaption>Fig. 15. Half-coated plate - Second in-plane flexural mode de-icing (250 Vpk, 10 s).</figcaption></figure>
<figure><img src="image_29.png" /><figcaption>Fig. 16. Fully-coated plate - Second in-plane flexural mode de-icing (10 s).</figcaption></figure>

<figure><img src="image_30.png" /><figcaption>Fig. 17. Wearlon plate - Fracture mechanism depending on the ice length for the first out-of-plane flexural mode.</figcaption></figure>

adhesion strength for the Wearlon coating was 290 kPa, which is significantly lower than the 740 kPa measured for bare aluminum under similar conditions.

Regarding Wearlon's toughness, according to [17], material based on silicone-epoxy does not have low toughness. Furthermore, according to [17], the toughness decreases with the thickness. Low interfacial coating thickness is in the µm range, as is the case for Grad300 (0.3 µm), but not for Wearlon (a few hundred µm). All these factors confirm that the Wearlon coating is not a low-interfacial coating.

## 5.2. Experimental results

In previous tests with the Grad300 plate, it was shown that the effectiveness of electromechanical resonant de-icing systems is improved by applying a low-toughness coating. This is not the case with the Wearlon coating, which is rather characterized by a low shear strength. Tests are performed with this coating under the same conditions as before to confirm the need for low toughness to improve de-icing and the limitations of low-shear-strength coatings in improving the performance of electromechanical resonant de-icing systems.

### 5.2.1. First out-of-plane flexural mode

The first out-of-plane flexural mode is again used to analyze the fracture mechanisms and, as before, the tests are performed with different ice layer lengths. The considered ice coverages are again 100%, 80%, and 60% of the sample length, each with an ice thickness of 3 mm. The

de-icing procedure is not varied and each test was conducted at least twice.

The Wearlon-coated sample displays the same fracture mechanisms as bare aluminum, as shown in Fig. 12. When fully covered with ice or with a 80% ice coverage, both the Wearlon coated and the bare aluminum samples demonstrate a cohesive fracture mechanism, as illustrated in Figs. 12(a) and 17(a) and in Fig. 12(b) and 17(b). When ice coverage is reduced to 60%, the fracture mechanism in both samples transitions from cohesive to adhesive, as depicted in Figs. 12(c) and 17(c). It can be concluded that the coated sample behaves similarly to the bare sample, and that the low-shear-strength coating does not significantly impact the de-icing mechanism obtained with the first out-of-plane flexural mode and thus the mode I fracture mechanism.

### 5.2.2. Second in-plane flexural mode and second extensional mode

As before, tests in the IWT were conducted to assess the effect of the Wearlon coating coupled with electromechanical resonant de-icing systems, operating using mode II and mode III fracture. These fracture modes are obtained by exciting the second extensional mode and the second in-plane flexural mode of the sample. This time, only one polished aluminum plate was manufactured: on one half, the plate presented a layer of the hydrophobic Wearlon coating, while the other half was left bare.

The second extensional mode was first studied. As illustrated in Fig. 18(a), the results indicate that the coated side of the plate (left) did not display a better de-icing behavior compared to the uncoated
<figure><img src="image_31.png" /><figcaption>Fig. 18. Half-coated plate - Second extensional mode de-icing (200 Vpk, 10 s). The right-most picture coincides with the final configuration at $t = 10$ s.</figcaption></figure>

<figure><img src="image_32.png" /><figcaption>Fig. 19. Half-coated plate - Second in-plane flexural mode de-icing (250 Vpk, 10 s).</figcaption></figure>

side (right). At the end of excitation, ice adhered to both sides of the surface.

The experiment was repeated with a rime-like ice. As illustrated in Fig. 18(b), the de-icing process was not entirely successful. Only a portion of the surface was de-iced, with no significant differences observed between the coated and uncoated parts. Consequently, the application of the coating did not demonstrate any clear advantage.

The half-coated plate was subsequently tested using the second in-plane flexural mode. Two distinct ice blocks, each 3 mm in thickness, were formed on the surface to separate the behavior of the two sides. As shown in Fig. 19(a), following activation, only a small ice block on the coated (blue) side detached, with some limited adhesive propagation observed on the same side after 2 s. Due to the difficulty in detecting adhesive propagation on the uncoated side, it is unclear whether the same effect occurred there. After 10 s of excitation, no further de-icing was observed on either side of the plate. A second test was conducted at a frequency of 7.1 kHz using a rime-like ice layer. In line with previous results, the application of 250 Vpk caused the detachment of a small ice block on the coated side, with no additional de-icing effects observed (Fig. 19(b)).

## 6. Conclusions

Two anti-icing coatings were evaluated for their effectiveness in promoting fracture propagation in the context of a resonant electromechanical ice protection system. The first coating, called Grad300, is a low-interfacial-toughness coating. The second coating, Wearlon, is a commercially available low-shear-strength coating.

Tests were performed with three resonant modes, in which fracture occurs under different loading conditions. The first tests were performed with the first out-of-plane flexural mode. It was shown that, while the fracture mechanism in Grad300 transitioned from cohesive to adhesive at a different ice length than aluminum, thus confirming a change in fracture behavior. However, this did not result in an improvement in de-icing performance. This is a limitation of out-of-plane flexural modes, where the energy release rate decreases significantly as the fracture spreads.

Subsequent de-icing experiments performed in the icing wind tunnel focused on two other resonant modes: the second extensional mode and the second in-plane flexural mode. To facilitate accurate comparison between coated and uncoated surfaces, two half-coated prototypes were fabricated. IWT results indicated a significant improvement in de-icing performance with Grad300 compared to the bare substrate. However, for Wearlon, the performance on coated and bare sections was similar. To conclude, the Grad300 coating performed better with in-plane modes, which exhibit a more stable energy release rate as the fractures propagate and involve modes II and III fracture mechanisms, than with the first out-of-plane flexural mode.

This paper raises three main considerations.

First, it is now evident how important it is to fully characterize the interfacial properties of a coating to better predict the fracture mechanisms when coatings are adopted for a hybrid system in combination with a resonant electromechanical ice protection system. In most cases, either the interfacial shear strength or the toughness is provided, and for the latter, only one of the three quantities, $G_{Ic}$, $G_{IIc}$ and $G_{IIIc}$, is often measured. A comprehensive characterization of the coating would
enable a more accurate selection of coatings to be paired with specific resonant modes.

Second, in the literature on anti-icing coatings, low-shear strength coatings have been identified as a solution for numerous industrial applications. This study demonstrated that coatings with only a low interfacial shear strength may have limited applicability for resonant electromechanical de-icing systems.

Third, the gain in power for resonant electromechanical de-icing systems combined with a low-interfacial-toughness coating can be estimated using [8]. A reduction in toughness by half results in a reduction in surface power consumption by half.

To further this study, additional tests could be performed in a wind tunnel where ice properties can be certified, and flight tests could be conducted to confirm the results with in-flight ice.

In future studies, the durability of the coatings could also be investigated. Understanding the number of de-icing cycles a coating can withstand before experiencing performance degradation is crucial for assessing long-term effectiveness. This aspect is particularly important when considering the potential for future industrial applications, where repeated de-icing operations will be necessary.

### CRediT authorship contribution statement

**G. Gastaldo:** Writing – original draft, Methodology, Formal analysis, Data curation, Conceptualization. **G. Hernández-Rodríguez:** Writing – review & editing, Formal analysis, Data curation, Conceptualization. **V. Pommier-Budinger:** Writing – review & editing, Supervision, Methodology, Conceptualization. **M. Budinger:** Writing – review & editing, Supervision, Methodology, Conceptualization. **J. Pothin:** Data curation. **A.M. Coclite:** Writing – review & editing, Supervision, Methodology.

### Declaration of competing interest

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

### Acknowledgements

This project has received funding from the European Union's Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No. 956703 (SURFICE Smart surface design for efficient ice protection and control).

### Data availability

Data will be made available on request.

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