# Development and assessment of an adhesively bonded assembly geometry adapted for both ELS test and toward hygro-mechanical aging evaluation

Arij Fawaz, Emilie Lepretre, Xavier Chapeleau, Jean-François David, Sylvain Chataigner

<figure><img src="image_1.png" /></figure>

## ► To cite this version:

Arij Fawaz, Emilie Lepretre, Xavier Chapeleau, Jean-François David, Sylvain Chataigner. Development and assessment of an adhesively bonded assembly geometry adapted for both ELS test and toward hygro-mechanical aging evaluation. Theoretical and Applied Fracture Mechanics, 2026, 141 (A), pp.105301. 10.1016/j.tafmec.2025.105301. hal-05394703

HAL Id: hal-05394703

https://hal.science/hal-05394703v1

Submitted on 9 Dec 2025

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

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

Distributed under a Creative Commons Attribution 4.0 International License
<figure><img src="image_3.png" /></figure>

# Development and assessment of an adhesively bonded assembly geometry adapted for both ELS test and toward hygro-mechanical aging evaluation

Arij Fawaz<sup>a,b,*</sup>, Emilie Lepretre<sup>a</sup>, Xavier Chapeleau<sup>b</sup>, Jean-François David<sup>a</sup>, Sylvain Chataigner<sup>a</sup>

## ARTICLE INFO

**Keywords:**

Structural adhesive bonding

Fracture mechanics

End-loaded Split test (ELS)

Digital image correlation (DIC)

Distributed optical fiber sensor

## ABSTRACT

Structural adhesive bonding has gained significant attention in recent years. However, its durability in harsh environments, such as marine ones, remains insufficiently examined due to a lack of comprehensive research. One reliable approach for assessing the strength of bonded assemblies is the fracture mechanics, which involves conducting experimental tests in different loading modes to determine their fracture toughness. These tests can be performed before and after aging conditions to evaluate the mechanical properties evolution of the bonded assembly in response to aging. While mode I may occur, mode II is usually dominant in bonded joints; thus, only mode II is considered in this study. The selected mode II test is the End-Loaded Split (ELS) test. Most studies have focused on either the mechanical test setup or the aging setup, but have lacked a combined approach. This paper introduces a new sample configuration that merges both the ELS test setup and the hygro-mechanical frame. To validate the new sample design, a comparison of the fracture toughness values and of the cohesive zone models (CZMs), obtained after fracture data elaboration, is made between this new configuration and a standard ELS sample geometry. For the fracture toughness measurement, all specimens were instrumented with distributed optical fiber sensor to monitor crack propagation as well as Digital Image Correlation system to calculate the J-integral values from which the CZM can be derived. One major conclusion is that the results are repeatable, confirming that the new sample design is valid for the upcoming aging study.

## 1. Introduction

Metallic offshore structures require regular maintenance and reinforcement due to their exposure to harsh environments, particularly seawater. Various joining techniques are available for repairing and reinforcing these structures, including structural bonding. Structural bonding offers significant advantages over other joining methods by mitigating issues related to stress singularities, avoiding substantial weight addition, and ensuring more uniform stress distribution across the bonded zone [1–3]. However, one of the primary limitations of structural bonding is the limited knowledge regarding its durability under varying aging conditions, such as creep, humid aging, fatigue, or coupled aging conditions [3–12].

To evaluate the durability of bonded assemblies, their mechanical properties need to be examined using a robust method, such as the one based on Linear Elastic Fracture Mechanics (LEFM) [13]. In this approach, mechanical characterization tests can be conducted in mode I

(opening mode), mode II (shear mode), and mixed-mode loading conditions. These destructive tests aim to investigate interface behavior through determination of the strain energy release rate and then by using the test data for modeling approaches. One of the most widely adopted methods for modeling the interfacial behavior of bonded assemblies is the Cohesive Zone Model (CZM) [14,15]. The CZM describes the relationship between local stress and local strain at the interface of materials or within a material, highlighting the initiation and propagation of cracks, as well as the evolution of damage and failure of interfaces. In bonded assemblies, the shear mode has been identified as the predominant loading mode [16].

In offshore environment, bonded assemblies are subjected to hygrothermal conditions combined with permanent loadings. Prior studies have already revealed the effects of hydrothermal conditions [17] or creep conditions [8,18] on the mechanical behavior of bonded assemblies. Some authors [19] demonstrated that immersion in distilled water reduces adhesive strength more significantly compared to seawater immersion. Fernandes et al. [20] underlined the influence of

<footnote><sup>a</sup>MAST/SMC, Université Gustave Eiffel, Bouguenais 44344, France</footnote>

<footnote><sup>b</sup>COSYS/SII-14S, Université Gustave Eiffel, Inria, Bouguenais 44344, France</footnote>

<footnote>* Corresponding author at: MAST/SMC, Université Gustave Eiffel, Bouguenais 44344, France.</footnote>

<footnote>E-mail address: arij.fawaz@univ-eiffel.fr (A. Fawaz).</footnote>
<table><thead><tr><th colspan="2">Nomenclature</th></tr></thead><tbody><tr><td>ELS</td><td>End-Loaded Split test</td></tr><tr><td>DIC</td><td>Digital Image Correlation</td></tr><tr><td>LEFM</td><td>Linear Elastic Fracture Mechanics</td></tr><tr><td>CZM</td><td>Cohesive Zone Model</td></tr><tr><td>3ENF</td><td>Three-Point End-Notched Flexure test</td></tr><tr><td>4ENF</td><td>Four-Point End-Notched Flexure test</td></tr><tr><td>t<sub>1</sub></td><td>Thickness of the upper adherend in configuration 1 and configuration 2 samples</td></tr><tr><td>t<sub>2</sub></td><td>Thickness of the lower adherend in configuration 1 samples</td></tr><tr><td>t'<sub>2</sub></td><td>Thickness of the lower adherend 1 in configuration 2 samples</td></tr><tr><td>t"<sub>2</sub></td><td>Thickness of the lower adherend 2 in configuration 2 samples</td></tr><tr><td>b</td><td>sample's width</td></tr></tbody></table><table><tbody><tr><td>l</td><td>sample's length</td></tr><tr><td>T<sub>g</sub></td><td>Glass transition temperature of the adhesive</td></tr><tr><td>E</td><td>Young's modulus of the adhesive</td></tr><tr><td>Δ<sub>clamp</sub></td><td>Clamp correction</td></tr><tr><td>E<sub>1</sub></td><td>The specimen's flexural modulus</td></tr><tr><td>C</td><td>Compliance of the specimen</td></tr><tr><td>a<sub>0</sub></td><td>Length of the initial artificial crack</td></tr><tr><td>a<sub>p</sub></td><td>Length of a real pre-crack</td></tr><tr><td>L</td><td>The initial free length</td></tr><tr><td>ROI</td><td>Region of Interest</td></tr><tr><td>FPZ</td><td>Fracture Process Zone</td></tr><tr><td>θ<sub>P</sub></td><td>Rotation angle at the load application point</td></tr><tr><td>ECM</td><td>Experimental Compliance Method</td></tr><tr><td>SBT</td><td>Simple Beam Theory method</td></tr><tr><td>CBTE</td><td>Corrected Beam Theory with Effective crack length</td></tr><tr><td>R<sup>2</sup></td><td>Coefficients of determination</td></tr></tbody></table>

three moisture conditions (55 % RH, 75 %RH and distilled water) on fracture response of composite bonded joints. They obtained smaller reduction of fracture energy decreases slightly in the case of exposure to 55 % and 75 % RH while it is strongly reduced when samples were immersed in distilled water. Significant research has been dedicated to understanding the diffusion of humidity in bulk adhesives [4,21–25] and bonded assemblies [4,7,26]. Grangeat et al. [4] found that diffusion is faster and more significant in bonded assemblies than in bulk adhesives, highlighting the impact of the interfacial zone. The authors in [27,28] found that the water absorption can result in a decrease in the glass transition temperature of the adhesive.

Likewise, researchers have investigated the impact of creep on the long-term performance of bonded joints by studying both single-lap joints [11,29] and double-lap joints [30] under constant load. The authors in [30] demonstrated that pre-creep loading of bonded structures can greatly enhance the fracture energy and static strength of the joints. Queiroz et al. [31] examined the creep behavior of single-lap joints SLJs consisting of a metallic substrate bonded with an epoxy-based adhesive. They tested these SLJs at different applied load equal to 100 %, 80 %, 70 % and 60 % of the average tensile strength of the joints (τ<sub>u</sub>). As they decreased the applied load from 80 % to 70 % of τ<sub>u</sub>, the average time until rupture increased from 8 h to 1768.5 h (over 200 times greater). Thus, increasing the applied creep load by just 10 % can significantly impact the creep life of adhesive joints, particularly those bonded with epoxy adhesives.

Several mode II mechanical characterization tests exist in the literature, such as the Three-Point End-Notched Flexure (3ENF), the Four-Point End-Notched Flexure (4ENF) and the End-Loaded Split (ELS) tests. Among these, the 4ENF and ELS tests are known to offer greater stability in crack propagation compared to the 3ENF test [33–35]. In this study, the standardized ELS test [36] is selected as the mode II mechanical characterization method. Sample geometry for ELS test consists of two perfectly symmetrical and identical bonded adherends. With this geometry, it is not possible, via a bending test, to apply a constant tensile stress inside the bonded joint (the neutral axis is located at the middle of the bonded joint) and at a sufficiently high level for mechanical aging. Thus, a new sample geometry is proposed in this study, meeting both the ELS test specifications and the requirements of the creep aging campaigns based on bending test.

Despite numerous studies focusing only on creep or moisture diffusion, there is a lack of relevant research on their combined effects under humid and creep aging conditions [32]. Therefore, our study aims to investigate the combined effect of hydro-mechanical conditions on the mechanical properties of bonded joints. To do that, a new bonded assembly geometry is needed to fit both the aging conditions and the

mechanical characterization test. The aim of this article is to demonstrate the relevance of the new specimen configuration proposed. First, the new bonded joint design is described in detail, including the criteria for its selection. Subsequently, experimental investigations on this joint, prior to aging, are presented, based on ELS tests only. All samples are instrumented with Digital Image Correlation (DIC) and distributed optical fiber sensors to monitor crack propagation. Finally, the fracture toughness values, the J-integral, and the CZM are evaluated for both configurations: the standard symmetrical bonded joint and the newly proposed design.

## 2. Design and preparation of studied adhesively bonded samples

### 2.1. Specimen design

In this study, two specimen designs of bonded assemblies are investigated, labeled as configuration 1 samples and configuration 2 samples. Configuration 1 includes all specimens with identical (same elastic properties) and symmetrical (same dimensions) adherends. The lower adherend (t<sub>2</sub>) and the upper adherend (t<sub>1</sub>) have thus the same thickness and are made of the same material (Fig. 1).

Configuration 2 is a newly proposed specimen design allowing for the combination of both the creep setup and the geometry of the ELS test sample.

In this study, a four-point bending configuration was chosen for the creep setup. This design ensures a constant and identical stress value in the X-direction σ<sub>XX</sub> for each section between the two load application points. The moment remains constant in the middle of the adhesive layer between the two load application points, while stress singularities occur at these points. These singularities are addressed through the introduction of a pre-crack. As a result, the remaining uncracked portion of the adhesive is subjected to a region of constant moment. Furthermore, to achieve a non-zero stress value in the adhesive and at the adherend/ adhesive interfaces, a non-symmetric sample is selected in which the upper adherend is thicker than the lower one. (Fig. 2). Both adherends have the same young modulus.

During creep, the applied load will be chosen so as not to induce any crack propagation, since the specimen will be tested using the ELS test after creep aging. To ensure that the adhesive joint experiences shear forces during the ELS test, the neutral axis should be inside the adhesive layer. To do that, an additional plate is bonded to the thinner adherend (the lower adherend 1), until its stiffness matches that of the upper adherend (as shown in Fig. 3). Consequently, the modified lower adherend consists of three layers: the thin lower adherend having a thickness of t'<sub>2</sub>, a small adhesive layer (adhesive 2), and the second
<figure><img src="image_4.png" /><figcaption>Fig. 1. Configuration 1 specimen.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 2. A 4-point non-symmetrical bending creep test.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 3. Configuration 2 specimen.</figcaption></figure>

bonded adherend of $t''_2$ thickness. Furthermore, the applied creep load will be selected to remain within the elastic deformation range, without any permanent deformation. This means that even if the specimen shape is slightly warped when placed in the creep frame, it returns to a flat shape once removed. Thus, there will be no curvature in the assembly before bonding the third plate (i.e., lower adherend 2).

Configurations 1 and 2 have the same length of $l=300$ mm and the same width of $b = 15$ mm. This small width was chosen to achieve water saturation more quickly. In configuration 1, both adherends have a thickness of 5 mm, and the adhesive layer is approximately 1 mm thick (± 0.15 mm). For configuration 2, the selected dimensions are as follows: $t_1 = 5$ mm, $t'_2 = 0.6$ mm and $t''_2 = 4$ mm. The thickness of adhesive 1 is around 1 mm (± 0.15 mm), whereas adhesive 2 has a thickness of approximately 0.4 mm (± 0.05 mm). All steel plates were supplied with a precision of $10^{-2}$mm.

## 2.2. Material properties

For configurations 1 and 2, all the adherends are high-strength steel plates. The upper adherend and lower adherend 2 are made of STRENX 700, with a yield strength of 700 MPa, while lower adherend 1 is a high-strength black strapping steel with a yield strength of 925 MPa. The lower adherend 1 is of a different type than the other adherends since it was not feasible, according to many manufacturers and suppliers we contacted them, to cut the STRENX 700 plates along their thickness to

achieve a 0.6 mm thickness. Therefore, we used a different type of steel that is commercially available with an average thickness of 0.6 mm, requiring only cutting to the desired width and length.

Despite the fact that the interface where an artificial pre-crack is inserted is almost identical from a mechanical perspective to the interface between high-yield steel and adhesive 1 (adhesive 1/lower adherend interface for configuration 1 and adhesive 1/lower adherend 1 for configuration 2), these two interfaces differ chemically. This discrepancy arises from the differing nature of the adherends used, which can impact adhesion, as the type of substrate plays a significant role in the adhesion process.

Two commercial adhesives with different chemical compositions were selected for this research. The adhesive 1, used in both configurations, is an epoxy-based adhesive, with a glass transition temperature $T_g$ of 91 °C and a Young's modulus $E$ of 3100 MPa according to its technical data sheet. The adhesive 2, used in configuration 2 samples only, is a methacrylate adhesive with $T_g = 85$ °C and $E$ ranging between 1200 and 1700 MPa, as specified in its technical datasheet. It is important to note that only the properties of adhesive 1 are investigated in this study, while adhesive 2 is used only to achieve specimen symmetry. The adhesive 2 should not be the weakest element of the bonded assembly, ensuring that crack propagation occurs only along adhesive 1 and not adhesive 2. Moreover, the adhesive 2 was selected in such a way as to not affect the properties of adhesive 1 during its curing conditions. Therefore, adhesive 2 was chosen with a curing condition at room
temperature (25 °C for 24 h), with no post-curing. The selection of these adhesives was driven by their industrial relevance and frequent use in marine environment, which represents the case and condition of this research.

## 2.3. Samples preparation methodology

Before bonding, the adherends were sanded using a sandblasting machine, achieving an average roughness of 3.5 µm (± 0.5 µm), and then cleaned with acetone. To maintain a constant thickness of 1 mm for adhesive 1, 1 mm thick shims were used on each side of the specimen. For adhesive 2, a plastic fishing line with a diameter of 0.4 mm was used to ensure a constant adhesive thickness of 0.4 mm.

After bonding, all specimens were cured according to the adhesive supplier's technical data sheet: adhesive 1 at 80 °C for 16 h and adhesive 2 at 25 °C for 24 h.

# 3. Mechanical tests, instrumentation and determination of critical energy release rate

## 3.1. Clamp calibration for ELS test

The ELS test is a shear fracture mechanics test used to evaluate the fracture toughness of adhesive joints by applying a tensile load at the end of a pre-cracked bonded specimen, while the opposite end is clamped with a block that slides laterally on bearings (see Fig. 4). One of the main limitation of the ELS test is the clamping variability of the sample [33,37]. Thus, the ISO 15114 standard [36] suggests a clamp calibration correction process, before conducting the ELS test, in order to obtain both the ELS clamp correction $\Delta_{clamp}$ and the specimen's flexural modulus $E_1$. A graph of $C^{1/3}$ (C is the compliance of the specimen, i.e., the ratio between the displacement value of the load application point and the applied load) versus the free length L (distance between the load application point and the clamping fixture) can be plotted following the procedure indicated in the standard, and a linear regression of this data is conducted as expressed in Eq. (1):

$$C_3^1 = \alpha (L + |\Delta_{clamp}|) \quad (1)$$

Where $\alpha$ is the slope value from which the flexural modulus of the specimen $E_1$ can be calculated by using Eq. (2). In this equation, b is the sample width and h the upper adherend height.

$$E_1 = \frac{1}{2b(h \times \alpha)^3} \quad (2)$$

After the calibration, the ELS test was performed by applying a vertical load at the pre-cracked end of the specimen, inducing crack

propagation along the adhesive layer (see Fig. 5). The loading procedure was performed via a 3R traction/compression machine at a speed of 1 mm/min.

For all specimens, the initial free length is $L = 100$ mm and the first test is done with an artificial crack consisting of a Teflon insert (0.21 mm thick) measuring $a_0 = 75$ mm. This initial test is used only to establish a real crack front rather than an artificial one. The real pre-crack was obtained by propagating an initial artificial crack created using a Teflon insert, as recommended by the ELS standard. In fact, pre-cracking in mode II allows prevents from insert-induced crack initiation and unstable crack propagation. The obtained pre-crack length is denoted $a_p$. The study focuses only on the subsequent tests featuring a real crack front and varying ratios of $a_p/L$ ranging from 0.6 to 0.75. The ratio $a_p/L$ was selected to be greater than 0.55 to enhance the stability of crack propagation during the test, in accordance with the ISO 15114 standard [36]. Moreover, due to the total length of the specimen (300 mm), the two ends were used to led ELS test.

## 3.2. Instrumentation

The specimen is equipped with a single mode polyimide coated optical fiber bonded to the center of the top surface of the upper adherend (Fig. 6), as proposed in [38]. The optical fiber is used as sensor with high spatial resolution distributed optical fiber sensing system (Luna ODISI-B), allowing continuous monitoring of strain along the upper adherend during the test. Typically, strain values obtained along the entire fiber length correspond to strain gauges of 0.65 mm length spaced at equal intervals of 0.65 mm.

The strain-distributed optical fiber sensor was primarily used to assess the crack length during the ELS test. The strain profiles, derived at each time step and at intervals of 0.65 mm from the optical fiber, were analyzed. By assuming that the maximum strain corresponds to the crack front, the position of the crack front can be identified [39], allowing for the determination of the crack length. This approach facilitates the calculation of the $a_p/L$ ratio and the mode II fracture toughness values for each test. The final crack position was also obtained based on data from the fiber optical sensor.

A Digital Image Correlation (DIC) system was also employed and consists of two 5 MP Basler acA2440-75um cameras, each equipped with Kowa LR1015WM52 lenses (50 mm focal length). Camera stereo-correlation angle is 15 degrees and the cameras were placed at a fixed distance of 30 cm from the sample's edge, where a fine speckle pattern was applied (Fig. 7). The camera sensor has a resolution of 2448 pixels in the X-direction (corresponding to the sample length) and 2048 pixels in the Y-direction (corresponding to the sample thickness), which defines the digital image resolution used for Digital Image Correlation (DIC) analysis.

<figure><img src="image_7.png" /><figcaption>Fig. 4. Calibration setup for an ELS test performed on a pre-cracked bonded assembly.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Fig. 5. ELS test setup for a pre-cracked bonded assembly.</figcaption></figure>
<figure><img src="image_9.png" /><figcaption>Fig. 6. Position of the optical fiber on the samples.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Fig. 7. Speckle pattern applied on the edge of the specimen.</figcaption></figure>

An airbrush was used to create a black-on-white speckle pattern, with speckle sizes ranging between 0.05 mm and 0.3 mm. Based on the implementation parameters (such as size of the speckle, contrast of the speckle pattern, lighting conditions, position of the cameras and their calibration), the physical pixel size is of approximately 0.05 mm and the Correli software recommends an optimal mesh size of 16 × 16 pixels for the analysis (Fig. 8).

A Region of Interest (ROI) is selected to contain the initial and final crack fronts, including the Fracture Process Zone (FPZ) and a section named SS'. The FPZ refers to the region near the crack tip where the material undergoes complex interactions due to stress and damage. It is

characterized by microstructural changes, such as the initiation and growth of cracks or voids, or plasticity, which influence the overall fracture behavior. SS' section is a vertical section (across the entire thickness of the bonded assembly) positioned as a compromise distance between two conditions (Fig. 9): (1) SS' should be sufficiently distant from the clamping edge to avoid the influence of the clamping zone on crack propagation (this distance was determined to be a maximum of 10 mm from the clamping edge, based on the optical fiber data from all tests), and (2) SS' should be far enough from the initial crack tip (pre-crack length) to ensure that the contour used for energy calculation fully encompasses the entire FPZ.

Thanks to the DIC data, the sliding displacement $\delta$ between upper and lower adherends can be deduced from the horizontal displacement fields. This parameter is essential to calculate later on the rotation angle at the SS' section. Due to meshing singularities near the edges of the assembly, the total displacements in section SS' is estimated by linear extrapolation of the two extreme displacement measurements obtained within the ROI.

It is worth noting that, in this study, crack length was determined exclusively using the optical fiber sensor, as DIC provided less accurate results in mode II due to the influence of the FPZ on the displacement fields. DIC was used solely to obtain displacement fields within the defined ROI for the calculation of the J-integral.

Finally, to assess the rotation angle $\theta_p$ at the load application point, a muRata SCA121T-D03 inclinometer was used which provides a measuring range $\pm 90^\circ$ with an accuracy of $\pm 1^\circ$ and a resolution of 0.0025$^\circ$, as specified by the manufacturer. This rotation angle is needed for the J-integral approach more detailed in the following part.

### 3.3. Theoretical measurement of the ELS crack tip

To monitor crack propagation using the previously described optical fiber, it is essential to understand the corresponding strain profiles and how the crack tip position can be estimated from the strain profiles of

<figure><img src="image_11.png" /><figcaption>Fig. 8. 16 × 16 pixels meshing in the ROI.</figcaption></figure>
<figure><img src="image_12.png" /><figcaption>Fig. 9. (a) Horizontal displacement field for a sample from configuration 1, with an initial crack length of 69.45 mm; (b) Schematic representation of the region of interest (ROI) at the edge of the bonded assembly.</figcaption></figure>

the continuous optical fiber. By applying beam theory, the strain at the top surface of a bonded assembly, tested via an ELS test, can be expressed via two strain components: $\epsilon_{xx1}$ and $\epsilon_{xx2}$. The strain $\epsilon_{xx1}$ corresponds to Path A, as indicated in Fig. 10, representing the top surface of the bonded assembly in the pre-crack region (i.e., without adhesive). In this region, the sample behaves as a superposition of two separate beams (no friction considered) where each beam carries half of the bending moment. The Young's modulus for this part is that of the steel adherend $E_s$ and the second moment of area (also known as the area moment of inertia) $I_{z,1}$ is provided in Eq. (3). The strain $\epsilon_{xx2}$ corresponds to the strain over the remaining top surface of the bonded assembly, i.e., Path B (uncracked part of the specimen), where an adhesive layer is present between the two steel plates. The second moment of area of the adhesive layer $I_{a(z,2)}$ and that of the two adherends $I_{s(z,2)}$, in this zone, are given by Eqs. (4) and (5) respectively. The expressions for $\epsilon_{xx1}$, $\epsilon_{xx2}$, are provided in Eqs. (6) and (7), respectively.

$$I_{z,1} = 2 \times \frac{bh_s^3}{12} \qquad (3)$$

$$I_{a(z,2)} = \frac{bh_a^3}{12} \qquad (4)$$

$$I_{s(z,2)} = \frac{b}{12} \left[ (h_a + 2h_s)^3 - h_a^3 \right] \qquad (5)$$

$$\epsilon_{xx1} = - \frac{M_z}{E_s \cdot I_{z,1}} \frac{h_s}{2} \qquad (6)$$

$$\epsilon_{xx2} = - \frac{M_z}{E_a I_{a(z,2)} + E_s I_{s(z,2)}} \left( h_s + \frac{h_a}{2} \right) \qquad (7)$$

In the previous equations b represents the sample width, $h_a$ corresponds to the thickness of the adhesive layer, $E_a$ denotes the Young's modulus of the adhesive layer, and $M_z$ represents the bending moment component about the x-axis. A symmetrical bonded assembly is considered in this part where the thickness of adherend is denoted as $h_s$, representing both the upper and lower adherend thickness ($h_s = t_1 = t_2$).

This model has several key limitations: it assumes that the fracture process zone (FPZ) has a negligible effect on the derived strain profiles, and it supposes that the crack front is sufficiently separated from the load application point to avoid any interference.

### 3.4. Determination of the critical energy release rates

To calculate the mode II fracture toughness value, $G_{IIc}$, for crack initiation and propagation stages, three methods are proposed in the ELS test standard: the Experimental Compliance Method (ECM), the Simple Beam Theory method (SBT) and the Corrected Beam Theory with Effective crack length (CBTE).

The first two methods require experimental determination of the crack length. The ECM method relies on a cubic correlation between compliance and the measured crack length, as described in Eqs. (8) and (9). The parameter $C_0$ represents the intercept on the C-axis, while m corresponds to the slope; both $C_0$ and m are constants. The SBT method, in addition to the crack length, requires the flexural modulus of the specimen $E_I$ obtained through the calibration process (Eq. (10)). In contrast, the CBTE method does not require direct measurement of the crack length. Instead, the crack length is corrected to an effective crack length $a_e$, which account for clamping effects and incorporates calibration corrections (Eq. (11)). The mode II fracture toughness based on the CBTE method is defined by Eq. (12).

$$G_{IIc} = \frac{3P^2 a^2 mF}{2b} \qquad (8)$$

$$C = C_0 + ma^3 \qquad (9)$$

<figure><img src="image_13.png" /><figcaption>Fig. 10. Schematic representation of the analytical strain profile at the top surface of a bonded assembly subjected to an ELS test.</figcaption></figure>
$$G_{\text{IIC}} = \frac{9P^2 a^2 F}{4b^2 h^3 E_1} \qquad (10)$$

$$a_e = \left[ \frac{1}{3} \left( 2b \frac{C}{N} h^3 E_1 - (L - \Delta_{\text{clamp}})^3 \right) \right]^{1/3} \qquad (11)$$

$$G_{\text{IIC}} = \frac{9P^2 a_e^2 F}{4b^2 h^3 E_1} \qquad (12)$$

In these equations, $a$ denotes the crack length, $C$ the compliance of the specimen, $P$ the applied load, $h$ the height of a single adherend and $b$ the sample width. The term $F$ refers to a correction factor typically used in ELS tests to account for large deflections due to significant displacements. $N$ is another correction factor. Further details on the calculation of the correction factors $F$ and $N$ can be found in the ISO 15114 standard [36].

One of the main limits of these methods is the fact that they are based on the Linear Elastic Fracture Mechanics (LEFM) assumptions. This means that the Fracture Process Zone (FPZ) is assumed to be small compared to any of the specimen's relevant dimensions, including width, thickness, or crack length. However, for adhesively bonded assemblies subjected to mode II loading, the FPZ is relatively large [40] and thus it is comparable to any significant specimen dimension. As a result, significant nonlinear effects may arise, making the LEFM assumptions invalid for analyzing the failure and fracture of bonded joints.

To overcome the limitation of the LEFM assumptions, a method based on the non-linear fracture mechanics should be used. One of the methods that has received a great deal of attention in this nonlinear context is the J-integral approach [41], known also as the contour integral.

As there is a limitation of LEFM assumptions in mode II for bonded joints due to the large FPZ, this study introduces the use of optical fiber measurements to precisely estimate FPZ length. This information, obtained prior to DIC analysis, allowed for a tailored ROI that fully captured the FPZ. Consequently, the J-integral was calculated over the appropriate zone, yielding values that more accurately reflect the FPZ's non-linear and inelastic behavior, thus providing a more reliable alternative to the classical CBTE fracture toughness value. The ROI, besides fully covering the FPZ, is also located at a certain distance from the clamping area to prevent the measurement of energy contributions unrelated to crack propagation.

Pérez-Galmès et al. [42] proposed and validated a J-integral closed-form solution for an ELS test (Eq. (13)). A suitable contour integration path is selected taking into account the total FPZ and a section SS' that lies at distance $L_s$ from the clamping fixture. This J-integral formula requires the measurement of the rotation at the load application point, which is provided using the inclinometer, along with the rotation and deformation at the section SS', which can be derived from the DIC data. Pérez-Galmès et al. [42] simplified the required data by estimating the deformation at SS' section using simple beam theory assumptions, eliminating the need for additional outputs from the DIC analysis. Moreover, the J-integral formula, presented in Eq. 14, was also corrected to account for large displacements, as the ELS test induces significant vertical displacements. It is important to note that several assumptions are made in this J-integral solution: (1) The strain profile at section SS' is assumed to be linear, (2) the longitudinal strain profile is estimated using Simple Beam Theory, and (3) the rotation angle at section SS' is considered equal to that at the crack tip.

$$J_{\text{ELS}} = \frac{3[P\cos(\theta_p)]^2}{5G_{12}b^2h} + \frac{P\cos(\theta_p)}{b} \tan(\theta_p - \theta_g) - \frac{E_1 h}{3} \epsilon_g^2 \qquad (13)$$

$$J_{\text{ELS}} = \frac{3[P\cos(\theta_p)]^2}{5G_{12}b^2h} + \frac{P\cos(\theta_p)}{b} \tan(\theta_p - \theta_g) - \frac{E_1 h}{3} \left( \frac{3}{2} \frac{P(L - L_s)}{E_1 b h^2} \right)^2 \qquad (14)$$

Where $G_{12}$ is the shear modulus of the adherend, $\Theta_g$ is the rotation angle obtained from the displacement profile at SS' section derived from

DIC data and $\Theta_p$ is the rotation angle measured directly by the inclinometer placed at the load displacement point.

For the calculation of the J-integral value for configuration 2 samples, the sliding is calculated as being twice that of the upper adherend. Since the sliding in the reconstructed lower adherend is influenced by the soft adhesive layer (adhesive 2), we assumed that the sliding in the reconstructed lower adherend is equal to that of the upper adherend, which is not affected by the presence of adhesive 2. This assumption was validated based on the following conditions: (1) the position of the neutral axis was confirmed to be at the mid-thickness of the epoxy layer (within ±0.1 mm), as verified through the selected dimensions of the steel plates (particularly their thicknesses) and the strain profiles obtained from DIC; and (2) the reconstructed lower adherend and the upper adherend exhibit equivalent stiffness. Moreover, the strain profiles derived from DIC are piecewise linear.

# 4. Results and discussion

## 4.1. ELS test results: Load-displacement curves and clamp calibration

Fig. 11 and Fig. 12 present the load-displacement curves for configuration 1 and configuration 2 respectively. For repeatability purposes, multiple tests were conducted on samples with varying $a_p/L$ ratios: six tests for configuration 1 and six tests for configuration 2. The load-displacement curves indicate stable crack propagation across all samples. Specifically, after reaching the maximum load, crack propagation initiates, leading to a decline in load until the first local minimum is reached. This interval, between the maximum load and the subsequent first minimum, becomes the critical region of interest, forming the basis for fracture toughness calculations.

Fig. 13 illustrates the load-displacement curves for samples with an $a_p/L$ ratio around 70% (±2%). The curves show comparable initial stiffness in both cases; however, a notable 15% difference in the average maximum load is observed between the two configurations. Samples from configuration 2 exhibit higher loads at larger displacements and are therefore more resilient. This difference may be due to the sand-blasting procedure performed to bond the third plate (i.e., lower adherend 2) in the configuration 2 samples. Indeed, this sandblasting could indirectly cause compression forces in the adhesive 1 layer through the forces applied to the lower adherend 1 during the process.

Following the clamp calibration procedure, the average flexural modulus $E_1$ was determined to be approximately 179.45 GPa for samples from configuration 1, while samples from configuration 2 exhibited an average value of 184.20 GPa. Thus, $E_1$ for configuration 1 samples is slightly lower than that for configuration 2 samples. Additionally, the average calibration correction $\Delta_{\text{clamp}}$ was also calculated to be 39.41 mm for configuration 1 and 38.09 mm for configuration 2. The clamp

<figure><img src="image_14.png" /><figcaption>Fig. 11. Load-displacement curves for configuration 1 samples.</figcaption></figure>
<figure><img src="image_15.png" /><figcaption>Fig. 12. Load-displacement curves for configuration 2 samples.</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>Fig. 13. Load-displacement curves for configuration 1 and configuration 2 samples with an ap/L ratio around 70% (±2%).</figcaption></figure>

calibration results indicated that $\Delta_{clamp}$ is nearly identical for both configurations, suggesting that the clamping process is performed in a very similar manner.

## 4.2. Determination of crack length through optical fiber analysis

Fig. 14 illustrates the strain curves at various time steps, ranging from $t_0 = 0$ s to $t_8 = 224$ s, for a sample from configuration 1 with an $a_p/L$ ratio of 69.45 %. The load is applied downward at the position $x = 0$ mm. The initial crack length is located at $x = a_p = 69.45$ mm, and the clamping fixture is at $x = L = 100$ mm.

During the ELS test, all strain profiles exhibit two peaks (Fig. 10): one on the right, corresponding to the fixed support (clamping edge), and one on the left, associated with the crack tip. At $t_0 = 0$ s, there is no peak, as no load is applied, and a reference is established based on the initial deformation profile of the optical fiber. Once the test begins, a downward load is applied at the designated point, and as the load increases, two peaks begin to emerge. In Fig. 14, during the loading phase and just before the crack propagation, the maximum strain was at the point A (at $a_p = 69.45$ mm). As the applied load increases, the crack started to propagates slowly from point A to point B until reaching its maximum value (at point C), where the final crack length can be directly deduced from the graph. It was observed that, in all tests, the crack can propagate up to a maximum distance of 6 to 10 mm from the fixed support. This zone, beyond which the crack cannot propagate, highlights the effect of clamping in the ELS test setup.

This procedure for the measurement of the crack length $a_p$ was previously validated in an earlier study conducted by [16]. In that study, the crack length measured by the optical fiber was verified through visual inspections. A dye penetrant was applied at the end of the test to highlight the initial and final crack tips. The results confirmed the accuracy of the crack length measurements obtained using the optical fiber.

More particularly, for the determination of the crack front, the optical fiber interrogator was synchronized with the 3R traction/compression machine, enabling the acquisition of both load and displacement data at each time step from the optical fiber system. The microcrack initiation phase was identified from the resulting load-displacement curve. This phase can be associated to the point at which the curve begins to deviate from linearity, occurring before the maximum load is reached. This deviation point, observed on the load-displacement curve, was considered the onset of microcrack initiation [43]. After the maximum load is reached, macrocrack propagation begins; therefore, the peak observed in the strain profiles at this stage is associated with the macrocrack tip.

Finally, for all samples from configuration 1, the crack always occurred at the lower adherend/adhesive 1 interface, while for those from configuration 2, the crack propagated at the lower adherend 1/adhesive 1 interface. Therefore, the failure mode is interfacial for all the

<figure><img src="image_17.png" /><figcaption>Fig. 14. (a) Top surface strain profiles at different times for a sample from configuration 1, with an initial crack length of 69.45 mm; and (b) the corresponding load-displacement curve.</figcaption></figure>
samples (Fig. 15). The same bonding protocol for attaching the Teflon insert to the steel adherend was previously employed in the study by Sourisseau [16], where both adhesive and cohesive failure modes were observed, depending on the loading condition (mode I, mode II, or mixed-mode). Thus, it could be considered in our study that the presence of the Teflon insert at the interface did not promote the initiation of the observed interfacial crack.

### 4.3. Strain energy release rate and J-integral computation

Table 1 presents the average mode II fracture toughness $G_{IIIC}$ values for both configurations, calculated using the three previously described data reduction methods: ECM, SBT and CBTE. The corresponding standard deviations are also reported. As stable crack propagation was achieved in all samples from both configurations, the $G_{IIIC}$ values were determined based on the mean plateau of the fracture toughness versus crack length curve for each test.

According to the results presented in Table 1, the mean $G_{IIIC}$ values obtained using the ECM, SBT, and CBTE methods exhibit differences between configurations 1 and 2 of approximately 9%, 13%, and 14%, respectively. These differences between both configurations should be taken into account for the upcoming aging tests.

Furthermore, significant differences of more than 50% are observed between the mode II fracture toughness values obtained using the SBT method and the one obtained with the ECM and the CBTE method. This variation can be primarily attributed to the various assumptions inherent to each data reduction method:

- The ECM accounts for adhesive deformation by linking the specimen's compliance to an equivalent crack length. However, ECM results are highly dependent on compliance measurements and thus require precise calibration.

- The SBT method is generally considered less accurate. Similar to the ECM method, it oversimplifies fracture mechanics by neglecting the impact of adhesive deformations, nonlinear effects, and crack tip plasticity. It ignores energy dissipation at the crack tip, leading, in our case, to an underestimation of the fracture energy.

- The CBTE method was found to be the most accurate among these three data reduction methods [36], it considers the calibration effect. However, it has the limitation of being affected by clamping variability,

<caption>Table 1</caption>

Mean mode II fracture toughness values for configurations 1 and 2, according to three data reduction methods (ECM, SBT, and CBTE), along with their corresponding standard deviations (SD).

<table><thead><tr><th rowspan="2"></th><th rowspan="2"></th><th colspan="3">G<sub>IIIC</sub> (N/mm)</th></tr><tr><th>ECM</th><th>SBT</th><th>CBTE</th></tr></thead><tbody><tr><td rowspan="2">Configuration 1</td><td>Average</td><td><strong>0.84</strong></td><td><strong>0.41</strong></td><td><strong>0.94</strong></td></tr><tr><td>SD</td><td>0.30</td><td>0.06</td><td>0.15</td></tr><tr><td rowspan="2">Configuration 2</td><td>Average</td><td><strong>0.77</strong></td><td><strong>0.46</strong></td><td><strong>1.07</strong></td></tr><tr><td>SD</td><td>0.12</td><td>0.14</td><td>0.19</td></tr></tbody></table>

as the mode II fracture toughness formula based on this method requires the clamp calibration parameter.

According to the ELS test standard [36], the CBTE method has demonstrated the highest reproducibility and robustness and is therefore the preferred approach to follow. Thus, only the CBTE method will be adopted in the remainder of this study.

For the calculation of the J-integral, the position of the SS' section should be defined. For example, Oshima et al. [44] showed that the plastic zone can extend over 40 mm during mode II fracture toughness experiments, thus they selected all ROIs to be larger than 40 mm to sufficiently large to capture the entire plastic zone. In this study, the SS' section was placed 6 mm from the clamping zone, corresponding to a distance between 21 mm and 25 mm from the initial crack front. Indeed, according to the fiber optic strain profiles, the initial crack front (which appears as a peak in the strain curves) begins to widen and shift slightly before reaching the maximum force ($F_{max}$). The distance between this initial peak and the last peak observed just before the onset of macroscopic crack propagation (i.e., just before reaching $F_{max}$ prior to failure) was measured for all tests and was taken as an estimate of the FPZ length. The maximum value obtained was 17 mm. Therefore, the SS' section was positioned between 21 mm and 25 mm from the initial crack front (depending on the propagation length and the $a_p/L$ ratio), in order to ensure that the entire FPZ was included within the J-integral contour. Additionally, SS' was placed 6 mm away from the clamping fixture to avoid its influence. Indeed, based on all ELS tests carried out, the optical fiber data indicated that there is a region of approximately 6 mm near the clamping area where crack propagation does not occur, due to the

<figure><img src="image_18.png" /><figcaption>Fig. 15. Interfacial failure mode for configuration 1 and configuration 2 samples (Areas outlined in red indicate regions where crack propagation occurred in mode II, while areas outlined in black represent regions with no crack propagation, resulting from specimen opening at the end of testing). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>
mechanical constraint imposed by the fixture.

The *J*-integral values were calculated for both configurations based on Eq. (14). A comparison between the mean values of *G*<sub>IIC</sub> based on the CBTE method and the mean values of the *J*-integral is made in Table 2.

The average values of *G*<sub>IIC</sub> and the *J*-integral are higher for samples with configuration 2 compared to those with configuration 1. This difference can be mainly attributed to presence of the softer, more flexible adhesive layer (adhesive 2) likely contributes to the variation by affecting the shear deformation behavior in the lower adherend of configuration 2. It may also be associated with the bonding process of the third plate in configuration 2 samples (i.e., lower adherent 2), where its bonding requires sandblasting of lower adherent 1, leading to compressive forces on adhesive 1 induced by the sandblasting. However, the compressive force was applied indirectly via the lower adherend 1, not directly to the adhesive 1 layer. As a result, the induced compressive stress in the adhesive is minimal and unlikely to affect its mechanical behavior significantly. Additionally, the *G*<sub>IIC</sub> values calculated using the CBTE method exceed the *J*-integral values by 12% and 11% for configurations 1 and 2, respectively. This small discrepancy primarily arises from the LEFM assumptions of the CBTE data reduction method.

### 4.4. CZM determination through the direct method: *J*-integral

Fig. 16 and Fig. 17 illustrate the variation of the *J*-integral as a function of local sliding for configurations 1 and 2, respectively. The corresponding *J*-integral polynomial approximation with the corresponding coefficients of determination (*R*<sup>2</sup>) for configuration 1 and 2 are presented in Table 3 and Table 4 respectively. In all cases, the *R*<sup>2</sup> values exceeded 0.9935, indicating a high level of fitting accuracy. The local sliding values were extracted from the DIC analysis at the S-S' section, as previously described.

From these *J*-integral vs. sliding curves, the CZM can be deduced by deriving the equation *J*-integral = *f*(*δ*). Fig. 18 and Fig. 19 illustrate the CZM for the six samples from configuration 2 and the six samples from configuration 2, respectively.

From these experimental data, the mean bilinear cohesive law was outlined based on the respective average values obtained in both configurations, as presented in Table 5. The main defined parameters were: the maximum reached shear stress *τ*<sub>max</sub> with the sliding value at this point *δ*<sub>max</sub> and the sliding values at failure *δ*<sub>failure</sub>.

Comparison of the two mean CZM curves for both configurations reveals differences (Fig. 20): the initial slope is lower for configuration 2, the maximum stress reached is 32% higher for configuration 2, with half the sliding value at this point, and the sliding at failure is 33% higher for configuration 2. These differences between the two configurations may be attributed to the presence of two different interfaces. Indeed, in configuration 2, the crack propagates at the adhesive 1/lower adherent interface, while in configuration 2, it propagates at the adhesive 1/lower adherent 1 interface, which is of a different nature than the lower adherent in configuration 2. These differences may also be attributed to the sandblasting performed during the bonding of the third plate in configuration 2 samples.

To validate the assumption that the observed difference is due to the variation in adhesion of adhesive 1 to the two types of steel adherends used, one possible approach would be to manufacture two groups of bonded assemblies. Both groups would consist of symmetrical bonded joints using adhesive 1. In the first group, the adherends are made from

<table><caption>**Table 2**
Mean values of $G_{IIC}$ and *J*-integral for ELS samples of configurations 1 and 2.</caption><thead><tr><th></th><th></th><th>G<sub>IIC</sub>-CBTE (N/mm)</th><th>J-integral (N/mm)</th></tr></thead><tbody><tr><td rowspan="2">Configuration 1</td><td>Average</td><td><strong>0.94</strong></td><td><strong>0.84</strong></td></tr><tr><td>SD</td><td>0.15</td><td>0.15</td></tr><tr><td rowspan="2">Configuration 2</td><td>Average</td><td><strong>1.07</strong></td><td><strong>0.96</strong></td></tr><tr><td>SD</td><td>0.19</td><td>0.15</td></tr></tbody></table>

<figure><img src="image_19.png" /><figcaption>**Fig. 16.** *J*-integral values as a function of local sliding for configuration 1 samples.</figcaption></figure>

<figure><img src="image_20.png" /><figcaption>**Fig. 17.** *J*-integral values as a function of local sliding for configuration 2 samples.</figcaption></figure>

<table><caption>**Table 3**
*J*-integral polynomial approximation for ELS samples of configuration 1, with the corresponding coefficient of determination *R*<sup>2</sup>.</caption><thead><tr><th></th><th>J-integral = f(δ)</th><th>R<sup>2</sup></th></tr></thead><tbody><tr><td>#1 Configuration 1</td><td>-132,811 δ<sup>4</sup> + 10,500 δ<sup>3</sup> + 94,28 δ<sup>2</sup> + 21,119 δ</td><td>0.9990</td></tr><tr><td>#2 Configuration 1</td><td>-352,108 δ<sup>4</sup> + 29,914 δ<sup>3</sup> - 436,86 δ<sup>2</sup> + 71,175 δ</td><td>0.9984</td></tr><tr><td>#3 Configuration 1</td><td>-196,442 δ<sup>4</sup> + 19,492 δ<sup>3</sup> - 229,95 δ<sup>2</sup> + 49,651 δ</td><td>0.9987</td></tr><tr><td>#4 Configuration 1</td><td>-602,870 δ<sup>4</sup> + 47,734 δ<sup>3</sup> - 704,88 δ<sup>2</sup> + 66,176 δ</td><td>0.9960</td></tr><tr><td>#5 Configuration 1</td><td>-102,993 δ<sup>4</sup> + 277,73 δ<sup>3</sup> + 599,15 δ<sup>2</sup> - 36,579 δ</td><td>0.9935</td></tr><tr><td>#6 Configuration 1</td><td>-241,401 δ<sup>4</sup> + 9435,3 δ<sup>3</sup> + 520,21 δ<sup>2</sup> - 35,983 δ</td><td>0.9983</td></tr></tbody></table>

<table><caption>**Table 4**
*J*-integral polynomial approximation for ELS samples of configuration 2, with the corresponding coefficient of determination *R*<sup>2</sup>.</caption><thead><tr><th></th><th>J-integral = f(δ)</th><th>R<sup>2</sup></th></tr></thead><tbody><tr><td>#1 Configuration 2</td><td>66,942 δ<sup>4</sup> + 7546,4 δ<sup>3</sup> - 30,397 δ<sup>2</sup> - 0,9763 δ</td><td>0.9948</td></tr><tr><td>#2 Configuration 2</td><td>-43,506 δ<sup>4</sup> + 3966,8 δ<sup>3</sup> + 69,091 δ<sup>2</sup> + 49,073 δ</td><td>0.9997</td></tr><tr><td>#3 Configuration 2</td><td>106,180 δ<sup>4</sup> + 15,834 δ<sup>3</sup> - 523,01 δ<sup>2</sup> + 95,281 δ</td><td>0.9989</td></tr><tr><td>#4 Configuration 2</td><td>-114,934 δ<sup>4</sup> + 16,343 δ<sup>3</sup> - 516,94 δ<sup>2</sup> + 87,086 δ</td><td>0.9982</td></tr><tr><td>#5 Configuration 2</td><td>-15,126 δ<sup>4</sup> - 437,56 δ<sup>3</sup> + 303,03 δ<sup>2</sup> - 14,417 δ</td><td>0.9974</td></tr><tr><td>#6 Configuration 2</td><td>-78,877 δ<sup>4</sup> + 12,276 δ<sup>3</sup> - 458,83 δ<sup>2</sup> + 11,2763 δ</td><td>0.9973</td></tr></tbody></table>
<figure><img src="image_21.png" /><figcaption>Fig. 18. The CZM derived from the experimental data for 6 samples from Configuration 1 with the corresponding mean bilinear cohesive law.</figcaption></figure>

<figure><img src="image_22.png" /><figcaption>Fig. 19. The CZM derived from the experimental data for 6 samples from configuration 2 with the corresponding mean bilinear cohesive law.</figcaption></figure>

<table><caption>**Table 5**
The mean values of the CZM parameters obtained experimentally.</caption><thead><tr><th></th><th>τ<sub>max</sub> (MPa)</th><th>δ<sub>max</sub> (mm)</th><th>δ<sub>failure</sub> (mm)</th></tr></thead><tbody><tr><td>Configuration 1</td><td>26.69<br>± 3.21</td><td>0.04<br>± 0.01</td><td>0.06<br>± 0.01</td></tr><tr><td>Configuration 2</td><td>20.22<br>± 4.37</td><td>0.06<br>± 0.01</td><td>0.08<br>± 0.01</td></tr></tbody></table>

STRENX 700 steel, while in the second group, they are made from high-strength black strapping steel. The first group has already been investigated through the 'Configuration 1' samples presented in this study. However, manufacturing and testing samples for the second group is more challenging, as the black strapping steel was only available from the manufacturer in a thickness of 0.6 mm. This thickness is significantly below the minimum required for mechanical characterization tests, which typically require much thicker adherends. As a result, this comparison could not be carried out in the present work.

<figure><img src="image_23.png" /><figcaption>Fig. 20. Bilinear cohesive law derived from the experimental tests for configurations 1 and 2.</figcaption></figure>

## 5. Conclusion

This study validated a new bonded assembly geometry, configuration 2, designed to enable the ELS test under creep aging conditions. Steel-to-steel assemblies using configuration 2 were compared in their unaged state to a standard symmetrical geometry, configuration 1. All samples were made from high-yield-strength steel and bonded with the same commercial epoxy adhesive. To compare both configurations, a fracture mechanics-based approach was employed by using destructive ELS tests on all bonded assemblies. Both configurations exhibited similar initial stiffness; however, higher load values were achieved for configuration 2 samples. This difference can be attributed to the addition of a third plate in configuration 2 assemblies, leading to a compression effect induced by sandblasting.

Mode II fracture toughness $G_{IIC}$ was calculated using three LEFM-based methods from the ELS test standard: ECM, SBT, and CBTE. Results varied across methods, but as CBTE shows the highest repeatability according to the ES test standard, it was primarily used. Accurate crack length measurement, essential for some methods and $a_p/L$ ratio determination, was achieved using a high-resolution optical fiber for continuous crack-tip monitoring. To overcome LEFM limitations, the J-integral method from non-linear fracture mechanics was applied using DIC. Configuration 2 consistently showed higher J-integral and $G_{IIC}$ values, calculated via the CBTE method. $G_{IIC}$ values slightly exceeded J-
integral results by 12% for configuration 1 and 11% for configuration 2.

Furthermore, CZMs were derived from the experimental results for both configurations. The CZMs revealed that configuration 2 samples exhibited a lower initial stiffness, a 32% higher maximum stress for configuration 2, and a 33% greater sliding displacement at failure for configuration 2. The difference between the two CZM configurations could be explained by the presence of two distinct interfaces or the sandblasting procedure realized to bond the third plate in configuration 2 samples.

Overall, this study identified both similarities and differences between the two configurations, which must be considered in future aging campaigns. The proposed configuration 2 and the associated testing procedure can also be adapted for other materials, such as composite materials or stainless steel, and can incorporate different adhesives. However, one of the main limitations is the ability to obtain materials of varying thickness, particularly very thin ones.

Further investigations on the new configuration 2 are recommended. Multiple aging campaigns are currently underway, focusing exclusively on configuration 2 samples to evaluate their durability under various aging conditions: humid aging, creep aging, and coupled hygro-mechanical aging to investigate the combined effects of water diffusion and mechanical loading on the durability of bonded assemblies.

Moreover, as a perspective for future work, to fully validate the proposed geometry of configuration 2 samples and the test method, it would be necessary to include examples of brittle, intermediate, and ductile adhesives and compare their performance across both configurations.

## CRediT authorship contribution statement

**Arij Fawaz:** Writing – review & editing, Writing – original draft, Project administration. **Emilie Lepretre:** Supervision. **Xavier Chapel-eau:** Supervision. **Jean-François David:** Methodology. **Sylvain Chataigner:** Supervision.

## 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

The authors would like to acknowledge the technical teams of the MAST/SMC laboratory and COSYS/SII laboratory at Université Gustave Eiffel, the Weamec/Intermer project as well as the 'Région Pays de La Loire' for co-funding this study.

## Data availability

Data will be made available on request.

## References

[1] V.M. Karbhari, Rehabilitation of metallic civil infrastructure using fiber-reinforced polymer (FRP) composites: a materials and systems overview at the adhesive bond level, in: Rehabilitation of Metallic Civil Infrastructure Using Fiber Reinforced Polymer (FRP), Composites, Elsevier, 2014, pp. 3–10, https://doi.org/10.1533/9780857096654.1.3.

[2] L. Mishnaevsky, Repair of wind turbine blades: review of methods and related computational mechanics problems, Renew. Energy 140 (2019) 828–839, https://doi.org/10.1016/j.renene.2019.03.113.

[3] A.D. Orcesi, A. Feraille, S. Chataigner, Fatigue strengthening of steel structures using high modulus CFRP plates: development of a life-cycle analysis approach, Constr. Build. Mater. 227 (2019) 116628, https://doi.org/10.1016/j.conbuildmat.2019.08.009.

[4] R. Grangeat, M. Girard, F. Jacquemin, C. Lupi, Method of characterizing the interphase's mean water diffusion properties of a bonded assembly in immersion,

J. Adhes. 98 (3) (2022) 207–226, https://doi.org/10.1080/00218464.2020.1828080.

[5] B. De Parscau Du, F. Plessix, P. Lefébure Jacquemin, S. Le Corre, Characterization and modeling of the polymerization-dependent moisture absorption behavior of an epoxy-carbon fiber-reinforced composite material, J. Compos. Mater. 50 (18) (2016) 2495–2505, https://doi.org/10.1177/0021998315606510.

[6] M. Heshmati, R. Haghani, M. Al-Emrani, Dependency of cohesive laws of a structural adhesive in mode-I and mode-II loading on moisture, freeze-thaw cycling, and their synergy, Mater. Des. 122 (2017) 433–447, https://doi.org/10.1016/j.matdes.2017.03.016.

[7] M. Kim, Y. Kim, P. Kim, J.-H. Roh, J. Park, Humidity aging effect on adhesive strength of composite single-lap joint, Int. J. Aeronaut. Space Sci. 18 (1) (2017) 56–62, https://doi.org/10.5139/IJASS.2017.18.1.56.

[8] R.A. Queiroz, E.M. Sampaio, V.J. Cortines, N.R. Rohem, Study on the creep behavior of bonded metallic joints, Appl. Adhes. Sci. 2 (1) (2014) 8, https://doi.org/10.1186/2196-4351-2-8.

[9] I.A. Ashcroft, D.J. Hughes, S.J. Shaw, Mode I fracture of epoxy bonded composite joints: 1. Quasi-static loading, Int. J. Adhes. Adhes. 21 (2) (2001) 87–99, https://doi.org/10.1016/S0143-7496(00)00038-5.

[10] J. Crank (Ed.), *Diffusion in Polymers*, 3. print, Acad. Pr. London, 1977.

[11] R.S. Ashofteh, H. Khoramishad, Creep behavior of polymeric adhesive joints exposed to different environmental conditions, Polym. Compos. 41 (8) (2020) 3218–3226, https://doi.org/10.1002/pc.25613.

[12] W.K. Loh, A.D. Crocombe, M.M. Abdel Wahab, I.A. Ashcroft, Environmental degradation of the interfracture fracture energy in an adversely bonded joint, Eng. Fract. Mech. (2002) 2113–2128.

[13] M. Mehrabi, L.M. Martulli, A. Bernasconi, M. Carboni, Estimating crack tip position in adhesively bonded joints subjected to mode II quasi-static loading, Fatigue Fract. Eng. Mater. Struct. 47 (4) (2024) 1262–1280, https://doi.org/10.1111/ffe.14237.

[14] L.F.M. da Silva, A. Öchsner, R.D. Adams, Eds., *Handbook of Adhesion Technology*, Berlin, Heidelberg, Springer Berlin Heidelberg, 2011, https://doi.org/10.1007/978-3-642-01169-6.

[15] L.F.M. Da Silva, R.D.S.G. Campilho, *Advances in Numerical Modeling of Adhesive Joints*. in SpringerBriefs in Applied Sciences and Technology, Berlin, Heidelberg, Springer Berlin Heidelberg, 2012, https://doi.org/10.1007/978-3-642-23608-2.

[16] Q. Sourisseau, Development of a Robust Methodology for the Design Assessment of Bonded Reinforcements on Steel Structures Use of Cohesive Zone Model and Distributed Optical fiber for Characterization, PhD thesis, Nantes Université, Nantes, 2022.

[17] A. Ameli, N.V. Datla, M. Papini, J.K. Spelt, Hygrothermal properties of highly toughened epoxy adhesives, J. Adhes. 86 (7) (2010) 698–725, https://doi.org/10.1080/00218464.2010.482405.

[18] M. Loiseau, S. Chataigner, R. Créac'hadec, E. Lepretre, M.-O. Quéméré, J.-P. Court, Impact of the load level on the creep behaviour of adversely bonded fastener in tension: experimental investigations, analytical and numerical modelling, J. Adhes. Sci. Technol. (2023) 1–18, https://doi.org/10.1080/01694243.2023.2168586.

[19] M. Al-Harthi, R. Kahraman, B. Yilbas, M. Sunar, B.J.A. Aleem, Influence of water immersion on the single-lap shear strength of aluminum joints bonded with aluminum-powder-filled epoxy adhesive, J. Adhes. Sci. Technol. 18 (15–16) (2004) 1699–1710, https://doi.org/10.1163/1568561042708386.

[20] R.L. Fernandes, M.F.S.F. De Moura, R.D.F. Moreira, Effect of moisture on pure mode I and II fracture behaviour of composite bonded joints, Int. J. Adhes. Adhes. 68 (2016) 30–38, https://doi.org/10.1016/j.ijadhadh.2016.01.010.

[21] G. Quino, A. Pellegrino, V.L. Tagarielli, N. Petrinic, Measurements of the effects of pure and salt water absorption on the rate-dependent response of an epoxy matrix, Compos. Part B Eng. 146 (2018) 213–221, https://doi.org/10.1016/j.compositesb.2018.03.044.

[22] A. Rudawska, The effect of the salt water aging on the mechanical properties of epoxy adhesives compounds, Polymers 12 (4) (2020) 843, https://doi.org/10.3390/polym12040843.

[23] M. Lettieri, M. Frigione, Effects of humid environment on thermal and mechanical properties of a cold-curing structural epoxy adhesive, Constr. Build. Mater. 30 (2012) 753–760, https://doi.org/10.1016/j.conbuildmat.2011.12.077.

[24] A. Ilioni, P.-Y. Le Gac, C. Badulescu, D. Thévenet, P. Davies, Prediction of mechanical behaviour of a bulk epoxy adhesive in a marine environment, J. Adhes. 95 (1) (2019) 64–84, https://doi.org/10.1080/00218464.2017.1377616.

[25] L. Silva, S. Tognana, W. Salgueiro, Study of the water absorption and its influence on the young's modulus in a commercial polyamide, Polym. Test. 32 (1) (2013) 158–164, https://doi.org/10.1016/j.polymertesting.2012.10.003.

[26] R. Leger, A. Roy, J.C. Grandidier, A study of the impact of humid aging on the strength of industrial adhesive joints, Int. J. Adhes. Adhes. 44 (2013) 66–77, https://doi.org/10.1016/j.ijadhadh.2013.02.001.

[27] B. De Nève, M.E.R. Shanahan, Water absorption by an epoxy resin and its effect on the mechanical properties and infra-red spectra, Polymer 34 (24) (1993) 5099–5105, https://doi.org/10.1016/0032-3861(93)90254-8.

[28] S.G. Prolongo, M.R. Gude, A. Ureña, Water uptake of epoxy composites reinforced with carbon nanofillers, Compos. Part Appl. Sci. Manuf. 43 (12) (2012) 2169–2175, https://doi.org/10.1016/j.compositesita.2012.07.014.

[29] A. Khabazaghdam, B. Behjat, M. Yazdani, L.F.M. Da Silva, E.A.S. Marques, X. Shang, Creep behaviour of a graphene-reinforced epoxy adhesively bonded joint: experimental and numerical investigation, J. Adhes. 97 (13) (2021) 1189–1210, https://doi.org/10.1080/00218464.2020.1742114.

[30] R.M. Carneiro Neto, A. Akhavan-Safar, E.M. Sampaio, J.T. Assis, L.F.M. da Silva, Effect of creep on the mode II residual fracture energy of adhesives, J. Appl. Polym. Sci. 138 (47) (2021) 51387, https://doi.org/10.1002/app.51387.
[31] R.A. Queiroz, E.M. Sampaio, V.J. Cortines, N.R. Rohem, Study on the creep behavior of bonded metallic joints, 2014, pp. 1–12.

[32] X. Han, A.D. Crocombe, S.N.R. Anwar, P. Hu, W.D. Li, The Effect of a Hot-Wet Environment on Adhesively Bonded Joints Under a Sustained Load, J. Adhes. 90 (5–6) (2014) 420–436, https://doi.org/10.1080/00218464.2013.853176.

[33] A.J. Brunner, B.R.K. Blackman, P. Davies, A status report on delamination resistance testing of polymer-matrix composites, Eng. Fract. Mech. 75 (9) (2008) 2779–2794, https://doi.org/10.1016/j.engfracmech.2007.03.012.

[34] M. Pérez-Galmés, J. Renart, C. Sarrado, A.J. Brunner, A. Rodríguez-Bellido, Towards a consensus on mode II adhesive fracture testing: experimental study, Theor. Appl. Fract. Mech. 98 (2018) 210–219, https://doi.org/10.1016/j.tafmec.2018.09.014.

[35] S. Abdel-Monsef, J. Renart, L. Carreras, A. Turon, P. Maimí, Effect of environment conditioning on mode II fracture behaviour of adhesively bonded joints, Theor. Appl. Fract. Mech. 112 (2021) 102912, https://doi.org/10.1016/j.tafmec.2021.102912.

[36] ISO 15114:2014 standard, Fibre-reinforced plastic composites — Determination of the mode II fracture resistance for unidirectionally reinforced materials using the calibrated end-loaded split (C-ELS) test and an effective crack length approach, 2014.

[37] B.R.K. Blackman, A.J. Brunner, J.G. Williams, Mode II fracture testing of composites: a new look at an old problem, Eng. Fract. Mech. 73 (16) (2006) 2443–2455, https://doi.org/10.1016/j.engfracmech.2006.05.022.

[38] Q. Sourisseau, E. Lepretre, S. Chataigner, X. Chapeleau, L. Mouton, S. Paboeuf, Use of high spatial resolution distributed optical fiber to monitor the crack propagation of an adhesively bonded joint during ENF and DCB tests, Int. J. Adhes. Adhes. 115 (2022) 103124, https://doi.org/10.1016/j.ijadhadh.2022.103124.

[39] A. Panerai, B. Oneda, L.M. Martulli, A. Bernasconi, M. Carboni, Distributed backface strain sensing of composite adhesively bonded joints under mode II fatigue loading, Compos. Part B Eng. 291 (2025) 111964, https://doi.org/10.1016/j.compositesb.2024.111964.

[40] J. Bertrand, J. Jumel, J. Renart, J.-B. Kopp, Theoretical assessment of ELS test data reduction technique using virtual testing, Int. J. Fract. 229 (2) (2021) 195–213, https://doi.org/10.1007/s10704-021-00549-4.

[41] J.R. Rice, A path independent integral and the approximate analysis of strain concentration by notches and cracks, J. Appl. Mech. 35 (2) (1968) 379–386, https://doi.org/10.1115/1.3601206.

[42] M. Pérez-Galmés, J. Renart, C. Sarrado, A. Rodríguez-Bellido, J. Costa, A data reduction method based on the J -integral to obtain the interlaminar fracture toughness in a mode II end-loaded split (ELS) test, Compos. Part Appl. Sci. Manuf. 90 (2016) 670–677, https://doi.org/10.1016/j.compositesa.2016.08.020.

[43] B.R.K. Blackman, A.J. Kinloch, M. Paraschi, The determination of the mode II adhesive fracture resistance, GIIC, of structural adhesive joints: an effective crack length approach, Eng. Fract. Mech. 72 (6) (2005) 877–897, https://doi.org/10.1016/j.engfracmech.2004.08.007.

[44] S. Oshima, A. Yoshimura, Y. Hirano, T. Ogasawara, K.-T. Tan, In-situ observation of microscopic damage in adhesively bonded CFRP joints under mode I and mode II loading, Compos. Struct. 227 (2019) 111330, https://doi.org/10.1016/j.compstruct.2019.111330.