Strength prediction of nanoparticle-reinforced adhesive and hybrid joints under unaged and hygrothermal conditions using machine learning and experimental methods

Abstract

This study investigates the effects of adding fullerene and single-walled carbon nanotubes (SWCNT) on the strength and durability of bonded and bonded/bolted joints, specifically for composite-to-composite (CTC) and composite-to-aluminum (CTA) substrates under three-point bending, both before and after hygrothermal aging. Samples were categorized into neat specimens, specimens with added fullerene, specimens with added SWCNT, and specimens with a combination of 50% SWCNT and 50% fullerene. Results show that the optimal nanoparticle ratio differs for bonded versus bonded/bolted joints. Nanoparticles significantly reduced degradation from hygrothermal exposure, preventing interfacial debonding and slowing strength loss. Mixed formulations improved cohesive strength and shifted failure from the adhesive interface to within the adhesive layer, enhancing joint performance and durability under both unaged and aged conditions. Furthermore, six machine learning models—ridge regression, decision tree, random forest regressor, gradient boosting regressor, support vector regression, and neural networks—were applied to predict the static strength of joints. The support vector regression and decision tree models demonstrated superior performance for bonded joints, while ridge regression and gradient boosting regressor were most effective for bonded/bolted joints. The analysis highlights that joint type, substrate, nanoparticle type and percentage, and environmental aging significantly influence adhesive performance. This study offers valuable insights into the aging and durability of bonded and dissimilar joints, providing a framework to enhance joint performance and reduce the risk of failure during operational use.

Keywords

Machine learning nano particle dissimilar joint strength hygrothermal ageing

Introduction

In many real-world applications within the aerospace and automotive industries, it is often necessary to combine carbon fiber-reinforced polymer (CFRP) with aluminum alloy to form a complete structure. These two lightweight materials are widely used together in these fields.¹ The selection of an appropriate joining method in engineering applications is crucial and requires careful consideration of the available options. Mechanical fasteners, such as bolts, rivets, or pins, are commonly used, but they can damage composites and create stress concentrations, potentially increasing the likelihood of early fatigue crack initiation and growth under cyclic loading.^2–4 Adhesive bonding, on the other hand, offers advantages such as lightweight construction, high sealing properties, durability under fatigue loading, and uniform stress distribution.^5–7 However, structures bonded with adhesives can be brittle and susceptible to hygrothermal environments, leading to safety and maintenance concerns.^8,9 To improve the efficiency of adhesive joints, various techniques can be employed, including geometrical modifications, surface treatments, hybrid joints combining bonding and mechanical methods, and the addition of metallic and non-metallic powders.^10–14 The existing body of literature provides a substantial amount of research on the quasi-static mechanical characteristics of hybrid joints. These studies primarily focus on analyzing failure modes,^15–17 utilizing simulation techniques,^18,19 and optimizing designs.^20,21

Furthermore, nanotechnology has introduced a novel strategy for enhancing the mechanical properties of materials. A common approach involves incorporating nanoparticles into adhesive systems, which improves adhesion, load-carrying capacity, crack resistance, and slows down crack propagation within the bonding layer.^22–25 Carbon nanotubes (CNTs), in both single-wall (SWCNT) and multi-wall (MWCNT) forms, have been used as additives to enhance interlaminar strength, toughness, thermal resistance, and environmental durability.^26–28 Studies have shown that hybrid nanoparticles are more effective than single nanoparticles due to their synergistic interactions.^29,30 The amount of nanoparticles added is crucial; insufficient amounts have little effect, while excessive amounts can lead to agglomeration and reduced mechanical properties.³¹ Environmental factors are a critical consideration for composites, particularly for joints in real-world applications.^32–34 The susceptibility of adhesive joints to environmental conditions, such as moisture and high temperatures, can impact their mechanical performance and weaken the adhesive-adherend interface.^35–38 Hygrothermal aging can trigger degradation mechanisms, leading to reduced strength and an increased risk of interfacial peeling.^39–42 The effect of hygrothermal aging on hybrid joints is complex, and understanding their mechanical behavior in challenging environmental conditions is essential.⁴³

Data-driven approaches, such as machine learning, have made significant advancements for various applications, including damage detection, the prediction of mechanical properties, and the improvement of design processes. These methods are particularly valuable due to their ability to analyze large datasets and provide accurate predictions.^44–46 Jing Wang et al.⁴⁷ investigated the accelerated aging of glass/epoxy composites under heat-humidity conditions and compared the results with natural aging. They utilized tensile strength data and machine learning models, including linear regression, polynomial regression, artificial neural networks (ANN), random forest regression, and support vector regression (SVR), to predict natural aging times from accelerated aging data. Similarly, Milad Bazli et al.⁴⁸ explored the use of machine learning to predict the durability of fiber-reinforced polymers (FRP), highlighting the importance of high-quality datasets and demonstrating the transformative impact of these technologies on structural engineering. Aghabalaei et al.^49,50 investigated the application of machine learning to predict the mechanical properties and durability of composite materials and bonded connections under humid conditions. They developed an ANN-based micromechanics approach to examine the modulus perpendicular to the fibers in epoxy composites, utilizing finite element analysis and statistical methods to build predictive models from microstructural data. Additionally, they assessed the durability of concrete-to-FRP bonded joints using a comprehensive database and machine learning models, including ANN and ensemble methods, to predict failure modes and bond strength. Both studies emphasize the effectiveness of machine learning in structural design and durability assessment under moisture exposure. Zewen Gu et al.⁵¹ developed black-box and grey-box machine learning models to predict the failure loads of single lap adhesive joints using geometric and material variables. By analyzing 300 Finite Element (FE) model samples and validating the accuracy with experiments, they created deep neural network and genetic programming models. Their study explores the relationships between design variables, leading to optimal structural and material designs for joint strength. Tian et al.⁵² examined the hydrothermal behavior of CFRPs, focusing on long-term prediction models, the mechanisms of property degradation, and water absorption dynamics. They underscored the importance of selecting appropriate prediction methods, including experimental and mechanical approaches, as well as machine learning-based methods.

Although many studies have been conducted on the aging behavior of adhesive joints and the effects of adding nanoparticles to adhesives, most of the existing research has focused on the addition of MWCNTs and graphene nanoplatelets (GNPs) under static force conditions, as well as on the aging behavior of adhesive joints. However, these studies often neglect the complexities involved in dissimilar joint substrates. This gap means that the intricate interactions between composite-to-metal dissimilar joints, which are common in real-world applications, remain underexplored. Therefore, understanding the aging process of composite joints is crucial, and comprehensive research is urgently needed to predict the mechanical properties of both similar and dissimilar bonded and bonded/bolted joints under realistic conditions. Furthermore, while most studies have investigated the effects of adding MWCNTs and GNPs to adhesives, limited information is available on the impact of adding fullerene, SWCNTs, and their combinations on the mechanical properties of single lap joints (SLJs). Nasibulin et al.⁵³ observed that combining fullerene with SWCNTs leads to the formation of a new nanoparticle, known as nanobuds, which possess a unique particle geometry. This distinct geometry could potentially enhance the mechanical properties of adhesive joints, highlighting the need for further investigation in this area. Additionally, due to the time-consuming nature or impracticality of performing natural aging tests, predicting the strength of similar (composite-to-composite) and dissimilar (composite-to-aluminum) bonded and bonded/bolted joints under hygrothermal conditions is of great importance.

For the first time, this study investigates the influence of adding fullerene, single-walled carbon nanotubes (SWCNTs), and nano buds nanoparticles on the strength of bonded and bonded/bolted joints with composite-to-composite (CTC) and composite-to-aluminum (CTA) substrates under three-point bending, both before and after hygrothermal aging. The research explores how effectively five commonly used machine learning models—ridge regression, decision tree, random forest regressor, gradient boosting regressor, support vector regression, and neural networks—can predict the mechanical behavior of these joints under unaged and hygrothermal conditions. By integrating experimental results with machine learning, this study enhances the understanding of adhesive and hybrid joint aging, particularly in dissimilar joints (composite-to-metal), and offers new insights into their behavior when exposed to various environmental aging conditions. The goal is to improve safety measures, support informed decision-making, and increase sustainability by evaluating adhesive joints under realistic environmental conditions.

Experimental details

Materials

In this study, single lap joints (SLJs) were constructed using carbon fiber-reinforced polymer (CFRP) with a thickness of 3.2 mm and Aluminum 5083 with a thickness of 2 mm. SLJs were classified as CFRP-to-CFRP (CTC) when both adherends were CFRP composites, and as CFRP-to-Aluminum (CTA) when one of the substrates was a CFRP composite. The CFRP substrates used in the study were comprised of 3k T200 fabric woven in a 0/90 sequence, consisting of a total of fourteen layers. These adherends were treated with HR520 and LR520 resins using a vacuum infusion process. During this process, a vacuum pressure of approximately −100 kPa (1 bar) was applied to drive the resin into the laminate. For curing the composite plates, they underwent an initial 24-h placement at room temperature, followed by a subsequent post-curing process at 60°C for a duration of 10 h in an oven. The CFRP adherends were subsequently cut into samples measuring 100 × 25 mm² for testing. Similarly, the AL adherends were cut from a larger sheet using a CNC laser, producing specimens with the same dimensions of 100 × 25 mm². The adhesive used was HB9940 from Axson (Sika, France), with the resin-to-hardener ratio of 100:90 with a viscosity of 430,000 cps. The mechanical properties of the adhesive and adherends used in this research is shown in Table 1.

Table 1.

Mechanical properties of the adhesive and adherends.

	Tensile strength (MPa)	Yield stress (MPa)	E (GPa)	Poisson’s ratio ( $ν$ )
Axson HB9940	30	-	2.5	0.2
CFRP	600	-	43.7	0.1
AL5083	300	145	71.4	0.33

To increase the force applied to the joints, socket head screws were utilized. Additionally, self-locking nuts and steel washers were incorporated into all joints to provide support and prevent loosening of the screws. The samples (both bonded/bolted and bonded) were designed with their geometrical configuration and dimensions according to the guidelines provided by ASTM D5868. Specific details can be found in Figure 1.

Figure 1.

Specimen geometries for bonded/bolted and bonded.

The attributes of nano additives, including their size, shape, and functionalization, significantly affect the strength of the bond between the nanoparticles and the epoxy matrix, as well as their dispersion in adhesive materials. These factors also influence the durability, mechanical strength, and physical properties of the adhesive.⁵⁴ Therefore, it is essential to consider the impact of various nanoparticle shapes on the microstructural mechanisms, durability, and ultimate strength of the adhesive joints.

The procurement of SWCNT powder (>90%, OD 1-2 nm, length 5-30 µm) was sourced from US Research Nanomaterials Inc., while Fullerene C60 with 99.5% purity was obtained from EMFUTUR Nanomaterials and Associated Products Technologies in Spain. The motivation for selecting these two powders for investigation stems from a previous study conducted by Nasibulin et al.,⁵³ which revealed that using these nanoparticles together leads to the formation of nano buds. Nano buds are composite structures consisting of a SWCNT bonded to a fullerene molecule, serving as a nucleation site for the growth of a second SWCNT that develops into a “bud” shape attached to the primary nanotube. As shown in Figure 2(A), in Nano Buds, one or more C60 fullerene molecules are covalently attached to the side wall of a single-walled nanotube.⁵⁵ This distinct structure can act as a molecular support and provide complementary surface bonding between nanoparticles and adjacent materials, helping to prevent matrix slippage in composite materials and increase their mechanical strength.⁵⁶ The SEM micrograph depicting these particles is shown in Figure 2(B).

Figure 2.

(A) Process of connecting Fullerene to SWCNT and the creation of Nano Buds.⁵⁷ (B) SEM images of Fullerene and SWCNT materials utilized in the research.

Nano-adhesive preparation

Achieving a homogeneous distribution of nanoparticles in adhesives is crucial for enhancing their mechanical properties. The effectiveness of the dispersion process—affected by factors such as magnetic stirrer power and duration—can impact particle distribution and agglomeration. Poor dispersion quality can lead to defects and uneven distribution, which can ultimately influence the static failure load of bonded joints. Therefore, employing a technique that ensures even particle distribution with minimal clumping and imperfections is essential. In this research, four sets of samples were examined using distinct adhesives: (I) neat adhesive, (II) adhesive reinforced with fullerene particles, (III) adhesive reinforced with SWCNT particles, and (IV) adhesive reinforced with both fullerene and SWCNT particles. Due to the high viscosity of the adhesive and the ineffectiveness of ultrasonic dispersion, a multi-step approach, inspired by the research of Nurziana Kong et al.,⁵⁸ was employed to evenly disperse fullerene and SWCNTs in the adhesive while minimizing defects.

To address the high viscosity of the adhesive, the nanoparticles were diluted in ethanol (99.5% absolute denatured C₂H₅OH from EMC2 Technology, Selangor, Malaysia) at a weight ratio of 1:10. The mixture was then subjected to magnetic stirring using a device from INTLLAB in Shenzhen, Guangdong, China, for 10 min at 2000 rpm. Afterward, to attain a homogeneous distribution of nanoparticles in the epoxy, a magnetic stirrer was utilized to mechanically mix the nano-ethanol particle solution into part A of the epoxy at a maximum speed of 2400 rpm. The mixture was allowed to stand at room temperature until the ethanol completely evaporated. The mixing process was continuously monitored to determine the weight difference of the solution at 30-min intervals. When the rate of evaporation dropped to nearly zero, it was considered that the ethanol had completely evaporated. This technique was specifically employed for the samples in groups II and III. In group IV, the prevention of agglomeration of the mixed nanoparticles was achieved by adding the SWCNT nanoparticles and stirring for 10 min, followed by the addition of fullerene nanoparticles and further mixing for another 10 min at the same speed. This sequential addition and stirring process was implemented to ensure a homogeneous dispersion of the nanoparticles in the matrix. In the subsequent stage, the procedure from the previous step was replicated. This involved combining the ethanol-nanoparticle solution with epoxy component A using a magnetic stirrer set at 2400 rpm. The resulting mixture was then left at room temperature to allow for the complete evaporation of the ethanol. The final step involved adding the prescribed amount of hardener adhesive (component B of the epoxy) to the mixture and stirring the blend with a spoon for 1 minute, after which it was applied to the sample adherends. Figure 3 depicts the steps involved in dispersing the nanoparticles to prepare the hybrid reinforced adhesive. This comprehensive approach ensured effective nanoparticle dispersion, overcoming the limitations of ultrasonic methods and achieving the desired mechanical properties in the adhesive joints.

Figure 3.

Nanoparticle dispersion methods.

Joint fabrication

To establish strong interfacial adhesion, it is essential to clean the surfaces that will be overlapped before bonding the adherends. This step is critical for eliminating potential contaminants or impurities that may interfere with the bonding process and weaken bond strength. For bonded joints, surface preparation was conducted to enhance sample strength, following the ASTM D2093 standard. The aluminum adherend surface was prepared according to the ASTM D3933-98 standard. Ultimately, the adherends were secured within a single lap joint (SLJ) fixture, as depicted in Figure 4. This fixture effectively immobilizes the adherends with respect to each other until the adhesive is fully cured, while simultaneously regulating the adhesive thickness to 0.3 mm. The process of preparing the bonded joint is illustrated in Figure 4.

Figure 4.

Preparation procedure of bonded specimens.

The single lap joints were then subjected to a curing process for 24 h at room temperature. Following this, they underwent post-curing by being exposed to a temperature of 70°C for 2 h. The initial step in creating a bonded/bolted joint involves performing the adhesive joint according to the specified procedure. In accordance with ASTM D5961, holes were drilled in the adherends using a CNC machine. The diameter of the holes was specifically designed to be 3.919 mm to accommodate bolts with a diameter of 3.979 mm. To prevent delamination during drilling, the method described in the study by Farid Gamdani et al.⁵⁹ was followed, which included placing a wooden board behind the samples. Subsequently, a torque meter was used to tighten the nut to 5 Nm. To examine the behavior of particles in adhesive specimens reinforced with fullerene, SWCNT, and a combination of both, scanning electron microscope (SEM) micrographs were taken, as shown in Figure 5.

Figure 5.

SEM image of an adhesive reinforced with 2.5% nanoparticles (fullerene, SWCNT, and their mixture) used in the research.

Hygrothermal ageing

To perform hygrothermal aging on the samples, they were immersed in tap water at a temperature of 53°C for a period of twenty days. The moisture absorption of the samples was quantified following the guidelines provided in ASTM D570. The results were finally calculated using equation (1).

\emptyset = \frac{W_{t} - W_{0}}{W_{0}} \times 100 %

(1)

Equation (1) is used to determine the percentage of humidity absorbed (∅) by a sample that has undergone hygrothermal conditions. It incorporates two weights: W_t, representing the sample’s weight after moisture absorption, and W₀, representing the sample’s weight before hygrothermal aging. By comparing these weights, the percentage of humidity absorbed can be calculated.

Testing procedure

The bonded/bolted and bonded joints underwent three-point bending static tests using a Santam STM-150 machine, following the ASTM D790 standard at a speed of 0.5 mm/min. The Santam STM-150 is equipped with a precise class 0.5 load cell with a capacity of 150 kN, ensuring accurate measurement of the applied load. Additionally, the machine features a precise displacement sensor for measuring crosshead displacement and operates with an AC servo motor and drive system with closed-loop control. The specimens were divided into four categories: (I) neat specimens (non-reinforced adhesive), (II) specimens enhanced with Fullerene nanoparticles at 1.5% and 2.5% V_f (volume fraction), (III) specimens enhanced with SWCNT at 1.5% and 2.5% V_f, and (IV) specimens enhanced with a combination of 50% SWCNT and 50% Fullerene nanoparticles at 1.5% and 2.5% V_f. All four categories were tested under both unaged and hygrothermal aged conditions, using two types of adherends—composite-to-composite (CTC) and composite-to-aluminum (CTA)—and two types of joints: bonded and bonded/bolted. In this study, ‘F' refers to adhesives reinforced with fullerene, ‘S' represents samples with SWCNT-reinforced adhesives, and ‘M' indicates a mixture containing 50-50% V_f of both fullerene and SWCNT. A total of 168 static tests were carried out, with each group undergoing three repetitions of the tests. Figure 6 depicts the CTA Static Three-point bending test.

Figure 6.

Static three-point bending test.

In Table 2, the selected V_f % values for nanoparticles are based on earlier research conducted by Rama Esmail et al.⁶⁰ In their study, they investigated the effects of fullerene nanoparticles, single-walled carbon nanotubes (SWCNTs), and a mixture of both on the mechanical properties of adhesive joints. The most effective concentration range for enhancing joint strength and durability was identified as being between 1.5% and 2.5% volume fraction (V_f). Within this range, the nanoparticles significantly improved the mechanical properties of the adhesive, such as tensile strength, without causing detrimental effects like excessive brittleness. However, increasing the nanoparticle content beyond the optimal value (above 2.5% V_f) led to the formation of agglomerated particles, which acted as stress concentrators and negatively impacted the static strength of the joints. Conversely, reducing the filler content percentage from the optimal value had a minimal effect on the static strength of joints compared to those without additives. This finding highlights the importance of selecting the appropriate amount of additives to achieve the desired level of static strength in the joints. The chosen ratios (1.5% and 2.5% volume fraction, V_f) ensured a uniform dispersion of nanoparticles within the adhesive matrix, thereby maximizing the reinforcing effect and maintaining the structural integrity of the joints. As a result, two V_f % values (1.5% and 2.5%) were used to prepare the nanoadhesive. Table 2 presents the scheduled experiments for static testing.

Table 2.

Tests scheduled for reinforcing joints with nanoparticles in static testing.

Types	Specimen	Nanoparticles	V_f %	Static tests
Types	Specimen	Nanoparticles	V_f %	Unaged	Hygrothermal
Bonded	CTC	Neat	-	Neat (st-U)	Neat (St-H)
		F (fullerene)	1.5	F (1.5st-U)	F (1.5st-H)
		F (fullerene)	2.5	F (2.5st-U)	F (2.5st-H)
		S (SWCNT)	1.5	S (1.5st-U)	S (1.5st-H)
		S (SWCNT)	2.5	S (2.5st-U)	S (2.5st-H)
		M (50 % SWCNT + 50 % fullerene (Mix))	1.5	M (1.5st-U)	M (1.5st-H)
		M (50 % SWCNT + 50 % fullerene (Mix))	2.5	M (2.5st-U)	M (2.5st-H)
	CTA	Neat	-	Neat (st-U)	Neat (St-H)
		F (fullerene)	1.5	F (1.5st-U)	F (1.5st-H)
		F (fullerene)	2.5	F (2.5st-U)	F (2.5st-H)
		S (SWCNT)	1.5	S (1.5st-U)	S (1.5st-H)
		S (SWCNT)	2.5	S (2.5st-U)	S (2.5st-H)
		M (50 % SWCNT + 50 % fullerene (Mix))	1.5	M (1.5st-U)	M (1.5st-H)
		M (50 % SWCNT + 50 % fullerene (Mix))	2.5	M(2.5st-U)	M (2.5st-H)
Bonded/bolted	CTC	Neat	-	Neat (st-U)	Neat (St-H)
		F (fullerene)	1.5	F (1.5st-U)	F (1.5st-H)
		F (fullerene)	2.5	F (2.5st-U)	F (2.5st-H)
		S (SWCNT)	1.5	S (1.5st-U)	S (1.5st-H)
		S (SWCNT)	2.5	S (2.5st-U)	S (2.5st-H)
		M (50 % SWCNT + 50 % fullerene (Mix))	1.5	M (1.5st-U)	M (1.5st-H)
		M (50 % SWCNT + 50 % fullerene (Mix))	2.5	M(2.5st-U)	M(2.5st-H)
	CTA	Neat	-	Neat (st-U)	Neat(St-H)
		F (fullerene)	1.5	F (1.5st-U)	F (1.5st-H)
		F (fullerene)	2.5	F (2.5st-U)	F (2.5st-H)
		S (SWCNT)	1.5	S (1.5st-U)	S (1.5st-H)
		S (SWCNT)	2.5	S (2.5st-U)	S (2.5st-H)
		M (50 % SWCNT + 50 % Fullerene (Mix))	1.5	M (1.5st-U)	M (1.5st-H)
		M (50 % SWCNT + 50 % Fullerene (Mix))	2.5	M (2.5st-U)	M (2.5st-H)

Model based on machine learning

Prediction approaches

This study focuses on predicting static load from empirical tests using machine learning models, emphasizing their complex and nonlinear relationships. Six diverse algorithms—ridge regression, decision tree, random forest regression, gradient boosting regression, support vector regression, and neural networks—were selected for their proven versatility in handling complex relationships in various fields, including force prediction. Each model brings distinct strengths to address the inherent complexities of nonlinear relationships: Ridge regression for managing multicollinearity, decision trees for interpretability, random forests for robustness, gradient boosting for high accuracy, support vector regression for combating overfitting, and neural networks for capturing intricate patterns. These algorithms are strategically chosen to optimize predictive performance by effectively leveraging the nonlinear dynamics present in static load prediction tasks, which encompass the intricate interactions among factors such as material properties, joint configurations, nanoparticle percentage, and aging conditions. By accounting for these complexities, the models can more accurately capture how variations in these elements influence the static strength of bonded and bonded/bolted joints.

Random forest (RF)

As depicted in Figure 7, Random Forest⁶¹ is an ensemble model consisting of multiple decision trees. These trees are trained using the bagging (bootstrap aggregation) method, where each tree has its own decision branches, leaf nodes, internal nodes, and root nodes. Input variables x = {x₁, x₂,…, x_n} traverse the decision paths through the internal nodes, which apply decision rules, until reaching a leaf node. The prediction for each tree is denoted as h_t(x), where t refers to a specific tree. The final prediction of the Random Forest model is obtained by aggregating the outputs of all T trees. For classification tasks, this aggregation is done via majority voting (equation (2)):

\hat{y} = majority_vote {h_{1} (x), h_{2} (x), \dots, h_{T} (x)}

(2)

Figure 7.

Structure and computational workflow of the random forest.

For regression tasks, the final output is the average of the predictions of all trees (equation (3)):

\hat{y} = \frac{1}{T} \sum_{t = 1}^{T} h_{t} (x)

(3)

Random Forest helps reduce overfitting by averaging or voting across many trees, making the model resilient to noise and outliers. The model is well-suited for classification tasks with high-dimensional data due to its scalability and ability to process data in parallel.

Ridge regression

Ridge regression,⁶² also known as Tikhonov regularization, is an extension of linear regression that addresses some limitations of the standard approach, particularly in the presence of multicollinearity or when the number of predictors exceeds the number of observations. Ridge regression modifies the linear regression objective by adding a penalty term, λ $\sum β_{i}^{2}$ , to the sum of squared residuals. This penalty term, controlled by the tuning parameter λ, shrinks the regression coefficients towards zero, reducing their variance. This regularization technique helps prevent overfitting and improves the model’s generalization to new data. The ridge regression model can be represented as:

y = β_{0} + β_{1} x_{1} + β_{2} x_{2} + \dots + β_{n} x_{n} + ϵ + λ \sum_{i = 1}^{n} β_{i}^{2}

(4)

In this formula, y represents the dependent variable or target, while β₀, β₁, …, β_n denote the coefficients associated with the corresponding predictors x₁, x₂, …, x_n. The term ϵ accounts for any error in the model. Additionally, λ is the regularization parameter that governs the extent of penalty applied to the coefficients, helping to shrink them towards zero. This regularization technique proves particularly valuable for high-dimensional datasets, where it strikes a balance between fitting the training data well and maintaining a simpler, more generalizable model.

Decision tree

Decision trees⁶³ are effective, non-parametric methods used for both regression and classification tasks. They are hierarchical structures that employ a divide-and-conquer approach. A labeled dataset ${D = {(xi, yi)}_{i = 1}^{N}$ can be used to construct decision trees, which can then be represented as a set of comprehensible rules. In the decision tree model, the input space X is partitioned into local regions R_j using a distance measure such as the Euclidean norm. For classification, the decision tree predicts the class label $\hat{y}$ based on the majority class in the region R_j where the input x falls, as represented in equation (5):

\hat{y} = mode {y_{i} ∣ x_{i} \in R_{j}}

(5)

where mode denotes the most frequent class label in the region R_j. For regression tasks, the decision tree predicts a continuous value

\hat{y}

as the average of the target values in the region Rj, as shown in equation (6):

\hat{y} = \frac{1}{| R_{j} |} \sum_{x_{i \in R_{j}}} y_{i}

(6)

where ∣R_j∣ represents the number of data points in the region R_j. The decision tree structure, as shown in Figure 8, consists of internal decision nodes that perform tests on features, decision nodes that represent the outcomes of these tests, and terminal nodes (or leaves) that provide the final prediction.

Figure 8.

Flowchart of decision tree.

Artificial neural network (ANN)

The ANN algorithm,⁶⁴ inspired by the human brain’s neural network, extracts features from large datasets using multi-layer nonlinear processing units for predictions. Its architecture includes a single-output layer, a hidden layer with many neurons, and a multi-input layer processing inputs x_i (where i = 1 to n). Each hidden layer neuron’s output serves as the input for subsequent layers. The training of the back-propagation (BP) neural network involves two steps:

Forward propagation where Inputs x_i are weighted by W_i, summed with a bias term b, and passed through an activation function F, resulting in the output y (as shown in equation (7)).

y = F (\sum_{i = 1}^{n} W_{i} x_{i} + b)

(7)

Backward propagation where the error function, typically measured as the difference between the predicted output and the actual output, is used to adjust the weights. When the error exceeds a set threshold, back-propagation updates the weights to minimize this error.

A neural network with multiple hidden layers is referred to as a deep neural network (DNN). Figure 9(A) and (B) illustrate the ANN and DNN architectures, respectively, and demonstrate their application as predictive models.

Figure 9.

(A) Configuration of a simple ANN incorporating feedback via back-propagation. (B) Visual representation illustrating the architecture of a DNN.

Support vector regression (SVR)

One effective tool for identifying nonlinear patterns, managing small datasets, and detecting high-dimensional relationships is SVR.⁶⁵ SVR constructs a hyperplane (equation (8)) to maximize class separation by mapping samples to a higher-dimensional space for linear separability. This approach enhances classification performance and broadens its applications for function approximation. While the parameters b and ω play an important role in defining the hyperplane, the mapping is represented by the transformation function ϕ(x) that maps the input data to this higher-dimensional space. SVR, derived from support vector machines (SVM), aims to minimize the difference between f(x), the model output, and the true value y, within an allowable error margin ε, specifically designed for single-sample datasets. Loss is incurred only when the difference exceeds ε, defining a 2ε band around f(x) for accurate predictions. SVR constructs a hyperplane in a high-dimensional space to minimize distances from points beyond this band, addressing this optimization through a convex optimization problem (equation (9)), as shown in Figure 10.

f (x) = b + ω^{T} \emptyset (x)

(8)

\min \frac{1}{2} {‖ ω ‖}^{2} + \sum_{i = 1}^{n} (ξ_{i}^{1} + ξ_{i}^{2}) \times C

(9)

Figure 10.

Using SVR to map data to high dimensions.

In SVR, slack variables $ξ_{i}^{2}$ and $ξ_{i}^{1}$ represent margin deviations, penalized by regularization parameter C. SVR uses kernels (non-linear, linear, sigmoid, RBF) to transform data and capture patterns. Class prediction is based on a decision function (equation (10)). Lagrange multipliers $α_{i}^{2}$ and $α_{i}^{1}$ , from the dual problem, use kernel function κ.

f (x) = \sum_{i = 1}^{n} (α_{i}^{2} + α_{i}^{1}) k (x_{i}, x) + b

(10)

Gradient boosting regressor

Gradient Boosting Regressor⁶⁶ is a sophisticated machine learning method that creates a series of decision trees one after the other. Every new tree is trained to correct the mistakes made by the previous ones. Gradient Boosting improves the model by minimizing a loss function, which for regression problems is usually the mean squared error (MSE). The loss function can be expressed as equation (11). Where y represents the actual values, $\hat{y}$ represents the predicted values, and n is the number of observations.

L (y, \hat{y}) = \frac{1}{n} \sum_{i = 1}^{n} {(y_{i} - {\hat{y}}_{i})}^{2}

(11)

This method gradually enhances the model’s performance by concentrating on the residuals, or the discrepancy between the actual and anticipated values, at each stage. The residuals (r_i) at each stage can be defined as equation (12).

r_{i} = y_{i} - {\hat{y}}_{i}

(12)

The outcome is an effective prediction model that can manage intricate patterns and relationships found in the data. However, methods like regularization and cross-validation are frequently used to improve Gradient Boosting’s generalization abilities because it can be prone to overfitting, particularly if the number of trees is high or the trees are excessively deep. Regularization techniques such as shrinkage (learning rate) and tree constraints (e.g., maximum depth, minimum samples per leaf) are applied to control the complexity of the model. Cross-validation is used to ensure that the model performs well on unseen data.

Development of model

Models for static load prediction from actual tests were developed using machine learning techniques.

Management of data

The dataset in this study, which focuses on forecasting static load (N) in material science applications, must be carefully prepared to ensure reliable model performance. First, one-hot encoding was applied to encode categorical variables such as “connection type,” “nanoparticle type,” and “condition.” This preprocessing step facilitated a comprehensive analysis of these qualitative features within the prediction models. Next, a stratified approach was used to split the dataset into training and testing subsets. This method ensured that the distribution of nanoparticle volume percentages (nanoparticle V_f %) remained consistent across both sets, preventing any imbalance that could skew model evaluation and validation. Data normalization techniques were employed to standardize the numerical features derived from the dataset. To capture potential nonlinear interactions between the predictors and the target variable, polynomial features up to the second degree were generated. These features were then normalized using StandardScaler, which ensures a zero mean and a standard deviation of one. This normalization process minimizes the influence of differing feature scales, supporting unbiased and reliable model training. Together, these data preparation methods enhance the robustness and reliability of the prediction models, enabling them to generalize effectively to new data and provide valuable insights for material science studies.

Fine-tuning of hyperparameters

An organized hyperparameter tuning method was employed to maximize the models' prediction performance. A cross-validated grid search was conducted for thorough parameter optimization of each model type. For linear models like Ridge Regression and Linear Regression, regularization parameters such as alpha were adjusted. For models like decision trees, random forests, gradient boosting, and support vector regression, various parameters were explored, including learning rate, number of estimators, maximum depth, and kernel coefficients. This optimization was performed within a five-fold cross-validation framework to enhance generalization capabilities and prevent overfitting. Additionally, a neural network architecture with multiple layers and dropout regularization was designed to avoid overfitting during training, with hyperparameters fine-tuned through iterative experimentation. This strategy systematically adjusts model parameters, improving prediction accuracy and reliability, and aligning empirical data with computational methods to provide valuable insights for material science applications.

Results and discussion

Moisture absorption

Table 3 presents the measurements of moisture absorption over a 20-day period, calculated using equation (1). It should be noted that the findings for CTC and CTA bonded/bolted joints during the ageing stage were taken from previous research ⁴³ for comparison purposes. Moisture absorption and degradation can occur in both the adhesive and the adherents. According to prior studies, when neat specimens were exposed to hygrothermal ageing, a higher percentage of moisture absorption was initially observed in the adhesive, followed by the CFRP adherents. The results show that the neat adhesive specimen, particularly the CTC bonded/bolted configuration, absorbed the greatest amount of moisture. In contrast, the lowest moisture absorption was recorded in the CTA bonded SLJ, which was reinforced with 2.5% V_f fullerene. Despite their differing hydrophilic and hydrophobic properties, both SWCNT and fullerene nano-additives demonstrated a reduction in water absorption, with fullerene-reinforced samples showing a greater reduction than those with SWCNTs. Additionally, the extent of water absorption decreased as the proportion of nano-additives increased.

Table 3.

Percentage of humidity absorption during hygrothermal ageing.

Types	Specimen	Nanoparticles	% age of water absorbtion (∅)
Bonded	CTC	Neat	0.105
		1.5% fullerene	0.035
		2.5% fullerene	0.024
		1.5% SWCNT	0.086
		2.5% SWCNT	0.073
		1.5% M ( 50 % SWCNT + 50 % Fullerene)	0.052
		2.5% M ( 50 % SWCNT + 50 % Fullerene)	0.043
	CTA	Neat	0.088
		1.5% fullerene	0.031
		2.5% fullerene	0.022
		1.5% SWCNT	0.072
		2.5% SWCNT	0.061
		1.5% M ( 50 % SWCNT + 50 % Fullerene)	0.041
		2.5% M ( 50 % SWCNT + 50 % Fullerene)	0.036
Bonded/bolted	CTC	Neat	0.120
		1.5% fullerene	0.043
		2.5% fullerene	0.029
		1.5% SWCNT	0.097
		2.5% SWCNT	0.081
		1.5% M ( 50 % SWCNT + 50 % Fullerene)	0.061
		2.5% M ( 50 % SWCNT + 50 % Fullerene)	0.048
	CTA	Neat	0.099
		1.5% fullerene	0.035
		2.5% fullerene	0.025
		1.5% SWCNT	0.083
		2.5% SWCNT	0.067
		1.5% M ( 50 % SWCNT + 50 % Fullerene)	0.047
		2.5% M ( 50 % SWCNT + 50 % Fullerene)	0.041

Experimental test results

The application of a load to the midpoint of a single-lap joint (SLJ) during a three-point bending test subjects the overlap region to both shear forces and bending moments. These forces are maximized at the midpoint of the overlap length and gradually diminish towards the supports. The resulting shear and peel stresses are most concentrated at the free edges of the adhesive layer, often causing failure to initiate at these points.^67,68 In SLJs, joint failure typically arises because the adhesive has lower strength compared to the adherents. This is particularly evident in three-point bending tests, where one side of the joint experiences tension while the other side is subjected to compression due to the geometry of the joint. Adhesive materials tend to exhibit greater strength under compression than under tension, leading to failure initiation on the tensile side of the joint, which then progresses toward the compressive side.⁶⁹

The experimental results from static bending tests on both aged and unaged SLJ specimens provide valuable insights. Figure 11 shows the comparison of failure loads in joints following hygrothermal aging with the initial failure loads across various reinforced specimen groups. Generally, joints reinforced with SWCNT exhibited higher average failure loads compared to those reinforced with fullerene, with differences ranging from 1% to 3.5% for bonded joints and 1% to 2.8% for bonded/bolted joints at reinforcement levels of 1.5% and 2.5% volume fraction (V_f). The highest failure loads were observed in specimens reinforced with a mixture of SWCNT and fullerene particles at 2.5% V_f. The performance of bonded and bonded/bolted joints varied depending on the percentage of nanoparticles. Bonded joints demonstrated improved outcomes at lower nanoparticle percentages, while bonded/bolted joints exhibited better performance at higher percentages. For example, the addition of 1.5% V_f SWCNT to non-aged bonded samples resulted in a 2% and 4% increase in SLJ failure loads for bonded-CTC and bonded-CTA configurations, respectively. However, increasing the nanoparticle content to 2.5% V_f caused slight reductions in failure loads, likely due to particle agglomeration and increased adhesive brittleness (Figure 11).

Figure 11.

Column charts: bending test results for bonded/bolted and bonded single lap joint.

Similar trends were observed with fullerene-reinforced SLJ samples. Notably, the best performance in bonded/bolted joints was achieved at a 2.5% V_f nanoparticle proportion, consistently outperforming the neat adhesive SLJ specimen in load-bearing capacity across unaged configurations (Figure 11(b)). Hygrothermal aging studies revealed that adding SWCNTs improved the adhesive’s resistance to degradation, while fullerene-reinforced SLJ configurations consistently exhibited higher failure loads than aged neat adhesive SLJ samples, likely due to fullerene’s hydrophobic nature enhancing resistance to hygrothermal effects. Despite previous studies reported decreases in failure loads following hygrothermal aging,^70,71 this study observed increases in failure loads for bonded-CTC and bonded-CTA specimens with a 2.5% V_f mixture of SWCNT and fullerene.⁷² This improvement was attributed to the ability of the nano-fillers to restrict polymer chain movement, thereby enhancing the material’s resistance to the weakening effects typically caused by hygrothermal aging.^73,74

In contrast, the bonded/bolted-CTC and bonded/bolted-CTA joints did not exhibit an increase in failure load after hygrothermal aging, suggesting that the bolts effectively prevent excessive elongation caused by adhesive relaxation, thereby preserving load-bearing capacity. Additionally, joints reinforced with a combination of SWCNTs and fullerenes at 2.5% V_f demonstrated significantly higher static failure loads in bonded/bolted configurations compared to bonded joints alone, highlighting the synergistic effect of the nanoparticles and bolts.⁴³ For industrial applications, the combined use of SWCNTs and fullerenes alongside bolts offers improved strength and cost-effectiveness. Comparative analyses revealed that hybrid joints with nanoparticles and bolts maintained higher failure loads under hygrothermal conditions compared to their non-nanoparticle counterparts, emphasizing the significance of this dual reinforcement strategy.⁴³

In summary, the study underscores the complex interplay between adhesive properties, reinforcement with nanoparticles, and the presence of mechanical fasteners in SLJ configurations, especially in dissimilar joints (composite-to-metal). It highlights the potential of combining SWCNTs and fullerenes with bolts to improve joint performance under varying environmental conditions, presenting a promising avenue for future research in enhancing adhesive joint strength across engineering disciplines.

The force-deflection curve of bonded/bolted single lap joints, as illustrated in Figure 12, demonstrates two distinct steps, whereas the curve for bonded joints shows only one step. The first step represents the adhesive bonding strength, while the second step indicates the strength of the bolted joint following adhesive failure. The behavior of the CTA joint in Figure 12 exemplifies this pattern. These results underscore the significant role of bolts in enhancing the mechanical performance of composite structures, suggesting the potential for developing advanced and efficient engineering systems. Additionally, the deformation of the adhesive material in bonded/bolted joints is considerably lower compared to that in bonded joints, owing to the pivotal role of the bolted joint. On average, the bonded/bolted specimens exhibited higher force levels than the bonded samples, emphasizing the importance of utilizing bonded/bolted joints in applications susceptible to hygrothermal aging. Similar findings were reported in the study conducted by Kim et al.⁷⁵

Figure 12.

Comparative analysis for static bending tests conducted on bonded/bolted and bonded.

Hybrid joints do not always enhance joint strength. The effectiveness of hybrid joints in amplifying joint strength is contingent upon the mechanical fastener outperforming the bonded joint.⁷⁶ However, if the mechanical fastener is weaker than the bonded joint, it contributes only marginally to the strength of the hybrid joint. Applying a tightening torque to bonded/bolted joints can enhance their load-carrying capacity. This tightening torque induces compression effects that reduce the likelihood of fractures in the adhesive layers of the materials. Additionally, the use of mechanical fasteners can improve a joint’s load-bearing capacity and resistance to damage by inhibiting crack propagation. As illustrated in Figure 13, the increased mean force observed in bonded/bolted joints can be attributed to two factors. First, the compressive force applied by the bolt and washer enhances friction between the composite layers, thereby limiting adhesive deformation. Second, the incorporation of steel washers in hybrid joints increases the clamping force and delays the propagation of adhesive cracks, resulting in an improved load-carrying capacity of the adhesive layer. Similar findings have been reported in other studies.^16,33,77

Figure 13.

Two factors boost average force in bonded/bolted joints.

Predictions of the machine learning

This study employs two statistical metrics—R² and RMSE—to comprehensively evaluate the performance of each machine learning algorithm (Table 4). R² assesses the correlation between predicted and actual values, with scores ranging from 0 to 1; higher R² values indicate more accurate predictions. RMSE, on the other hand, measures the discrepancies between predicted and observed values, with lower RMSE values signifying better prediction accuracy. Together, these metrics are crucial for evaluating regression models and determining the most suitable model for predicting static load.

Table 4.

Recorded force of of different joints.

Joint	Condition-substrate	Assessment criteria	Ridge regression	Decision tree	Random forest regressor	Gradient boosting regressor	Support vector regression	Neural networks
Bonded	Unaged-CTC	R²	0.61	0.91	0.88	0.63	0.97	0.1
	Unaged-CTC	RMSE	13.69	6.43	7.65	13.27	12.29	24.19
	Hygrothermal-CTC	R²	0.6	1	0.92	0.86	0.93	0.89
	Hygrothermal-CTC	RMSE	22.90	1.96	10	13.61	9.51	12
	Unaged-CTA	R²	0.68	0.75	0.96	0.68	0.85	0.1
	Unaged-CTA	RMSE	10.57	9.37	3.56	10.48	7.14	24.19
	HygrothermalCTA	R²	0.52	0.9	0.86	0.75	0.49	0.05
	HygrothermalCTA	RMSE	18.72	8.67	10.18	13.63	19.34	36.07
bonded/bolted	Unaged-CTC	R²	1	0.93	0.9	0.98	1	0.08
	Unaged-CTC	RMSE	1.57	7.49	9.2	3.69	0.48	35.6
	Hygrothermal-CTC	R²	1	0.99	0.96	1	1	0.9
	Hygrothermal-CTC	RMSE	0.73	2.67	7.31	0	0.1	10.74
	Unaged-CTA	R²	0.98	0.45	0.87	1	0.99	0.25
	Unaged-CTA	RMSE	3.76	20.18	9.98	0.53	2.29	23.57
	Hygrothermal-CTA	R²	0.98	0.04	0.39	0.7	0.17	0.01
	Hygrothermal-CTA	RMSE	4.46	34.84	27.78	19.34	32.37	45.75

Figures 14 and 15 show the results of actual tests and predicted examples of bonded and bonded/bolted joints based on six different machine learning models: Ridge regression, decision tree, random forest regressor, gradient boosting regressor, support vector regression, and neural networks. The experimental results reveal a non-linear relationship between input parameters such as joint type, substrate, type of nanoparticles, and V_f%. This indicates that the selection of input parameters involves complex mechanisms that are not adequately described by a simple linear relationship. The experimental data serve as a benchmark for evaluating the prediction accuracy of the machine learning models. Using the presented actual data, ridge regression, decision tree, random forest regressor, gradient boosting regressor, support vector regression, and neural networks models were employed to predict static load based on the experimental results. Each model uses distinct methods to discover and predict underlying patterns in the data. In the bonded joint category, support vector regression showed the highest accuracy for unaged CTC conditions with an R² value of 0.97, while the decision tree model performed best under hygrothermal CTC conditions, achieving a perfect R² of 1.00. For unaged CTA conditions, the random forest regressor was the most accurate with an R² of 0.96, and under hygrothermal CTA conditions, the decision tree again proved superior with an R² of 0.90. Conversely, neural networks consistently underperformed across all bonded conditions, with the lowest R² values ranging from 0.02 to 0.001.

Figure 14.

(a) to (f): The results of actual tests versus predicted tests of bonded joints based on six different machine learning models.

Figure 15.

(g) to (l): The results of actual tests versus predicted tests of bonded/bolted joints based on six different machine learning models.

In the bonded/bolted joint category, ridge regression, support vector regression, and gradient boosting regressor models exhibited perfect prediction accuracy (R² = 1) for unaged-CTC and hygrothermal-CTC conditions. However, neural networks remained the least accurate, especially under hygrothermal-CTA conditions, with an R² of 0.01. This comprehensive analysis underscores the significance of selecting appropriate machine learning models to accurately predict the static load and aging effects in composite joints, highlighting the superiority of decision tree and random forest regressor for bonded joints and ridge regression, support vector regression, and gradient boosting regressor for bonded/bolted joints. Examining the effect of the substrate type (CTC and CTA) on the results reveals notable differences. In the bonded joint category, models generally performed better with the CTA substrate compared to the CTC substrate, particularly under hygrothermal conditions. For example, the random forest regressor achieved an R² of 0.96 for unaged-CTA compared to 0.88 for unaged-CTC. However, this trend is not consistent across all models; for instance, the decision tree model performed equally well (R² of 1) for both substrates under hygrothermal-CTC conditions. In the bonded/bolted joint category, the improvement in prediction accuracy with CTA is more pronounced. Ridge regression, support vector regression, and gradient boosting regressor models achieved perfect R² values (1) for hygrothermal-CTA, suggesting that the CTA substrate allows for more accurate predictions under aging conditions. The substrate type significantly affects the models' performance, with CTA generally providing better prediction accuracy, possibly due to its material properties that offer more consistent and predictable responses to aging.

Furthermore, a comparison of the results between bonded and bonded/bolted joints indicates that adding a bolted connection generally improves prediction accuracy across various machine learning models. For instance, ridge regression, gradient boosting regressor, and support vector regression achieved perfect R² values (1) in bonded/bolted joints for both unaged CTC and hygrothermal CTC conditions, marking a noticeable improvement compared to their performance in purely bonded joints. The inclusion of bolted connections likely enhances structural integrity and load distribution, leading to more consistent and predictable behavior under different conditions. This improved predictability is reflected in the higher R² values across models when a bolted connection is present. However, neural networks still exhibited poor performance in bonded/bolted joints, indicating that while the addition of bolts can enhance prediction accuracy, the choice of model remains crucial. Overall, incorporating a bolted connection appears to facilitate better predictive performance by machine learning models, emphasizing both the combined mechanical benefits and the need for sophisticated algorithms to accurately capture the complex interactions within composite materials.

Advantages and disadvantages of ML methods

Selecting the appropriate machine learning model to predict the static strength of bonded and bonded/bolted joints—both composite-to-composite (CTC) and composite-to-aluminum (CTA)—under hygrothermal conditions requires a comprehensive understanding of each model’s unique strengths and limitations. Ridge Regression is beneficial for handling multicollinearity in linear data and provides regularization, which helps prevent overfitting. However, it still struggles with non-linear relationships and requires careful tuning of the regularization parameter. Decision trees offer easy interpretability and can model both linear and non-linear relationships. However, they are prone to overfitting, especially with complex datasets, and their performance can be unstable across different training sets. In contrast, random forest regression enhances accuracy by averaging the results of multiple decision trees, making it robust against noise and overfitting. While it performs well with both linear and non-linear data, it can be computationally intensive and less interpretable due to its ensemble nature. Gradient boosting regressor excels at capturing complex patterns through iterative refinement of predictions, often leading to high accuracy. Nevertheless, it can be computationally demanding and requires careful hyperparameter tuning to prevent overfitting. SVR is adept at modeling non-linear relationships through its use of kernel functions but can become computationally expensive with larger datasets and is sensitive to hyperparameter choices. Lastly, neural networks are highly effective for modeling intricate non-linear relationships, making them suitable for a wide array of applications. However, they demand substantial computational power, large datasets for optimal performance, and significant training time. Moreover, ANNs are often criticized for their lack of interpretability in real-world scenarios. Table 5 summarizes the advantages and disadvantages of the various machine learning models.

Table 5.

Advantages and disadvantages ML methods.

ML models	Key advantages	Key disadvantages
SVR	• Excellent at capturing non-linear relationships	• Computationally expensive for large datasets
	• Effective for small- to medium-sized datasets	• Sensitive to the choice of hyperparameters
	• Flexibility through different kernel functions	• Requires careful tuning
ANNs	• Capable of modeling complex non-linear relationships	• Requires large datasets for optimal performance
	• Versatile with various data types	• Computationally intensive
	• High performance in handling intricate patterns	• Lacks interpretability
	• High performance in handling intricate patterns	• Time-consuming training process
Ridge regression	• Effective for linear relationships with regularization	• Limited to linear relationships
	• Effective for linear relationships with regularization	• Performance can drop on non-linear data
	• Reduces overfitting by penalizing large coefficients	• Sensitive to multicollinearity
Random forest regression	• High accuracy and robustness	• Computationally intensive due to ensemble nature
	• Handles both linear and non-linear data
	• Resistant to overfitting and noise	• Difficult to interpret
Gradient boosting regressor	• Excellent performance for complex patterns through boosting	• Computationally demanding, especially with large datasets
	• Can optimize for various loss functions	• Requires careful tuning to avoid overfitting
	• Flexibility with hyperparameters for tuning	• Slower training times compared to simpler models
Decision tree	• Simple to understand and interpret.	• Prone to overfitting, especially with deep trees
	• Handles both numerical and categorical data	• Sensitive to small changes in data
	• Can capture non-linear relationships	• May require pruning to improve performance

Feature importance in bonded versus bonded/bolted joints

The study of feature importance for static test results between bonded joints and bonded/bolted joints reveals pronounced differences in the influencing factors. For bonded joints, the unaged condition results indicate that the type of nanoparticles used is the dominant factor, accounting for 73.1% of the variance in test outcomes. The substrate type and the volume fraction percentage (V_f %) each play a secondary role, contributing approximately 13.5%. When subjected to hygrothermal conditions, the importance of nanoparticles remains high at 49.2%, but the significance of V_f % rises sharply to 45.0%, while the influence of the substrate diminishes to a mere 5.8%.

In contrast, the bonded/bolted joints display a fundamentally different distribution of importance. For unaged conditions, the substrate type emerges as the most critical factor, explaining 66.9% of the variance. The importance of nanoparticles drops significantly to 28.5%, and V_f % further declines to just 4.6%. Under hygrothermal conditions, this pattern persists: the substrate type continues to dominate with a 58.2% contribution to variance, while the nanoparticles and V_f % contribute 22.6% and 19.2%, respectively. These findings underscore a crucial point: decisions and insights derived from the analysis of bonded joints do not necessarily extend to bonded/bolted joints. In bonded joints, both the presence of nanoparticles and their concentration play significant roles in both unaged and hygrothermal conditions. However, in bonded/bolted joints, the introduction of a screw fundamentally shifts the dynamics. The substrate type becomes the principal factor influencing performance, with its importance vastly overshadowing that of the nanoparticles and their concentration. This shift highlights that the mechanical addition of a screw alters the performance characteristics of the joint, making the substrate’s properties far more influential while reducing the relative impact of the nanoparticle type and concentration.

In summary, while nanoparticles and their concentration are critical in determining the performance of bonded joints, their significance is substantially reduced in bonded/bolted joints, where the substrate type takes precedence. This distinction is crucial for designing and optimizing joint performance in different configurations, ensuring that the unique factors influencing each type are adequately considered. Figure 16 depicts the Feature importance in bonded and bonded/bolted Joints.

Figure 16.

Feature importance in bonded and bonded/bolted joints.

Failure mode

The ASTM D5573-99 standard classifies the modes of failure in bonded specimens. According to this standard, there are seven categories of failure, including adhesive failure (AF), cohesive failure (CF), thin layer cohesive failure (TLCF), fiber tear failure (FTF), light fiber tear failure (LFTF), stock break, and mixed failure. In contrast, bolted single-lap joints (SLJs) exhibit different modes of failure, such as shear out (SO), net tension (NT), tear out (TO), and bearing failure (BF). For bonded/bolted joints, the failure mode is a combination of both bonded and bolted failure modes.

In out-of-plane loading, adhesive joints experience tensile forces at one free end, while the opposite free end is subjected to compression. These opposing forces generate positive peel stress in the tensile region and negative peel stress in the compressive region. Consequently, a crack initiates at the tip of the joint where positive peel stress is applied (causing crack opening) and propagates towards the opposite tip (where crack closure occurs). This ultimately leads to rapid and unavoidable failure.⁷⁸

Figure 17 illustrates the failure modes observed in neat, 2.5% V_f fullerene, 2.5% V_f SWCNT, and 2.5% V_f mixed samples, both before and after hygrothermal ageing, for CTC and CTA bonded joints. The analysis of these failure modes provides insights into the mechanical performance and durability of the joints under different conditions. The unaged samples exhibited a combination of cohesive and adhesive failure modes across all joint types, but the proportion of each failure type varied. Specifically, neat adhesive samples predominantly displayed adhesive failure, characterized by a clean separation at the adhesive-substrate interface. This mode of failure suggests weaker bond strength and indicates that the adhesive’s internal strength was not fully utilized during the bending tests. Consequently, the neat samples had the lowest level of cohesive failure, which correlates with their lower strength performance. In contrast, the samples reinforced with nanoparticles—especially the mixed samples containing 2.5% V_f of both fullerene and SWCNT—showed a significant increase in cohesive failure. Cohesive failure occurs within the adhesive layer itself, leaving adhesive residues on both substrates. This mode of failure is desirable because it signifies that the adhesive bond to the substrate is stronger, and the material’s internal strength is being fully utilized before fracturing. The higher prevalence of cohesive failure in the mixed samples indicates that the addition of nanoparticles effectively enhances the adhesive’s internal strength and overall bond performance. The impact of nanoparticles on the adhesive failure modes was evident in the improved bond strength and the increased cohesive failure area relative to the adhesive failure area. Nanoparticles, by reinforcing the adhesive matrix, distribute the stress more evenly and improve the resistance to crack initiation and propagation. This enhancement leads to a more robust adhesive bond, shifting the failure mode from adhesive failure to cohesive failure. After exposing the samples to hygrothermal aging, distinct changes in failure modes were observed. Samples that did not exhibit any strength improvement post-aging typically experienced Adhesive Failure or a mixture of adhesive and cohesive failure. This finding indicates that hygrothermal aging adversely affected the bond strength, causing the adhesive-substrate interface to weaken. The exposure to moisture and elevated temperatures likely degraded the adhesive properties, leading to failure at the interface rather than within the adhesive layer. Conversely, samples that demonstrated increased strength after hygrothermal aging exhibited a predominant shift towards cohesive failure, with only a minor proportion of adhesive failure. This shift is significant because cohesive failure, even after aging, suggests that the adhesive’s internal strength remains high and that the bond integrity is maintained despite environmental degradation. The presence of nanoparticles likely contributes to this resilience by enhancing the adhesive’s ability to withstand environmental stresses, thus preserving or even improving the joint strength.

Figure 17.

Visual representation of damage in bonded SLJs: A comparison between unaged and aged samples of CTC and CTA after static bending.

In summary, the presence of nanoparticles, especially in mixed formulations, significantly influences the failure modes by enhancing cohesive strength and shifting failure from the adhesive interface to within the adhesive layer. This shift is beneficial as it indicates improved joint performance and durability, both under normal and environmentally aged conditions. Cohesive failure remains the most advantageous failure mode, reflecting the material’s peak strength and robust bond integrity.

The surfaces of bonded/bolted samples with varying volumes of reinforcement (neat, 2.5% V_f of fullerene, 2.5% V_f of SWCNT, and 2.5% V_f of mixed SLJ) were examined before and after hygrothermal aging, as depicted in Figure 18. The outcomes demonstrate distinct levels of cohesive and adhesive failure across CTC and CTA joints in unaged samples. Notably, the most effective failure type, cohesive failure, was predominantly observed in the samples reinforced with 2.5% V_f SWCNT and 2.5% V_f mixed nanoparticles, indicating superior strength during the bending tests. This result underscores the significant enhancement in adhesion strength and the expansion of cohesive failure regions due to the incorporation of nanoparticles, compared to the adhesive regions. One critical issue observed after hygrothermal aging is the occurrence of interfacial debonding (NT) in the neat adhesive specimens, leading to a substantial decline in their lifespan. This degradation highlights the vulnerability of unreinforced adhesives to environmental factors. In aged bonded/bolted specimens of CTC and CTA joints, the failure modes evolved into a mixture of adhesive and cohesive failures, with varying proportions. The presence of nanoparticles in the adhesive matrix played a crucial role in mitigating the degradation of adhesive properties during hygrothermal exposure by inhibiting the formation of interfacial debonding (NT). The observed decrease in strength and the reduction in the number of cycles to failure in adhesive specimens post-hygrothermal aging emphasize the necessity for regular testing and monitoring of adhesive performance over time. The study’s findings suggest that the choice of nanoparticles significantly impacts the adhesive’s failure modes and overall performance under environmental stress. Therefore, selecting the appropriate type of nanoparticle for a specific application is crucial to enhancing joint durability and performance.

Figure 18.

Visual representation of damage in bonded/bolted SLJs: A comparison between aged and unaged samples of CTC and CTA after static bending.

Overall, these findings indicate that the type and volume of nanoparticles in the adhesive can profoundly affect its performance when subjected to hygrothermal ageing. A strong correlation exists between the joint’s strength and its specific fracture pattern. The shift in failure modes under hygrothermal conditions underscores the significant influence of environmental factors on the failure behavior of SLJs. Understanding these failure modes is vital for improving the design and optimization of adhesively bonded joints, particularly in industrial applications exposed to demanding and harsh conditions. Figure 18 illustrates the failure modes observed in neat, 2.5% V_f fullerene, 2.5% V_f SWCNT, and 2.5% V_f mixed samples, both before and after hygrothermal ageing, for CTC and CTA bonded/bolted joints.

Conclusions

This article investigates the impact of incorporating fullerene and SWCNT nanofillers on the static strength of bonded/bolted and bonded single-lap joints (SLJs) under a three-point bending load, both before and after exposure to hygrothermal conditions. Furthermore, the study aims to predict the static strength of both bonded and bonded/bolted joints—specifically CTC (composite to composite) and CTA (composite to aluminum)—under hygrothermal conditions using machine learning methods based on experimental data. Given the nonlinear relationships among input parameters such as joint type, substrate, type and percentage of nanoparticles (V_f %), and environmental aging (hygrothermal conditions), predicting the static strength of joints provides valuable insights into their aging characteristics and durability.

The presence of nanoparticles in the adhesive matrix played a crucial role in mitigating the degradation of adhesive properties during hygrothermal exposure. This is evidenced by the inhibition of interfacial debonding and the substantial decrease in the rate of strength reduction in adhesive specimens following hygrothermal aging.

The addition of fullerene and SWCNT nanofillers to the adhesive joints not only improved moisture resistance but also enhanced the static load capacity of the joints. This improvement was particularly notable in the mixed nanoparticle samples (50% fullerene and 50% SWCNT), which demonstrated superior performance in static bending tests.

Six machine learning models—ridge regression, decision tree, random forest regressor, gradient boosting regressor, support vector regression, and neural networks—were employed to predict the static strength of the joints under various conditions. The best-performing models for bonded joints were support vector regression and decision tree, while ridge regression and gradient boosting regressor excelled in predicting bonded/bolted joints. In contrast, neural networks consistently underperformed. Model performance varied with substrate type and joint configuration, type and percentage of nanoparticles (V_f %), highlighting the need for careful model selection to optimize predictive accuracy under different conditions.

The incorporation of nanoparticles, particularly in mixed formulations, significantly influences the failure modes by enhancing cohesive strength and shifting failure from the adhesive interface to within the adhesive layer. This shift is beneficial, as it indicates improved joint performance and durability under both normal and environmentally aged conditions. Cohesive failure remains the most advantageous failure mode, reflecting enhanced joint resilience.

For industrial applications, particularly in the aerospace and automotive sectors, the combined use of SWCNTs and fullerenes alongside bolts offers enhanced strength and cost-effectiveness. The addition of a bolt to the bonded joint resulted in an increase in static failure load of 26–36% compared to the bonded joint alone. Furthermore, hybrid joints maintained higher failure loads under hygrothermal conditions compared to their non-nanoparticle counterparts, underscoring the significance of this dual reinforcement strategy.

Overall, the analysis of feature importance revealed that joint type, substrate, type and percentage of nanoparticles (V_f %), and environmental aging can profoundly affect adhesive performance. Specifically, the choice of joint configuration (bonded vs. bonded/bolted) significantly influenced the prediction accuracy of the machine learning models. The bonded/bolted joints exhibited improved structural integrity and load distribution, leading to more consistent and accurate predictions.

The research conducted a thorough analysis of the correlation between machine learning-predicted samples and experimental samples, providing valuable insights into the aging and durability characteristics of bonded and bonded/bolted joints. By integrating experimental data with machine learning models, the accuracy of static strength predictions is improved, thereby contributing to a deeper understanding of the aging processes of adhesive joints.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Sajjad Karimi

Data availability statement

Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.

References

Pramanik

Basak

Dong

, et al. Joining of carbon fibre reinforced polymer (CFRP) composites and aluminium alloys– a review. Compos Appl Sci Manuf 2017; 101(oct): 1–29.

Gay

Lefebvre

Bergamo

, et al. Fatigue performance of a self-piercing rivet joint between aluminum and glass fiber reinforced thermoplastic composite. Int J Fatig 2012; 83(feb): 127–134.

Liu

Zhuang

Luo

, et al. Joining mechanism and damage of self-piercing riveted joints in carbon fibre reinforced polymer composites and aluminium alloy. Thin-Walled Struct 2023; 182: 110233.

Karimi

Ahmadi

Klenin

, et al. An experimental investigation on the influence of environmental ageing on strength and fatigue behavior of different single lap joints. Compos Struct 2023; 322: 117423.

Ahmed

Masmoudi

Bissonnette

, et al. Bond behavior of CFRP reinforcement systems with concrete under static and fatigue loading. Construct Build Mater 2024; 426: 136000.

, et al. Investigating the failure behavior of hygrothermally aged adhesively bonded CFRP-aluminum alloy joints using modified arcan fixture. Thin-Walled Struct 2023; 182: 110303.

Zhao

Karimi

. An experimental investigation of static and fatigue behavior of various adhesive single lap joints under bending loads subjected to hygrothermal and thermal conditions. J Adhes 2023; 100(9): 845–866. DOI: 10.1080/00218464.2023.2270431.

Wang

Lin-yu-wen

, et al. Hygrothermal ageing effect on the water diffusion in glass fiber reinforced polymer (GFRP) composite: experimental study and numerical simulation. Compos Sci Technol 2022; 230: 109762.

Ulus

Burak Kaybal

. Out-of-plane static loading performance of lightweight aluminum/composite FML structures for retrofitting applications: effectiveness of bonded, bolted and hybrid bonded/bolted joining techniques under hydrothermal aging environment. Construct Build Mater 2023; 403: 133124.

10.

Xie

You

Tao

, et al. Experimental and theoretical study on mechanical behaviors of CFRP–steel interface. Thin-Walled Struct 2023; 182: 110208.

11.

de Barros

Kenedi

Ferreira

, et al. Influence of mechanical surface treatment on fatigue life of bonded joints. J Adhes 2017; 93(8): 599–612.

12.

Luo

Song

, et al. A novel method for improving interfacial joining strength of vacuum brazed TiAl/GH3536 thin-walled structure by Au coating. Thin-Walled Struct 2023; 190: 110915.

13.

Tang

Soutis

, et al. Multiscale analysis of the compressive behaviour of polymer-based composites reinforced by hybrid Al2O3/Al fibres. Compos Sci Technol 2024; 255: 110718.

14.

Ghosh

Kumar

Preeti

, et al. Superior dissimilar adhesive joint of mild steel and aluminium using UDM processed epoxy based TiO2 nano-filler composite adhesive. Compos B Eng 2016; 99: 224–234.

15.

Ekrem

Avcı

. Effects of polyvinyl alcohol nanofiber mats on the adhesion strength and fracture toughness of epoxy adhesive joints. Compos B Eng 2018; 138: 256–264.

16.

Lopez-Cruz

Laliberte

Lessard

. Investigation of bolted/bonded composite joint behaviour using design of experiments. Compos Struct 2017; 170(jun): 192–201.

17.

Karimi

. Enhancing mechanical properties of GFRP–aluminum joints through Z pinning: a low velocity shear impact study. J Adhes Sci Technol. 2024; 1–14. doi:10.1080/01694243.2024.2375282.

18.

Zhang

Liu

, et al. Numerical analysis of hybrid (bonded/bolted) FRP composite joints: a review. Compos Struct 2021; 262(apr): 113606.

19.

Zhang

Liu

, et al. Research in failure behaviors of hybrid single lap aluminum-CFRP (plain woven) joints. Thin-Walled Struct 2021; 161: 107488.

20.

Jiang

Liao

Gao

, et al. Comparative study on joining quality of electromagnetic driven self-piecing riveting, adhesive and hybrid joints for Al/steel structure. Thin-Walled Struct 2021; 164: 107903.

21.

Cheng

Guo

, et al. Tensile properties of a hybrid bonded/bolted joint: parameter study. Compos Struct 2020; 245(aug): 112329.

22.

Soltannia

Mertiny

Taheri

. Static and dynamic characteristics of nano-reinforced 3D-fiber metal laminates using non-destructive techniques. J Sandw Struct Mater 2021; 23(7): 3081–30112.

23.

Rezvani Tavakol

Yarmohammad Tooski

Jabbari

, et al. Effect of graphene nanoparticles on the strength of sandwich structure inspired by dragonfly wings under low‐velocity impact. Polym Compos 2021; 42(10): 5249–5264.

24.

Fallahi

Moini Jazani

Molla-Abbasi

. Design and characterization of high-performance epoxy adhesive with block copolymer and alumina nanoparticles in aluminum-aluminum bonded joints: mechanical properties, lap shear strength, and thermal stability. Polym Compos 2022; 43(3): 1637–1655.

25.

Farzad

Hossein Seyedkashi

Hossein Pol

. Experimental study of mechanical properties and failure mechanisms of metal–composite laminates reinforced with multi-walled carbon nanotubes. Thin-Walled Struct 2023; 183: 110377.

26.

Zamani

da Silva

LFM

Nejad

, et al. Experimental study on mixing ratio effect of hybrid grapheme nanoplatelet/nano-silica reinforcement on the static and fatigue life of aluminum-to-GFRP bonded joints under four-point bending. Compos Struct 2022; 300: 116108.

27.

Monteiro

Avila

. The carbon nanotubes effect into single-lap joint failure modes and load capacity: a micromechanical analysis. Mater Res 2017; 20(suppl 1): 143–152.

28.

Akpinar

. Effect of nanostructured reinforcement of adhesive on thermal cycling performance of a single-lap joint with composite adherends. Compos B Eng 2019; 175: 107106.

29.

Özbek

Çakır

. MWCNT and nano-silica hybrids effect on mechanical and fracture characterization of single lap joints of GFRP plates. Int J Adhesion Adhes 2022; 117: 103159.

30.

Min

Liu

Shen

, et al. Unique synergistic effects of graphene oxide and carbon nanotube hybrids on the tribological properties of polyimide nanocomposites. Tribol Int 2018; 117: 217–224.

31.

Mehmet

VÇ

. The synergistic effect of hybrid nano-silica and GNP additives on the flexural strength and toughening mechanisms of adhesively bonded joints. Int J Adhesion Adhes 2023; 122: 103333.

32.

Starkova

Aiello

Aniskevich

. Long-term moisture diffusion in vinylester resin and CFRP rebars: a 20-year case study. Compos Sci Technol 2023; 242: 110167.

33.

Long

Xue

, et al. Polarization Raman spectroscopy characterizations of microscopic stress in 3D angle-interlock woven composites during thermo-oxidative ageing. Compos Sci Technol 2024; 247: 110423.

34.

Vivek

Puplampu

Murray

, et al. Degradation in interfacial shear strength of carbon fiber/ vinyl ester composites due to long-term exposure to seawater using push-out tests. Compos Sci Technol 2023; 241: 110131.

35.

Zheng

Wang

, et al. On failure mechanisms in CFRP/Al adhesive joints after hygrothermal aging degradation following by mechanical tests. Thin-Walled Struct 2021; 158: 107184.

36.

De'Nève

Shanahan

. Water absorption by an epoxy resin and its effect on the mechanical properties and infra-red spectra. Polymer 1993; 34: 5099–5105.

37.

Galvez

Abenojar

Martinez

. Effect of moisture and temperature on the thermal and mechanical properties of a ductile epoxy adhesive for use in steel structures reinforced with CFRP. Compos B Eng 2019; 176: 107194.

38.

Zhang

, et al. Effects of moisture ingress on the mesoscale mechanical properties of epoxy adhesives under elevated temperature. Polym Test 2021; 94: 107049.

39.

Jin

Xuan

, et al. Influence of cyclical hygrothermal aging on mechanical response and structural durability of composite bolted interference-fit joints. Thin-Walled Struct 2022; 173: 108997.

40.

Calabrese

Fiore

. A simplified predictive approach to assess the mechanical behavior of pinned hybrid composites aged in salt-fog environment. Compos Struct 2020; 249: 112589.

41.

Liu

Guo

Hebdon

, et al. Behaviors of GFRP- steel bonded joints under cyclic loading after hygrothermal aging. Construct Build Mater 2020; 242: 118106.

42.

Zhang

Feng

, et al. Performance evolution of epoxy adhesive and CFRP-steel epoxy-bonded joints subjected to hygrothermal exposure. Construct Build Mater 2024; 429: 136445.

43.

Karimi

Rezvani Nasab

Afshari

, et al. Effect of hygrothermal and thermal aging on the fatigue and static strength of mechanical and hybrid single lap joint. Compos Struct 2023; 309: 116692.

44.

Ding

Hou

Xia

, et al. Predictions of macroscopic mechanical properties and microscopic cracks of unidirectional fibre-reinforced polymer composites using deep neural network (DNN). Compos Struct 2022; 302: 116248.

45.

Shimamoto

Akiyama

. Estimating the mechanical residual strength from IR spectra using machine learning for degraded adhesives. J Adhes 2022; 98(15): 2423–2445.

46.

Ramalho

GMF

Lopes

Silva

LFM

. Structural health monitoring of adhesive joints using lamb waves: a review. Struct Contr. Hlth 2022; 29(1): e2849.

47.

Wang

Karimi

Zeinalzad

, et al. Using machine learning and experimental study to correlate and predict accelerated aging with natural aging of GFRP composites in hygrothermal conditions. Construct Build Mater 2024; 438: 137264.

48.

Machello

Bazli

Rajabipour

, et al. Using machine learning to predict the long-term performance of fibre-reinforced polymer structures: a state-of-the-art review. Construct Build Mater 2023; 408: 133692.

49.

Aghabalaei Baghaei

Hadigheh

. Durability assessment of FRP-to-concrete bonded connections under moisture condition using data-driven machine learning-based approaches. Compos Struct. 2021; 114576.

50.

Aghabalaei Baghaei

Hadigheh

. Artificial neural network prediction of transverse modulus in humid conditions for randomly distributed unidirectional fibre reinforced composites: a micromechanics approach. Compos Struct 2024; 337: 118073.

51.

Liu

Hughes

, et al. A parametric study of adhesive bonded joints with composite material using black-box and grey-box machine learning methods: deep neuron networks and genetic programming. Compos B Eng 2021; 217: 108894.

52.

Xiao

Tian

Xian

. Hydrothermal ageing of carbon fiber reinforced polymer Composites applied for construction: a review. J Mater Res Technol 2023; 27: 1017–1045.

53.

Nasibulin

Pikhitsa

Jiang

, et al. A novel hybrid carbon material. Nat Nanotechnol 2007; 2(3): 156–161. DOI: 10.1038/nnano.2007.37.

54.

Zamani

Alaei

Silva

LFM

, et al. On the static and fatigue life of nano-reinforced Al-GFRP bonded joints under different dispersion treatments. Fatig Fract Eng Mater Struct 2022; 45(4): 1088–10110.

55.

Mirderikvand

Shamlouei

. Novel nanobuds from C20 with C30, C40, C50, C60 and C70 fullerene: structural, electrical and optical properties and solvent effect. J Mol Liq 2023; 377: 121550.

56.

Azadi

Shamlouei

. DFT design of novel nano-bud from B12N12 and C60 fullerene. Diam Relat Mater 2023; 136: 109909.

57.

Yang

Wang

Huang

, et al. Effects of nanobuds and heat welded nanobuds chains on mechanical behavior of carbon nanotubes. Comput Mater Sci 2015; 109: 49–55.

58.

Kong

Khalil

Fricke

. Moisture absorption behavior and adhesion properties of GNP/epoxy nanocomposite adhesives. Polymers 2021; 13: 1850. DOI: 10.3390/polym13111850.

59.

Gamdani

Boukhili

Vadean

. Tensile strength of open-hole, pin- loaded and multi-bolted single-lap joints in woven composite plates. Mater Des 2015; 88: 702–712.

60.

Esmail

Alaei

Eskandarijam

, et al. Effect of presence of SWCNT and Fullerene nano particles in the adhesive of CFRP single lap joint on the lap shear strength subjected to hygrothermal conditions. J Adhes Sci Technol 2023; 37: 3013–3029.

61.

Breiman

. Random forests. Mach Learn 2001; 45: 5–32. DOI: 10.1023/A:1010933404324.

62.

Hoerl

Kennard

. Ridge regression: biased estimation for nonorthogonal problems. Technometrics 1970; 12(1): 55–67.

63.

Costa

Pedreira

. Recent advances in decision trees: an updated survey. Artif Intell Rev 2023; 56: 4765–4800. DOI: 10.1007/s10462-022-10275-5.

64.

Rumelhart

Hinton

Williams

. Learning representations by back-propagating errors. Nature 1986; 323: 533–536. DOI: 10.1038/323533a0.

65.

Smola

Schölkopf

. A tutorial on support vector regression. Stat Comput 2004; 14: 199–222. DOI: 10.1023/B:STCO.0000035301.49549.88.

66.

Friedman

. Greedy function approximation: a gradient boosting machine. Ann Stat 2001; 29(5): 1189–1232.

67.

Apalak

Engin

. Effect of adhesive free-end geometry on the initiation and propagation of damaged zones in adhesively bonded lap joints. J Adhes Sci Technol 2004; 18(5): 529–559.

68.

Apalak

Gunes

. Elastic flexural behaviour of an adhesively bonded single lap joint with functionally graded adherends. Mater Des 2007; 28(5): 1597–1617.

69.

Esmaeili

Razavi

Bayat

, et al. Flexural behavior of metallic fiber-reinforced adhesively bonded single lap joints. J Adhes 2018; 94(6): 453–472.

70.

Khoramishad

Alizadeh

da Silva

LFM

. Effect of multi-walled carbon nanotubes and silicon carbide nanoparticles on the deleterious influence of water absorption in adhesively bonded joints. J Adhes Sci Technol 2018; 32(16): 1795–1808.

71.

Jojibabu

Ram

Deshpande

, et al. Effect of carbon nano-filler addition on the degradation of epoxy adhesive joints subjected to hygrothermal aging. Polym Degrad Stabil 2017; 140(2017): 84–94.

72.

Gude

Prolongo

Urena

. Hygrothermal ageing of adhesive joints with nanoreinforced adhesives and different surface treatments of carbon fibre/epoxy substrates. Int J Adhesion Adhes 2013; 40: 179–187.

73.

Pramoda

Liu

. Effect of moisture on the dynamic mechanical relaxation of polyamide-6/clay nanocomposites. J Polym Sci B Polym Phys 2004; 42: 1823–1830. DOI: 10.1002/polb.20061.

74.

Starkova

Chandrasekaran

Prado

LASA

, et al. Hydrothermally resistant thermally reduced graphene oxide and multi-wall carbon nanotube based epoxy nanocomposites. Polym Degrad Stabil 2013; 98: 519–526.

75.

Kim

Lopez-Cruz

Heidari-Rarani

, et al. An experimental study on the mechanical behaviour of bonded and hybrid bonded- bolted composite joints using digital image correlation (DIC) technique. Compos Struct 2021; 276: 114544.

76.

Reza Borghei

Behjat

Yazdani

. The impact of graphene nanoparticle additives on the strength of simple and hybrid adhesively bonded joints. J Compos Mater 2019; 53(23): 3335–3346.

77.

Matsuzaki

Shibata

Todoroki

. Improving performance of GFRP/aluminum single lap joints using bolted/co-cured hybrid method. Compos Appl Sci Manuf 2008; 39: 154–163.

78.

Doğan

Bulut

Erkliğ

, et al. Mechanical and low velocity impact characterization of carbon/glass hybrid composites with graphene nanoplatelets. Mater Res Express 2019; 6: 085304. DOI: 10.1088/2053-1591/ab1c03.