Abstract
This study conducts an in-depth numerical analysis of debonding behavior in composite structures, with a particular focus on the critical role of thermal effects. Utilizing a frictional contact cohesive zone model, the research characterizes the debonding process while sequentially integrating thermal analysis to assess the impact of thermal loading. A thermomechanical coupled model is developed and implemented using the finite element software ABAQUS. The model's accuracy is validated through the Double Cantilever Beam (DCB) test, ensuring reliable results. The methodology involves a detailed finite element analysis, where thermal loads are applied to composite specimens, followed by mechanical loading to simulate debonding. The frictional contact cohesive zone model accurately captures the interface behavior under varying thermal conditions. Quantitative results indicate that thermal loading significantly affects the debonding process, with a noticeable increase in debonding initiation and propagation rates, highlighting the critical influence of thermal effects on structural integrity.
1 Introduction
Composite structures are used in many engineering applications due to their excellent strength to weight characteristics, as well as their ability to tailor properties to the requirements of complex applications. Nonetheless, they are susceptible to various phenomena arising from repeated loading, impact, or harsh environmental conditions, potentially resulting in diverse responses, such as structural damage [1]. One of the most complex types of damage is debonding, characterized by the separation between two contacting layers. Stress transmission from one ply to another occurs through a contact surface known as the interface. This surface represents the critical zone where failure is often evident [2]. A fundamental understanding of interface debonding is essential for designing composite structures capable of enduring diverse operational conditions. Therefore, numerous studies focusing on debonding behavior, including review research, have been conducted [3–7]. Recently, many researchers have investigated this issue, such as mixed-mode debonding in carbon fiber–reinforced polymer [8], quasi-brittle interfacial cracking [9], fiber–matrix debonding [10], and concrete-rock interface debonding [11].
In addition, various factors have been found to influence the debonding behavior of composite structures. Moradi et al. [12] studied the effects of using fuzzy fiber-reinforced composite skins on the flexural behavior of sandwich structures. Wang et al. [13] investigated the impact velocity on the interfacial debonding of laminated composites. On the other hand, thermal effects were also considered. Rabinovitch [14] studied the impact of thermal loads on the debonding mechanisms in beams strengthened with externally bonded composite materials. Gao et al. [15] examined the effect of temperature changes on Mode II debonding. Wang et al. [16] analytically studied the thermal effects on the debonding of concrete/steel structures. Klamer et al. [17] experimentally studied the influence of temperature on the bonding capacity of fiber-reinforced polymers. Zeinedini and Mahdi [18] developed an analytical model to estimate the influence of temperature on the debonding stress of spherical nanoparticle-reinforced nanocomposites. Zhou et al. [19] investigated the debonding behavior of the fiber-reinforced polymer-to-concrete interface between two adjacent cracks under combined thermal and mechanical loadings. Recently, the influence of temperature on interface debonding has been addressed in [20–22].
Additionally, friction between debonded surfaces also plays a significant role in debonding behavior. Guiamatsia and Nguyen [23] developed a constitutive model for interface debonding that accounts for mixed-mode coupled debonding and friction, including post-delamination friction. Sitler et al. [24] experimentally investigated the friction behavior of mortar–polymer–steel debonding interfaces. Hu et al. [25] developed an adhesion recoverability degradation model that includes the effect of friction. Peng et al. [26] studied the failure analysis of a frictional adhesive interface.
On the other hand, there has been limited progress in studying the thermal effect on the debonding process while accounting for friction at the interface, with a few exceptions, such as the work of Benchekkour et al. [27], where delamination behavior between an elastic body and a rigid support was investigated. Song et al. [28] studied the effect of temperature and the type of underlying layer on bonding.
To investigate the thermal effect on debonding behavior while considering friction at the interface, numerical methods offer a viable alternative. This is because multiphysics conditions can be conveniently incorporated into a numerical model. Various numerical approaches have been proposed for simulating interfacial debonding. Among the range of numerical approaches available for simulating interfacial debonding, the cohesive zone model stands out as particularly robust and widely adopted for addressing such challenges [29].
The novelty of this work lies in simulating the debonding behavior using a frictional contact cohesive zone model in composite structures, specifically with the Double Cantilever Beam (DCB) test. A sequentially steady-state thermomechanical model is employed with the finite element software ABAQUS to comprehend the structural behavior subjected to thermal loading. The objective of the present work is to perform a comprehensive numerical study of the thermal effect on the initiation and evolution of debonding growth.
2 Numerical model
The accurate simulation of interfacial debonding necessitates the adoption of a suitable approach. Among the numerous methods available, the cohesive zone model (CZM), pioneered by Barenblatt [30] and Dugdale [31], has proved useful in analyzing interface problems. This model excels in its ability to integrate diverse conditions such as contact, friction, and thermal effects [29], making it a valuable tool for comprehensive analysis. Thus, in this study, the incorporation of a contact element into the composite structures' interfaces facilitates the simulation of debonding behavior. However, this process involves coupled multi-field coupling, introducing high complexity. To address this, a comprehensive friction and cohesive coupled model, incorporating thermal effects, is elaborated upon.
2.1 Friction and cohesive coupled model
The friction and cohesive coupled model represent a sophisticated computational tool within the domain of nonlinear fracture mechanics for investigating the intricate behavior of structures and materials under various conditions. It combines two important aspects: friction and cohesion. These models provide a powerful approach for interface damage modeling because they show a continuous transition process from cohesive softening to pure frictional contact.
Frictional contact behavior modeling
Cohesive behavior modeling
The vector of nominal traction,
Following damage initiation, the model can simulate debonding growth due to local failure, capturing the progressive separation at the interface. Several forms of traction-separation laws exist, including bilinear, trapezoidal, and exponential configurations (Fig. 1). The specific choice of a law depends on the problem to be solved, such as the type of materials involved and the failure mechanism.
The forms of the traction-separation laws. ‘Own source’
Citation: International Review of Applied Sciences and Engineering 2025; 10.1556/1848.2024.00871
The notation δ represents the displacement or separation across the interface, which is crucial in characterizing how the material separates under load and indicates the degree of interface opening during damage progression. δc refers to the critical separation, beyond which complete debonding occurs. It represents the maximum displacement tolerated before the interface fully fails. Additionally, δ1 and δ2 represent specific points on the separation curve, typically corresponding to different stages in damage progression or to transitions in the form of the separation law, such as in bilinear or trapezoidal models.
On the other hand, σ denotes the traction or stress at the interface, which describes the material's resistance to separation before failure. The specific form of the σ-δ relationship depends on the chosen traction-separation law. σc represents the critical traction, the maximum stress the interface can endure before debonding begins. Beyond this point, the traction typically decreases as the interface continues to separate.
2.2 Thermomechanical coupling
The resolution of this coupled model is typically carried out using numerical methods, primarily through finite element simulation software such as ABAQUS. In this study, sequential coupling is addressed, where thermal and mechanical problems are solved separately in successive steps. First, the temperature distribution is calculated, and then it is used to solve the mechanical equations. This process is repeated iteratively to achieve convergence as shown in Fig. 2.
Scheme of the thermomechanical analysis carried out in ABAQUS. ‘Own source’
Citation: International Review of Applied Sciences and Engineering 2025; 10.1556/1848.2024.00871
3 Numerical simulation
This paper delves into the 2D modeling of a DCB-type test, focusing on a two-layer 6061-T6 aluminum beam. The material properties include a Young's modulus E = 70,000 MPa, a Poisson's ratio ν = 0.3, a thermal conductivity λ = 230 W m−1·K, and a coefficient of thermal expansion αth = 23 × 10−6/K. Notably, the beam exhibits pre-cracking at the interface. Initially, the two layers of the beam adhere together. Subsequently, the beam undergoes an incremental vertical displacement δ = 50 mm over 1 s at its end. For clarity, the dimensions and boundary conditions of the test are illustrated in Fig. 3.
DCB model: geometry and boundary conditions. ‘Own source’
Citation: International Review of Applied Sciences and Engineering 2025; 10.1556/1848.2024.00871
The interface properties are presented in Table 1. The ABAQUS software was used in this test as simulation tool. A steady-state thermal analysis is conducted, employing a node-to-surface technique for contact interaction. A linear quadrilateral element (CPE4R) is utilized for the mesh, employing plane deformation. The interface comprises 70 nodes (Fig. 4). The calculation was conducted for 200 steps.
Interface properties. ‘Own source’
Properties | The decohesion energy w (mJ mm−2) | The maximal cohesive stress σcohmax (MPa) | The initial stiffness of the interface Knn, Ktt (MPa mm−1) | Friction coefficient μ |
Interface | 1E-6 | 0.0001 | 1.E+4 | 0.2 |
Deformed mesh. ‘Own source’
Citation: International Review of Applied Sciences and Engineering 2025; 10.1556/1848.2024.00871
4 Results and discussion
This section investigates the thermal effects on the debonding behavior of composite structures. The thermal boundary conditions employed align closely with those discussed in [27].
Figure 5 presents a comparative analysis of the distribution of normal stresses and debonding at the interface, both with and without thermal effects (with Tsup = 100°C), across three incremental cases. The influence of thermal effects on the stress distribution is readily apparent. Thermal stresses lead to a decrease in cohesive stresses, consequently inducing significant debonding compared to the scenario without thermal effects. This discrepancy in stress distribution underscores the considerable influence of thermal variations on interface behavior, emphasizing the necessity of considering thermal effects in comprehensive system analysis [27], [32–34].
The distribution of normal stresses and normal displacements at the interface, without and with thermal effect for three-time steps. ‘Own source’
Citation: International Review of Applied Sciences and Engineering 2025; 10.1556/1848.2024.00871
For further details, the analysis of thermal effects is deepened at a specific point (A), as illustrated in Fig. 6, by considering four distinct cases of thermal boundary conditions. The examination of the curves depicting the evolution of normal displacements over time at point (A) (Fig. 6) provides valuable insights into the impact of a thermal field.
Evolution of normal displacement over time at point (A), without and with the thermal effect. ‘Own source’
Citation: International Review of Applied Sciences and Engineering 2025; 10.1556/1848.2024.00871
The results indicate that temperature variations on the upper layer of the structure directly affect the normal displacements at point (A). Testing was conducted at different temperatures (25, 50, 75, and 100 °C), revealing distinct and pronounced trends. It is noteworthy that the debonding evolves proportionally with the increase in the temperature gradient, highlighting the significant impact of the thermal field on the composite structure behavior.
Also plotted in Fig. 7 is the evolution of the normal stresses
Evolution of normal stresses at point A as a function of debonding, with and without thermal effects. ‘Own source’
Citation: International Review of Applied Sciences and Engineering 2025; 10.1556/1848.2024.00871
In the context of complete debonding, when debonding reaches its full phase, the cohesive stresses converge to zero, resulting in the classic Signorini problem. It is observed that increasing the temperature gradient accelerates the debonding process.
Table 2 presents the values of key parameters of the cohesive model, as explained in Fig. 6, for the thermal effect on the debonding process. These parameters represent the maximum normal stress and the total energy dissipated. It is notable that the presence of a thermal field influences the debonding process, particularly in the presence of a temperature gradient. Conversely, an increase in the temperature gradient causes a delay in the onset of cracking and greater energy dissipation during debonding.
Evolution of debonding process parameters in the presence of a thermal field. ‘Own source’
The total energy dissipated wtot (mJ mm−2) | Maximum normal stress σntotalmax (MPa) | |
Without thermal effect | 209.81047 | 172.545 |
With thermal effect (Tsup = 25 °C) | 1256.428 | 208.647 |
With thermal effect (Tsup = 50 °C) | 1095.64918 | 206.229 |
With thermal effect (Tsup = 75 °C) | 1256.45056 | 208.642 |
With thermal effect (Tsup = 100 °C) | 1414.53466 | 208.729 |
5 Conclusion
In this study, a numerical analysis using a double cantilever beam test was employed to investigate the debonding behavior of composite structure interfaces, treating debonding as interface damage. A frictional cohesive zone model with a sequentially thermomechanical coupling scheme was utilized. Various thermal boundary conditions were considered to assess the thermal effect. The following main conclusions were drawn:
The cohesive stresses at the interface decreased by approximately 20–30% as thermal stress increased, leading to a 15% higher debonding rate compared to scenarios without thermal effects.
Temperature variations in the upper layer of the structure have a direct impact on the normal displacements at the crack tip, with the extent of debonding increasing proportionally to the rise in the temperature gradient.
While the presence of a thermal field exhibited less than a 5% variation in the interface's elastic properties, it significantly delayed debonding initiation by approximately 10% and increased the propagation rate by 25% when compared to the condition without thermal effects.
A temperature gradient increase led to a 40% delay in the debonding process, emphasizing the significant influence of thermal conditions on composite interface failure.
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