## 1 Introduction  
Composite materials play a crucial role in aerospace applications due to their exceptional strength-to-weight ratio, corrosion resistance, and design flexibility. They are extensively used in aircraft structures, such as wings and fuselages, to reduce weight, improve fuel efficiency, and enhance performance. However, one of the significant challenges associated with composite materials in aerospace is the occurrence of delamination. Delamination refers to the separation of layers within a composite laminate, which can weaken the structure and compromise its integrity. Investigating the problem of delamination is essential because often this type of damage is not visible and can propagate under service loads leading to catastrophic failures, especially in critical components subjected to high mechanical loads and environmental stresses [1]. Understanding the mechanisms and factors influencing delamination is crucial for developing effective preventive measures and design guidelines to ensure the safety and reliability of composite structures in aerospace applications. By addressing the issue of delamination, aerospace engineers can optimize composite material performance, extend component lifespan, and enhance overall aircraft safety [2, 3]. Unlike traditional homogeneous materials, composite materials exhibit non-linear fracture behavior due to their heterogeneous microstructure and complex damage mechanisms. Delamination propagation is influenced by mechanisms such as fiber bridging, matrix toughening, and fiber pull-out, which contribute to energy dissipation and crack deviation, thus enhancing the material's resistance to fracture and playing a crucial role in determining the fracture behavior and overall durability of composite structures [4]. Fiber bridging represents the main toughening mechanism, it occurs when reinforcing fibers bridge across the delaminated interface, effectively resisting crack propagation, and enhancing the material's fracture toughness, the energy needed to advance a pre-existing delamination within a composite laminate [5; 6; 7]. The R-curve refers to the resistance curve, representing the relationship between crack extension and fracture toughness. The R-curve effect indicates that as the crack propagates, the fracture toughness increases until it reaches a steady-state value, reflecting the material's ability to resist crack growth [8]. Understanding and characterizing the R-curve behavior is essential for predicting the structural integrity and failure behavior of composite materials under various loading conditions, facilitating the design of robust and reliable composite structures for aerospace applications. The standard experimental tests used to determine the fracture toughness for composite materials are intended for delamination propagation in unidirectional specimens, where the fiber bridging and the R-curve effect is often negligible [9; 10]. However, in real structural applications, delamination often occurs between plies oriented at different angles, resulting in a range of damage mechanisms, mainly fiber bridging, that contribute to an increase in fracture toughness as the delamination advances [11; 12]. Several works can be found in the literature that address the R-curve effect on the delamination propagation both numerically and experimentally. In [13; 14; 15] researchers experimentally studied the effect of the fiber orientation at the interface on the delamination propagation in standard Double cantilever Beam (DCB), End-Notched Flexure (ENF), and Mixed-Mode Bending (MMB) specimens, achieving consistent values of the fracture toughness at the onset, while significantly different R-curve behavior, with large increases in the fracture toughness as the delamination advances.