features are considered explicitly, allow accurate predictions to be made without the need for complex material models. Two widely used numerical techniques for modelling crack initiation and propagation in small-scale brittle or semi-brittle materials are the phase-field fracture method (PFM) [1; 2] and the cohesive zone model (CZM) [3; 4; 5]. Two PFM approaches are widely used to simulate crack initiation and propagation in brittle or semi-brittle materials, namely, the standard phase-field fracture model (SPFM) [1; 2] and the cohesive phase-field fracture model (CPFM) [6; 7]. The main difference between SPFM and CPFM lies in the consideration of the length scale parameter, which determines the thickness of the diffused crack region. In SPFM, the length scale parameter is inherently dependent on the fracture toughness of the material. This dependence can lead to challenges in the accurate modeling of crack propagation, especially in materials with considerable heterogeneity [8; 9; 10; 11]. In contrast, CPFM decouples the length scale parameter from the material properties, making it more suitable for small-scale simulations. In CPFM, crack propagation is controlled by a traction-separation law embedded in the phase-field, which enables the modelling of cohesive cracking and debonding phenomena without predefined fracture zones [12]. This makes CPFM particularly advantageous for the simulation of fractures in composite materials with interfaces. CZM is widely used to simulate fracture in brittle and semi-brittle materials, especially those with significant heterogeneity. CZM is divided into two categories: intrinsic and extrinsic approaches [13; 14]. The extrinsic method dynamically introduces CIEs during simulation, while the intrinsic method embeds CIEs in the material prior to simulation, making it effective for modelling weak interfaces. Interested readers are referred to [15; 16; 17; 18; 19; 20; 21; 22; 23; 24] for further practical applications of CZM. In this work, the intrinsic approach is used to define weak interfaces. Despite its effectiveness, the intrinsic CZM requires predefined fracture zones, which can be challenging for multiphase microstructures due to the complexity of implementation and computational cost. Recently, PFM has gained popularity in the simulation of crack initiation and propagation in multiphase materials with a interface phase. These simulations consider both matrix cracking and interface debonding. Based on how the interface is treated, two main approaches can be identified. In the first, the interface is approximated with a finite width and its failure is modelled using an auxiliary phase-field parameter [25; 26; 27; 28; 29; 30]. Here, the interface fracture energy is derived from CZM or mathematical approximations taking into account other phases. In the second approach, the interface is assumed to have zero thickness, and CIEs are used to simulate debonding [41; 42; 43; 44; 45; 46; 47]. This method avoids approximating the interface width, but requires the fracture zone to be identified in advance. Figure 1 gives an overview of these fracture approaches. Small-scale simulations face two main challenges: they are computationally expensive, especially for multiphase materials, and the simulation of crack initiation and propagation adds complexity that further increases the computational burden. This challenge is particularly significant in the FE2 approach, where performing small-scale simulations at each  
Figure 1: Application of finite element methods for simulating fracture in heterogeneous materials: The hybrid fracture approach integrates CZM for interface debonding and PFM for matrix cracking. integration point in macroscale models is very resource intensive. Given these obstacles, it is crucial to choose a numerical approach that minimises complexity while reducing computational cost.