The main aim of the current study is to explore direction-dependent fracture initiation and propagation within an arbitrary anisotropic solid. In particular, the specific objective is to develop an anisotropic cohesive phase-field (PF) fracture model. In this model, weak and strong anisotropy is considered both in the strain energy and fracture energy. This is achieved by considering contributions to strain energy of fiber and matrix as in the case of fiber-reinforced composites (FRC) together with introducing anisotropy in fracture energy through higher-order structural tensors. Motivated from earlier works of Van den Bosch et al. (Eng Fract Mech 73:1220–1234, 2006), the PF fracture model is integrated with a coupled exponential cohesive zone law which considers both normal and tangential components of separation. Such a cohesive PF description has a strong micromechanical basis for fracture, requiring interface fracture toughness and ultimate traction in normal and tangential directions. \(C^0\) and \(C^1\) approximations are used for modeling the weak and strong anisotropy. Several numerical examples are presented to demonstrate the usefulness of the model developed herein. The obtained numerical results are validated with the experimental results from the literature. The anisotropic fracture resulting in either intergranular or transgranular failure of polycrystalline material is analyzed by adopting a coupled anisotropic phase field and cohesive zone approach.

当前研究的主要目的是探索任意各向异性固体内与方向相关的断裂萌生和扩展。特别是，具体目标是开发各向异性内聚相场（PF）断裂模型。在该模型中，应变能和断裂能均考虑了弱各向异性和强各向异性。这是通过考虑纤维和基体应变能的贡献（如纤维增强复合材料（FRC）的情况）以及通过高阶结构张量引入断裂能的各向异性来实现的。灵感来自 Van den Bosch 等人的早期作品。 (Eng Fract Mech 73:1220–1234, 2006)，PF 断裂模型与耦合指数内聚区定律相结合，该定律考虑了分离的法向分量和切向分量。这种内聚性 PF 描述具有强大的断裂微观力学基础，需要界面断裂韧性以及法向和切向方向的极限牵引力。\(C^0\)和\(C^1\)近似用于对弱和强各向异性进行建模。提出了几个数值示例来证明本文开发的模型的有用性。所得数值结果与文献中的实验结果进行了验证。采用耦合各向异性相场和内聚区方法分析导致多晶材料沿晶或穿晶失效的各向异性断裂。