The phase-field approach has proven to be a powerful tool for the prediction of crack phenomena. When it is applied to inelastic materials, it is crucial to adequately account for the coupling between dissipative mechanisms present in the bulk and fracture. In this contribution, we propose a unified phase-field model for fracture of viscoelastic materials. The formulation is characterized by the pseudo-energy functional which consists of free energy and dissipation due to fracture. The free energy includes a contribution which is related to viscous dissipation that plays an essential role in coupling the phase-field and the viscous internal variables. The governing equations for the phase-field and the viscous internal variables are deduced in a consistent thermodynamic manner from the pseudo-energy functional. The resulting model establishes a two-way coupling between crack phase-field and relaxation mechanisms, i.e. viscous internal variables explicitly enter the evolution of phase-field and vice versa. Depending on the specific choice of the model parameters, it has flexibility in capturing the possible coupled responses, and the approaches of recently published formulations are obtained as limiting cases. By means of a numerical study of monotonically increasing load, creep and relaxation phenomena, rate-dependency of failure in viscoelastic materials is analysed and modelling assumptions of the present formulation are discussed.

相场方法已被证明是预测裂纹现象的有力工具。当它应用于非弹性材料时，充分考虑本体和断裂中存在的耗散机制之间的耦合是至关重要的。在这一贡献中，我们提出了一种用于粘弹性材料断裂的统一相场模型。该公式的特点是伪能量泛函，它由自由能和断裂引起的耗散组成。自由能包括与粘性耗散相关的贡献，粘性耗散在耦合相场和粘性内部变量中起重要作用。相场和粘性内部变量的控制方程以一致的热力学方式从伪能量泛函推导出来。结果模型建立了一个裂纹相场和松弛机制之间的双向耦合，即粘性内部变量明确地进入相场的演化，反之亦然。根据模型参数的特定选择，它在捕获可能的耦合响应方面具有灵活性，并且最近发布的公式的方法是作为限制情况获得的。通过对单调增加的载荷、蠕变和松弛现象的数值研究，分析了粘弹性材料的破坏率依赖性，并讨论了当前公式的建模假设。