In this study, a finite deformation phase-field formulation is developed to investigate the effect of hygrothermal conditions on the viscoelastic-viscoplastic fracture behavior of epoxy nanocomposites under cyclic loading. The formulation incorporates a definition of the Helmholtz free energy, which considers the effect of nanoparticles, moisture content, and temperature. The free energy is additively decomposed into a deviatoric equilibrium, a deviatoric non-equilibrium, and a volumetric contribution, with distinct definitions for tension and compression. The proposed derivation offers a realistic modeling of damage and viscoplasticity mechanisms in the nanocomposites by coupling the phase-field damage model with a modified crack driving force and a viscoelastic-viscoplastic model. Numerical simulations are conducted to study the cyclic force-displacement response of both dry and saturated boehmite nanoparticle (BNP)/epoxy samples, considering BNP contents and temperature. Comparing numerical results with experimental data shows good agreement at various BNP contents. In addition, the predictive capability of the phase-field model is evaluated through simulations of single-edge notched nanocomposite plates subjected to monolithic tensile and shear loading.

翻译：本研究建立了一种有限变形相场公式，用于探究湿热条件对循环载荷下环氧纳米复合材料粘弹性-粘塑性断裂行为的影响。该公式引入了亥姆霍兹自由能的定义，其中考虑了纳米颗粒、水分含量和温度的影响。自由能被加性分解为偏斜平衡部分、偏斜非平衡部分和体积贡献部分，并对拉伸和压缩状态分别进行了定义。通过将相场损伤模型与修正的裂纹驱动力及粘弹性-粘塑性模型耦合，所提出的推导为纳米复合材料的损伤与粘塑性机制提供了真实建模。通过数值模拟，研究了干燥与饱和勃姆石纳米颗粒（BNP）/环氧树脂试样的循环力-位移响应，并考虑了BNP含量和温度的影响。将数值结果与实验数据对比，发现不同BNP含量下均表现出良好的一致性。此外，通过模拟受单调拉伸和剪切载荷的单边缺口纳米复合材料板，评估了相场模型的预测能力。