Fracture prediction is indispensable for polymers, like rubbers, which have a broad range of applications mainly due to their high extensibility. The phenomenon known as strain-induced crystallization further contributes to the fracture toughness of certain rubbers. In this study, a criterion based on internal bond energy, incorporating the effects of crystallization, is proposed to predict fracture initiation in rubber-like materials with pre-existing cracks. First, a multi-scale mechanical model is developed for characterizing the behavior of rubber when subjected to both uniaxial and biaxial deformation states. At the microscale, both the amorphous and crystalline chain segments are modeled as elastic in order to consider the energy contribution by the molecular bond distortions. This internal energy is considered along with the entropic and crystalline free energy for each chain. In the chain model, the effects of loading condition and the relative orientation of a chain on its crystallinity are taken into account. At the macroscopic scale, an existing crystallinity distribution function is adapted and a mixed finite element formulation with an augmented Lagrangian multiplier is utilized to impose the incompressibility constraint. A non-affine maximal advance path constraint based homogenization model is utilized for bridging the two scales. Its potential to account for anisotropy in the stretched network compels the model to be preferable due to its physical significance, for the purpose of fracture modeling. The rigidity of the crystallites is accounted for by proposing a crystallite distortion energy in addition to the critical bond dissociation energy, for fracture initiation to occur. The model is validated by comparison with existing experimental results for both crystallizing and non-crystallizing rubbers. In addition to its potential to predict the material behavior when subjected to uniaxial and biaxial loading, the capability of the model to quantitatively estimate the effect of crystallization on fracture initiation is also verified.

断裂预测对于像橡胶这样的聚合物来说是必不可少的，因为它们具有广泛的应用范围，这主要是由于它们的高延展性。称为应变诱导结晶的现象进一步有助于某些橡胶的断裂韧性。在这项研究中，提出了一种基于内部键能的标准，结合了结晶的影响，用于预测具有预先存在裂纹的类橡胶材料的断裂起始。首先，开发了一种多尺度力学模型，用于表征橡胶在单轴和双轴变形状态下的行为。在微观尺度上，无定形和结晶链段都被建模为弹性的，以考虑分子键扭曲对能量的贡献。这种内能与每条链的熵和晶体自由能一起考虑。在链模型中，考虑了加载条件和链的相对取向对其结晶度的影响。在宏观尺度上，采用现有的结晶度分布函数，并利用具有增广拉格朗日乘子的混合有限元公式来施加不可压缩约束。基于非仿射最大前进路径约束的同质化模型用于桥接两个尺度。考虑到拉伸网络中的各向异性的潜力，由于其物理意义，模型更适合用于裂缝建模。除了临界键离解能之外，还通过提出微晶畸变能来解释微晶的刚性，用于发生断裂。该模型通过与结晶和非结晶橡胶的现有实验结果进行比较来验证。除了在单轴和双轴载荷下预测材料行为的潜力之外，该模型还验证了定量估计结晶对断裂起始影响的能力。