基于物理和化学的热化学老化弹性体相场方法本构框架
Physics and chemistry-based constitutive framework for thermo-chemically aged elastomer using phase-field approach
AI总结：
本文提出一种基于物理和化学的本构框架，结合相场方法预测热化学老化弹性体的应力响应与脆性破坏，仅需四个材料属性并通过交联密度演化表征老化效应，经解析、有限元实现和实验验证表明其能准确预测老化弹性体力学行为。
摘要：
我们提出一个基于物理和化学的本构框架，用于预测热化学老化弹性体的应力响应，并利用相场方法捕捉其脆性破坏。在氧气存在下的高温老化会使弹性体的大分子网络发生复杂化学反应，从而引发两种主要机制：断链和交联。化学交联导致硬化行为，这是老化弹性体脆性响应的特征。在本工作中，我们首先修正亥姆霍兹自由能，以纳入热化学驱动的交联过程的影响。然后，我们为这一本构描述配备相场，通过基于应变的断裂准则来捕捉由此引发的脆性破坏。我们表明，所提出的框架是自洽的，并且只需要四个主要材料属性，这些属性因热化学老化而产生的演化完全由基于化学表征实验获得的交联密度变化来表征。所建立的本构框架首先在均匀杆单轴拉伸情形下进行解析求解，以揭示四个材料属性之间的相互联系。随后，该框架通过商业有限元软件Abaqus中的用户单元子程序（UEL）在有限元（FE）环境中进行数值实现，以模拟更复杂的几何形状和加载状态。最后，该框架针对文献中已有的一组实验结果进行了验证。对比结果证实，所提出的本构框架能够准确预测热化学老化弹性体的力学响应。文中还提供了进一步的数值算例，以展示演化中的材料属性对含有预存裂纹的试件响应的影响。
英文摘要：
We propose a physics and chemistry-based constitutive framework to predict the stress responses of thermo-chemically aged elastomers and capture their brittle failure using the phase-field approach. High-temperature aging in the presence of oxygen causes the macromolecular network of elastomers to undergo complex chemical reactions inducing two main mechanisms: chain-scission and crosslinking. Chemical crosslinking contributes to the stiffening behavior characterizing the brittle response of aged elastomers. In this work, we first modify the Helmholtz free energy to incorporate the effect of thermo-chemically-driven crosslinking processes. Then, we equip the constitutive description with phase-field to capture the induced brittle failure via a strain-based criterion for fracture. We show that our proposed framework is self-contained and requires only four main material properties whose evolution due to thermo-chemical aging is characterized entirely by the change of the crosslink density obtained based on chemical characterization experiments. The developed constitutive framework is first solved analytically for the case of uniaxial tension in a homogeneous bar to highlight the interconnection between all four material properties. Then, the framework is numerically implemented within a finite element (FE) context via a user-element subroutine (UEL) in the commercial FE software Abaqus to simulate more complicated geometries and loading states. The framework is finally validated with respect to a set of experimental results available in the literature. The comparison confirms that the proposed constitutive framework can accurately predict the mechanical response of thermo-chemically aged elastomers. Further numerical examples are provided to demonstrate the effects of evolving material properties on the response of specimens containing pre-existing cracks.
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