CONSTITUTIVE MODELLING OF SILICONE ADHESIVE CONSIDERING MULLINS EFFECT
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摘要:硅酮结构胶广泛应用于建筑玻璃幕墙的粘接, 准确掌握其力学行为是实现可靠粘接的保证. 目前常用的唯象超弹性模型忽视了材料微观结构特性, 无法描述本构行为机理; 经典的熵弹性模型往往缺乏对聚合物网络非仿射变形、缠结效应等特性的考虑. 上述不足导致了已有模型难以有效模拟硅酮胶的力学行为, 尤其是循环加载下的显著Mullins效应. 为此, 文章基于非仿射网络模型, 根据分子链分布的微球模型对宏观−微观变形转换关系进行修正, 将受载下分子链构象的演化扩展至有限个方向. 在此基础上, 基于网络演化理论提出抽象交联网络和缠结网络的演化函数描述循环加载下聚合物网络的演化过程, 以模拟Mullins效应. 文章构建的修正非仿射网络模型结合了硅酮胶的微观结构特性和变形机制, 可以描述聚合物网络非仿射变形、缠结约束效应、分子链的有限拉伸性以及空间分布特性. 与文献硅酮胶材性试验数据和其他本构模型预测结果的对比表明, 修正非仿射网络模型可有效地模拟硅酮胶多种变形模式下的力学行为, 且可描述Mullins效应的残余变形和模量退化现象, 对硅酮胶的设计计算具有参考意义.Abstract:Silicone adhesive has been widely used in assembly glass curtain walls. To achieve a reliable bonding system, an effective description of material behavior is required. However, commonly used phenomenological hyperelastic models have not considered the microstructure properties of materials and cannot describe the mechanisms of their mechanical behaviors, while the classical entropic hyperelastic models often do not consider the non-affine deformation, entanglement effect or other features of polymer network. The above deficiencies make it difficult for the existing models to effectively simulate the mechanical behavior of silicone adhesive, especially the significant Mullins effect under cyclic loading. For these reasons, in this paper, based on the non-affine network model and microsphere model of polymer chain distribution, we modified the macro-micro deformation transformation and the evolution of chain conformation to consider spatial distribution of polymer chains in finite directions. Based on the modified model, network alteration functions are proposed for crosslinked and entangled network respectively using network alteration theory. These functions describe the evolution of polymer network under cyclic loading to model Mullins effect. Considering the microstructure properties and deformation mechanisms of silicone adhesive, the modified non-affine network model can describe the characteristics of polymer network, including non-affine deformation, entanglement effect, finite chain extensibility and spatial chain distribution. The comparisons with the experimental data and other model results demonstrate the capability of the modified model to accurately predict the mechanical behavior of silicone adhesive under various loading conditions, as well as the permanent set and modulus degradation of Mullins effect, which shows good potential in engineering applications.
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Parameter Definition Expression ${G_c}$ crosslink modulus $nkT{g^2}\left( {1 - {2 \mathord{\left/ {\vphantom {2 u}} \right. } u}} \right)$ ${G_e}$ entanglement modulus ${ { {n_e}kT} }/{2}$ ${\lambda _{{\rm{max}}} }$ finite chain extensibility $\dfrac{1}{g}\sqrt {\dfrac{N}{ {1 - {2 \mathord{\left/ {\vphantom {2 u} } \right. } u} } } }$ $n$ chain density of crosslink network $k$ Boltzmann’s constant $T$ temperature $g$ affine/non-affine deformation parameter $u$ crosslink functionality, i.e. the number of chains connected at a crosslink ${n_e}$ chain density of entanglement network 
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Test Specimen/mm Loading conditions/(mm·min−1) uniaxial tension (UT) 
R.T. 5 uniaxial compression (UC) 
R.T. 0.174 simple shear (SS) 
R.T. 0.21 cyclic uniaxial tension (CUT) 
R.T. 3.75 下载:
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表 3单调加载模型参数
Table 3.Parameters for monotonic loading
Parameter Definition Fitting result/MPa $G_0^c$ initial crosslink modulus 1.38 $G_0^e$ entanglement modulus 0.20 下载:
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表 5循环加载模型参数
Table 5.Parameters for cyclic loading
Parameter Definition Fitting result $\varLambda_{m,\max }^0$ nominal maximum chain stretch 2.05 ${a_c}$ crosslink network alteration parameter 0.47 ${a_e}$ entanglement network alteration parameter 1.22 下载:
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