碳纤维增强形状记忆聚合物复合材料的热-力学行为建模与影响因素碳纤维增强形状记忆聚合物复合材料的热-力学行为建模与影响因素
Modeling and influence factors of the thermo-mechanical behaviors of the carbon fiber reinforced shape memory polymer composites

采用变形梯度分解的方法，基于热力学内变量理论，构建了适用于描述碳纤维增强形状记忆聚合物（CF/SMP）复合材料热-力学行为的热黏弹性本构模型。模型中考虑了材料的结构松弛效应和应力松弛效应，且适用于有限变形条件。依据该模型研究了一种CF/SMP薄板在受到单向均布载荷作用且处于平面应力状态时的碳纤维有效应变影响因素。理论上证实了虽然碳纤维的容许应变很小，但合理取向的纤维分布形式能使其应用于有限变形条件下而不被破坏。此外，分析了该CF/SMP形状记忆热-力学循环过程中形状记忆效应（SME）的影响因素。结果表明，碳纤维含量的增大和纤维倾斜角的减小会导致CF/SMP刚度增大，从而降低其形状固定率。此外，碳纤维体积含量和温度变化率对升温回复阶段也存在一定影响。上述研究方法和结果能对单向连续CF/SMP的设计与应用提供一定理论指导。 The method of decomposition of deformation gradient and thermodynamics with internal state variables were used to describe the thermo-mechanical behavior of the carbon fiber reinforced shape memory polymer (CF/SMP) composite. A thermo-viscoelastic constitutive model incorporated with stress and structural relaxation was developed in the work. The model can be applied to the finite deformation condition. In the simulation, the CF/SMP lamina was under the unidirectional stress and in the condition of plane stress state. The influence factors of carbon effective strain of the lamina were studied based on the constitutive model. It is proved that the properly ranged carbon fiber can be used in the CF/SMP under the condition of finite deformation condition, though the tolerant strain of the carbon fiber is rather small. In addition, the influence factors of the shape memory effect (SME) of the CF/SMP during a typical thermo-mechanical shape memory cycle were studied here. It is demonstrated that the CF/SMP with the higher volume fraction and smaller inclination angle has the higher stiffness which will result in the lower shape ratio. In addition, the carbon fiber volume fraction and heating rate may also have effect on the recovery process. The research in the paper could provide a basis for design and application of the CF/SMP in engineering. 国家自然科学基金（11572153）；江苏省自然科学基金（BK20170759；BK20151467）；南京工程学院科研基金（ZKJ201603）；江苏高校优秀科技创新团