【作者】 李勇；

【导师】 杜星文；

【作者基本信息】 哈尔滨工业大学 ， 工程力学， 2006， 博士

【摘要】 银纹化是玻璃态高聚物所特有的一种现象。聚合物的银纹损伤是一个复杂的多层次阶段,从微观层次的分子链间缠结链段的重排、滑移、取向、解缠及断链,到细观层次的银纹引发,生长及断裂,直到后继的微裂纹的产生、扩展、串接最终导致材料整体破坏。银纹能够承载一定的拉应力;银纹化高聚物的力学性能是银纹损伤和银纹增韧两方面竞争的结果,这说明银纹化高聚物损伤的模型不同于一般的损伤材料,应该反映它所特有的损伤机理。在标准线性固体模型的基础上,通过引进率相关弹簧和作者已建立的非线性Bingham流体模型,建立了小变形条件下的高聚物一维非线性粘弹模型;并根据对应原理,将此模型推广到各向同性材料中,建立了三维非线性粘弹模型。其次,根据Noll三原则、功共轭原理、真应力原则,选择Updated Lagrange坐标系以及第二类P-K应力张量和Green应变张量,将小变形条件下的三维粘弹性本构进行推广,建立了Euler坐标系下的有限变形条件下的三维粘弹性模型。最后,根据非平衡态热力学及其内变量理论,建立了一维有限变形粘弹性模型。首次引入分形理论对高聚物的银纹损伤进行研究。首先,根据银纹的特点阐述了其分形维数的区间为[0 , 2)。银纹的分形维数不仅表征了高聚物的空穴化程度而且表征了材料的微纤化水平。其次,在利用分形维数建立的损伤变量和韧化函数的基础上,定义了一个全新的概念:银纹变量。它可以表征银纹损伤和银纹增韧对材料的共同作用。在有限变形条件下,通过面积转换,定义了新的分形维数计算方法,建立了有限变形条件下的银纹变量。新的银纹变量能够更加客观的刻画材料的损伤程度,因为它有效地剔除有限变形过程中弹性变形和塑性变形对银纹分形维数的影响。最后,利用已建立的银纹变量,根据Kachanov-Rabotnov的有效应力理论,建立了银纹化高聚物在小变形条件和有限变形条件下的一维和三维的分形损伤模型。利用分形维数对银纹进行了定量化分析。通过蠕变试验,采集了PMMA在不同应力和不同时间的蠕变银纹图像,并采用盒维法计算了其分形维数。试验证明,蠕变银纹引发的应力阀值随时间的增长呈指数关系降低,并最终趋于常数;蠕变银纹的分形维数与应力呈线性关系,与时间呈指数关系;在达到应力阀值的瞬间,能产生大量银纹,导致银纹的分形维数产生阶跃。根据实验结果,建立了蠕变银纹的分形维数与应力、时间的关系式。更多还原

【Abstract】 The crazing phenomenon is unique to amorphous glassy polymers. The crazing damage evolves in three different levels: the orientating, untwisting and breaking of macromolecular chains in microscopic state; the initiation, growth and breakdown of crazes in mesoscopic layer; the formation, expansion and rupture of mesocracks in macroscopic view. A craze can sustain a definite amount of tensile stress and the mechanical properties of crazing polymers are the competitive result between crazing damage and toughening, which means the damage model of crazing polymers should be distinguished from other materials due to their particular damage mechanism.Based on the standard linear solid model, a one-dimensional nonlinear viscoelastic model of polymers for small deformation is set up to describe strain- rate-dependency elasticity and nonlinear viscosity. The corresponding three- dimensional model is developed by generalizing the one-dimensional nonlinear viscoelastic model according to the correspondence principle.The former construction serves as a starting point for the development of a three-dimensional, finite deformation, viscoelastic constitutive model. So the Updated Lagrange coordinate system and the second Piola-Kirchhoff stress tensor/the Green strain tensor are selected to extend small-strain model on the base of the Noll principles, the work conjugation theory and the true stress principle. A one-dimensional, finite strain, viscoelastic constitutive model is proposed according to the nonequilibrium thermodynamics and its internal variable theory.The fractal theory is introduced to study crazes for the first time. Firstly, it is proved that the interval of fractal dimension of crazes is [0 , 2). The fractal dimension represents the fiberizing degree and the cavitating level of polymers. Secondly, a new concept—crazing variable is defined base on the damage variable and the toughening equation set up by the fractal dimension of crazes, which allows the two important properties of crazing: damage and toughening. The finite-strain crazing variable is proposed by use of the new computing method of fractal dimension modified by area transformation under the condition更多还原