【作者】 唐俊；

【导师】 聂昕；

【作者基本信息】 湖南大学 ， 机械工程， 2021， 硕士

【摘要】 随着时代进步和对材料需求的增加,新材料技术得到快速发展,其中复合材料具有优异的综合力学性能,受到广大学者和工程师的青睐。然而,在复合材料的结构设计和制造工艺过程中,充斥着各种各样的不确定性因素,这些不确定性因素对复合材料的力学性能有显著影响。因此,对复合材料力学性能进行不确定性分析具有重要工程意义。本文以纤维增强复合材料周期性单胞为研究对象,采用基于渐进均匀化方法的随机多尺度理论对纤维增强复合材料力学性能进行了不确定性研究。首先,基于渐进均匀化方法推导了n相复合材料的随机多尺度理论,并编写代码实现了两相和三相复合材料的随机多尺度分析程序的开发,实现了结果的可视化。而且,利用蒙特卡洛模拟方法验证了随机多尺度理论的有效性及程序编写的准确性。其次,基于BORSA方法对ABAQUS进行二次开发实现了非连续纤维增强复合材料的周期性单胞随机参数化建模。将纤维直径、长度、纤维取向角以及纤维位置参数设置为随机变量,便可得到非连续纤维增强复合材料的随机单胞模型。随机单胞模型能有效地模拟真实纤维复合材料的细观几何形态。随后,分别以单向非连续纤维增强复合材料和随机分布纤维增强复合材料为研究对象,分析了组分材料(玻纤和聚丙烯高聚物)的弹性模量不确定性对宏观性能不确定性的影响。研究表明:对于单向纤维增强复合材料而言,纤维纵向的等效弹性模量不确定性程度主要受纤维弹性模量不确定性的影响,受基体弹性模量不确定性的影响较小;纤维横向等效弹性模量和等效剪切模量的不确定性程度主要受基体弹性模量不确定性的影响,而对纤维弹性模量不确定性的影响并不敏感。对于随机分布纤维增强复合材料而言,等效弹性模量和等效剪切模量的不确定性程度基本受基体弹性模量不确定性的影响,而受纤维弹性模量不确定性的影响极小,这与单向纤维复合材料相比有很大差异。由此可知完全不同的纤维取向会改变组成相材料弹性模量不确定性对宏观性能不确定性的影响机制。还研究了随机分布纤维增强复合材料组成相材料的弹性模量不确定性对细观应力不确定性的影响,发现玻纤模量不确定性对整个单胞各处细观应力不确定性均有影响,并且影响程度由玻纤内部到界面再到基体逐渐减弱。基体模量不确定性对基体细观应力不确定性程度影响极大,对纤维内部的细观应力不确定性基本无影响,纤维表面(或者界面处)的细观应力不确定性程度受到纤维和基体材料不确定性因素的共同影响。材料模量参数的不确定性对界面处的应力不确定性的影响程度最大。此外,在同时考虑材料不确定性和细观几何不确定性影响的情况下,对单向纤维增强复合材料的均匀化模量采用混合高斯分布进行了概率分布估计,发现纤维体积分数对宏观性能不确定性的影响显著,等效弹性模量和等效剪切模量的标准差随纤维体积分数的增加而增加。纤维长度越大,等效弹性模量标准差亦越大,等效剪切模量标准差对纤维长度的增加不敏感。最后,在传统的纤维增强复合材料细观失效准则基础上,提出了考虑不确定性因素的细观失效准则。为纤维增强复合材料的细观失效研究或损伤演化分析,提供一种指导性思路。此外在考虑材料性能参数不确定性的情况下分析了在不同置信水平下的细观应力,并与传统分析结果进行了对比。更多还原

【Abstract】 With the progress of the times and the increasing demand for materials,new material technology has been developed rapidly.Composite materials have excellent comprehensive mechanical properties,which are favored by the majority of scholars and engineers.However,there are a variety of uncertain factors in the process of structural design and manufacturing process of composite materials,which have a significant impact on the mechanical properties of composite materials.Therefore,the uncertainty analysis of the mechanical properties of composites is of great engineering significance.In this paper,the stochastic multi-scale theory based on the asymptotic homogenization method is used to study the uncertainty of the mechanical properties of fiberreinforced composites.Initially,the stochastic multi-scale theory of n-phase composites is derived based on the asymptotic homogenization method,and the code is written to realize the development of the stochastic multi-scale analysis program of two-phase and three-phase composites,and the visualization of the results is realized.Moreover,Monte Carlo Simulation is used to verify the effectiveness of stochastic multi-scale theory and the accuracy of programming.Moreover,ABAQUS was redeveloped to realize the stochastic parametric modeling of periodic RVE of discontinuous fiber reinforced composites based on BORSA method.By setting the parameters of fiber diameter,fiber length,fiber orientation angle and fiber centroid position as random variables,the random RVE model of discontinuous fiber reinforced composites can be obtained.The geometry of real fiber composites at microscale can be simulated by the generated random RVE model.Then,the impact of the elastic modulus uncertainty of component materials(glass fiber and polypropylene polymer)on the uncertainty of macroscale properties is analyzed by taking unidirectional discontinuous fiber reinforced composites and randomly distributed fiber reinforced composites as the research objects,respectively.The results show that: For unidirectional fiber reinforced composites,the uncertainty of the equivalent elastic modulus in the longitudinal direction of the fiber is mainly affected by the uncertainty of the elastic modulus of the fiber,and is less affected by the uncertainty of the elastic modulus of the matrix;the uncertainty of the equivalent elastic modulus in the transverse direction of the fiber and the equivalent shear modulus is mainly affected by the uncertainty of the elastic modulus of the matrix,but is not sensitive to the uncertainty of the elastic modulus of the fiber.For randomly distributed fiber reinforced composites,the uncertainty of equivalent elastic modulus and equivalent shear modulus is basically affected by the uncertainty of matrix elastic modulus,while the uncertainty of fiber elastic modulus has little effect,which is quite different from unidirectional fiber reinforced composites.It can be seen that completely different fiber orientations can change the influence mechanism of elastic modulus uncertainty of constituent materials on macroscopic properties uncertainty.The influence of the elastic modulus uncertainty of randomly distributed fiber reinforced composites on the uncertainty of microscopic stress is also studied.It is found that the glass fiber modulus uncertainty has an influence on the microscopic stress uncertainty throughout the whole RVE,and the degree of influence gradually decreases from the inside of the glass fiber to the interface and then to the matrix.The uncertainty of matrix modulus has a great influence on the uncertainty of microscopic stress of matrix,but has no influence on the uncertainty of microscopic stress inside the fiber.The uncertainty of microscopic stress on fiber surface(or interface)is affected by the uncertainty of fiber and matrix collectively.The uncertainty of the material modulus parameters has the greatest influence on the stress uncertainty at the interface.In addition,the probability distribution of homogenization modulus of unidirectional fiber-reinforced composites is estimated by Gaussian mixture distribution considering both material uncertainty and geometric uncertainty at microscale.It is found that the fiber volume fraction has a significant effect on the uncertainty of macroscopic properties.The standard deviation of equivalent elastic modulus and equivalent shear modulus increases with the increase of fiber volume fraction.The standard deviation of equivalent elastic modulus increases with the increase of fiber length,and the standard deviation of equivalent shear modulus is insensitive to the increase of fiber length.Finally,a microscopic failure criterion considering uncertainties is proposed based on the traditional microscopic failure criterion of fiber reinforced composites.It provides a guiding idea for the microscopic failure research or damage evolution analysis of fiber reinforced composites.In addition,the microscopic stress under different confidence levels is analyzed considering the uncertainty of material properties,and the results are compared with those of traditional analysis.更多还原