复合材料粘弹性本构关系与热应力松弛规律研究Ⅰ:理论分析

基于均匀化理论研究了复合材料粘弹性分析的多尺度方法, 以及复合材料等效热应力松弛规律。引入了等效粘弹性热应力系数张量和等效时变热膨胀系数的概念, 建立了含温度变化的复合材料热粘弹性本构关系, 并给出了基于均匀化理论的复合材料粘弹性松弛模量、等效热应力松弛系数和等效时变热膨胀系数的预测方法。对特殊复合材料的粘弹性性质进行了分析, 结果表明: (1) 复合材料的粘弹性本构关系具有与常规材料的本构关系类似的形式, 但一般复合材料的热应力松弛规律与常规材料不同, 其热膨胀不能瞬时完成, 而具有明显的时变性质;(2) 空心材料的热膨胀具有瞬时性质, 其等效时变热膨胀系数与基体材料的热膨胀系数相同, 其热应力松弛规律与基体材料的松弛规律相同;(3) 当各组分材料的松弛模量的各分量可分解成不同的系数与相同的时间函数的乘积时, 复合材料的等效时变热膨胀系数与时间无关, 其松弛规律与常规材料的松弛规律完全相同。     

形状记忆纤维热粘弹性基体复合材料的力学行为

应用热粘弹性理论和Voigt混合律,在变温场中针对马氏体逆相变过程建立了NiTi形状记忆纤维热粘弹性基体复合材料的应力-应变关系,在逆相变过程和基体呈现热粘弹态阶段,由于基体松弛其模量减小,在跃阶拉应力的作用下,复合材料的压缩应变迅速增大,纤维回复应力先增大后减小;在跃阶拉应变的作用下,复合材料的应力增加先变缓然后加快直至稳定,较高的温度和材料参数对NiTi纤维热粘弹性基体复合材料的力学行为和纤维的作动性能有明显的影响.     

粘弹性复合材料中的渐近均匀化方法

主要研究了由各向同性线弹性加强体和各向同性线粘弹性基体组成的复合材料的问题。在已有的线弹性多层材料的渐近均匀化方法的基础上,应用弹性-粘弹性对应原理,在Carson域中求解粘弹性问题,通过两次运用均匀化方法,得到一类单向强化复合材料的有效模量的表达式。反演可得到单向强化复合材料的有效松弛模量在时间域中的表达式,并且与其它结果进行了比较。     

等效介质理论数值法计算复合材料的热膨胀系数

本文用一套等效介质理论的数值方法计算了球状微粒掺杂之各向同性复合材料及单向纤维增强之横观各向同性复合材料之线热膨胀系数,得到合理的结果,并与Schapery式、Kerner式之计算及实验值作出比较,显示了等效介质理论于复合材料热弹性能计算之适用性.      

基于细观力学的纤维沥青混凝土有效松弛模量

为了研究纤维沥青混凝土的本构模型,将其视为以沥青混合料为粘弹性基体,纤维为弹性夹杂的两相复合材料。对基于复合材料细观力学理论建立的有效模量表达式进行了修正,提出了纤维沥青混凝土的割线有效松弛模量。以聚酯纤维沥青混凝土为例进行了有效松弛模量的解析分析和模拟蠕变实验的有限元分析,分析结果与试验数据的比较表明,该文提出的割线有效松弛模量模型对于纤维沥青混凝土粘弹性力学行为具有很好的预测能力。应用该模型对路面弯沉变形进行了有限元分析,结果表明:纤维的加入有效的改善了沥青混凝土路面的粘弹性性能。     

沥青混合料热粘弹性本构关系试验测定及其力学应用

基于热粘弹性力学理论,就不同的温度条件下沥青混合料的应力松弛特征开展了试验研究,应用热流变简单材料的时温等效原理对试验结果进行了分析和参数拟合,根据试验结果建立了描述沥青混合料粘弹特性的广义Maxwell模型;通过理论推导提出了沥青混合料非定常和非均匀变温条件下增量型热粘弹性本构关系,在此基础上,给出应用本构关系进行沥青路面热粘弹性力学分析的数值实现方法;通过对TSRST试验的模拟,对得到的沥青混合料热粘弹性本构关系及其数值实现方法的合理性进行了验证,并给出一个工程计算实例。     

残余应力对复合材料弹2塑性变形的影响

从细观力学的角度给出了分析残余应力对一般复合材料塑性性能影响的一种解析方法, 该方法基于应力二阶矩的割线模量法及Ponte Castaneda 和W illis 给出的弹性细观模型。有残余应力时, 所提的细观解析模型能够同时考虑纤维形状, 体积百分比, 纤维取向及纤维的分布对复合材料变形的影响。计算结果表明, 残余应力的存在会引起复合材料拉压变形的不对称, 材料宏观的拉压硬化曲线又与复合材料的细观结构参数密切相关。对单向复合材料, 本文作者对其等效割线热膨胀系数, 拉压应力-应变曲线的有限元分析结果与给出的细观解析模型定量吻合。      

EMC材料参数对微电子封装器件热应力的影响

利用动态机械分析仪测定环氧模塑封(EMC)材料的粘弹性数据,并用广义麦克斯韦模型表征了EMC材料的粘弹松弛特性;利用热机械分析仪获得了EMC材料在不同温度时的尺寸变化量,并通过线性拟合得到了EMC材料的热膨胀系数。使用有限元软件MSC Marc分别模拟了基于EMC粘弹性、弹性两种不同性质时,QFN器件在-55~+125℃温度条件下热应力分布,并分析了热膨胀系数对热应力的影响。结果表明:QFN器件的最大热应力出现在粘接剂、芯片和EMC材料的连接处,有限元分析中EMC的材料性质和热膨胀系数会对热应力产生较大影响。     

PP木纤维复合材料热粘弹性力学特性研究

通过对PP木纤维复合材料进行应变率为10-4～10-2s-1、温度为90、130、170℃下的单向应力条件下的力学性能试验,结果表明,PP木纤维复合材料的力学响应对温度和应变率都是敏感的,并且升高温度与降低应变率对PP木纤维复合材料的力学性能有等效的影响。利用Maxwell模型提出了该PP木纤维复合材料的一个非线性热粘弹性本构方程,拟合出了相应的粘弹性参数。利用该本构模型模拟了PP木纤维复合材料的热压缩实验,理论计算所得应力-应变曲线与实验结果吻合较好。     

树脂基三维编织复合材料粘弹性能的数值预报

建立了基于三细胞模型数值预报三维编织复合材料粘弹性能的方法。首先构造了三维编织复合材料的三细胞模型并施加周期性边界条件,随后利用标准线性固体模型模拟树脂基体的粘弹性能,导出基体的松弛模量,再通过有限元计算及Prony级数拟合,得到三种胞元的粘弹性参数。然后根据三种胞元的体积分数和粘弹性参数,利用三个标准线性固体模型并联,模拟得到三维编织复合材料沿编织方向的粘弹性参数和蠕变本构关系。最后,分析了编织角和纤维体积含量对粘弹性能的影响。     

Micromechanics modeling of fatigue failure mechanisms in a hybrid polymer matrix composite

Initiation of fatigue damage for a hybrid polymer matrix composite material was studied via 3-Dimensional viscoelastic representative volume element modeling in order to gain further understanding. It was found that carbon fiber reinforced composites perform better in fatigue loading, in comparison to glass fiber reinforced composites, due to the fact that the state of stress within the matrix material was considerably lower for carbon fiber reinforced composites eliminating (or at least prolonging) fatigue damage initiation. The effect of polymer aging was also evaluated through thermal aging of neat resin specimens. Short-term viscoelastic material properties of unaged and aged neat resin specimens were measured using Dynamic Mechanical Analysis. With increasing aging time a corresponding increase in storage modulus was found. Increases in the storage modulus of the epoxy matrix subsequently resulted in a higher state of predicted stress within the matrix material from representative volume element analyses. Various parameters common to unidirectional composites were numerically investigated and found to have varying levels of impact on the prediction of the initiation of fatigue damage.     

Analysis of viscoelastic laminated composite plates

A micromechanics analysis is performed for the determination of the five independent elastic moduli of unidirectional fiber composites. By considering viscoelastic phases and by using the correspondence principle and the inversion of the Laplace transform, the five time-dependent functions which characterize the effective behavior of viscoelastic composites are established. The predicted time-dependent behavior is applied for the analysis of viscoelastic laminated plates. The resulting viscoelastic effects are shown, and comparison between the results obtained within the classical laminated plate theory and the first-order shear deformation theory is discussed.     

Time-dependent response of active composites with thermal, electrical, and mechanical coupling effect

The mechanical and physical properties of materials change with time. This change can be due to the dissipative characteristic of materials like in viscoelastic bodies and/or due to hostile environmental conditions and electromagnetic fields. We study time-dependent response of active fiber reinforced polymer composites, where the polymer constituent undergoes different viscoelastic deformations at different temperatures, and the electro-mechanical and piezoelectric properties of the active fiber vary with temperatures. A micromechanical model is formulated for predicting effective time-dependent response in active fiber composites with thermal, electrical, and mechanical coupling effects. In this micromechanical model limited information on the local field variables in the fiber and matrix constituents can be incorporated in predicting overall performance of active composites. We compare the time-dependent response of active composites determined from the micromechanical model with those obtained by analyzing the composites with microstructural details. Finite element (FE) is used to analyze the composite with microstructural details which allows quantifying variations of field variables in the constituents of the active composites.     

The effect of particle shape on the mechanical properties of filled polymers

The existing models for predicting the elastic moduli of polymers dispersed with particles of shape other than spheres and continuous fibres are reviewed. The applicability and limitation of these equations are discussed. The emphasis of the review is to seek a unified understanding and approach to the effect of particle shape at finite concentration on the elastic moduli, thermal expansion coefficient, stress concentration factor, viscoelastic relaxation modulus and creep compliance of filled polymers. The effects of anisotropic particle shape on mechanical properties of polymeric composites are clearly illustrated. Attention is also drawn to the relationship between elastic moduli, thermal expansion, creep elongation and stress relaxation moduli.     

复合材料热膨胀性能研究

本文研究了单向纤维增强复合材料的热膨胀性能。引进界面粘结系数C,利用热弹性理论推导出经C修正后的线膨胀系数计算公式。由MOM型综合热分析仪测量了玻璃纤维和碳纤维复合材料在不同界面情况及不同纤维体积含量时的线膨胀系数。理论计算值与实测值相当接近,相对误差小于10%。     

有一定取向性的碳纤维增强尼龙6复合材料弹性模量的实验和理论研究

纤维增强热塑性聚合物基复合材料注塑成型后往往被认为是各向同性复合材料。然而,注塑成型后纤维会具有一定的取向性,从而使复合材料试样呈现各向异性的特点。为了合理预测此类复合材料的弹性模量,本文对碳纤维增强尼龙6复合材料注塑试样内部的纤维长度和取向分布情况进行了测试和分析,得出了纤维取向的分布规律。随后结合单向纤维增强聚合物基复合材料力学模型和层叠理论,构造出了适用于有一定取向性的纤维增强树脂基复合材料弹性模量预测理论模型,其理论结果和拉伸实验结果吻合较好,表明该预测模型的准确性比较高。      

用均匀化方法预测单向纤维复合材料热膨胀行为

本文利用均匀化方法研究了单向纤维复合材料的热膨胀行为。建立了热膨胀系数与组分材料性能、体分比之间的关系,得到了纤维/基体性能比值对横向热膨胀系数的影响比对纵向系数的影响更重要的结论。通过均匀化方法和四种已有的理论方法之间的相互比较,以及同实验值对比,分析了各理论方法的精度,验证了均匀化方法的可靠性。      

Effect of fiber arrangement on mechanical properties of short fiber reinforced composites

The present paper developed a three-dimensional (3D) “tension–shear chain” theoretical model to predict the mechanical properties of unidirectional short fiber reinforced composites, and especially to investigate the distribution effect of short fibers. The accuracy of its predictions on effective modulus, strength, failure strain and energy storage capacity of composites with different distributions of fibers are validated by simulations of finite element method (FEM). It is found that besides the volume fraction, shape, and orientation of the reinforcements, the distribution of fibers also plays a significant role in the mechanical properties of unidirectional composites. Two stiffness distribution factors and two strength distribution factors are identified to completely characterize this influence. It is also noted that stairwise staggering (including regular staggering), which is adopted by the nature, could achieve overall excellent performance. The proposed 3D tension–shear chain model may provide guidance to the design of short fiber reinforced composites.