复合材料粘弹性本构关系与热应力松弛规律研究Ⅱ:数值分析

给出了预测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均匀化方法的有限元数值实现步骤, 研究了单向纤维复合材料随温度变化的粘弹性本构关系, 以及热应力松弛规律和热膨胀系数的时变特征。单向纤维复合材料的一维热变形分析数据显示了热应变对时间的强烈依赖关系;以数值形式给出的等效热应力松弛模量对时间的依赖关系表明, 等效的热应力松弛模量对时间的依赖性较弱, 其冲击模量和渐近模量只相差0.4 %。     

纤维复合材料粘弹性动态性能的细观力学分析

建立了纤维增强复合材料粘弹性动态性能的细观力学模型.首先建立了树脂基体相各向同性的粘弹性模型,模型参数由纯树脂基体材料的蠕变试验获取,在此基础上分别建立了针对单向和正交铺层复合材料的横观各相同性、正交各相异性的细观粘弹性模型.对单向、正交铺层复合材料进行了静态和动态试验,分别通过试验和上述理论模型得到了其阻尼比、动态储存模量、损耗模量和损耗因子,理论预测与试验结果吻合.     

各向异性热粘弹性流体动力润滑理论

本文在弹性流体动力润滑理论的基础上,把各向同性线弹性的材料性能假设扩展为各向异性热粘弹性,建立了各向异性热粘弹性流体动力润滑理论,以适应复合材料齿轮和复合材料滚动轴承的工程设计需要。      

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.      

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。     

S-2/F46复合材料低速冲击损伤及剩余弯曲性能

考察了单向、正交和准各向同性S-2 /F46复合材料低速冲击后的剩余弯曲强度和模量,结合冲击损伤形貌比较了其冲击损伤模式及演化过程.单向复合材料的冲击损伤呈突变式发展,而正交和准各向同性复合材料则呈多阶段渐进式发展,弯曲性能衰减也呈现相应模式.只有当试样的结构完整性损失较大时弯曲性能才明显下降,其衰减的临界冲击能以单向复合材料最大,正交复合材料最小.此外,角铺层复合材料弯曲模量比强度衰减更严重.     

基于单胞解析模型的单向复合材料强度预报方法

基于单胞解析模型,建立一种从复合材料细观组分到宏观单向板的强度预报方法。根据连续介质力学和均匀化方法构建细-宏观关联矩阵,通过该关联矩阵将细观组分材料的弹性和损伤性能传递到宏观单向板中。考虑复合材料细观损伤状态,当纤维和基体满足各自强度准则时失效,并通过失效因子折算成刚度的衰减。在此基础上,结合有限元分析,实现复合材料单向板纵横向拉伸模拟,从而预报单向板的拉伸强度。结果表明:该方法预报的模量和强度与实验值基本一致,验证了该方法的有效性与高效性。     

UD-Cf/SiC陶瓷基复合材料的高温拉伸性能

采用两种形状(纺锤形、矩形)的拉伸试样对热压单向M40JB-C_f/SiC和T800-C_f/SiC复合材料进行了高温拉伸强度测试,得到了C_f/SiC复合材料的拉伸强度,并对纺锤形试样断裂应变的表达式进行修正,得出了复合材料的弹性模量。M40JB-C_f/SiC复合材料1300℃的拉伸强度及模量分别为374 MPa和134 GPa, 1450 ℃的拉伸强度及模量为338 MPa和116 GPa,T800-C_f/SiC复合材料1300 ℃拉伸强度和模量为392 MPa 和115 GPa。测试结果与试样的断裂方式密切相关,在有效部位断裂的测试结果大于在非有效区断裂的测试结果。M40JB-C_f/SiC复合材料的拉伸断裂应力-应变曲线表现出塑性变形的非线弹性破坏特征,而T800-C_f/SiC主要表现为线弹性特征。      

三维均匀化方法预测编织复合材料等效弹性模量

本文将基于小参数渐近展开和摄动方法的均匀化理论与有限元方法结合起来应用于三维编织复合材料弹性本构的数值模拟。通过对三维编织结构等效模量的数值计算 ,结果表明本文的方法可得到较为准确的等效模量 ,并较其它解法大大降低了计算量。     

关于横观各向同性体在其各向同性面内弹性问题的一个常数

研究了在平面应力和平面应变情况下, 横观各向同性材料在其各向同性面内的应力2应变关系以及用位移表达的平衡方程可以被表示成与各向同性材料完全相同的形式。这种等同关系是通过引入一个与横观各向同性材料的泊松比有关的常数得到的。该常数的引入消除了已发表的文献中求解横观各向同性材料平面问题时出现的矛盾。这个常数的引入也便于正确计算单向纤维增强复合材料的横向切变模量。      

Fourier series expansion in non-orthogonal coordinate system for the homogenization of linear viscoelastic periodic composites

The Eshelby method and the Fourier series are used in order to determine the linear elastic and viscoelastic properties of composites with periodically distributed inclusions in a non-orthogonal coordinate system. The relaxation moduli provided by the proposed method are compared with the moduli obtained via FEM for a unidirectional composite. This comparison gives good results. The procedure results very useful for periodic composites with hexagonal symmetry, such as some transversely isotropic composites.     

Efficient techniques for predicting viscoelastic behavior of sublaminates

Even for linear elastic behavior, stress analysis of thick laminated composites can be very computation intensive if every lamina is modeled discretely. In such cases, modeling of individual lamina is impractical and the homogenization method for sublaminates becomes essential. In the current work, 3D homogenization formulas for an elastic sublaminate, which were derived by the authors in previous work, were utilized to determine the 3D effective properties for a viscoelastic sublaminate. The properties were determined by three methods that exploited the 3D elastic homogenization formulas: (i) quasi-elastic method, (ii) correspondence principle, and (iii) direct time integration of the incremental viscoelastic equations. The finite element method with discrete modeling of the plies was used to obtain reference solutions. The effective viscoelastic properties obtained using the three methods based on the elastic homogenization formulas were in very good agreement with the reference solution. Among these methods, the quasi-elastic method was found to be both accurate and the simplest method in determining the effective properties. The methods were also used to predict the stress response of a sublaminate to different strain histories. The direct time integration method using the 3D elastic homogenization formulas performs accurately and efficiently for this problem.     

Vibration isolation using open or filled trenches

The problem of isolating structures from surface waves by open or filled trenches under conditions of plane strain is numerically studied. The soil is assumed to be an isotropic, linear elastic or viscoelastic nonhomogeneous (layered) half-space medium. Waves generated by the harmonic motion of a rigid surface machine foundatin are considered. The formulation and solution of the problem are accomplished by the frequency domain boundary element method. The Green's function of Kausel-Peek-Hull for a thin layered half-space is employed and this essentially requires only a discretization of the trench perimeter and the soil-foundation interface. The proposed methodology is used for the solution of a number of vibration isolation problems and the effect of soil inhomogeneity on the wave screening effectiveness of trenches is discussed.     

On numerical evaluation of effective material properties for composite structures with rhombic fiber arrangements

This paper deals with unidirectional fiber reinforced composites with rhombic fiber arrangements. It is assumed, that there is a periodic structure on micro level, which can be taken by homogenization as a representative volume element (RVE) for the composite, where the composite phases have isotropic or transversely isotropic material characterizations. A special procedure is developed to handle the primary non-rectangular periodicity with common numerical homogenization techniques based on FE-models. Due to appropriate boundary conditions applied to the RVE elastic effective macroscopic coefficients are derived. Results are listed and compared with other publications and good agreements are shown. Furthermore new results are presented, which exhibit the special orthotropic behavior of such composites caused by the rhombic fiber arrangement.     

Dynamic steady-state crack propagation in a transversely isotropic viscoelastic body

The problem considered herein is the dynamic, subsonic, steady-state propagation of a semi-infinite, generalized plane strain crack in an infinite, transversely isotropic, linear viscoelastic body. The corresponding boundary value problem is considered initially for a general anisotropic, linear viscoelastic body and reduced via transform methods to a matrix Riemann–Hilbert problem. The general problem does not readily yield explicit closed form solutions, so attention is addressed to the special case of a transversely isotropic viscoelastic body whose principal axis of material symmetry is parallel to the crack edge. For this special case, the out-of-plane shear (Mode III), in-plane shear (Mode II) and in-plane opening (Mode I) modes uncouple. Explicit expressions are then constructed for all three Stress Intensity Factors (SIF). The analysis is valid for quite general forms for the relevant viscoelastic relaxation functions subject only to the thermodynamic restriction that work done in closed cycles be non-negative. As a special case, an analytical solution of the Mode I problem for a general isotropic linear viscoelastic material is obtained without the usual assumption of a constant Poissons ratio or exponential decay of the bulk and shear relaxation functions. The Mode I SIF is then calculated for a generalized standard linear solid with unequal mean relaxation times in bulk and shear leading to a non-constant Poissons ratio. Numerical simulations are performed for both point loading on the crack faces and for a uniform traction applied to a compact portion of the crack faces. In both cases, it is observed that the SIF can vanish for crack speeds well below the glassy Rayleigh wave speed. This phenomenon is not seen for Mode I cracks in elastic material or for Mode III cracks in viscoelastic material.     

Boundary element method homogenization of the periodic linear elastic fiber composites

The paper presented is devoted to the Boundary Element Method based homogenization of the periodic transversely isotropic linear elastic fiber-reinforced composites. The composite material under consideration has deterministically defined elastic properties while its components are perfectly bonded. To have a good comparison with the FEM-based computational techniques used previously, the additional Finite Element discretization is presented and compared numerically against BEM homogenization implementation on the example of engineering glass–epoxy composite. The homogenization method proposed has rather general characteristics and, as it is shown, can be easily extended on n-component composites. On the contrary, we can consider and homogenize the heterogeneous media with randomly defined material properties using Monte-Carlo simulation technique or second order perturbation second probabilistic moment approach.     

聚合物基复合材料有效蠕变响应与单轴拉伸行为的细观力学模拟

基于变分渐近均匀化理论框架建立表征线性黏弹性聚合物基复合材料有效蠕变响应和宏观应力-应变行为的细观力学模型。从线性黏弹性聚合物基复合材料本构方程中构建能量泛函变分表达式出发,采用变分渐近法求解线性黏弹性聚合物基复合材料的有效蠕变柔度系数,并以此为基础计算聚合物基复合材料的时变和单轴拉伸行为。通过算例验证了构建模型的适用性和准确性。由于所有计算均在时间域内完成,不再需要传统线黏弹性复合材料使用的Laplace转换和反演,计算效率大为提高。      

Micromechanical analysis of stress relaxation response of fiber-reinforced polymers

The paper describes a micromechanical method to determine the stress relaxation response of polymer composites consisting of linearly viscoelastic matrices and transversely isotropic elastic fibers. A representative unit cell is subjected to some prescribed axial and shear loadings to study and quantify the time-dependent behavior of composite materials. Closed-form analytical expressions are derived describing the anisotropic viscoelastic response of composite materials as functions of matrix and fiber properties. The present analytical expressions are employed to determine the stress relaxation behavior of a graphite/epoxy composite and the results are compared with the finite element analysis of the micromechanical model. Very good correlation between analytical expressions and numerical results is illustrated for the linearly anisotropic viscoelastic response of composite materials.     

Boussinesq’s viscoelastic problem on normal concentrated force on a half-space surface

A problem on the action of a normal concentrated force on the surface of viscoelastic half-space (Boussinesq’s viscoelastic problem) is solved. The relations of the theory of linear isotropic viscoelasticity are used as determining relations. The two relaxation functions corresponding to shift and volumetric expansion states are accepted to be independent. The forms of these functions are not defined concretely. Exact formulae for displacements, strains and stresses components are represented. The used solution method may be used for the solution of a series of problems of the theory of linear isotropic viscoelasticity as well.     

Vibration isolation using open or filled trenches

The problem of structural isolation from ground transmitted vibrations by open or infilled trenches under conditions of plane strain is numerically studied. The soil medium is assumed to be linear elastic or viscoelastic, homogeneous and isotropic. Horizontally propagating Rayleigh waves or waves generated by the motion of a rigid foundation or by surface blasting are considered in this work. The formulation and solution of the problem is accomplished by the boundary element method in the frequency domain for harmonic disturbances or in conjunction with Laplace transform for transient disturbances. The proposed method, which requires a discretisation of only the trench perimeter, the soil-foundation interface and some portion of the free soil surface on either side of the trench appears to be better than either finite element or finite difference techniques. Some parametric studies are also conducted to assess the importance of the various geometrical, material and dynamic input parameters and provide useful guidelines to the design engineer.