多元多层平纹机织CMC-SiC弹性常数的多尺度均匀化高效预测方法

多元多层碳化硅陶瓷基复合材料(Silicon carbide ceramic matrix composites,CMC-SiC)等效弹性常数的准确、高效预测是实现材料性能优化与结构计算分析的重要基础.本文以多元多层平纹机织CMC-SiC为研究对象,建立了其多尺度微结构有限元模型,采用均匀化方法依次在纤维丝和纤维束尺度上进行了弹性性能常数的计算.通过合理的等效,简化了多元多层微结构有限元模型的复杂性,提高了等效性能的均匀化计算效率.数值计算结果与实验结果证实吻合较好,验证了本文提出的微结构模型以及预测方法的有效性.     

玻纤增强注塑件的均匀化弹性力学参数研究

基于均匀化方法,根据长玻纤增强聚丙烯(LGFR-PP)的微观特征,建立了非连续长玻纤增强复合材料的代表性体积单元(RVE),通过有限元方法模拟预测了复合材料的宏观等效弹性力学参数,与注塑样条拉伸性能测试结果进行了比较。研究表明,通过在玻纤两侧增加聚丙烯(PP)分布,所采用的RVE较传统连续纤维的有限元模型更为合理;当玻纤成单一取向时,玻纤增强聚丙烯为一种横观各向同性材料;改变玻纤取向与拉伸方向之间的角度,拉伸方向的等效模量先微幅减小,再迅速降低,而后趋于稳定。利用均匀化方法预测非连续长玻纤增强注塑件的等效弹性力学性能具有较高的工程可行性,能进一步为玻纤增强注塑件的结构服役性能分析提供科学依据。     

非均匀材料界面裂纹的Cell-Based光滑有限元法

为提高非均匀材料界面裂纹尖端断裂参数的求解精度,基于非均匀材料界面断裂力学、Cell-Based光滑有限元(Cell-SFEM)和非均匀材料的互交作用积分法,提出了求解非均匀材料界面裂纹尖端断裂参数的CellBased光滑有限元法,推导了基于Cell-Based光滑有限元法的非均匀材料的互交作用积分法,对非均匀材料间的界面裂纹尖端处正则应力强度因子进行了求解,并与参考解进行了比较,讨论了互交积分区域大小和光滑子元个数与正则应力强度因子的关系。数值算例结果表明:本方法具有很高的计算精度,对积分区域大小不敏感,可为设计、制造抗破坏非均匀材料提供依据。     

基于均匀化方法的多孔材料细观力学特性数值研究

本文把均匀化理论与有限元法相结合 ,应用于多孔材料的弹性本构数值模拟 ,利用位移渐进展开建立了均匀化有限元列式。通过对正方形孔洞蜂窝材料有效模量的计算比较 ,表明本文方法可得到较准确的有效模量 ;同时还考察了胞壁固体相的力学性能参数vs 对宏观力学性能的影响 ,得到了与一些理论公式相同的结论。最后 ,本文对胞壁中含有弹性增强相的多孔材料的力学性能进行了数值研究 ,并利用二次均匀化方法给出定量的计算结果     

基于均匀化方法的多孔材料细观力学特性数值研究

本文把均匀化理论与有限元法相结合,应用于多孔材料的弹性本构数值模拟,利用位移渐进展开建立了均匀化有限元列式。通过对正方形孔洞蜂窝材料有效模量的计算比较,表明本文方法可得到较准确的有效模量;同时还考察了胞壁固体相的力学性能参数vs对宏观力学性能的影响,得到了与一些理论公式相同的结论。最后,本文对胞壁中含有弹性增强相的多孔材料的力学性能进行了数值研究,并利用二次均匀化方法给出定量的计算结果。     

多维非经典热传导问题的时间2空间多尺度高阶均匀化分析

采用一种时间-空间多尺度高阶渐近均匀化分析方法,模拟了热冲击载荷条件下多维微尺度多相周期性结构中的非经典热传导问题。通过引入放大空间尺度和缩小时间尺度,在不同时间尺度上获得由空间非均匀性引起的波动效应和非局部效应。根据高阶均匀化理论在空间和时间上进行均匀化,消去缩小时间尺度,确定各阶等效均匀化热传导系数的关系并对该系数进行数值求解,获得了多维非傅里叶热传导高阶非局部温度场控制方程。进而对二维周期性多相材料中的非傅里叶热传导问题进行分析,结果证明了本文中所提出的多维非傅里叶热传导高阶非局部模型的正确性与有效性。     

梯度涂层材料中裂纹问题的非均匀元分析

本文采用非均匀等参有限元的方法研究了薄膜梯度涂层/均匀基材中的界面裂纹问题,并与双材料界面裂纹情况进行了对比计算。研究表明:在均匀基材上采用梯度涂层,与双材料相比可以有效地降低裂尖场应力强度因子;同时还分析了涂层厚度与梯度参数对界面应力强度因子的影响。结果表明:当薄膜厚度大于或等于裂纹长度时,应力强度因子(KI、KII)对其尺度的变化显得不敏感;对梯度参数的影响而言,当材料性能曲线的幂指数m大于1时,裂尖场的应力强度因子KII相对KI很小且基本不随m变化,因此裂尖场与均匀材料情况类似;当m小于1时,应力强度因子KII随m减小而急剧增大,裂尖场由KI及KII控制,断裂趋于混合型。     

基于多尺度渐进均匀化理论手性瓦声学性能计算

基于多尺度渐进均匀化理论,建立手性结构瓦的等效弹性常数计算方法。给出多尺度均匀化方法的详细推导过程,通过对比二维手性结构瓦基于所获得的等效弹性常数振动传递结果和详细手性结构建模的计算结果,验证该方法的正确性。利用得到的弹性常数计算某加筋板敷设手性结构瓦的水下辐射声压,该计算结果和试验结果量级基本一致。这表明多尺度渐进均匀化得到的等效弹性常数能够用于实艇敷设手性结构瓦的隔声计算,具有一定的工程应用价值。     

基于均匀化方法的节理岩体等效弹性性能预测

假定节理岩体具有均质的宏观结构和非均质的周期性分布的细观结构,利用均匀化方法,根据材料周期性特点,通过摄动理论建立依赖于两尺度坐标变量而变化的渐进位移场,推导出反映节理岩体细观结构的控制方程,并结合有限元法,数值模拟得到其宏观等效弹性模量。将算例得到的等效弹性模量与Taylor方法、自洽方法及Hashin-Shtrikman结果进行对比分析,证实了均匀化算法的合理性。同时探讨了节理岩体的弹性性能与组份性能及细观结构的关系,并考察了节理岩体的岩质材料泊松比对宏观力学性能的影响。     

弹性接触颗粒状周期性结构材料力学分析的均匀化方法(Ⅰ) ——局部RVE分析

研究工作目的是建立弹性接触颗粒状组成周期性结构材料力学分析的均匀化模型。首先对具有周期性构造的弹性接触颗粒材料力学的微观(小尺度)与宏观两级均匀化方法的研究现状进行了简要回顾,进而发展了问题局部RVE分析的有限元求解技术,该方法考虑了弹性接触体的粘着界面特性,并基于参变量变分原理提出了问题求解的参数二次规划算法,为宏观均匀化分析工作打下基础。      

Multi-scale analysis of the early damage mechanics of ferritized ductile iron

A multiscale computational homogenization method for the modeling of hydro-mechanical coupling problem for quasi-brittle materials is developed. The present method is based on an asymptotic expansion homogenization combined with the semi-concurrent finite element modelling approach. Modified periodic boundary conditions and a molecular dynamics (MD) based inclusion or filler generation procedure are devised for the hydro-mechanical coupling problem. A modified elastic damage constitutive model and a damage induced permeability law have been developed for the hydraulic fracturing. The statistical convergence of the microscale representative volume element (RVE) model regarding the RVE characteristic size is studied. It was found that the RVE characteristic size is determined by both the mechanical and hydraulic properties of the RVE simultaneously. The present method is validated by the experimental results for brittle material. The damage zone and crack propagation path captured by the present method is compared with the experimental results (Chitrala et al. in J Pet Sci Eng 108:151–161, 2013). The results show that the present method is an effective for the modelling of hydro-mechanical coupling for brittle materials.     

A second-order two-scale homogenization procedure using C^{1} macrolevel discretization

The present study deals with a second-order two-scale computational homogenization procedure for modeling deformation responses of heterogeneous materials at small strains. The macro to micro transition and the application of generalized periodic boundary conditions on the representative volume element (RVE) at the microlevel are investigated. The structure at macroscale level is discretized by the \(C^{1}\) two dimensional triangular finite elements, while the \(C^{0}\) quadrilateral finite element is used for the discretization of the RVE. The finite element formulations and the new proposed multiscale scheme have been implemented into the finite element software ABAQUS using user subroutines derived. Due to the \(C^{1}-C^{0}\) continuity transition, an additional integral condition on microlevel fluctuation field has to be imposed, as expected. The integration has been performed using various numerical integration techniques and the results obtained are compared in a few examples. It is concluded that only trapezoidal rule gives a physically based deformed shape of the RVE. Finally, the efficiency and accuracy of the proposed multiscale homogenization approach are demonstrated by the modeling of a shear layer problem, usually used as a benchmark in multiscale analyses.     

Multiscale approach with RSM for stress–strain behaviour prediction of micro-void-considered metal alloy

This paper presents the concept of using a representative volume element (RVE) in a multiscale approach to predict the macroscopic stress–strain behaviour of a cast SS316L specimen under tension up to the point prior to necking. RVE models with various micro-void spatial configurations were built, and the effects of micro-voids and strain rate on the material properties (e.g., yield strength, ultimate tensile strength (UTS), ultimate tensile strain and strain hardening coefficient) were analysed. The spatial configuration of the micro-voids inside the cast SS316L specimen was acquired by the X-ray CT scanning system and each micro-void in the gauge length part was converted into a matching RVE model in the finite element (FE) analysis. Response surface methodology (RSM) was employed to investigate the effect of RVE configurations, i.e., the size of the RVE and the shape and spatial location of the micro-voids, on the material properties (yield strength and UTS) of the cast SS316L specimen at the macroscopic level, and then the optimal levels of the RVE configuration were determined. The stress–strain curve from the simulation did show a good agreement with the experimental results and hence the proposed concept was verified.     

纤维丝束带复合材料的有效性能预测与实验测试

依据纤维丝束带复合材料的相关几何结构参数值和所确定的纤维丝束带特征体积单元（RVE）模型几何结构尺寸,以有限元软件MSC.Patran/Nastran为平台建立纤维丝束带复合材料RVE有限元模型并在模型中置入相应的制备缺陷。各类制备缺陷的置入均采用删除网格单元的方法,置入裂纹型制备缺陷时偏移裂纹两侧单元相对面以获得当前裂纹宽度,置入孔洞型制备缺陷时尽量模拟其真实形貌。根据复合材料力学关于材料各性能参数的定义和细观力学基本理论推导了有限元计算细观力学（FECM）方法预测复合材料有效弹性性能和有效热膨胀性能的过程。根据FECM方法预测了不含制备缺陷、含单一制备缺陷和含各类制备缺陷时的弹性常数和有效热膨胀系数。结果表明:各类制备缺陷的存在均会使弹性模量和剪切模量减小,泊松比和热膨胀系数可能增大也可能减小。通过与实验测试结果对比分析可知,数值预测结果普遍比实验测试结果偏大,但总体效果较为理想,最大相对误差为6.04%。      

A comparison of homogenization and standard mechanics analyses for periodic porous composites

Composite material elastic behavior has been studied using many approaches, all of which are based on the concept of a Representative Volume Element (RVE). Most methods accurately estimate effective elastic properties when the ratio of the RVE size to the global structural dimensions, denoted here as , goes to zero. However, many composites are locally periodic with finite . The purpose of this paper was to compare homogenization and standard mechanics RVE based analyses for periodic porous composites with finite . Both methods were implemented using a displacement based finite element formulation. For one-dimensional analyses of composite bars the two methods were equivalent. Howver, for two- and three-dimensional analyses the methods were quite different due to the fact that the local RVE stress and strain state was not determined uniquely by the applied boundary conditions. For two-dimensional analyses of porous periodic composites the effective material properties predicted by standard mechanics approaches using multiple cell RVEs converged to the homogenization predictions using one cell. In addition, homogenization estimates of local strain energy density were within 30% of direct analyses while standard mechanics approaches generally differed from direct analyses by more than 70%. These results suggest that homogenization theory is preferable over standard mechanics of materials approaches for periodic composites even when the material is only locally periodic and is finite.     

Effective properties of three-phase electro-magneto-elastic composites

Coupling between the electric field, magnetic field, and strain of composite materials is achieved when electro-elastic (piezoelectric) and magneto-elastic (piezomagnetic) particles are joined by an elastic matrix. Although the matrix is neither piezoelectric nor piezomagnetic, the strain field in the matrix couples the electric field of the piezoelectric phase to the magnetic field of the piezomagnetic phase. This three-phase electro-magneto-elastic composite should have greater ductility and formability than a two-phase composite in which the electric field and the magnetic field are coupled by directly bonding two brittle materials. A finite element analysis (FEA) and micromechanics based averaging of a representative volume element (RVE) are performed in this work to determine the effective dielectric, magnetic, mechanical, and coupled-field properties of an elastic matrix reinforced with piezoelectric and piezomagnetic fibers as functions of the phase volume fractions, the fiber arrangements in the RVE, and the fiber material properties with special emphasis on the poling directions of the piezoelectric and piezomagnetic fibers. The effective magneto-electric moduli of this three-phase composite are found to be less than the effective magneto-electric moduli of a two-phase piezoelectric/piezomagnetic composite, because the elastic matrix is not stiff enough to transfer significant strains between the piezomagnetic and piezoelectric fibers.     

三维编织复合材料紧固件剪切强度预报

建立了三维缎纹编织复合材料代表性体积单元(RVE)和紧固件剪切试件模型,引入周期性边界条件,建立了材料的宏观力学性能预报方法,并采用跨尺度计算方法对不同受载角度下的紧固件剪切破坏过程进行了有限元模拟。进行了三维缎纹编织复合材料紧固件的剪切试验,有限元计算结果与试验结果吻合较好,验证了本方法的可行性。分析了不同受载角度对剪切破坏模式及强度的影响,结果表明,该编织复合材料剪切强度随受载角度增大而降低,且具有不同的损伤起始位置和扩展过程。     

Evaluations of the effective material properties of carbon nanotube-based composites using a nanoscale representative volume element

Carbon nanotubes (CNTs) possess extremely high stiffness, strength and resilience, and may provide the ultimate reinforcing materials for the development of nanocomposites. In this paper, the effective mechanical properties of CNT-based composites are evaluated using a 3-D nanoscale representative volume element (RVE) based on continuum mechanics and using the finite element method (FEM). Formulas to extract the effective material constants from solutions for the RVE under three loading cases are derived based on the elasticity theory. An extended rule of mixtures, based on the strength of materials theory for estimating the effective Young’s modulus in the axial direction of the RVE, is applied for comparisons with the numerical solutions based on the elasticity theory. Numerical examples using the FEM are presented, which demonstrate that the load carrying capacities of the CNTs in a matrix are significant. With additions of the CNTs in a matrix at volume fractions of only about 2% and 5%, the stiffness of the composite can increase as many as 0.7 and 9.7 times for the short and long CNT cases, respectively. These simulation results are consistent with the experimental ones reported in the literature.     

Effects of Interphase Damage and Residual Stresses on Mechanical Behavior of Particle Reinforced Metal-Matrix Composites

Mechanical behavior of aluminum matrix composites reinforced with SiC particles are predicted using an axisymmetric micromechanical finite element model. The model aims to study initiation and propagation of interphase damage subjected to combination of thermal and uniaxial loading. Effects of manufacturing process thermal residual stresses and interphase de-bonding are considered. The model includes a square Representative Volume Element (RVE) from a cylindrical unit cell representing a quarter of SiC particle surrounded by Al-3.5wt.%Cu matrix. Suitable boundary conditions are defined to include effects of combined thermal and uniaxial tension loading on the RVE. An appropriate damage criterion with a linear relationship between radial and shear stresses for interphase damage is introduced to predict initiation and propagation of interphase de-bonding during loading. A damage user subroutine is developed and coupled to the finite element software to model interphase damage. Overall Stress-strain behavior of particulate metal-matrix composite by considering residual stresses is compared with experimental data to estimate interphase strength. Effects of thermal residual stresses in elastic, de-bonding and plastic zones of composite system are discussed in details. Furthermore, parametric study results show high influence of interphase strength on the overall mechanical behavior of composite material.     

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.