Stress analysis of two-dimensional cellular materials with thick cell struts

Finite element analyses (FEA) were performed to thoroughly validate the collapse criteria of cellular materials presented in our previous companion paper. The maximum stress (von-Mises stress) on the cell strut surface and the plastic collapse stress were computed for two-dimensional (2D) cellular materials with thick cell struts. The results from the FEA were compared with those from theoretical criteria of authors. The FEA results were in good agreement with the theoretical results. The results indicate that when bending moment, axial and shear forces are considered, the maximum stress on the strut surface gives significantly different values in the tensile and compressive parts of the cell wall as well as in the two loading directions. Therefore, for the initial yielding of ductile cellular materials and the fracture of brittle cellular materials, in which the maximum stress on the strut surface is evaluated, it is necessary to consider not only the bending moment but also axial and shear forces. In addition, this study shows that for regular cellular materials with the identical strut geometry for all struts, the initial yielding and the plastic collapse under a biaxial state of stress occur not only in the inclined cell struts but also in the vertical struts. These FEA results support the theoretical conclusion of our previous companion paper that the anisotropic 2D cellular material has a truncated yield surface not only on the compressive quadrant but also on the tensile quadrant.     

确定均质化法中精确周期性边界条件的新解法及其在复合材料刚度预测中的应用

通过引进新的特征函数,提出一种新的求解方法,将均质化法中计算特征函数的非奇次积分方程转化为奇次积分方程,得到具有精确的周期性边界条件的均质化方法。利用该方法预测孔洞材料、短纤维增强复合材料刚度的变化,所得结果与用经典方法得到的结果进行比较,验证该方法的可靠性。对于短纤维增强复合材料,分析纤维排列方式对刚度的影响,这是经典的Halpin—Tsai法和Mori—Tanaka法无法预测的,因而文中的方法具有更高的精确度和更广的适应性。     

含固有缺陷复合材料有效弹性性能预报

根据缺陷在复合陶瓷中分布特点,将缺陷简化为刚度为0的椭球夹杂,嵌入到横观各向同性基体中,建立含缺陷复合材料的细观结构模型。应用相互作用直推估计法推导含缺陷胞元的有效刚度,结合刚度体平均化方法,假设胞元空间随机分布,得到复合材料的等效刚度表达式,分析横观各向同性基体中缺陷体积分数、取向和形状对材料等效刚度的影响,并进一步讨论缺陷周围基体各向异性的影响。结果表明,缺陷存在导致材料弹性性能明显降低,在缺陷体积分数较小时,弹性常数对缺陷体积分数更加敏感;缺陷形状对弹性常数有较大影响,当缺陷接近于薄片状时,缺陷厚度对弹性常数影响明显,而缺陷平面形状对弹性常数基本没有影响;当片状缺陷垂直于基体中弹性模量较大的轴时,缺陷对材料有效性能的降低作用更显著,考虑缺陷周围基体各向异性是很有必要的。     

A morphological elastic model of general hexagonal columnar structures

A general three-dimensional (3D) anisotropic hexagonal model of columnar structure with non-uniform strut morphology is developed. This model covers several types of cellular structure such as two-dimensional (2D) hexagonal and square honeycombs, and 3D hexagonal and rhombic cellular materials of rod-like columnar structure. The effective elastic constants are determined taking account of bending, axial, and shear deformations of the struts. Unlike the theoretical work of other investigators for 2D honeycombs, considering bending, axial and shearing deformations of struts, the present model not only produces transverse isotropy for regular hexagonal columnar structure but also provides a consistent Poisson's ratio when applied to a square honeycomb. The effect of tapered strut morphology on the elastic properties of cellular structures is investigated. For the general hexagonal columnar structures, the bending compliance is the dominant function for the in-plane elastic constants of 2D and 3D structures (excluding the in-plane shear modulus of rhombic structures) and the out-of-plane shear moduli of 3D structures, but the axial compliance is dominant for the in-plane shear modulus of 2D and 3D rhombic structures and the out-of-plane Young's modulus of 3D structures. For cellular materials with the same relative density, the presence of taper increases values of the effective Young's and shear moduli for which the bending compliance is dominant, but decreases those for which the axial compliance is dominant. It is found that the effective elastic properties of cellular materials are dependent not only on the relative density but also on strut morphology both in cross-section geometry and its variation along the strut length which the present model takes account of. These results illustrate the importance of the strut morphology in calculating the effective elastic properties of cellular materials.     

小尺寸材料弹性常数超声测量系统的研制及其应用

提出一种小尺寸材料弹性常数测量的新方法——利用线聚焦超声传感器和超声浸水技术同时测定纵波和漏表面波的波速，求得材料的弹性常数。基于PXI-8186嵌入式控制器构建了小尺寸材料弹性常数测控系统，利用LabVIEW软件平台开发了小尺寸材料弹性常数自动测量软件。实验结果表明，该方法可以实现小尺寸材料弹性常数的测量，测量结果具有很好的重复性。     

Effects of defects on in-plane properties of periodic metal honeycombs

The effects of missing or fractured cell walls on in-plane effective elastic stiffness and initial yield strength of square and triangular cell metal honeycombs are investigated using finite element analysis. Due to the change of localized deformation mode, the in-plane properties of defected honeycombs can differ significantly from those of intact metal honeycombs, depending on cell type and stress state. First, the effect of the size of a statistical volume element of honeycomb cells with randomly removed cell walls is explored by using different numbers of cells with 5% of walls removed, subject to periodic boundary conditions. The size of a representative volume element (statistically homogeneous) is determined for each considered in-plane property. Next, the effective in-plane properties of square cell and triangular cell honeycombs are, respectively, calculated as a function of increasing number density of randomly removed cell walls. Finally, the sensitivities of axial compressive effective properties of these honeycombs to missing cell walls are compared with that of a previously analyzed hexagonal cell honeycomb. The results indicate that some in-plane properties sharply diminish with defect density, while others exhibit more gradual decay. In compression, the effective elastic stiffness and initial yield strength of triangular cell honeycombs are least sensitive to defects among those considered.     

The effects of non-periodic microstructure and defects on the compressive strength of two-dimensional cellular solids

The utility of unit cell models that assume periodic microstructures may be limited when applied to cellular materials that have non-periodic microstructures. We analyzed the effects of non-periodic microstructure and defects on the compressive failure behavior of Voronoi honeycombs using finite element analysis. Our results indicate that the non-periodic arrangement of cell walls in random Voronoi honeycombs (with cells approximately uniform in size) results in higher strains in a small number of cell walls compared to periodic, hexagonal honeycombs. Consequently, the Voronoi honeycombs were approximately 30% weaker than periodic, hexagonal honeycombs of the same density. The strength difference between the Voronoi and periodic honeycombs depended slightly on density, due to density-dependent interactions between failure modes (i.e. plastic collapse and elastic buckling). Defects, introduced by removing cell walls at random locations, caused a sharp decrease in the effective mechanical properties of both Voronoi and periodic honeycombs (e.g. a 10% reduction in density due to defects caused a 60% reduction in the strength of Voronoi honeycombs). The sensitivity to defects was comparable for thin-walled, elastomeric honeycombs (relative density 0.015) and for thicker walled, plastic honeycombs (relative density 0.15). The properties degraded to zero when 35% of the cell walls were removed, consistent with the percolation limit for a two-dimensional network of hexagonal cells. When four or more adjacent cell walls were removed, the localized band of cell collapse passed through the defect site and the effective strength and modulus were reduced, indicating that even those defects which have a negligible effect on density can alter the failure pattern as well as the effective properties of honeycombs with cells of approximately equal size and strength.     

各向异性材料应力应变分析方法的研究

由于各向异性材料的弹性常数随方向而变化 ,这就使通常用于各向同性材料的光弹性贴片法的基本方程失效。本文从光弹性贴片法的基本原理出发 ,给出正交各向异性板内任一点的应力计算公式 ,同时也提出了正交各向异性板厚度效应的修正系数。文中对带圆孔正交各向异性板孔边应力分布做了光贴片实验并与文献 [2 ]中的有关数值解进行了比较 ,验证了本文工作的正确性     

铺层结构三维等效弹性常数研究

从铺层结构的三维宏观弹性特性出发,利用三维层压结构理论,获得了复合层板的三维弹性常数的等效公式。以MATLAB为平台,编写模块化程序,将层压结构理论运用于某大型回转机械平行铺层和环状铺层结构的三维弹性常数等效中,输入每个单层结构的弹性参数,该程序可自动生成部件等效刚度矩阵、柔度矩阵和等效弹性常数;结合APDL参数化语言建立有限元模型,对等效前后的结构进行模态分析比较。结果表明,等效前后部件前三阶固有频率的变化率都小于5%,说明该方法对此类复合铺层结构的三维弹性常数等效是可行的。     

颗粒增强复合材料有效弹性模量的预报

用细观力学的方法对陶瓷颗粒增强金属基复合材料进行研究,把材料简化为三相模型,陶瓷粒子和基体壳简化为椭球形二相胞元,用Mori-Tanaka法建立二相胞元的刚度预报模型.结果表明,二相胞元为横观各向同性,具有5个独立的弹性常数.据二相胞元方位的随机性,由应力应变换轴公式和物理方程确定复合材料的平均应变,进而得到复合材料的等效弹性模量和等效泊松比以及等效刚度模量的理论计算公式,并通过对所建模型的分析,确定各参量与陶瓷颗粒含量之间的关系.     

基于Voronoi随机模型研究多孔材料的动态特性

利用随机Voronoi技术生成2维随机模型,结合有限元分析方法系统研究多孔材料在x1-x2平面内冲击载荷作用下的动态特性.模型包含胞孔形状的不规则性和孔壁厚度的不均匀性,以及孔壁的随机不完整性.模拟结果发现,在中低速冲击时Voronoi模型并不出现如规则蜂窝模型一样的"X"和"V"形的变形,而出现几条局部随机变形带;在冲击速度比较高时,局部变形带并不明显,在冲击面端附近区域出现"I"形的变形.发现平台冲击压力和胞孔形状不规则度之间具有比较复杂的关系;很小的孔边不完整性将会造成材料强度很大的"丢失";尽管组成多孔材料的母材是理想弹-塑性材料,但应用Voronoi随机模型描述的多孔材料是一应变率敏感材料.     

State space solution for thick laminated piezoelectric plates with clamped and electric open-circuited boundary conditions

Based on the theories of 3-D elasticity and piezoelectricity and by assuming appropriate boundary functions, the state equation for laminated piezoelectric plate is established. By using the transfer matrix and recursive solution approach, an analytical solution that satisfies all boundary conditions, including the conditions on the top and bottom surfaces, of the laminates is presented. The solution can take into account all the independent elastic and piezoelectric constants for orthotropic and piezoelectric materials and satisfies the continuity conditions between plies of the laminates. Numerical examples are given at the end of the paper to verify the effectiveness of the present method. The results are compared with those of existing analytical and finite element models.     

从微观角度研究铝的宏观力学性能

从微观角度进行了分子模拟,建立了铝的晶胞,依据第一性原理,计算出其弹性系数矩阵,结合宏观尺度的微元体,建立了微元体的弹性性能和晶胞之间的弹性系数的关系,得到的模拟计算结果和实验值非常接近.     

非线性超声谐振方法及在结垢检测中的应用研究

针对压力容器和管道安全运行需要,发展了一种非线性超声谐振结垢检测方法。从理论上分析非线性细观弹性材料因迟滞效应引起的非线性弹性本构关系。研究发现,随着超声波激励幅值的增加,迟滞导致的非线性效应主要表现为超声波谐振频率向低频偏移和谐振频谱品质因数的变化。对涂有不同厚度模拟结垢的板试件进行非线性超声谐振检测试验,研究了激励电压水平对基波及二次谐波谐振频谱的影响规律,提出基于二次谐波弹性迟滞非线性系数和耗散迟滞非线性系数的结垢层厚度表征方法。在此基础上,将非线性超声谐振检测方法应用于实际工程中炉管结垢层检测,结果表明,利用二次谐波的弹性迟滞非线性系数和耗散迟滞非线性系数能较好反映炉管结垢状况。研究工作为实际工程中炉管结垢层检测提供了新的思路和方法。     

Transport properties in fibrous elastic rhombic composite with imperfect contact condition

In this contribution, effective elastic moduli are obtained by means of the asymptotic homogenization method (AHM), for oblique two-phase fibrous periodic composites with two models (spring and interphase) of imperfect contact conditions. This work is an extension of previous reported results, where only perfect contact for elastic or piezoelectric composites for square and hexagonal arrays were considered. The constituents of the composites exhibit transversely isotropic properties. A doubly periodic parallelogram array of cylindrical inclusions under longitudinal shear is considered. The behavior of the shear elastic coefficient for different geometry arrays related to the angle of the cell is studied. As validation of the present method, some numerical examples and comparisons with theoretical and experimental results verified that the present model is efficient for the analysis of composites with presence of imperfect interface and parallelogram cell. The effect of the arrangement of the cells on the shear effective property is observed. The present method can provide benchmark results for other numerical and approximate methods.     

Measurement of elastic constants of limited-size piezoelectric ceramic sample by ultrasonic method

Measurement of material elastic constants for limited-size samples by ultrasonic method is described and validated. Based on acoustic microscope technology, the material elastic constants are determined by longitudinal wave and leak surface wave velocities simultaneously measured by developed ultrasonic system with a line-focus PVDF transducer. In this paper, the elastic constants of limited-size Cr₂O₃ doping on 0.2 PZN–0.8 PZT piezoelectric ceramic wafer sample are determined and the measurement errors are analyzed. The experimental results show this ultrasonic system can be used for measurement of material elastic constants for limited-size samples with high measurement precision, and the relative errors for Poisson’s ratio and Young’s module measurements are, respectively, less than 1% and 3%. It can satisfy the requirement of engineering and science research. Furthermore, it is suitable to measure elastic constants of both isotropic and anisotropic materials by ultrasonic method with help of developed ultrasonic system.     

Experimental X-ray elastic constants of 3OHGV and St45 steels

Measured X-ray elastic constants of 30HGV and St45 steels are presented. The algorithm for the calculation of the X-ray elastic constants and their errors on the basis of diffractometer measurement are presented. Experimental results are compared with theoretical elastic constants. The influence of the surface layer strain of specimen on the experimental results is considered.     

A generalized self-consistent estimate for the effective elastic moduli of fiber-reinforced composite materials with multiple transversely isotropic inclusions

The effective elastic properties of a fiber-reinforced composite material with multiple transversely isotropic inclusions are estimated by the use of a generalized self-consistent method, which considers strong interactions between the inclusion and matrix as well as among inclusions. The accuracy of this method is established by comparing to the closed-form analytic solutions by Christensen when the matrix and inclusion are isotropic. Furthermore, current predictions from the generalized self-consistent method for a composite with multiple inclusions correspond well with the numerical results from finite element analysis. The generalized self-consistent method can be particularly useful in establishing micromechanics models of natural biological composite materials such as cortical bone to examine the dependence of the elastic properties of cortical bone on its porosity.     

A new model to predict effective elastic constants of composites with spherical fillers

In this study, a new model to predict the effective elastic constants of composites with spherical fillers is proposed. The original Eshelby model is extended to a finite filler volume fraction without using Mori-Tanaka’s mean field approach. When single filler is embedded in the matrix, the effective elastic constants of the composite are computed. The composite is in turn considered as a new matrix, where new single filler is again embedded in the matrix. The predicted results by the present model with a series of embedding procedures are compared with those by Mori-Tanaka, self-consistent, and generalized self-consistent models. It is revealed through parametric studies such as stiffness ratio of the filler to the matrix and filler volume fraction that the present model gives more accurate predictions than Mori-Tanaka model without using the complicated numerical scheme used in self-consistent and generalized self-consistent models.     

Effects of tricyclazole (5-methyl-1,2,4-triazol[3,4] benzothiazole), a specific DHN-melanin inhibitor, on the morphology of Fonsecaea pedrosoi conidia and sclerotic cells

The influence of tricyclazole (5-methyl-1,2,4-triazol[3,4]benzothiazole), a specific DHN-melanin inhibitor, on the cell walls and intracellular structures of Fonsecaea pedrosoi conidia and sclerotic cells was analyzed by transmission electron microscopy (TEM), deep-etching, and field emission scanning electron microscopy. The treatment of the fungus with 16 microg mL(-1) of tricyclazole (TC) did not significantly affect fungal viability, but electron microscopy observations showed several important morphological differences between TC-treated and non-TC treated cells. Control sclerotic cells presented patched granules, with an average diameter of 47 nm, on the cell surface, which were absent in TC-treated cells. Also, TC-treated sclerotic cells showed an undulated relief. TC treatment leads to an accumulation of electron lucent vacuoles in the fungal cytoplasm of both conidia and sclerotic cells, and treated conidia observed by deep etching showed a relevant thickening of the fungal cell wall. Together, these observations support the previous data of our group that F. pedrosoi synthesizes melanin in intracellular organelles. In addition, we suggest that melanin is not only an extracellular constituent but could also be dispersing all over the cell walls and could have an effective role in cross-linking different cell wall compounds that help maintain the regular shape of the cell wall.