基于三角对称共晶团断裂的复相陶瓷极限应力预报模型

根据复相陶瓷内三角对称共晶团的特殊结构形式,基于共晶团细观损伤断裂机理建立复相陶瓷极限应力预报模型,为分析复相陶瓷的断裂机理提供理论依据。首先,基于共晶团内纤维端部的应力集中效应,考虑共晶团内基体出现微观塑性流动的特性,利用位错塞积理论和内聚键破裂条件,确定三角对称共晶团的本征断裂应力。然后,基于沿共晶团晶向的微观损伤应变,确定加载函数,考虑三角对称共晶团细观断裂过程中的中性加载条件,计算共晶团的细观损伤断裂应力。最后,考虑三角对称共晶团尺寸的随机性和方向任意性,引入"临界区"概念,在共晶团尺寸和方向服从二维完全随机分布条件下,得到复相陶瓷极限应力的理论预报模型。结果表明,复相陶瓷的极限应力主要由三角对称共晶团的细观损伤极限应力确定,三角对称共晶团内纤维夹杂体积含量和尺寸对极限应力有重要影响。     

含片状缺陷共晶复合陶瓷的细观强度模型

根据缺陷在共晶复合陶瓷中的分布特点,假设缺陷为片状、缺陷周围介质为横观各向同性,建立了含缺陷共晶复合材料的细观力学模型;根据损伤理论定义了胞元等效外载应力场,依据等效夹杂理论得到了含缺陷各向异性基体复合材料 Griffith 强度,考虑缺陷的空间分布随机性得到了复合材料强度与缺陷尺寸、缺陷体积含量等参数的关系。结果表明：强度与缺陷半径的-1/2次方成线性关系,且缺陷尺寸较小时强度变化明显;片状缺陷体积含量对强度影响显著,尤其当缺陷含量小于3%时,少量缺陷即可造成强度极大地下降;缺陷形状及基体的各向异性对强度也有着重要影响,各向同性基体中片状缺陷不为圆形时,缺陷始终从短轴开始扩展,各向异性基体中片状缺陷为圆形时,则缺陷首先从弹性模量大的方向上扩展,最终缺陷形状和弹性模量满足特定的比例关系。     

含片状缺陷共晶复合陶瓷的细观强度模型

根据缺陷在共晶复合陶瓷中的分布特点,假设缺陷为片状、缺陷周围介质为横观各向同性,建立了含缺陷共晶复合材料的细观力学模型;根据损伤理论定义了胞元等效外载应力场,依据等效夹杂理论得到了含缺陷各向异性基体复合材料Griffith强度,考虑缺陷的空间分布随机性得到了复合材料强度与缺陷尺寸、缺陷体积含量等参数的关系。结果表明:强度与缺陷半径的-1/2次方成线性关系,且缺陷尺寸较小时强度变化明显;片状缺陷体积含量对强度影响显著,尤其当缺陷含量小于3%时,少量缺陷即可造成强度极大地下降;缺陷形状及基体的各向异性对强度也有着重要影响,各向同性基体中片状缺陷不为圆形时,缺陷始终从短轴开始扩展,各向异性基体中片状缺陷为圆形时,则缺陷首先从弹性模量大的方向上扩展,最终缺陷形状和弹性模量满足特定的比例关系。     

含共晶界面陶瓷复合材料的损伤应变场分析

研究了含共晶界面陶瓷复合材料的损伤应变场及其尺度效应。根据含共晶界面复合陶瓷的细观结构特性,利用含共晶界面陶瓷复合材料中三相胞元内的应力场分布规律,得出棒状共晶体内的无损应变场分布规律。针对棒状共晶体内存在损伤的现象,通过引入损伤变量,利用三相模型法得到了棒状共晶体内存在损伤时的应变场分布规律;根据应变和纤维状夹杂直径之间的关系,分析了棒状共晶体内的损伤应变场及其尺度效应。结果表明,含共晶界面陶瓷复合材料内三相胞元中基体、界面相和纤维夹杂内的损伤应变场对纤维夹杂直径具有明显的尺度效应。     

含强约束界面片状夹杂复合陶瓷热膨胀系数预报

以含强约束界面相片状夹杂复合陶瓷的细观结构为基础,建立含片状夹杂、强约束界面相、基体氛围和有效介质组成的四相模型,将片状夹杂、强约束界面相和基体氛围构成的三相胞元看作复合夹杂,根据Eshelby理论,确定了含同向片状夹杂复合陶瓷的有效热膨胀系数的解析表达式,复合陶瓷为横观各向同性,有2个独立的热膨胀系数.定量分析表明含同向片状夹杂的强约束界面复合陶瓷的有效热膨胀系数具有明显的尺度效应.     

Al2O3基陶瓷刀具材料摩擦磨损特性及其有限元分析

以添加TiC、Ti（C,N）和SiCw 3种Al2O3基陶瓷刀具材料作为研究对象,在MRH-3型高速环-块摩擦磨损试验机上研究3种陶瓷刀具材料在相同试验条件下的摩擦磨损性能,通过扫描电子显微镜对陶瓷的磨损表面进行观察,并利用ANSYS有限元软件分析计算磨损时的应力分布．结果表明,Al2O3基陶瓷刀具材料的摩擦磨损特性与其添加剂的种类有关,其抗磨性能由大到小顺序依次为Al2O3／SiCw〉Al2O3／Ti（C,N）〉Al2O3／TiC．Al2O3基陶瓷刀具的摩擦磨损性能与其硬度（H）、弹性模量（E）和断裂韧性（KIC）有关,磨损率W随E／H增加而增大,随KIC增加而减小．Al2O3／TiC陶瓷刀具材料的磨损机理以粘着磨损为主,Al2O3／Ti（C,N）和Al2O3／SiCw陶瓷刀具材料的磨损机理主要为磨粒磨损．     

Al2O3陶瓷材料应变率相关的动态本构关系研究

采用改进的SHPB实验方法对Al2O3陶瓷的动态力学性能进行了研究,得到了材料在较高应变率范围内的动态应力应变曲线。结果表明,Al2O3陶瓷为弹脆性材料,其动态应力应变呈非线性关系,在较高的应变率范围内,陶瓷材料的动态应力应变关系是应变率相关的;材料的初始弹性模量、破坏应力、破坏应变值随应变率的增大而增大。基于损伤力学的基本理论,给出了Al2O3陶瓷的一维损伤型线性弹脆性本构模型。根据SHPB实验结果确定模型中的参数,得到了Al2O3陶瓷应变率相关的损伤型动态本构方程。     

爆炸成型弹丸对Al2O3装甲陶瓷材料的侵彻实验研究

用爆炸成型弹丸(explosively formed projectile, EFP)对Al2O3装甲陶瓷材料进行了侵彻（depth of penetration, DOP）实验,得到了99Al2O3装甲陶瓷对模拟EFP的质量防护因数和差分防护因数及他们随陶瓷块厚度的变化规律,初步评估了99Al2O3装甲陶瓷对EFP的抗侵彻性能,解释了装甲陶瓷对EFP的抗侵彻过程和机理。研究结果表明,增加约束可以提高陶瓷的抗侵彻性能。     

压入实验界面端奇异性研究

纤维压入实验是复合材料界面剪切强度细观实验方法之一,其试件通常由复合材料中切割下来制备而成,从中选取单根纤维,进行压入试验,所以被选中的纤维可看成是被纤维和纯基本材料构成的横观各向同性复合材料所包裹。本文以此为依据,建立了横观各向同性复合材料基体包裹各向同性纤维的轴对称模型,采用逐次渐近等求解方法,得到了求解该模型界面端应力奇异性指数的特征方程,并计算了碳纤维／环氧树脂、碳纤维／铝和碳纤维／Al2O3压入试件界面端奇异性随碳纤维体积百分含量的变化情况。     

三维立方准晶椭球夹杂的Eshelby张量

准晶体颗粒复合智能材料具有优异的物化性能和应用前景。不同于传统的各向同性材料,三维立方准晶体材料包含声子场,相位子场,及声子-相位子耦合场。为更好地研究准晶体颗粒夹杂问题,揭示准晶体材料夹杂问题的物理现象,本文利用本征应变公式和柯西留数定理,考虑椭球体夹杂,获得了三维立方准晶材料夹杂问题的Eshelby张量,并给出了统一的表达式。进而,当三维立方准晶夹杂形状为球形、棒状、扁平状和带状时,获得了封闭形式的三维立方准晶Eshelby张量表达式。同时,给出了椭球体长径比变化时Eshelby张量的变化规律,这对研究准晶体颗粒夹杂问题具有重要的理论意义。     

Characterization of Anisotropic Polymeric Foam Under Static and Dynamic Loading

An orthotropic polymeric foam with transverse isotropy (Divinycell H250) used in composite sandwich structures was characterized at various strain rates. Uniaxial experiments were conducted along principal material axes as well as along off-axis directions under tension, compression, and shear to determine engineering constants, such as Young??s and shear moduli. Uniaxial strain experiments were conducted to determine mathematical stiffness constants, i. e., C _ij . An optimum specimen aspect ratio for these tests was selected by means of finite element analysis. Quasi-static and intermediate strain rate tests were conducted in a servo-hydraulic testing machine. High strain rate tests were conducted using a split Hopkinson Pressure Bar system built for the purpose using polymeric (polycarbonate) bars. The polycarbonate material has an impedance that is closer to that of foam than metals and results in lower noise to signal ratios and longer loading pulses. It was determined by analysis and verified experimentally that the loading pulses applied, propagated along the polycarbonate rods at nearly constant phase velocity with very low attenuation and dispersion. Material properties of the foam were obtained at three strain rates, quasi-static (10^?4 s^?1), intermediate (1 s^?1), and high (10³ s^?1) strain rates. A simple model proposed for the Young??s modulus of the foam was in very good agreement with the present and published experimental results.     

Extreme conditions of elastic constants and principal axes of anisotropy

This paper describes the derivation of extreme conditions of each elasticity coefficient (Young’s modulus, shear modulus, et al.,) for the general case of linear-elastic anisotropic materials. The stationarity conditions are obtained, and they determine the orthogonal coordinate systems being the principal axes of anisotropy, where the number of independent elasticity constants decreases from 21 to 18 and, in some cases of anisotropy, to 15 or lower. The example of a material with cubic symmetry is given.     

Localized acoustic waves at twist boundaries in transversely isotropic media

Existence criteria and basic characteristics are analytically found for elastic waves localized at a twist boundary in transverse isotropic media. The boundary is formed by two identical semi-infinite bodies with non-collinear principal axes parallel to the interface. The analysis is based on the Stroh formalism specified to the case of transverse isotropy. The dispersion equation is presented in a general form and explicitly solved for small misorientations. The waves in the sector situated between the directions of transverse isotropy in the sub-media of the bicrystal are explicitly described.     

Failure criteria for transtropic,pressure dependent materials

A convenient criterion in the 3D-principal stress space for describing the yielding and failure behaviour of transversely isotropic (transtropic) materials, presenting also the strength differential effect (SDE) along the three principal stress axes, is the elliptic-paraboloid failure criterion (EPFC). The general properties of the EPFC were examined previously for the general anisotropic material with SDE and its validity was established by comparing it with other criteria and the real behaviour of various anisotropic materials. In this paper the particular properties of materials showing a transverse isotropy were studied and important results were established which simplify considerably the complicated expressions established in the case of total anisotropy. The particular properties of the EPFC for transtropic materials were also compared with experimental evidence and were found to be in agreement with it.     

The symmetry approximation for nonsymmetric permeability tensors and its consequences for mass transport

It is well known that the permeability has a tensor character. In practical applications, this is accounted for by the introduction of three principal permeabilities — three scalars — and three mutually orthogonal principal axes. In this paper, it is investigated whether this is always the exact way of describing anisotropy and, if not, what the consequences of the principal axes approximation are for flow and transport. First, it is shown that spatial upscaling may result in nonsymmetric large-scale permeability tensors, for which principal axes do not exist. However, it is possible to define generalized principal axes: three principal axes for the flux and three for the pressure gradient, with only three principal permeabilities. Since nonsymmetric permeability tensors are undesirable in practical applications, an approximation method making the nonsymmetric permeability symmetric is introduced. The important conclusion is then that the exact large-scale flux and large-scale pressure gradient do not have the same directions as the approximate flux and approximate pressure gradient. A practical consequence is that the principal axes approximation results in a difference between flux and transport direction. When considering miscible displacement or transport of mass dissolved in groundwater, the velocity component normal to the flux direction may be considered as a contribution to the transverse macro dispersion.     

Variational analysis of transverse cracking and local delamination in [θm/90n]s laminates

A displacement-based variational model is developed to study the effects of transverse cracking and local delaminations in symmetric composite laminates. In the model, the crack shape is assumed to be a function of crack density and delamination length. Using a variational approach with the principle of minimum potential energy, governing equations are derived. The effective Young’s modulus E_x and energy release rate G are theoretically examined as a result of local delaminations.     

On Compressible Materials Capable of Sustaining Axisymmetric Shear Deformations. Part 4: Helical Shear of Anisotropic Hyperelastic Materials

Conditions on the form of the strain energy function in order that homogeneous, compressible and isotropic hyperelastic materials may sustain controllable static, axisymmetric anti-plane shear, azimuthal shear, and helical shear deformations of a hollow, circular cylinder have been explored in several recent papers. Here we study conditions on the strain energy function for homogeneous and compressible, anisotropic hyperelastic materials necessary and sufficient to sustain controllable, axisymmetric helical shear deformations of the tube. Similar results for separate axisymmetric anti-plane shear deformations and rotational shear deformations are then obtained from the principal theorem for helical shear deformations. The three theorems are illustrated for general compressible transversely isotropic materials for which the isotropy axis coincides with the cylinder axis. Previously known necessary and sufficient conditions on the strain energy for compressible and isotropic hyperelastic materials in order that the three classes of axisymmetric shear deformations may be possible follow by specialization of the anisotropic case. It is shown that the required monotonicity condition for the isotropic case is much simpler and less restrictive. Restrictions necessary and sufficient for anti-plane and rotational shear deformations to be possible in compressible hyperelastic materials having a helical axis of transverse isotropy that winds at a constant angle around the tube axis are derived. Results for the previous case and for a circular axis of transverse isotropy are included as degenerate helices. All of the conditions derived here have essentially algebraic structure and are easy to apply. The general rules are applied in several examples for specific strain energy functions of compressible and homogeneous transversely isotropic materials having straight, circular, and helical axes of material symmetry.     

The Stress Response of Functionally Graded Isotropic Linearly Elastic Rotating Disks

The purpose of this research is to investigate the effects of material inhomogeneity on the response of linearly elastic isotropic solid circular disks or cylinders, rotating at constant angular velocity about a central axis. The work is motivated by the recent research activity on functionally graded materials (FGMs), i.e., materials with spatially varying properties tailored to satisfy particular engineering applications. The analog of the classic problem for a homogeneous isotropic rotating solid disk or cylinder is considered. The special case of a body with Young"s modulus depending on the radial coordinate only, and with constant Poisson"s ratio, is examined. For the case when the Young"s modulus has a power-law dependence on the radial coordinate, explicit exact solutions are obtained. It is shown that the stress response of the inhomogeneous disk (or cylinder) is significantly different from that of the homogeneous body. For example, the maximum radial and hoop stresses do not, in general, occur at the center as in the case for the homogeneous material. Furthermore, for the case where the Young"s modulus increases with radial distance from the center, it is shown that radially symmetric solutions exist provided the rate of growth of the Young"s modulus is, at most, cubic in the radial variable. It is also shown for the general inhomogeneous isotropic case how the material inhomogeneity may be tailored so that the radial and hoop stress are identical throughout the disk. This revised version was published online in August 2006 with corrections to the Cover Date.     

A mechanics-of-materials model for predicting Young’s modulus of damaged woven fabric composites involving three damage modes

An analytical model for damaged woven fabric composites is developed using the theory of advanced mechanics of materials. The analysis is based on Castigliano’s second theorem and utilizes a damaged mosaic model laminate. Three damage modes (i.e., transverse yarn cracking, interface debonding, and sliding with friction at the interface) are considered. Only one independent interfacial parameter, the friction coefficient between warp and fill yarns, is introduced in the analysis. A closed-form formula is provided for estimating effective Young’s modulus of damaged woven laminates. A parametric study of some 192 sample cases of two different composite systems (i.e., glass fiber/epoxy and ceramic fiber/ceramic) is conducted to illustrate the application and significance of the newly derived analytical model. The numerical values of the effective Young’s modulus for the special case involving only transverse yarn cracking (the first damage mode) estimated by the present mechanics-of-materials model agree fairly well with those predicted by an elasticity-based model [Int. J. Solids Struct. 38 (2001) 855]. For the general case involving all three damage modes simultaneously, the present model reveals the complex nature of Young’s modulus reduction in a quantitative manner, which differs from existing models.     

Unit cell debonding analyses for arbitrary orientation of plastic anisotropy

Debonding of rigid inclusions embedded in the elastic–plastic aluminum alloy Al 2090-T3 is analyzed numerically using a unit cell model taking full account of finite strains. The cell is subjected to overall biaxial plane strain tension and periodical boundary conditions are applied to represent arbitrary orientations of plastic anisotropy. Plastic anisotropy is considered using two phenomenological anisotropic yield criteria, namely Hill [Proceedings of the Royal Society of London A 193 (1948) 281] and Barlat et al. [International Journal of Plasticity 7 (1991) 693]. For this material plastic anisotropy delays debonding compared to plastic isotropy except for the case of Hill’s yield function when the tensile directions coincided with the principal axes of anisotropy. For some inclinations of the principal axes of anisotropy relative to the tensile directions, the stress strain responses are identical but the deformation modes are mirror images of each other.