Effect of surface/interface stress on the plastic deformation of nanoporous materials and nanocomposites

Surface and interface play an important role on the overall mechanical behaviors of nanostructured materials. We investigate the effect of surface/interface stress on the macroscopic plastic behaviors of nanoporous materials and nanocomposites, where both the surface/interface residual stress and surface/interface elasticity are taken into account. A new second-order moment nonlinear micromechanics theory is developed and then reduced to macroscopically isotropic materials. It is found that the effect of surface/interface residual stress is much more prominent than that of the surface/interface elasticity, causing strong size effect as well as asymmetric plastic deformation for tension and compression. The variation of yield strength is more prominent with smaller pore/inclusion size or higher pore/inclusion volume fraction. For a representative nanoporous aluminum, the surface effect becomes significant when the pore radius is smaller than about 50 nm. When hard inclusions are embedded in a ductile metal matrix, the interface effect and resulting size effect are much smaller than that of nanoporous materials. The results may be useful for evaluating the mechanical integrity of nanostructured materials.     

Analysis and simulation for tensile behavior of anisotropic open-cell elastic foams

Based on the elongated Kelvin obtained to investigate the tensile behavior Kelvin model＇s periodicity and symmetry in model, a simplified periodic structural cell is of anisotropic open-cell elastic foams due to the whole space. The half-strut element and elastic deflection theory are used to analyze the tensile response as done in the previous studies. This study produces theoretical expressions for the tensile stress-strain curve in the rise and transverse directions. In addition, the theoretical results are examined with finite element simulation using an existing formula. The results indicate that the theoretical analysis agrees with the finite element simulation when the strain is not too high, and the present model is better. At the same time, the anisotropy ratio has a significant effect on the mechanical properties of foams. As the anisotropy ratio increases, the tensile stress is improved in the rising direction but drops in the transverse direction under the same strain.     

DYNAMIC RESPONSE OF SATURATED POROUS ELASTIC FOUNDATION UNDER POROSITY ANISOTROPY$^{\bf 1)}$

由于不同的沉积条件和应力状态, 天然土体通常表现出一定的各向异性特征. 文章研究地基上表面受温度载荷和机械载荷时, 孔隙率各向异性参数变化对饱和多孔弹性地基热-水-力耦合动力响应问题的影响. 基于Lord-Shulman广义热弹性理论, 结合孔隙率各向异性基本假设, 建立了孔隙率各向异性饱和多孔弹性地基热-水-力耦合动力响应模型, 利用正则模态法推导出无量纲竖向位移、超孔隙水压力、竖向应力和温度分布的解析表达式并加以图示. 正则模态法是一种利用加权残差求得解析解的方法, 相较于其他方法能快速求解偏微分方程. 当孔隙率各向异性参数为1时, 可将该各向异性耦合动力响应模型退化为热-水-力耦合动力响应模型验证该地基模型的合理性. 着重分析了孔隙率各向异性参数变化对不同物理量的影响. 结果表明: 孔隙率各向异性参数变化对物理量均有一定影响. 在地基上表面受温度载荷作用时, 对超孔隙水压力和竖向应力影响最为明显; 在地基上表面受机械载荷作用时, 对超孔隙水压力和温度影响明显. 整体而言, 无论地基上表面受何种载荷, 随着各向异性参数增大, 峰值逐渐减小, 在地基深度增加方向峰值所在位置向靠近地基上表面方向移动.     

孔隙率各向异性下饱和多孔弹性地基动力响应

由于不同的沉积条件和应力状态, 天然土体通常表现出一定的各向异性特征. 文章研究地基上表面受温度载荷和机械载荷时, 孔隙率各向异性参数变化对饱和多孔弹性地基热-水-力耦合动力响应问题的影响. 基于Lord-Shulman广义热弹性理论, 结合孔隙率各向异性基本假设, 建立了孔隙率各向异性饱和多孔弹性地基热-水-力耦合动力响应模型, 利用正则模态法推导出无量纲竖向位移、超孔隙水压力、竖向应力和温度分布的解析表达式并加以图示. 正则模态法是一种利用加权残差求得解析解的方法, 相较于其他方法能快速求解偏微分方程. 当孔隙率各向异性参数为1时, 可将该各向异性耦合动力响应模型退化为热-水-力耦合动力响应模型验证该地基模型的合理性. 着重分析了孔隙率各向异性参数变化对不同物理量的影响. 结果表明: 孔隙率各向异性参数变化对物理量均有一定影响. 在地基上表面受温度载荷作用时, 对超孔隙水压力和竖向应力影响最为明显; 在地基上表面受机械载荷作用时, 对超孔隙水压力和温度影响明显. 整体而言, 无论地基上表面受何种载荷, 随着各向异性参数增大, 峰值逐渐减小, 在地基深度增加方向峰值所在位置向靠近地基上表面方向移动.      

采用瓣叶复合材料的生物心脏瓣膜的力学分析

采用微观组织结构分析及宏观复合材料分析结合的方法,分析了猪主动脉瓣的非线性复合材料性质,提出了一种适用于猪主动脉瓣的非线性复合材料本构模型,用提出的非线性复合材料本构模型,对闭合承载状态下的等厚度与变厚度几何模型的猪主动脉瓣的应力分布及变形进行了有限元数值模拟,发现：与各向同性瓣叶相比,单向增强复合材料的瓣叶不但具有较强的承载能力,而且具有较大的柔软性。     

Elliptical inclusion in an anisotropic plane: non-uniform interface effects

We study the plane deformation of an elastic composite system made up of an anisotropic elliptical inclusion and an anisotropic foreign matrix surrounding the inclusion. In order to capture the influence of interface energy on the local elastic field as the size of the inclusion approaches the nanoscale, we refer to the Gurtin-Murdoch model of interface elasticity to describe the inclusion-matrix interface as an imaginary and extremely stiff but zero-thickness layer of a finite stretching modulus. As opposed to isotropic cases in which the effects of interface elasticity are usually assumed to be uniform (described by a constant interface stretching modulus for the entire interface), the anisotropic case considered here necessitates non-uniform effects of interface elasticity (described by a non-constant interface stretching modulus), because the bulk surrounding the interface is anisotropic. To this end, we treat the interface stretching modulus of the anisotropic composite system as a variable on the interface curve depending on the specific tangential direction of the interface. We then devise a unified analytic procedure to determine the full stress field in the inclusion and matrix, which is applicable to the arbitrary orientation and aspect ratio of the inclusion, an arbitrarily variable interface modulus, and an arbitrary uniform external loading applied remotely. The non-uniform interface effects on the external loading-induced stress distribution near the interface are explored via a group of numerical examples. It is demonstrated that whether the nonuniformity of the interface effects has a significant effect on the stress field around the inclusion mainly depends on the direction of the external loading and the aspect ratio of the inclusion.     

FeCrAl合金材料织构对其宏观力学本构关系的影响研究

FeCrAl合金具有优良的高温抗氧化性和耐辐照性能,是事故容错核燃料包壳的重要候选材料. 其在加工过程和热处理过程中易形成α纤维织构（<110>//RD）和γ纤维织构（<111>//ND）,会影响材料的宏观力学性能与深加工成形能力. 本研究针对具有不同织构的多晶FeCrAl合金,建立了代表性体元模型, 使用晶体塑性有限元方法,在ABAQUS/Explicit中模拟材料单轴加载下的宏观应力应变曲线,分析不同织构对FeCrAl合金宏观力学本构关系的影响. 计算结果表明,对于具有α织构、γ织构和晶粒无择优取向的材料,在轧向上的应力应变曲线差异较小. γ织构会引起材料强烈的各向异性,在轧面法向上的屈服强度远高于轧向和横向上的屈服强度,这是因为晶粒的<111>方向平行于加载方向,滑移系难以启动. 提高γ纤维织构的比例,将增大轧面法向上的屈服强度. 本研究可以为优化FeCrAl合金材料织构、加工条件和材料力学性能提供参考.     

FeCrAl合金材料织构对其宏观力学本构关系的影响研究

FeCrAl合金具有优良的高温抗氧化性和耐辐照性能,是事故容错核燃料包壳的重要候选材料. 其在加工过程和热处理过程中易形成α纤维织构（<110>//RD）和γ纤维织构（<111>//ND）,会影响材料的宏观力学性能与深加工成形能力. 本研究针对具有不同织构的多晶FeCrAl合金,建立了代表性体元模型, 使用晶体塑性有限元方法,在ABAQUS/Explicit中模拟材料单轴加载下的宏观应力应变曲线,分析不同织构对FeCrAl合金宏观力学本构关系的影响. 计算结果表明,对于具有α织构、γ织构和晶粒无择优取向的材料,在轧向上的应力应变曲线差异较小. γ织构会引起材料强烈的各向异性,在轧面法向上的屈服强度远高于轧向和横向上的屈服强度,这是因为晶粒的<111>方向平行于加载方向,滑移系难以启动. 提高γ纤维织构的比例,将增大轧面法向上的屈服强度. 本研究可以为优化FeCrAl合金材料织构、加工条件和材料力学性能提供参考.     

Mechanics of corrugated surfaces

Experimental studies of the surface stress of solids typically work with surfaces that are not perfectly planar. The experiment then probes an effectively averaged surface stress. The evolution of the surface morphology, for instance during film growth or reconstruction, is also affected by the surface stress acting on a corrugated surface. Here, we analyze the mechanics of rough surfaces in a continuum framework. In a generalization of the approach of Weissmüller and Duan [2008. Phys. Rev. Lett. 101, 146102] to solids with anisotropic elasticity, anisotropic surface stress and anisotropic roughness, we focus on the effectively averaged surface stress that determines the mean compensating stress in the bulk. Important concepts are the projection of out-of-plane stresses at inclined segments of a surface into the macroscopic surface plane, and the transverse coupling between the out-of-plane and in-plane components of the surface-induced stress in the bulk. We show that the coupling of the surface stress at a corrugated surface into a planar substrate depends on the geometry of the corrugation exclusively through the surface orientation distribution function. Special geometries are inspected with an eye on illustrating the impact of anisotropic elasticity as well as geometric anisotropy, which both feed into the anisotropy of the effective surface stress.     

Evolution of plastic anisotropy in amorphous polymers during finite straining

The large strain deformation response of amorphous polymers results primarily from orientation of the molecular chains within the polymeric material during plastic straining. Molecular network orientation is a highly anisotropic process, thus the observed mechanical response is strongly a function of the anisotropic state of these materials. Through mechanical testing and material characterization, the nature of the evolution of molecular orientation under different conditions of state of strain is developed. The role of developing anisotropy on the mechanical response of these materials is discussed in the context of assessing the capabilities of several models to predict the state of deformation-dependent response. A three-dimensional rubber elasticity spring system that is capable of capturing the state of deformation dependence of strain hardening is used to develop a tensorial internal state variable model of the evolving anisotropic polymer response. This fully three-dimensional constitutive model is shown to be successfully predictive of the true stress vs. true strain data obtained in our isothermal uniaxial compression and plane strain compression experiments on amorphous polycarbonate (PC) and polymethylmethacrylate (PMMA) at moderate strain rates. A basis is established for providing the polymer designer with the ability to predict the flow strengths and deformation patterns of highly anisotropic materials. A companion paper by Arruda, Boyce, and Quintus-Bosz [in press] shows how the model developed herein is used to predict various anisotropic aspects of the large strain mechanical response of preoriented materials. Additional work has been done to extend the model to include the effects of strain rate and temperature in Arruda, Jayachandran, and Boyce [in press].     

Wave propagation analysis of a functionally graded magneto-electro-elastic nanobeam rest on Visco-Pasternak foundation

Wave propagation analysis of a nanobeam made of functionally graded magneto-electro-elastic materials with rectangular cross section rest on Visco-Pasternak foundation is studied in this paper. For modeling the axial, rotation and transverse deformations, Timoshenko beam model is used. Fundamental magneto-electro-elastic equations of the model are derived for a general functionally graded beam excited to electric and magnetic potentials. Surface elasticity is employed for more confident modeling the behavior of nanobeam. Using Hamilton principle and calculation of kinetic and strain energies, the equations of motion are derived. Considering the harmonic wave propagation of infinite domain yields characteristic equation of the system in terms of different parameters of model. The effects of different parameters such as non-homogeneous index, wave number and residual surface stress are investigated on the different phase velocities corresponding to modes of deformation. One can find that increasing the non-homogeneous index and wave number leads to decrease in wave propagation phase velocities.     

沉积方向和粒径组成对砂土力学特性的影响

运用砂土毛细效应所形成的假凝聚力制备具有不同沉积方向的试样,开展三轴固结排水剪切试验,研究粒径组成对初始各向异性砂土力学特性的影响,分析了粒径组成、沉积方向、强度特性和体积变化之间的相互关系.研究结论表明,试样剪切带的形成受到颗粒级配的影响,它是应力应变关系中陡降阶段的产生原因.沉积方向对粗砂和细砂的偏应力峰值强度均有...     

皮质骨断裂力学行为的实验研究

采用稳态裂纹扩展和疲劳裂纹扩展的实验, 研究了牛皮质骨横向和纵向裂纹扩展的断裂力学行为. 沿着两个方向制备了紧凑拉伸(CT)试件. 由于试件尺寸的限制,采用数值计算方法确定了裂纹尖端应力强度因子与裂纹长度的关系. 在实验中, 采用数字图像相关法精确测定裂纹尖端的位置. 由于裂纹沿横向扩展时有较大的偏斜, 将采用$J$积分测量其断裂韧性. 实验结果表明, 在裂纹扩展的一定范围内, 皮质骨的断裂韧度随着裂纹不断扩展而增大, 即表现出上升的阻力曲线(R-curve)性质.而皮质骨的横向裂纹扩展的断裂韧度要远远大于纵向裂纹扩展的断裂韧度, 表现出各向异性的阻力曲线行为. 在疲劳裂纹扩展中, 纵向疲劳裂纹扩展率要大于横向疲劳裂纹扩展率, 这说明皮质骨具有各向异性的疲劳裂纹扩展性质.      

任意多椭圆孔多裂纹无限大各向异性板应力强度因子求解的一种新方法

采用各向异性体平面弹性理论中的复势方法,应用保角变换技术,以F aber级数为工具,导出含任意多椭圆孔和裂纹群无限大各向异性板在远场载荷作用下其应力场和位移场的级数解,并在此基础上利用断裂力学方法确定裂纹尖端的应力强度因子,通过算例讨论了材料参数及裂纹、孔的尺寸等对应力强度因子的影响规律,得出了一些有益的结论。数值结果表明本文方法具有计算精度高、收敛速度快、方便快捷等优点,有利于全面系统地研究各参数对结构断裂性能的影响。     

具有表面效应的压电半空间中的表面波

纳米科技的快速发展使压电纳米结构在纳米机电系统中得到广泛应用,形成了诸如纳米压电电子学等新的研究方向.与传统的宏观压电材料相比,在纳米尺度下压电材料往往呈现出不同的力学特性,而造成这种差异的原因之一便是表面效应.本文基于Stroh公式、Barnett-Lothe积分矩阵及表面阻抗矩阵,研究计入表面效应的任意各向异性压电半空间中的表面波传播问题,导出了频散方程.针对横观各向同性压电材料,假设矢状平面平行于材料各向同性面,发现Rayleigh表面波和B-G波解耦,并得到各自的显式频散方程.结果表明,Rayleigh表面波的波速小于偏振方向垂直于表面的体波,而B-G波的波速小于偏振方向垂直于矢状平面的体波.以PZT-5H材料为例,用数值方法考察表面残余应力和电学边界条件对表面波频散特性的影响发现:表面残余应力只对第一阶Rayleigh波有明显的影响;电学开路情形的B-G波比电学闭路情形的B-G波传播快.本文工作可为纳米表面声波器件的设计或压电纳米结构的无损检测提供理论依据.     

Asymptotic approach to analyze singular stress state in anisotropic multi-material: Application to the rivets

The problem of stress singularities due to multi-material junctions is described in this paper. A semi-analytical approach is proposed based on an asymptotic model in the case of anisotropic linear elasticity in three dimensions. The advantage of the present method is the quasi-explicit knowledge of the stress and displacement fields around the junctions. Thus, after a brief explanation of the approach leading to the mechanical fields around the singular line at the junction between different materials, numerical results are presented concerning various configurations of an assembly with rivets included in a bi-layer composite that illustrate this method.     

Elastic field of an isotropic matrix with a nanoscale elliptical inhomogeneity

In traditional continuum mechanics, the effect of surface energy is ignored as it is small compared to the bulk energy. For nanoscale materials and structures, however, the surface effects become significant due to the high surface/volume ratio. In this paper, two-dimensional elastic field of a nanoscale elliptical inhomogeneity embedded in an infinite matrix under arbitrary remote loading and a uniform eigenstrain in the inhomogeneity is investigated. The Gurtin–Murdoch surface/interface elasticity model is applied to take into account the surface/interface stress effects. By using the complex variable technique of Muskhelishvili, the analytic potential functions are obtained in the form of an infinite series. Selected numerical results are presented to study the size-dependency of the elastic field and the effects of surface elastic moduli and residual surface stress. It is found that the elastic field of an elliptic inhomogeneity under uniform eigenstrain is no longer uniform when the interfacial stress effects are taken into account.     

显式模拟类橡胶材料应力软化引起的不可恢复变形及其各向异性特征

类橡胶材料在经过初次加载后会产生应力软化现象, 也就是Mullins效应. 实验证明应力软化现象会导致材料产生不可恢复变形, 同时引入各向异性特征. 本文基于对数应变构造一个多轴可压缩应变能函数, 先引入耗散来表征应力软化现象, 再引入依赖耗散大小的不可恢复变形量以及各向异性特征量, 使得新模型既可以表征Mullins效应, 又能模拟应力软化作用下产生的不可恢复变形和各向异性特征. 本文在各向同性形函数的基础上, 通过球坐标系的思想, 进一步发展并提出了一个任意方向适用的各向异性形函数. 新模型在材料尚未发生软化(耗散为0)的情况下, 表现出各向同性; 一旦发生应力软化(耗散大于0), 则变为各向异性. 随着加载?卸载循环的累积, 耗散逐渐变大, 不可恢复变形也随之变大直到达到一个稳定的值, 各向异性特性也逐渐变得明显. 新方法得到的结果可以精确匹配经典的实验数据, 并预测不同方向的应力软化现象以及由此产生的不可恢复变形和各向异性特征.      

ANISOTROPIC STRENGTH CRITERION BASED ON T CRITERION AND THE TRANSFORMATION STRESS METHOD 1)

岩土材料通常呈现出成层水平分布特点, 即可将其视为横观各向同性材料, 横观各向同性对于岩土材料的变形以及强度值都会产生显著的影响. 基于已提出的t强度准则, t强度准则是基于各向同性单元体中存在有效滑移面来构建的, 并根据该空间有效滑移面上主剪应力与主法向应力的比值达到一定阈值为破坏条件. 在空间中存在有效滑移面与物理沉积面, 基于上述两个面在空间的位置关系, 用两面夹角作为表征横观各向同性对剪切强度影响程度的参量, 并假定当该夹角值越大, 则各向异性对强度贡献程度越大, 对应更大的应力比强度值, 反之, 则对应更小的应力比强度值. 基于上述思路并类比将其推广为正交三维各向异性准则, 基于三维各向异性材料的三维沉积面, 提出了三维特征沉积面的概念, 并基于空间滑移面与三维特征沉积面之间的夹角作为度量各向异性程度的变量, 提出了基于两面角作为参量考虑原生各向异性的应力比强度公式, 并利用该应力比强度公式来修正已提出的t强度准则, 最终建立了考虑各向异性影响的t准则公式. 在上述准则基础上, 考虑将各向异性应力空间转换为各向同性应力空间的思路, 在各向异性t准则基础上, 推导得到了基于各向异性强度t准则的变换应力公式, 利用变换应力公式可以将传统的以p, q为变量的各向同性本构模型转变为可考虑各向异性的三维本构模型. 通过对岩土材料的强度以及真三轴条件下的应力应变关系试验数据预测, 验证了所提的各向异性t准则及其变换应力公式的有效性及适用性.