Three-dimensional micromechanical modeling of voided polymeric materials

A three-dimensional micromechanical unit cell model for particle-filled materials is presented. The cell model is based on a Voronoi tessellation of particles arranged on a body-centered cubic (BCC) array. The three-dimensionality of the present cell model enables the study of several deformation modes, including uniaxial, plane strain and simple shear deformations, as well as arbitrary principal stress states.The unit cell model is applied to studies on the micromechanical and macromechanical behavior of rubber-toughened polycarbonate. Different load cases are examined, including plane strain deformation, simple shear deformation and principal stress states. For a constant macroscopic strain rate, the different load cases show that the macroscopic flow strength of the blend decreases with an increase in void volume fraction, as expected. The main mechanism for plastic deformation is broad shear banding across inter-particle ligaments. The distributed nature of plastic straining acts to reduce the amount of macroscopic strain softening in the blend as the initial void volume fraction is increased. In the case of plane strain deformation, the plastic flow is observed to initiate across inter-particle ligaments in the direction of constraint. This particular mode of deformation could not have been captured using a two-dimensional, plane strain idealization of cylindrical voids in a matrix.The potential for localized crazing and/or cavitation in the matrix is addressed. It is observed that the introduction of voids acts to relieve hydrostatic stress in the matrix material, compared to the homopolymer. It is also seen that the predicted peak hydrostatic stress in the matrix is higher under plane strain deformation than under triaxial tension (with equal lateral stresses), for the same macroscopic stress triaxiality.The effect of void volume fraction on the macroscopic uniaxial tension behavior of the different blends is examined using a Considère construction for dilatant materials. The natural draw ratio was predicted to decrease with an increase in void volume fraction.     

Electroelastic behavior modeling of piezoelectric composite materials containing spatially oriented reinforcements

In this work, a modeling of electroelastic composite materials is proposed. The extension of the heterogeneous inclusion problem of Eshelby for elastic to electroelastic behavior is formulated in terms of four interaction tensors related to Eshelby’s electroelastic tensors. Analytical formulations of interaction tensors are presented for ellipsoidal inclusions. These tensors are basically used to derive the self-consistent model, Mori–Tanaka and dilute approaches. Numerical solutions are based on numerical computations of these tensors for various types of inclusions. Using the obtained results, effective electroelastic moduli of piezoelectric multiphase composites are investigated by an iterative procedure in the context of self-consistent scheme. Generalised Mori–Tanaka’s model and dilute approach are re-formulated and the three models are deeply analysed. Concentration tensors corresponding to each model are presented and relationships of effective coefficients are given. Numerical results of effective electroelastic moduli are presented for various types of piezoelectric inclusions and for various orientations and compared to existing experimental and theoretical ones.     

A micromechanical analysis of elastoplastic behavior of porous materials

In this paper, we present a micromechanical analysis of elastoplastic behavior of porous materials. The non-uniform transformation field analysis (NTFA) is used and the non-uniform distribution of local plastic strain in the solid matrix is taken into account. Comparisons with the classical Gurson's model and standard FEM solution are presented.     

On consistent micromechanical estimation of macroscopic elastic energy,coherence energy and phase transformation strains for SMA materials

An apparatus of micromechanics is used to isolate the key ingredients entering macroscopic Gibbs free energy function of a shape memory alloy (SMA) material. A new self-equilibrated eigenstrains influence moduli (SEIM) method is developed for consistent estimation of effective (macroscopic) thermostatic properties of solid materials, which in microscale can be regarded as amalgams of n-phase linear thermoelastic component materials with eigenstrains. The SEIM satisfy the self-consistency conditions, following from elastic reciprocity (Betti) theorem. The method allowed expressing macroscopic coherency energy and elastic complementary energy terms present in the general form of macroscopic Gibbs free energy of SMA materials in the form of semilinear and semiquadratic functions of the phase composition. Consistent SEIM estimates of elastic complementary energy, coherency energy and phase transformation strains corresponding to classical Reuss and Voigt conjectures are explicitly specified. The Voigt explicit relations served as inspiration for working out an original engineering practice-oriented semiexperimental SEIM estimates. They are especially conveniently applicable for an isotropic aggregate (composite) composed of a mixture of n isotropic phases. Using experimental data for NiTi alloy and adopting conjecture that it can be treated as an isotropic aggregate of two isotropic phases, it is shown that the NiTi coherency energy and macroscopic phase strain are practically not influenced by the difference in values of austenite and martensite elastic constants. It is shown that existence of nonzero fluctuating part of phase microeigenstrains field is responsible for building up of so-called stored energy of coherency, which is accumulated in pure martensitic phase after full completion of phase transition. Experimental data for NiTi alloy show that the stored coherency energy cannot be neglected as it considerably influences the characteristic phase transition temperatures of SMA material.     

Evolution of the micromechanical properties of impacted granular materials

The impact of a projectile on a granular material induces important changes in the micromechanical properties of the impacted material. These changes are studied using a Discrete Element Method model of the impact. The numerical results show that the impact first entails an energy propagation from the impact point to the limit of the sample through the existing force chains. A significant kinetic energy and a total breakage of the existing contact force chains are the main consequences of the energy propagation. During the long recovery balance phase observed after the energy propagation phase, frictional processes cause the kinetic energy dissipation. The motions of the particles and the numerous contact openings first prevent the formation of stable force chains. However, for long durations after the beginning of the impact, contact openings stop. The balance recovery phase therefore finally results in the creation of new stable contact force networks.     

A micromechanical model of toughening behavior in the dual-phase composite

The fabrication of a special kind of dual-phase composite consisting of a hard matrix and ductile phase, such as metals with bimodal grain size distribution, is a promising strategy for improving the tensile ductility of nanocrystalline (nc)/ultrafine-grained (ufg) materials (Wang et al., 2002). This strategy is, however, challenged by the low reproducibility from low controllability of microstructural parameters and the existence of counterexamples (Prasad et al., 2009). The key to meet these challenges is to control the bimodal microstructural parameters to enable quantificational investigation of the relation between mechanical properties and microstructural parameters, and then set up a correlative quantitative model. In this paper, a new micromechanical model based on the propagation and multiplication of localized deformation bands is developed. To assess the model, a series of hypo-eutectoid Cu–Al alloys with controllable bimodal structures are prepared and their stress–strain curves in tension, together with those of bimodal copper (Wang et al., 2002) and bimodal Al–Mg alloys (Han et al., 2005) are predicted. Close agreement between the model-predicted and experimental results is obtained. The strength and uniform ductility of bimodal materials are observed in strong relation to the microstructural and constitutive parameters of volume fraction, strain hardening coefficient, and size of the coarse-grained ductile phase. Additionally, appropriate microstructural and constitutive parameters to achieve effective toughening can also be estimated according to the model.     

A micromechanical model for predicting thermal properties and thermo-viscoelastic responses of functionally graded materials

This study introduces a micromechanical model for predicting effective thermo-viscoelastic behaviors of a functionally graded material (FGM). The studied FGM consists of two constituents with varying compositions through the thickness. The microstructure of the FGM is idealized as solid spherical particles spatially distributed in a homogeneous matrix. The mechanical properties of each constituent can vary with temperature and time, while the thermal properties are allowed to change with temperature. The FGM model includes a transition zone where the inclusion and matrix constituents are not well defined. At the transition zone, an interchange between the two constituents as inclusion and matrix takes place such that the maximum inclusion volume contents before and after the transition zone are less than 50%. A micromechanical model is used to determine through-thickness effective thermal conductivity, coefficient of thermal expansion, and time-dependent compliance/stiffness of the FGM. The material properties at the transition zone are assumed to vary linearly between the two properties at the bounds of the transition zone. The micromechanical model is designed to be compatible with finite element (FE) scheme and used to analyze heat conduction and thermo-viscoelastic responses of FGMs. Available experimental data and analytical solutions in the literature are used to verify the thermo-mechanical properties of FGMs. The effects of time and temperature dependent constituent properties on the overall temperature, stress, and displacement fields in the FGM are also examined.     

An efficient approximate numerical method for modeling contact of materials with distributed inhomogeneities

This research explores the influence of distributed non-interpenetrating inhomogeneities on the contact of inhomogeneous materials via a new efficient numerical model based on Eshelby’s Equivalent Inclusion Method. The half-space contact of a sphere with an inhomogeneous material is considered, and the solutions take into account interactions between all inhomogeneities. The efficiency and solution accuracy of the proposed method are demonstrated through comparative studies with those of an existing numerical method and the finite element method. The influence of spatial inhomogeneity orientations on the contact elastic field is investigated and parametric studies are conducted for the effect of arbitrarily distributed inhomogeneities on the stress field of the materials. The significance of the influences of inhomogeneity distribution parameters on the inverse volumetric stress integral is quantified and the corresponding data are fitted into selected several formulas as a step towards understanding the rolling contact fatigue life of the materials.     

Dynamic compressive behavior of thick composite materials

The effect of strain rate on the compressive behavior of thick carbon/epoxy composite materials was investigated. Falling weight impact and split Hopkinson pressure bar systems were developed for dynamic characterization of composite materials in compression at strain rates up to 2000 s^–1. Strain rates below 10 s^–1 were generated using a servohydraulic testing machine. Strain rates between 10 s^–1 and 500 s^–1 were generated using the drop tower apparatus. Strain rates above 500 s^–1 were generated using the split Hopkinson pressure bar. Unidirectional carbon/epoxy laminates (IM6G/3501-6) loaded in the longitudinal and transverse directions, and cross-ply laminates were characterized. The 90-deg properties, which are governed by the matrix, show an increase in modulus and strength over the static values but no significant change in ultimate strain. The 0-deg and cross-ply laminates show higher strength and ultimte strain values as the strain rate increases, whereas the modulus increnases only slightly over the static value. The increase in strength and ultimate strain observed may be related to the shear behavior of the composite and the change in failure modes. In all cases, the dynamic stress-strain curves stiffen as the strain rate increases. The stiffening is lowest in the longitudinal direction and highest in the transverse direction.     

纤维增强复合材料风机叶片宏细观一体化有限元分析An unified FEM for macroscopic and mesoscopic analysis of fiber reinforced composite fan blades

为了建立纤维增强复合材料风机叶片宏观性能和细观组分的直接关联,得到一般有限元分析时无法获得的细观参量值,利用FORTRAN程序把细观力学的失效／损伤分析模块,嵌入到有限元软件ABAQUS中的USD‐FLD 用户子程序中,建立了风机叶片宏细观一体化模型。该模型能够实现基于细观组分级损伤／失效判据的宏细观渐进损伤分析和强度预报功能。该模型计算结果与文献中的试验结果有较好的一致性。     

插秧机微机械陀螺随机误差分析及建模

微机械陀螺广泛应用于组合导航系统.以插秧机 GPS/INS 组合导航系统为研究背景,针对微机械陀螺的误差进行了研究.为了提高插秧机组合导航系统的定位精度,首先通过分析微机械陀螺的工作原理对微机械陀螺的误差来源和分类进行了深入的分析,说明微机械陀螺的随机误差是影响插秧机组合导航系统定位精度的一个主要因素.然后基于时间序列的分析建立了微机械陀螺的 AR 随机误差模型,并利用此模型采用 Kalman 滤波算法对采集的试验数据进行处理.实验结果表明,在采用 AR模型后,微机械陀螺的随机误差的方差减小了一个数量级,随机误差的幅值也明显减小.     

Rate dependent properties of perovskite type tetragonal piezoelectric materials using micromechanical model

In this paper, a three-dimensional micromechanical model is presented for simulation of the rate dependent properties of certain perovskite type tetragonal piezoelectric materials. The model is based on linear constitutive, nonlinear domain switching, and linear kinetics theories. The simulation starts with a virgin bulk material of randomly oriented grains. Then the material is electrically loaded with an alternating voltage of various frequencies, which are in the order of 0.01 Hz to 1 Hz. An energy equation in combination with a probability function is used to determine the onset of the domain switching inside the grains. Such a probability function leads to a better phenomenological model for the domain switching even for electrical loadings, which are in a range far below the coercive fields. The propagation of the domain wall during the domain switching process in grains is modeled by means of linear kinetics relations after domain nucleation. The response of the bulk ceramic is predicted by averaging the response of individual grains using Euler angles for the transformation from local coordinates of the grains to global coordinate. Electric displacement hysteresis loops for different frequencies and amplitudes of the alternating electric fields are simulated. A simple micromechanical model without the probabilistic approach is compared with the one that takes it into account. Both models give important insights into the rate dependency of piezoelectric materials, which was observed in some experiments reported in the literature.     

2D编织陶瓷基复合材料应力-应变行为的试验研究和模拟

本文对2D编织陶瓷基复合材料拉伸应力-应变行为进行了试验研究和理论模拟。将2D编织结构简化为：正交铺层结构和纤维束波动结构。基于基体随机开裂、纤维随机断裂的统计分布理论,得到正交铺层结构的应力-应变关系;基于体积平均方法,将纤维束波动部分分割为若干子单元;由于纤维束的波动使各子单元材料方向与加载方向不一致,因此考虑了各子单元的线性行为和非线性行为对材料响应的影响,同时引入强度分析模型,得到纤维束波动部分的应力-应变关系。结合正交铺层部分和纤维束波动部分的应力-应变关系,得到2D编织结构的应力-应变行为,理论与试验吻合较好。     

Non-elliptic elastic materials and the modeling of elastic-plastic behavior for finite deformation

For illustrative purposes this paper treats a special problem in the theory of finite deformations of elastic materials whose associated displacement equations of equilibrium do not remain elliptic at all strains. The typical deformation arising in this problem possesses a discontinuous gradient, so that quasi-static motions involving such equilibrium states may be dissipative. For a special class of such “non-elliptic” elastic materials, it is shown that the macroscopic response in the problem treated may be precisely of the form associated with elastic—perfectly plastic behavior. The counterparts of yield, plastic strain and plastic strain rate are determined by the underlying elastic strain energy function.     

双周期圆截面纤维复合材料平面问题的解析法

结合双准周期Riemann边值问题理论与Eshelby等效夹杂原理，为双周期圆截面纤维复合材 料平面问题发展了一个实用有效的解析方法，获得了问题的全场级数解并与有限元结果进行 了比较. 该方法为非均匀材料的力学性质分析和复合材料等新材料的微结构设计提供了 一个有效的计算工具，也可用来评估有限元等数值与近似方法的精度.     

An experimental investigation of losipescu specimen for composite materials

A detailed experimental evaluation of the losipescu specimen tested in the modified Wyoming fixture is presented. Moiré interferometry is employed to determine the deformation of unidirectional and cross-ply graphite-epoxy specimens. The results of the moiré experiments are compared to those from the traditional strain-gage method. It is shown that the strain-gage readings from one surface of a specimen together with corresponding data from moiré interferometry on the opposite face documented an extreme sensitivity of some fiber orientations to twisting. A localized hybrid analysis is introduced to perform efficient reduction of moiré data, producing whole-field strain distributions in the specimen test sections.     

Effective properties and stress-strain state of composite materials made by the method of centrifugal reinforcement

Institute of Mechanics of the Ukrainian Academy of Sciences, Kiev. Ivano-Frankovskii Institute of Oil and Gas. Translated from Prikladnaya Mekhanika, Vol. 25, No. 4, pp. 93–98, April, 1989.     

Homogenization method for strength and inelastic behavior of nanocrystalline materials

Homogenization techniques are used for modeling the so-called “breakdown” of the Hall–Petch law in the case of nanocrystalline (NC) materials. In this paper, the NC material is modeled as a composite material composed of two phases: the grain core (inclusion) and the grain boundaries (matrix). The deformation of the inclusion phase has a viscoplastic component that takes into account the dislocation glide mechanism as well as Coble creep. The boundary phase is modeled as an amorphous material with a perfect elastic–plastic behavior. An application of the model is developed on pure copper under tensile load. The results are compared with various experimental data.