Multicycle Indentation for Evaluation of Polymer Material Viscoelastic Characteristics

The evaluation of viscoelastic characteristics by an indentation test is required in order to separate the viscoelastic deformation and plastic deformation from the measured penetration depth. In this study, a multicycle indentation test is performed in order to separate these deformations and to evaluate the viscoelastic characteristics of acrylonitrile butadiene styrene (ABS) and polybutylene terephthalate (PBT). In the multicycle indentation test, two or more indentation tests are conducted at the same specimen position. After the first cycle, the indentation test is performed on the impression; thus, an evaluation formula for obtaining the viscoelastic characteristics is proposed, and the validity of this formula is confirmed by finite element analysis. As a result, the evaluated creep compliances of both materials are close the value evaluated by tensile testing. Therefore, it is concluded that the proposed method is applicable to the evaluation of viscoelastic characteristics.     

Rheological characterization of continuous fiber—reinforced viscous fluid

The present paper describes a micromechanical technique to determine rheological properties of viscous fluid reinforced with unidirectional continuous fibers. Fluid viscosity is described by a shear thinning model and high viscosity is considered for continuous fibers having considerable rigidity compared to net fluid. The microstructure is identified by a representative volume element that is subjected to equivalent macroscopic deformation fields. The energy balance and periodicity conditions are considered to relate deformation and stress in macro and micro-levels. It is shown that response of viscous fluid reinforced with rigid fibers depends on deformation history as well as rate-of-deformation in the transverse intraply shear and transverse squeeze flows. An orthotropic viscous constitutive equation is derived to describe response of such materials. The material viscosities are evaluated for viscous fluid reinforced with different fiber volume fractions during deformation applied in different rates of deformation. The results are used to derive the functions predicting effective anisotropic viscosities of reinforced fluid.     

On the Measurement of two Independent Viscoelastic Functions with Instrumented Indentation Tests

In the present paper, a methodology for complete characterization of linear isotropic viscoelastic material with spherical instrumented indentation test is proposed. The developed method allows for measuring two independent viscoelastic functions, shear relaxation modulus and time-dependent Poisson’s ratio, from the indentation test data obtained at non-decreasing loading, but otherwise arbitrary. Finite element modelling (FEM) is relied upon for validating the proposed methodology and for quantifying the influence of experimental variables on the measurements accuracy. Spherical indentation experiments are performed on several viscoelastic materials: polyoxymethylene, bitumen and bitumen-filler mastics. The viscoelastic material functions obtained with the indentation tests are compared with the corresponding results from the standard mechanical tests. Numerical and experimental results presented indicate that the methodology proposed allows mitigating the machine compliance and loading rate effects on the accuracy of the viscoelastic indentation tests.     

A 3/D finite element approach for metal matrix composites based on micromechanical models

Based on analytical considerations by Dvorak and Bahel-El-Din, a 3/D finite element material law has been developed for the elastic-plastic analysis of unidirectional fiber-reinforced metal matrix composites. The material law described in this paper has been implemented in the finite element code ABAQUS via the user subroutine UMAT. A constitutive law is described under the assumption that the fibers are linear-elastic and the matrix is of a von Mises-type with a Prager-Ziegler kinematic hardening rule. The uniaxial effective stress-strain relationship of the matrix in the plastic range is approximated by a Ramberg-Osgood law, a linear hardening rule or a nonhardening rule. Initial yield surface of the matrix material and for the fiber reinforced composite are compared to show the effect of reinforcement. Implementation of this material law in a finite element program is shown. Furthermore, the efficiency of substepping schemes and stress corrections for the numerical integration of the elastic-plastic stress-strain relations for anisotropic materials are investigated. The results of uniaxial monotonic tests of a boron/aluminum composite are compared to some finite element analyses based on micromechanical considerations. Furthermore a complete 3/D analysis of a tensile test specimen made of a silicon-carbide/aluminum MMC and the analysis of an MMC inlet inserted in a homogenous material are shown.     

基于均匀化理论韧性复合材料塑性极限分析

运用细观力学中的均匀化方法分析了韧性复合材料的塑性极限承载能力.从反映复合材料细观结构的代表性胞元入手,将均匀化理论运用到塑性极限分析中,计算由理想刚塑性、Mises组分材料构成的复合材料的极限承载能力.运用机动极限方法和有限元技术,最终将上述问题归结为求解一组带等式约束的非线性数学规划问题,并采用一种无搜索直接迭代算法求解.为复合材料的强度分析提供了一个有效手段.     

Measurement of the Viscoelastic Properties of Bitumen Using Instrumented Spherical Indentation

Indentation testing as a tool for determination of the viscoelastic mechanical properties of bitumen is examined in some detail using theoretical, numerical as well as experimental methods. In particular Brinell indentation is analysed and simple but rigorous formulae for a complete characterization of linear viscoelastic materials are presented. Numerical methods (finite element methods) are used in order to verify and substantiate these relations for an experimental situation. Indentation experiments are then performed on bitumen and special efforts are made in order to avoid size effects, i. e. anomalous results due to the fact that the indented specimens are too small and as a result, far field boundary conditions will influence the interpretation of the experimental output. The mechanical properties determined experimentally by indentation are compared with corresponding results from standard mechanical tests, and the results are encouraging considering the fact that non-linear effects are also influencing the outcome of the experiments.     

短纤维增强三元乙丙橡胶横观各向同性黏-超弹性本构模型

短纤维增强三元乙丙橡胶包覆薄膜,是一种应用于固体火箭发动机缠绕包覆装药的新型复合材料.为了描述其在工作过程中受振动、冲击等载荷作用时的力学行为,基于黏弹性理论和纤维增强连续介质力学理论,提出了一种考虑应变率强化效应的横观各向同性黏-超弹本构模型.模型中应变能函数被分解为超弹性应变能和黏性应变能,其中超弹性应变能包括表征各向同性的橡胶基体应变能和表征各向异性的纤维拉伸应变能,黏性应变能采用表征橡胶和纤维黏性响应的宏观唯象模型.选取表征各应变能的函数形式,经过数学变换、替代、叠加,求解确定最终的应力应变形式,明确模型参数获取的具体步骤,将预测结果与实验结果对比分析,准确性较高.研究表明:该模型能有效预测材料在低应变率下纤维方向为0?～45?的非线性率相关力学特性;模型形式易于实现有限元开发,对固体火箭发动机装药结构完整性分析具有参考价值.     

基于微米力学实验的页岩I型断裂韧度表征

页岩断裂韧度($K_{IC})$是页岩气储层水力压裂设计的基础参数之一,由于组成的非均质性,常规宏观力学测量方法存在制样困难、力学解释参数不连续、精度偏低等问题. 如何及时获取页岩的断裂特性,确保安全高效的工程施工,是当前面临的一大问题. 因此,提出了基于微米力学实验的页岩Ⅰ型断裂韧度分析方法,可用于页岩微裂纹起裂、发育直至形成宏观裂纹的机理研究,进行页岩宏观Ⅰ型断裂韧度预测. 基于页岩多尺度组成分析,开展了维氏压头和玻氏压头的页岩微米力学实验,分析了页岩残余压痕与压头间的相似关系、有效测试载荷以及压头参数的优化与选择. 分析了不同压入载荷下的页岩细观断裂韧度分布特征,开展了宏观巴西圆盘实验,验证页岩微米力学测试方法的适用性. 研究结果表明,在有效载荷范围内的页岩细观Ⅰ型断裂韧度波动性较小,当压入载荷过大时,由于岩样压痕区域出现局部剥落导致断裂韧度测量值偏小. 与宏观实验的比对分析显示,微米力学实验的$K_{IC}$平均值为0.86 MPa$\cdot \sqrt{m}$,直槽切缝巴西圆盘实验得到的$K_{IC}$平均值为0.92 MPa$\cdot \sqrt{m}$,两类方法的统计平均值较为接近,页岩局部组成的非均质性使得微米力学测量结果较宏观测试更为分散. 研究结果可用于页岩宏观Ⅰ型断裂韧度预测,为有效解决页岩气储层水力压裂参数评价提供新的思路和方法.      

Viscoelastic Deformation of a Reinforced Plate with a Crack

The deformation of a viscoelastic reinforced composite is studied. The composite has an axis of elastic symmetry and consists of transversally isotropic fibers and a viscoelastic matrix, which differ by the volume concentration and mechanical characteristics. The material is modeled by a transversely isotropic homogeneous linearly viscoelastic medium with some averaged characteristics. A plate fabricated from the composite in question is weakened by a through mode I crack and is subjected to constant tensile forces. The viscoelastic properties of the matrix material are described by a convolution operator. The Volterra principle is used to derive expressions for the viscoelastic characteristics and crack opening. The irrational function of the integral operator that describes the crack opening is expanded into an operator continued fraction and is represented as the sum of base operators     

纳米颗粒增强镍基MEMS器件材料的蠕变性能研究

利用同步辐射LIGA微铸复合工艺,将纳米氧化物增强颗粒复合到微电子机械系统(MEMS)结构材料中。制作了专用夹具,采用微力材料试验机测量了纳米Al2O3颗粒增强镍基复合材料的强度为1GPa;将恒加载速率/载荷法和恒载荷法相结合,利用纳米压痕仪测量了该材料的室温蠕变速率敏感指数m。结果表明,LIGA复合技术得到的纳米颗粒增强镍基复合材料具有较高的强度;MEMS器件材料在室温下会发生蠕变;材料在相同压深下最大载荷不随加载速率而改变,加载段粘弹性和粘塑性变形极少;主要由局部高应力导致压痕蠕变;材料的蠕变速率敏感指数m值为0.004,说明纳米Al2O3颗粒可有效增强基体材料的抗蠕变能力;且不同恒.P/P下获得的m值基本相同,表示此种材料对加载速率不敏感。     

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。     

Buckling test and optimum design of fiber reinforced composite plates under compression

In this paper, the conclusion that the experimental results coincide with theoretical analysis has been got through buckling test of 283 composite rectangular plates. It is confirmed that the critical loads of composite plates calculated by buckling theoretical formula of anisotropic plate are reliable. The selections of optimal content of matrix and optimal off-axis which make fiber reinforced composite plates reach biggest critical loads are also discussed in this paper. The result of analysis may be used in the design for the products.     

Spherical indentation of incompressible rubber-like materials

In recent years, indentation tests have been proven very useful in probing mechanical properties of small volumes of materials. However, a class of materials that very little has been done in this direction is rubber-like materials (elastomers). The present work investigates the spherical indentation of incompressible rubber-like materials. The analysis is performed in the context of second-order hyperelasticity and is accompanied by finite element computations and an extensive experimental program with spherical indentors of different radii. Uniaxial tensile tests were also performed and it was found that the initial elastic modulus correlates well with the indentation response. The experiments suggest stiffer indentation response than that predicted by linear elasticity, which is somehow counter-intuitive, if the uniaxial material response is to be considered. Regarding the uniqueness of the inverse problem, that is to establish material properties from spherical indentation tests, the answer is disappointing. We prove that the inverse problem does not give unique answer regarding the constitutive relation, except for the initial stiffness.     

Estimates of thermoelastic characteristics of composites reinforced by short anisotropic fibers

We construct a mathematical model describing thermomechanical interaction between composite structure elements (isotropic particles of the matrix and anisotropic short fibers) and the macroscopically isotropic elastic medium with desired thermoelastic characteristics. At the first stage of this model, the self-consistency method is used to obtain relations determining the elasticity moduli of the composite, and at the second stage, the model permits determining its linear thermal expansion coefficient. The dual variational statement of the linear thermoelasticity problem in an inhomogeneous solid permits obtaining two-sided estimates for the bulk elasticity modulus, shear modulus, and linear thermal expansion coefficient of the composite under study. The calculated dependencies presented in the paper permit predicting the thermoelastic characteristics of a composite reinforced by anisotropic short fibers (including those in the form of nanostructure elements).     

DETERMINATION OF CREEP PARAMETERS FROM INDENTATION CREEP EXPERIMENTS

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Orientation effect on the Boussinesq indentation of a transversely isotropic piezoelectric material

Three-dimensional finite element analysis was used to study the effect of the angle between the loading direction and the axisymmetric direction on the indentation behavior of a transversely isotropic piezoelectric half-space by a cylindrical indenter of flat end. Two cases were considered in the analysis, which included (a) the indentation by an insulating indenter, and (b) the indentation by a conducting indenter. Both the indentation load and the indentation-induced potential were found to be proportional to the indentation depth. Using the simulation results and the analytical relationship for the indentation by a rigid, insulating indenter, semi-analytical relationships were developed between the indentation load and the indentation depth and between the indentation-induced potential on the indenter and the indentation depth for the conducting indenter, respectively. The proportionality between the indentation-induced potential and the indentation depth is only a function of the angle between the loading direction and the poling direction, independent of the type of indenters, which may be used to measure the relative direction of the loading axis to the axisymmetric axis of transversely piezoelectric materials from the indentation test.     

Growth of a penny-shaped crack with a nonsmall fracture process zone in a composite

The paper studies the stress rupture behavior of a reinforced viscoelastic composite through which a penny-shaped mode I crack propagates under a constant load. The composite has hexagonal symmetry and consists of elastic isotropic fibers and viscoelastic isotropic matrix. The material is modeled as a transversely isotropic homogeneous viscoelastic medium with effective characteristics. The crack is in the isotropy plane. The ring-shaped fracture process zone at the crack front is modeled by a modified Dugdale zone with time-dependent stresses. The viscoelastic properties of the matrix are characterized using a resolvent integral operator. Use is made of Volterra's principle, the method of operator continued fractions, and the theory of precritical crack growth in viscoelastic bodies. The problem is reduced to nonlinear integral equations. Numerical results are obtained for certain components of the composite, constant volume fractions, and different fracture strengths Translated from Prikladnaya Mekhanika, Vol. 44, No. 8, pp. 45–51, August 2008.     

Experimental and numerical study of the effect of silica filler on the tensile strength of a 3D-printed particulate nanocomposite

Polymers are commonly found to have low mechanical properties, e.g., low stiffness and low strength. To improve the mechanical properties of polymers, various types of fillers have been added. These fillers can be either micro- or nano-sized; however; nano-sized fillers are found to be more efficient in improving the mechanical properties than micro-sized fillers. In this research, we have analysed the mechanical behaviour of silica reinforced nanocomposites printed by using a new 5-axis photopolymer extrusion 3D printing technique. The printer has 3 translational axes and 2 rotational axes, which enables it to print free-standing objects. Since this is a new technique and in order to characterise the mechanical properties of the nanocomposites manufactured using this new technique, we carried out experimental and numerical analyses. We added a nano-sized silica filler to enhance the properties of a 3D printed photopolymer. Different concentrations of the filler were added and their effects on mechanical properties were studied by conducting uniaxial tensile tests. We observed an improvement in mechanical properties following the addition of the nano-sized filler. In order to observe the tensile strength, dog-bone samples using a new photopolymer extrusion printing technique were prepared. A viscoelastic model was developed and stress relaxation tests were conducted on the photopolymer in order to calibrate the viscoelastic parameters. The developed computational model of nano reinforced polymer composite takes into account the nanostructure and the dispersion of the nanoparticles. Hyper and viscoelastic phenomena was considered to validate and analyse the stress–strain relationship in the cases of filler concentrations of 8%, 9%, and 10%. In order to represent the nanostructure, a 3D representative volume element (RVE) was utilized and subsequent simulations were run in the commercial finite element package ABAQUS. The results acquired in this study could lead to a better understanding of the mechanical characteristics of the nanoparticle reinforced composite, manufactured using a new photopolymer extrusion 5-axis 3D printing technique.     

Optimisation de renforts composites internes de structures tridimensionnelles

The reinforcement of a 3D structure with composite panels is considered. The behaviour of those panels are to be optimized considering the external loading of the 3D structure. The study is within the framework of anisotropic linear elasticity. The 3D model takes into account the rigidity induced by Kirchhoff–Love plate reinforcement. An optimization of the behavior characteristics of the composite reinforcement (density and orientation of fibers at each point) is presented.     

Homogenization estimates for fiber-reinforced elastomers with periodic microstructures

This work presents a homogenization-based constitutive model for the mechanical behavior of elastomers reinforced with aligned cylindrical fibers subjected to finite deformations. The proposed model is derived by making use of the second-order homogenization method [Lopez-Pamies, O., Ponte Castañeda, P., 2006a. On the overall behavior, microstructure evolution, and macroscopic stability in reinforced rubbers at large deformations: I—theory. J. Mech. Phys. Solids 54, 807–830], which is based on suitably designed variational principles utilizing the idea of a “linear comparison composite.” Specific results are generated for the case when the matrix and fiber materials are characterized by generalized Neo-Hookean solids, and the distribution of fibers is periodic. In particular, model predictions are provided and analyzed for fiber-reinforced elastomers with Gent phases and square and hexagonal fiber distributions, subjected to a wide variety of three-dimensional loading conditions. It is found that for compressive loadings in the fiber direction, the derived constitutive model may lose strong ellipticity, indicating the possible development of macroscopic instabilities that may lead to kink band formation. The onset of shear band-type instabilities is also detected for certain in-plane modes of deformation. Furthermore, the subtle influence of the distribution, volume fraction, and stiffness of the fibers on the effective behavior and onset of macroscopic instabilities in these materials is investigated thoroughly.