Analysis of stress concentrations in unidirectional composites taking into account the tensile load in the matrix

A modified shear-lag model accounting for the effect of the tensile stiffness of the matrix is proposed for solving the stress redistribution due to the failure of fibers and matrix in unidirectionally fibre-reinforced composites. The advantages of this model are simple, reasonable and accurate by comparison with the other similar modified shear-lag models. It can be further extended to study the stress redistribution with interfacial damage between fibres and matrix. This paper quantitatively discusses the influence of the tensile stiffness ratio of matrix to fibre and of the fibre volume fraction on the stress concentration in the fibres and matrix adjacent to cut fibres and matrix, and suggests that the influence of the matrix stiffness on the stress concentration can be neglected when the matrix stiffness is low, such as polymer matrix composites, and the fibre volume fraction is high. For other cases such as ceramic and metal matrix composites, the tensile load of the matrix cannot be neglected in the shearlag analysis. The project supported by the Guangdong Provincial Natural Science Foundation of China.     

Design,Manufacture, and Quasi-Static Testing of Metallic Negative Stiffness Structures within a Polymer Matrix

A composite material system comprised of a monostable negative stiffness (NS) structure within a polymer matrix was designed, fabricated, and experimentally evaluated. The monostable negative stiffness (NS) structure was designed using a combination of analytical and numerical models and manufactured in stainless steel. The NS structure was arranged in parallel with different polymer matrices to experimentally evaluate the effects of the matrix properties on the overall stiffness and energy dissipation of the composite NS-matrix system when loaded in uniaxial compression. A strong influence of the matrix properties on the stiffness and energy absorption capacity of the composite system was observed. Unlike conventional composites for which there is a natural tradeoff between stiffness and energy absorption capacity, the composite NS-matrix system enhanced stiffness while simultaneously improving energy absorption relative to a neat matrix, but only when the stiffness of the matrix was carefully matched to the stiffness of the NS structure.     

颗粒增强复合材料的屈服极限

基于渐近均匀化方法,导出了颗粒增强复合材料的屈服准则,给出了初始屈服应力的解析表达式。因为颗粒增强体的弹性模量远比弹塑性基体的弹性模量高,这个模量差在增强体和基体中产生了装配刚度。解局部问题可以得到该装配刚度。从屈服应力的表达式可以看出,增强体和基体两者的平均装配刚度和剪切模量之比决定了屈服应力的提高程度。给出了两个数值算例。采用菱形十二面体单胞求解了局部问题。取单胞形状为菱形十二面体的优点是增强体的体积比可以高达74%。     

A unified model for polystyrene–nanorod and polystyrene–nanoplatelet melt composites

We present a unified constitutive model capable of predicting the steady shear rheology of polystyrene (PS)–nanoparticle melt composites, where particles can be rods, platelets, or any geometry in between, as validated against experimental measurements. The composite model incorporates the rheological properties of the polymer matrix, the aspect ratio and characteristic length scale of the nanoparticles, the orientation of the nanoparticles, hydrodynamic particle–particle interactions, the interaction between the nanoparticles and the polymer, and flow conditions of melt processing. We demonstrate that our constitutive model predicts both the steady rheology of PS–carbon nanofiber composites and the steady rheology of PS–nanoclay composites. Along with presenting the model and validating it against experimental measurements, we evaluate three different closure approximations, an important constitutive assumption in a kinetic theory model, for both polymer–nanoparticle systems. Both composite systems are most accurately modeled with a quadratic closure approximation.     

Nanoparticle debonding strength: A comprehensive study on interfacial effects

The most appealing feature of nanofilled polymers is the perspective of obtaining surprisingly high mechanical properties at low nanofiller volume fractions. The knowledge of nanostructure–property relationships is however essential for the design of these materials.In the present work, a model for the critical hydrostatic tension related to nanoparticle debonding is presented. The model accounts for some important issues inherently related to the nanoscale with particular reference to surface elastic stresses on the nanoparticle periphery and the emergence of a zone of altered chemistry surrounding the nanoparticle. The analytical solution suggests that the range of nanoparticle radii where interfacial effects do affect the solution is limited to the nanometer scale. In more details, considering the interphase and surface elastic properties used in the analysis, it has been found that for stiff particles with radius between 10 nm and 100 nm (silica, alumina and other metal oxide nanoparticles) the prominent role is played by the interphase elastic properties. Surface elastic constants were found to have, instead, only a negligible effect.     

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.     

Microstructure and mechanical properties of three-dimensional five-directional braided composites

Three-dimensional (3D) five-directional braided composites are significant structural materials in the fields of astronauts and aeronautics. On the basis of the 3D five-directional braiding process, three types of microstructural unit cell models are established with respect to the interior, surface and corner regions. The mathematical relationships among the structural parameters, such as fiber orientation, fiber volume fraction, the yarn packing factor, are derived. By using these three unit cell models, a micromechanical prediction procedure is described to simulate the stiffness and strength properties of 3D five-directional braided composites. Only the in situ constituent fiber and matrix properties of the composites and the fiber volume proportion are required in the simulation. The stress states generated in the constituent fiber and matrix materials are explicitly correlated with the overall applied load on the composites. The predictive stiffness and strength are in good agreement with available experimental data, which demonstrates the applicability of the present analytical model.     

界面特性对短纤维金属基复合材料蠕变行为的影响

基于短纤维增强金属基复合材料(MMC)的单纤维三维模型(三相)，利用粘弹性有限元分析方法对影响金属基复合材料的蠕变行为的因素进行了较为系统的分析。研究中主要讨论了界面特性和纤维取向角对金属基复合材料的蠕变性能的影响。研究结果发现，界面特性诸如厚度、模量和应力指数都对纤维最大轴应力和稳定蠕变率产生影响：稳态蠕变率随界面模量的增大而逐渐减小，当高于基体模量时基本保持不变；纤维轴应力的变化与蠕变率正好相反。稳态蠕变率随界面厚度、应力指数的增加而增大；而轴应力则随之减小。同时不同的纤维取向也影响金属基复合材料蠕变时的轴应力分布和稳态蠕变率。     

The effects of the interphase and strain gradients on the elasticity of layer by layer (LBL) polymer/clay nanocomposites

A synergistic stiffening effect observed in the elastic mechanical properties of LBL assembled polymer/clay nanocomposites is studied via two continuum mechanics approaches. The nanostructure of the representative volume element (RVE) includes an effective interphase layer that is assumed to be perfectly bonded to the particle and matrix phases. An inverse method to determine the effective thickness and stiffness of the interphase layer using finite element (FE) simulations and experimental data previously published in Kaushik et al. (2009), is first illustrated. Next, a size-dependent strain gradient Mori–Tanaka (M–T) model (SGMT) is developed by applying strain gradient elasticity to the classical M–T method. Both approaches are applied to LBL-assembled polyurethane–montmorillonite (PU–MTM) clay nanocomposites. Both two-dimensional (2D) and three-dimensional (3D) FE models used in the first approach are shown to be able to accurately predict the stiffness of the PU–MTM specimens with various volume fractions. The SGMT model also accurately predicts the experimentally observed increase in stiffness of the PU–MTM nanocomposite with increasing volume fraction of clay. An analogy between the strain gradient effect and the role of an interphase in accounting for the synergistic elastic stiffening in nanocomposites is provided.     

Effective mechanical properties of unidirectional composites in the presence of imperfect interface

In this paper, the equivalent inclusion method is implemented to estimate the effective mechanical properties of unidirectional composites in the presence of an imperfect interface. For this purpose, a representative volume element containing three constituents, a matrix, and interface layer, and a fiber component, is considered. A periodic eigenstrain defined in terms of Fourier series is then employed to homogenize non-dilute multi-phase composites. In order to take into account the interphase imperfection effects on mechanical properties of composites, a stiffness parameter in terms of a matrix and interphase elastic modulus is introduced. Consistency conditions are also modified accordingly in such a way that only the part of the fiber lateral stiffness is to be effective in estimating the equivalent composite mechanical properties. Employing the modified consistency equations together with the energy equivalence relation leads to a set of linear equations that are consequently used to estimate the average values of eigenstrain in non-homogeneous phases. It is shown that for composites with both soft and hard reinforcements, largest stiffness parameter that indicates complete fiber–matrix interfacial debonding causes the same equivalent lateral properties.     

Multi-scale modeling of tensile behavior of carbon nanotube-reinforced composites

A multi-scale representative volume element (RVE) for modeling the tensile behavior of carbon nanotube-reinforced composites is proposed. The RVE integrates nanomechanics and continuum mechanics, thus bridging the length scales from the nano- through the mesoscale. A progressive fracture model based on the modified Morse interatomic potential is used for simulating the behavior of the isolated carbon nanotubes and the FE method for modeling the matrix and building the RVE. Between the nanotube and the matrix a perfect bonding is assumed until the interfacial shear stress exceeds the corresponding strength. Then, nanotube/matrix debonding is simulated by prohibiting load transfer in the debonded region. Using the RVE, a unidirectional nanotube/polymer composite was modeled and the results were compared with corresponding rule-of-mixtures predictions. A significant enhancement in the stiffness of the polymer owing to the adding of the nanotubes is predicted. The effect of interfacial shear strength on the tensile behavior of the nanocomposite was also studied. Stiffness is found to be unaffected while tensile strength to significantly decrease with decreasing the interfacial shear strength.     

Rheometric properties of micron-sized CaCO3 suspensions stabilised by a physical polyol/silica gel for polyurethane foams

This article considers the rheometric properties of mixtures containing a micron-sized mineral filler of calcium carbonate (CaCO₃) in a polymer matrix gelled by adding colloidal silica (CS). These mixtures, consisting of a polymer matrix (polyols, catalysts, surfactant) are used to produce polyurethane foams. The suspending phase (polymer matrix/CS) has a yield stress that has been linked to fractal aggregation of the colloidal filler. Suspensions without any colloidal silica (polymer matrix/CaCO₃), show aggregation of CaCO₃ which is most probably due to the adsorption of catalysts present in the polymer matrix. Beyond a critical CaCO₃ volume fraction, a yield stress is detected indicating a 3D connected structure. In the case of suspensions containing colloidal silica (polymer matrix/CaCO₃/SC), the yield stress is due to a combination of the fractal network formed by the colloidal silica and aggregation of the micron-sized particles of CaCO₃.     

A theory of plasticity for carbon nanotube reinforced composites

Carbon nanotubes (CNTs) possess exceptional mechanical properties, and when introduced into a metal matrix, it could significantly improve the elastic stiffness and plastic strength of the nanocomposite. But current processing techniques often lead to an agglomerated state for the CNTs, and the pristine CNT surface may not be able to fully transfer the load at the interface. These two conditions could have a significant impact on its strengthening capability. In this article we develop a two-scale micromechanical model to analyze the effect of CNT agglomeration and interface condition on the plastic strength of CNT/metal composites. The large scale involves the CNT-free matrix and the clustered CNT/matrix inclusions, and the small scale addresses the property of these clustered inclusions, each containing the randomly oriented, transversely isotropic CNTs and the matrix. In this development the concept of secant moduli and a field fluctuation technique have been adopted. The outcome is an explicit set of formulae that allows one to calculate the overall stress-strain relations of the CNT nanocomposite. It is shown that CNTs are indeed a very effective strengthening agent, but CNT agglomeration and imperfect interface condition can seriously reduce the effective stiffness and elastoplastic strength. The developed theory has also been applied to examine the size (diameter) effect of CNTs on the elastic and elastoplastic response of the composites, and it was found that, with a perfect interface contact, decreasing the CNT radius would enhance the overall stiffness and plastic strength, but with an imperfect interface the size effect is reversed. A comparison of the theory with some experiments on the CNT/Cu nanocomposite serves to verify the applicability of the theory, and it also points to the urgent need of eliminating all CNT agglomeration and improving the interface condition if the full potential of CNT reinforcement is to be realized.     

The structure of colloidal polyethylenimine–silica nanocomposite microparticles

Deposition of silica from an organosilane tetraethoxysilane (TEOS) onto parent polyethylenimine (PEI) microgel particles produces a novel PEI–silica nanocomposite, which possesses greater adsorption capacity for copper ions than either parent material. This study explores factors governing interactions of silica with the PEI matrix, along with structural features of resulting PEI–silica composite particles, to explain their properties and determine their application potential. The influence of initial TEOS/PEI mass ratio and the duration of silica deposition on the final silica content and distribution in the composite are studied. A comparative analysis of the structural architecture of chemically etched silica remnants, original PEI–silica composite particles and the parent PEI-microgel is carried out using X-ray photoelectron spectroscopy, small-angle X-ray scattering, and electron microscopy techniques. It is found that silica sol nanoparticles are evenly distributed throughout the PEI-microgel framework and interlinked with it via electrostatic interactions, enabling a structural model of the PEI–silica nanocomposite to be proposed. The chemical stability of resulting nanocomposite particles in parallel with the parent PEI-microgel is tested and shown to be robust for more than 100 days of storage in aqueous dispersions across a range of pH conditions, highlighting the application potential for these particles in copper capture.     

模型复合材料弹塑性界面应力分析

由纤维增强弹塑性基体所产生的界面具有弹塑性力学行为。考虑到一般材料的塑性变形都遵循幂硬化规律,对模型复合材料的界面进行弹性和应变硬化状态下的变形规律及其应力分析。以纤维拔出试验为研究模型,将界面分成弹性区和塑性区。利用界面应力剪滞理论,分别建立弹性区和塑性区的界面力学基本方程。选择适当的位移函数满足基本方程及埋入纤维的边界条件,再按位移函数求出弹性区和塑性区的界面剪应力。推导出平均界面剪应力与纤维     

EFFECTIVE SPECIFIC HEATS OF SPHERICAL PARTICULATE COMPOSITES WITH INHOMOGENEOUS INTERPHASES

基于细观力学复合球模型研究了含非均匀界面相粒子填充复合材料的有效热弹性性质,重点讨论了界面相性质的径向分布对有效比热的影响. 首先,将非均匀界面相沿径向离散为多个同心球壳,每个球壳内的材料性质假设是均匀的. 基于上述离散模型,利用含界面相的复合球模型,推导了复合材料的有效体积模量、有效热膨胀系数及有效比热的数值求解表达式;进一步,假设界面相的性质沿径向连续变化,建立了一组微分方程,上述有效性质依赖于该微分方程组的解. 特别地,当界面相杨氏模量为幂次分布时,通过求解该微分方程组得到了有效比热等热弹性性质的解析解. 算例结果表明,应用此方法预测的有效热膨胀系数与实验结果吻合良好;界面相热膨胀系数的径向分布对有效比热和有效热膨胀系数均有显著的影响,而界面相弹性模量的径向分布对有效比热有显著的影响,对有效热膨胀系数的影响相对较小.     

含非均匀界面相粒子填充复合材料的有效比热

基于细观力学复合球模型研究了含非均匀界面相粒子填充复合材料的有效热弹性性质,重点讨论了界面相性质的径向分布对有效比热的影响. 首先,将非均匀界面相沿径向离散为多个同心球壳,每个球壳内的材料性质假设是均匀的. 基于上述离散模型,利用含界面相的复合球模型,推导了复合材料的有效体积模量、有效热膨胀系数及有效比热的数值求解表达式;进一步,假设界面相的性质沿径向连续变化,建立了一组微分方程,上述有效性质依赖于该微分方程组的解. 特别地,当界面相杨氏模量为幂次分布时,通过求解该微分方程组得到了有效比热等热弹性性质的解析解. 算例结果表明,应用此方法预测的有效热膨胀系数与实验结果吻合良好;界面相热膨胀系数的径向分布对有效比热和有效热膨胀系数均有显著的影响,而界面相弹性模量的径向分布对有效比热有显著的影响,对有效热膨胀系数的影响相对较小.      

Ag2S纳米粒子原位合成以增强PAI涂层机械和摩擦学性能

借助单源前驱体热分解在聚酰胺酰亚胺(PAI)涂层中原位合成了硫化银(Ag₂S)纳米粒子,并通过调节单源前驱体的含量进一步调控纳米粒子尺寸. 采用X射线衍射仪和高分辨场发射扫描电镜对原位合成Ag₂S纳米粒子的物相结构、形貌、尺寸和尺寸分布进行了表征和分析;详细研究了Ag₂S纳米粒子对PAI涂层机械性能和摩擦学性能的影响;对其增强机制进行了探讨. 结果表明:PAI涂层中原位合成的Ag₂S纳米粒子粒径较小而且分散均匀,且调节单源前驱体能有效调控Ag₂S纳米粒子的尺寸和尺寸分布. Ag₂S纳米粒子的原位引入(优化质量分数为5.0%)有效改善了PAI涂层的机械性能和摩擦学性能,其摩擦学性能的增强归因于机械强度的提高和诱导转移膜的形成.      

Mechanisms of stress transfer and interface integrity in carbon/epoxy composites under compression loading. Part II: Numerical approach

The finite element method is used to get an insight into the micromechanics of the compressive behaviour of carbon fibre composites. First the developed model is validated with existing experimental data and good agreement between predictions and experiments was found. Then the FE model is used to derive the complete stress field in the fibre and the matrix in the vicinity of a fibre fracture location. It was found that the perturbation of the stress field occurs mainly in the direction transverse to the fibre axis and this could explain the failure modes observed in composites tested in compression. Finally, a parametric study was performed on the effect of matrix modulus and matrix yield stress on the compressive fragmentation process.     

Investigation of the Effects of Environmental Fatigue on the Mechanical Properties of GFRP Composite Constituents Using Nanoindentation

Background

Fatigue failure criteria for fibre reinforced polymer composites used in the design of marine structures are based on the micromechanical behaviour (e.g. stiffness properties) of their constituents. In the literature, there is a lack of information regarding the stiffness degradation of fibres, polymer matrix and fibre/matrix interface regions affected by environmental fatigue.

Objective

The aim of present study is to characterize the stiffness properties of composite constituents using the nanoindentation technique when fatigue failure of composites is due to the combined effect of sea water exposure and cyclic mechanical loads.

Methods

In the present study, the nanoindentation technique was used to characterize the stiffness properties of composite constituents where the effects of neighbouring phases, material pile up and viscoplasticity properties of the polymer matrix are corrected by finite element simulation.

Results

The use of finite element simulation in conjunction with nanoindentation test data, results in more accurate estimation of projected indented area which is required for measuring the properties of composite constituents. In addition, finite element simulation provides a greater understanding of the stress transfer between composite constituents during the nanoindentation process.

Conclusions

Results of nanoindentation testing on the composite microstructure of environmentally fatigue failed composite test coupons establish a strong link to the stiffness degradation of the fiber/matrix interface regions, verifying the degradation of composite constituents identified by scanning electron microscopy (SEM) and energy dispersive X-ray spectroscopy (EDX) analysis.