Stiffness and Energy Dissipation of Polymer Matrix Composites Containing Embedded Metallic Negative Stiffness Structures

Background

Conventional composites used in damping applications exhibit an undesirable tradeoff between stiffness and energy dissipation. Recent research demonstrates that it is possible to simultaneously achieve increased stiffness and energy dissipation for a configuration of a viscoelastic polymer matrix placed in parallel with a negative stiffness structure (NSS). This configuration resulted in energy dissipation equal to the sum of its components but is difficult to implement in practice.

Objective

In this paper, an alternative configuration is investigated in which the NSS is embedded simultaneously in series and parallel with the matrix. The main objectives are to examine the tradeoff between the stiffness and energy dissipation of the composite and to identify the mechanisms for enhanced energy dissipation.

Methods

To achieve this, FEA models were used to match the stiffness of a polymer matrix with that of a metallic NSS. Multiple specimens were manufactured and tested under quasi-static compressive loads to determine the force versus displacement curves and calculate the energy dissipation and stiffness.

Results

These tests demonstrate that the total energy dissipation of the composite can be greater than the sum of its components, while maintaining the benefit of increasing the stiffness and damping capacity simultaneously. The results also demonstrate that the applied strain rate plays a critical role in activating the NSS, which is essential to achieve the desired increase in energy dissipation.

Conclusions

The results indicate that localized strain and strain rate at the interface between the NSS and polymer matrix are the main contributors to achieving energy dissipation beyond the sum of its components. Furthermore, it was demonstrated that the strain rate affects the activation of the NSS and therefore composites containing mechanically activated NSS must be designed for the strain rate of interest.

     

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.     

Role of the polymer phase in the mechanics of nacre-like composites

Although strength and toughness are often mutually exclusive properties in man-made structural materials, nature is full of examples of composite materials that combine these properties in a remarkable way through sophisticated multiscale architectures. Understanding the contributions of the different constituents to the energy dissipating toughening mechanisms active in these natural materials is crucial for the development of strong artificial composites with a high resistance to fracture. Here, we systematically study the influence of the polymer properties on the mechanics of nacre-like composites containing an intermediate fraction of mineral phase (57 vol%). To this end, we infiltrate ceramic scaffolds prepared by magnetically assisted slip casting (MASC) with monomers that are subsequently cured to yield three drastically different polymers: (i) poly(lauryl methacrylate) (PLMA), a soft and weak elastomer; (ii) poly(methyl methacrylate) (PMMA), a strong, stiff and brittle thermoplastic; and (iii) polyether urethane diacrylate-co-poly(2-hydroxyethyl methacrylate) (PUA-PHEMA), a tough polymer of intermediate strength and stiffness. By combining our experimental data with finite element modeling, we find that stiffer polymers can increase the strength of the composite by reducing stress concentrations in the inorganic scaffold. Moreover, infiltrating the scaffolds with tough polymers leads to composites with high crack initiation toughness K_IC. An organic phase with a minimum strength and toughness is also required to fully activate the mechanisms programmed within the ceramic structure for a rising R-curve behavior. Our results indicate that a high modulus of toughness is a key parameter for the selection of polymers leading to strong and tough bioinspired nacre-like composites.     

Static and fatigue behaviour of glass-fibre-reinforced polypropylene composites

This paper is concerned with fatigue of polypropylene/glass-fibre thermoplastic composites produced from a bi-directional woven cloth mixture of E glass fibres and polypropylene fibres. The latter becomes the matrix after the application of heat and pressure. This composite was manufactured with a fibre volume fraction V_f of 0.338. The effect of layer design on the static and fatigue performance was investigated. The S–N curves, the rise in the temperature of the specimens during the tests and the loss of stiffness, were obtained and discussed. The loss of stiffness was related to the rise of temperature and stress release observed in the material. The effect of load rate on the static properties was also studied and discussed accordingly.     

Une condition de déviation des fissures dans les CMC et les multicouches

A crack deflection criterion is proposed on the basis of the Cook and Gordon mechanism. The stress state induced by a crack was computed in an elementary cell of bimaterial using the finite element method. An interface failure criterion was established in terms of strengths and elastic moduli of constituents. A master curve was produced. It allows matrix crack deflection to be predicted with respect to constituents properties and interface strength. The model can be used also to evaluate the strength of interfaces and interphases in ceramic matrix composites and in multilayers. To cite this article: S. Pompidou, J. Lamon, C. R. Mecanique 333 (2005).     

Modelling of fibre pull-out in cracked fibre reinforced composites with linear elastic fracture mechanics

A method of finite element modelling the fracture mechanics of a fibre reinforced cement composite is presented. It embodies the use of beam elements with negative extensional stiffness. The method compares favourably with experimental work. Whilst fibre reinforced cement composites are used in this work, the techniques used are applicable to any type of fibre composite material.     

Influence of applied in-plane strain on transverse thermal conductivity of 0°/90° and plain weave ceramic matrix composites

A computationally economic finite-element-based stress analysis model, developed previously by the authors, has been extended to predict the thermal behaviour of ceramic matrix composites with strain-induced damage. The finite element analysis utilises a solid element to represent a homogenised orthotropic medium of a heterogeneous uni-directional tow. The non-linear multi-axial strain dependent thermal behaviour has been discretised by multi-linear curves, which have been implemented by a user defined subroutine, USDFLD, in the commercial finite element package, ABAQUS. The model has been used to study the performance of two CMC composites: a SiC (Nicalon) fibre-calcium aluminosilicate (CAS) matrix, 0°/90° cross-ply laminate Nicalon-CAS; and, carbon fibre-dual carbon-SiC matrix (C/C-SiC), plain weave laminate DLR-XT. The global through-thickness thermal conductivity degradation with composite uni-axial strain has been predicted. Comparisons have been made between the predictions and experimental data for both materials, and good agreement has been achieved. For the Nicalon-CAS 0°/90° cross-ply the dominant mechanism of thermal conductivity degradation is combined fibre failure and associated wake debonding; and, for the DLR-XT plain weave the same mechanisms act in combination with out-of-plane shear failure.     

Progressive failure analysis of tow-placed, variable-stiffness composite panels

The past developments on tow-placement technology led to the production of machines capable of controlling fibre tows individually and placing them onto the surface of a laminate with curvilinear topology. Due to the variation of properties along their surface, such structures are termed variable-stiffness composite panels.In previous experimental research tow-steered panels have shown increased buckling load capacity as compared with traditional straight-fibre laminates. Also, numerical analyses by the authors showed that first-ply failure occurs at a significant higher load level. The focus of this paper is to extend those analyses into the postbuckling progressive damage behaviour and final structural failure due to accumulation of fibre and matrix damage. A user-developed continuum damage model implemented in the finite element code ABAQUS^® is employed in the simulation of damage initiation and material stiffness degradation.In order to correctly predict the buckling loads of tow-steered panels under compression, it is of crucial importance to take into account the residual thermal stresses resulting from the curing process. Final failure of tow-steered panels in postbuckling is predicted to within 10% difference of the experimental results. Curvilinear-fibre panels have up to 56% higher strength than straight-fibre laminates and damage initiation is also remarkably postponed. Tow-steered designs also show more tolerance to central holes than traditional laminates.     

Stiffness properties of particulate composites containing debonded particles

This paper considers the problem of determining the nonlinear bimodular stiffness properties, i.e., the tensile and compressive Young’s moduli and Poisson’s ratios, and the shear modulus, of particulate composite materials with particle–matrix interfacial debonding. It treats the general case in which some of the particles are debonded while the others remain intact. The Mori–Tanaka approach is extended to formulate the method of solution for the present problem. The resulting auxiliary problem of a single debonded particle in an infinite matrix subjected to a remote stress equal to the average matrix stress, for which Eshelby’s solution does not exist, is solved by the finite element method accounting for the particle–matrix separation and contact at the debonded particle–matrix interface. Because of the nonlinear nature of the problem, an iterative process is employed in calculating the stiffness properties. The predicted stiffness properties are compared to the exact solutions of the stiffness properties of particulate composites with body-centered cubic packing arrangement.     

Shear wave propagation in layered composites with degraded matrices at locations of imperfect bonding

Biodegradable polymers find an increasing number of applications in different fields of engineering and medicine due to their environmental-friendly degradation. The process of degradation of biodegradable polymer constituents and the bonding quality between the constituents in composites can be identified by the analysis of the phononic band structure. The present article considers a layered composite, in which the matrix degradation is modeled by a multitude of layers with decreasing values of their mechanical properties. Bonding between the inclusion and the degrading matrix is taken into account by a linear elastic bonding model in the first case and by a viscoelastic model in the second case.     

金属基纳米复合材料等效弹性模量的均匀化方法数值模拟

均匀化理论利用位移场双尺度渐近展开建立有限元列式，本文将其与有限元通用程序相结合，应用于金属基复合材料的弹性本构数值模拟。通过对不同尺度增强相金属基复合材料等效模量的数值模拟，考察了均匀化方法的适用情况。数值计算结果表明，对常规尺度增强相金属基复合材料，均匀化方法可以较准确地预测其等效弹性模量；对纳米增强相金属基复合材料，该方法仍可给出较好的预测，但存在某种程度的系统偏差。通过对纳米尺度增强机理的分析讨论，认为纳米增强相与基体材料问的界面效应可能有别于连续介质假设，指出可以考虑采用离散原子-连续介质耦合模型改进数值模拟结果。     

The effective properties of composites with fiber-end cracks

The paper describes use of self-consistent finite element method (SCFEM) for predicting effective properties of fiber composite with partially debonded interface. The effective longitudinal Young's modulus and shear modulus for unidirectional fiber reinforced composites with fiber-end cracks are calculated. Numerical results show that the effective properties are considerably influenced by the fiber-end cracks. The effects of microstructural parameters, such as fiber volume fraction, modulus ratio of the constituents and fiber aspect, on the effective properties of the composites were discussed. The project supported by the National 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.     

The effect of microstructural morphology on the elastic,inelastic, and degradation behaviors of aluminum–alumina composites

Micromechanical models with idealized and simplified shapes of inhomogeneities have been widely used to obtain the average (macroscopic) mechanical response of different composite materials. The main purpose of this study is to examine whether the composites with irregular shapes of inhomogeneities, such as in the aluminum–alumina (Al–Al₂O₃) composites, can be approximated by considering idealized and simplified shapes of inhomogeneities in determining their overall macroscopic mechanical responses. We study the effects of microstructural characteristics, on mechanical behavior (elastic, inelastic, and degradation) of the constituents, and shapes and distributions of the pores and inclusions (inhomogeneities), and thermal stresses on the overall mechanical properties and response of the Al–Al₂O₃ composites. Microstructures of a composite with 20% alumina volume content are constructed from the microstructural images of the composite obtained by scanning electron microscopy (SEM). The SEM images of the composite are converted to finite element (FE) meshes, which are used to determine the overall mechanical response of the Al–Al₂O₃ composite. We also construct micromechanics model by considering circular shapes of the inhomogeneities, while maintaining the same volume contents and locations of the inhomogeneities as the ones in the micromechanics model with actual shapes of inhomogeneities. The macroscopic elastic and inelastic responses and stress fields in the constituents from the micromechanics models with actual and circular shapes of inhomogeneities are compared and discussed.     

Statistical Assessment of Tensile Static,Creep and Fatigue Strengths for Unidirectional CFRP

Background

The tensile strength along the longitudinal direction of unidirectional carbon fiber reinforced plastics (CFRPs) constitutes important data for the reliable design of CFRP structures. Our earlier reports proposed the formulations for the statistical static, creep, and fatigue strengths of CFRP based on Christensen’s model of the viscoelastic crack kinetics.

Objective

This study is concerned with the statistical assessment of the tensile static, creep, and fatigue strengths of unidirectional CFRPs by using the proposed formulations and the characterization of the long-term strengths of unidirectional CFRPs.

Method

First, the proposed formulations for the time-dependent and temperature-dependent statistical static, creep, and fatigue strengths of CFRP are introduced. Second, the tensile static, creep and fatigue strengths of unidirectional CFRP are measured statistically at various temperatures using resin-impregnated CFRP strands as tensile test specimens by measuring the viscoelasticity of the matrix resin. Finally, the master curves showing the long-term life of these strengths are constructed by substituting these measured data into the formulations.

Results

The results clarify that the formulations are applicable with high reliability over wide ranges of time and temperature for the statistical tensile static, creep and fatigue strengths of unidirectional CFRP except above the glass transition temperature of the matrix resin. Therefore, the fatigue strength degradation phenomena of unidirectional CFRPs can be expressed by the time- and temperature-dependent part due to the viscoelastic behavior of the matrix resin and the number of load cycle-dependent parts.

Conclusions

The long-term life prediction of unidirectional CFRPs under static, creep and fatigue tension loadings can be determined by ascertaining the mechanical properties of the CFRP and matrix resin in the proposed formulations.

     

Local shrinkage and stress induced by thermo-oxidation in composite materials at high temperatures

The paper is concerned with the modelling, simulation and experimental characterisation of local shrinkage strains and stresses induced by thermo-oxidation phenomena in the IM7/977-2 carbon/epoxy composite material at elevated temperatures. The oxygen concentration and mechanical fields were established through a coupled model constructed from a unified multiphysical approach and the thermodynamics of irreversible processes. The model was implemented in the ABAQUS^® finite element commercial code. Simulations of thermo-oxidation-induced matrix shrinkage were run at a local scale, i.e., the scale of the elementary constituents of the composite, the fibre and the matrix. The experimental assessment was done at the same scale, and the local matrix shrinkage profiles were measured by confocal interferometric microscopy.A good agreement was found between the simulated and measured profiles, validating the unified model. The thermo-oxidation induced stress field was analysed to understand the influence of the environment on the onset of damage in composite materials at elevated temperature.     

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.     

纤维/金属网增强层板低速冲击损伤机理和演化

本文首先通过落锤低速冲击实验测试了纯玻璃纤维增强环氧树脂复合材料和304不锈钢丝网(SSWM)/玻璃纤维混杂复合材料的力学性能,探究了SSWM嵌入数量对混杂复合材料抗冲击性能的影响．随后采用Abaqus有限元软件建立了混杂复合材料的低速冲击模型,分别采用三维Hashin失效准则和Jason-Cook破坏准则模拟了纤维/基体和SSWM的损伤;建立了基于表面接触的内聚力模型来模拟界面分层;编写了VUMAT用户子程序定义混杂复合材料层合板的渐进失效过程．结果表明：相较于纯玻璃纤维增强环氧树脂层合板,SSWM/玻璃纤维混杂增强环氧树脂层合板的抗冲击性能更优,其中铺层形式为铺层III的混杂复合材料抗冲击性能最佳．通过对比发现有限元仿真结果与实验结果吻合良好,表明建立的模型适用于SSWM/玻璃纤维混杂增强环氧树脂复合材料低速冲击损伤的评估．通过分析仿真结果发现混杂复合材料的低速冲击损伤主要是冲击区域的纤维断裂、基体破坏和层间分层;SSWM通过吸收和传递冲击能量从而提升了混杂复合材料的抗冲击性能．     

On the problem of interfacial damage in fibre-reinforced composites under variable loads

In this paper, the theoretical background for the failure analysis of fibre-reinforced composites under variable repeated loads in the framework of direct methods is presented. It is based on a local shakedown analysis in a representative volume element of the composite and the use of averaging techniques to study the influence of each component (matrix, fibre and interface) on the macroscopic response of such composite.     

压电复合材料粘接界面断裂有限元模拟

根据数字化FRMM(Fix-Ratio Mix-Mode)断裂试验,得到了压电复合材料试件的断裂韧性和位移及应变场。本文在试验的基础上,通过非线性有限元软件ABAQUS及用户子程序UMAT进行了模拟分析,采用基于损伤力学的粘聚区模型(CZM)对压电复合材料界面的起裂和脱胶扩展进行了分析,并与VCCT方法进行了比较。计算得到的荷载位移曲线更接近于试验结果,但在裂纹扩展路径上的吻合需要对粘聚区法则进一步修正。通过进一步对CZM参数进行分析,表明界面粘结强度和界面刚度对计算结果的影响很大。研究结果表明,粘聚区模型可以很好地表征压电复合材料弱粘接界面脱胶断裂问题。