On the local elastic–plastic behaviour of the interface in titanium/silicon carbide composites

The purpose of this study is to conduct a high-resolution nonlinear finite element analysis of the elastic–plastic behaviour of titanium/silicon carbide composites subject to transverse loading. This class of metal matrix composites is designed for the next generation of supersonic jet engines and deserves careful assessment of its behaviour under thermo mechanical loads. Three aspects of the work are accordingly examined. The first is concerned with the development of a representative unit cell capable of accurately describing the local elastic–plastic behaviour of the interface in metal matrix composites under thermal and mechanical loads. The second is concerned with the determination of the influence of mismatch in the mechanical properties between the inhomogeneity and the matrix upon the induced stress fields and the plastic zone development and its growth. The third is concerned with unloading and the role played by the interface upon residual stresses. It is found that the maximum interfacial stress in the matrix appears in the case involving cooling from the relieving temperature with subsequent applied compressive loading. It is also found that the mismatch in mechanical properties between the matrix and the inhomogeneity introduces significant changes in the stress distribution in the matrix. Specifically, it is observed that the maximum radial and tangential stresses in the matrix take place at the interface. The plastic deformation of the matrix leads to a relaxation of these stresses and assists in developing a more uniform interfacial stress distribution. However, the matrix stresses and the resulting equivalent plastic strains still reach their maximum values at that interface. The results show similarities in the patterns of the interfacial stress distribution and plastic zone development for all ranges of fibre volume fractions and loading levels examined. However, they also show marked differences in both the magnitude and patterns of matrix stress distribution between the adjacent inhomogeneities as a result of interaction effects between the fibres.     

Effect of elastic–plastic matrix on thermo-mechanical response of continuous anisotropic fiber-reinforced composites

Based on a concentric cylinder model, the analytical elastic–plastic solution of deformations and stresses for the composites reinforced with transversely isotropic, circumferentially orthotropic and radially orthotropic fibers subjected to axisymmetric thermo-mechanical loading is developed. How the plasticity, volume fraction, physical and mechanical properties of the matrix affect the elastic–plastic thermo-mechanical response of the composites is investigated. The plasticity of the matrix decreases greatly the axial compressive stress in the matrix, but more noticeably increases the axial compressive stress in the fiber. For the composites reinforced with transversely isotropic, circumferentially orthotropic and radially orthotropic fibers, decreasing the volume fraction, thermal expansion coefficient and Young's modulus, and increasing the yield stress and hardening parameter of the matrix can lower the maximum equivalent stress of the fiber. However, increasing the yield stress and hardening parameter of the matrix raises the maximum equivalent stress of the matrix.     

Micromechanics based analysis of randomly distributed fiber reinforced composites using simplified unit cell model

The geometry of the simplified unit cell (SUC) model [Aghdam MM, Smith DJ, Pavier MJ. Finite element micromechanical modeling of yield and collapse behavior of metal matrix composites. J Mech Phys Solids 48 (2000) 499–528] is extended to study effects of random fiber arrangement on the mechanical and thermal characterizations of unidirectional composites. The representative volume element (RVE) considered in the model consists of an r × c unit cells in which fibers are surrounded randomly by matrix cells. The presented model is general and can be used to predict the behavior of a fibrous composite subjected to thermal and mechanical, normal and shear, loading. The model also is capable of analyzing various combinations of these loading conditions such as off-axis test of unidirectional coupons. Both random and repeating fiber arrays can be considered in the model. Results for the overall thermal and elastic properties of a SiC/Ti metal matrix composite (MMC) show good agreement with both the finite element and other analytical models with repeating fiber arrays. Results of transverse properties also revealed that hexagonal array assumption for fiber arrangement is more realistic than square array assumption.     

形状记忆合金短纤维增强弹塑性基体复合材料的力学行为

基于Eshelby等效夹杂方法和Mori-Tanaka的平均化理论推导了针对SMA短纤维增强弹塑性基体复合材料的细观力学模型。利用此模型,分析了这种复合材料的力学行为,讨论了材料温度、纤维体积分数和纤维特征形状等参数对复合材料残余应力和残余应变的影响。这对复合材料的分析和设计都有重要的意义。      

On the matrix cracking stress and the redistribution of internal stresses in brittle-matrix composites

A concept is proposed to increase the matrix cracking stress of some brittle-matrix composites by taking advantage of the redistribution of internal stresses that occurs when a composite with phases that have dissimilar creep behavior is subjected to thermomechanical loading. The concept is elaborated through the stress analysis of a model unidirectional composite with constituents that exhibit linear viscoelastic behavior. It is shown that if a composite with a matrix that is less creep resistant than the fibers is subjected to a treatment involving both thermal and mechanical loading (e.g. creep test), stresses can be transferred from the matrix to the fibers, resulting in the stress–relaxation of the matrix. Furthermore, it is also shown that by the elastic recovery of the fibers, the matrix can be subjected to large compressive residual stresses at the end of the treatment. The conditions for the viability of this concept and the implications of fiber overloading and potential loss of composite-like behavior are discussed.     

Residual stresses in fibre- and whisker-reinforced aluminium alloys during thermal cycling measured by X-ray diffraction

Residual stresses have been determined using X-ray diffraction in two different metal matrix composites, viz. a squeeze-cast Al-2%Mg matrix with 10, 20 or 26 vol.% Al₂O₃ fibres and an extruded AA 6061 alloy with 25 vol.% SiC whiskers. The composites have been studied after thermal cycling between 240 or 250 °C and room temperature succeeded in some cases by quenching to liquid nitrogen temperature. On the squeeze-cast composite, stresses were measured at room temperature and in situ at 240 °C. X-ray stress determinations were compared with the stress values calculated by a modified Eshelby model for equivalent inclusions. By the model, the stresses can be accurately predicted for both composite systems. Thermally induced plastic relaxation reduces the residual stresses. The degree of reduction depends on the reinforcement volume fraction, the difference in coefficient of thermal expansion between the phases and the magnitude of the temperature drop. At elevated temperature the stresses are less responsive to reiterated quenching and heating.     

基于宏微观分析的碳纤维增强高分子复合材料强度性能表征

微观力学强度理论(MMF)是一种新型的基于物理失效模式的复合材料强度理论。通过对碳纤维/树脂(UTS50/E51)复合材料单向层合板进行纵向、横向静载拉伸、压缩和弯曲试验, 得到层合板的基本力学性能和宏观强度指标。建立了碳纤维增强树脂基复合材料微观力学模型, 获取树脂基体和纤维不同位置的机械载荷应力放大系数和热载荷应力放大系数。结合获取的应力放大系数及试验测得的单向层合板宏观强度, 计算出层合板组分的MMF强度特征值。绘制了基于MMF强度理论的层合板破坏包络线, 并与Tsai-Wu失效准则预测结果进行对比。实现了对UTS50/E51层合板MMF强度特征值的表征。     

Finite-element modeling of initial matrix failure in CFRP under static transverse tensile load

The failure of transversely loaded unidirectional CFRP has been investigated by the use of mechanical and thermo-mechanical test methods and finite-element analysis. The case considered here is characterized by a high interfacial strength between fiber and matrix, so that matrix failure governs the fracture process of the composite. On the basis of the experimental results, the parabolic and other failure criteria were applied to the FE calculations. The failure dependence of the resin on the actual stress state could be described. Furthermore, the influence of thermal residual stresses on the initial matrix failure has been investigated, and the actual stiffnesses and thermal expansion changes of the epoxy resins and the composites as a function of temperature have been determined experimentally. The results of the mechanical and thermo-mechanical tests performed on the pure resins and on the composites were incorporated into a finite-element analysis and compared with the transverse tensile properties of the composite laminates. In the FE analysis, the local fiber-volume fraction was varied over a wide range in order to investigate its influence on the thermal residual stresses and transverse composite strength. The results could explain the low strain to failure of transverse laminates under tensile loading.     

Effects of Interphase Damage and Residual Stresses on Mechanical Behavior of Particle Reinforced Metal-Matrix Composites

Mechanical behavior of aluminum matrix composites reinforced with SiC particles are predicted using an axisymmetric micromechanical finite element model. The model aims to study initiation and propagation of interphase damage subjected to combination of thermal and uniaxial loading. Effects of manufacturing process thermal residual stresses and interphase de-bonding are considered. The model includes a square Representative Volume Element (RVE) from a cylindrical unit cell representing a quarter of SiC particle surrounded by Al-3.5wt.%Cu matrix. Suitable boundary conditions are defined to include effects of combined thermal and uniaxial tension loading on the RVE. An appropriate damage criterion with a linear relationship between radial and shear stresses for interphase damage is introduced to predict initiation and propagation of interphase de-bonding during loading. A damage user subroutine is developed and coupled to the finite element software to model interphase damage. Overall Stress-strain behavior of particulate metal-matrix composite by considering residual stresses is compared with experimental data to estimate interphase strength. Effects of thermal residual stresses in elastic, de-bonding and plastic zones of composite system are discussed in details. Furthermore, parametric study results show high influence of interphase strength on the overall mechanical behavior of composite material.     

Stress distributions in single shape memory alloy fiber composites

Shape memory alloy (SMA) in the form of wires or short fibers can be embedded into host materials to form SMA composites that can satisfy a wide variety of engineering requirements. The recovery action of SMA inclusions induced by elevated temperature can change the modal properties and hence the mechanical responses of entire composite structures. Due to the weak interface strength between the SMA wire and the matrix, interface debonding often occurs when the SMA composites act through an external force or through actuation temperature or combination of the two. Thus the function of SMAs inside the matrix cannot be fully utilized. To improve the properties and hence the functionality of SMA composites it is therefore very important to understand the stress transfers between SMA fibers and matrix and the distributions of internal stresses in the SMA composite. In this paper, a theoretical model incorporating Brinson’s constitutive law of SMA for the prediction of internal stresses is successfully developed for SMA composites, based on the principle of minimum complementary energy. A typical two-cylinder model consisting of a single SMA fiber surrounded by epoxy matrix is employed to analyze the stress distributions in the SMA fiber, the matrix, and at the interface, with important contributions of the thermo-mechanical effect and the shape memory effect. Assumed stress functions that satisfy equilibrium equations in the fiber and matrix respectively are utilized, as well as the principle of minimum complementary energy, to analyze the internal stress distributions during fiber pull-out and the thermal loading process. The entire range of axisymmetric states of stresses in the SMA fiber and matrix are developed. The results indicate substantial variation in stress distribution profiles for different activation and loading scenarios.     

Finite element analysis of the stress distribution in a thermally and transversely loaded Ti–6Al–4V/SiC fibre composite

The load transfer between fibre and matrix in a metal matrix composite (MMC) depends on the properties and conditions of the fibre/matrix interfacial region. The objective of this investigation is to gain a better understanding of the stresses generated within a continuously reinforced MMC, particularly at this interface. Finite element analysis is used to investigate the effect of thermal and transverse mechanical loading on the SiC/Ti–6Al–4V composite system. The effect on the stress field of a carbon coating on the SiC fibres is also investigated. The results indicate that the interfacial region affects the stress distribution, with the presence of the carbon coating significantly altering the stress profiles generated. It is also found that the residual stresses generated as a result of cooling down the composite from processing temperature, has a marked effect on the stress profile and the behaviour of the composite when subsequent mechanical loading is applied.     

Matrix cracking with frictional bridging fibres in continuous fibre ceramic composites

Interfacial debonding and matrix cracking due to residual axial stresses have been analysed for unidirectional fibre-reinforced ceramic composites. The analytical solutions for the crack-opening displacement, the axial displacement of the composite due to interfacial debonding, and the critical residual axial stress for matrix cracking have been obtained. The solutions were then compared with those for tensile loading in the fibre direction. Three issues related to Part I, i.e. the effective fracture toughness of the composite, the critical loading stress for matrix cracking in the presence of residual stresses, and the debonded fibre length due to loading, were also addressed in the present study.     

Fibre-matrix bond strength studies of glass,ceramic, and metal matrix composites

An indentation test technique for compressively loading the ends of individual fibres to produce debonding has been applied to metal, glass, and glass-ceramic matrix composites; bond strength values at debond initiation are calculated using a finite-element model. Results are correlated with composite longitudinal and interlaminar shear behaviour for carbon and Nicalon fibre-reinforced glasses and glass-ceramics including the effects of matrix modifications, processing conditions, and high-temperature oxidation embrittlement. The data indicate that significant bonding to improve off-axis and shear properties can be tolerated before the longitudinal behaviour becomes brittle. Residual stress and other mechanical bonding effects are important, but improved analyses and multiaxial interfacial failure criteria are needed to adequately interpret bond strength data in terms of composite performance.     

Prediction of local hygroscopic stresses for composite structures – Analytical and numerical micro-mechanical approaches

The aim of this article is to propose an analytical micro-mechanical self-consistent approach dedicated to mechanical states prediction in both the fiber and the matrix of composite structures submitted to a transient hygroscopic load. The time and space dependent macroscopic stresses, at ply scale, are determined by using continuum mechanics formalism. The reliability of the new approach is checked, for carbon–epoxy composites, through a comparison between the local stress states calculated in both the resin and fiber according to the new closed-form solutions and the equivalent numerical model.     

Coupled heat conduction and thermal stress analyses in particulate composites

This study introduces two micromechanical modeling approaches to analyze spatial variations of temperatures, stresses and displacements in particulate composites during transient heat conduction. In the first approach, a simple micromechanical model based on a first order homogenization scheme is adopted to obtain effective mechanical and thermal properties, i.e., coefficient of linear thermal expansion, thermal conductivity, and elastic constants, of a particulate composite. These effective properties are evaluated at each material (integration) point in three dimensional (3D) finite element (FE) models that represent homogenized composite media. The second approach treats a heterogeneous composite explicitly. Heterogeneous composites that consist of solid spherical particles randomly distributed in homogeneous matrix are generated using 3D continuum elements in an FE framework. For each volume fraction (VF) of particles, the FE models of heterogeneous composites with different particle sizes and arrangements are generated such that these models represent realistic volume elements “cut out” from a particulate composite. An extended definition of a RVE for heterogeneous composite is introduced, i.e., the number of heterogeneities in a fixed volume that yield the same expected effective response for the quantity of interest when subjected to similar loading and boundary conditions. Thermal and mechanical properties of both particle and matrix constituents are temperature dependent. The effects of particle distributions and sizes on the variations of temperature, stress and displacement fields are examined. The predictions of field variables from the homogenized micromechanical model are compared with those of the heterogeneous composites. Both displacement and temperature fields are found to be in good agreement. The micromechanical model that provides homogenized responses gives average values of the field variables. Thus, it cannot capture the discontinuities of the thermal stresses at the particle-matrix interface regions and local variations of the field variables within particle and matrix regions.     

Numerical study of the effects of reinforcement/matrix interphase on stress-strain behavior of YAl2 particle reinforced MgLiAl composites

For the potential influence produced by the reinforcement/matrix interphase in particle reinforced metal matrix composites (PMMCs), a unit cell model with transition interphase was proposed. Uniaxial tensile loading was simulated and the stress/strain behavior was predicted. The results show that a transition interphase with both appropriate strength and thickness could affect the failure mode, reduce the stress concentration, and enhance the maximum strain value of the composite.     

高体积含量颗粒增强复合材料的一个细观力学模型Ⅱ: 弹塑性与损伤分析

在高体积含量颗粒增强复合材料细观弹性分析的基础上, 引入了细观塑性和细观损伤模型: 基体用服从Von Mises 屈服准则的理想弹塑性材料模拟, 用沿圆柱形基体轴线方向的平均应力(即对称面上的应力) 来判断基体的屈服, 并将基体的塑性部分简化为圆柱状轴对称区域。建立了基体和颗粒/ 基体界面统一的损伤准则, 该准则同时考虑了最大应变和三轴应力的影响, 通过对细观塑性和细观损伤在空间取向上的平均, 建立了材料宏观模量的折减法则。用该细观力学模型, 数值模拟了一种实际金属基复合材料的强度实验, 理论模型与实验结果吻合。