Influences of interfacial bonding strength and scatter of fibre strength on tensile behaviour of unidirectional metal matrix composites

The influences of interfacial bonding strength and scatter of strength of fibres on tensile behaviour of unidirectional metal matrix composites, whose matrix has low yield stress in comparison to the strength of fibres, were studied using the Monte-Carlo simulation technique using two-dimensional model composites. The following results were found. The strength of composites increases with increasing bonding strength, especially when the bonding strength exceeds the shear yield stress of the matrix and then remains nearly constant. The strength of composites is very sensitive to bonding strength when the scatter of fibre strength is large, but not when it is small. The fracture mode varies from non-cumulative to cumulative with increasing scatter of fibre strength for both cases of weak and strong interfacial bondings. The fracture surface becomes irregular when bonding strength becomes low and scatter of fibre strength becomes large. The applicability of the Rosen and Zweben models and the rule of mixtures to predict the strength of composites was examined.     

Reliability approach to the tensile strength of unidirectional CFRP composites by Monte-Carlo simulation in a shear-lag model

A numerical technique based on the Monte-Carlo method in a shear-lag model is developed to simulate the tensile strength and fracture process for a unidirectional carbon-fiber-reinforced-plastic (CFRP) composite. The technique improves on the conventional approach by using an r_min method that can determine the stresses working on the fiber and matrix elements as the damage progresses. The r_min method is based on tracking the incremental ratio of the strength of an element to its stress. The present model includes the effect of the sliding frictional forces around fiber breaks caused by debonding between the fiber and matrix. Statistical properties of the tensile strength were obtained through simulation runs involving 100 samples for each value of the frictional force parameter. Also studied was the size effect in composite strength with increasing numbers of fibers, N, where it was found numerically that mean strength varies linearly as 1/[ln(N)]^1/2 and coefficient of variation varies linearly as 1/ln(N), as suggested from a simple theory.     

基于内聚力模型的形状记忆合金短纤维增强树脂基复合材料的模拟分析

通过单纤维拔出实验和单轴拉伸实验, 测定了形状记忆合金(SMA)增强树脂基复合材料的界面脱粘剪切强度和单向随机分布SMA短纤维增强复合材料的拉伸强度。根据蒙特卡罗法和边界条件控制方程, 编写了适于软件调用的单向随机分布短纤维增强复合材料的APDL语言生成程序, 建立数值模拟模型。基于指数型内聚力模型, 对SMA纤维与环氧树脂基体界面分离(即界面脱粘)过程进行了有限元模拟。结果表明: 相同纤维体积分数下, 随着纤维长细比的减小, 复合材料整体弹性模量逐渐降低; 温度驱使SMA纤维弹性模量发生变化, 可以有效提高复合材料整体弹性模量。     

Simulation and analysis of shape memory alloy fiber reinforced composite based on cohesive zone model

Shape memory alloy (SMA) composite has been wildly used in engineering fields as a smart structure. The interface between SMA fiber and matrix plays an important role in determining the effective response of the composites, since it is the medium through which stress transfer occurs. Therefore, it is necessary to investigate how the variation of interfacial properties affects the overall behavior of the composites. In this paper, the interfacial shear strength and ultimate strength of composites are evaluated based on pull-out tests and uniaxial tensile tests, respectively. An algorithm for the automatic generation of unidirectional random distribution short-fiber reinforced composites is developed by using Monte-Carlo method and boundary condition control equation via ANSYS Parameter Design Language (APDL). Cohesive zone model (CZM) approach is used to characterize the interfacial traction separation relationships. Uniaxial tensile test is simulated using finite element method to study the overall macroscopic behavior of the composite through varying fiber ratios and ambient temperatures. The effects of interfacial debonding process, fiber ratios and ambient temperatures on the response of composites are discussed under the same fiber volume fraction.     

含界面相三维全五向编织复合材料拉伸行为模拟及失效机制研究

基于三维全五向（Q5D）编织复合材料的细观结构模型,通过引入界面相单元,建立了含界面相Q5D编织复合材料单轴拉伸损伤失效分析模型。应用Python语言实现对ABAQUS的二次开发,将Linde等提出的失效准则和Von-Mises应力准则分别用于纱线和基体的渐进损伤判断,并确定材料的整体失效模式;对于界面相,采用Quads准则进行损伤判断。利用周期性位移边界条件,对含界面相Q5D编织复合材料的纵向拉伸应力-应变行为进行了渐进损伤数值模拟,详细讨论了在纵向拉伸载荷作用下材料的细观损伤起始、扩展和最终失效的演化过程,分析了材料的细观损伤失效机制,预测了材料的极限破坏强度,并研究了界面相性能对材料整体力学行为的影响规律。研究结果表明,数值模拟结果与实验值吻合较好,验证了渐进损伤模型的有效性,为该类材料的力学分析和优化设计奠定了基础。     

Microscopic failure mechanisms of fiber-reinforced polymer composites under transverse tension and compression

The mechanical behavior of unidirectional fiber-reinforced polymer composites subjected to tension and compression perpendicular to the fibers is studied using computational micromechanics. The representative volume element of the composite microstructure with random fiber distribution is generated, and the two dominant damage mechanisms experimentally observed – matrix plastic deformation and interfacial debonding – are included in the simulation by the extended Drucker–Prager model and cohesive zone model respectively. Progressive failure procedure for both the matrix and interface is incorporated in the simulation, and ductile criterion is used to predict the damage initiation of the matrix taking into account its sensitivity to triaxial stress state. The simulation results clearly reveal the damage process of the composites and the interactions of different damage mechanisms. It can be concluded that the tension fracture initiates as interfacial debonding and evolves as a result of interactions between interfacial debonding and matrix plastic deformation, while the compression failure is dominated by matrix plastic damage. And then the effects of interfacial properties on the damage behavior of the composites are assessed. It is found that the interfacial stiffness and fracture energy have relatively smaller influence on the mechanical behavior of composites, while the influence of interfacial strength is significant.     

双随机分布细观分析模型与复合材料性能预报

发展了一种细观力学有限元分析方法——拟真实的参数化双随机分布模型, 该模型综合考虑了纤维增强树脂基复合材料的真实微结构特点和纤维单丝综合力学性能测试结果的离散性特征, 模拟了复合材料中纤维排列和强度分布的随机性。借助移动窗口法研究了该参数化双随机分布模型的可靠性, 确定了其代表性体积单元的尺寸。基于能量法原理推导了单向复合材料的弹性模量预测公式, 结合能量法和渐进失效分析方法, 利用该细观力学有限元方法分别预测了单向纤维增强树脂基复合材料T300/5228的弹性模量和强度性能。数值模拟结果和大部分试验结果吻合良好, 表明发展的细观力学有限元方法能够较好地预测复合材料的力学性能。      

基于单胞解析模型的单向复合材料强度预报方法

基于单胞解析模型,建立一种从复合材料细观组分到宏观单向板的强度预报方法。根据连续介质力学和均匀化方法构建细-宏观关联矩阵,通过该关联矩阵将细观组分材料的弹性和损伤性能传递到宏观单向板中。考虑复合材料细观损伤状态,当纤维和基体满足各自强度准则时失效,并通过失效因子折算成刚度的衰减。在此基础上,结合有限元分析,实现复合材料单向板纵横向拉伸模拟,从而预报单向板的拉伸强度。结果表明:该方法预报的模量和强度与实验值基本一致,验证了该方法的有效性与高效性。     

2D-SiC/SiC复合材料拉伸加卸载行为

为了研究国产2D-SiC/SiC复合材料的拉伸损伤行为以及低周循环载荷作用下的力学性能,通过试验和建立加卸载细观力学模型,对其拉伸加卸载行为进行了探讨。建立了单向连续纤维增强陶瓷基复合材料加卸载细观力学模型,得到了初始加载、卸载和重新加载时的应力-应变关系;利用断裂统计方法得到了基体裂纹数随应力变化的关系和复合材料失效判断条件。经过应力转化,将该模型应用于国产二维编织SiC/SiC复合材料。对单向加载试件,采用正交试验方法和最小二乘法得到基体Weibull模量和界面剪切阻力,通过控制材料失效强度与试验结果一致,得到纤维Weibull模量。由上述参数确定的2D-SiC/SiC复合材料拉伸循环加卸载应力-应变曲线与实测曲线吻合很好。通过Matlab编程得到2D-SiC/SiC复合材料单向加载时基体开裂过程图。结果表明,2D-SiC/SiC复合材料失效时,基体裂纹分布相对比较均匀;基体裂纹数随应力单调增加,未出现持平段,表明材料失效时,基体裂纹还没有达到饱和。     

Verification and prediction of residual strength of C/SiC composites under non-stress oxidation

This article describes the strength behavior of C/SiC composites under non-stress oxidation. The oxidation kinetics model of a ceramic matrix composite contains both a reaction-controlled process and a diffusion-controlled process. The oxidation process has an effect on the fiber volume fraction, radius, and the composite interface shear stress. We obtained the residual strength of unidirectional C/SiC composites under 400–900 °C oxidation with non-stress environments by combining the mass loss rate model with the strength failure model at room temperature. This model considers the different components of the system to be subject to oxidation at different temperature ranges. Then, the influence of oxidation temperature, oxidation time, and fiber volume fraction on residual strength was studied. Experiments on C/SiC composites at 650 and 800 °C in an air environment with non-stress conditions were then performed, and the theoretical results of C/SiC composites were in good agreement with the experimental data.     

Tensile strength of fibre-reinforced metal matrix composites with non-uniform fibre spacing

The influence of non-uniform fibre spacing on the strength of unidirectional fibre-reinforced metal matrix composites was studied by means of a Monte-Carlo computer simulation experiment. The influence of yield stress of the matrix and scatter of the fibre strength on the strength of composites were also studied for both uniform and non-uniform fibre spacings. It was demonstrated that (1) the strength of composites with non-uniform fibre spacing is lower than that with uniform spacing due to the high stress concentration arising from the breakage of fibres, and (2) the reduction in strength of composites due to the non-uniformity increases with increasing scatter of fibre strength. For both cases of uniform and non-uniform spacings, the following tendencies were observed : (a) the strength of composites increases but then decreases with increasing yield stress of matrix, (b) it is very sensitive to yield stress of the matrix when the scatter of fibre strength is large but not when it is small, and (c) it decreases but then increases with increasing scatter of fibre strength when the yield stress of the matrix is high, while it decreases monotonically with increasing scatter of fibre strength when the yield stress is low.     

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.     

Monte Carlo simulation on tensile failure process of unidirectional carbon fiber reinforced nano-phased epoxy

This paper presents an analytical approach which combines the modified shear-lag model and Monte Carlo simulation technique to simulate the tensile failure process of unidirectional T700 carbon reinforced composite. Two kinds of matrix were investigated in the present paper, one is neat epoxy and the other one is SiC nano-particle filled epoxy. In the model, the strength of the fiber elements is randomly allocated by the Monte Carlo method, the elastic properties of the matrix elements and the friction after the interfaces breakage are definitely allocated. Using this model, the deformation, damage and failure process of the composite are simulated on the microscopic level, the tensile stress–strain relationship is well predicted. The relationship between mechanical properties of the fiber, matrix and composites was discussed. The analysis also shows that, compared with the neat system, nano-phased composite exhibits 10% improvement in tensile strength, which agrees with the experimental data.     

Statistical prediction of fatigue failure of fibre reinforced composite materials

A statistical approach is proposed to evaluate the residual strength and life of unidirectional and angle-ply composite laminates subjected to in-plane tensile cyclic stresses. The method is based on the extension of previous static failure criteria describing independently the fibre failure and matrix failure modes, combined with the statistical nature of fatigue failure of fibre-reinforced composites. The static and fatigue strengths of composite laminates at any off-axis angle are evaluated using the fatigue failure functions for the three principal failure modes, which are determined from the fatigue behaviour of unidirectional composites subjected to longitudinal and transverse tension as well as in-plane shear stresses. The evaluations of the fatigue strength of unidirectional E-glass/epoxy laminates under off-axis fatigue loading and angle-ply S-glass/epoxy laminates under in-plane fatigue loading show good agreement between theoretical predictions and experimental results.     

Multi-scale modeling, stress and failure analyses of 3-D woven composites

The very complex, multi-level hierarchical construction of textile composites and their structural components commonly manifests via significant property variation even at the macro-level. The concept of a “meso-volume” (introduced by this author in early 1990s) is consistently applied in this work to 3-D stress/strain and failure analyses of 3-D woven composites at several levels of structural hierarchy. The meso-volume is defined as homogeneous, anisotropic block of composite material with effective elastic properties determined through volumetrically averaged 3-D stress and strain fields computed at a lower (“finer”) level of structural hierarchy and application of generalized Hooke’s law to the averaged fields. The meso-volume can represent a relatively large, homogenized section of a composite structural component, a lamina in laminated composite structure, a homogenized assembly of several textile composite unit cells, a single homogenized unit cell, a resin-impregnated yarn, a single carbon fiber, even a carbon nanotube assembly. When composed together, distinct meso-volumes constitute a 3-D Mosaic model at the respective hierarchy level. A multi-scale methodology presented in this paper first illustrates 3-D stress/strain analysis of the Mosaic unidirectional composite, computation of its effective elastic properties and their further use in 3-D stress/strain analysis of the Mosaic model of 3-D woven composite Unit Cell. The obtained 3-D stress/strain fields are then volumetrically averaged within the Unit Cell, and its effective elastic properties are computed. The predicted effective elastic properties of 3-D woven composite are compared with experimental data and show very good agreement. Further, those effective elastic properties are used in 3-D simulations of three-point bending tests of 3-D woven composite; theoretical predictions for central deflection show excellent agreement with experimental data. Finally, a 3-D progressive failure analysis of generic 3-D Mosaic structure is developed using ultimate strain criterion and illustrated on the 3-D woven composite Unit Cell. The predicted strength values are compared to experimental results. The presented comparisons of theoretical and experimental results validate the adequacy and accuracy of the developed material models, mathematical algorithms, and computational tools.     

REINFORCEMENT FRACTURE AND TENSILE DUCTILITY IN SPHERE-REINFORCED METAL-MATRIX COMPOSITES

Abstract— Sphere-reinforced metal-matrix composites are modelled as a three dimensional array of hexagonal cylinders, each one with a broken or intact spherical reinforcement at its centre. Using this model, the stress-strain response of the composite in uniaxial tension was obtained. A parametrical analysis of the influence of matrix and reinforcement properties as well as volume fraction on the ductility of these composites was performed. It was found that the decrease in ductility with respect to the unreinforced matrix depended mainly on the reinforcement/matrix strength ratio and on the defect distribution in the particulates.     

单向纤维增强陶瓷基复合材料单轴拉伸行为

采用细观力学方法对单向纤维增强陶瓷基复合材料的单轴拉伸应力-应变行为进行了研究。采用Budiansky-Hutchinson-Evans（BHE）剪滞模型分析了复合材料出现损伤时的细观应力场,结合临界基体应变能准则、应变能释放率准则以及Curtin统计模型三种单一失效模型分别描述陶瓷基复合材料基体开裂、界面脱粘以及纤维失效三种损伤机制,确定了基体裂纹间隔、界面脱粘长度和纤维失效体积分数。将剪滞模型与3种单一失效模型相结合,对各个损伤阶段的应力-应变曲线进行模拟,建立了准确的复合材料强韧性预测模型,并讨论了界面参数和纤维韦布尔模量对复合材料损伤以及应力-应变曲线的影响。与室温下陶瓷基复合材料单轴拉伸试验数据进行了对比,各个损伤阶段的应力-应变、失效强度及应变与试验数据吻合较好。     

Thermoplastic matrix continuous filament composites of Kevlar® aramid or graphite fiber

Key static mechanical properties and laminating processes of thermoplastic matrix continuous filament composites reinforced with Kevlar® aramid or graphite fibers are presented and discussed. A tow of Kevlar or graphite impregnated with a thermoplastic matrix from a proprietary melt-coating process involving injection of a melted thermoplastic polymer can be consolidated into a sound, void-free composite laminate by compression molding. The unidirectional composites of Kevlar 49 or graphite from the melt-coated tows possess mechanical properties superior to those of similar composites prepared by other processes such as yarn cowinding and film laminating. The unidirectional composites of Kevlar 49 with thermoplastic matrices prepared from the melt-coated tows are equivalent or superior to those using Epon® epoxies or polyvinylester in flexural, shear and compressive strengths. Using J-polymer, a polyamide copolymer and a proprietary Du Pont resin candidate as a thermoplastic matrix model, a static mechanical test data base has been developed for graphite/thermoplastic matrix composites showing significant advantages in damage tolerance, compression after impact, and interlaminar fracture toughness. Although the unidirectional compressive strength of graphite/epoxy composites has been shown to correlate with matrix modulus, the thermoplastic matrix composites show no such correlation.     

Effect of Moisture and Temperature on the Compressive Failure of CCF300/QY8911 Unidirectional Laminates

CCF300/BMI composites are relevant materials for supersonic aircraft due to their high specific properties. However in aeronautical applications, the composites are exposed to severe environmental conditions, and it is known that hot and humid environments can degrade some aspects of the material performance especially the compressive strength. In this paper, the effect of moisture and temperature on the compressive failure of unidirectional CCF300 carbon fiber reinforced bismaleimide(BMI) matrix composites were studied. Also scanning electron microscope (SEM) was employed for fractographic investigations. It is observed that the plastic deformations at the fiber/matrix and interlaminar interface as well as residual stresses lower the compressive strength of the material. The failure of specimens tested in hot and wet conditions always occurs as a result of out-of-plane microbuckling that is attributed to the reduction of matrix strength. In addition, the fiber microbuckling model, fiber kinking model and combined model were employed for the compressive strength prediction of the UD CCF300/QY8911 composites subjected to different environment conditions. The comparison was done between these models. Results show that the combined model is more suitable for the compressive strength prediction of CCF300/QY8911 composite systems when suffering severe environment conditions.