Transverse failure of carbon fiber composites: Analytical sensitivity to the distribution of fiber/matrix interface properties

An analytic differentiation method is presented to calculate the sensitivity of the transverse failure response of carbon fiber composite laminates to the distribution parameters of the fiber/matrix interface properties. The method starts with the evaluation of the sensitivities of the transverse failure response with respect to the interface properties of each fiber, ie, the cohesive failure strength and the critical displacement jump. These individual sensitivities are then used to calculate the sensitivities with respect to the mean and standard deviation of the interface properties. The derived sensitivities are implemented in a nonlinear interface-enriched generalized finite element method solver specially developed for this application. The interface-enriched generalized finite element method solver combines a cohesive modeling of the fiber/matrix interface failure with finite element meshes that do not conform to the composite microstructure. The approach is first demonstrated on a model material involving a one-dimensional domain containing N cohesive interfaces described by randomly selected cohesive failure properties. The method is then applied to the more complex problem of a composite laminate involving a large number of fibers.     

Modeling the Tensile Strength of Carbon Fiber − Reinforced Ceramic − Matrix Composites Under Multiple Fatigue Loading

An analytical method has been developed to investigate the effect of interface wear on the tensile strength of carbon fiber ? reinforced ceramic ? matrix composites (CMCs) under multiple fatigue loading. The Budiansky ? Hutchinson ? Evans shear ? lag model was used to describe the micro stress field of the damaged composite considering fibers failure and the difference existed in the new and original interface debonded region. The statistical matrix multicracking model and fracture mechanics interface debonding criterion were used to determine the matrix crack spacing and interface debonded length. The interface shear stress degradation model and fibers strength degradation model have been adopted to analyze the interface wear effect on the tensile strength of the composite subjected to multiple fatigue loading. Under tensile loading, the fibers failure probabilities were determined by combining the interface wear model and fibers failure model based on the assumption that the fiber strength is subjected to two ? parameter Weibull distribution and the loads carried by broken and intact fibers satisfy the Global Load Sharing criterion. The composite can no longer support the applied load when the total loads supported by broken and intact fibers approach its maximum value. The conditions of a single matrix crack and matrix multicrackings for tensile strength corresponding to multiple fatigue peak stress levels and different cycle number have been analyzed.     

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。     

Effect of fiber,matrix and interface properties on the in-plane shear deformation of carbon-fiber reinforced composites

The effect of fiber, matrix and interface properties on the in-plane shear response of carbon-fiber reinforced epoxy laminates was studied by means of a combination of experiments and numerical simulations. Two cross-ply laminates with the same epoxy matrix and different carbon fibers (high-strength and high-modulus) were tested in shear until failure according to ASTM standard D7078, and the progressive development of damage was assessed by optical microscopy in samples tested up to different strains. The composite behavior was also simulated through computational micromechanics, which was able to account for the effect of the constituent properties (fiber, matrix and interface) on the macroscopic shear response. The influence of matrix, fiber and interface properties on each region and on the overall composite behavior was assessed from the experimental results and the numerical simulations. After the initial elastic region, the shear behavior presented two different regions, the first one controlled by matrix yielding and the second one by the elastic deformation of the fibers. It was found that in-plane shear behavior of cross-ply laminates was controlled by the matrix yield strength and the interface strength and was independent of the fiber properties.     

Evaluation of time-dependent change in fiber stress profiles during long-term pull-out tests at constant loads using Raman spectroscopy

Constant-load pull-out tests were carried out on single-fiber model composite specimens for 500 to 1,000 hours in order to investigate the time-dependent change in fiber axial stress profiles resulting from matrix creep in unidirectional continuous fiber-reinforced composites. Three resins used as the matrix materials, in which single carbon fibers were embedded, were normal epoxy, a blend with a more flexible epoxy, and UV-curable acrylic. The time-dependent change in fiber stress profiles in the constant-load pull-out tests was measured using Raman spectroscopy, and creep and relaxation tests for the matrix resins themselves were performed. It was observed that the normal epoxy matrix composite exhibited only a negligible change in the fiber stress profile with time whereas the flexible epoxy and UV-curable acrylic matrices allowed, respectively, considerable and significant changes. These observations were shown to be consistent with the creep and stress relaxation test results of the matrix resins. It was also found that the time-dependent change in fiber stress was much slower in the experiment than in the prediction based on perfect bonding at the fiber/matrix interface. The interfacial slip that occurred in the composites tested could be responsible for the gradual variation in fiber stress profiles.     

Analysis of matrix damage evolution in laminated composite plates

A new model has been developed to investigate matrix cracking in laminated fibrous composite structures. The model can predict matrix cracking and its effect on stiffness reduction. It can also compute the load transfer from the cracked matrix to surrounding fibers. The model is based on the micromechanical concept of the fiber and matrix as well as the matrix material degradation concept as matrix cracking progressed. The micromechanical concept uses a rectangular cell geometry representing a fiber and its surrounding matrix while the material degradation concept uses an empirical expression of a Weibull type function. Two material constants are required for matrix cracking. The constants were obtained from an experiment on matrix cracking. With those constants, the present model predicts the matrix cracking in other cases. The predicted solutions were comparable to the experimental data.     

Statistical issues in the fracture of brittle-matrix fibrous composites

This paper reviews recent work and presents new results on statistical aspects of the failure of composites consisting of brittle fibers aligned in a brittle matrix. The failure process involves quasi-periodic matrix cracking in planes perpendicular to the fiber, frictional sliding of the fibers in fiber break zones, and fiber bridging of cracks in a load-sharing framework that may vary from global to fairly local. First, we review the overall statistical features of the failure process, and identify certain issues in terms of critical geometric, statistical and mechanical parameters. This leads to two interesting cases, one where the spacing of matrix cracks is small relative to the length scale of load transfer in the fibers, and one where it is larger. Next we consider ‘characteristic’ bundles in the composite which capture essential features of the statistics of the failure process, and develop their distributions for strength in terms of certain characteristic stress and length scales. We then model the composite as a chain arrangement of such bundles both longitudinally and laterally, as the scale of load transfer among fibers in a bundle may be smaller than the full composite cross-section. This scale, though not precisely quantified, depends on such things as the stiffness of the matrix relative to the fibers, the volume fraction of the matrix and the spacing of periodic cracks. We then consider the strength distribution for the composite on the basis of the failure of the weakest characteristic bundle. We also consider issues related to fiber pull-out and the work of fracture as well as the possibility of severe strain localization especially within the bundle triggering overall failure. Substantial reductions in strength are predicted for smaller bundle sizes, but composite reliability is typically very high and the size effect very mild. Finally, we mention limited comparisons with Monte Carlo simulations and experimental results.     

Experimental Analysis of the Influence of Structural Parameters on the Behavior of Glass-Fiber Reinforced Polypropylene Composites

In a composite material reinforced by short random fibers, damage results from different elementary failure mechanisms such as matrix microcracking, fiber pull out, failure of the fiber/matrix interface, failure of fibers, etc. These damages influence greatly the macroscopic behavior of composite materials. To obtain good mechanical performance of a composite material, it is important to optimize the fiber ratio and the quality of the fiber/matrix interface, which have a direct influence on the damage mentioned above. The main objective of this study is to determine the influence of structural parameters on the evolution of damage for two types of polypropylene glass-fiber reinforced composites. In parallel with the classical approach of the mechanical theory of damage, which consists in load–unload tensile tests, the use of acoustic emission allows one to follow in real time the character and the importance of damage mechanisms in the course of loading. In addition, fractographic analysis makes it possible to confirm different assumptions and conclusions from this study.     

Can carbon nanotubes grown on fibers fundamentally change stress distribution in a composite?

In carbon fiber reinforced polymer composites the onset of damage occurs at the fiber/matrix interface, where stress concentrations are the highest due to the property mismatch of the two materials. This article reports results of a modelling study indicating that carbon nanotubes (CNTs) grown on fibers are effective in suppressing stress concentrations at the fiber/matrix interface. In the case of high density CNT forests, they can even fundamentally change a profile of the interfacial stress. The study is performed using a novel two-scale finite element model of a nano-engineered composite based on the embedded regions technique.     

Micromechanisms of damage in unidirectional fiber reinforced composites: 3D computational analysis

Numerical micromechanical investigations of the mechanical behavior and damage evolution of glass fiber reinforced composites are presented. A program code for the automatic generation of 3D micromechanical unit cell models of composites with damageable elements is developed, and used in the numerical experiments. The effect of the statistical variability of fiber strengths, viscosity of the polymer matrix as well as the interaction between the damage processes in matrix, fibers and interface are investigated numerically. It is demonstrated that fibers with constant strength ensure higher strength of a composite at the pre-critical load, while the fibers with randomly distributed strengths lead to the higher strength of the composite at post-critical loads. In the case of randomly distributed fiber strengths, the damage growth in fibers seems to be almost independent from the crack length in matrix, while the influence of matrix cracks on the beginning of fiber cracking is clearly seen for the case of the constant fiber strength. Competition between the matrix cracking and interface debonding was observed in the simulations: in the areas with intensive interface cracking, both fiber fracture and the matrix cracking are delayed. Reversely, in the area, where a long matrix crack is formed, the fiber cracking does not lead to the interface damage.     

Modeling Strength Degradation of Fiber-Reinforced Ceramic-Matrix Composites Subjected to Cyclic Loading at Elevated Temperatures in Oxidative Environments

In this paper, the strength degradation of non-oxide and oxide/oxide fiber-reinforced ceramic-matrix composites (CMCs) subjected to cyclic loading at elevated temperatures in oxidative environments has been investigated. Considering damage mechanisms of matrix cracking, interface debonding, interface wear, interface oxidation and fibers fracture, the composite residual strength model has been established by combining the micro stress field of the damaged composites, the damage models, and the fracture criterion. The relationships between the composite residual strength, fatigue peak stress, interface debonding, fibers failure and cycle number have been established. The effects of peak stress level, initial and steady-state interface shear stress, fiber Weibull modulus and fiber strength, and testing temperature on the degradation of composite strength and fibers failure have been investigated. The evolution of residual strength versus cycle number curves of non-oxide and oxide/oxide CMCs under cyclic loading at elevated temperatures in oxidative environments have been predicted.     

单纤维界面强度光弹性实验和理论研究

利用光弹性实验和有限元计算两种方法对单丝拔出复合材料模型的界面剪应力进行了研究。从计算和实验两个方面证明,当在纤维自由端施加一轴向拉力后,在单丝与基体界面的埋入端附近将出现剪应力的最大值。然后,沿着单丝的埋入方向,剪应力迅速降低,在界面区的中间趋于最小值,并且基本稳定不变。由此证明,单丝增强复合材料中界面的应力传递主要集中在单丝的埋入端附近,并且在这一区域最先达到危险应力,发生界面的脱胶破坏,引起整个试件的失效。     

Continuous micro-indenter push-through technique for measuring interfacial shear strength of fiber composites

This paper describes a continuous push-through, micro-indentation technique for measuring the fiber-matrix interfacial shear strength. E-glass fibers embedded perpendicular to the plane of thin polished specimens of epoxy matrix, with and without coupling agents, were indented with a micro-indenter until failure of the interface occurred and the fibers were pushed through the epoxy. The results show over 60% higher interfacial shear strength for fibers with coupling agent than for fibers without coupling agent. Average shear strength values obtained via the indentation technique are in good agreement with those obtained from the single-fiber-composite test. Absence of acoustic emission signals for debonding of the fibers coupled with no sudden drops in load vs indentation depth suggest that in this geometry the debonding is a slow, continuous process for both fiber surface treatments.     

单纤维拔出方法表征CFRP界面强度的研究

提出了单根碳纤维从环氧树脂基体中拔出的一种简易方法，在国内首次实现了用该方法表征碳纤维增强树脂基复合材料（ＣＦＲＰ）界面粘合性能的技术。     

Stress Concentrations Caused by Embedded Optical Fiber Sensors in Composite Laminates

The fiber optic sensor (FOS) embedded perpendicular to reinforcing fibers causes an `Eye' shaped defect. The length is about 16 times fiber optic radius (R_Fos) and height is about 2R_Fos. The eye contains fiber optics in the center surrounded by an elongated resin pocket. Embedding FOS causes geometric distortion of the reinforcing fiber over a height equal to 6 to 8 R_Fos. This defect causes severe stress concentration at the root of the resin pocket, the interface (in the composite) between the optical fiber and the composite, and at 90° to load direction in the composite. The stress concentration was calculated by finite element modeling of a representative micrograph. The FE results agreed reasonably with analytical and experimental data in the literature for a similar problem. The stress concentration in axial direction was about 1.44 and in transverse direction at the interface was -0.165 and at resin pocket was 0.171. Under tensile loading, the initial failure was by transverse matrix cracking (fiber splitting) at the root of the resin pocket, then that lead to final fracture by fiber breakage. Under compression loading, the failure initiation was by interfacial cracking due to large transverse tensile stress and the final fracture was by compression. Fracture stress calculated from the analysis using the maximum stress criteria agreed reasonably with test data.     

Simulation of Acoustic Emission in Planar Carbon Fiber Reinforced Plastic Specimens

The simulation of acoustic emission waveforms resulting from failure during mechanical loading of carbon fiber reinforced plastic structures is investigated using a finite element simulation approach. For this investigation we focus on the dominant failure mechanisms in fiber reinforced structures consisting of matrix cracking, fiber breakage and fiber-matrix interface failure. To simulate the failure process accurately, we present a new acoustic emission source model that is based on the microscopic source geometry and micromechanical properties of fiber and resin. We demonstrate that based on this microscopic source model these failure mechanisms result in excitation of macroscopic plate waves. The propagation of these plate waves is described using a macroscopic three-dimensional model geometry which includes contributions of reflections from the specimen boundaries. We further present a model of the acoustic emission sensors used in experiments to simulate the influence of aperture effects. To enhance the understanding of correlation between macroscopically detectable acoustic emission signals and microscopic failure mechanisms we simulate the response to different source excitation times, crack surface displacements and displacement directions. The results obtained show good agreement with fundamental assumptions about the crack process reported by various other authors. The simulated acoustic emission signals obtained are compared to experimentally measured waveforms during four-point bending experiments of carbon fiber reinforced plastic structures. The simulated signals of fiber-breakage, matrix-cracking and fiber-matrix interface failure show systematic agreement with the respective experimental signals.     

基于细观有限元方法的复合材料横向力学性能分析

横向断裂是制约复合材料结构设计的关键点,传统细观模型因为不能充分考虑组分性能、体积分数和纤维形状及分布情况而不能有效预测材料横向力学性能。采用改进的随机序列吸收算法建立具有随机纤维分布的复合材料代表性体积单胞模型,考虑基体破坏和界面脱粘两种失效模式和固化过程中产生的残余应力,对模型在横向拉、压、剪3种载荷下的力学行为进行仿真计算。分析了不同界面强度对复合材料力学性能的影响规律。仿真结果与实验数据对比表明:横向模量预测误差在7%以内,压缩和剪切的强度误差在8%以内,结果一致性较好,表明该模型能够有效预测复合材料横向力学性能。     

连续碳化硅纤维增强钛基(SiCf/Ti)复合材料的制备技术及界面特性研究综述

连续碳化硅纤维(SiCf)由于具有比强度、比模量高,耐磨性、热稳定性好等性能优点,常作为增强体制备SiC纤维增强钛基复合材料。与钛合金基体相比,其具有密度更低、强度更高、疲劳蠕变性能大幅提升等优点,但横向性能却明显下降。因此,该类材料常被设计制作成单向增强性部件,广泛应用在航空航天等领域,如发动机的传动轴、整体叶环、盘类及风扇叶片等多种复合材料的结构件。碳化硅纤维增强钛基复合材料的性能主要由碳化硅纤维的性能、基体性能及纤维与基体之间的结合界面性能决定。目前批量生产的SiC纤维性能较差,界面结合状态与复合材料性能之间关系的研究开展较少,还不能为钛基复合材料构件设计提供足够的数据支持。因此,近年来研究者们主要从SiCf/Ti基复合材料力学行为的研究角度出发,探究不同基体及纤维类型、复合材料制备工艺方法、界面特性及产物对SiCf/Ti基复合材料界面结合力及破坏机制的影响,获得了大量有价值的数据,以期开发出成本低、产物稳定性好、可批量生产SiCf/Ti基复合材料的制造工艺方法。目前较为成熟的碳化硅纤维有英国DERA-Sigma公司提供的Sigma系列SiCf及美国Textron公司提供的SCS系列SiCf,后者强度最高达到6 200 MPa。SiCf/Ti基复合材料的制备工艺包括金属箔-纤维-金属箔工艺(FFF)、单层带工艺(MT)、基体-涂层纤维工艺(MCT)等,制备复合材料的工艺根据零部件的用途来定,FFF适用于制备板材等大尺寸构件,MCT适用于制备叶环、轴、管、叶片等复杂结构件。界面是增强体与基体之间的纽带和桥梁,界面结构设计、界面反应控制及反应产物均影响着界面的力学特性。在SiCf/Ti基复合材料的纤维和基体之间添加过渡层能够减缓它们之间的相互扩散及化学反应,过渡层选用反应层和惰性涂层组成的双层涂层较好。界面反应产物受涂层成分、基体组织、复合和热处理工艺、环境因素等的影响,增强纤维及基体性能、优选制备工艺、控制界面反应及产物有利于提高复合材料的力学性能。本文总结了连续SiC纤维(SiCf)增强钛基复合材料的应用研究现状,详述了SiCf/Ti基复合材料的钛合金基体材料、SiCf的种类及性能,SiCf与SiCf/Ti基复合材料的制备方法,分析了SiCf/Ti基复合材料界面结构设计及反应产物,阐明了界面力学特性与复合材料性能的关系,指出国内SiCf/Ti基复合材料发展的重点应放在高性能SiC纤维的研究与开发、界面层设计及界面与性能的关系以及复合材料分析检测手段三个方面,为SiCf/Ti基复合材料的制备及其今后的实际应用提供了参考。     

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.     

Leaky guided wave propagation along imperfectly bonded fibers in composite materials

Leaky guided modes propagating along embedded fibers in a composite material can be used for characterizing the fiber-matrix interface. This principle can be applied to real composites containing small-diameter fibers by using laser interferometric detection of very fine lateral resolution on the order of a few microns. The main purpose of this paper is to develop the analytical tools needed to assess the sensitivity of guided wave inspection to interface properties in composite materials. Typically, the sound velocity is much lower in the matrix than in the fiber and the guided modes are strongly attenuated by leaking their energy into the matrix as they propagate. As a result, the velocity of the lowest-order axisymmetric longitudinal mode decreases while its attenuation increases with increasing interfacial stiffness between the fiber and the matrix. It is shown that loose fibers can be readily identified from early signals produced by fast guided modes. In the case of a well-bonded fiber-matrix interface, these guided modes are slowed down and strongly attenuated by the loading of the matrix depending on the fiber diameter and the interfacial stiffness of the interface. Interestingly, the relative difference between the well-bonded and free fibers is greater at low frequencies. Therefore, good sensitivity to the sought interfacial stiffness can be achieved at a few MHz, i.e., when the fiber diameter is still much smaller than the acoustic wavelength. Our analytical results show that the leaky guided mode technique is mainly sensitive to the transverse interfacial stiffness of the fiber-matrix interface. At typical ultrasonic frequencies between 1 and 20 MHz, the technique works best in the 10¹¹–10¹³ N/m³ interfacial stiffness range which is one or two orders of magnitude lower than the optimal sensitivity range of the more conventional bulk velocity and reflection methods.