Fatigue behavior of laminated composites with a circular hole under in-plane uniaxial random loading

A modified fiber failure fatigue model is presented to evaluate the behavior of laminated composites with a central circular hole under in-plane uniaxial random/block loading. The analytical model presented is based on minimum strength model and fiber failure criterion under static loading available in the literature. The analysis starts with the determination of location of a characteristic curve around the hole and the stress state along the characteristic curve under in-plane uniaxial fatigue loading. Number of cycles to failure and location of failure are determined under given fatigue loading condition. Based on ply-by-ply analysis, ultimate fatigue failure and the corresponding number of cycles are determined. Degradation of material strength as a function of applied number of cycles is considered in the model presented. Random loading case is analyzed based on rainflow counting technique. Analytical predictions are compared with the experimental results for uniaxial block loading.     

A micromechanical analysis of fiber crack propagation in composite materials due to transverse tensile loads

The fiber crack propagation in composites due to transverse tensile loads is studied using a micromechanical model and Linear Elastic Fracture Mechanics. To approach the problem, a three domain cylindrical model is introduced to simulate the fiber cracking. The model problem is then solved by the dislocation and singular integral equation techniques. The stress intensity factors of the fiber crack are calculated for various situations. It is found that fiber anisotropy has hardly any effect on the fiber crack propagation; “reverse composites” (composites in which fiber is less stiff than the matrix, such as Nicalon/SiC ceramic composite) virtually eliminate fiber crack propagation.     

Fatigue behavior of laminated composites with a circular hole under in-plane multiaxial loading

A modified fiber failure fatigue model is presented for characterizing the behavior of laminated composites with a central circular hole under in-plane multiaxial fatigue loading. The analytical model presented is based on minimum strength model and fiber failure criterion under static loading available in the literature. The analysis starts with the determination of location of a characteristic curve around the hole and the stress state along the characteristic curve under in-plane multiaxial fatigue loading. Number of cycles to failure and location of failure are determined under given fatigue loading condition. Based on ply-by-ply analysis, ultimate fatigue failure and the corresponding number of cycles are determined. Analytical predictions are compared with the experimental results for uniaxial and multiaxial fatigue loading cases. A good match is observed. Further, studies are carried out for different in-plane biaxial tension–tension and biaxial compression–compression loading cases.     

Statistical modelling of compression and fatigue damage of unidirectional fiber reinforced composites

A statistical computational model of strength and damage of unidirectional carbon fiber reinforced composites under compressive and cyclic compressive loading is presented in this paper. The model is developed on the basis of the Budiansky–Fleck fiber kinking condition, continuum damage mechanics concept and the Monte-Carlo method. The effects of fiber misalignment variability, fiber clustering, load sharing rules on the damage in composite are studied numerically. It is demonstrated that the clustering of fibers has a negative effect of the damage resistance of a composite. Further, the static compressive loading model is generalized for the case of cyclic compressive loading, with and without microdegradation of the matrix, and with and without random variations of loading. It was observed that the random variations of loading shorten the lifetime of the composite: the larger the variability of applied load, the shorter the lifetime.     

Micromechanical modeling of interface damage of metal matrix composites subjected to off-axis loading

A three dimensional micromechanics based analytical model is presented to investigate the effects of initiation and propagation of interface damage on the elastoplastic behavior of unidirectional SiC/Ti metal matrix composites (MMCs) subjected to off-axis loading. Manufacturing process thermal residual stress (RS) is also included in the model. The selected representative volume element (RVE) consists of an r × c unit cells in which a quarter of the fiber is surrounded by matrix sub-cells. The constant compliance interface (CCI) model is modified to model interfacial de-bonding and the successive approximation method together with Von-Mises yield criterion is used to obtain elastic–plastic behavior. Dominance mode of damage including fiber fracture, interfacial de-bonding and matrix yielding and ultimate tensile strength of the SiC/Ti MMC are predicted for various loading directions. The effects of thermal residual stress and fiber volume fraction (FVF) on the stress–strain response of the SiC/Ti MMC are studied. Results revealed that for more realistic predictions both interface damage and thermal residual stress effects should be considered in the analysis. The contribution of interfacial de-bonding and thermal residual stress in the overall behavior of the material is also investigated. Comparison between results of the presented model shows very good agreement with finite element micromechanical analysis and experiment for various off-axis angles.     

基体局部软化对纤维/环氧树脂复合材料力学行为影响的数值分析

聚合物基体的变形局部化在复合材料破坏过程中起着重要作用。采用有限元分析方法, 借助用户材料子程序(UMAT), 描述了具有应变软化特点的高聚物弹塑性的本构关系, 研究了纤维/环氧树脂复合材料在拉伸破坏过程中基体局部变形的演化规律, 分析了基体的局部应变软化对纤维/环氧树脂复合材料应力的影响。结果表明: 纤维的应力分布及基体的塑性变形具有不均匀性; 基体局部变形降低了邻近断点的完好纤维的应力集中程度; 随着纤维间距的增加, 邻近断点的完好纤维的应力集中区域变宽, 而且应力集中程度降低。     

Stress Corrosion Cracking of Basalt/Epoxy Composites under Bending Loading

The purpose of this research is to study the stress corrosion behavior of basalt/epoxy composites under bending loading and submerged in 5% sulfuric acid corrosive medium. There are limited numbers of research in durability of fiber reinforced polymer composites. Moreover, studies on basalt fibers and its composites are very limited. In this research, mechanical property degradation of basalt/epoxy composites under bending loading and submerged in acidic corrosive medium is investigated. Three states of stress, equal to 30%, 50% and 70% of the ultimate strength of composites, are applied on samples. High stress states are applied to the samples to accelerate the testing procedure. Mechanical properties degradation consists of bending strength, bending modulus of elasticity and fracture energy of samples are examined. Also, a normalized strength degradation model for stress corrosion condition is presented. Finally, microscopic images of broken cross sections of samples are examined.     

Microstructure and mechanical properties of Al–2Mg alloy base short steel fiber reinforced composites prepared by vortex method

Fabrication and characterization of cast Al–2Mg alloy matrix composites reinforced with short steel fibers are dealt with in the present study. Three types of steel fiber were used: uncoated, copper coated and nickel coated. All the composites were prepared by the liquid metal route using vortex methods. When tested in tension, all composites exhibited improvement in strength due to high relative strength of steel fibers. The ductility was lowered except for the composite with copper coated fibers. Copper coated fiber reinforced composites gave the highest strength. Higher strength accompanied with appreciable ductility demonstrated by composites with copper coated fibers is attributed to the solid solution and fiber strengthening as well as good bonding at the interface. Composites reinforced with uncoated and Ni coated steel fibers did not exhibit strengthening to the level exhibited with copper coated fibers because brittle intermetallic phases are formed at the interface. These phases promote initiation and facilitate propagation of cracks. The observed fracture mechanism of composites was dimple formation, fiber breakage and pullout of fibers. Fracture surface of uncoated and Ni coated composites showed extensive pull out of fibers as well as fiber breakage confirming the above inference. In case of the copper coated composites dimple formation and coalescence was more extensive. EDX analysis showed a build up Cu, Ni, and Fe at the interface.     

连续变化界面层对复合材料弹性性能影响

界面层对复合材料的变形和破坏有着重要的影响,实际界面层的性能是随位置而连续变化的,但目前大多数考虑界面层影响的工作都假设界面层材料性能均匀或分层均匀。假设界面层的性能是空间位置的幂函数形式,给出了具有上述界面层的纤维和球形夹杂在球压和剪切载荷下的解,然后利用平均场方法建立了上述复合材料的有效弹性性质与微结构的联系。还将上述方法与均匀界面层模型进行了比较,计算结果表明,界面层的性质对复合材料有效性质和局部应力的分布有着重要影响。      

针刺C/SiC复合材料应力-应变模型及试验验证

研究了室温下针刺C/SiC复合材料的静拉伸应力-应变行为。基于显微CT技术重构的微观型貌,选取恰当的代表体积单元,建立了针刺C/SiC复合材料应力-应变性能预测的单胞模型。基于可实现任意加卸载下单向纤维增强C/SiC复合材料应力-应变计算的界面摩擦模型,由材料的细观组分性能计算出单向纤维束层的应力-应变响应,然后将单向纤维束层的应力-应变响应代入到单胞模型中,通过有限元法计算得到针刺C/SiC复合材料的整体应力-应变响应。进行了针刺C/SiC复合材料静拉伸试验,测得材料的应力-应变响应,计算结果与试验吻合较好。      

Experimental and analytical study on fiber-kinking failure mode of laminated composites

Compressive behavior of composite materials has received significant attention in recent years. In the present work, a recently developed strain based fiber kinking model and stress based ones for unidirectional laminated composites are compared with experimental results. These models are implemented into a finite element code and the obtained results for glass/epoxy (Type C) ASNA 4197 unidirectional composites are presented and discussed in detail. Experimental investigations on compressive strength and kink band formation were also performed for several specimens with various dimensions and off-axis angles made of the same glass/epoxy prepreg composite material. A special compressive fixture was also fabricated in order to ensure that the specimens are in full contact with the loading machine elements and also to eliminate the potential bending moments.Comparison between the experimental and analytical results indicated that the proposed fiber kinking model and the developed code can be used to predict the compressive strength of laminated composites due to fiber kinking mode.     

单向纤维增强复合材料强度的统计分析

在本文中,我们提出了一个用于研究单向纤维增强复合材料中纤维载荷集中的剪滞分析模型。用此模型推导出了包含r根断纤维的裂纹的尖端纤维的载荷集中因子的解析表达式,并由此计算了裂纹尖端纤维的最大载荷集中因子,其计算结果与Hedgepeth[2]的结果非常一致。其次,我们提出了平均载荷集中因子的概念,并通过载荷集中因子的大小定义了裂纹尖端纤维的影响长度。它的物理意义明确,而且,在裂纹的扩展过程中是逐渐增大的,这与实际情况相符。在前面分析的基础上,应用裂纹临界核模型[2,3],我们对单向纤维增强复合材料的强度问题进行了统计分析,其计算结果与实验值是一致的,其中使用平均载荷集中因子计算所得到的强度值与实验值更接近。数值结果说明了裂纹临界核模型的正确性以及用平均载荷集中因子和影响长度进行裂纹扩展分析的可行性。     

Modeling of electromechanical behavior of woven SiC/SiC composites

A coupled electro-mechanical model was developed to predict the mechanical behavior of woven SiC/SiC ceramic matrix composites and electrical resistance response to mechanical damages in the composites. The matrix is explicitly included in the model such that the matrix cracking and fiber break can be linked to the electrical resistance change during loading. The results show that the electrical resistance increases linearly with an increase of matrix crack density and the number of fiber breaks. The predictions are compared to the experimental results on 2D woven SiC/SiC ceramic composites. With proper materials parameters input, the models can accurately predict the stress–strain curve and electrical resistance change during the loading. The model is further compared to an analytical solution of electromechanical coupling to get an insight into the electrical–mechanical interaction mechanisms in the composites.     

Investigation of mechanical behavior of transverse stitched T-joints with PR520 resin in flexure and tension

An investigation of the mechanical behavior of transverse stitched T-joints using a fiber insertion process and PR520 toughened epoxy resin was undertaken. Experimental and numerical analysis was performed under flexure loading and preliminary experiments were conducted under tensile loading. These conditions were selected as representative of the in-service loads found in the application of this type of joint in industry. Experiments were conducted to determine the modes of failure and ultimate failure strength for each load condition. Flexure specimens were instrumented with strain gages to measure far field strains. Initial and ultimate damage moment is investigated and failure mechanisms are discussed. The results indicate that the flexural specimens fail in part from unsymmetrical loading of the fiber insertions and in part from high stress concentration in the “resin-rich” fillet region. Tensile specimens have symmetric loading of both sets of fiber insertions and initially fail due to matrix cracking at the web-to-flange interface. Both flexure and tension specimens are shown to exhibit additional load-carrying capability beyond initial failure indicating a significant damage tolerance. A linear elastic finite element model was developed for flexural loading and results are compared to experimental data.     

碳/碳复合材料疲劳损伤失效试验研究

对单向碳/碳复合材料纵向拉-拉疲劳特性及面内剪切拉-拉疲劳特性进行了试验研究; 对三维四向编织碳/碳复合材料的纵向拉-拉疲劳特性及纤维束-基体界面剩余强度进行了试验研究。使用最小二乘法拟合得到了单向碳/碳复合材料纵向及面内剪切拉-拉疲劳加载下的剩余刚度退化模型及剩余强度退化模型, 建立了纤维束-基体界面剩余强度模型。结果显示: 单向碳/碳复合材料在87.5%应力水平的疲劳载荷下刚度退化最大只有8.8%左右, 在70.0%应力水平的疲劳载荷下, 面内剪切刚度退化最大可达30%左右; 三维四向编织碳/碳复合材料疲劳加载后强度及刚度均得到了提高; 随着疲劳循环加载数的增加, 三维四向编织碳/碳复合材料中纤维束-基体界面强度逐渐减弱。      

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.     

Dual scale non-linear stress analysis of a fibrous metal matrix composite

Precise estimation of local stress profiles in individual phases of a fiber reinforced metal matrix composite is a crucial concern for design of composites. Stress profiles are significantly affected by plastic relaxation of soft matrix. In this work, an analytical model was developed to compute local stress profiles in individual phases of fibrous metal matrix composites. To this end, embedded cell cylindrical composite model was applied in which a layered concentric cylinder consisting of a fiber-, matrix- and homogenized composite layers was used. Mean field micromechanics was integrated into the conventional elasticity solution process so that micro-macro dual scale analysis could be performed. The algorithm was formulated in an iterative incremental structure which was able to perform plastic analysis. This also allows temperature dependence of flow stress to be considered. Taking copper-SiC system as a reference composite, stress profiles were obtained for mechanical and thermal loading cases. For comparison, independent finite element analyses were carried out for two different unit cell models. Excellent agreement between analytical and numerical solutions was found for the mechanical loading case even for plastic range. In the case of thermal loading, however, plastic solutions revealed notable difference in quantity, especially for the axial stress component.     

PET短纤维/硅灰石晶须/硅树脂混杂材料的拉伸性能表征

研究了PET短纤维和硅灰石晶须混杂增强硅树脂复合材料的拉伸性能。结果表明,相对少量硅灰石晶须加入到PET/硅树脂体系中会降低PET纤维的增强效果,材料的拉伸强度降低,但当硅灰石晶须的加入量很多时,材料的拉伸强度反而会明显提高。笔者对硅灰石晶须的加入量对PET短纤维增强系数的影响进行了定量分析。     

Micromechanical modeling of load transfer in fibrous composites

A unified analytical treatment is presented for the study of micromechanical stress distribution in unidirectional fibrous composites loaded with various thermal and mechanical loads. Two models are considered to represent the composite. Both use a concentric cylindrical system with the difference that one requires laterally free while the other requires laterally constrained outer boundaries, broadly describing situations of plane stress and plane strain, respectively. The present work has been motivated by the recent work of McCartney (McCartney, Proc. Roy. Soc. London, Ser. A 425 (1989) 215–244) who analyzed the laterally free system, and by our previous work (Nayfeh, Fibre Sci. Technol. 10 (1977)) in which we analyzed the laterally constrained one. For axisymmetric loading, and upon adopting some appropriate restrictions on the radial behavior of some field quantities, an elasticity-based procedure reduces the two-dimensional field equations, which hold in both the fiber and matrix components, together with the appropriate interface and boundary conditions, to a quasi-one-dimensional system. The resulting system is capable of identifying the stress distribution in each component as influenced by the other component via the readily identifiable interaction (transfer) terms. The model is general and applicable to a large variety of situations. These include situations of matrix cracking, fiber break and even regions of slip at the fiber–matrix interface. As a by-product, the model was capable of obtaining the classical Lamé solutions (the iso-strain case) as a degenerate case. Confidence in the modeling was gained when it identically reproduced all of the numerical examples presented by McCartney. Numerical results that parallel some of the ones presented by McCartney are included in the form of comparisons between results obtained based upon the laterally constrained and the laterally free systems.     

Effective mechanical properties of “fuzzy fiber” composites

In this paper we investigate the mechanical behavior of carbon fiber composites, where the carbon fibers are coated with radially aligned carbon nanotubes. For this purpose we develop a general micromechanics method for fiber composites, where fibers are coated with radially aligned microfibers (“fuzzy fiber” composites). The mechanical effective properties are computed with a special extension of the composite cylinders method. The in-plane shear modulus is determined using an extended version of the Christensen’s generalized self consistent composite cylinders method. The proposed methodology provides stress and strain concentration tensors. The results of the method are compared with numerical approaches based on the asymptotic expansion homogenization method. The combination of composite cylinders method and Mori–Tanaka method allows us to compute effective properties of composites with multiple types of “fuzzy fibers”. Numerical examples of composites made of epoxy resin, carbon fibers and carbon nanotubes are presented and the impact of the carbon nanotubes length and volume fraction in the overall composite properties is studied.