Optimizing strength and toughness of nanofiber-reinforced CMCs

Nanofibers used in current ceramic matrix composites (CMCs) are usually wavy and of finite length. Here, a shear-lag model for predicting the tensile strength and work of fracture of a composite containing a “single matrix crack”, as a function of all the material parameters including constant plus Coulomb interfacial friction, is presented for a CMC containing wavy, finite-length nanofibers having a statistical distribution of strengths. Literature results are recovered for straight infinite fibers, with strength and toughness depending on a characteristic strength σ_c and a characteristic length δ_c. For nanofibers of finite length L, radius of curvature R, and with Coulomb friction coefficient μ, the strength and toughness are found to depend only on σ_c, δ_c, and two new dimensionless parameters μδ_c/R and L/δ_c. Parametric results for a typical carbon nanotube CMC show an optimal region of morphology (L and R) that maximizes composite strength and toughness, exceeding the properties of composites with straight (R=∞) and/or long (L=∞) reinforcements. Therefore, while factors such as the nanofiber strength distribution and the nanofiber–matrix interface sliding resistance may not be easily controlled, the tuning, via processing, of purely geometrical properties of the nanofibers (L and R) alone can aid in maximizing composite properties. These results have important application in hybrid CMCs such as “fuzzy fiber” CMCs, where micron-scale fibers are covered with a forest of nanofibers such that the nanofiber array can bridge longitudinal cracks and thus improve delamination resistance.     

Effects of stress ratio on fatigue life of carbon-carbon composites

Cyclic loading causes cumulative damage and therefore degrades the inelastic properties of composite materials. Present work investigates the damage development under tension-tension fatique, and the effect of stress ratio on the fatigue life of carbon-carbon (C/C) composites at room temperature at a frequency of 3 Hz. The fatigue damage has been identified through ultrasonic non-destructive technique, optical microscopy and scanning electron microscopy.From the S-N curve it has been observed that the endurance strength of C/C composite is quite high; approximately 85% of the ultimate tensile strength. The fatigue life of C/C composites has also been observed to increase with the stress ratio. Matrix cracks, filament splitting within the yarns, complete delamination and the nucleation of the interfacial flaws have been identified as the failure mechanisms during the fatigue tests. On the other hand, the failure modes during the static test were found to be complete fiber fracture accompanied by partial delamination. A statistical fatigue life distribution for carbon-carbon composites has also been presented in this paper.     

Creep-rupture lifetime simulation of unidirectional metal matrix composites with and without time-dependent fiber breakage

A numerical simulation for predicting the axial creep-rupture lifetime of continuous fiber-reinforced metal matrix composites is proposed, based on the finite element method. The simulation model is composed of line elements representing the fibers and four-node isoparametric plane elements representing the matrix. While the fibers behave as an elastic body at all times, the matrix behaves as an elasto-plastic body at the loading process and an elasto-plastic creep body at the creep process. It is further assumed in the simulation that the fibers are fractured not only in stress criterion but time-dependently with random nature. Simulation results were compared with the creep-rupture lifetime data of a boron-aluminum composite with 10% fiber volume fraction experimentally obtained. The simulated creep-rupture lifetimes agreed well with the averages of the experimental data. The proposed simulation is further carried out to predict a possibility of creep-rupture for the composite without time-dependent fiber breakage. It is finally concluded that the creep-rupture of a boron-aluminum composite is closely related with the shear stress relaxation occurring in the matrix as well as time-dependent fiber breakage.     

缝纫复合材料层合板面内拉伸强度研究

旨在研究由缝纫引起的材料弹性性质的变化并对缝纫复合材料层合板面内拉伸强度进行理论预测。认为缝纫引起的面内纤维偏转是缝纫影响复合材料面内力学性能的主要原因，引入最大纤维偏转角和变形区宽度两个结构参数，提出了描述材料非均匀性的纤维弯曲模型。采用多层次多尺度模拟的方法得到层合板非均匀的材料性质。通过二维有限元分析对单向拉伸载荷作用下的面内强度进行理论预测，得到与试验数据相吻合的结果，进而分析了缝纫密度对拉伸强度的影响。     

Uncertainties of unidirectional composite strength under tensile loading and variation of environmental condition

A probabilistic strength model is developed for unidirectional composites with fibers in hexagonal arrays. The model assumes that, a central core of broken fibers surrounded by unbroken fibers which are subjected to unidirectional tensile loading. The proposed approach consists in using a modified shear lag model to calculate the ineffective lengths and stress concentrations around fiber breaks. The main feature in the model lies in incorporating the variation of composite properties due to temperature and moisture, in order to predict degradation of fibers and matrix characteristics. The strength degradation is often seen as a result of changes in ineffective lengths at fiber breaks, leading to stress concentrations in intact neighboring fibers. As fiber breaks are intrinsically random, the variability of input data allows us to describe the probabilistic model by using the Monte-Carlo method. The sensitivities of the mechanical response are evaluated regarding the uncertainties in design variables such as Young’s modulus of fibers and matrix, fiber reference strength, shear yield stress, fiber volume fraction and shear parameter defining the shear stress in the inelastic region.     

On the axial propagation of kink bands in fiber composites : Part i experiments

In many fiber composites, longitudinal compressive failure leads to the formation of kink bands. It has been found that these kink bands, once formed, can be made to propagate (broaden) in a steady-state manner at a constant stress level called the propagation stress (σ_P) . This is a characteristic stress of the material which, for the AS4⧹PEEK composite used in the study reported here, is approximately 40% of its compressive strength. This phenomenon is investigated experimentally using a special confining set-up that allows direct observation of the propagation process. For the composite studied, the kink bands have a repeatable inclination (β) of approximately 15°, and the fibers within the bands are rotated to about 30° in the absence of a load. When loaded to σ_P, however, they are found to rotate further to 40°, that is, substantially greater than the 2β reported elsewhere. The mechanism of propagation is found to be a bend-break-rotate sequence undergone by short segments of fibers at the edge of the kink band. It is well known that polymeric matrix composites such as the one used in this study exhibit rate-dependent behavior. Experimental results are presented which show that the kink band propagation stress is also rate dependent.     

Multi-Scale Experiments and Interfacial Mechanical Modeling of Carbon Nanotube Fiber

The multi-scale deformation and interfacial mechanical behavior of carbon nanotube fibers with multi-level structures are investigated by experimental and theoretical methods. Multi-scale experiments including uniaxial tensile testing, in situ Raman spectroscopy, and scanning electron microscopy are conducted to measure the mechanical response of multi-level structures within the fiber under tension. A two-level interfacial mechanical model is then presented to analyze the interfacial bonding strength of mesoscopic bundles and microscopic nanotubes. The evolution characteristics of multi-scale deformation of the fiber are described based on experimental characterization and interfacial strength analysis. The strengthening mechanism of the fiber is further studied. Comprehensive analysis shows that the property of multi-level interfaces is a critical factor for the fiber strength and toughness. Finally, the method of improving the mechanical properties of fiber-based materials is discussed. The result can be used to guide multi-level interface engineering of carbon nanotube fibers and fiber-based composites to produce high performance materials.     

复合材料层合板面内渐进损伤分析的CDM模型简

基于连续介质损伤力学,提出了一个预测复合材料层合板面内渐进损伤分析的模型,它包括损伤表征、损伤判定和损伤演化3 部分. 模型能够区分纤维拉伸断裂、纤维压缩断裂、纤维间拉伸损伤和纤维间压缩损伤4 种损伤模式,定义了与4 个损伤模式对应的损伤状态变量,导出了材料主轴系下损伤前后材料本构之间的关系. 损伤起始采用Puck 准则判定,损伤演化由特征长度内应变能释放密度控制. 假定材料服从线性应变软化行为,建立了损伤状态变量关于断裂面上等效应变的渐进损伤演化法则. 模型涵盖了复合材料面内损伤起始、演化直至最终失效的全过程. 完成了含孔[45/0/-45/90]_2S 层合板在拉伸和压缩载荷下失效分析,结果表明该模型能合理进行层合板的强度预测和损伤失效分析.     

一种新的界面脱粘和纤维拔出模型

对纤维增强复合材料中界面的脱粘和纤维的拔出行为进行了研究,通过纤维间距d来考虑纤维之间的相互影响,改变脱粘段的剪切强度和粘结段的临界能量释放率,推导出了纤维拉拔荷载和纤维脱粘长度之间的变化关系,与StangH的模型进行了对比,当纤维间距较大时,纤维之间的相互影响相对较小,此时与StangH的单根纤维拉拔情况较为相符,但当纤维间距较小时,由于临近纤维的影响,使得在相同脱粘长度的情况下,纤维拉拔荷载和纤维拔出端位移有减小的趋势,改变复合材料板层的厚度,由于影响了基体的变形,界面的脱粘和纤维的拔出行为也受到了相应的影响。     

Nonlinear viscoelastic multi-scale repetitive unit cell model of 3D woven composites with damage evolution

Three-dimensional (3D) textile composites have great potential applications to aircrafts and high speed vehicles because of the high strength/weight ratios and the capabilities of manufacturing complex, net-shape preforms. This paper reports the nonlinear viscoelastic responses and damage mechanisms of one kind of 3D textile composites, named as 3D orthogonal woven composite (3DOWC) under quasi-static tensile loading based on a micro/meso-scale repetitive unit cells (RUCs) model. In the RUCs model, the resin is described with a nonlinear viscoelastic material and the fibers/tows with an elastic material. The damage initiation and propagation in resin are simulated by the post-damage constitutive models with maximum principal theory failure criteria. The fibers/tows impregnated with resin are defined by elastic transverse-isotropic material model with ultimate strengths failure of ‘expanded smeared crack’ both along and perpendicular to fibers/tows axis direction. The engineering parameters and ultimate strengths of homogenized fibers/tows filled with matrix in meso-RUCs model are transferred from the numerical analysis of the micro-RUCs. The results are compared with experimental and theoretical values of RUC deformation and damage initiation and propagation under monotonic axial loading. The methodology of establishing the nonlinear visco-elastic multi-scale model of 3D textile composites without introducing the real fabric architecture in finite element analyses is explained. With the multi-scale RUCs model, the mechanical behaviors of other kinds of 3D textile composites can also be predicted.     

On the effect of fiber creep-compliance in the high-temperature deformation of continuous fiber-reinforced ceramic matrix composites

Creep models for unidirectional ceramic matrix composites reinforced by long creeping fibers with weak interfaces are presented. These models extend the work of Du and McMeeking (1995) [Du, Z., McMeeking, R. 1995. Creep models for metal matrix composites with long brittle fibers. J. Mech. Phys. Solids 43, 701–726] to include the effect of fiber primary creep present in the required operational temperatures for ceramic matrix composites (CMCs). The effects of fiber breaks and the consequential stress relaxation around the breaks are incorporated in the models under the assumption of global load sharing and time-independent stochastics for fiber failure. From the set of problems analyzed, it is found that the high-temperature deformation of CMCs is sensitive to the creep-compliance of the fibers. High fiber creep-compliance drives the composite to creep faster, leading however to greater lifetimes and greater overall strains at rupture. This behavior is attributed to the fact that the greater the creep-compliance of the fibers, the higher the creep rate but the slower the matrix stress relaxation – since the matrix must deform with a rate compatible with the more creep-resistant fibers – and therefore the less the load carried by the main load-bearing phase, the fibers. As a result, fewer fibers fail and less damage is accumulated in the system. Moreover, the greater the creep-compliance of the fibers, the slower the matrix shear stress relaxation – and thus the lower the levels of applied stress for which this effect becomes important. The slower the shear stress relaxes, the slower the “slip” length increases. Due to the Weibull nature of the fibers, the fiber strengths at the smaller gauge length of the slip length are stronger; therefore fewer fibers undergo damage. Hence, high fiber creep-compliance is desirable (in the absence of any explicit creep-damage mechanism) in terms of composite lifetime but not in terms of overall strain. These results are considered of importance for composite design and optimization.     

A periodic unit-cell simulation of fiber arrangement dependence on the transverse tensile failure in unidirectional carbon fiber reinforced composites

The effect of fiber arrangement on transverse tensile failure in unidirectional carbon fiber reinforced composites with a strong fiber-matrix interface was studied using a unit-cell model that includes a continuum damage mechanics model. The simulated results indicated that tensile strength is lower when neighboring fibers are arrayed parallel to the loading direction than with other fiber arrangements. A shear band occurs between neighboring fibers, and the damage in the matrix propagates around the shear band when the interfacial normal stress (INS) is sufficiently high. Moreover, based on the observation of Hobbiebrunken et al., we reproduced the damage process in actual composites with a nonuniform fiber arrangement. The simulated results clarified that the region where neighboring fibers are arrayed parallel to the loading direction becomes the origin of the transverse failure in the composites. The cracking sites observed in the simulation are consistent with experimental results. Therefore, the matrix damage in the region where the fiber is arrayed parallel to the loading direction is a key factor in understanding transverse failure in unidirectional carbon fiber reinforced composites with a strong fiber/matrix interface.     

A new Monte Carlo model for predicting the mechanical properties of fiber yarns

Understanding the complicated failure mechanisms of hierarchical composites such as fiber yarns is essential for advanced materials design. In this study, we developed a new Monte Carlo model for predicting the mechanical properties of fiber yarns that includes statistical variation in fiber strength. Furthermore, a statistical shear load transfer law based on the shear lag analysis was derived and implemented to simulate the interactions between adjacent fibers and provide a more accurate tensile stress distribution along the overlap distance. Simulations on two types of yarns, made from different raw materials and based on distinct processing approaches, predict yarn strength values that compare favorably with experimental measurements. Furthermore, the model identified very distinct dominant failure mechanisms for the two materials, providing important insights into design features that can improve yarn strength.     

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．     

Competing mechanisms in the wear resistance behavior of biomineralized rod-like microstructures

The remarkable mechanical properties observed in biological composite materials relative to those of their individual constituents distinguish them from common engineering materials. Some naturally occurring high-performance ceramics, like the external veneer of the Chiton (Cryptochiton stelleri) tooth, have been shown to have superior hardness and impressive abrasion resistance properties. The mechanical performance of the chiton tooth has been attributed to a hierarchical arrangement of nanostructured magnetite rods surrounded with organic material. While nanoindentation tests provide useful information about the overall performance of this biological composite, understanding the key microstructural features and energy dissipation mechanisms at small scales remains a challenging task. We present a combined experimental/numerical approach to elucidate the role of material deformation in the rods, debonding at the rod interfaces and the influence of energy dissipation mechanisms on the ability of the microstructure to distribute damage under extreme loading conditions. We employ a 3D finite element-based micromechanical model to simulate the nanoindentation tests performed in geological magnetite and cross-sections of the chiton tooth. This proposed model is capable of capturing the inelastic deformation of the rods and the failure of their interfaces, while damage, fracture and fragmentation of the mineralized rods is assessed using a probabilistic function. Our results show that these natural materials achieve their abrasion resistant properties by controlling the interface strength between rods, alleviating the tensile stress on the rods near the indentation tip and therefore decreasing the probability of catastrophic failure without significantly sacrificing resistance to penetration. The understanding of these competing energy dissipating mechanisms provides a path to the prediction of new combination of materials. In turns, these results suggest certain guidelines for abrasion resistance rod-like microstructures in composites with high volume fraction of brittle minerals or ceramics with tailored performance for specific applications.     

Melt shear rheology of carbon nanofiber/polystyrene composites

The rheological behavior and morphology of carbon nanofiber/polystyrene (CNF/PS) composites in their melt phase have been characterized both through experimental measurements and modeling. Composites prepared in the two different processes of solvent casting and melt blending are contrasted; melt-blended and solvent-cast composites were each prepared with CNF loadings of 2, 5, and 10 wt%. A morphological study revealed that the melt blending process results in composites with shorter CNFs than in the solvent-cast composites, due to damage caused by the higher stresses the CNFs encounter in melt blending, and that both processes retain the diameter of the as-received CNFs. The addition of carbon nanofiber to the polystyrene through either melt blending or solvent casting increases the linear viscoelastic moduli, G′ and G″, and steady-state viscosity, η, in the melt phase monotonically with CNF concentration, more so in solvent cast composites with their longer CNFs. The melt phase of solvent-cast composites with higher CNF concentrations exhibit a plateau of the elastic modulus, G′, at low frequencies, an apparent yield stress, and large first normal stress difference, N ₁, at low strain rates, which can be attributed to contact-based network nanostructure formed by the long CNFs. A nanostructurally-based model for CNF/PS composites in their melt phase is presented which considers the composite system as rigid rods in a viscoelastic fluid matrix. Except for two coupling parameters, all material constants in the model for the composite systems are deduced from morphological and shear flow measurements of its separate nanofiber and polymer melt constituents of the composite. These two coupling parameters are polymer–fiber interaction parameter, σ, and interfiber interaction parameter, C _I. Through comparison with our experimental measurements of the composite systems, we deduce that σ is effectively 1 (corresponding to no polymer–fiber interaction) for all CNF/PS nanocomposites studied. The dependence of CNF orientation on strain rate which we observe in our experiments is captured in the model by considering the interfiber interaction parameter, C _I, as a function of strain rate. Applied to shear flows, the model predicts the melt-phase, steady-state viscosities, and normal stress differences of the CNF/PS composites as functions of shear rate, polymer matrix properties, fiber length, and mass concentration consistent with our experimental measurements.     

Macroscopic behavior and field fluctuations in viscoplastic composites: Second-order estimates versus full-field simulations

This work presents a combined numerical and theoretical study of the effective behavior and statistics of the local fields in random viscoplastic composites. The full-field numerical simulations are based on the fast Fourier transform (FFT) algorithm [Moulinec, H., Suquet, P., 1994. A fast numerical method for computing the linear and nonlinear properties of composites. C. R. Acad. Sci. Paris II 318, 1417-1423], while the theoretical estimates follow from the so-called “second-order” procedure [Ponte Castañeda, P., 2002a. Second-order homogenization estimates for nonlinear composites incorporating field fluctuations: I—Theory. J. Mech. Phys. Solids 50, 737-757]. Two-phase fiber composites with power-law phases are considered in detail, for two different heterogeneity contrasts corresponding to fiber-reinforced and fiber-weakened composites. Both the FFT simulations and the corresponding “second-order” estimates show that the strain-rate fluctuations in these systems increase significantly, becoming progressively more anisotropic, with increasing nonlinearity. In fact, the strain-rate fluctuations tend to become unbounded in the limiting case of ideally plastic composites. This phenomenon is shown to correspond to the localization of the strain field into bands running through the composite along certain preferred orientations determined by the loading conditions. The bands tend to avoid the fibers when they are stronger than the matrix, and to pass through the fibers when they are weaker than the matrix. In general, the “second-order” estimates are found to be in good agreement with the FFT simulations, even for high nonlinearities, and they improve, often in qualitative terms, on earlier nonlinear homogenization estimates. Thus, it is demonstrated that the “second-order” method can be used to extract accurate information not only for the macroscopic behavior, but also for the anisotropic distribution of the local fields in nonlinear composites.     

Macroscopic strength estimates for metal matrix composites embedding a ductile interphase

The influence of an interphase region on the macroscopic strength of unidirectional fiber-reinforced metal-matrix composites (MMCs) is investigated. The three phases of the composite are supposed to be elastic-perfectly plastic and to conform with J₂-plasticity. First, theoretical bounds to the macroscopic strength are derived, according to homogenization theory for heterogeneous periodic media: the gap between these bounds is quite narrow for certain stress conditions, volumetric proportions of the constituents, and ratios of the interphase-to-matrix strength. Then, a numerical model previously developed by Taliercio (2005) is employed to predict the macroscopic response of three-phase MMCs under any 3D stress through the analysis of a single representative unit cell. The model is applied to the numerical identification of the macroscopic strength properties of MMCs under uni-, bi- and triaxial stresses, in cases where the theoretical bounds are not sufficiently close to identify the actual macroscopic yield surface. The influence of the weakening interphase on the predicted macroscopic strength is critically discussed. A decrease in interphase strength is found to affect the transverse tensile and shear strength of the composite to a moderate extent, whereas the macroscopic longitudinal shear strength is extremely sensitive to the interphase strength.     

基于Cosserat近场动力学的纤维混凝土破坏模拟

本文基于Cosserat近场动力学发展了一种纤维混凝土的近场动力学模型,对纤维混凝土的破坏现象进行研究。该模型考察了物质点独立的转动自由度和物质点间的力偶作用,而且有表征微结构尺寸的内禀长度,相比于传统的近场动力学模型,更适合描述纤维混凝土这类胶结颗粒材料的力学行为。本文采用完全离散的方式对纤维进行建模,引入了纤维拔出实验中拔出位移和切应力的关系,并且采用组构张量描述纤维的局部分布。数值算例部分模拟了单纤维拔出实验、带预制裂纹的平板拉伸实验和三点弯曲梁实验。数值结果和已有的数值模型以及实验进行了对比,验证了所提出模型的正确性。此外,本文还调查了微结构对纤维混凝土破坏的影响,数值结果显示Cosserat剪切模量和内禀长度会影响裂纹的局部分布,但是不会改变裂纹的主方向。