Constitutive modeling of fiber composites with a soft hyperelastic matrix

This paper presents an experimental and numerical study of unidirectional carbon fiber composites with a silicone matrix, loaded transversally to the fibers. The experiments show nonlinear behavior with significant strain softening under cyclic loading. The numerical study uses a plane-strain finite element continuum model of the composite material in which the fiber distribution is based on experimental observations and cohesive elements allow debonding to take place at the fiber/matrix interfaces. It is found that accurate estimates of the initial tangent stiffness measured in the experiments can be obtained without allowing for debonding, but this feature has to be included to capture the non-linear and strain-softening behavior.     

纤维增强陶瓷基复合材料的D失效判据

经典唯象强度理论适用于正交各向异性线弹性体.对于非线性纤维增强复合材料,通过加卸载试验和损伤力学的分析方法,可以得到一种虚拟的线性化应力-应变关系;依据损伤等效假设,针对线性损伤和非线性损伤,对基于应力的经典二次失效准则进行变换,建立了一种基于损伤的强度理论,即"D失效判据",这一强度理论可以作为经典判据的补充和扩展.针对平纹编织C/SiC复合材料的拉/剪组合试验,进行了实例计算,结果表明:利用D失效判据预测的失效包络线比蔡-希尔准则的预测曲线低,而且,失效曲线的形式与材料的损伤演化规律相关.     

Modeling oxidation damage of continuous fiber reinforced ceramic matrix composites

For fiber reinforced ceramic matrix composites(CMCs),oxidation of the constituents is a very important damage type for high temperature applications. During the oxidizing process,the pyrolytic carbon interphase gradually recesses from the crack site in the axial direction of the fiber into the interior of the material. Carbon fiber usually presents notch-like or local neck-shrink oxidation phenomenon,causing strength degradation. But,the reason for SiC fiber degradation is the aw growth mechanism on its surface. A micromechanical model based on the above mechanisms was established to simulate the mechanical properties of CMCs after high temperature oxidation. The statistic and shearlag theory were applied and the calculation expressions for retained tensile modulus and strength were deduced,respectively. Meanwhile,the interphase recession and fiber strength degradation were considered. And then,the model was validated by application to a C/SiC composite.     

Neutral nano-inhomogeneities in hyperelastic materials with a hyperelastic interface model

We examine the existence of neutral nano-inhomogeneities in a hyperelastic inhomogeneity-matrix system subjected to finite plane deformations when uniform (in-plane) external loading is imposed on the matrix. We incorporate nanoscale interface effects by representing the material interface as a separate hyperelastic membrane, perfectly bonded to the surrounding bulk material. We show that for any type of hyperelastic bulk material and practically any type of hyperelastic membrane representing the interface, neutral nano-inhomogeneities do exist but are necessarily circular in shape. We show further that the radius of the circular neutral nano-inhomogeneity is determined by the (uniform) external loading (which must be hydrostatic) and the respective strain energy density functions associated with the hyperelastic bulk and interface materials.     

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.     

Influence of fiber architecture on the inelastic response of metal matrix composites

This three-part paper focuses on the effect of fiber architecture (i.e. shape and distribution) on the elastic and inelastic response of unidirectionally reinforced metal matrix composites (MMCs). The first part provides an annotated survey of the literature; it is presented as an historical perspective dealing with the effects of fiber shape and distribution on the response of advanced polymeric matrix composites and MMCs. A summary of the state of teh art will assist in defining new directions in this quickly reviving area of research. The second part outlines a recently developed analytical micromechanics model that is particularly well suited for studying the influence of these effects on the response of MMCs. This micromechanics model, referred to as the generalized method of cells (GMC), can predict the overall inelastic behavior of unidirectional, multiphase composites, given the properties of the constituents. The model is also general enough to predict the response of unidirectional composites that are reinforced by either continuous or discontinuous fibers, with different inclusion shapes and spatial arrangements, in the presence of either perfect or imperfect interfaces and/or interfacial layers. Recent developments on this promising model, as well as directions for future enhancements of the model's predictive capability, are included. Finally, the third part provides qualitative results generated by using GMC for a representative titanium matrix composite system, SCS-6/TIMETAL 21S. The results presented correctly demonstrate the relative effects of fiber arrangement and shape on the longitudinal and transverse stress-strain and creep behavior of MMCs, with both strong and weak fiber/matrix interfacial bonds. Fiber arrangements included square, square-diagonal, hexagonal and rectangular periodic arrays, as well as a random array. The fiber shapes were circular, square, and cross-shaped cross-sections. The effect of fiber volume fraction on the stress-strain response is also discussed, as is the thus-far poorly documented strain rate sensitivity effect. In addition to the well-documented features of the architecture-dependent behavior of continuously reinforced two-phase MMCs, new results are presented about continuous multiphase internal architectures. Specifically, the stress-strain and creep responses of composites with different size fibers and different internal arrangements and bond strengths are investigated; the aim was to determine the feasibility of using this approach to enhance the transverse toughness and creep resistance of titanium matrix composites (TMCs).     

Damping in ceramic matrix composites with matrix cracks

The paper presents an analytical solution capable of predicting the effect of matrix cracking in ceramic matrix composites (CMC) on damping. The cracking scenarios considered in the paper include through-the-thickness cracks and cracks terminating at the layer interfaces. The increase in damping associated with matrix cracking is mostly due to the frictional energy dissipation along the damaged fiber–matrix interfaces adjacent to the bridging cracks whose plane of propagation intersects the fiber axis. Damping increases with a higher density of matrix cracks. The loss factor is affected by the angle of the lamina relative to the direction of the applied load. The loss factor is also influenced by the frequency and magnitude of local dynamic stresses. Examples of distributions of the local loss factor along the axis of a CMC beam subject to pulsating loads of various frequencies are shown in the paper.     

Effects of matrix inelasticity on the overall hysteretic behavior of TiNi-SMA fiber composites

The effects of the inelastic deformation of the matrix on the overall hysteretic behavior of a unidirectional titanium–nickel shape-memory alloy (TiNi-SMA) fiber composite and on the local pseudoelastic response of the embedded SMA fibers are studied under the isothermal loading and unloading condition. The multiaxial phase transformation of the SMA fibers is predicted using the phenomenological constitutive equations which can describe the two-step deformation due to the rhombohedral and martensitic transformations, and the inelastic behavior of the matrix material using the standard nonlinear viscoplastic model. The average behavior of the SMA composite is evaluated with the micromechanical method of cells. It is observed that the inelastic deformation of the matrix due to prior tension results in a compressive stress in the matrix after unloading of the SMA composite and this residual stress impedes the complete recovery of the pseudoelastic strain of the SMA fibers. This explains that a closed hysteresis behavior of the SMA composite is no longer observed in contrast with the case that an elastic behavior of matrix is assumed. The predicted local stress–strain behavior indicates that the cyclic response of matrix is crucial to the design of the hysteretic performance of the SMA composite under the repeated loading conditions.     

An experimental study of dynamic delamination of thick fiber reinforced polymeric matrix composites

Dynamic delamination of thick fiber reinforced polymeric matrix composite laminates is investigated using optical techniques and high-speed photography. The laminates used in this work are graphite/epoxy fiber reinforced, 65 percent fiber volume fraction, composite plates consisting of 48 plies (6 mm plate thickness). Two different laminate layups are tested: a quasi-isotropic arrangement and a unidirectional arrangement. The experimental setup consists of 152 mm×152 mm square plates impact loaded in an outof-plane configuration using a high-speed gas gun. Impact speeds range from 1 m/s to 30 m/s. Real-time imaging of the laminate out-of-pane displacement is performed using the lateral shearing interferometer of coherent gradient sensing (CGS) in conjunction with high-speed photography. Onset of dynamic delamination can be observed, and quantities such as delamination speeds (in some cases up to 1800 m/s) are measured and reported. A brief comparison is made with dynamic fracture experiments of the same material conducted in a separate study.     

Elastic properties of obliquely wound composites with a damaged matrix

Special Design and Technological Office, Institute of Mechanics, Academy of Sciences of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 25, No. 2, pp. 82–89, February, 1989.     

Nonlinear strain properties of particulate composites with a metallic matrix

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 27, No. 5, pp. 32–37, May, 1991.     

A new variational estimate for the effective response of hyperelastic composites

A variational method for predicting the effective properties of hyperelastic composites in terms of available estimates for “hyperelastic comparison composites” is proposed. In some cases this estimate can produce a lower bound on the effective energy-density function. This nonlinear-comparison variational procedure is specialized to classes of fiber and statistically isotropic composites with the aid of appropriate choices of comparison composites with neo-Hookean phases. The end results are given in terms of closed-form expressions for the effective strain energy-density functions, from which the stress-strain relations can be extracted analytically. Explicit analytical estimates for the overall responses of composites whose phases behaviors are governed by the Gent model are obtained. The results for the fiber composites are compared with corresponding finite element simulations of periodic fiber composites as well as with other available estimates. A fine agreement between the predictions obtained via the various estimates is revealed even in the limit of infinite contrast between the properties of the phases.     

Residual strength of a fiber reinforced metal matrix composite with a crack

The residual strength of a cracked unidirectional fiver reinforced metal matrix composite is studied. We propose a bridging model based on the Dugdale strip yielding zones in the matrix ahead of the crack tips that accounts for ductile deformations of the matrix and fiber debonding and pull-out in the strip yielding zone. The bridging model is used to study the fracture of an anisotropic material and its residual strength is calculated numerically. The predicted results for a SiC/titanium composite agree well with the existing experimental data. It is found that a higher fiber bridging stress and a larger fiber pull-out length significantly contribute to the composite's residual strength. The composite's strength may be more notch-insensitive than the corresponding matrix material's strength depending on several factors such as fiber-matrix interface properties and the ratio of the matrix modulus to an ‘effective modulus’ of the composite.     

短切碳纤维C/SiC陶瓷基复合材料的动态劈裂拉伸实验

为了探究C/SiC陶瓷基复合材料的动态断裂力学行为和破坏形态,利用分离式霍普金森压杆(split Hopkinson pressure bar,SHPB)装置对3种不同短切碳纤维体积分数的C/SiC陶瓷基复合材料进行了动态劈裂实验,并利用扫描电子显微镜扫描了C/SiC复合材料试件的破坏界面,分析了C/SiC陶瓷基复合材料的失效特征和增韧机理。实验结果表明：C/SiC复合材料在冲击劈裂实验过程中,同一短切碳纤维体积分数下试件的动态抗拉强度随着冲击气压的增大而增大; 短切碳纤维体积分数为16.0%时, 材料的抗拉强度最低; 冲击后,试件的整体破坏情况与冲击气压、短切碳纤维体积分数有关。

     

Stress concentrations in composites with interface sliding,matrix stiffness and uneven fiber spacing using shear lag theory

The stress concentrations near a single fiber break in a unidirectionally reinforced fiber composite are investigated using a shear lag theory within the framework of finite elements. A model for uniformly spaced, well bonded fibers embedded in a matrix that cannot carry axial loads that was formulated previously is first introduced. The solution of this problem involves Fourier transforms and requires only a two-dimensional numerical integration. The work described in the current paper characterizes the stress concentrations around a single fiber break in the presence of fiber/matrix interface sliding, axial matrix stiffness and uneven fiber spacing. Due to the introduction of these complicating factors, the model no longer lends itself to the simple Fourier transformation solution method. For the case of interface sliding a new method is developed to handle sliding in any shear lag system. For the cases of axial matrix stiffness and uneven fiber spacing a finite element code specifically written for this problem is used to determine the fiber stresses. The results are discussed in the context of global versus local load sharing, and the effects on composite failure.     

Axisymmetric response of a cracked fiber in matrix

Solved is the problem of a penny-shaped crack in a fiber surrounded by a finite radius matrix subjected to uniform axial strain. The stress intensity factor at the crack edge and the maximum stresses at the interface are examined. These quantities depend on the elastic moduli of the fiber and the matrix, the interface properties, the fiber volume fraction and the crack length. The axisymmetric results are compared with those in plane extension. They are discussed in relation to possible crack growth directions depending on assumed interface strength.     

High-temperature metal matrix composites

This paper presents an overview of studies of creep-one of the most important characteristics of high-temperature materials. A structural model of creep and methods of accelerated creep tests are considered, and the effect of structural parameters on the creep resistance is studied. The problem of fracture toughness of metal matrix composites is analyzed. The possibility of designing composites with the necessary balance of high-temperature strength, fracture toughness, and oxidation resistance (heat resistance), in particular, composites operated at temperatures of 1400–1600°C is demonstrated by the example of a molybdenum oxide composite.