Fiber-reinforced Brittle Matrix Composites Research Articles

3D-Damage Model for Fiber-Reinforced Brittle Composites with Microcracks and Imperfect Interfaces

A three-dimensional (3D) micromechanics-based evolutionary damage model is proposed to predict the effective elastic behavior of continuous fiber-reinforced brittle matrix composites with microcracks and imperfect interfaces. Eshelby’s tensor for a circular cylindrical inclusion with slightly weakened interface is adopted to model continuous fibers with imperfect interfaces. The nucleation of microcracks is simulated by employing the continuum damage model. A multilevel damage modeling process in accordance with Weibull’s probabilistic function is incorporated into the micromechanical framework to describe the sequential evolution of imperfect interfaces in the composites. Numerical examples corresponding to uniaxial loadings in the longitudinal and transverse directions are solved to illustrate the potential of the proposed damage model. Furthermore, the present prediction is compared with available experimental data in the literature to highlight the applicability of the proposed model.

Effect of Coulomb friction on the fiber/matrix debonding and matrix cracking in unidirectional fiber-reinforced brittle-matrix composites

A model for a macroscopic crack transverse to bridging fibers is developed based upon the Coulomb friction law, instead of the hypothesis of a constant frictional shear stress usually assumed in fiber/matrix debonding and matrix cracking analyses. The Lame formulation, together with the Coulomb friction law, is adopted to determine the elastic states of fiber/matrix stress transfer through a frictionally constrained interface in the debonded region, and a modified shear lag model is used to evaluate the elastic responses in the bonded region. By treating the debonding process as a particular problem of crack propagation along the interface, the fracture mechanics approach is adopted to formulate a debonding criterion allowing one to determine the debonding length. By using the energy balance approach, the critical stress for propagating a semi-infinite fiber-bridged crack in a unidirectional fiber-reinforced composite is formulated in terms of friction coefficient and debonding toughness. The critical stress for matrix cracking and the corresponding stress distributions calculated by the present Coulomb friction model is compared with those predicted by the models of constant frictional shear stress. The effect of Poisson contraction caused by the stress re distribution between the fiber and matrix on the matrix cracking mechanics is shown and discussed in the present analysis.

Irregular lattice model for quasistatic crack propagation

An irregular lattice model is proposed for simulating quasistatic fracture in softening materials. Lattice elements are defined on the edges of a Delaunay tessellation of the medium. The dual (Voronoi) tessellation is used to scale the elemental stiffness terms in a manner that renders the lattice elastically homogeneous. This property enables the accurate modeling of heterogeneity, as demonstrated through the elastic stress analyses of fiber composites. A cohesive description of fracture is used to model crack initiation and propagation. Numerical simulations, which demonstrate energy-conserving and grid-insensitive descriptions of cracking, are presented. The model provides a framework for the failure analysis of quasibrittle materials and fiber-reinforced brittle-matrix composites.

A modeling study on residual stress-induced interfacial debonding and stress–strain behavior of weakly bonded UD composites

Abstract Residual stress-induced interfacial debonding and its influence on stress–strain behavior of unidirectional fiber-reinforced brittle matrix composites with weak interface were studied using mini-composite model by means of the two-dimensional shear lag analysis combined with a Monte Carlo method. Damages (fracture of fiber, matrix and interface) were accumulated intermittently, resulting in serrated stress–strain curve. In this process, the residual stresses changed the strain, order and location of occurrence of damages, and consequently the shape of stress–strain curve and strength of composite. Under the existence of compressive and tensile axial residual stresses in fiber and matrix, respectively, the fracture of the matrix and the debonding from the fracture-ends of matrix were enhanced, while the fracture of fiber and the debonding from the fracture-ends of fiber were suppressed. The residual stress-induced premature fracture of the matrix, followed by debonding, reduced the strength of composite.

THE EFFECTS OF POISSON CONTRACTION ON MATRIX CRACKING IN BRITTLE-MATRIX COMPOSITES

The effects of Poisson contraction on matrix cracking in unidirectional fiber-reinforced brittle-matrix composites are studied in this paper. The fibers, initially held in the matrix by a compressive pressure due to the thermal expansion mismatch, are subjected to frictional slipping over the matrix as soon as a fiber-bridged crack is formed. The friction between the fibers and the matrix is assumed to follow the Coulomb friction law. A shear-lag model, which includes the Poisson contraction and the friction due to the relative fiber/matrix slipping, is adopted to calculate the stress and strain fields in the fibers and matrix. Using the energy balance approach, a relation for the critical matrix cracking stress for propagating of a semi-infinite fiber-bridged crack is derived. The results obtained show that the Poisson contraction has a strong effect on the predicted matrix cracking stress in brittle-matrix composites, especially in composites with a stiff matrix.

309 繊維強化セラミックス基複合材料における界面はく離とブリッジングによる高靭性化(OS セラミックス,CMC及びMMC)

309 繊維強化セラミックス基複合材料における界面はく離とブリッジングによる高靭性化(OS セラミックス,CMC及びMMC)

A tensile strength model for unidirectional fiber-reinforced brittle matrix composite

A model for the ultimate tensile strength of unidirectional fiber-reinforced brittle matrix composite is presented. In the model, transverse matrix crack spacing and change in debonding length between the fiber and the matrix is continuously monitored with increasing applied load. A detailed approximate stress analysis, together with a Weibull failure statistics for fiber fracture, are used to determine the probability of fiber fracture and fiber fracture location in the composite. Results of the model are consistent with experimental data. It is suggested from the results that the strength and toughness of the composite are significantly influenced by the Weibull modulus of the fiber and the fiber/matrix interfacial shear stress. A higher fiber Weibull modulus results in a lower composite strength while a higher fiber/matrix interfacial shear stress results in a composite with higher strength but lower toughness. A moderate variation in matrix strength and fiber/matrix interfacial shear strength does not significantly affect the strength of the composite.

Strain Redistribution around Holes and Notches in Fiber-Reinforced Cross-Woven Brittle Matrix Composites

Strain Redistribution around Holes and Notches in Fiber-Reinforced Cross-Woven Brittle Matrix Composites

Effects of crack—fiber interactions on crack growth rate in fiber-reinforced brittle matrix composite under cyclic loading: model experiment

The crack—fiber interaction process and measurement of the crack growth rate of a fiber-reinforced brittle matrix composite have been studied using a single SiC fiber-reinforced polymethyl methacrylate (PMMA) model composite. The change in interfacial shear sliding stress due to cyclic loading—unloading was obtained by a thin specimen push-back test. The interfacial shear sliding stress decreased slightly after cyclic loading and this behaviour originated from wear of the sliding interface. The crack growth rate of the composite, d a/d N, vs. crack length relation was strongly affected by the interaction process. Elastic constraint before interface partial symmetrical debonding and crack bowing after this debonding were the major sources of d a/d N reduction of the composite. After the matrix crack surrounded the fiber, d a/d N was slowed by the crack-shielding mechanism originating from fiber bridging. This process continued throughout the tested number of applied cycles, because the interfacial shear sliding stress transfer operated during cyclic loading. The three-dimensional crack—fiber interaction process during crack propagation and its effects on d a/d N under cyclic loading in a fiber-reinforced brittle matrix composite were discussed.

Analysis of debonding and frictional sliding in fiber-reinforced brittle matrix composites: basic problems

Using the axisymmetric cylindrical composite model, a comprehensive finite element analysis (FEA) has been carried out for a single fiber pullout problem. The FEA completely satisfies the mechanical boundary conditions and mechanical continuities over the fiber—matrix interface. Thermally induced stresses due to thermal expansion mismatch and the Coulomb frictional shear stress transfer at the debond interface are used in the FEA. The debond length is determined based on the calculated interfacial debond crack tip energy release rate. Shear and axial stress distributions along the fiber—matrix interface and the singular stress field in the crack tip are also obtained. The numerical results are used to discuss basic problems: (i) interface mechanical boundary conditions and mechanical continuity near the debond crack tip, (ii) singularity of thermal residual stress and loading stress fields, (iii) slip and stick conditions at the debond interface, and (iv) influence of frictional resistance on the debond crack energy release rate. The differences of the FEA results from the analytical ones based on Lame´solution with Coulomb frictional shear sliding resistance are discussed with a special attention to the four basic problems. Limitations of the conventional analytical solutions are also pointed out based on the present FEA results.

Crack-face fiber bridging: Finite element analysis, analytical model, and experimental result

Prior to considering crack-face bridging, the stress/strain-field ahead of the crack tip in the compact tension (CT) geometry is numerically assessed by means of finite element method (FEM). The stress field along the crack line which has a decreasing profile of tensile stresses from the crack tip converts to monotonically increasing compressive stresses toward the back face of the CT specimen via a rotational center. Based on these stress-field analyses, a novel crack-face bridging model for fiber-reinforced brittle matrix composites is presented. The application of the model to the experimental result of a 2D-C/C composite enables one to estimate the crack-face fiber bridging stresses and their distribution profile.

Ultimate strength prediction of continuous fiber-reinforced brittle matrix composites

A model to predict ultimate strength of continuous fiber-reinforced brittle matirix composites has been developed. A statistical theory for the strength of the uniaxially fiber-reinforced brittle matrix composite is presented. Material of matrix is assumed to be homogeneous and isotropic, so that the strength of material is anywhere constant, whilst that of fiber is considered to show Weibull statistical distribution. The theory may be utilized to optimize the biaxial and multidirectional tensile strength properties of laminated materials. The composite strength is estimated by assuming no interacting matrix cracks. The frictional shear stress caused by bridging fibers is involved in the strength computation. The predicted strength is compared to experimental results with LAS-Glass/Nicalon fiber composite.

Crack-Bridging Force in Random Ductile Fiber Brittle Matrix Composites

The behavior of fiber-reinforced composites is governed by the crack-bridging force provided by the fibers, which can be obtained by the analysis of debonding and bending of fibers across a crack. In this paper, a micromechanical model for the analysis of crack-bridging force is developed. As fiber debonding has been extensively studied in the literature, the present work focuses on the component of crack-bridging force due to fiber bending, which is obtained by analyzing the bending of an elastoplastic beam on an elastic foundation with variable stiffness along the fiber. The possibility of matrix spalling below the fiber is also considered. Some of the assumptions made in the model are verified with more accurate analyses. Model prediction of the maximum crack-bridging force in metallic fiber-reinforced brittle matrix composites is found to be in reasonably good agreement with experimental results. A parametric study of the model reveals the existence of an optimal range of fiber yield strength that can provide the most desirable crack-bridging behavior.

Tailoring interfacial shear strength of SiC fiber-reinforced brittle matrix composites

The interfacial shear strength of Nicalon SiC fiber-reinforced glass-ceramic matrix composites was aimed to be tailored via two methods: (1) varying of the thickness of the carbon-rich interfacial layer between the fiber and the matrix by controlling hot pressing period and (2) formation of the secondary interfacial layer, TaC, at the carbon/matrix boundary by doping the Ta 2O 5 matrix addition. In the series of composites with varying carbon-rich layer thickness, fiber/matrix debonding mostly occurred at the carbon/matrix boundary and hence the increase in the carbon-rich layer thickness did not cause any apparent changes in the interfacial shear strength. In the TaC formed series of composites, the interfacial shear strength was affected considerably by the presence of the TaC phase at carbon/matrix boundary. The Ta 2O 5 addition to control the quantity of the TaC phase has shown to be a useful method to tailor the interfacial shear strength of SiC fiber/glass-ceramic composites.

Notch-sensitivity and shear bands in brittle matrix composites

Matrix cracking, fiber breaking and interface sliding cause nonlinear deformation in fiber-reinforced brittle matrix composites. When a notched sample is loaded in tension, the nonlinear deformation usually localizes around the notch, spreads the stress in the ligament more evenly, and thereby leads to a higher fracture load. We simulate the interplay of two deformation mechanisms: a tensile band ahead of, and shear bands perpendicular to, a notch. The shear deformation evens out the stress distribution in the tensile band, and the strength of the tensile band sets the extent of the shear deformation. Each band is simulated by a traction-deformation law. The work of fracture is computed from a small-scale inelastic problem, and the fracture loads of notched samples from a large-scale inelastic problem. Several important conclusions emerge from the simulation. First, weak shear bands can substantially increase the work of fracture. Second, the fracture loads of notched samples are well correlated with the unnotched strength, work of fracture and notch size, by a formula independent of the shear band description. The results of the simulation are used to explain the available experimental data, and to suggest an evaluation procedure for notch-sensitivity.

On large scale sliding in fiber-reinforced composites

A critical e xamination is made of the use of the line-spring model to represent fiber bridging of matrix cracks in the analysis of failure phenomena in fiber-reinforced brittle matrix composites. Attention is focused on composite systems designed to undergo fiber debonding and sliding when matrix cracking occurs. For most composites of this class, it is found that the distance along the fiber within which sliding occurs is often too large to justify use of the line-spring representation. A model which allows for large scale sliding (the LSS model) is proposed and applied to three problems : a matrix crack emerging from a semi-infinite unbridged through-crack in a uni-directional fiber-reinforced composite, the same problem for the finite length unbridged through-crack, and matrix cracking of a cross-ply composite. Primary emphasis is placed on the stress concentration in the bridging fibers. Predictions from the LSS model are compared with those from the line-spring model. In general, the line-spring model is found to overestimate the stress concentration in critically located fibers. A discussion of the significance of the lower estimates of the stress concentration factors is given for several composite systems.

The role of the fiber/matrix interface in the first matrix cracking of fiber-reinforced brittle-matrix composites

Details of the microfracture mechanics and mechanisms of first matrix cracking are addressed for unidirectionally reinforced brittle-matrix composites. The fracture toughness of first matrix cracking is experimentally determined by the controlled surface flaw method. Toughening is achieved by the composite approach through the crack-tip stress shielding processes of the fiber/matrix interface debonding in the frontal process zone as well as the internal elastic stress partition between the fiber and the matrix due to the difference in their elastic moduli. The toughness improvement by the elastic stress partition combined with the interface debonding process is studied using a carbon-fiber/carbon-matrix composite and three different types of carbon-fiber/Si 3N 4-matrix composites.

On matrix cracking in fiber reinforced ceramics

This paper addresses critical stress at the propagation of a fiber-bridged matrix crack of arbitrary length in fiber-reinforced brittle matrix composites. The formulation of the problem follows the approach adopted earlier by Marshall, Cox and Evans, but a new shear-lag model that accounts for the matrix shear deformation above the slipping region is used here to derive the relationship between the crack opening displacement and the crack surface closure traction. The inclusion of the matrix shear deformation above the slipping region significantly affects the calculated crack tip stress intensity factor and the prediction of the critical stress at the propagation of the crack. Illustrative examples are cited using three available composite systems of SiC-borosilicate, C-borosilicate and Nicalon-lithium-aluminosilicate (LAS).

Stochastic Aspects of Matrix Cracking in Brittle Matrix Composites

A computer simulation of multiple cracking in fiber-reinforced brittle matrix composites has been conducted, with emphasis on the role of the matrix flaw distribution. The simulations incorporate the effect of bridging fibers on the stress required for cracking. Both short and long (steady-state) flaws are considered. Furthermore, the effects of crack interactions (through the overlap of interface slip lengths) are incorporated. The influence of the crack distribution on the tensile response of such composites is also examined.

Transverse fracture in laminated fiber-reinforced brittle matrix composites

Cracking during uniaxial tensile loading of laminated fiber-reinforced composites usually begins in the 90° layer (with fibers normal to the axis of loading). When such transverse cracks in the 90° ply reach the 0° ply, they are arrested by the fibers in the 0° ply so that the transverse crack growth is restricted in the 90° ply. Such crack growth eventually leads to extensive cracking of the 90° ply. The critical applied stress for the propagation of these transverse cracks in the 90° layers, which is referred to as the cracking stress, is obtained based on a distributed spring model which simulates the constraining effect provided by the intact 0° layers to transverse cracks in the 90° layers. First, the spring stress—stretch relation is derived analytically based on a modified shear-lag model and its accuracy is verified using a boundary element method calculation. The spring stress—stretch relation takes into account the interface behavior that frictional slip can occur at the ply interfaces. The cracking stress, which is dependent on the crack length in the 90° ply, is evaluated based on the bridging spring stress—stretch relation. For cracks with lengths much larger than the ply thickness, the steady-state cracking stress is obtained in closed form. For shorter cracks, the cracking stress is obtained by solving an integral equation. Finally, the theoretical results for long cracks are compared with experimental data for a laminated SiC fiber, calcium—alumino-silicate (CAS) glass matrix composite.