Brittle Matrix Composites Research Articles

The influence of crack trapping on the toughness of fiber reinforced composites

Frictional crack bridging is the main mechanism of toughening in brittle fiber\\brittle matrix composites. In addition, the fibers may have a second beneficial effect : they tend to trap cracks propagating through the solid, and may cause them to arrest. The effectiveness of crack trapping increases with the fracture toughness of the interface between fibers and matrix. In contrast, crack bridging tends to be more effective if the interface between fibers and matrix has a low fracture toughness. In this paper, we study the competing effects of crack trapping and bridging in a brittle fiber\\brittle matrix composite. A numerical method is used to predict in three dimensions the path of a crack as it bypasses rows of fibers in an ideally brittle matrix. The results are used to deduce the influence of crack trapping on the toughness of the composite. In addition, a simple model of frictional crack bridging is used to compare the relative effects of crack trapping and bridging. It is shown that, in general, the influence of bridging greatly exceeds that of trapping. However, if the fibers have a low tensile strength and there is a large resistance to sliding between fibers and matrix, crack trapping can be significant : in this case, the best composite toughness is achieved by using a tough interface between fibers and matrix.

Fracture toughness and R-Curve behavior of laminated brittle-matrix composites

The fracture toughness and resistance-curve behavior of relatively coarse-scale, niobium/niobium aluminide (Nb/Nb3Al) laminated composites have been examined and compared to other Nb/Nb3Al composites with (in situ) Nb particulate or microlaminate reinforcements. The addition of high aspectratio Nb reinforcements, in the form of 20 vol. pct of 50- to 250-µm-thick layers, was seen to improve the toughness of the Nb3Al intermetallic matrix by well over an order of magnitude, with the toughness increasing with Nb layer thickness. The orientation of the laminate had a small effect on crack-growth resistance with optimal properties being found in the crack arrester, as compared to the crack divider, orientation. The high fracture toughness of these laminates was primarily attributed to large (∼1- to 6-mm) crack-bridging zones formed by intact Nb layers in the crack wake; these zones were of sufficient size that large-scale bridging (LSB) conditions generally prevailed in the samples tested. Resistance-curve modeling using weight function methods permitted the determination of simple approximations for the bridging tractions, which were then used to make smallscale bridging (SSB) predictions for the steady-state toughness of each laminate.

Conditions for matrix crack deflection at an interface in ceramic matrix composites

This paper describes a numerical approach developed to simulate the mechanism of matrix crack deflection at the fibre/matrix interface in brittle matrix composites. For this purpose, the fracture behaviour of a unit cell (microcomposite) consisting of a single fibre surrounded by a cylindrical tube of matrix was studied with the help of a finite element model. A fracture mechanics approach was used to design a criterion for deflection at the fibre/matrix interface of an annular crack present in the matrix. The analysis of the fracture behaviour of SiC/SiC and SiC/glass ceramics microcomposites shows that the introduction of a low modulus and low toughness interfacial layer at the fibre/matrix interface (e.g. a carbon coating) greatly favours matrix crack deflection at the interphase/fibre interface.

Analysis of interfacial sliding in brittle-matrix composites during push-out and push-back tests

The aim of this work was to study the friction mechanisms in single-filament model composites (SiC/Pyrex), as the fibre slides into the matrix, and to analyse the modification of friction conditions as interface degradation proceeds. Results obtained by push-out and push-back tests on thin sheets of a single-filament model composite are presented and discussed. The push-out set-up used was classical in principle, except that the stiffness of the device can be easily changed. When this stiffness is high, the pushing force is steady (friction under steady regime) and exhibits a well pronounced seating drop, during push-back, as the fibre reaches its original position. When the stiffness becomes low, the load–displacement curve exhibits large serrations because the friction is now in the stick-slip regime. The dependence of the serration characteristics on specimen thickness is described and discussed. The bifurcation between steady sliding and stick-slip regimes is discussed with respect to the jerky nature of the slip at the microscopic scale, because slip needs to break contacts between asperities of the rough surfaces. As the number of push-out/push-back cycles increases, these serrations progressively disappear. This phenomenon can be explained by the progressive degradation of the sliding surfaces. A simple model describing the degradation kinetics was proposed.

On the matrix cracking stress and the redistribution of internal stresses in brittle-matrix composites

A concept is proposed to increase the matrix cracking stress of some brittle-matrix composites by taking advantage of the redistribution of internal stresses that occurs when a composite with phases that have dissimilar creep behavior is subjected to thermomechanical loading. The concept is elaborated through the stress analysis of a model unidirectional composite with constituents that exhibit linear viscoelastic behavior. It is shown that if a composite with a matrix that is less creep resistant than the fibers is subjected to a treatment involving both thermal and mechanical loading (e.g. creep test), stresses can be transferred from the matrix to the fibers, resulting in the stress–relaxation of the matrix. Furthermore, it is also shown that by the elastic recovery of the fibers, the matrix can be subjected to large compressive residual stresses at the end of the treatment. The conditions for the viability of this concept and the implications of fiber overloading and potential loss of composite-like behavior are discussed.

The fracture toughness of a particulate-reinforced brittle matrix

An analytical modeling approach capable of evaluation of principal micromechanical processes taking place in brittle matrix composites reinforced by ductile particles is presented. The model addresses the effects associated with discrete particle distribution and particle—matrix interface properties. As is well known, the reinforcing mechanism is based on formation of a system of restrictive forces imposed on the crack surfaces by the plastic particles behind the propagating crack front. The particles form a bridging zone and, thus, constrain the crack opening. This is the principal aspect of the toughening mechanism in these systems. The analytical approach is based on these physical features; it enforces the natural stress state surrounding the particles and the constant volume plastic flow of the particles, and does not rely on an approximation of the stress-crack opening displacement relationship of the representative cell. The analysis allows one to trace the crack propagation through this system. This detailed analysis explains certain aspects of the particulate reinforcement mechanism not discussed in the literature previously. The resistance curves are presented for several composite systems.

Characterization of matrix damage in metal matrix composites under transverse loads

A volume integral equation method is used to investigate the mechanics of damage evolution in a unidirectional SiC/Ti composite under transverse loading. It is shown that the most likely mechanism of the damage is the initiation of partial fiber debonding followed by transverse cracking (in brittle matrix composites, e.g., SiC/Ti3Al) or plastic yielding (in ductile matrix composites, e.g., SiC/Ti-15-3). The matrix damage has been observed to occur at extremely low transverse loads and a rational explanation of this phenomenon does not appear to have been given previously in the literature. Our results indicate that the initiation of matrix cracking or yielding can be explained if microcracks are present in the fiber-matrix interface zone. In absence of the microcracks the stresses in the matrix are too low to cause any damage.

Evaluation on the fracture toughness and strength of fiber reinforced brittle matrix composites

It is well known in the fracture mechanics community that the performance of brittle materials, such as different types of ceramics which have low fracture toughness, improves significantly when fibers are added into the material. This is because the presence of fibers deters the crack propagation. Fibers bridge the gap between two adjacent surfaces of the crack and reduce the crack tip opening displacement, thus make it harder to propagate. Several investigators have experimentally studied how the length, diameter and volume fraction of fibers affect the fracture toughness of fiber reinforced brittle matrix composite materials. However, to this date not much work has been done to develope a micro-mechanics based simplified mathematical model of fiber reinforced composites that can quantitatively explain the increase of the fracture toughness and strength of a composite with volume fraction, length and diameter of fibers, used for strengthening the composite, this is what is attempted in this paper.

Interfacial bond conditions and stress distribution in a two-dimensionally reinforced brittle-matrix composite

A model has been developed for the stress distribution at the fibre/matrix interface in a brittle-matrix composite with a 2D woven reinforcement, which accounts for the interfacial bond conditions and is based on a shear-lag analysis. The modified shear-lag model equations fulfil the equilibrium condition between the interfacial regions exactly, incorporate the thermal stresses explicitly, and can cope with an interface under radial tension. The uniaxial shear-lag model is consecutively applied to the longitudinal tows with their surrounding intertow matrix and to the longitudinal fibres within their intratow matrix mantle. The presence of transverse tows and fibres can be adequately represented by attributing a normal tensile strength to the interface, associated to the restraining effect of the transverse reinforcement geometry. With material data from tensile tests on an Al 2O 3(f)/SiC composite the model parameters are determined, together with the in situ composite properties which are difficult to obtain experimentally. The model is subsequently incorporated into a numerical approach to describe a pull-out experiment.

Predicting the Thermal Shock Resistance of Fiber Reinforced Brittle Matrix Composites

The development of flaw-tolerant fiber-reinforced glass, glass-ceramic and ceramic matrix composites has resulted in a new family of high-temperature capability structural materials exhibiting quasi-ductile fracture behavior. While a great deal of research efforts have been devoted to study the mechanical behavior of these materials at both room and elevated temperatures, investigation of their behavior when subjected to abrupt thermal gradients, i.e. under thermal shock conditions, has received much less consideration. This is surprising, as the high-temperature applications for which these composite materials are candidate, e.g. in gas turbine engines, will inevitably involve some kind of thermal shock loading. It is therefore important to understand the materials` response under severe thermal transients and to be able to predict their thermal shock resistance. The topic of the present article is the development of an approach for the prediction of {Delta}{Tc} from data of the composite constituents and of the thermal shock conditions. The approach developed is compared with available experimental data on silicate matrix composites.

Micromechanics and effective transverse elastic moduli of composites with randomly located aligned circular fibers

Based on the two-dimensional (plane-strain) micromechanical fiber interaction framework, effective transverse elastic moduli of two-phase brittle matrix composites containing many randomly located yet unidirectionally aligned circular fibers are investigated in this paper. The fibers are characterized as infinitely long and equal-sized inclusions. By employing the local pairwise fiber interaction formulation coupled with the ensemble-area averaged field equations, the proposed approximate analysis leads to a novel, higher-order (in fiber volume fraction), and accurate method for the prediction of effective transverse elastic moduli of two-phase fiber reinforced composites. In addition, the proposed micromechanical approach is extended to predict the effective transverse shear velocities of fiber suspensions with randomly located aligned rigid fibers. Comparisons with experimental data, Hashin's variational bounds, and improved three-point bounds are also presented to illustrate the predictive capability of the proposed method for fiber-reinforced composites.

Non-axisymmetric matrix cracking and interface debonding in unidirectional brittle matrix composites

A discrete fiber model is developed in this paper and applied to study the problem of non-axisymmetric matrix cracking and interface debonding in unidirectional brittle-matrix fiber-reinforced composite materials subjected to an axial tensile load in the fiber direction. In this model, it is assumed that the interface debond remains open. Considering the non-axisymmetry of the matrix crack and interface debond, a three-dimensional stress analysis is introduced into the above model. The variational approach based on the principle of minimum potential energy is employed to obtain the numerical results for stress and displacement fields. On the basis of Irwin—Kies compliance calibration formulation, the strain energy release rates associated with the matrix crack and the interface debond are calculated. The competition between these two modes is then assessed by comparing the corresponding toughnesses. It is shown that the magnitude of the toughness of the fiber/matrix interface plays a predominant role on the debond initiation and extension. The stabilities of the debond and the matrix crack extension are investigated.

Micromechanics versus macromechanics: a combined approach for metal matrix composite constitutive modelling

The cyclic constitutive behaviour description of long fibre metal matrix composites needs to take into account viscoplasticity of the matrix, damage of the constituents and interfaces, manufacture residual stresses and damage deactivation effects. In order to incorporate in the model the main constituent characteristics and the composite parameters (volume fractions, fibre shape and arrangements) a combined approach is proposed, i.e. that of using a micromechanics-based analysis for the thermo-elastoviscoplasticity of the composite with damaging effects when the damage is active (i.e. when the microcracks are open). The developed model is based on transformation field analysis and on the effective stress-effective strain space within the continuum damage mechanics of the constituents. The particularization to a two-phase material permits an explanation of the macroscopic constitutive operators of the composite. The obtained macroscopic model is then formulated in such a way as to describe the damage deactivation effects that take place under cyclic conditions for compressive-like loadings. The formalism is extended from that developed previously for elastic brittle ceramic matrix composites, taking into account the possible deactivation for a given (or varying) non-zero strain. The deactivation criterion ensures the continuity of the stress-strain response for any multiaxial loadings. The proposed model is then applied to a SiC/Ti metal matrix composite, with unidirectional long fibres.

On the micromechanical failure modes in a class of ideal brittle matrix composites. Part 2. Uncoated-fiber composites

On the micromechanical failure modes in a class of ideal brittle matrix composites. Part 2. Uncoated-fiber composites

On the micromechanical failure modes in a class of ideal brittle matrix composites. Part 1. Coated-fiber composites

An intensive study is carried out to investigate the veracity of an elasticity model called the axisymmetric damage model (ADM) to predict the micromechanical failure modes in a number of ideal unidirectional composites made from silicon carbide fibers and various glass matrices with uniform fiber spacing. In Part 1, the specimens contain two fiber coatings. Detailed experiments are conducted to study the fracture process by observation of surface cracking and through SEM micrographic analysis. Failure scenarios postulated through the ADM are consistent with the observed behavior using the measured constituent properties. Some of the features of the composites predicted in this work are: (1) Numerous matrix microcracks, approximately normal to and bridging the fibers, are observed. For the present materials, matrix crack initiation precedes the onset of nonlinearity of the composite stress-strain curve. A semiempirical model derived earlier and a mechanistic crack growth model are used to study this behavior. (2) Carbon mounds (or mountains), which are roughly triangular in cross-section and have a base width of approximately 5 μm, occur in the specimens. Their location displays a sensitive dependence on the properties of the glass matrix. The ADM suggests the origin of this phenomenon and the loading condition leading to it. (3) A massive degree of debonding is observed within the interfacial region. Again, the nature of this debonding is quite sensitive to the properties of the glass matrix, among other things. The model results are consistent with debonding initiated by radial tension and having continued growth under shear stress. (4) The progressive matrix cracking process is statistical in nature as the distance between successive microcracks varies considerably with position at their initiation. Calculation of the matrix stress field ahead of the interfacial debond leads to bounds, which surround the experimental observations, on the average spacing as a function of applied and residual stresses. (5) Multiple fiber breaks suggest stress transfer has taken place in some regions such that high values of the redistributed fiber axial stress have developed. It is inferred that such failures can only take place in regions where the interface is continuous, while the model results are consistent with the observed failure stress in the fibers. We conclude with an evaluation of the quality of the model and the definition of future research and data needs required to further solidify our findings. We also offer some comments on the implications with regard to our understanding of the behavior of ceramic matrix composites. The well-controlled microgeometry of these composites and the overall consistency of their behavior with analytical models suggest that they can be regarded as truly pedigreed materials.

Computational modeling of damage evolution in unidirectional fiber reinforced ceramic matrix composites

A finite element model for investigating damage evolution in brittle matrix composites was developed. This modeling is based on an axisymmetric unit cell composed of a fiber and its surrounding matrix. The unit cell was discretized into linearly elastic elements for the fiber and the matrix and cohesive elements which allow cracking in the matrix, fiber-matrix interface, and fiber. The cohesive elements failed according to critical stress and critical energy release rate criteria (in shear and/or in tension). The tension and shear aspects of failure were uncoupled. In order to obtain converged solutions for the axisymmetric composite unit cell problem, inertia and viscous damping were added to the formulation, and the resulting dynamic problem was solved implicitly using the Newmark Method. Parametric studies of the interface toughness and strength and the matrix toughness were performed. Details of the propagation of matrix cracks and the initiation of debonds were also observed.

Experimental simulation of matrix cracking and debonding in a model brittle matrix composite

A model composite material system was designed to simulate typical damage mechanisms in unidirectional fiber reinforced brittle matrix composites. Experiments were performed at low to high quasistatic, macroscopic loading rates (e˙=10^(−5)−10^(−3)s^(−1)). At all loading rates reversal of the transverse strain was observed and was correlated to matrix cracking and debonding. The optical method of coherent gradient sensing (CGS) was used to obtain qualitative information regarding the stress fields and to observe the progression of damage. It was found that the sequence of damage formation (damage path) depended on the macroscopic loading rate. At lower loading rates periodic matrix cracks developed; minimal debonding of the reinforcement-matrix interface occurred only much later in the experiment. At higher loading rates extensive debonding followed propagation of the initial matrix crack, and periodic cracking was not observed. Several features of the material response of the model material system were also observed in a previously studied unidirectional ceramic matrix composite.

Continuous vs discontinuous bridged-crack model for fiber-reinforced materials in flexure

Two different nonlinear fracture mechanics models are proposed for analysis of the constitutive flexural behavior of brittle-matrix composites with localized or distributed continuous ductile reinforcements. The models analyze the potential crises for brittle crack propagation and reinforcement yielding or debonding and can be fitted into the general framework of the bridged-crack model. A rigid-plastic bridging law is assumed. Local discontinuous phenomena, as well as a ductile to brittle transition in the constitutive relationship, when a characteristic dimension of the body decreases, are predicted. A comparison between the continuous and discontinuous formulations shows that, in the limit case of a sufficiently high number of localized reinforcements, the theoretical models converge to the same global results.

Reversal in Failure Scaling Transition of Fibrous Composites

A nonlinear fracture mechanics model is proposed for analysis of the flexural behavior of brittle-matrix composites with uniformly distributed secondary phases. In accordance with the Barenblatt-Dugdale model the bridging or cohesive zone of the material is replaced by a fictitious crack along which a closing traction distribution is applied. The dimensionless formulation brings out the parameters synthetically controlling the structural behavior and the size-scale effects. Different scaling transitions are predicted in the flexural behavior of the composite depending on different modeling of the toughening mechanisms. When a homogenized toughening mechanism for the whole composite is considered along with closing tractions as a linearly decreasing function of the crack opening displacement, a ductile to brittle transition is found as the beam depth increases. On the other hand, when the matrix toughness and the toughening mechanism of the reinforcements are separately modeled, and the closing tractions have a constant value until a critical crack opening displacement, a double brittle-ductile-brittle transition is found. Experimental tests on fiber-reinforced mortar beams in bending are successfully simulated.

Localized stress redistribution after fibre fracture in brittle matrix composites

Abstract A model is detailed that describes the redistribution of stress, after individual fibre failure, amongst the intact reinforcing fibres of a ceramic matrix composite. The load drop carried by a single fibre when it breaks is balanced by extra loads in the intact fibres which are calculated using elastic solutions and variational mechanics. The magnitude of stress redistribution is shown to follow a d − m relationship, where d is the distance from the broken fibre and m depends on the fibre volume fraction and a non-dimensional parameter that normalizes the influence of the stress and the elastic properties of the composite. The model has been applied to two composites, SiC/SiC and CAS/SiC. It is shown that the stress redistribution is localized in both composites, the stress increments in the closest intact fibres being more than one order of magnitude greater than predicted by the assumption of global stress redistribution.