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Analysis and model of the crack bridging mechanisms in a ductile fiber reinforced ceramic matrix composite
Abstract
The force resisting the opening of a crack in a brittle matrix composite that is bridged by ductile fibers was studied (Acta Mater. 46(18) (1998) 6381; Acta Mater. 45(9) (1997) 3609). to gain a generic understanding of the crack-bridging process by ductile reinforcements. The matrix was alumina, initially containing a parallel array of fine cylindrical holes. Molten Al was cast into the holes to produce the fibers in situ. A crack was gently introduced to traverse the specimen. The matrix halves were pulled apart in a controlled manner to open the crack. The resisting force increased proportionally to the crack opening over a wide range until a force plateau was reached. Thereafter the force diminished very gradually until failure intervened. Analysis of this counter-intuitive behavior indicated that the excellent adhesion between the fiber and the matrix in combination with the large thermal expansion mismatch must have led to extensive but spotty debonding already from the start of the start of the crack opening. In spite of the well-known ductility of the fibers, the bridging showed quasi-elastic behavior over much of the crack opening. Necking appeared to be suppressed until the separation approached failure. Detailed modeling is offered to provide interpretation of this observed behavior.
... One of the reasons for the enhanced mechanical properties is the role of crack-bridging by ductile metal ligaments. 3 Aluminide intermetallics (FeAl, AlNb 3 and AlTi 3 ) are attractive for high temperature applications due to their high melting points (T m > 1000 • C) and relatively low densities. The incorporation of aluminide intermetallics as reinforcing phases in a ceramic matrix may improve the potential applications of such composites at high temperatures. ...
... 8,9 The i-3A process is based on pressure infiltration of liquid Alalloys into a porous preform, which is composed of Al 2 O 3 and a reactive oxide (such as TiO 2 , Nb 2 O 5 or Fe 2 O 3 ). In TiO 2 based CMC, a reduction reaction takes place, where Al 3 Ti is produced by the reduction of TiO 2 by Al according to: 10,11 3TiO 2 + 13Al → · · · → 3Al 3 Ti + 2α-Al 2 O 3 (1) ...
... As expected, the sample is partially composed of ␣-Al 2 O 3 . The reduction of TiO 2 intensifies, and results in a large amount of (Al-Si) 3 Ti. The presence of this specific phase was confirmed by EDS in SEM, and TEM combined with selected area diffraction (SAD). ...
The reactions that take place during the formation of ceramic matrix composites that are based on α-Al2O3–(Al–Si)3Ti interpenetrating networks were analysed. A reactive preform was pressure infiltrated with an Al–Si alloy. After pressure infiltration, the composite did not react in a full manner and further thermal annealing was required. The reduction of TiO2 by the liquid Al–Si alloy results in the formation of (Al-Si)3Ti (Al60Si12Ti28). The formation of (Al–Si)3Ti is governed by the consumption of TiO that is formed as an intermediate phase during the reduction of TiO2.
... An approach, how such long debond length might develop under the given constraint due to thermal mismatch stresses is given elsewhere. 37 The decreasing part of the curves is, however, expected to occur due to a severe necking of the ligaments down to fracture. The calculated bridging relation for the network material, however, is unexpected. ...
Incorporation of metal into brittle ceramics results in an increase in fracture toughness, which can lead to an increase in strength, reliability and thermal shock resistance of the composite compared to monolithic ceramics. The basic material specific property, which controls the enhancement of the mechanical properties, is the bridging stress relation of the metal reinforcements. This relation was calculated from measured profiles of loaded cracks (COD) for fiber reinforced model composites and interpenetrating network composites in the system Al2O3/Al. Results are compared with directly measured bridging stress relations for the model materials. The bridging relations are further used to model the R-curve behavior of the composites which are compared with experimentally measured ones. Limitations of the applied procedure are discussed as well as the influence of specimen geometry and flaw size.
... This is clearly dependent on the interfacial bond strength, which thus affects both fibre pull-out and fibre plasticity. There have been various observations, over an extended period [16,18,20,21,[24][25][26][27][28][29][30][31][32], concerning the extent and nature of fibre pull-out and plastic deformation in MFCs. In general, it is recognised [20][21][22]24] that strong interfacial bonding is likely to impose greater constraint on fibre plasticity, and hence limit the plastic work done. ...
A model is presented for prediction of the fracture energy of ceramic–matrix composites containing dispersed metallic fibres. It is assumed that the work of fracture comes entirely from pull-out and/or plastic deformation of fibres bridging the crack plane. Comparisons are presented between these predictions and experimental measurements made on a commercially-available composite material of this type, containing stainless steel (304) fibres in a matrix predominantly comprising alumina and alumino-silicate phases. Good agreement is observed, and it’s noted that there is scope for the fracture energy levels to be high (∼20 kJ m−2). Higher toughness levels are both predicted and observed for coarser fibres, up to a practical limit for the fibre diameter of the order of 0.5 mm. Other deductions are also made concerning strategies for optimisation of the toughness of this type of material.
The toughening of brittle materials with a ductile layer greatly enhances the composite fracture toughness. The behavior of a single constrained ligament is what characterize this enhancement. In this article, an approach based on geometrical correction function of necking is proposed to model the bridging ligament response and compared with experimental single Ni-ligament test using digital image correlation (DIC) technique.
A composite of metal and brittle ceramic layers have increased fracture toughness as compared to ceramic monoliths. The property controlling the toughness enhancement is the, ‘bridging-stress’, exerted by the ductile phase astride the crack in the ceramic. This bridging-stress is a function of the crack-opening displacement (COD) which is a function of the size of the crack and the position along its profile. Depending on the accuracy of estimation of the bridging-stress, the modeled R-curve and experimental one match. In this study, a weight function based approach to generate the R-curve is reported and compared with the experimental results for Al2O3/Ni multilayer laminates.
A metal/ceramic laminate has increased fracture toughness as compared to the ceramic monoliths. The toughness enhancement is controlled by the closure (‘bridging-stresses’) exerted by the metallic bridging layers (‘ligaments’) astride the crack in the ceramic layers. The crack-opening-displacement (COD) carries information on the level and location of these stresses. If the COD profile is known, the bridging-stresses and consequently, the R-curve behavior of the composite can be modeled. In this study, a weight-function-based approach is used to generate the R-curve and is compared with experimental results for Al2O3/Ni multilayer laminates.
The pull-out of a ductile fibre from a brittle matrix was analysed in Part I [1] using a shear-lag model. However, the analysis is formidable due to the consideration of Poisson's effect along the sliding length. This consideration is essential when the debonded fibre-matrix interface is subjected to Coulomb friction during fibre pull-out. To simplify the analysis, Poisson's effect is treated in an average sense in the present study, whereas it was treated pointwise in Part I. The present simplified solutions are in excellent agreement with the previous more rigorous and more complex solutions. The simplified model thus provides adequate solutions for the pull-out of a ductile fibre from a brittle matrix, and can be readily used for further applications.
The role of fiber debonding and sliding on the toughness of intemetallic composites reinforced with ductile fibers is examined. The toughness is shown to be a function of the matrix/fiber interface properties, residual stresses and the volume fraction, size and flow behavior of the fibers. Mechanical testing and in situ microstructural observations were carried out on a Ti-25at.%Ta-50at.%Al intermetallic matrix reinforced with W-3Re fibers. The fibers were coated with a thin oxide layer in order to induce debonding and prevent interdiffusion between the fiber and the matrix. The ductility, high strength and debond characteristics of coated tungsten-rhenium fibers promote a large increase in toughness. However, the mismatch in thermal expansion coefficients is the source of large residual tensile stresses in the matrix that induces spontaneous matrix cracking. Matrix cracking and composite toughness are examined as a function of the interfacial properties, residual stresses and properties of the fiber.
The aim of the work is to gain a better understanding of the microprocesses involved in the fracture of ductile phase reinforced CMCs with an interpenetrating network microstructure, especially the processes involved in deformation and fracture of the ductile phase and its subsequent influence upon overall mechanical performance of the material. A model material is produced comprising regularly oriented aluminium fibers located within an alumina matrix. Compact tension samples, each produced with fibers oriented at 30, 60 or 90 to the fracture plane, are used to produce crack growth resistance curves and are then sliced to produce samples which are used to test the stress-extension, Ï(u), behavior of the ductile fibers. Fracture surfaces are analyzed within the SEM. The Ï(u) behavior and fracture process of the fibers is modeled using both a dislocation pile-up model and FEM analysis. Comparison is made with a geometric ductile deformation model from the literature. The models are found to describe well the Ï(u) experimental data and also the crack growth resistance results. It is found that ductile phase deformation and fracture is highly sensitive to the level of mechanical constraint upon the fiber. This is influenced by factors such as the porosity in the fiber, the interface strength and fiber orientation relative to the crack plane. Fiber diameter significantly affects Ï(u) behavior also.
This study examines theoretically the strength characteristics of ductile particle reinforced brittle materials in which the strength enhancement is derived from the crack bridging process. The crack bridging is characterized by rectilinear and linear softening bridging laws that relate the crack surface traction to the crack opening displacement. The composite strength is expressed in terms of two non-dimensional parameters that combine the effects of the flaw size, elastic modulus, matrix toughness, and the bridging-law parameters. It is shown that such composites can be substantially more flaw tolerant than the monolithic matrices owing to a narrowing of the strength distribution. The role of interface debond length is also examined. It is shown that there exists optimal debond lengths of which the composite strength is maximized. In contrast, the steady state toughness increases monotonically with debond length. The implications of these results on the design of composite microstructures are briefly described.
An experimental investigation into the debonding and pull-out of nickel wires from epoxy resin and cement paste matrices has been carried out. Above a critical embedded length both the debonding and pull-out stresses attain limiting values. A theory based on the model of a yielded zone travelling up the wire behind a debonding front was shown to describe the observed dependence of the limiting debonding stress on the yield stress, diameter and surface roughness of the wire. Pull-out behaviour subsequent to debonding was explained using this model in terms of an unyielded plug at the end of the wire. Orientation of the wire to the loading direction was found to raise the limiting debonding and pull-out stresses due to enhanced friction at the wire exit point.
A brittle solid can be toughened by dispersing ductile inclusions in it. The degree of toughening depends on the properties, volume fraction and size of the ductile inclusions and on the strength of the interface between inclusion and matrix. Experiments and models are described which quantify the influence of interface strength. The experiments use a sandwich of lead bonded between two glass plates, in such a way that debonding can be controlled. Cracks are introduced into the glass, and the behaviour of the lead at and near the crack tip is examined. The way in which debond and crack-orientation influence the work of fracture is explored.
Thermal expansion data for Al2O3/Al interpenetrating network composites, obtained using a dilatometer, are analysed to determine the residual stress during, and after, thermal cycling between room temperature and 600°C. A rigorous technique, using the effective medium approximation method, is applied, utilizing unconstrained thermal strains of the individual phases which are determined experimentally. Coefficients of thermal expansion are predicted as a function of metal content and temperature. Residual stresses are calculated using two approaches: (1) a “macroscopic” approach which considers total composite strain and (2) a “micromechanical” approach which considers time dependent effects in the metal phase. Predictions agree well with experimental data and neutron diffraction measurements, and provide a mechanistic understanding of the thermo-mechanical behaviour of the material.
The toughening of brittle matrices by the dispersion of a ductile phase has provided composite materials with important property combinations. However, the characteristics of the ductile phase that generate optimum toughness have yet to be adequately established. This article presents some observations in several composite systems of toughening by a plastic stretching mechanism and describes models of the stretching process. Some of the salient aspects of toughening emerge from a comparison between theory and experiment. In particular, ductile phases having a large uniaxial work of fracture and large mean strain for hole initiation tend to most effectively augment the toughness of brittle matrices, especially in conjuction with appreciable residual compression in the matrix, induced by thermal expansion mismatch.
The incorporation of metals into brittle solids is a successful way to improve their mechanical properties. In the present study, emphasis is placed on the roughness increase of such composites, shown by their R-curve behaviour. Although the increased toughness has been experimentally verified in many eases, the theoretical prediction is still a question of concern. The material specific property which controls the toughening effect is the bridging stress relation of the metal reinforcements. In a first part of this paper, a theoretical calculation of this bridging relation from crack opening displacement measurements will be presented. In a second part, a variety of bridging relations will be used to demonstrate their effect on the R-curve behaviour of a composite. Both calculations will be verified with experimental results of an Al/Al2O3 model composite material, where the bridging relation was also measured experimentally. 1998 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved.
Brittle solids can be toughened by incorporating ductile inclusions into them. The inclusions bridge the crack and are stretched as the crack opens, absorbing energy which contributes to the toughness. To calculate the contribution to the toughness it is necessary to know the force-displacement curve for an inclusion, constrained (as it is) by the stiff, brittle matrix. Measured force-displacement curves for highly constrained metal wires are described and related to the unconstrained properties of the wire. The constraint was achieved by bonding the wire into a thick-walled glass capillary, which was then cracked in a plane normal to the axis of the wire and tested in tension. Constraint factors as high as 6 were found, but a lesser constraint gives a larger contribution to the toughness. The diameter of the wires (or of the inclusions) plays an important role. Simple, approximate, models for the failure of the wires are developed. The results allow the contribution of ductile particles to the toughness of a brittle matrix composite to be calculated.
The aim of the study is to investigate the thermal expansion behavior and internal residual strains in metal reinforced ceramic matrix composites (CMCs). A variety of Al2O3/Al CMCs with an interpenetrating network structure were produced using a pressure infiltration technique. The samples contained two variations in the average ligament diameter of the metal phase of 0.15 μm and 1 μm and metal contents ranging from 13 to 40 vol.%. Coefficients of thermal expansion (CTEs) were found to vary significantly with temperature. It is proposed that this indicates an influence of the flow characteristics of the metal. Comparisons are made with well known methods for predicting CTEs of metal/ceramic composites. Overall strain increases with temperature scaled proportionally with metal content. Comparisons were made with uninfiltrated porous ceramic preforms and a pure metal sample. Hysteresis was observed between the heating and cooling of the composite samples at constant rate.
The addition of a dispersed ductile phase to a brittle material can lead to significant increases in fracture resistance compared to the untoughened matrix material. Often the important mechanism appears to be bridging by intact ductile ligaments behind the advancing crack tip. Although a framework for predicting toughness enhancements from bridging mechanisms exists, the required detailed model of ligament deformation which would provide the load-extension relation for a typical ligament has not been available. In this paper, numerical modeling of a plastically deforming ligament constrained by surrounding elastic matrix material is performed and the relevant toughness enhancement information extracted. Comparison is made to model experiments as needed to investigate such deformation processes as well as to toughnesses measured for technologically important composites. The results suggest that debonding along the interface between the ligament and the matrix may enhance the toughening effect of a ductile phase.
Studies in Large Plastic Flowand Fracture” (Mc-Graw Hill
- P W Bridgman