Fracture of brittle particles in a ductile matrix

Prerequisites for precipitate cracking in a yielding ductile matrix have been examined. A statistical model based on the fibre loading model combined with weakest link fracture theory is presented. With the model it is possible to estimate the effect of different variables on the particle fracture probability quantitatively. The predictions made are in excellent agreement with experimental results for a variety of different precipitate types. The result can be applied to calculate the probability of cleavage fracture for steels.

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Résumé On examine les conditions pour lesquelles un précipité fragile se rompt dans une matrice ductile en déformation plastique. On présente un modèle statistique basé sur les modèles de chargement d'une fibre et combiné avec la théorie de la rupture de la liaison la plus faible. Avec ce modèle, il est possible d'estimer quantitativement l'effet de diverses variables sur la probabilité de rupture d'une particule. Les prédictions qui sont avancées sont en excellent accord avec les résultats expérimentaux, pour une gamme de divers types de précipités. Les résultats peuvent être appliqués au calcul de la probabilité de rupture par clivage dans le cas des aciers.

     

Cavity growth in ductile particles bridging a brittle matrix crack

The addition of a dispersed ductile phase in a brittle ceramic can result in an increased fracture toughness, mainly due to plastic dissipation during crack bridging. The large elastic-plastic deformations of a ductile particle intercepted by a brittle matrix crack are here analysed numerically with main focus on the effect of the growth of a single void in the particle centre, as has been observed experimentally. Particle-matrix debonding is incorporated in the numerical model, represented in terms of a cohesive zone formulation, and so is the effect of initial residual stresses induced by the thermal contraction mismatch during cooling from the processing temperature. The bridging behaviour is studied for different combinations of material parameters, and the void growth behaviour is related to previous results for cavitation instabilities in elastic-plastic solids.     

Effects of residual stress on toughening of brittle polycrystals

The effects of residual stress on toughening of brittle polycrystalline materials, in the absence of microcracking, were investigated by considering the mode I stress intensity factor reduction at the tip of a stationary crack under combined applied and residual stress loading. Toughness enhancement associated with a number of model singular and non-singular residual stress fields was evaluated. The singular residual stress fields were used to model grain-sized thermal expansion anisotropy due to grain-orientation differences in a polycrystal. The numerical results indicate that residual stress can significantly toughen a stationary crack against initiation. For the same average value of residual stress, toughness enhancement due to singular residual stress fields is more substantial than that due to non-singular residual stress fields. Sample toughness enhancement results are presented for a single-phase polycrystal failing by intergranular fracture.     

Pull-out of a ductile fibre from a brittle matrix

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.     

Pull-out of a ductile fibre from a brittle matrix

Pull-out of a ductile fibre from a brittle matrix has been analysed using a shear lag model. Debonding at the fibre-matrix interface and yielding of the fibre occurred during the pull-out process. Both Poisson's contraction of the fibre and Coulomb friction of the debonded interface were considered. The debond length, which consists of an elastic zone length and a plastic zone length, was also analysed. When the fibre has a finite embedded length, it was found that necking prior to full pull-out of the fibre was required to optimize the toughening of a brittle matrix due to plastic deformation of the fibres. The essential material properties to achieve this are addressed.     

Analysis of crack extension paths and toughening in a two phase brittle particulate composite by the boundary element method

Crack extension in a two-phase composite consisting of a brittle matrix and cylindrical particles is simulated using a linear elastic boundary element program. Three crack extension paths: (i) deflection around the particle (ii) growing along the interface, and (iii) penetrating the particle are addressed. These depend on the elastic constant mismatch of the matrix and the particle. Toughening is considered through the ratio of the stress intensity factors. Cracks will readily grow along a weak matrix/particle interface, while a strong/stiff particle may force the crack to deflect around it, if the interface is strong. Inversely a crack easily penetrates a compliant particle. For the combination of a strong particle and a moderate strength interface, high toughening can be obtained when the crack tip is arrested. A strategy for the update of element configuration when the crack intersects the interface is also presented, which lays the foundation for analyzing the toughening promoted by ductile particles using the boundary element method based on elastoplastic mechanics. This revised version was published online in July 2006 with corrections to the Cover Date.     

Benefits of toughening a vinyl ester resin matrix on structural materials

A commonplace vinyl ester resin blended with a core-shell polymer additive has been used as a matrix for some typical structural commercial materials to determine the benefits of increased matrix toughness. In a simulation of polymer concrete, the tougher matrix was found to increase the toughness of the concrete by a small amount. Unexpectedly the flexural strength was increased by 30% which has been ascribed to the greater damage tolerance of the matrix. In composites with fibre glass cloth, the interlaminar toughness is also improved. An application of extreme value statistics showed that the change in resin toughness due to blending was fully transferred to the composite, and also allowed an estimation of the effect of the reinforcement on toughness.     

The cracking of composites consisting of discontinuous ductile fibres in a brittle matrix — effect of fibre orientation

The effect of the orientation of metal wires on the opening of a crack in a brittle-matrix composite has been studied. The force arising from the plastic bending of a wire which is weakly bonded to the matrix and which crosses the matrix crack at an angleθ to the crack face normal has been measured in model resin-wire composites and good agreement is found with a simple theory based on the calculation of the force needed to produce a plastic hinge in a cantilever beam. The force passes through a maximum at a small crack opening, of the order of one wire diameter, and decreases with further crack opening. The The largest force is obtained for a value ofθ of approximately 45°. For wires whose length approaches the critical length, the force and the total work of fracture arising from the bending of the wire are small compared to the values arising from the interfacial shear stress resisting pull-out; the contributions due to bending and interfacial shear stress are of comparable magnitudes for wires which are approximately one-fifth of the critical length.     

Size effect in Ni-coated TiC particles for metal matrix composites

Nickel (Ni) particles have been coated on the surface of titanium carbide (TiC) particles to enhance the dispersion of TiC particles into a molten metal and to achieve an improvement in the mechanical and thermal properties of the metal matrix. The adhesion of Ni particles on the surface of TiC particles is induced by the attractive force between the TiC with a negative charge and the Ni cation in an aqueous solution. The powders prepared with the relatively large particle sizes of 1, 4, and 40 microm show both TiC and Ni phases, whereas that prepared with a particle size of 0.02 microm shows complex phases of Ni, TiC, and TiO2 (titanium dioxide). The TiO2 phase is caused by the oxidation reaction between the TiC and oxygen. The 1 microm powder shows that the Ni is located only around the TiC without any self-aggregation and the TiC and Ni particles are isolated in the 4 and 40 microm powders, as confirmed in TEM images. The particle size is the essential factor in fabricating highly efficient Ni-coated TiC particles for metal matrix composites.     

Prediction of first matrix cracking in micro/nanohybrid brittle matrix composites

The classical Aveston–Cooper–Kelly shear-lag model for predicting the first matrix cracking strength in a brittle matrix composite is extended to the case of a hybrid brittle matrix composite containing both micro-scale and nano-scale fibers. First, closed-form solutions for the stresses in the two types of fibers and the matrix are derived. These are then used along with an energy analysis to predict the matrix cracking stress as a function of relevant material parameters. The analysis is applied to a typical Nicalon-SiC/CVI-SiC ceramic matrix composite containing additional nanofibers, for a wide range of nanofiber properties. A few volume percent of small diameter, moderate-stiffness nanofibers is predicted to provide significant strengthening and reduced crack opening while maintaining acceptable post-cracking fiber stresses. Various issues in the design of such micro/nanohybrid composites are then discussed.     

The debonding and pull-out of ductile wires from a brittle matrix

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.     

On the validity of the Weibull failure model for brittle particles

The Weibull theory of material strength and fracture assumes that the Weibull modulus m is a material parameter, which does not depend on shape and size of the loaded object. Based on large data sets from single-particle fracture experiments with brittle materials (glass, clinker cement, limestone), the authors show that the Weibull modulus of nearly spherical particles seems to decrease with increasing particle diameter. A possible explanation is that the inner structure of the particles depends on their size so that small particles are much stronger than large ones. Received: 9 December 1999     

The propagation of cracks in composites consisting of ductile wires in a brittle matrix

Two types of fracture toughness specimens, double cantilever beam and single-edge notch, were constructed from nickel wires in an epoxy resin matrix. The critical stress intensity factor to cause propagation of an unbridged matrix crack arrested at a wire was found to be greater than that for plain resin. Subsequent crack propagation could be described by taking account of the stress intensity factor due to known forces in the crack-bridging wires which subtracted from that due to the applied forces. The debonding and pull-out behaviour observed previously in single-wire specimens was confirmed in the multi-wire fracture toughness specimens.     

Fracture mechanics of brittle matrix ductile fiber composites

A model to predict the increase in critical flaw size or stable crack growth potential which can occur by the inclusion of ductile fibers in a brittle matrix is considered. The model is based upon the super-position of two known stress intensity solutions; one for the crack opening mode resulting from a remotely applied stress and the second, an opposing stress intensity that results from a crack closing force exerted by unbroken fibers spanning the crack surfaces. The extent of stable growth possible is computed at the ultimate stress of the brittle phase as functions of fiber strength and of volume fraction for various amounts of fiber rupture. A hot pressed beryllium matrix is used as an example. The crack surface displacement over which a given fiber is capable of deforming without rupture is found to be sensitive to the fiber-matrix interface strength. The factors leading to maximum crack surface displacement without rupture are a high strain hardening capability of the fiber and an interface designed to fail at fiber stresses between yield and ultimate strengths.