Fracture of a brittle particulate composite

Previous models for crack-particle interactions in brittle composites are modified to account for penetrable obstacles, obstacle shape and secondary crack interactions. The modified model is applied to a glass-unbonded nickel sphere composite system, the experimental aspects of which were summarized in Part 1. Increases in fracture energy are explained in terms of local crack blunting. It is shown that these results fall, as expected, between those for an entirely sharp crack front and an entirely blunt one.     

Fracture of a brittle particulate composite

A study was made of the fracture process in a model brittle composite containing nickel spheres in a glass matrix. The macroscopic fracture characteristics of the system were determined by fracture surface energy, fracture strength and elastic modulus measurements. The microstructures of the composites were defined using quantitative microscopy and the fracture process was studied by the technique of ultrasonic fractography. This procedure traced changes in the crack front configuration and local crack velocity as the crack interacted with the array of nickel particles.     

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.

     

Fracture statistics of brittle materials with surface cracks

Several different statistical fracture theories are developed for materials with cracks confined to the surface. All assume that crack planes are normal to the surface, but are otherwise randomly oriented. The simplest theory assumes that only the component of stress normal to the crack plane contributes to fracture. This theory is in fair agreement with biaxial fracture data on Pyrex glass obtained by Oh. When the contribution of shear is included in the analysis, the crack shape has to be considered. Several shapes are examined and the corresponding fracture statistics are derived. Two failure criteria are employed. In one the fracture occurs when the maximum tensile stress on some part of the crack surface reaches the intrinsic strength of the material. The other is based on a critical strain energy release rate. The assumption of shear-sensitive cracks leads to improved agreement with experiment, but really good agreement appears to require the assumption that the cracks have a preferred orientation.     

An estimation of plastic zones in a plate with a central hole

A method is described for estimating the size of the plastic zone developing around a central hole in a finite width plate subjected to a monotonically increasing tensile load from a knowledge of the elastic stress field only. The plate is assumed to be subjected to plane stress conditions and to be made from an elastic, linearly strain-hardening material. Yielding is considered to occur when the Mises criterion is satisfied. Stresses within the plastically deformed area of the plate are evaluated by means of the Prandtl-Reuss incremental flow rule together with strains increments calculated from the elastic stress distributions. The predicted plastic zone sizes correlate well with those determined experimentally by other workers.