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Meccanica

, Volume 28, Issue 3, pp 209–215 | Cite as

A structural model of ceramics: Multiple fracture

  • Vladimir Kobelev
  • Alexander Richter
Article
  • 24 Downloads

Abstract

The processes of deformation of ceramics containing multiple internal defects, and the dissemination of microcracks, are analyzed by considering an infinite periodic grid of underformable hexagonal grains connected with elastic bondings. The model of ceramics and the stress distribution at the vicinity of the local break, together with a discussion of the experimental data, were studied in the first part of the paper [1]. The model is based on the assumption that the strength of grains is higher than that of bondings, and the cracks in the material spread through the bondings. To calculate the stress state of the medium, a numerical method, based on Green's function and the superposition principle, is used. Defects, presented by failed bondings, are placed by polarization dipoles of forces and moments applied to the grains adjacent to the defect. The stress distributions in the perfect medium, loaded by the external loads and polarization dipoles, and in the medium, containing micro-cracking, should be the same. This condition allows us to obtain simultaneous linear equations in terms of polarization dipoles and to determine the stress state of the medium. The failure of bondings is characterized by the von Mises strength criterion. The results of numerical modeling of the origination of a microcrack from a system of defects, and its dissemination for various loading, are presented.

Key words

Ceramics Micromechanics Fracture 

Sommario

Le modalita' di deformazione di materiali ceramici in presenza di difetti interni c la propagazione di microfratture sono analizzate considerando una griglia periodica di grani esagonali rigidi collegati tra loro mediante elementi elastici. Il modello di materiale ceramico, lo stato di sforzo in vicinanza di una frattura e la discussione di dati sperimentali sono stati presentati nella prima parte dell'articolo [1]. Il modello si basa sull'potesi che la rigidezza dei grani sia decisamente superiore a quella dei legami e chc le cricche si diffondano attraverso i legami medesimi. Per calcolare lo stato di sforzo si utilizza un metodo basato sulle funzioni di Green e sul principio di sovrapposizione. I difetti, rappresentati dai legami interrotti, sono rimpiazzati da dipoli di polarizzazione applicati ai grani adiacenti al difetto. Lo stato di sforzo nel materiale perfetto in presenza di carichi esterni e di dipoli, e nel materiale con microcricche sono considerali uguali. Questa condizione consente di ottenere un sistema linearc di equazioni in funzione di dipoli di polarizzazione e di determinare lo stato di sforzo. Il criterio di Mises e' utilizzato per individuare la rottura dei legami elastici. Vengono presentati, per diverse condizioni di carico, i risultati di simulazioni numeriche relative all'insorgere e alla propagazione di microfratture a partire da un'insieme di difetti.

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Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • Vladimir Kobelev
    • 1
  • Alexander Richter
    • 1
  1. 1.Institute for Problems in MechanicsRussian Academy of ScienceMoscowRussia

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