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Stochastic analysis of the fracture of solids with microcracks

Abstract

The present study is concerned with the stochastic formulation of the failure of solids with microcracks. The analysis is directed towards the development of microcracks in a given material structure due to the application of an external constant load. The formulation is based on the theory of stochastic population processes and that of point processes. The consideration of certain aspects of the “extreme value” theory is however necessary in characterizing the evolution of the microcrack population. It is shown to be convenient to first consider a collection of microcracks in a specific material domain (microdomain) which is regarded as a “family of objects” and represented by its state so that: {z1, z2 ..., z n }=z ⊂ Z ⊂\(\mathfrak{X}\), where Z is the state space and\(\mathfrak{X}\) a general probabilistic function space. Governing equations for the development of microcracks are derived and the results of the analysis are then compared with experimental observations obtained from short-time creep tests on a class of high temperature materials.

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Axelrad, D.R., Frydrychowicz, W. Stochastic analysis of the fracture of solids with microcracks. Z. angew. Math. Phys. 46, 507–523 (1995). https://doi.org/10.1007/BF00917441

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Keywords

  • State Space
  • Function Space
  • Probabilistic Function
  • Point Process
  • Creep Test