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Microscopic origins of stochastic crack growth

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1035)

Abstract

Physical arguments are made to obtain a mathematical model of the stochastic growth of surface fatigue cracks in a ductile metal alloy. The model is a set of coupled partial differential equations for the expected statistical density of cracks per unit area. The differential equations describe the smooth, deterministic local evolution of crack states, with the stochastic effects of abrupt local changes of material in the crack path appearing as transitions between distinct subspaces of single crack state space. Results are related to observables such as statistical distributions of crack growth rate and of time for at least one crack to reach macroscopic length.

Keywords

  • Crack Length
  • Plastic Zone
  • Stress Amplitude
  • Short Crack
  • Lifetime Distribution

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. E.W. Montroll and M.F. Shlesinger, this volume.

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© 1983 Springer-Verlag

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Pardee, W.J., Morris, W.L., Cox, B.N. (1983). Microscopic origins of stochastic crack growth. In: Hughes, B.D., Ninham, B.W. (eds) The Mathematics and Physics of Disordered Media: Percolation, Random Walk, Modeling, and Simulation. Lecture Notes in Mathematics, vol 1035. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0073271

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  • DOI: https://doi.org/10.1007/BFb0073271

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12707-9

  • Online ISBN: 978-3-540-38693-3

  • eBook Packages: Springer Book Archive