On the analysis of cracking under a combined quadratic thermal flux and a quadratic mechanical loading

B. Wu, D. Peng, R. Jones

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This paper analyses the problem of a crack in an orthotropic material subjected to combined quadratic mechanical loading and a quadratic thermal flux. Attention is focused on the problem of a partially insulated crack. Applying the Fourier transform technique and the superposition principle enables closed form solutions to be obtained for the temperature field, the elastic displacements, and the stress intensity factors. Explicit closed form solutions have been presented. The results reveal that the thermal resistance through the crack region greatly influences the solution. It is found that the energy release rate (J Integral) can be either positive or negative depending on the combination of the thermal and mechanical loads. This finding, i.e., the potential for a negative J integral, is confirmed by finite element analysis. A negative energy release rate is clearly not physically valid. The practical implications of this finding are not yet clear.

Original languageEnglish
Pages (from-to)182-197
Number of pages16
JournalApplied Mathematical Modelling
Publication statusPublished - 1 Apr 2019


  • Energy release rate
  • Fourier transform
  • Fracture mechanics
  • Orthotropic material
  • Stress intensity factors
  • Thermos-mechanical loads

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