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Thermoelastic stress analysis under nonadiabatic conditions

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Abstract

Thermoelastic stress analysis is a full-field stress measurement technique complementary to local techniques like strain gages. Generally, the heat transfer inside the material is neglected with respect to the frequency of the cyclical loading. An adiabaticity criterion is established to assert this simplification as a function of the thermal diffusion length and the spatial stress gradients. Under nonadiabatic conditions, heat diffusion attenuates the spatial temperature gradients, which leads to an underestimation of stress concentrations. Analytical and numerical considerations allow for the quantification of the spatial resolution. Finally, several inverse techniques can restore the thermally attenuated contrasts.

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Abbreviations

a :

thermal diffusivity (m2·s−1)

c p :

specific heat at constant pressure (J·kg−1·K−1)

E :

Young's modulus (GPa)

f :

frequency (Hz)

j :

complex unityj=(−1)0,5

k :

thermal conductivity (W·m−1·K−1)

K 0 :

Bessel's function of second kind

q :

heat source (W·m−3)

t :

time (s)

T :

instantaneous temperature (K)

T 0 :

initial specimen temperature (K)

α:

coefficient of thermal expansion (K−1)

Δ:

Laplace's operator

μ:

thermal diffusion length μ=(2a/ω)0,5 (m)

ν:

Poisson's coefficient

ω:

2πf

φ:

phase shift (rd)

ρ:

density (kg·m−3)

σI :

first invariant of Cauchy's stress tensor (MPa)

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Authors and Affiliations

  1. Laboratoire d'Energétique et d'Optique, Université de Reims Champagne-Ardenne, Moulin de la Housse, B.P. 1039, F-51687, Reims Cedex 2, France

    S. Offermann (Senior Lecturer), J. L. Beaudoin (Senior Lecturer) & C. Bissieux (Senior Lecturer)

  2. Hochschule für Technik und Wirtschaft der Saarlandes, Goebenstr. 40, D-66117, Saarbrücken, Germany

    H. Frick (Professor)

Authors
  1. S. Offermann
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  2. J. L. Beaudoin
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  3. C. Bissieux
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  4. H. Frick
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Offermann, S., Beaudoin, J.L., Bissieux, C. et al. Thermoelastic stress analysis under nonadiabatic conditions. Experimental Mechanics 37, 409–413 (1997). https://doi.org/10.1007/BF02317306

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  • DOI: https://doi.org/10.1007/BF02317306

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