Abstract
A technique for measuring local stresses in metallic specimens is proposed and tested. The technique depends on the experimental measurement of temperature changes in stressed members due to adiabatic elastic deformation. At a free boundary in a body under plane stress, these temperature changes are directly related to the value of the tangential principal stress. The technique is suited for measurement of stress-concentration effects, since the temperature changes can be measured with thermocouples featuring extremely small junctions.
A simple stress-concentration geometry, the finitewidth strip with a central circular hole, is chosen as a model system for this study. Heat transfer in this geometry due to the temperature gradients produced by elastic deformation is analyzed. It is shown that the ratio of the temperature change at a reference section to the change at the locale of the stress concentration can be used to determine the stress-concentration factor, allowing for heat-transfer effects. An experimental measurement system capable of obtaining reproducible results with the thermal-measurement technique is described, and experimental results are given for the model geometry which agree favorably with theoretical predictions. Application of the technique to other problems is discussed.
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Abbreviations
- C P :
-
heat capacity at constant pressure
- D :
-
hole diameter
- F :
-
loading function
- \(\dot F\) :
-
time derivative of loading function
- H :
-
relaxation function
- K :
-
stress-concentration factor
- \(\hat K\) :
-
stress-concentration factor, from temperature change ratio
- L :
-
minimum ligament distance
- N Fo :
-
kt o /W 2
- r :
-
polar coordinate
- S AB :
-
Seebeck coefficient
- T :
-
temperature
- T a :
-
ambient temperature
- t :
-
time
- t o :
-
unloading time
- W :
-
width of strip
- x :
-
length coordinate
- α:
-
linear-thermal-expansion coefficient
- θ:
-
polar coordinate
- k :
-
thermal diffusivity
- λ:
-
ratio of hole diameter to strip width=D/W
- ρ:
-
density
- σ∞ :
-
uniform uniaxial stress far from hole
- ΔΘ:
-
change in sum of principal stresses during deformation
- ΔT :
-
temperature change due to thermoelastic effect
- ΔT hole :
-
peak temperature change at root of hole during deformation
- ΔT plate :
-
peak temperature change at reference section during deformation
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Taken in part from dissertation of R. W. Dunlap, submitted in partial fulfillment of the requirements for degree of Doctor of Philosophy at the University of Michigan, Ann Arbor, Mich.
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Dunlap, R.W., Hucke, E.E. & Ragone, D.V. Local stress measurement using the thermoelastic effect. Experimental Mechanics 8, 154–163 (1968). https://doi.org/10.1007/BF02326342
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DOI: https://doi.org/10.1007/BF02326342