Abstract
A new experimental procedure to determine the loads carried by the fluid (air) and matrix components of a polymeric foam is presented. Testing is carried out in a sealed chamber equipped with a differential pressure transducer to measure changes in the chamber air pressure and a load cell to measure the load applied to the specimen. Multiexposure photographs are used to determine lateral specimen expansion at various degrees of compression. From these data the amount of air trapped and compressed within the foam can be determined. Theoretical analyses suggest and tests confirm that for the strain rates used here the trapped air undergoes isothermal compression. By treating compression of the air trapped in the specimen as an isothermal process, an equivalent volume-average pore pressure can be determined, and the load carried by the fluid phase calculated. The load carried by the polymer matrix component is the difference between the total response and the fluid component. The energy input into each phase during compression can then be calculated.
The effectiveness of the procedure is demonstrated by displacement-controlled compression tests of 50×100×100-mm semi-rigid, polyurethane foam specimens. Two types of foam were compressed to 75-percent strain at nominal strain rates of 1.4/s and 14/s. Calculated values show a high degree of repeatability.
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Abbreviations
- A :
-
Ram cross-sectional area
- Bi:
-
Biot number
- d :
-
pore diameter
- E aij :
-
energy input into fluid phase between statesi and
- E mij :
-
energy input into matrix phase between statesi andj
- h :
-
convection heat-transfer coefficient
- i, j :
-
two states of the system (typically a reference state and a subsequent state)
- k :
-
thermal conductivity of the medium
- L :
-
characteristic length
- m ej :
-
mass of expelled air at statej
- m si , m sj :
-
mass of air in specimen at statesi andj, respectively
- n :
-
coefficient characterizing the polytropic compression of a gas
- pi, pj :
-
air pressure at statesi andj, respectively
- p ci , p cj :
-
pressure of air in chamber at statesi andj, respectively
- p aj :
-
pore-average fluid pressure in specimen at statej
- Δpc :
-
change in chamber pressure
- ν:
-
dummy variable of integration representing volume
- \(\upsilon _i^c ,\upsilon _j^c \) :
-
chamber volume at statesi andj, respectively
- \(\upsilon _i^e \) :
-
equivalent volume of air expelled from the specimen at statej
- \(\upsilon _i^m ,\upsilon _i^m \) :
-
volume of matrix at statesi andj, respectively
- \(\upsilon _i^p ,\upsilon _i^p \) :
-
volume of pore air at statesi andj, respectively
- \(\upsilon _i^s ,\upsilon _i^s \) :
-
specimen volume at statesi andj, respectively
- z j :
-
ram displacement (positive when into chamber)
- ε:
-
average uniaxial strain in specimen
- ρ j :
-
mass density of chamber air at statej
- ε :
-
average uniaxial stress in matrix
- \(\sigma _j^t \) :
-
average effective total uniaxial stress in specimen
- τ:
-
thermal time constant
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Rehkopf, J.D., Brodland, G.W. & McNeice, G.M. Experimentally separating fluid and matrix contributions to polymeric foam behavior. Experimental Mechanics 36, 1–6 (1996). https://doi.org/10.1007/BF02328691
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DOI: https://doi.org/10.1007/BF02328691