抄録
The relaxation spectrum curves for apples and potatoes were determined from the relaxation test, in which the product in natural shape was loaded between parallel plates until the deflection reached some predetermined value and the force required to maintain the deflection was measured and recorded as a function of time.
For estimating the relaxation function from the recorded relaxation force, the following two methods were introduced:
1) Hertz's contact theory was extended to the viscoelastic case by generalization of Alfrey's theorem saving that in the case of the second boundary value problem for the non-homogenious strain in isotropic compressible viscoelastic media characterized by linear relations between the components of stress, strain and their derivatives with respect of time, the strain distribution was identical with that in an compressible elastic material under the same surface displacement. From these results, we derived the following equation by which to evaluate the relaxation function of the product:
φ(t)=μp(t)/p
where φ(t): the after-effect function.
p(t): the compressible force recorded as a function of time.
p(t): the calculated compressible force in a compressible elastic body of the same shape.
μ: the modulus of rigidity.
The after-effect function in compression was determined from the above-mentioned after-effect function multiplied by 2(1+ν).
where ν: Poisson's ratio.
2) The method of O'brien, M., Gentry, J. P. and Gibson, R. C. for determining the modulus of elasticity was extended to the viscoelasticity and the ellipsoid of revolutionshaped material whose center axis being parallel with the compression plates and the relaxation function was determined by the following equation:
φ(t)=p(t)/(α2D1/D2)
where α: the deflection.
D1: the diameter of the product.
D2: the length of the center axis of the product.
From the relaxation function, the relaxation spectrum was determined by the method of Alfrey's approximation and Schapery's direct method of approximation.
The Poisson's ratio in Hertz theory was measured by using the rosette type strain gage.
