抄録
In order to describe the elastic constants of the orthotropic plate having the unknown principal direction under a plane stress condition, we have to determine 4 more independent elastic constants in addition to that in the principal direction. If we try to evaluate these values by an ordinary tensile test, we have no alternative but to carry out the tensile tests in the directions other than the principal direction (the tensile tests of off-angle). However, there are always some difficulties in the off-angle tests. The present report describes a method of determining the principal direction and elastic constants of an orthotropic plate by carrying out the compressive tests on the ring specimens cut out from the plate.
When an orthotropic ring is compressed in θ direction against its principal direction, the deflection δc of the ring will be approximately described as follows:
δc=f(El, E', Et, sin2θ, cos2θ), 1/E'=1/2(1/Glt-2νlt/El)
Here, El, Et, νlt and Glt are its Young's modulus, Poisson's ratio and shear modulus in the principal direction, respectively. Since the relation of δc-θ assumes the center of symmetry at θ=0°and 90°, we can determine the principal direction by finding out the symmetric point of the δc-θ' curve obtained by the compressive tests in several θ' directions against its reference axis.
After the principal direction has been determined, compressive tests are carried out in the directions of 0°and 90°on the open ring samples made from the ring by cutting off one part. Then, the values of elastic constants are obtained from the values of δc and deflection δh of the open ring by the following procedure.
First, the constants c1, c2 and c3 are calculated by the next equations.
δ'c or h=2I/PR3δc or h
c1=1/π[δ'h(0°)-δ'h(90°)]
c2=15π/8[2δ'c(45°)-δ'c(0°)-δ'c(90°)]-10c12/62π/[δ'h(0°)+δ'h(90°)]
c3=[δ'h(0°)+δ'h(90°)]/2π-c2/4
Here, P is the load, R is the mean radius of the ring and I is the moment of inertia of area. The value of elastic constants are obtained by the following equations.
El=1/c3-c1
Et=1/c3+c1
E'=1/c3+c2
In order to separate νlt and Glt from the evaluated value of E', we have to introduce other tests. As far as we deal with usual 2-dimensional stress problem, however, we have only the values of El, Et and E' to be solved, being relieved of the trouble of separating them. The present method enables us to determine the principal direction and the values of necessary elastic constants by cutting one ring out from a small portion of a given original plate and testing it.
