While compression testing the sample is compressed between the bearing
surfaces of the testing machine. Thereat the friction between these surfaces and
the ends of the sample influence significantly. If this friction would be equal to
zero (what is actually not true), then there would be a uniform (homogenouse)
deflected mode in the sample for any relative height of the cylindrical sample
h/R
,
where
h
— half of the height of the sample, and
R
— its radius. However, due to
the influence of friction between the ends of the sample and the bearing surfaces
of the testing machine stress state in the sample differs from the homogeneous
stress greatly and strength characteristics, determined according to the test results
of short samples, are substantially exaggerated compared with the strength of the
base material. Strength characteristics determined while testing cubic samples can
not be used for calculating the product. So it is important to determine such sizes of
the sample for compression that friction at the ends of the sample wouldn’t be more
than the strength characteristics of the material and did not affect the uniformity
of the deflected mode in the strain measurement. This article is devoted to this
task.
The character of distribution of deformation in the samples with different
relative height was investigated numerically.
The problem of squeezing cylinder between two rigid plates was solved by
the finite element method (FEM) [5, 6]. Friction at the ends of the sample was
taken: a) infinite; b) zero. The cylinders with the relative height
h/R
= 0
,
5
; 1,0;
1,5; 2,0; 3,0 were calculated. The problem was solved in the elastic formulation.
Because of the symmetry only a quarter of the cylinder, which was divided into
200 (with radius 10 and height 20) finite elements, was considered.
Figure 1 shows the variation of axial
ε
z
, radial
ε
r
, and tangential
ε
θ
deformation in the surface layer of elements depending on the height for samples
with different relative height. Deformation was calculated relative to the average
axial deformation
Δ
h/h
, wheare
Δ
h
was determined by the movement of the
bearing surfaces of the testing machine.
Figure 2 shows the dependence of the size of the zone with uniform distribution
of axial strain for samples with different relative heights.
It is seen that this dependence is nonlinear. The solid curve corresponds to the
size of the zone, where the deviation of an axial deformation from the uniform
does not exceed 1%, and the dashed curve — a deviation is not more than 5%.
The same dependences for the radial and tangential deformation have the same
character. These curves are obtained, when the coefficient of friction between the
end of the sample and a reference surface of the testing machine is infinitely
large. When the coefficient of friction is equal to zero, then the distribution of
deformation will be uniform for any dimensions of the sample. This corresponds
to the dashed-dotted line in Figure 2.
With the help of figure 2 you can determine the dimensions of the sample,
which has homogeneous (uniform) deflected mode in the area of measuring
deformation. For example, for a sample of 20 mm in diameter at the base of
ISSN 0236-3941. Вестник МГТУ им. Н.Э. Баумана. Сер. “Машиностроение” 2014. № 3 137
