Page 150 - Mechanical Behavior of Materials

Section 4.6 Compression Test 151

m = n = 0.1955 Ans.
b
b = 2.79634, H = 10 = 625.7 Ans.

Hence, the equation is ˜σ B = 625.7 ˜ε 0.1955 MPa.
p
The foregoing fit is based on the last nine data points in Table E4.1. The first four plastic
strain values in Table E4.1 for nonzero force are very small values judged to be meaningless,
as arising from subtracting two nearly equal quantities that include experimental error. The next
four did not appear to lie on the straight line trend in Fig. 4.21 and so were also excluded.
The true fracture stress and strain are simply the values from the last line of Table E4.1, as
this corresponds to the fracture point:
˜ σ fB = 649 MPa, ˜ ε f = 1.091 Ans.

4.6 COMPRESSION TEST

Some materials have dramatically different behavior in compression than in tension, and in some
cases these materials are used primarily to resist compressive stresses. Examples include concrete
and building stone. Data from compression tests are therefore often needed for engineering
applications. Compression tests have many similarities to tension tests in the manner of conducting
the test and in the analysis and interpretation of the results. Since tension tests have already
been considered in detail, the discussion here will focus on areas where these two types of tests
differ.

4.6.1 Test Methods for Compression
A typical arrangement for a compression test is shown in Fig. 4.22. Uniform displacement rates in
compression are applied in a manner similar to a tension test, except, of course, for the direction
of loading. The specimen is most commonly a simple cylinder having a ratio of length to diameter,
L/d, in the range 1 to 3. However, values of L/d up to 10 are sometimes used where the primary
objective is to accurately determine the elastic modulus in compression. Specimens with square or
rectangular cross sections may also be tested.
The choice of a specimen length represents a compromise. Buckling may occur if the L/d ratio
is relatively large. If this happens, the test result is meaningless as a measure of the fundamental
compressive behavior of the material. Buckling is affected by the unavoidable small imperfections
in the geometry of the test specimen and its alignment with respect to the testing machine. For
example, the ends of the specimen can be almost parallel, but never perfectly so.
Conversely, if L/d is small, the test result is affected by the details of the conditions at the end.
In particular, as the specimen is compressed, the diameter increases due to the Poisson effect, but
friction retards this motion at the ends, resulting in deformation into a barrel shape. This effect can
be minimized by proper lubrication of the ends. In materials that are capable of large amounts of
deformation in compression, the choice of too small of an L/d ratio may result in a situation where