Page 174 - Mechanical Behavior of Materials

Section 4.10 Summary 175

Hence, for t/r 1 = 0.1, we have γ 2 /γ 1 = 1.10, or a 10% variation, as stated earlier, and similarly a
25% variation for t/r 1 = 0.25.
The testing of thin-walled tubes in torsion is not nearly as prevalent as tension testing. But it
nevertheless provides a viable alternative for characterizing the fundamental stress–strain behavior
of materials.

4.10 SUMMARY

A variety of relatively simple mechanical tests are used to evaluate materials properties. The results
are used in engineering design and as a basis for comparing and selecting materials. These include
tests involving tension, compression, indentation, impact, bending, and torsion.
Tension tests are frequently used to evaluate stiffness, strength, ductility, and other character-
istics of materials, as summarized in Table 4.5. One property of interest is the elastic modulus E,
a measure of stiffness and a fundamental elastic constant of the material. Poisson’s ratio ν can also
be obtained if transverse strains are measured. The yield strength σ o characterizes resistance to the
beginning of plastic deformation, and the ultimate tensile strength σ u is the highest engineering
stress the material can withstand.
Ductility is the ability to resist deformation without fracture. In a tension test, this is
characterized by the percent elongation at fracture, 100ε f , and by the percent reduction in area.
Also, detailed analysis of test results can be done by using true stresses and strains, which consider
the finite changes in gage length and cross-sectional area that may occur. Additional properties can
then be obtained, notably, the strain hardening exponent n and the true fracture stress and strain, ˜σ fB
and ˜ε f .
If a material is tested under conditions where significant creep strain occurs during the tension
test, then the results are sensitive to strain rate. At a given temperature, increasing the strain rate
usually increases the strength, but decreases the ductility. Qualitatively similar effects occur for a
given strain rate if the temperature is decreased. These effects are important for most engineering
metals only at elevated temperature, but they are significant in many polymers at room temperature.
Compression tests can be used to measure similar properties as tension tests. These tests are
especially valuable for materials used primarily in compression, such as concrete and building stone,
and for other materials that behave in a brittle manner in tension, such as ceramics and glass. In these
materials, the strength and ductility are generally greater in compression than in tension, sometimes
dramatically so.
Hardness in engineering is usually measured by using one of several standard tests that measure
resistance to indentation by a ball or sharp point. The Brinell test uses a 10 mm ball, and the Vickers
2
test a pyramidal point. Both evaluate hardness as the average stress in kg/mm on the surface area
of the indentation. The values obtained are similar, but the Vickers test is useful for a wider range
of materials. Rockwell hardness is based on the depth of indentation by a ball or conical diamond
point. There are several Rockwell hardness scales to accommodate various materials.
Notch-impact tests evaluate the ability of a material to resist rapid loading where a sharp notch
is present. The impact load is applied by a swinging pendulum or a falling weight. Details of
specimen size and shape and the manner of loading differ for various standard tests, which include
the Charpy, Izod, and dynamic tear tests.