Page 136 - Mechanical Behavior of Materials

Section 4.4 Trends in Tensile Behavior 137

(b) If the test were interrupted at ε = 0.0070, the stress–strain path during unloading would
be expected to approximately follow the elastic modulus slope E, as shown in Fig. E4.1(b).
Noting from Table E4.1(b) that the stress value corresponding to this strain is σ = 267.6MPa,
the elastic strain ε e recovered, and the plastic strain ε p remaining, are estimated to be

σ 267.6MPa
ε e = = = 0.00133, ε p = ε − ε e = 0.00700 − 0.00133 = 0.00567 Ans.
E 201,200 MPa

The original gage length of 50.8 mm would be permanently stretched by a L corresponding to
the plastic strain, where ε p = L/L i , so that the new length is

L = L i + L = L i + ε p L i = 50.8mm + 0.00567(50.8mm) = 51.09 mm Ans.

4.4 TRENDS IN TENSILE BEHAVIOR

A wide variety of tensile behaviors occur for different materials. Even for a given chemical
composition of a material, the prior processing of the material may have substantial effects on the
tensile properties, as may the temperature and strain rate of the test.

4.4.1 Trends for Different Materials
Engineering metals vary widely as to their strength and ductility. This is evident from Table 4.2,
where engineering properties from tension tests are given for a number of metals. Relatively high
strength polymers in bulk form are typically only 10% as strong as engineering metals, and their
elastic moduli are typically only 3% as large. Their ductilities vary quite widely, some being quite
brittle and others quite ductile. Properties of some commercial polymers are given in Table 4.3 to
illustrate these trends.
Rubber and rubber-like polymers (elastomers) have very low elastic moduli and relatively low
strengths, and they often have extreme ductility. Ceramics and glasses represent the opposite case,
as their behavior is generally so brittle that measures of ductility have little meaning. Strengths in
tension are generally lower than for metals, but higher than for polymers. The elastic moduli of
ceramics are relatively high, often higher than for many metals. Some typical values of ultimate
tensile strength and elastic modulus have already been given in Table 3.10.
The tensile behavior of composite materials is, of course, strongly affected by the details of
the reinforcement. For example, hard particles in a ductile matrix increase stiffness and strength,
but decrease ductility, more so for larger volume percentages of reinforcement. Long fibers have
qualitatively similar effects, with the increase in strength and stiffness being especially large for
loading directions parallel to large numbers of fibers. Whiskers and short chopped fibers generally
produce effects intermediate between those of particles and long fibers. Some of these trends are
evident in Table 4.4, where data are given for various SiC reinforcements of an aluminum alloy.