Page 56 - Mechanical Behavior of Materials

Section 2.5 Inelastic Deformation 55

Table 2.2 Elastic Modulus and Strength of Single-Crystal
Whiskers and Strong Fibers and Wires
Elastic Modulus Tensile Strength Ratio
3
Material E,GPa (10 ksi) σ u ,GPa (ksi) E/σ u
(a) Whiskers
SiC 700 (102) 21.0 (3050) 33
Graphite 686 (99.5) 19.6 (2840) 35
Al 2 O 3 420 (60.9) 22.3 (3230) 19
α-Fe 196 (28.4) 12.6 (1830) 16
Si 163 (23.6) 7.6 (1100) 21
NaCl 42 (6.09) 1.1 (160) 38

(b) Fibers and wires
SiC 616 (89.3) 8.3 (1200) 74
Tungsten 405 (58.7) 24.0 (3500) 17
(0.26 μm diameter)
Tungsten 405 (58.7) 3.9 (570) 104
(25 μm diameter)
Al 2 O 3 379 (55.0) 2.1 (300) 180
Graphite 256 (37.1) 5.5 (800) 47
Iron 220 (31.9) 9.7 (1400) 23
Linear polyethylene 160 (23.2) 4.6 (670) 35
Drawn silica glass 73.5 (10.7) 10.0 (1450) 7.4
Source: Data in [Kelly 86].

Theoretical tensile strengths around σ b = E/10 are larger than the actual strengths of solids by
a large amount, typically by a factor of 10 to 100. This discrepancy is thought to be due mainly to the
imperfections present in most crystals, which decrease the strength. However, small whiskers can be
made that are nearly perfect single crystals. Also, thin fibers and wires may have a crystal structure
such that strong chemical bonds are aligned with the length direction. Tensile strengths in such
cases are indeed much higher than for larger and more imperfect samples of material. Strengths in
the range from E/100 to E/20, corresponding to one-tenth to one-half of the theoretical strength,
have been achieved in this way, lending credence to the estimates. Some representative data are
given in Table 2.2.

2.5 INELASTIC DEFORMATION

As discussed in the previous section, elastic deformation involves the stretching of chemical bonds.
When the stress is removed, the deformation disappears. More drastic events can occur which
have the effect of rearranging the atoms so that they have new neighbors after the deformation is
complete. This causes an inelastic deformation that does not disappear when the stress is removed.
Inelastic deformation that occurs almost instantaneously as the stress is applied is called plastic
deformation, as distinguished from creep deformation, which occurs only after passage of time
under stress.