Page 339 - Biomedical Engineering and Design Handbook Volume 1, Fundamentals

316 BIOMATERIALS

room temperature. These polymers have a high modulus and high ultimate tensile strength, but low
ductility and toughness. Ductile polymers are semicrystalline polymers such as polyethylene and
PTFE that have a T below room temperature for the amorphous polymer content. The crystals lend
g
strength, but the rubbery amorphous regions offer toughness. These polymers have lower strength
and modulus, but greater toughness than brittle polymers. Elastomers have low moduli since they
have T well below room temperature, but they can return to their original shape following high
g
extensions since cross-links prevent significant polymer chain translations.
Mechanical properties of polymers, unlike other engineering materials, are highly strain rate and
temperature dependent. Modulus increases with increasing strain rate and decreasing temperature
(see Fig. 13.8 for schematic diagram). The strain rate dependence for mechanical properties shows
that polymers exhibit viscous behavior in addition to solid or elastic behavior.

Increasing
strain rate

Stress

Decreasing
temperature

Strain
FIGURE 13.8 Schematic diagram showing strain rate and temperature
dependence of polymer mechanical properties. [Reproduced from
Encyclopedia of Materials Science and Engineering. M. B. Bever (ed.).
Cambridge, MA: MIT Press, 1986, p. 2917.]

For an elastic solid, stress σ is a linear function of the applied strain ε and there is no strain rate
dependence. Elastic modulus E is the slope of the stress versus strain curve. An elastic material can
be modeled as a spring, while viscous materials can be modeled as a dashpot. For a fluid (viscous
material), stress is proportional to strain rate (dε/dt) and unrelated to strain. Viscosity η is the slope
of the stress versus strain rate curve. Figure 13.9 shows the stress/strain relationship for elastic solids
and the stress/strain-rate relationships for viscous liquids.

σ σ η
E

ε dε/dt

FIGURE 13.9 Stress/strain relationship for elastic solids and the stress/strain-rate rela-
tionships for viscous liquids.