Page 278 - T. Anderson-Fracture Mechanics - Fundamentals and Applns.-CRC (2005)

1656_C006.fm Page 258 Monday, May 23, 2005 5:50 PM

258 Fracture Mechanics: Fundamentals and Applications

Let us begin the discussion of fracture in plastics by reviewing some of the basic principles of
polymeric materials.

6.1.1 STRUCTURE AND PROPERTIES OF POLYMERS
A polymer is defined as the union of two or more compounds called mers. The degree of
polymerization is a measure of the number of these units in a given molecule. Typical engineering
plastics consist of very long chains, with the degree of polymerization on the order of several
thousand.
Consider polyethylene, a polymer with a relatively simple molecular structure. The building
block in this case is ethylene (C H ), which consists of two carbon atoms joined by a double bond,
4
2
with two hydrogen atoms attached to each carbon atom. If sufficient energy is applied to this
compound, the double bond can be broken, resulting in two free radicals that can react with other
ethylene groups:

H H HH
| | | |
−
C = C energy + → C C −
| | | |
H H HH

The degree of polymerization (i.e., the length of the chain) can be controlled by the heat input,
catalyst, as well as reagents that may be added to aid the polymerization process.

6.1.1.1 Molecular Weight
The molecular weight is a measure of the length of a polymer chain. Since there is typically a
distribution of molecule sizes in a polymer sample, it is convenient to quantify an average molecular
weight, which can be defined in one of two ways. The number average molecular weight is the
total weight divided by the number of molecules:

n
NM i
i
M = i= ∑ 1 n (6.1)
∑ N
n
i=1 i

where N is the number of molecules with molecular weight M . The number average molecular
i
i
weight attaches equal importance to all molecules, while the weight average molecular weight
reflects the actual average weight of molecules by placing additional emphasis on the larger
molecules:
n
NM i 2
i
M = i= ∑ 1 (6.2)
∑ NM
n
w
i=1 i i