ABSTRACT
Fractures, cracks, or damage may originate from different aspects: debonding of atoms, nucleation, or growth and coalescence of microcracks and microcavities (Lemaitre, 2001). From an engineering materials point of view, the following damage categories can be defined:
1. Brittle or quasi-brittle failure — fracture occurs without significant irreversible strain
2. Ductile failure — failure at large plastic strain at low temperature (~1/4 of the melting temperature)
3. Creep failure — failure at large plastic strain at high temperature (>1/3 of the melting temperature)
4. Fatigue failure — failure due to repetitious loading either above or below yield stress; may be further classified into low-cycle, high-cycle, and gigacycle fatigue damage
It must be emphasized that any fracture or crack mechanism is closely related to the material’s microstructure. In polymers, these mechanisms are dominated by the long and flexible macromolecules (Schirrer, 2001). Macromolecules are long series of monomers whose backbones are composed of linked carbon atoms. The cone angle of carbon atoms is fixed at about 70º (Figure 4.1). Therefore, the relative position of the linked carbon atom chain, i.e., the macromolecular backbone, is limited to some extent. The stiffness of the monomer and the space it occupies dictate the stiffness of the macromolecule. A large condensed assembly of macromolecules is the polymer. It may exist in either amorphous or crystalline structure, depending on its temperature. At material temperatures below its glass transition temperature,
T
, the macromolecules assume a glassy or amorphous disordered structure in which the smallest elementary volume of the material is about the size of the monomer. At temperatures above
T
, the material is said to be in the “rubbery” state. Figure 4.2 shows a typical modulus vs. temperature relationship for a polymer. In the glassy state, interactions between nonlinked atoms are strong, and any applied load is distributed atom to atom. When a small elastic load is applied, all carbon-carbon bonds are stressed, and their cone angles are strained. Larger loads lead to nonrecoverable plastic deformations. In the rubbery state, molecular interaction at the atomic level does not exist. Under applied loads, the entanglements deform about each other, and the atoms are free to twist on the carbon-carbon cone. The elastic properties are due primarily to the entropy variations of the entanglement positions, which are nearly proportional to the macroscopic strain (Schirrer, 2001). True rubbery materials may exhibit linearity between applied stress and strain up to strain levels of 10.
