138
BULK NANOSTRUCTURED MATERIALS
Figure 6.6. A crack in a two-dimensional rectangular lattice.
next bond at the bottom of the crack and it breaks. This process of crack propagation
continues until eventually the material separates at the crack. A crack provides a
mechanism whereby a weak external force can break stronger bonds one by one.
This explains why the stresses that induce fracture are actually weaker than the
bonds that hold the atoms of the metal together. Another kind of mechanical failure,
is the brittle-to-ductile transition, where the stress-strain curve deviates from linearity, as seen in Fig. 6.3. In this region the material irreversibly elongates before
fracture. When the stress is removed after the brittle to ductile transition the material
does not return to its original length. The transition to ductility is a result of another
kind of defect in the lattice called a dislocation. Figure 6.7 illustrates an edge
dislocation in a two-dimensional lattice. There are also other kinds of dislocations
such as a screw dislocation. Dislocations are essentially regions where lattice
deviations from a regular structure extend over a large number of lattice spacings.
Unlike cracks, the atoms in the region of the dislocation are bonded to each other,
but the bonds are weaker than in the normal regions. In the ductile region one part of
the lattice is able to slide across an adjacent part of the lattice. This occurs between
sections of the lattice located at dislocations where the bonds between the atoms
8
0
0
0
0
0
0
0
0
8
0
Q
0
0
0
Q
0
0
0
0
0
0
0
Q
0
0
Figure 6.7. An edge dislocation in a two-dimensional rectangular lattice.
BULK NANOSTRUCTURED MATERIALS
Figure 6.6. A crack in a two-dimensional rectangular lattice.
next bond at the bottom of the crack and it breaks. This process of crack propagation
continues until eventually the material separates at the crack. A crack provides a
mechanism whereby a weak external force can break stronger bonds one by one.
This explains why the stresses that induce fracture are actually weaker than the
bonds that hold the atoms of the metal together. Another kind of mechanical failure,
is the brittle-to-ductile transition, where the stress-strain curve deviates from linearity, as seen in Fig. 6.3. In this region the material irreversibly elongates before
fracture. When the stress is removed after the brittle to ductile transition the material
does not return to its original length. The transition to ductility is a result of another
kind of defect in the lattice called a dislocation. Figure 6.7 illustrates an edge
dislocation in a two-dimensional lattice. There are also other kinds of dislocations
such as a screw dislocation. Dislocations are essentially regions where lattice
deviations from a regular structure extend over a large number of lattice spacings.
Unlike cracks, the atoms in the region of the dislocation are bonded to each other,
but the bonds are weaker than in the normal regions. In the ductile region one part of
the lattice is able to slide across an adjacent part of the lattice. This occurs between
sections of the lattice located at dislocations where the bonds between the atoms
8
0
0
0
0
0
0
0
0
8
0
Q
0
0
0
Q
0
0
0
0
0
0
0
Q
0
0
Figure 6.7. An edge dislocation in a two-dimensional rectangular lattice.