Page 20 - Mechanical Behavior of Materials

Section 1.2 Types of Material Failure 21

Figure 1.2 Axial member (a) subject to loading and unloading, showing elastic deformation
(b) and both elastic and plastic deformation (c).

1.2.1 Elastic and Plastic Deformation
Deformations are quantified in terms of normal and shear strain in elementary mechanics of
materials. The cumulative effect of the strains in a component is a deformation, such as a bend, twist,
or stretch. Deformations are sometimes essential for function, as in a spring. Excessive deformation,
especially if permanent, is often harmful.
Deformation that appears quickly upon loading can be classed as either elastic deformation or
plastic deformation, as illustrated in Fig. 1.2. Elastic deformation is recovered immediately upon
unloading. Where this is the only deformation present, stress and strain are usually proportional.
For axial loading, the constant of proportionality is the modulus of elasticity, E, as defined in
Fig. 1.2(b). An example of failure by elastic deformation is a tall building that sways in the wind and
causes discomfort to the occupants, although there may be only remote chance of collapse. Elastic
deformations are analyzed by the methods of elementary mechanics of materials and extensions of
this general approach, as in books on theory of elasticity and structural analysis.
Plastic deformation is not recovered upon unloading and is therefore permanent. The difference
between elastic and plastic deformation is illustrated in Fig. 1.2(c). Once plastic deformation begins,
only a small increase in stress usually causes a relatively large additional deformation. This process
of relatively easy further deformation is called yielding, and the value of stress where this behavior
begins to be important for a given material is called the yield strength, σ o .
Materials capable of sustaining large amounts of plastic deformation are said to behave in a
ductile manner, and those that fracture without very much plastic deformation behave in a brittle
manner. Ductile behavior occurs for many metals, such as low-strength steels, copper, and lead,
and for some plastics, such as polyethylene. Brittle behavior occurs for glass, stone, acrylic plastic,