4. If a material does not have a distinct yield
point, a yield strength can be specified
using a graphical procedure such as the
offset method
5.
6. Brittle materials, such as gray cast iron, have
very little or no yielding and so they can
fracture suddenly.
7.
8.
9.
10. If the load is reapplied, the atoms in the material will
again be displaced until yielding occurs at or near the
stress and the stress–strain diagram continues along
the same path as before, Fig. 3–14b. It should be
noted, however, that this new stress–strain diagram,
defined by now has a higher yield point a
consequence of strain-hardening. In other words, the
material now has a greater elastic region; however, it
has less ductility, a smaller plastic region, than when
it was in its original state.
11. Strain hardening is used to establish a higher
yield point for a material. This is done by
straining the material beyond the elastic limit,
then releasing the load. The modulus of
elasticity remains the same; however, the
material’s ductility decreases
12. • Strain energy is energy stored in a material due to its
deformation. This energy per unit volume is called strain-
energy density. If it is measured up to the proportional limit, it
is referred to as the modulus of resilience, and if it is
measured up to the point of fracture, it is called the modulus
of toughness. It can be determined from the area under the
diagram.
As a material is deformed by an external loading, it
tends to store energy internally throughout its
volume. Since this energy is related to the strains in
the material, it is referred to as strain energy.
13. • For applications, it is sometimes convenient to
specify the strain energy per unit volume of
material. This is called the strain-energy
density, and it can be expressed as
• If the material behavior is linear elastic, then
Hooke’s law applies, and therefore we can
express the elastic strain-energy density in
terms of the uniaxial stress as
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33. • The nature of this failure apparently results from the fact that
there are microscopic imperfections, usually on the surface of
the member, where the localized stress becomes much
greater than the average stress acting over the cross
section.As this higher stress is cycled, it leads to the formation
of minute cracks. Occurrence of these cracks causes a further
increase of stress at their tips or boundaries, which in turn
causes a further extension of the cracks into the material as
the stress continues to be cycled. Eventually the cross-
sectional area of the member is reduced to the point where
the load can no longer be sustained, and as a result sudden
fracture occurs. The material, even though known to be
ductile, behaves as if it were brittle
