Geology Reference
In-Depth Information
stretching force
F
to its end faces (Fig. 3.2(a)).The rele-
vant elastic modulus isYoung's modulus
E
, defined by
Elastic
field
Ductile field
Fracture
point
longitudinal stress F A
longitudinal strain
E
=
l l
D
Yield
point
Note that extension of such a rod will be accompanied
by a reduction in its diameter; that is, the rod will suffer
lateral as well as longitudinal strain.The ratio of the lateral
to the longitudinal strain is known as
Poisson's ratio
(
s
).
The
bulk modulus K
expresses the stress-strain ratio in
the case of a simple hydrostatic pressure
P
applied to a
cubic element (Fig. 3.2(b)), the resultant volume strain
being the change of volume
D
v
divided by the original
volume
v
Strain
Fig. 3.1
A typical stress-strain curve for a solid body.
known as the principal axes of stress, and the normal
stresses acting in these directions are known as the
princi-
pal stresses
. Each principal stress represents a balance of
equal-magnitude but oppositely-directed force compo-
nents.The stress is said to be compressive if the forces are
directed towards each other and tensile if they are
directed away from each other.
If the principal stresses are all of equal magnitude
within a body the condition of stress is said to be
hydro-
static
, since this is the state of stress throughout a fluid
body at rest. A fluid body cannot sustain shearing stresses
(since a fluid has no shear strength), hence there cannot
be shear stresses in a body under hydrostatic stress. If the
principal stresses are unequal, shearing stresses exist
along all surfaces within the stressed body, except for the
three orthogonal planes intersecting in the principal
axes.
A body subjected to stress undergoes a change of
shape and/or size known as
strain
. Up to a certain limit-
ing value of stress, known as the
yield strength
of a ma-
terial, the strain is directly proportional to the applied
stress (Hooke's Law). This elastic strain is reversible so
that removal of stress leads to a removal of strain. If the
yield strength is exceeded the strain becomes non-linear
and partly irreversible (i.e. permanent strain results), and
this is known as plastic or ductile strain. If the stress is in-
creased still further the body fails by fracture. A typical
stress-strain curve is illustrated in Fig. 3.1.
The linear relationship between stress and strain in the
elastic field is specified for any material by its various
elas-
tic moduli
, each of which expresses the ratio of a particu-
lar type of stress to the resultant strain. Consider a rod of
original length
l
and cross-sectional area
A
which is ex-
tended by an increment
D
l
through the application of a
volume stress P
volume strain
K
=
v v
D
In a similar manner the
shear modulus
(
m
) is defined as
the ratio of shearing stress (
t
) to the resultant shear strain
tan
q
(Fig. 3.2(c))
shear stress
shear strain
tan
t
=
m
q
Finally, the
axial modulus
y
defines the ratio of longi-
tudinal stress to longitudinal strain in the case when there
is no lateral strain; that is, when the material is con-
strained to deform uniaxially (Fig. 3.2(d))
longitudinal stress F A
longitudinal strain uniaxial
y
=
)
l l
(
D
3.3 Seismic waves
Seismic waves are parcels of elastic strain energy that
propagate outwards from a seismic source such as an
earthquake or an explosion. Sources suitable for seismic
surveying usually generate short-lived wave trains,
known as pulses, that typically contain a wide range of
frequencies, as explained in Section 2.3. Except in the
immediate vicinity of the source, the strains associated
with the passage of a seismic pulse are minute and may be
assumed to be elastic. On this assumption the propaga-
tion velocities of seismic pulses are determined by the
elastic moduli and densities of the materials through
