a negative slope and the inelastic mechanisms
operating there are responsible for a degradation
of the load-carrying capacity as the sample continues to shorten and the failure process develops.
The sample is said to be in a brittle state because it is
accumulating permanent strain as the magnitude
of the compressive stress decreases. Unloading
during this brittle deformation along the dashed
path results in a larger permanent strain, eЈ p , and
reloading returns approximately to the original
curve. Tests typically end at a strain limited by the
apparatus (e.g. point D) or complete failure of the
sample.
9.2.1 Soft and stiff testing machines
Given a well-designed testing machine, the testing
procedure to determine strength is straightforward: load the sample until it starts to lose its
capacity to carry the load, and record the extreme
value of stress. However, to understand the process of failure one must understand the mechanical interplay between the sample and the testing
machine. It turns out that the machines can play
a strong, and even dominant, role in the outcome
of mechanical property tests and experiments.
Indeed, the particular action of these machines
has strongly influenced our understanding of how
rock specimens behave when they are fracturing,
so we need to understand this action and ask if
it might duplicate the behavior of the Earth
during natural deformation events. This action, as
we learn in this section, depends upon whether
the machine is soft or stiff relative to the rock
sample.
For many discussions of extension and shear
fracturing in the literature of rock mechanics the
stress–strain curve after failure initiates is not
shown because the testing machine was incapable
of tracking these quantities accurately during the
rapid failure event. Shortly after reaching the peak
stress (Fig. 9.5, point C), the data stream was terminated because the specimen disintegrated into
a pile of rock chips and dust with a loud bang. As
early as 1943 it was clear that explosive disintegration was not necessarily a natural behavior, but
rather “elastic energy is stored in the cylinder and
in the machine . . . and the release of this energy
causes the breakdown of the cylinder” (Whitney,
1943). Curiosity about the post-peak-stress part of
the stress–strain curve led researchers to try to
capture the complete stress–strain curve and to understand what influence the testing machine might
have on the specimen behavior during failure
(Hudson et al., 1972; Jaeger and Cook, 1979, p. 177).
Consider the schematic illustration of a
testing machine (Fig. 8.25) and note that it is composed of two basic components: an hydraulic actuator (including piston and cylinder, rod, and platen)
for applying a force to the specimen and a reaction
frame (tie-bars and cross-heads) for supporting this
force. When fluid pressure is increased in the
actuator the piston is driven downward applying
a compression to the specimen and shortening it.
The downward directed force is transmitted
through the specimen to the lower cross-head.
The actuator also applies an equivalent upward
directed force to the upper cross-head so the tiebars are placed in tension and elongate, while the
cross-head bends. Both the actuator and the reaction frame deform and are capable of storing
elastic energy. If the mechanical parts of the
testing machine combine to be very much stiffer
than the rock specimen, the machine would
deform very little and we could ignore its role in
the test. However, specimens are explosively disintegrated in some testing machines because
the energy stored in the machine is released into
the specimen even though no fluid is pumped
into the actuator to do additional work. In other
words, the system composed of the machine and
the specimen self-destructs.
To understand this process the initial deformation of the specimen is idealized (Fig. 9.6a)
with a spring of constant stiffness, C s . The
machine frame is idealized with two springs of
stiffness C m /2 in parallel and tied together with an
upper and lower rigid bar. All of these springs are
tied to a rigid basal support which is taken as the
reference frame for measuring displacements.
The vertical y-axis is positive downward so forces
and displacement acting downward are positive.
Two applied forces idealize the actuator: F s acting
downward on the specimen spring and F m acting
upward on the rigid bar joining the two machine
springs (Fig. 9.6b). These forces are identical in
magnitude and opposite in direction, so F s ϭϪF m .
Under the applied force, F s , the specimen spring
contracts and its upper end moves toward the
9.2 STRENGTH OF LABORATORY SAMPLES
339
operating there are responsible for a degradation
of the load-carrying capacity as the sample continues to shorten and the failure process develops.
The sample is said to be in a brittle state because it is
accumulating permanent strain as the magnitude
of the compressive stress decreases. Unloading
during this brittle deformation along the dashed
path results in a larger permanent strain, eЈ p , and
reloading returns approximately to the original
curve. Tests typically end at a strain limited by the
apparatus (e.g. point D) or complete failure of the
sample.
9.2.1 Soft and stiff testing machines
Given a well-designed testing machine, the testing
procedure to determine strength is straightforward: load the sample until it starts to lose its
capacity to carry the load, and record the extreme
value of stress. However, to understand the process of failure one must understand the mechanical interplay between the sample and the testing
machine. It turns out that the machines can play
a strong, and even dominant, role in the outcome
of mechanical property tests and experiments.
Indeed, the particular action of these machines
has strongly influenced our understanding of how
rock specimens behave when they are fracturing,
so we need to understand this action and ask if
it might duplicate the behavior of the Earth
during natural deformation events. This action, as
we learn in this section, depends upon whether
the machine is soft or stiff relative to the rock
sample.
For many discussions of extension and shear
fracturing in the literature of rock mechanics the
stress–strain curve after failure initiates is not
shown because the testing machine was incapable
of tracking these quantities accurately during the
rapid failure event. Shortly after reaching the peak
stress (Fig. 9.5, point C), the data stream was terminated because the specimen disintegrated into
a pile of rock chips and dust with a loud bang. As
early as 1943 it was clear that explosive disintegration was not necessarily a natural behavior, but
rather “elastic energy is stored in the cylinder and
in the machine . . . and the release of this energy
causes the breakdown of the cylinder” (Whitney,
1943). Curiosity about the post-peak-stress part of
the stress–strain curve led researchers to try to
capture the complete stress–strain curve and to understand what influence the testing machine might
have on the specimen behavior during failure
(Hudson et al., 1972; Jaeger and Cook, 1979, p. 177).
Consider the schematic illustration of a
testing machine (Fig. 8.25) and note that it is composed of two basic components: an hydraulic actuator (including piston and cylinder, rod, and platen)
for applying a force to the specimen and a reaction
frame (tie-bars and cross-heads) for supporting this
force. When fluid pressure is increased in the
actuator the piston is driven downward applying
a compression to the specimen and shortening it.
The downward directed force is transmitted
through the specimen to the lower cross-head.
The actuator also applies an equivalent upward
directed force to the upper cross-head so the tiebars are placed in tension and elongate, while the
cross-head bends. Both the actuator and the reaction frame deform and are capable of storing
elastic energy. If the mechanical parts of the
testing machine combine to be very much stiffer
than the rock specimen, the machine would
deform very little and we could ignore its role in
the test. However, specimens are explosively disintegrated in some testing machines because
the energy stored in the machine is released into
the specimen even though no fluid is pumped
into the actuator to do additional work. In other
words, the system composed of the machine and
the specimen self-destructs.
To understand this process the initial deformation of the specimen is idealized (Fig. 9.6a)
with a spring of constant stiffness, C s . The
machine frame is idealized with two springs of
stiffness C m /2 in parallel and tied together with an
upper and lower rigid bar. All of these springs are
tied to a rigid basal support which is taken as the
reference frame for measuring displacements.
The vertical y-axis is positive downward so forces
and displacement acting downward are positive.
Two applied forces idealize the actuator: F s acting
downward on the specimen spring and F m acting
upward on the rigid bar joining the two machine
springs (Fig. 9.6b). These forces are identical in
magnitude and opposite in direction, so F s ϭϪF m .
Under the applied force, F s , the specimen spring
contracts and its upper end moves toward the
9.2 STRENGTH OF LABORATORY SAMPLES
339