91
same magnitude as the incident wave propagates in the opposite direction from the clamp towards the end of the incident bar.
Since the longitudinal and shear mechanical impedances at the bar end are sufficiently large, the reflected unloading wave
counteracts the torque and tensile force in the incident bar to zero as it propagates back from the bar end. Hence, the duration
of the incident wave is the time required for the wave to travel twice the pre- stressed section of the bar.
It is noted that the torsional wave will reach the specimen with a slight delay with respect to the tensile wave due to the
difference in wave speeds. The synchronization of the two waves is a critical issue in designing the TTHB system, which is
reasonably achieved by locating the clamp very close to the specimen in the present design. The distance between the clamp
and the bar/specimen interface is selected so that the waves traveling at distinct speeds in the incident bar would reach the
specimen within 10 μs (this tolerance for time difference is originally adopted by [6]).
16.3.2 Stored Loads
The torque T T and force F T required to break the specimen are calculated by Eqs. (16.1) and (16.2). As engineering materials
exhibit a rate-dependent behavior, the shear strength τ and the tensile strength σ t correspond to the specific required shear and
longitudinal strain rates,
g and
e , respectively. T T and F T represent the amplitudes of the transmitted torsional and tensile waves.
T
J
r
T
s
s
=
t
(16.1)
F
A
T
s t
= s
(16.2)
where, J s and A s are moment of inertia and across section area of the specimen, respectively.
The amplitudes of the reflected torsional and tensile waves, T R and F R , which are related to the required torsional and
tensile strain rates, respectively, are determined from Eqs. (16.3) and (16.4).
T
c J l
r
R
s
s
s
=
× × -
( )
r
g
2
(16.3)
F
cA l
R
s
=
× × -
( )
r
e
2
(16.4)
where, l s and r s are the gauge length and average radius of the considered thin-walled specimen, ρ denotes the density of the
bar material, c s and c are the longitudinal and shear wave velocities of the bar, respectively. J and A are moment of inertia
and cross-sectional area of the bar.
The amplitude of the incident torsional or tensile waves, T I or F I , is then the sum of the amplitudes of the corresponding
transmitted and reflected waves. When the incident wave is generated via the rapid release of tensile and torsional elastic
energies stored in a section of the input bar the amplitude of the incident waves is equal to half that of the stored load. The
torque and force to be stored, T S and F S are therefore calculated as:
T
T
T T
S
I
T
R
=
=
-
(
)
2
2
(16.5)
F
F
F F
S
I
T
R
=
=
-
(
)
2
2
(16.6)
16.3.3 Instrumentation
The noncontact photon Doppler velocimetry (PDV) and the traditional strain gauge technique are instrumented in the TTHB
system. The PDV technique is a 1-D Fourier transform analysis of a heterodyne laser interferometry signal used for accurate
velocity measurements of materials subjected to dynamic events. The technique has been initially developed to better
16 The Development of Split Hopkinson Tension-Torsion Bar for the Understanding of Complex Stress States at High Rate
same magnitude as the incident wave propagates in the opposite direction from the clamp towards the end of the incident bar.
Since the longitudinal and shear mechanical impedances at the bar end are sufficiently large, the reflected unloading wave
counteracts the torque and tensile force in the incident bar to zero as it propagates back from the bar end. Hence, the duration
of the incident wave is the time required for the wave to travel twice the pre- stressed section of the bar.
It is noted that the torsional wave will reach the specimen with a slight delay with respect to the tensile wave due to the
difference in wave speeds. The synchronization of the two waves is a critical issue in designing the TTHB system, which is
reasonably achieved by locating the clamp very close to the specimen in the present design. The distance between the clamp
and the bar/specimen interface is selected so that the waves traveling at distinct speeds in the incident bar would reach the
specimen within 10 μs (this tolerance for time difference is originally adopted by [6]).
16.3.2 Stored Loads
The torque T T and force F T required to break the specimen are calculated by Eqs. (16.1) and (16.2). As engineering materials
exhibit a rate-dependent behavior, the shear strength τ and the tensile strength σ t correspond to the specific required shear and
longitudinal strain rates,
g and
e , respectively. T T and F T represent the amplitudes of the transmitted torsional and tensile waves.
T
J
r
T
s
s
=
t
(16.1)
F
A
T
s t
= s
(16.2)
where, J s and A s are moment of inertia and across section area of the specimen, respectively.
The amplitudes of the reflected torsional and tensile waves, T R and F R , which are related to the required torsional and
tensile strain rates, respectively, are determined from Eqs. (16.3) and (16.4).
T
c J l
r
R
s
s
s
=
× × -
( )
r
g
2
(16.3)
F
cA l
R
s
=
× × -
( )
r
e
2
(16.4)
where, l s and r s are the gauge length and average radius of the considered thin-walled specimen, ρ denotes the density of the
bar material, c s and c are the longitudinal and shear wave velocities of the bar, respectively. J and A are moment of inertia
and cross-sectional area of the bar.
The amplitude of the incident torsional or tensile waves, T I or F I , is then the sum of the amplitudes of the corresponding
transmitted and reflected waves. When the incident wave is generated via the rapid release of tensile and torsional elastic
energies stored in a section of the input bar the amplitude of the incident waves is equal to half that of the stored load. The
torque and force to be stored, T S and F S are therefore calculated as:
T
T
T T
S
I
T
R
=
=
-
(
)
2
2
(16.5)
F
F
F F
S
I
T
R
=
=
-
(
)
2
2
(16.6)
16.3.3 Instrumentation
The noncontact photon Doppler velocimetry (PDV) and the traditional strain gauge technique are instrumented in the TTHB
system. The PDV technique is a 1-D Fourier transform analysis of a heterodyne laser interferometry signal used for accurate
velocity measurements of materials subjected to dynamic events. The technique has been initially developed to better
16 The Development of Split Hopkinson Tension-Torsion Bar for the Understanding of Complex Stress States at High Rate