ACOUSTO-THERMAL MICROSTRUCTURE
CHARACTERIZATION
N. Meyendorf, H. Roesner, J. Frouin, J. Maurer, and S. Sathish
University of Dayton Research Institute - Center for Materials Diagnostics,
University of Dayton, 300 College Park, Dayton, OH 45469-0121
ABSTRACT. The paper shows that the acousto-thermal principal is capable of characterizing
microstructure changes due to fatigue in Ti-6Al-V4. The results are discussed in terms of internal
friction and compared to low frequency, high stress thermographic characterization and nonlinear acoustics. The dislocation structure of the fatigued titanium alloy was characterized by
transmission electron microscopy.
INTRODUCTION
Characterization of the microstructural damage due to fatigue and the estimation
of the remaining lifetime of a component is one of the great challenges of
nondestructive materials evaluation. A large number of papers can be found in the
literature concerning these topics. [1-4] are some examples. However, for most of the
published results, a very limited set of specimens (usually only one type of material)
and a very limited variation of loading conditions are used to evaluate nondestructive
techniques. Most of these results indicate that an NDE parameter varies with fatigue
life. However, the inverse problem is not solved. An NDE parameter measured at a
component is usually not sufficient to determine a lifetime expectation. Additionally,
for practical applications, variations in microstructure of the undamaged material and
uncertainties in knowledge about the loading conditions have to be considered.
Therefore, NDE approaches that relate to established destructive test methods have the
advantage that they can refer to the brought experience of fatigue specialists using
destructive tests.
For example, internal friction is a well-established technique for destructive
materials characterization. Cyclic mechanical loading generates heat due to internal
microplastic deformation, internal friction, and non-adiabatic thermal elastic effects.
These thermal effects are very sensitive to the mechanical properties and the
microstructure of the loaded material. The current study discusses the development of a
new thermal parameter that can be used to characterize the fatigue damage from the
heat generated per loading cycle.
PHYSICAL BACKGROUND
Dynamic mechanical loading of a material induces thermal effects that are
CP657, Review of Quantitative Nondestructive Evaluation Vol. 22, ed. by D. O. Thompson and D. E. Chimenti
© 2003 American Institute of Physics 0-7354-0117-9/03/S20.00
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related to its mechanical properties. The total temperature change, AT, of a material
due to cyclic mechanical loading is a superposition of the thermoelastic temperature
variation, ATei, the temperature due to heat dissipation, ATdiSS> and the temperature
variation, ATioss, due to heat energy exchange with the environment controlled by the
specific boundary conditions:
AT(t) = T(t)-T0 = ATel(t) + ATdiss(t) + ATloss(t)
(1)
Here, TO is the absolute reference temperature corresponding to the temperature
at time t = 0. In the following discussion adiabatic conditions are assumed, thus the
temperature decrease due to heat exchange with the environment, ATioss, is neglected.
The thermoelastic temperature change, under adiabatic conditions, is a
reversible thermodynamic effect caused by a change in material's free energy due to
elastic deformation. The thermoelastic temperature change due to a sinusoidal
mechanical loading at the frequency f (s"1) can be expressed as [5]:
ATel
( t ) = - a ' T o - < ? a . sin( 2icf • t)
P'CP
(2>
Here, aa [Pa] is the amplitude of the mechanical stress, a [K"1] is the coefficient
of thermal expansion, p[kg m"3] is the density and cp [J kg"1 K"1] is the specific heat at
constant pressure. This temperature change is directly related to the applied mechanical
stress, thus, it can be utilized for stress characterization.
Dynamic elastic deformations may also be accompanied by reversible anelastic
deformations, or at higher stress levels by irreversible plastic deformations. A result of
the non-elastic deformation is mechanical damping, whereby the mechanical energy is
transformed into dissipated heat energy. The dissipated heat produces a secondary
mechanically induced temperature effect, which superimposes the thermoelastic
temperature change [6-7]. In contrary to the thermoelastic effect under adiabatic
conditions, the generation of the dissipated heat is a thermodynamically irreversible
process. The temperature change ATdiSS is directly related to the generated and
accumulated dissipated heat Qdiss [J m~3] in the material and it can be described as
follows [8]:
ss
P'CP
The generation of dissipated heat is a thermodynamically irreversible process.
This effect is exhibited during cyclic periodic loading by the mechanical hysteresis.
Mechanical hysteresis is the result of a phase shift between the stress (a) and strain (e)
during a mechanical loading cycle. A phase shift always appears when the strain
amplitude, ea? consists of anelastic strain, eaneb or plastic strain, ep, in addition to the
elastic deformation.
Even at very small stresses, e.g., during ultrasonic loading, heat dissipation is
generated that can be measured experimentally [6]. Under these very low stress
conditions, reversible time dependent anelastic deformations are responsible for the
mechanical damping, generating very small mechanical hysteresis. The entire
mechanical energy loss per single mechanical loading cycle, Wmech> is then transformed
into heat energy qaiss- Some of the mechanisms activated under these low stress
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Standing wave
patterns
FIGURE 1: Thermosonic images of fatigued metal sheets (experiments at Wayne State University,
Detroit).
conditions have been described as Granato-Liicke damping, ferromagnetic damping or
thermoelastic damping [9,10].
EXPERIMENTS
Thermosonic experiments with fatigued metal sheets showed indications of
fatigue cracks (as expected) and additionally, a periodic temperature structure, which is
related to standing wave patterns. The increased temperature in this periodic structure
is located at positions of higher excitation amplitude and so increased heat dissipation
(Figure 1).
To quantify this effect, dogbone fatigue specimens of the titanium alloy Ti-6Al4V were manufactured and fatigued during interrupted fatigued experiments. After
each block of several thousand fatigued cycles, the specimens were removed from the
fatigued machine and excited by a power ultrasonic system for about 5 seconds. The
system was designed in a way that the maximum of the standing wave is generated in
the gage section of the fatigued specimen. The temperature as a function of ultrasonic
loading time was measured with a thermal camera (Figure 2).
Characteristic differences in the heating process were found for fatigued and
non-fatigued specimens. The temperature in the gage section of the mechanical loaded
specimen should show a time dependence as indicated schematically in Figure 2. The
periodic temperature oscillation caused by the thermo-elastic effect can be ignored for
the excitation frequency of 20 kHz as used in the experiments. The mean temperature
of the specimen should initially increase approximately linear with time (Stage 1). If
the thermal conductivity has to be considered and the process is not more adiabatic, the
mean temperature will deviate from this initial slope (Stage 2) and will approach a
saturation value for long loading periods (Stage 3). The duration for the Stage 1 with
approximately linear increase of a mean temperature depends on the thermal
conductivity. Based on FEM modeling, this period was found to be approximately 7
seconds for the titanium alloy used. For copper this time decreases to 0.14 seconds [11].
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Stage 1
Stage 2
Stage 3
FIGURE 2: Temperature of fatigue specimens during power ultrasonic loading (schematic).
A parameter that is independent of specimen size, thermal conductivity and
other random conditions can be determined from this initial slope (ATdiss). As indicated
in Figure 2, the temperature increment per loading cycle corresponds directly to the
energy generated per hysteresis cycle Aqdiss. The damping coefficient known from
internal friction experiments r|' is the energy generated per hysteresis cycle, divided by
the maximum work to elongate the specimen (see Figure 2). Therefore, the thermal
parameter ATdiss can be related directly to internal friction experiments. Figure 3 shows
that the parameter increases approximately linear with the number of fatigued cycles for
the investigated Ti alloy. Also, the dislocation density increases nearly linear with the
fatigue life for the investigated material. This was the result of a detailed quantitative
investigation using transmission electron microscopy. The dislocation density was
determined from electron microscopy as a function of fatigue cycles for the same
material and similar loading conditions [12].
Slope:
1.2*10-8mK
Fatigue life:
N = 81,065
Slope:
1.6*10-8mK
Fatigue life:
N = 72,693
20,000
40,000
60,000
80,000
N [cycles]
FIGURE 3: Temperature increment per loading cycle (power ultrasonic loading) as function of fatigue
life of specimen.
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Dislocation density:
A(0)= 0.2*10-5nnr2
Dislocation density variation: A(90%)/A(0) = 20
Loading frequency
Max. Stress
Variation of the
parameter as
^
function of
fatigue cycle
number N for
two specimens
For 1... 100 MHz
A(90%) = 10*10-5nnr2
Mechanical Loading Power Ultrasonics
30 Hz
20kHz
500 MPa
50 MPa
Nonlinear Acoustics
10 MHz
0.5 MPa
9
N
N
4
4
rf prop. A* L and (3 prop. A* L
N
[J-H. Cantrell et all.]
Dislocation
FIGURE 4: Comparison of experimental results (schematic) for fatigued Ti -6A1-4V specimens. (0)
means virgin specimen (90%) means specimen after (90%) of fatigue life.
DISCUSSION OF RESULTS
The experiments outlined above were part of a 5 years program on
nondestructive evaluation of fatigue of titanium alloys [13]. By using these results we
are able to compare the results to other experiments, which have used much lower and
much higher loading frequencies. Thermographic results using high stress low
frequency loading have been published and referenced [14, 15]. The experimental
procedure and data analysis was similar as outlined above but the loading frequency
was only 30 Hz (compared to 20 kHz used for the above experiments). The thermal
parameter AT&SS for the temperature increment generated per hysteresis cycle was 3
orders of magnitude larger compared to power ultrasonic excitation and showed a linear
increase with fatigue life similar to the above results (see Figure 4).
The nonlinear acoustic parameter (3 was measured at the frequency of 10 MHz
with transducers mounted on top and bottom of the fatigue specimen. This procedure
allowed measuring the nonlinearly parameter continuously during the fatigue
experiment [16]. The results illustrated schematically in Figure 4 indicate an increase
of the nonlinearity parameter with fatigue life. However, a saturation behavior was
found towards the end of the fatigue experiment. The nonlinearity parameter (3 cannot
directly be compared to the internal friction parameter t|' (like the dissipation
temperature increment for mechanical loading and power ultrasonic loading). However,
it can be found from the literature that the contribution of the dislocations to (3 is
proportional to the dislocation density A multiplied by L4. L is the loop length [17]. A
similar relation for the ultrasonic absorption follows from the Koehler-Granato-Luecke
theory and has been experimentally verified for the 1 to 100 MHz frequency range
[18, 19]. Ultrasonic absorption means the transfer of ultrasonic energy into heat.
However, during an increasing number of fatigue cycles an increasing number of
dislocations are generated. Dislocations form dislocation patterns and subgrain
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Moving dislocations
Local plastic deformation
AT • =a*o m+1
m: Ramberg-Osgood Exponent
Oscillating Dislocations
pinned by point defects
grain
b°undaries •••
'H'-'H'o prop. A
Atdlss-ATdiss0prop.A
Dependence of
concentration of
pinning points and
Temperature expected
Dislocation / phonon
interaction
P prop. A* L4
formation of dislocation
network reduces free
dislocation length L and
modifies process
FIGURE 5: Schematic variation of damping coefficient (from temperature increment per cycle) and
nonlinearly parameter (3 as function of fatigue life of Ti-6Al-4V specimens. Microscopic explanations for
low frequency (30 Hz) loading (left), power ultrasonic (20 kHz) loading (center), and nonlinear acoustic
(10 MHz) experiments (right).
structures. This results in a decrease of L and an increase of contributions from
dislocation dipole pares. This might explain the saturation of (3 for higher fatigue cycle
numbers.
Figure 4 compares the damping parameter T)' and the non-linear acoustic
parameter p for the different experiments. Parameters to generate the fatigue damage
were similar for all experiments and comparable to the conditions used for the
transmission electron microscopic experiments. While the dislocation density increases
by a factor of 20 from the virgin to the 90 percent fatigued specimen, the damping
parameter increases by a factor of 10 for experiments with a low frequency mechanical
loading (30 Hz). In comparison the increase in damping parameter for power ultrasonic
loading (20 KHz) was only by a factor of 1.5. A relatively high offset was found in
these experiments. The nonlinear acoustics parameter (10MHz) shows a slightly larger
increase. However, saturation was found for a high fatigue cycle number.
A possible explanation for these different behaviors for different loading
frequencies could be found in the different dissipation mechanisms (Figure 5). For very
low frequencies and high stress amplitudes microplastic deformations have to be
considered. The author showed in an earlier paper [14] that dissipated heat could be
related to the nonlinearity of the stress/strain curve. The temperature increment is a
function of the applied stress with an exponent resulting from the Ramberg-Osgood
relation. The dominant damping effect for the high frequencies used in nonlinear
acoustic experiments is dislocation/phonon interaction, which should result in a higher
damping compared the medium stimulation frequencies (20 kHz). The main source for
heat dissipated by the power ultrasonic loading with 20 kHz should be the oscillation of
dislocations that are pinned at grain boundaries and point defects. A damping
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parameter proportional to dislocation density is expected. However, in this frequency
range, also reorientation or vibration of point defects will significantly contribute due to
the internal damping. Snoek effect is one of the most popular effects of this type (for
carbon in iron). This damping effect should be responsible for the high offset, which
was found for this type of loading.
SUMMARY
Cyclic mechanical loading generates heat due to internal microplastic
deformation, internal friction, and non-adiabatic thermal elastic effects. These thermal
effects are very sensitive to the mechanical properties and microstructure of the loaded
material. The current study discusses the development of a new thermal parameter that
can be used to characterize the fatigue damage of the material from the heat generated
per loading cycle. The thermal parameter was measured during short-term (5 seconds)
cyclic loading as a function of fatigue life for the titanium alloy Ti-6Al-4V. Power
ultrasonic loading is a very efficient loading technique. For the material under
investigation dislocation density as well as the heat increment generated during one
loading cycle increases nearly linear with fatigue life. However, the amount of heat
generated and the sensitivity of the thermal parameter to fatigue life varies significantly
with loading amplitude and frequency. The results have been discussed in terms of
internal friction phenomenon.
ACKNOWLEDGEMENTS
The authors would like to acknowledge DARPA and the Air Force Office of
Scientific Research for funding the reported research under DARPA-MURI Grant
Number F49620-96-1-0442. We especially would like to acknowledge L.D. Favro and
Xiaoyan Han for performing the Thermosonic experiments presented in Figure 1 and
Dr. Victoria Kramb and Cindy O'Brien for help preparing of the paper.
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