The characterization of modern materials in terms of their constitutive
models (ranging from the elastic and inelastic deformation characteristics, to
the damage and fracture mechanics behaviour) is of great interest for the design
of mechanical structures as well as for material qualification purposes.
We investigate the characteristics of wave propagation, vibration, crack
advance, elasto-plastic and rate dependent deformation in solids, and viscous
behaviour of fluids. The mechanical properties of each material can be
derived from their influence on these processes.
Our research on material behaviour ranges from MEMS to steam turbine
components, from composites, to bitumen, to biological tissues (biomechanics).
Based on the Patent "Method and Device for Measuring the Characteristics of an
Oscillating System" (M. Sayir, J. Dual, J. Goodbread; K. Haeusler, US Pat. No.
4920787, EU Pat. No. 749 570 B1) a number of devices based on this principle
were developed at the Center of Mechanics, in the fields of visco- and
rheometry, to measure viscous and elastic properties of fluids and soft solids
and tissue:
[Top]
High
Frequency Dynamical Rheometry on Confined Emulsions
Authors: Alexandre Romoscanu,
Mahir B. Sayir, Klaus
Häusler, A. Burbidge
In this work, we explore the application of high frequency oscillating probes
as a measuring device for the rheological properties of fluid samples. The
working principle of the probes used here is based on the dynamical
behaviour of a resonator around its lower resonant frequencies. The
dynamical behaviour is quantified with the help of the resonant frequency
as well as the slope of the phase shift between driving force and measured
deflection around the resonant frequency as shown in Fig. 1. Interpretation of
the measured data is performed by modelling the resonator/fluid system under the
assumption of adequate constitutive equations for both the resonator and sample.
A subsequent comparison between computed and measured values allows us to
quantitatively link the measured dynamic behaviour of the system with the
rheological properties of the fluid sample.
Fig. 1
The only constraints on the resonator geometry are a shear strain of the
fluid sample, as well as sufficient sensitivity, usually reached through
maximizing the contact surface between resonator and fluid.. We presently work
with tube and rod resonators, which are suitable for online measurements, as
well as rotational and translational thin film geometries, where the fluid
sample is confined in a gap whose thickness is of the same order of magnitude as
the penetration depth of the shear wave in the fluid, typically some hundred
microns. These geometries allow the measurement of heterogeneous media such as
emulsions and suspensions. A typical thin film translational probe with
adjustable gap thickness is shown in Fig. 2. Confinment of the fluid sample in a
gap prevents the emergence of dispersed phase depletion layers in the vicinity
of the oscillatong wall and increases the instrument's sensitivity.
Homogeneization theories allow us to link the measured dynamical behaviour
of the resonator/fluid system with important heterogeneous medium parameters
like dispersed phase volume fraction, inclusion size and interfacial tension.
Fig. 2
[Top]
Wave
Propagation in Asphalt Concrete
Author: Andreas Hochuli, Mahir
B. Sayir
(from the 1998 brochure)
Asphalt concrete is a mix of stones, bitumen and pores filled with air,
forming a solid with large inhomogeneities. Using structural waves with
wavelengths larger than the characteristic dimension of the inhomogeneities, the
global stiffness of the structure is obtained nondestructively. Since bitumen is
viscoelastic, the material stiffness of asphalt concrete depends on the
frequency of dynamic loads and on the temperature.
We perform the following experiment: A transducer produces bending waves in
an asphalt concrete plate. We measure the displacement at two different points (
Figure 1 ). Fitting the experimental results to theoretical models, we can
determine both the global tensile and shear moduli as a function of the
frequency and the temperature.
Figure 1: Surface of the asphalt concrete plate prepared
for the bending wave propagation experiment
To check the results obtained from wave propagation experiments, we also
determine the resonance frequencies of the specimen. With this kind of
experiments we are able to measure the elastic as well as the viscoelastic
properties of the specimen from the phase-response of the structure. However,
the geometry and the boundary conditions of the asphalt concrete must be known
exactly, because they influence the resonance frequencies.
A transducer excites longitudinal vibrations in an asphalt concrete bar. We
change the frequency of the excitation until the bar vibrates at its resonance
mode. The mode of the resonance is checked by measuring the displacements at
several points along the bar by means of a laser-interferometer. The
supporting wires are placed in the nodes of the oscillation mode to minimize
their influence on the oscillation. The measurements are compared to theoretical
predictions. This enables us to determine the elastic and viscoelastic material
properties.
[Top]
Moduli
Determination of Undamaged and Damaged Composite Plates
Authors: Zeynep Eroglu, Mahir
B. Sayir
(from the 1998 brochure)
The material constants of undamaged and damaged crossply (bidirectional,
0o-90o) fiber-reinforced composite plates are determined. Consequently, the
influence of damage on moduli reduction is investigated.
As indicated in the chapter Dynamic Crack Propagation and Damage in Composite
Structures, damage can be correlated to reduction of effective moduli. In order
to quantify moduli reduction due to damage, first, the moduli of undamaged
composite plates are determined by phase velocity measurements with the help of
a heterodyne Laser-Doppler interferometry system (see See Heterodyne
Laser-Interferometer with Phase-Demodulation. ). The dispersion curves of the
flexural waves propagating in a composite plate are obtained from plotting phase
velocities c over a certain frequency (or wave number, k) range. In an undamaged
plate, there is a good correspondence between the experimental phase velocities
and the curves from the theoretical calculations (solid lines in Figure 1 ) not
only in 0o and 90o principal directions, but also in the in-between directions
(each 15o).
Figure 1: Dispersion curves of a composite plate
(02/90/03/90/03/90/02). Experimental data (symbols) and theoretical curves in 0
and 90 principal directions and 45o direction with flexural moduli determined
as: E33 = 97.04 GPa, G13 = 3.87 GPa, E22 = 26.78 GPa, G12 = 2.62 GPa, n32 =
0.27, n12 = 0.45, n31 = 0.45.
In order to evaluate the influence of damage on the various moduli, the
plates are exposed to cyclic flexural fatigue loading and the damage level is
inspected and controlled by an acoustic emission testing system.
The dispersion curves obtained from phase velocity measurements versus wave
numbers of Figure 2 indicate the influence of damage on the in-plane effective
tensile moduli (E33, E22) and out-of-plane effective shear moduli (G13, G12)
derived from the flexural stiffness in the two principal directions. The curves
(a) and (b) show the results for the undamaged plate. In (b) the experimental
values do not follow a single theoretical curve. To obtain a proper fit, the
moduli for the lower and higher frequency region have to be adjusted separately
(part (d) of Figure 2 ). Thus damage introduces a frequency-range dependency of
the effective moduli.
Furthermore, the results indicate that the fatigue damage reduces the shear
moduli more than the tensile moduli in the "strong" principal
direction (direction 3).
The fatigue loading of the composite plates to induce damage, the acoustic
emission tests and some ultrasonic testing measurements were carried out at
EMPA. The wave propagation measurements were performed at our Institute.
Figure 2: The bending moduli of a composite plate
(0/90/02/90/02/90/02/90/02/90/0) determined by phase velocity measurements prior
to and after damage. Points are from experimental measurements, curves are from
theoretical calculations. (a-) and (b-) prior to and after damage in 0o
principal direction, (c-) and (d-) prior to and after damage in 90o principal
direction, respectively. Standard error estimates are given as sy,x.
[Top]
Rheology
of Bitumen
Andreas Hochuli, Lily D. Poulikakos, Mahir
B. Sayir
in conjunction with EMPA
(from the 1998 brochure)
In some applications involving impact loading, the rheological behaviour of
bitumen in the high frequency ranges may be important in determining its
performance as a binder. Unfortunately, the frequencies of classical dynamic
shear rheometers for measuring complex viscosities are usually limited to 50-100
Hz. With this first motivating argument in mind, we performed a series of
measurements on bitumen "B 40/50" at a frequency of 5.3 kHz, using a
new torsional dynamic resonance rheometer developed at the Institute of
Mechanics.
Figure 1: Rheometer embedded in bitumen
Since the working frequencies are in the kHz range, the device is very robust
in environments involving spurious low-frequency vibrations. Even occasional
impact disturbances do not affect the readings after a few measuring cycles of
the order of milliseconds. Hence, the method is adapted for in situ measurements
and for monitoring in properly prepared road segments. The above-mentioned
series of measurements in the laboratory were performed under controlled
temperature varying between 40° and 100°C. Since in the kHz range only a
relatively thin (less than 10 mm thick) boundary layer of bitumen around the
vibrating rod is participating in the torsional vibration motion, inhomogeneous
distributions of temperature in the bitumen sufficiently far from the boundary
layer do not affect directly the measurements, as long as the temperature near
the moving boundary layer is known. This and other features of the resonance
rheometer contribute to a considerable simplification of the measurement
procedure with respect to classical methods, even under laboratory conditions.
Another important characteristic of the resonance rheometer is that the
amplitude can be maintained at very low levels (the measured maximum value of
the shear strain in the bitumen at 100 °C was 4. 10-4, it decreased to 5. 10-5
for 45°C). Thus nonlinear effects can be avoided, and the bitumen can be
modelled quite accurately as a linear viscoelastic fluid. Finally, while
comparing our results to classical measurements in the Hz-range and fitting
the data both at low and high frequencies to appropriate theoretical models, we
found that the behaviour at high frequencies involving short relaxation times
affect the accuracy of the model even at low frequencies and should be taken
into consideration in theoretical models trying to cover a wide spectrum of
frequencies.
Figure 2: Real part of the viscosity in a double
logarithmic scale as a function of frequency
Figure 3: Imaginary part of the viscosity in a double
logarithmic scale as a function of frequency
The new resonance rheometer has proven to be a useful tool for the
characterization of bitumen by means of its complex viscosity. Currently a
series of tests are planned in cooperation with EMPA in order to characterize
bituminous materials used in expansion joints of bridges. Using the resonance
rheometer the amount of damage due to fatigue and/or crack initiation can be
determined. This information can be used in evaluation of the expected useful
life of the material as well as future design.
[Top]
Experimental
Evaluation of Materials under Thermo-Mechanical Shock Conditions
Stefan Messmer, Mahir B.
Sayir
(from the 1998 brochure)
The choice of an optimal material combination for structures with
thermo-mechanical shock loads is more complex than for conventionally loaded
structures. There are many important failure mechanisms and, therefore,
experiments are necessary to evaluate an optimal material. During the last few
years a testing device has been developed to simulate the fatigue behaviour of
different materials under realistic conditions. Thermo mechanical shock loads
are typical for all kinds of combustion engines or several military
applications.
The testing device will be presented briefly. It is built up around a pulsed
Nd:YAG-Laser with approx. 150 W mean and 10 kW peak power. The Laser is used to
heat specimens in a short time. We can simulate a temperature increase of more
than 1000°C in less than 1 ms. We call this loading thermo-mechanical shock
loading, because of the thermal stresses correlated to the shock heating.
One of the key problems of this type of testing device is the influence of
the laser on the emissivity of the surface of the specimen. On the one hand, the
energy absorbtion of the surface depends on the emissivity, on the other hand,
the laser treatment changes the emissivity of the specimen. To get reproducible
testing conditions, the temperature of the surface has to be measured and
controlled. The only more or less reliable temperature measurement under the
given conditions uses infrared radiation to calculate temperature of the
surface. And again, the infrared radiation of the specimen depends on the
emissivity of the specimen. To ensure quality of the infrared temperature
readings, the change of emissivity is estimated during the experiment.
Figure 1: Experimental setup for thermo shock test with
Laser.
Figure 1 shows the principal setup of the testing device.
The laser light (wave length 1.06 m, not visible) is directed from the laser
resonator to the specimen. The focal point of the lens is well above the
specimen. The distance between the focal point and surface determines the
diameter of the heated region. This is one parameter to vary the heat flux per
unit area into the specimen. Within the laser region the material is heated up
very quickly (Heating time: 0.2 ms 20 ms, maximum temperature up to 1000°C).
The temperature of the material as a function of time during the laser pulse is
measured with an infrared camera. On its monitor the temperature of a single
line through the laser region can be shown as a function of time. From this
recording the maximum temperature value is evaluated and fed back into a
controller. The material temperature below the surface can be measured with a
thermocouple.
Figure 2: SEM-Picture of the surface of specimen 109.
This specimen has been loaded with 1000 Laser pulses of 1.5 ms duration,
creating peak temperatures of 600°C.The scale printed on the picture is 100 m.
Figure 3: Cut through Laser region. Surface layers and
cracks are well visible. The heat treatment with the laser leads to mechanical
stresses, plastic flow, cracking, oxidation and recristallisation.
Some typical test results are shown in the figures. Figure 2 shows the
surface of a steel specimen after 10'000 Laser pulses of 1.5 ms duration. The
surface shows a crack pattern that is aligned with scratches from the grinding
procedure. Also visible is some kind of erosion (oxidation). Figure 3 shows the
crack depth in a cut through the laser-heated region. An analysis of the crack
growth with respect to number of load cycles and peak temperature ( Figure 4 )
shows the main features of crack growth under thermo-mechanical shock loads. The
crack depth does not depend on the number of load cycles in the tested parameter
range, but it depends strongly on the peak temperature. This behaviour seems to
be paradox. The reason is that a thin layer of the specimen is influenced by
thermal shock loads, and only within this boundary layer plastic stress-strain
cycles as shown in Figure 4 will damage the material. Outside this boundary
layer there are no large cyclic stresses and the fracture will stop as soon as
they leave the boundary layer.
Figure 4: Mean crack depth as a function of peak
temperature and number of load cycles. The Weibull - Beta constant can be
interpreted as "mean crack depth". The crack depth does
not depend on number of load cycles.
Ceramic materials show a different behaviour . They behave linearly under
compression loads and, obviously, they do not show plastic behaviour .
Therefore, ceramic materials fails under compression, if the compression
stresses are high enough.
We have tested several types of steel specimens, stellite specimens,
pre-compressed and uncompressed ceramic specimens under several load types and
can now predict the behaviour of different materials in practical applications.
Acknowledgment: We would like to thank H. Oesch from s+w Bern for the support
of this project.
[Top]
Nanosonics:
Laser-based Ultrasonics at the Nanometer Scale
Authors: Dieter M.
Profunser, Jacqueline Vollmann
Research group: Jürg Dual
See report
on page Micro- and Nanomechanics
[Top]
Mechanical
Properties of Microstructures
Authors: Jürg Dual, Edoardo
Mazza, Gilbert Schiltges, Dirk Schlums
See report
on page Micro- and Nanomechanics
[Top]
Size
Effects in Thin Copper Foils
Author: Gerd Simons
Research group: Jürg
Dual
See report
on page Micro- and Nanomechanics
[Top]
02/24/09 | Stephan Kaufmann |
ZfM | ETH
