Mechanical spectroscopy

The Mechanical spectroscopy is a method in the materials science to the mechanical material properties, depending on the time or the frequency to be examined. The term was first used in 1990 by Leszek B. Magalas to describe the anelastic relaxation of materials.

Systematic studies of this phenomenon have been carried out since the 1940s (e.g. by Clarence Melvin Zener or Arthur S. Nowick and BS Berry).

Definition of terms

The term mechanical spectroscopy has both macroscopic and microscopic aspects. Macroscopically, the time-dependent or frequency-dependent behavior of the "intact" material is considered with exclusively elastic behavior . The behavior is predominantly linear (or the linear part is considered), so that the linear response theory can be used as a basis. Questions about strength , plasticity and breakage are ignored. The aim of the investigation is the function of the time-dependent response of a solid (e.g. strain ) to a time-dependent mechanical load (e.g. tension ). This function is dependent on time, frequency, temperature or amplitude and is called a spectrum . Hence the name "mechanical spectroscopy ". The influence of the atomic binding forces and defects (point defects, dislocations, etc.) is examined microscopically.

Anelasticity and viscoelasticity

If a material is anelastic , there is an unambiguous state of equilibrium between tension and elongation, but this does not occur immediately, but only after a time delay ( asymptotically ). Another condition of anelasticity is the complete decrease in deformation after unloading. If this is not the case, one speaks of viscoelasticity . In more recent work, however, the anelasticity is also referred to as viscoelasticity and the viscoelasticity as viscoplasticity. There are also various other names for these relaxation processes.

Functions and Spectra

left: Typical strain diagram of an anelastic relaxation with associated spring-damper diagram.
right: Typical strain diagram of a viscoelastic relaxation with associated spring-damper diagram.

A discrete spectrum for spring-damper systems of a Maxwell type.

To describe the anelastic behavior of the materials, one can use response functions or relaxation spectra. Spectra are particularly suitable for evaluating the relaxation time and the relaxation strength, since a distinction is made between the purely elastic part and the anelastic part. With the response functions, these components would have to be laboriously calculated. Anelastic relaxation is often based on thermal activation . Therefore the material damping can also be represented as a function of the temperature:

${\displaystyle Q^{-1}={\frac {\Delta }{2}}\operatorname {sech} \ {\frac {Q_{a}}{k_{\mathrm {B} }}}\left({\frac {1}{T}}-{\frac {1}{T_{\mathrm {P} }}}\right)}$

• ${\displaystyle Q^{-1}}$: Damping of the material
• ${\displaystyle \Delta }$: Relaxation strength
• ${\displaystyle Q_{a}}$: "Activation energy"
• ${\displaystyle k_{\mathrm {B} }}$: Boltzmann constant
• ${\displaystyle T_{\mathrm {P} }}$: Temperature in the peak

The opposite pole to anelastic relaxation is the static hysteresis .

Debye Peak

The solution for the ideal case (the anelastic standard body) is best obtained with the approach:

${\displaystyle \varepsilon =\varepsilon _{0}e^{i\omega t}}$; ${\displaystyle \sigma =(\sigma '+\sigma '')e^{i\omega t}=(M'+iM'')\varepsilon }$

• ${\displaystyle M(\omega )}$: Module of the material
• ${\displaystyle Q^{-1}=\tan {\phi }}$: Loss factor or material damping

In this case the relaxation maximum is at . This maximum is known as the Debye peak . ${\displaystyle {\frac {\Delta }{2}}}$ ${\displaystyle \omega \tau =1}$

Important types of relaxation spectra

0D effects

The anelastic relaxation via point defects is thermally activated and can only be caused by rearrangement of symmetry defects if their symmetry is lower than that of the crystal lattice .

Zener relaxation

The Zener relaxation is caused by the alignment of substitutive lattice atom pairs in the direction of stress or perpendicular to it.

Gorsky relaxation

The Gorsky effect is caused by the strain-induced movement of atoms in inhomogeneously deformed objects. Does it come B. to a bend in solids, some atoms migrate to the places where the atomic distance increases. This creates a diffusion flow. With Gorsky relaxation, however, the diffusion coefficient of rapidly diffusing interstitial atoms can be measured easily, such as B. of hydrogen atoms.

Snoek relaxation

While the Gorsky relaxation is caused by the volume expansion, the Snoek relaxation is caused by the reorientation of elastic dipoles.

The Snoek effect is created by the stress-induced movement of atoms inhomogeneously deformed objects. This causes a change in the elastic field, which is dependent on temperature and time.

Experimental methods

A DMA measuring device with which the vibrating reed method can also be carried out. The sample is clamped between the grips. Then an environmental chamber is placed over it in order to carry out measurements at different temperatures.

Overall, the numerous examination methods can be divided into four large groups (one static and four dynamic), which cover a huge range of at least 15 powers of ten on the time or frequency scale:

method	Elastic measurand	Anelastic measurand	application
Static tensile test	${\displaystyle E=\sigma /\varepsilon }$	${\displaystyle \sigma }$time-dependent ( constant) ${\displaystyle \varepsilon =}$ stress relaxation	Stress relaxation, creep
Subresonance Forced oscillation Excitation: ${\displaystyle \sigma =\sigma _{0}e^{i\omega t}}$	Strain amplitude ${\displaystyle \varepsilon _{0}}$	Loss angle ${\displaystyle \phi }$	forced vibrations
resonance	Resonance frequency ${\displaystyle f_{R}}$	damping ${\displaystyle Q^{-1}}$	free vibrations, standing wave
Ultrasonic pulse echo method	Speed ​​of sound ${\displaystyle c}$	Sound attenuation ${\displaystyle \alpha }$	running wave, pulse

While in the past mainly longitudinal and torsional pendulums were used in the experiments, nowadays the vibrating reed method has established itself. Here the temperature is usually changed continuously and the damping and the resonance frequency of the sample are measured.

Technical application

The Mechanical spectroscopy is used for the development of materials and production of components having desired damping characteristics, z. B. particularly low or particularly high attenuation.

Another possible application is the detection of hydrogen in metals.

See also

• Dynamic mechanical analysis

Individual evidence

1. ^ R. De Batist, LB Magalas: Mechanical Spectroscopy. In: RW Cahn, P. Haasen, EJ Kramer (Ed.): Materials Science and Technology. Volume 2B: Characterization of Materials. VCH, Weinheim 1994, ISBN 3-527-28265-3 .
2. ↑ C. Zener: Elasticity an Anelasticity in Metals. University of Chicago, Chicago 1948.
3. ↑ Arthur S. Nowick, BS Berry: Anelastic Relaxation in Crystalline Solids. Academic Press, New York 1972.
4. ^ LB Magalas: Mechanical Spectroscopy - Fundamentals. In: Solid State Phenomena. 89, 2003, pp. 1–22, doi: 10.4028 / www.scientific.net / SSP.89.1 .
5. ↑ MS Blanter, H. Neuhäuser, IS Golovin, H.-R. Sinning: Internal Friction in Metallic Materials, A Handbook. Springer Series in Materials Science, Vol. 90, Springer, Berlin Heidelberg New York 2007, ISBN 978-3-540-68757-3 .
6. ↑ R. Schaller, G. Fantozzi, G. Gremaud: Mechanical Spectroscopy Q ^ (- 1). Trans Tech Publications, Uetikon, Zurich 2001.
7. ↑ Alexander Strahl: Anelastic relaxations due to point defects and dislocations in Fe-Al alloys . 2006, urn : nbn: de: gbv: 084-11370 (dissertation, Technical University Carolo-Wilhelmina, Braunschweig).