Anelasticity and Mechanical Spectroscopy of Materials

Instructor: Igor S. Golovin

Course Summary

Anelastic behavior of metallic materials is their fundamental property which is particularly important during cyclic loading of products and designs. Ability of materials to dissipate the energy of mechanical vibrations may be useful or harmful property, depending on their functionality. High damping alloys are effective, and sometimes the only possible solution of suppressing of unwanted vibrations and, as a result, reducing noise. On the other hand, the experimental and theoretical analysis of energy dissipation spectra for mechanical vibrations, depending on their frequency and amplitude, as well as temperature, called mechanical spectroscopy, provides a unique opportunity to explore not only the structure but also the mobility of lattice defects: interstitial and substitution atoms, dislocations, grain boundaries and boundaries of magnetic domains and much more.

The main objective of this course is to show opportunities of mechanical spectroscopy in solving practical problems of physical and applied materials science, to master modern technology of the experiment; to identify processes and materials for which the characteristics of mechanical spectroscopy are the main criteria of operational reliability; and to discuss the relationship of the structural state of the material with its behavior under cyclic loading.

Course Format

Hours of lectureHours of discussionHours in laboratoryHours of independent studyTotal numbers of hours

Learning Outcomes

  • Acquisition of knowledge in the field of theoretical and experimental concepts of elastic and anelastic behavior of metallic materials under cyclic loading;
  • Demonstrate knowledge of physical mechanism of relaxations processes due to point defects, dislocations, grain boundaries etc.;
  • Be aware of new materials with special anelastic properties (high damping alloys, shape memory resonant acoustic and elastic elements of the membrane and others.);
  • Know the basic experimental techniques of mechanical spectroscopy of materials and have an ideas about the basic laws of formation of elastic and damping characteristics of the materials needed for engineering design and construction of new alloys and composites.

Course Content


  • Elasticity, anelasticity, visco-elasticity. Hooke law in complex form. Theory of elasticity as a background for modern engineering. Relaxation effects. Elasticity vs. Anelasticity or Engineers vs. Physicists: from Hooke to our days. Vibrations (from Violin Concert to Earthquake). How to find a submarine? Terms and definitions. Rheological approach.


  • Loading: static and dynamic loading. Relaxation processes. Dissipated energy.
  • Standard anelastic solid. Zener model for “standard solids”.
  • Debye equations. Thermally activated relaxation processes.
  • Frequency and temperature dependent damping spectra. Similarities and differences.
  • Point defects relaxations. Selection rule. Examples:
    • The Snoek effect — relaxation due to interstitial atoms “diffusion under stress” in bcc solution,
    • The Zener effect — relaxation due to reorientation of pairs of substitutional solute atoms.
  • Amplitude dependent damping. Granato and Lücke string model. “Dragging” and “break away” effects. Microplasticity. Contribution to damping from magnetic ordering.
  • Relaxation effects caused by interaction of dislocations and point defects (Bordoni, Hasiguti, and Köster’s effect).
  • Structural relaxation and relaxation due to phase transitions. Reversible martensitic transformation.


  • Phenomena:
    • Diffusion (low temperature)
    • Solubility
    • Interatomic interaction
    • Fatigue, microplasticity
    • Ageing, cold work
  • Materials:
    • Crystalline materials: metals, alloys, intermetallic compounds
    • Amorphous metallic materials and quasicrystals
    • Cellular materials (foams, sponges, sintered materials)
    • High damping materials

Reading List

  1. Blanter M.S., Golovin I.S., Neuhäuser H, Sinning H.-R. Internal Friction in Metallic Materials. A Handbook. Springer Verlag, 2007, p. 540
  2. A. S. Nowick and B. S. Berry, Anelastic Relaxation in Crystalline Solids, Academic Press, New York (1972).
  3. Schaller, R., Fantozzi, G., Gremaud, G. (Eds.) (2001) Mechanical Spectroscopy Q—1 2001 with Applications to Materials Science. Trans Tech Publications, Switzerland 2001.
  4. K. L. Ngai, Relaxation and Diffusion in Complex Systems, Springer (2011).


Class participation20%
Homework assignments30%
Final exam50%