### STP378: Cyclic Plastic Strain Energy and Fatigue of Metals

Morrow, JoDean

*Professor of theoretical and applied mechanics, University of Illinois, Urbana, Ill.*

Pages: 43 Published: Jan 1965

**Abstract**

At high cyclic stresses, repeated plastic strain is the predominant cause of energy dissipation in metals. Damping due to cyclic plastic strain energy may be distinguished from anelastic damping as follows: (1) there is usually a transient change in the shape and size of the hysteresis loop at the start of a cyclic test; (2) the cyclic rate of change and the cyclic steady-state shape and size of the loop are strongly dependent on the stress amplitude, but only weakly dependent on test frequency and temperature (damping peaks are rare) and (3) permanent micro- and macrostructural changes are observable in the metal, particularly the formation and cycle-dependent intensification of slip bands in which fissures nucleate and propagate to form microcracks which culminate in fatigue fracture.

Experimental techniques and methods of interpreting results are reviewed and typical phenomenological cycle-dependent deformation and fracture behavior of metals are illustrated. It is shown that a stable hysteresis loop quickly develops under cyclic conditions. The cyclic stress-strain curve is defined as the locus of tips of several stable loops obtained at different cyclic strain ranges. Expressions are presented for mathematically representing the individual loops and the locus of their tips, and a number of experimental methods are discussed for determining the stable cyclic stress-strain properties or the material constants in the mathematical expressions.

A set of six empirical fatigue fracture properties are defined for metals in terms of their resistance to completely reversed cyclic stress and strain. Past efforts to use mechanical hysteresis energy as a criterion for fatigue damage are reviewed, and a descriptive theory of fatigue based upon cumulative plastic strain energy as a criterion for fatigue damage and elastic strain energy as a criterion for fracture are developed. The theory quantitatively relates the fatigue properties of a metal to its cyclic stress-strain properties.

**Paper ID:** STP43764S

**Committee/Subcommittee:** E08.05

**DOI:** 10.1520/STP43764S

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