Dislocation behavior in fatigue IV. Quantitative interpretation of friction stress and back stress derived from hysteresis loops

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Abstract

The dislocation model developed in Parts I – III is examined quantitatively. According to this model loop patches result from random trapping of glide dislocations whereby a constant fraction of them are incorporated into the loop patches in each cycle. The dislocation density in these is equilibrated rather easily because of the low friction stress on the loops in prismatic glide. As another result of the low friction against prismatic glide the loop patches adjust towards optimum dislocation density such that the stored energy is minimized. This imparts to them volume elasticity and properties similar to Taylor lattices. The back stress, which was determined in Part II from an analysis of the hysteresis loops, is identified with the maximum elastic reaction of the dislocation lattice against the imposed strain at the end of each cycle. Correlated with this is a friction stress of closely similar magnitude arising firstly because relative motions of the dislocation lattices beyond the confines of their immediate energy minima are irreversible and secondly because of the anchoring of glide dislocations at loop patch surfaces through local loop polarization. This feature explains a major experimental result of Part II, namely the equality of the friction stress and the back stress except for that part of the friction stress which can be ascribed to jog dragging and point-defect hardening. With respect to deformations within the momentary energy valley the dislocations in the loop patches respond quasi-elastically as if the elastic constant of the material was too low. The magnitude of the apparent elastic constant depends on the configuration of the dislocation lattice. Comparison with the experimentally observed quasi-elastic behavior indicates that the lattice is nearly close packed. Further, comparison with the experimentally determined dislocation density in the loop patches at saturation suggests that in all cases about 10% of the glide dislocations become trapped in the loop patches. The magnitude of the back stress and its dependence on the number of cycles and fatigue strain range derived from the model is in almost perfect agreement with observations; in fact it is well within the limits of reliability of both theory and experiment. Another check of the theory is possible via the changes in hysteresis loop shape with the number of cycles beyond the cumulative strain at which the loop patches can accommodate the fatigue strain by simple “flipping”. The agreement between the predicted transformation of both stress and strain in proportion to the square root of the number of cycles and the observed changes in hysteresis loop shape was found to be excellent. These results and those of Parts II and III apply to the whole range of fatigue amplitude in the plateau region which is characterized by the formation of persistent slip bands at a stress of about 30 MPa.

References (18)

  • D. Kuhlmann-Wilsdorf et al.

    Mater. Sci. Eng.

    (1977)
  • D. Kuhlmann-Wilsdorf et al.

    Mater. Sci. Eng.

    (1979)
  • D. Kuhlmann-Wilsdorf

    Mater. Sci. Eng.

    (1979)
  • G.I. Taylor
  • F.R.N. Nabarro

    Adv. Phys.

    (1952)
    F.R.N. Nabarro

    Adv. Phys.

    (1952)
  • A. Seeger et al.

    Phys. Status Solidi

    (1966)
  • T.R. Duncan et al.

    J. Appl. Phys.

    (1968)
  • J.T. Moore et al.

    Phys. Status Solidi

    (1968)
  • G. Masing

    Z. Phys.

    (1947)
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