Derivation of Constitutive Equation for Describing Cyclic Deformation in Terms of Dislocation Dynamics and Its Application to Fatigue under Multiaxial Stress Loading.

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In the present study, the stress-strain field was calculated in the vicinity of the crack tip by means of the elastic-plastic finite-element method in annealed through-thickness-cracked copper specimens, where the constitutive equation derived on the basis of dislocation dynamics by the authors was modified to apply to cyclic loading analysis with large deformation. The analysis was carried out under cyclic loading at stress ratio R_<sigma>=-1. Then special attention was given to the strain and crack opening-closing behaviors with the cyclic hardening during first a few cycles. At the same time, calculated behaviors were compared with the test result measured by means of the grid method. The main results obtained are summarized as follows.(1) The cyclic hardening behavior was expressed quantitatively by the elastic-plastic finite-element method, using the constitutive equation derived on the basis of dislocation dynamics modified to apply to the large deformation.(2) From the load-controlled cyclic test, a cyclic strain range in the vicinity of the crack tip tended to decrease to the stable constant value with an increase in the number of stress cycles.(3) The calculated localized deformation behavior in the vicinity of the crack tip quantitatively and qualitatively described the test results very well. It suggested that this constitutive equation is effective to describe these behaviors.(4) The stress-strain hysteresis loop of the element that is located at the minimum cross section ahead of crack tip and variation of stress/strain distribution was shown by means of F.E.M.analysis. These result were in probable agreement with those obtained experimentally in (3).