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Circumferentially notched components of annealed copper were low-cycle fatigued under load-controlled condition being accompanied with mean load. In addition, their cyclic stress-strain responses were calculated under the corresponding loading conditions by means of elastic-plastic finite element method, where the constitutive equation proposed by the authors in their earlier paper was employed. The calculated nominal stress-diametral strain response at the minimum cross-section was in quite good agreement with the experiment, showing the validity of the present computation. The compressive mean stress generated at first one cycle at the notch-apex shakes down to be attenuated during the following cyclic loading under the condition of the load ratio Rp = -1.0, while this changes very slightly in the same direction during the further cyclic loadings at the Rp = -1/3 and 0. The stress ratio at the notch root Rσ is generally smaller than Rp, and the difference between them is much greater at Rp = -1/3 and 0 than at Rp = -1.0, in the sharper notch than in the duller notch, and under smaller applied cyclic loading than under the greater one. Incidentally, the tensile mean stress was yielded in the center region at the minimum cross-section of the notched components.

Cyclic stress-strain responses of annealed copper were numerically calculated in the minimum cross section of cylindrical notched components under axial load-controlled condition using elastic-plastic finite element method. The constitutive equation was developed for analyzing cyclic deformation by modifying the Johnston-Gilman's equation, which is derived from the concept of dislocation dynamics. The cyclic load-diametral displacement response of the notched component was in quite good agreement with the test result. The stress-strain response at a given position in the minimum cross section was calculated, which exhibited characteristic cyclic hardening. Then residual stress, mean stress, mean strain, and cyclic hardening behavior were successfully evaluated in the minimum cross section.

Circumferentially notched cylindrical components of annealed copper were cyclically strained under diametral-displacement-controlled conditions. The localized cyclic stress-strain responses at several locations in the minimum cross section including notch roots were calculated by introducing the constitutive equation for analyzing cyclic hardening behavior, which was derived on the basis of dislocation dynamics in our earlier paper, into the finite-element method. The calculations showed that the mean stress and strain were generated on the minimum cross section under diametral-displacement-controlled conditions with displacement ratio RDe=-l.0, and a convex axial stress distribution produced in the first tensile stroke changed to a distribution exhibiting greater stress at the outer locatins in the minimum cross section as the cyclic hardening process progresses. Meanwhile, the axial strain and the equivalent stress and strain increased at locations farther from the center in the minimum cross section throughout the entire cyclic straining process.

Rate dependence becomes more remarkable with increasing temperature in the inelastic behavior of engineering materials. When we deal with a stress/strain response in a structure, a sophisticated constitutive relationship must be applied to the stress analysis since the materials exhibit complicated characteristics under multiaxial stress states. The aim of this paper is to apply a unified constitutive model to finite element analysis of a notched cylinder. Experimental verification is carried out for a PCA material (Primary Candidate Alloy for a fusion reactor component). The local strain response near the notch root is measured by an electric-capacitance type strain gauge.

The tensile tests were performed for the sintered silicon nitride ceramic at displacement rates, δ=0.6, 0.06 and 0.006 mm/min in the temperature range from room temperature to 1400°C. According to the measurements of tensile displacement, the load P vs. displacementδrelationship was markedly influenced by test temperature and displacement rate. Young's modulus decreased with an increase in test temperature. The tensile strength was also reduced with increase in test temperature and decrease in displacement rate. The nominal stress-strain relationship was calculated from the measured P-δrelationship, under each test condition. Moreover, these stress-strain relationships were corrected so that the P-δcurve calculated using the elastic-plastic finite-element method agreed with the measured P-δcurve. The corrected stress-strain response seems to give the intrinsic response of the sintered silicon nitride ceramic at elevated temperatures. Furthermore, the development of the inelastic deformation zone was calculated through the elastic-plastic finite-element method on the basis of the corrected stress-strain curve at elevated temperatures.