The subloading surface model has been formulated and applied to the prediction of cyclic loading behavior of metals. However, the existing formulation of this model is limited to metals exhibiting only the cyclic hardening. In the present paper, the material functions prescribing the elastic-plastic transition are extended so as to describe the inverse and reloading behavior and the strain accumulation in cyclic loading more accurately for metals exhibiting not only the cyclic hardening but also the cyclic softening behavior. The experiments on the uniaxial cyclic loading of the seamless steel pipe P110 which exhibits the cyclic softening are performed for the mechanical ratcheting and the constant strain amplitudes. The simulations to the test data are performed by using the same set of material constants. Then, the validity of the extended model for the description of cyclic loading behavior of the seamless steel pipe is verified by comparisons with the test data.

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Numerical analysis method considering microstructure and deformation near the grain boundary is proposed in order to fundamentally evaluate strength properties of steels. The parameters that characterize grain shape, such as grain diameter, aspect ratio and grain orientation, are quantified for ferritic-phase steel. Two dimensional grain shapes reflecting the distribution of those parameters are modeled by the use of Voronoi tessellation that is the method to divide the region into arbitrary polygons. Stress distribution in the case of tensile load applied to such a set of grains is calculated by Finite Element Method (FEM). Mismatch of displacement near the grain boundary is also considered in the calculation as a boundary slip. Discontinuity of stress distribution on grain boundary is seen even though the single-phase steel is used and the same stress-strain property is given to all grains. Stress concentration around triple junction is also observed due to results of considering the mismatch of displacement near the grain boundary. The effects of distribution of grain shape parameters on stress distribution are investigated for the fundamental application of this analysis model and the difference of stress distribution is estimated. It can be mentioned that numerical analysis model in this paper is available for the evaluation of strength characteristics of steels.

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