On the Choice of an Offset-strain Value in Determining Yield Surfaces

Abstract

The choice of an offset-strain value in experimental determination of the yield surfaces, that controls the plasticity condition, the size and shape of the crack-tip plastic zone and the value of the correction factor for plasticity, is discussed. The results are illustrated by yield curves for aging steel in the metastable state under biaxial tension.1.Introduction. The shape and the size of the plastic zone near the crack tip affect fracture behavior of metallic materials, and the length of the plastic zone in the direction of crack propagation affects the correction factor in the expression for the effective crack length. The shape and size of the plastic zone are defined by the plasticity condition represented by the yield surface in the stress space. The yield surface depends on the yield strength, degree of anisotropy, character of strain hardening (in the case of subsequent yield surfaces), material structure and the offsetstrain value.Correlation of the plastic zone size with the strain hardening parameters and the plasticity condition were considered earlier on the example of mode I crack (Bastun, 1999). The influence of the material structure in the plastic zone on the fracture toughness characteristics was addressed in the work of Kaminsky and Nizhnik (1995). The problem of choice of the offset-strain value has been discussed from 1970's (Zyczkowski, 1981;Michno and Findley, 1976;Kachanov, 1971;Phillips, 1974), but it has not been fully clarified (Lebedev et al, 2000;Miastkowski and Szczebiot, 2001).2. Experimental procedure. We study, on the example of aging N18K8M5T steel, the yield surface for biaxial tension, for different offset-strain values δ (from 0 to 0.2%) and consider physical processes in the material in the range of small elastoplastic strains. The steel contains, in wt.%, 0.02C, 18.2Ni, 0.68Ti, 5.03Mo, 8.6Co, 0.11Al, 0.02Si, 0.005P, 0.005S) (Nizhnik and Usikova, 2005). The study was carried out using tubular specimens (the gauge length, outer diameter, and wall thickness are 100, 30, and 0.8 mm, respectively) fabricated from a cold-drawn rod. Blanks for specimens were subjected to austenization at temperature 860ºC (maintained for 25 min) with subsequent cooling to room temperature in the atmosphere of argon. As a result, the material has acquired the metastable structure of martensite, which represents a solid solution oversaturated with alloying elements. Biaxial tension was performed in accordance with the technique described in the works (Bastun, 1994; Bastun and Kaminskii, 2005), which involves loading specimens with an axial force and internal pressure along different rectilinear paths using a force type testing machine. 3. Results and discussion. As the preliminary tests showed, in the range of small elastoplastic strains the material exhibits substantial difference in the tensile and compressive strengths, with the tensile strength being higher. This fact is attributed to LETTERS IN FRACTURE AND MICROMECHANICS