Local Deformations And Analysis Of Phase Transformations

The local deformation was found in experiments is not same to traditional local deformation,such as Lüders-type deformation and local deformation of NiTi alloy tube under uniaxial tension or compression. All of local deformation generate from uniform deformation field. Stress and deformation gradient across interfaces between local deformation field and undeformation field are discontinuity. It is different from traditional local deformation. The present method of characterizing local deformation is that the geometric imperfection was brought in local deformation. But this method can not simulate discontinuity of Stress and deformation gradient across interfaces between local deformation field and undeformation field.In this paper, we establish a method that we regard local deformation field and undeformation field as elastic phase and plastic phase respectively, and analyze it by theory of phase transition in elastoplastic materials. Discontinuity of Stress and deformation gradient across interfaces between local deformation field and undeformation field are considered and continuity of traction and displacement across interface and the Maxwell relation is imposed. In this case, the inclination angle of the localized deformed band, the kink angle of the strip, the stresses field and strains in the localized deformed field can be predicted.In present paper, the local deformation in elastoplastic materials with strain-softening behaviour under uniaxial compression is simulated. As an illustration, a mechanical property curve of fine grained steel under uniaxial tension/compression is obtained from its peak-drop-plateau-type curve under uniaxial tension/compression by theory of phase transition. By analysis of phase transformation, the Maxwell stress, the inclination angle of the Lüders band, kink angle of the strip, and both stress and strain in the Lüders band are predicted analytically while local deformation. The predicted results are in reasonable agreement with the experimental measurements. In this paper, we also analyze local deformation in elastoplastic materials with strain-softening behavior under pure shear. Theoretical, the localized deformed band under plane shear still can appear. The direction of localized deformed band is identical with the direction of shear. As an illustration, a NiTi alloy plate under plane shear is numerically analyzed.We explain why no locally deformed spiral band was observed in experiments on thin-walled tubes under torsion (pure shear). That is to say, when the inclination angle of the localized deformed band is predicted to be , the localized deformed band cannot be observed in experiments. 90...