13th International Conference on Fracture June 16–21, 2013,Beijing, China -2- 2. Plasticity for austenitic steel with martensite phase transformation 2.1 Kinetics of Martensite Transformation The previous experimental observations confirm that the austenitic steel AISI304 transforms to martensite phase due to plastic deformations. The volume fraction of martensite phase increases with deformations. Olson and Cohen [7] studied the phase transformation and suggested an isotropic phase transformation law that describes the martensite content evolution as a function of plastic strain and temperature. The model was extended by Stringfellow et al [8] by incorporating the dependency of the stress triaxiality. According to the Stringfellow evolution of the martensite content, χ, depends on stress triaxiality η and plastic strain εp which reads χ= 1− χ ( ) Aεp +Bη ( ) (1) with the stress triaxiality η= σm / σe and the equivalent plastic strain εp = 2 3 εij p ε ij p .σm and σe denote hydrostatic stress and Mises stress, respectively. A and B are model parameters generally depending on the temperature and the stress state. For uniaxial material testing η is constant ( η=1/3 for uniaxial tension and -1/3 for uniaxial compression, respectively), so that the martensite content is a monotonic function of the plastic strain and can be expressed as χ=1−exp −Aεp ( ) . (2) The Stringfellow model predicts a monotonic relationship between the stress triaxialityrate without explicit effects of the stress triaxiality. Santacreu et al. [9] suggested an alternative evolution law reads χ= χmax − χ ( )mD Dε p ( )m−1 εp (3) with D= D0 +D1 η. (4) In the expressions above χmax denotes the maximum fraction for martensite transformation, D1 represent effects of stress triaxiality, m and D0 denote influences of plastic strain. In the original suggestion of Santacreu et al. [9] the parameter D should further related with the Lode angle, i.e. the third deviatoric stress invariant allowing to build the surface corner in the stress space. Since εp is non-negative, the martensite transformation is a monotonic function of time. Therefore, the model only considers austenite-martensite transformation, while the reverse transformation is prohibited. The total form of the Santacreu model reads ( ) ( ) max 1 exp p m D χ χ ε ⎡ ⎤ = − − ⎢ ⎥ ⎣ ⎦ (5) forgiving stress triaxlity. Both martensite transformation models predict a linear correlation between the plastic strain rate and transformation rate. Stringfellow addressed additionally that the transformation is further influenced by the stress triaxialityrate which is generally rather difficult to be identified in material testing. Furthermore, the martensite transformation may occur for varying stress triaxiality without plastic deformations, which is not confirmed in the stainless steel SS304. A major difference is the explicit expression to the stress triaxiality which allows to apply for FEM computations. In the present work the Santacreu model will be used for considering plasticity of the SS304 under consideration of the martensite transformation. 2.2 Plasticity with phase transformation The conventional J2 plasticity is applicable for the present stainless steel without considering
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