Inelastic constitutive models for the simulation of a cyclic softening behavior of modified 9Cr-lMo steel at elevated temperatures

In this paper, the inelastic constitutive models for the simulations of the cyclic softening behavior of the modified 9Cr-1Mo steel, which has a significant cyclic softening characteristic especially in elevated temperature regions, are investigated in detail. To do this, the plastic modulus, which primarily governs the calculation scheme of the plasticity, is formulated for the inelastic constitutive models such as the Armstrong-Frederick model, Chaboche model, and Ohno-Wang model. By implementing the extracted plastic modulus and the consistency conditions into the computer program, the inelastic constitutive parameters are identified to present the best fit of the uniaxial cyclic test data by strain-controlled simulations. From the computer simulations by using the obtained constitutive parameters, it is found that the Armstrong-Frederick model is simple to use but it causes significant overestimated strain results when compared with the Chaboche and the Ohno-Wang models. And from the ratcheting simulation results, it is found that the cyclic softening behavior of the modified 9Cr-1Mo steel can invoke a ratcheting instability when the applied cyclic loads exceed a certain level of the ratchet loading condition.

[1]  J. Chaboche,et al.  On the Plastic and Viscoplastic Constitutive Equations—Part II: Application of Internal Variable Concepts to the 316 Stainless Steel , 1983 .

[2]  W. Prager,et al.  A NEW METHOD OF ANALYZING STRESSES AND STRAINS IN WORK - HARDENING PLASTIC SOLIDS , 1956 .

[3]  Y. H. Kim,et al.  Effect of boron contents on weldability in high strength steel , 2007 .

[4]  J. C. Simo,et al.  Consistent tangent operators for rate-independent elastoplasticity☆ , 1985 .

[5]  Tasnim Hassan,et al.  Anatomy of coupled constitutive models for ratcheting simulation , 2000 .

[6]  J. Chaboche.  Constitutive equations for cyclic plasticity and cyclic viscoplasticity , 1989 .

[7]  Yukio Takahashi,et al.  Ratchetting of viscoplastic material with cyclic softening, part 1: experiments on modified 9Cr–1Mo steel , 2005 .

[8]  Yukio Takahashi,et al.  Ratchetting of viscoplastic material with cyclic softening, part 2: application of constitutive models , 2005 .

[9]  C. O. Frederick,et al.  A mathematical representation of the multiaxial Bauschinger effect , 2007 .

[10]  J. Chaboche,et al.  On the Plastic and Viscoplastic Constitutive Equations—Part I: Rules Developed With Internal Variable Concept , 1983 .

[11]  Jean-Louis Chaboche,et al.  On some modifications of kinematic hardening to improve the description of ratchetting effects , 1991 .

[12]  Jongsoo Lee,et al.  Constrained minimization utilizing GA based pattern recognition of immune system , 2007 .

[13]  N. Ohno,et al.  Kinematic hardening rules with critical state of dynamic recovery, part I: formulation and basic features for ratchetting behavior , 1993 .