Analysis on the determination of Chaboche and Bouc-Wen parameters for a quenched and tempered steel

High-strength metal alloys usually have a purely elastic behaviour during high-cycle fatigue regime. Nevertheless, some materials such as low alloy steels undergo plasticity even in high-cycle fatigue, and thus just considering a purely elastic behaviour significant prediction errors can be obtained. The Chaboche Isotropic-Kinematic Hardening (CIKH) [1, 2] model provides a versatile and realistic description of the material stress-strain behaviour under general multiaxial cyclic loadings. In this work, the global properties of the experimental cycles are introduced for the calibration. The imposed conditions are: the hysteresis areas, the peak stress values and the tangent slopes at the extreme points of the stabilized cycles, which represent the most significant loading parameters for the majority of the fatigue life loadings. The data just mentioned are taken from strain-controlled tests on plain specimens manufactured in steel 42CrMo4+QT. One linear and two non-linear backstress components of the kinematic hardening model are introduced. Two stabilized cycles are required to identify the main kinematic parameters whereas the asymptotic ratcheting rate, obtained from stress-controlled tests, is then used to determine the rate parameter of the slightly nonlinear backstress component. Finally, a fourth backstress component is added to improve the prediction near the elastic limit of the stabilized cycle of the strain-controlled test. Once the kinematic parameters are obtained, isotropic hardening laws can also be identified, by considering the evolution of the extreme points of the strain-controlled cycles before stabilization. Alternatively, the Bouc-Wen model [3, 4] can provide a reliable representation of nonlinear hysteretic phenomena, and a classic nonlinear least squares approach, based on the Levenberg- Marquardt algorithm, is employed to calculate the values of its constants. The performances of the two proposed techniques are compared, and a final discussion is provided. References [1] Chaboche, J.: Time-independent constitutive theories for cyclic plasticity, Int. J. Plast., 2 (2), 149–88 (1986). DOI: 10.1016/0749- 6419(86)90010-0 [2] Voce, E.: The relationship between stress and strain for homogeneous deformations, J. Inst. Met., 74, 537–562 (1948). [3] Bouc, R.: Forced vibrations of mechanical systems with hysteresis, Fourth Conference on Nonlinear Oscillations (Prague, Czechoslovakia, 5–9 September 1967), 315–321 (1967). [4] Wen, Y.K.: Method for Random Vibration of Hysteretic Systems, J. Eng. Mech. Div., 102 (2), 249–263 (1976). DOI: 10.1061/JMCEA3.0002106