Combined hardening parameters of steel CK45 under cyclic strain-controlled loading: Calibration methodology and numerical validation


  • Bahman Paygozar Department of mechanical engineering, TED University, Ankara, Turkey. Phone: +90-312-585-0270
  • S.A Dizaji Department of mechanical engineering, TED University, Ankara, Turkey
  • M.A Saeimi Sadigh Department of Mechanical Engineering, Azarbaijan Shahid Madani University, Tabriz, Iran



Combined hardening, Chaboche model, stabilized hysteresis curves


This study is to indicate the methodology of investigating the behavior of materials in the plastic domain while bearing cyclic loading i.e. low cycle fatigue. Materials under such loading, which experience huge amount of plastic deformation, are affected by the hardening or softening effects of loading which should be taken into account in all applications and numerical simulations as well. This work investigates the methodology of obtaining the nonlinear isotropic and kinematic hardening of steel CK45. To find the parameters of the above mentioned combined nonlinear isotropic/kinematic hardening one tensile test as well as three strain-controlled low cycle fatigue tests are carried out to extract the monotonic stress/strain curve and three diagrams of hysteresis curves, respectively. Then, four parameters necessary to simulate the nonlinear isotropic/ kinematic behavior of the material are extracted by means of curve fitting technique using MATLAB software. Afterwards, the accuracy of the data extracted from the experimental tests using the proposed methodology, are verified in a finite element package, ABAQUS, through implementing two user defined subroutines UMAT written in FORTRAN. It is indicated that the computed constants draw stress-strain curves much closer to experimental responses than isotropic hardening model does.  Eventually, the numerical results acquired by simulating the behavior of the sample under cyclic loading with importing the constants, calculated via combined hardening model, to ABAQUS reflects results highly close to the experimentally obtained response of the sample. It means that the procedure used to find the constants is accurate enough and consequently the constants computed are able to be used in both ABAQUS and subroutines.     


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How to Cite

B. Paygozar, S. Dizaji, and M. Saeimi Sadigh, “Combined hardening parameters of steel CK45 under cyclic strain-controlled loading: Calibration methodology and numerical validation”, J. Mech. Eng. Sci., vol. 14, no. 2, pp. 6848–6855, Jun. 2020.