In the last decade, instrumented indentation test has been widely used to determine the mechanical properties of different materials and especially for metals. The mechanical properties such as Young modulus, yield stress, hardening exponent, and stress-strain curve were determined with the help of the load–displacement curve of the continuous indentation test. The method consists of pushing an indenter in a material sample and the applied load and the indenter displacement are measured. In this research the load on the indenter was considered as cyclic and varied from zero to Fmax. Because of the Bauschinger effect, the hysteresis loops were formed. With the help of these hysteresis loops, nonlinear kinematic hardening parameters of the Armstrong–Freiderick (A-F) model can be determined. Spherical indenter was used and the sample was considered isotropic. The material behavior was modeled by the A-F rule. The test was modeled by the finite element method. An axi-symmetric mesh was used. The A–F model constants, C and γ, were varied to obtain their effects on the hysteresis loops. Maximum applied load was considered constant for different finite element modeling and the maximum and residual displacements were calculated from the simulations results. The normalized maximum and the residual displacements were increased as a function of the cycles. It was shown that these parameters value and their rate are dependent on the material model constants. These dependences were shown for different examples which can help to characterize the A-F model constants by the cyclic spherical indentation tests.

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