Optimum definition of true strain beneath a spherical indenter for deriving indentation flow curves

Several methods have been suggested for deriving indentation flow curves using the instrumented indentation technique, in which true stress and true strain are defined with indentation parameters. The definition of true stress is nearly the same in all methods, but the definitions of true strain fall into two categories, sine function and tangent function. We adopted the work-hardening exponent to determine the definition appropriate in obtaining accurate indentation flow curves. The work-hardening exponent was proven to be affected only by the definition of true strain and not by other parameters when the effect of real contact depth was eliminated using finite element analysis. The sine function yields too large work-hardening behaviors for materials that obey power-law work-hardening, but the tangent function evaluates them accurately. The definition based on the tangent function was thus determined to be more appropriate in deriving the indentation flow curve.