Linear strain hardening in elastoplastic indentation contact

<jats:p>Finite-element analyses for elastoplastic cone indentations were conducted in which the effect of linear strain hardening on indentation behavior was intensively examined in relation to the influences of the frictional coefficient (μ) at the indenter/material contact interface and of the inclined face angle (β) of the cone indenter. A novel procedure of “graphical superposition” was proposed to determine the representative yield stress <jats:italic>Y</jats:italic><jats:sub>R</jats:sub>. It was confirmed that the concept of <jats:italic>Y</jats:italic><jats:sub>R</jats:sub> applied to elastic-perfectlyplastic solids is sufficient enough for describing the indentation behavior of strainhardening elastoplastic solids. The representative plastic strain of ε<jats:sub>R</jats:sub> (plastic) ≈ 0.22 tan β, at which <jats:italic>Y</jats:italic><jats:sub>R</jats:sub> is prescribed, is applicable to the strain-hardening elastoplastic solids, affording a quantitative relationship of <jats:italic>Y</jats:italic><jats:sub>R</jats:sub> = <jats:italic>Y</jats:italic> + ε;<jats:sub>R</jats:sub> (plastic) × <jats:italic>E</jats:italic><jats:sub>P</jats:sub> in terms of the strain-hardening modulus <jats:italic>E</jats:italic><jats:sub>P</jats:sub>. The true hardness <jats:italic>H</jats:italic> as a measure for plasticity is estimated from the Meyer hardness <jats:italic>H</jats:italic><jats:sub>M</jats:sub> and then successfully related to the yield stress <jats:italic>Y</jats:italic> as <jats:italic>H</jats:italic> = <jats:italic>C</jats:italic>(β,μ) × <jats:italic>Y</jats:italic> for elastic-perfectly-plastic solids and as <jats:italic>H</jats:italic> = <jats:italic>C</jats:italic>(β,μ) × <jats:italic>Y</jats:italic><jats:sub>R</jats:sub> for strain-hardening solids, by the use of a β- and μ-dependent constraint factor <jats:italic>C</jats:italic>(β,μ) ranging from 2.6 to 3.2.</jats:p>