The elastic deformation on indenter is inevitable and has significant influences on indentation measurements. From a systematic finite element analysis for the indentation of elastic-perfectly plastic half-space by elastic spherical indenter, the piecewise linear characteristics of post-yield deformation are observed. Linear contact constitutive equations depending on elastic deformation of the indenter are derived by curve-fitting approach. An explicit theoretical contact model is presented to predict real contact radius, contact force and deformations of both contacting bodies ranging from elastic to finite plastic deformations. The applicability of the model is verified numerically and experimentally by static indentations and low-to-moderate velocity impacts.

压头的弹性变形是不可避免的，对压痕测量有重大影响。通过弹性球形压头对弹塑性半空间的压痕进行系统的有限元分析，观察了屈服后变形的分段线性特性。通过曲线拟合方法推导出取决于压头弹性变形的线性接触本构方程。提出了一个明确的理论接触模型来预测实际接触半径、接触力和两个接触体的变形，从弹性变形到有限塑性变形。该模型的适用性通过静态压痕和中低速度冲击在数值和实验上得到验证。