Unloading behavior of low velocity impact between elastic and elastic–plastic bodies

Unloading Behavior of Elastic-power-law Strain Hardening Materials Indented by Elastic Indenter

“…14 with n = 0 (elastic-perfectly plastic material),  =1.501 and 1.502. They are nearly as the same as  =1.5 for the Hertzian-type unloading law [43]. However, when n > 0,  is distinctly smaller than 1.5.…”

“…The shape of the residual cavity is assumed to be a spherical surface with a uniform radius res R after the indenter is unloaded and the material elastically recovers. This assumption was validated by Chen, Yin [43] for the elastic-perfectly plastic materials indented by elastic sphere. The importance of this assumption is that the elastic contact solution exists during the unloading of spherical indentation.…”

“…To predict the elastic-plastic contact behavior accurately, the unloading phase is as important as the loading phase [40][41][42][43][44]. The measurement of material properties, like yield strength, and elastic modulus is always relied on the analysis of the unloading phase [45].…”

“…Yin [36] and Chen, Yin [43] revised Strong's geometry similarity to calculate *e R by introducing a scaling factor. Different solving equations for *e R were suggested by Brake [53] and Big-Alabo, Harrison [28] for unloading during elastic-plastic and fully plastic loading phases, respectively.…”

“…Rodriguez, Alcala [70] showed that there are 26% and 17% permanent indentation errors for the spherical indenter and for the conical and Berkovich indenters, respectively, even though the reduce modulus are used in the conventional model to take into account the indenter elastic deformation. For the unloading behavior of elasticperfectly plastic materials, the indenter elastic deformation has been considered and found to have significant influence recently by Dong, Yin [36] and Chen, Yin [43]. A comprehensive study of unloading behavior for power-law strain hardening materials accounting for the indenter elasticity is still lacked.…”