On the correlation of indentation experiments

Abstract

The relationship between indentation pressure produced by cones, pyramids and spheres, and the mechanical properties of elastic-plastic materials is considered, based on previous work which uses the expansion of a cavity in an elastic-plastic material. According to the earlier model, there are three zones: a hydrostatic 'core' of which the indenter is embedded; a hemispherical shell, where plastic flow is taking place; and beyond this the elastic hinterland. An improved correlation with experimental results is obtained if it is assumed that the hemispherical core is a region in which the stresses are changing from purely hydrostatic to values which satisfy the Von Mises yield criterion. A further improvement results if a correction is made for the lack of geometric similarity of the strain field in indentations by spheres.

Two new expanding cavity models for indentation deformations of elastic strain-hardening materials

“…However, no detail was provided in Johnson (1985) regarding how the correction term was mathematically obtained, which makes it difficult for one to extend JohnsonÕs modification for elastic-perfectly plastic materials to elastic strain-hardening materials. In comparison, the modification by Studman et al (1977), which considers the variations in the stresses in the hemispherical core beneath the indenter from hydrostatic to other values that obey the von Mises yield condition, appears to be detailed, simple and also leads to better predictions (i.e., closer to the experimental data) than the original ECM of Johnson does. This modification, being also approximate (and thus nonunique), was motivated by the need to better correlate the predicted hardness values with experimentally measured ones and was based on the observation that there exists a jump (step-discontinuity) in r e (=r hh À r rr ) from r = a À , where r e = 0 due to the assumed hydrostatic stress state with r hh = r rr = r uu = Àp, to r = a + where r e = r y for elastic-perfectly plastic materials.…”

“…On the other hand, JohnsonÕs ECM in its original form is known to predict lower hardness values than experimentally measured ones (e.g., Studman et al, 1977). As a result, attempts have been made to modify the original ECM of Johnson (1970).…”

“…This modification, being also approximate (and thus nonunique), was motivated by the need to better correlate the predicted hardness values with experimentally measured ones and was based on the observation that there exists a jump (step-discontinuity) in r e (=r hh À r rr ) from r = a À , where r e = 0 due to the assumed hydrostatic stress state with r hh = r rr = r uu = Àp, to r = a + where r e = r y for elastic-perfectly plastic materials. Hence, the idea used in Studman et al (1977) to improve JohnsonÕs ECM for elastic-perfectly plastic materials is adopted to modify the two ECMs for elastic strain-hardening materials developed above. The modification procedure follows that used in Studman et al (1977) and is therefore excluded here.…”

“…Hence, the idea used in Studman et al (1977) to improve JohnsonÕs ECM for elastic-perfectly plastic materials is adopted to modify the two ECMs for elastic strain-hardening materials developed above. The modification procedure follows that used in Studman et al (1977) and is therefore excluded here. The major difference is that r y in the von Mises yield condition jr hh j r=a À r rr j r=a j = r y used there is now replaced by r e j r=a (i.e., the effective stress on the interface r = a).…”

Material Removal and Specific Energy in the Dynamic Scratching of Gamma Titanium Aluminides

“…The relation given by Eq. (8) [40,41]. In a typical adiabatic process, η could be as high as 1.0 [36].…”