The simulations described in this paper are essentially identical to
those carried out for a prev study [10].They were carried
out using the finite element code NIKE2D [15], which is an
implicit, finite deformation, large strain code for plane strain,
plane stress, and axisymmetric analyses. The model used for this
study consisted of 2466 4-node quadrilateral elements and 2579 nodes.
The analysis was conducted in axisymmetric mode, thus modeling a
conical indenter (following Bhattacharya and Nix [6]). The
included angle of the conical indenter was 136. (That is, the
angle between the indenter and the surface of the specimen was
22
.) The contact between the indenter and the specimen
surface was modeled using a slideline (adopting the terminology of the
NIKE codes) and the indenter was modeled using 66 elements. The
contact surface was assumed to be frictionless. The material model
used for the specimen was linearly elastic-perfectly plastic, as the
modeling of strain hardening has been shown to be relatively
unimportant for hardness simulation [6]. The indenter was
modeled as an elastic material with a stiffness (elastic modulus) 45
times that of the specimen. Higher stiffnesses tended to cause the
simulation to fail.
The nominal properties used for the analysis are shown in Table 1. The effect of the implantation is modeled by varying the yield strength of the specimen with depth from the surface. The yield stress distribution was assumed to match that of the implanted nitrogen ion concentration, which was found to be fairly linear. Hence, the yield stress in the implanted region of the finite element model was assumed to be linear, with a peak at the surface. No appreciable nitrogen was found deeper than 100 nm, so the yield stress was assumed to be a constant at depths greater than this value. In other words, the yield stress was maximum at the surface, dropped linearly to the bulk value (825 MPa) at a depth of 100 nm, and maintained this bulk value throughout the remainder of the sample. The linear region of the yield stress distribution was modeled using 15 different sets of material properties, so the implanted layer was modeled using 15 elements through its thickness. The elastic modulus was held constant throughout the sample.
