Strain Hardening From Elastic–Perfectly Plastic to Perfectly Elastic Flattening Single Asperity Contact

Abstract

For elastic contact, an exact analytical solution for the stresses and strains within two contacting bodies has been known since the 1880s. Despite this, there is no similar solution for elastic–plastic contact due to the integral nature of plastic deformations, and the few models that do exist develop approximate solutions for the elastic–perfectly plastic material model. In this work, the full transition from elastic–perfectly plastic to elastic materials in contact is studied using a bilinear material model in a finite element environment for a frictionless dry flattening contact. Even though the contact is considered flattening, elastic deformations are allowed to happen on the flat. The real contact radius is found to converge to the elastic contact limit at a tangent modulus of elasticity around 20%. For the contact force, the results show a different trend in which there is a continual variation in forces across the entire range of material models studied. A new formulation has been developed based on the finite element results to predict the deformations, real contact area, and contact force. A second approach has been introduced to calculate the contact force based on the approximation of the Hertzian solution for the elastic deformations on the flat. The proposed formulation is verified for five different materials sets.

Strain Hardening From Elastic-Perfectly Plastic to Perfectly Elastic Indentation Single Asperity Contact

“…A similar trend was observed in Ghaednia et al (2019), where the strain hardening effect on a flattening contact was studied, and the the same difference between the Hertzian theory and the FEM results was found. This result is likely due to neglecting the difference between indentation and flattening contact in Hertzian theory, where for both the cases the same effective radius of curvature is used.…”

“…A two-dimensional axisymmetric model similar to Ghaednia et al (2019) was developed in ANSYS Mechanical APDL 18.0 to simulate normal contact between a perfectly elastic sphere and an elastic-plastic flat. The sphere has a radius of 1 mm, and the flat is 3 mm thick and 5 mm wide.…”

“…The final mesh was selected to ensure that the results across both regimes were within 0.1% of the finest mesh considered. The final mesh is similar to the mesh used in Ghaednia et al (2019) except that a finer mesh was required on the flat's surface due to large pile-ups, Figure 1. The following conditions have been applied on the FE model: 1.…”

“…An extension of Kogut and Etsion (2002) to include bilinear strain hardening showed stable predictions for a large range of interfaces and material properties for a limited set of strain hardening coefficients (Shankar and Mayuram, 2008). In Ghaednia et al (2019), a new contact model for an elastic-plastic flattening contact was developed that included both bilinear strain hardening on the indenter and elastic deformations of the flat (which many previous flattening model considered rigid). The present analysis seeks to advance this research by investigating the role of hardening behavior for indentation.…”

“…In the previous work Ghaednia et al (2019), the effect of bilinear strain hardening for a flattening contact was studied. Even though the present work addresses a similar issue for indentation contact of bilinear materials, it is paramount that these two regimes be considered separately due to fundamental differences in their mechanics.…”