A proposed method based on combining the concepts of shape functions of the finite
element method (FEM) and a molecular dynamics (MD) technique was developed to
evaluate the chip formation and strain and stress distribution in the cutting of
single-crystal copper by a nano-scale mechanism. The displacement components for the
atom in any temporary situation during the nano-scale cutting could be found.
In this paper, the atom is regarded as a node and the lattice is regarded as an element.
Using the atom displacements calculated by the MD program and combining the concepts
of shape functions of FEM we calculate the equivalent strain for material deformation in
the atomic-scale cutting mechanism. The equivalent stress was derived from the equivalent
strain from the corresponding flow stress–strain curve, whereas the flow stress–strain curve
was obtained from the regression of the stress–strain curve of a nano-copper thin film
tension test simulation.
In addition, the chip atoms within the diamond space were moved along the tool surface
using a mathematical method. Also, this study introduced a new concept: 'a combined
Morse potential function and rigid tool space restrictions criterion as the chip separation
criterion' for the nano-scale cutting model.