Purpose: The complex mechanisms of tool wear in metal cutting have not been possible to investigate in detail by the experimental methods traditionally employed. However, as a result of both the continuous development of numerical methods, such as the Finite Element Method (FEM) and the development of ever more powerful computers, the evaluation of the chip formation process and the evolution of tool wear is now possible. Design/methodology/approach: In the work presented in this paper, numerical methods are employed to study the effect of a single embedded hard carbide particle on tool wear and tool tip deformation. An important advantage of this approach is that particle size and position can easily be changed, thus making it possible to investigate the influence of these parameters on tool wear. Findings: The results reveal that the position, and in particular the size of carbide particles, have a dramatic impact on tool wear. In particular, particles larger than a certain size (about 5μm) cause significant plastic deformation of the tool tip, when passing in sufficient proximity. Research limitations/implications: An effort has been made to obtain the corrected version of the stability polynomial, the corresponding stability region and the range of Re(z) for the RK-Butcher algorithm. Originality/value: The present article sheds some light on different numerical integration algorithms involved in robot arm model problem.