Analytical force model for orthogonal machining of unidirectional carbon fibre reinforced polymers (CFRP) as a function of the fibre orientation

Machining of carbon fibre reinforced polymer (CFRP) still represents a significant challenge due to its anisotropic material structure and brittle fracture behaviour. The material causes distinctive tool wear, which results in a significant increase of process forces. Analytical force models are crucial to optimise tool geometries and process parameters for efficient machining of CFRP with various fibre orientations. This research aims to develop an analytical force model for orthogonal machining which considers the influence of fibre orientation, tool geometry and increasing tool wear. The fibre orientation interval from 0° to 180° is sub-divided into four independent sub-models: (1) θ=0°=180°, (2) 15°≤θ≤75°, (3) θ=90° and (4) 105°+γ≤θ≤165°. For machining fibres with orientation (1) θ=0°=180°, the considered chip formation mechanisms are micro-buckling for axial loading and exceeding shear strength for transverse loading. Furthermore, spring back effects due to elastic deformation are taken into account. For fibre orientations in the range of (2) 15°≤θ≤75°, a bending beam surrounded by matrix material is modelled on elastic foundation, using minimum potential energy principle (MPEP) and WINKLER’s elastic foundation approach. After a first crack initiation at initial tool-fibre contact, further potential cracks due to bending of the now unilaterally supported fibres are taken into account. In the third sub-model (3) with the fibre orientation θ=90°, the modelled fibre fracture criterion is the local exceed of the compressive strength due to bending deformation. After the first crack initiation, further potential cracks are considered in the modelling approach, being affected by the varying tool-fibre contact point with progressing cutting motion. Using the same bending beam approach with MPEP for the sub-model (4) 105°+γ≤θ≤165°, the fibres are both axially compressed (buckling) and transversely bent during the cutting process. This superimposed combination results in a “peeling”-removal of the CFRP material. In order to consider tool wear effects, a characteristic description of the cutting edge is proposed using five micro-geometry parameters. The focus of this paper is on the force model, however simulation of tool wear is part of future research. The comparison of the simulated and experimental process forces, depending on the actual wear state and current tool micro-geometry shows a good correlation.