Y. Patel

Measuring fracture toughness from machining tests

Abstract An analysis of the forces involved in orthogonal cutting or machining is presented in which yielding on a shear plane is assumed. The fracture toughness Gc is included and it is observed that Gc may be determined by measuring the cutting and transverse forces together with the chip thickness for a range of cutting depths. This latter measurement enabled the shear plane angle ϕ to be determined experimentally. A simplified version of the analysis is also given in which ϕ is predicted by a cutting force minimization scheme. Neither scheme requires any details of the friction condition to be known since the transverse force is sufficient information for any type to be included in the analysis. A friction model including a coefficient of friction and an adhesion toughness is also utilized. Data for both polymer and metal cutting are taken from the literature and Gc is determined. In some datasets the tool rake angle α is also varied and the values of Gc and the yield stress σY are found to be independent of α. The force minimization method gives a good estimate of ϕ for most polymers. For metals (aluminium alloy, steel, and brass) the method worked well. For aluminium alloy Gc was independent of α and the predicted and measured ϕ values agreed. For steel and brass this was not so. Gc was mostly independent of α except at low values where high values of Gc were observed. A constant value of the coefficient of friction was observed for each α value but values for both the coefficient of friction and the adhesion toughness varied significantly with increasing rake angle.

Fundamentals of cutting

The process of cutting is analysed in fracture mechanics terms with a view to quantifying the various parameters involved. The model used is that of orthogonal cutting with a wedge removing a layer of material or chip. The behaviour of the chip is governed by its thickness and for large radii of curvature the chip is elastic and smooth cutting occurs. For smaller thicknesses, there is a transition, first to plastic bending and then to plastic shear for small thicknesses and smooth chips are formed. The governing parameters are tool geometry, which is principally the wedge angle, and the material properties of elastic modulus, yield stress and fracture toughness. Friction can also be important. It is demonstrated that the cutting process may be quantified via these parameters, which could be useful in the study of cutting in biology.

Blunt Cracks and Two Parameter Fracture Criteria

There is a concern in the fracture testing community about the influence of crack sharpness on measured toughness values. The notion of sufficiently sharp is intrinsic in the standards but does not define how sharp is sharp enough. This requires a definition of a crack tip radius below which the toughness will be Gc. A proposal is made here to modify the stress at a distance criteria in line with cohesive zones such that G GC and a critical stress σC is achieved. This provides a critical radius, ρC, below which, G = Gc. A comparison with FEA cohesive zone results supports the idea and comparison with data on uPVC conforms well to the suggested scheme to determine ρC. Some comments on self-blunting are also included.