A model for stresses, crack generation and fracture toughness calculation in scratched TiN-coated steel surfaces

The contact situation in a scratch tester, when a spherical rigid diamond tip is sliding with an increasing load over an elastic–plastic steel plate deposited with a 2 µm thick hard ceramic TiN coating is analysed. A three-dimensional finite element model (FEM) for describing the elastic and plastic behaviour and for calculating the stresses and strains has been developed. It shows that the maximum first principal tensile stress is generated in the tail part of the contact area. With increasing load a tetra-armed star shaped stress-field is generated around the contact. After about 1 mm of sliding a peak area of maximum first principal stress is formed in the back-tail region at the border of the scratch groove, creating the first visible angular cracks in the coating. This is in agreement with empirical observations. Once substantial plastic deformation of the substrate has occurred, the maximum tensile stresses are located behind the contact at a distance of 0.5–1 times the contact length from the back edge of the contact. These stresses have a horseshoe shaped ridge of maximum values with an opening in the sliding direction. The change of the state of deformation from sliding over the coating (sliding mode) to deforming the substrate plastically (ploughing mode) characterises the loss of load carrying capacity of the coated surface system. The model is used for calculating the fracture toughness of the coating. The critical fracture toughness is equal to the tensile stress times the square root of half of the crack spacing (K_c=ab/2) when the crack spacing is smaller than the crack length. For determining the fracture toughness of a 2 μm thick TiN coating on steel substrate a suitable crack field turned out to be the transversal tensile cracks in the scratched groove. For the studied case, the fracture toughness of the TiN coating was measured to be K_c=7 MPa m^0.5.