Wear 254 (2003) 278–291 A model for stresses, crack generation and fracture toughness calculation in scratched TiN-coated steel surfaces Kenneth Holmberg ∗ , Anssi Laukkanen, Helena Ronkainen, Kim Wallin, Simo Varjus VTT Industrial Systems, PL 1704, FIN-02044 VTT, Finland Received 10 April 2002; received in revised form 7 October 2002; accepted 1 November 2002 Abstract 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 m 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 = σ √ b/2) when the crack spacing is smaller than the crack length. For determining the fracture toughness of a 2 m 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 . © 2002 Elsevier Science B.V. All rights reserved. Keywords: Surface engineering; Coatings; Stress modelling; Fracture; Scratch test; Fracture toughness 1. Introduction There has been increased interest in the use of coatings on mechanical components, on tools in the production in- dustry, on disc drives in the computer industry, on preci- sion instruments, and on human replacement organs. New coating deposition techniques developed over the last two decades offer a wide variety of possibilities to tailor surfaces with many different materials and structures. In particular, chemical vapour deposition (CVD) and physical vapour de- position (PVD) techniques have made it possible to deposit thin coatings only about 1 m thick in a temperature range from very high temperatures (about 1000 ◦ C) down to room temperature. Coating materials such as TiN, TiC, Al 2 O 3 and more re- cently diamond, diamond-like carbon (DLC) and MoS 2 and their combinations as multilayers and dopants have been used with great success. In the best cases, these very thin ∗ Corresponding author. Tel.: +358-9-456-5370; fax: +358-9-456-7002. E-mail address: kenneth.holmberg@vtt.fi (K. Holmberg). coatings have decreased the coefficient of friction and the wear rate by one or two orders of magnitude. Super-low friction coefficients down to 0.001 in dry sliding have been measured [1,2]. The deposition techniques of thin coatings and their tribological behaviour and applications have been described by Holmberg and Matthews [3,4] and Holmberg et al. [5]. A tribological contact with two loaded surfaces in rela- tive motion is a very complex system that is not easy to un- derstand nor simulate or predict. The system becomes even more complex when coatings are introduced on the surfaces. Studies have been carried out at macrolevel, i.e. the compo- nent level, at microlevel, i.e. the surface asperity level, and at nanolevel, i.e. the molecular level [4,6,7]. One problem is that even the parameters used to describe friction and wear behaviour in coated tribological contacts are not clear. The parameters related to the macrogeometry of the contact and the topography are better defined, but the parameters defining the wear debris and surface layers are not well defined. Parameters related to load and speed are well controlled, as are the environmental parameters such as 0043-1648/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved. PII:S0043-1648(02)00297-1