Finite element modeling of fretting wear in anisotropic composite coatings: Application to HVOF Cr₃C₂–NiCr coating

Highlights

• Damage mechanics based cohesive zone finite element model for fretting wear in HVOF Cr₃C₂–NiCr coating.

• Individual phases of the coating were randomly assigned to resemble the microstructure from an SEM micrograph.

• Model predicts stress-based failure mechanisms in wear of HVOF Cr₃C₂–NiCr coating.

• Model also simulates partial and gross slip fretting wear profiles.

• Wear rate from the model is in close approximation to experimentally measured wear rate.

Abstract

This paper presents a two-dimensional (2D) plane strain finite element model to simulate fretting wear in composite cermet coating. The coating considered in this investigation is High Velocity Oxy-Fuel (HVOF) sprayed Cr₃C₂–NiCr with 55% volume fraction of Cr₃C₂. The material microstructure is modelled using Voronoi tessellations with a log-normal variation of grain size. Moreover, the individual phases of the material in the coating were assigned randomly to resemble the microstructure from an actual SEM micrograph. The ceramic carbide phase is orthorhombic and the cubic matrix possesses a high anisotropy index. As a result, each grain was modelled with random orientation to account for material anisotropy. The RVE dimensions were chosen such that its elastic response represented the overall response of a poly-aggregate. In order to simulate debonding of the ceramic carbide phase from the matrix, cohesive elements were used at the grain boundaries. Damage mechanics was used to model degradation of cohesive elements resulting from repeated fretting cycles. A grain deletion algorithm was developed to simulate removal of material from fretting wear. The crack patterns predicted from the model match closely with the patterns observed in experimental studies on wear of HVOF Cr₃C₂–NiCr coating. The model also predicts carbide pullout, a major damage mechanism in HVOF Cr₃C₂–NiCr coating subjected to wear. Experiments were also conducted to evaluate and corroborate the wear rate of HVOF Cr₃C₂–NiCr coating. The wear rate from the model matches closely with experiments at a constant load and displacement amplitude. The results from the model were then extended to obtain a fretting wear map under a combination of various loads and displacement amplitudes.

Introduction

Fretting is a phenomenon observed when small vibratory motion occurs between the surfaces in contact. Damage due to fretting typically involves competing mechanisms of corrosion, wear and fatigue. The term ‘fretting corrosion’ was first used by Tomlinson et al. [1] for closely fitted surfaces undergoing surface degradation. They presented conclusive evidences that the damage was caused by vibrations and was mechanical in nature rather than chemical. Suh [2] presented the delamination theory of wear, where he hypothesized that subsurface dislocation pile ups are responsible for creating voids. When multiple voids coalesce, they form a crack which eventually grows towards the surface leading to delamination. His theory agreed with the findings of Waterhouse [3], who described fretting corrosion as a form of mild wear, where early surface damage occurs by adhesion followed by removal of material through delamination. Using his theory, Suh also provided an explanation of the dependence of fretting wear rates on displacement amplitude, which were later classified by Vingsbo and Soderberg [4] as regimes of wear starting from pure sticking condition to sliding wear.

Although the conventional approach of investigating fretting phenomenon has been experimental in nature, there have been significant advancements in modeling the problem from analytical and numerical perspectives. Mindlin [5] studied the effects of tangential forces for elastic bodies in Hertzian contact. He predicted that slip would initiate at the edge of the contact and subsequently put forth an analytical solution of the stick region in terms of the contact width, coefficient of friction, normal and tangential force. Nowell and Hills [6] presented closed-form analytical solutions for shear traction distribution at different positions in a fretting cycle. Johansson [7] used finite element (FE) to simulate evolution of contact pressure in fretting. Szolwinski and Farris [8] showed that crack initiation and fatigue life in fretting fatigue followed Smith-Watson-Topper (SWT) multiaxial fatigue criterion. Goryacheva et al. [9] provided analytical solution of wear profile in partial slip for a 2D contact problem. McColl et al. [10] simulated fretting wear using an incremental wear approach based on Archard's wear equation [11]. Paulin et al. [12] also used a progressive wear approach to simulate fretting wear in Ti–6Al–4V. However, their approach was based on energy dissipated during fretting. Leonard et al. [13,14] developed a 2D model of fretting wear based on a combined discrete-finite element approach. Yue and Wahab [15] developed a 2D FE model to show that variable coefficient of friction has a considerable effect in running-in stage of gross-slip. Since wear debris plays a critical role in fretting, different authors [[16], [17], [18], [19]] have considered the influence of wear debris in their models. Semi-analytical methods have also been used to study fretting wear in dovetail joints at the turbine blade-disk interface [20,21].

Surface coatings such as chromium carbide (Cr₃C₂–NiCr) and tungsten carbide (WC–CoCr) are extensively used to mitigate surface damage due to fretting wear in machine components and increase their service life. These coatings are deposited using thermal spraying techniques such as HVOF process and offer excellent wear resistance [22]. The use of FE has also made it possible to investigate the influence of coating microstructure. Holmberg et al. [23,24] presented a Scanning Electron Microscope (SEM) image-based computational modeling technique for modeling of thermally sprayed multiphase WC-CoCr coating subjected to wear. Their model showed that stress concentration arises from a nonhomogeneous multiphase microstructure. Bolelli et al. [25] developed a microstructure sensitive FE model of thermally sprayed coatings. They used their model to evaluate the elastic modulus of HVOF sprayed WC-CoCr and WC-FeCrAl coatings and verified it experimentally with three-point bend tests. Further, their model also reproduced plastic flow and extrusion of the matrix at the edge of the contact, which is characteristic of the surface profile observed in sliding wear experiments.

The influence of crystallographic orientation of the material microstructure is also key area of focus in fretting analyses. Goh et al. [26,27] used a 2D crystal plasticity FE model to study the influence of plasticity at the grain level in fretting fatigue of Ti–6Al–4V. They found that a random distribution of crystallographic orientation in the microstructure is able to better capture the deformation response as compared to isotropic J₂ plasticity. Zhang et al. [28] used a three-dimensional (3D) Voronoi tessellation based fretting fatigue model to demonstrate the significant effect of grain size and crystallographic orientation on plastic deformation. More recently, Paulson et al. [29] and Vijay et al. [30,31] have shown that a random distribution of crystallographic orientation provides a higher fatigue life scatter when modeling rolling contact fatigue failure in bearings.

Repeated fretting cycles cause surface fatigue, due to which void formation takes place. This leads to progressive degradation of the material. Damage mechanics introduced by Chaboche [32] has been used to model material degradation in rolling contact fatigue [33,34], fretting [[35], [36], [37]] and axial fatigue [38], where damage accumulates on grain boundaries, which are treated as weak planes for crack initiation and propagation. Ghosh et al. [39] used damage mechanics and FE to simulate fretting wear in partial slip. They were able to demonstrate material removal from the edge of the contact with the use of a stress-based damage model for fretting wear. Leonard et al. [40] have demonstrated that damage accumulation follows a linear trend with fretting cycles and wear volume has also been shown to vary linearly with number of cycles/frictional energy in fretting [41,42]. More recently, Pereira and Wahab [43] used a damage mechanics based cohesive zone model for life estimation in fretting fatigue.

In this investigation, a fretting wear model of HVOF Cr₃C₂–NiCr coating is presented. The microstructure of multiphase Cr₃C₂–NiCr coating has been replicated in commercially available FE software; Abaqus using Voronoi tessellations. SEM micrograph of HVOF Cr₃C₂–NiCr coating shows that Cr₃C₂ grain size follows a log-normal distribution which was also incorporated in the model. These Voronoi polygons are randomly assigned Cr₃C₂ phase until the volume fraction of Cr₃C₂ in the RVE reached 55%. Material anisotropy was also considered in the model with random crystallographic orientation of the grains. The elastic modulus of the microstructure is shown to converge as the size of RVE increases. Moreover, cohesive elements were used at the grain boundaries and damage mechanics was used to accumulate damage due to repeated fretting cycles in these cohesive elements. Stress concentration due to a nonhomogeneous microstructure leads to surface as well as sub-surface cracks during fretting. This crack pattern follows similar trend as shown in experimental wear studies on HVOF Cr₃C₂–NiCr coating. Carbide pullout, which is a major failure mechanism in wear of HVOF Cr₃C₂–NiCr coating, is also predicted by the FE model. Further, experiments were conducted to validate the wear rate obtained from the model. A fretting wear map of HVOF Cr₃C₂–NiCr coating is also provided for a combination of loads and displacement amplitudes.