Finite element modeling of fretting wear in anisotropic composite coatings: Application to HVOF Cr3C2–NiCr coating
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.
Section snippets
Microstructure of the coating
In Cr3C2–NiCr coating, the spray powder typically consists of 75 % wt. of Cr3C2 phase and the remaining 25 % wt. is accounted by the NiCr matrix. However, during deposition, some Cr3C2 particles rebound from the substrate surface. As a result, the final microstructure of the coating contains lower proportion of carbide phase as compared to the original powder [44,45]. Cr7C3 is an additional compound of chromium carbide formed during the deposition process [46]. However, it is formed in
Subsurface stresses in the coating
The load balance step in fretting simulation of Hertzian line contact leads to generation of subsurface stresses in the coating. A theoretical solution of these stresses for homogeneous isotropic materials in available in literature [60]. A comparison was made between the stresses obtained from a homogeneous isotropic domain with Young's modulus and Poisson's ratio as and respectively and a heterogeneous anisotropic domain. No friction was considered for this comparison. The
Summary & conclusions
This paper presents a microstructure sensitive FE model for fretting wear of HVOF Cr3C2–NiCr coating. To represent the microstructure of the coating, Voronoi tessellations were used with random distribution of Cr3C2 phase. This was performed until the volume fraction of Cr3C2 reached 55%, which is characteristic of the HVOF Cr3C2–NiCr coating. To account for anisotropy of the cubic NiCr matrix and orthorhombic Cr3C2 phase, a procedure that allowed for random crystallographic orientation was
CRediT authorship contribution statement
Akshat Sharma: Conceptualization, Methodology, Software, Writing - original draft, Visualization. Akhil Vijay: Formal analysis, Investigation, Validation, Writing - review & editing. Farshid Sadeghi: Resources, Writing - review & editing, Supervision, Project administration.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
The authors would like to express their deepest appreciation to the sponsors of METL for their support to this project.
References (91)
The role of adhesion and delamination in the fretting wear of metallic materials
Wear
(1977)- et al.
On fretting maps
Wear
(1988) - et al.
Mechanics of fretting fatigue tests
Int J Mech Sci
(1987) - et al.
Mechanics of fretting fatigue crack formation
Wear
(1996) - et al.
Finite element simulation and experimental validation of fretting wear
Wear
(2004) - et al.
Finite element modelling of fretting wear surface evolution: application to a Ti-6A1-4V contact
Wear
(2008) - et al.
Finite element analysis of fretting wear under variable coefficient of friction and different contact regimes
Tribol Int
(2017) - et al.
A numerical simulation of fretting wear profile taking account of the evolution of third body layer
Wear
(2017) - et al.
Multiscale computation of fretting wear at the blade/disk interface
Tribol Int
(2010) - et al.
Influence of fretting wear on bladed disks dynamic analysis
Tribol Int
(2020)
Abrasive wear behaviour of WC-CoCr and Cr3C2 -20(NiCr) deposited by HVOF and detonation spray processes
Surf Coating Technol
Computational modelling based wear resistance analysis of thick composite coatings
Tribol Int
Wear resistance optimisation of composite coatings by computational microstructural modelling
Surf Coating Technol
Microstructure-based thermo-mechanical modelling of thermal spray coatings
Mater Des
Crystallographic plasticity in fretting of Ti-6AL-4V
Int J Plast
Plasticity in polycrystalline fretting fatigue contacts
J Mech Phys Solid
Microstructure sensitivity of fretting fatigue based on computational crystal plasticity
Tribol Int
Effects of crystal elasticity on rolling contact fatigue
Int J Fatig
A 3D finite element modelling of crystalline anisotropy in rolling contact fatigue
Int J Fatig
A continuum damage mechanics framework for modeling the effect of crystalline anisotropy on rolling contact fatigue
Tribol Int
Numerical modeling of sub-surface initiated spalling in rolling contacts
Tribol Int
An experimental study and fatigue damage model for fretting fatigue
Tribol Int
A damage model for fretting contact between a sphere and a half space using semi-analytical method
Int J Solid Struct
A microstructure based approach to model effects of surface roughness on tensile fatigue
Int J Fatig
A stress based damage mechanics model to simulate fretting wear of Hertzian line contact in partial slip
Wear
Rough surface and damage mechanics wear modeling using the combined finite-discrete element method
Wear
A novel modular fretting wear test rig
Wear
High temperature fretting wear prediction of exhaust valve material
Tribol Int
Fretting fatigue lifetime estimation using a cyclic cohesive zone model
Tribol Int
Dominant effect of carbide rebounding on the carbon loss during high velocity oxy-fuel spraying of Cr3C2-NiCr
Thin Solid Films
Sliding and abrasive wear behaviour of HVOF- and HVAF-sprayed Cr3C2-NiCr hardmetal coatings
Wear
Sliding wear behaviour of HVOF and HVAF sprayed Cr3C2-based coatings
Wear
Experimental investigation of fretting wear of coated spring clip and inlet ring in land-based gas turbines at elevated temperature
Wear
Rolling contact fatigue of case carburized steels
Int J Fatig
Large-scale 3D random polycrystals for the finite element method: generation, meshing and remeshing
Comput Methods Appl Mech Eng
Determining microhardness and elastic modulus of plasma-sprayed Cr3C2-NiCr coatings using Knoop indentation testing
Surf Coating Technol
Cr3C2-NiCr and WC-Ni thermal spray coatings as alternatives to hard chromium for erosion-corrosion resistance
Surf Coating Technol
The electronic, mechanical properties and theoretical hardness of chromium carbides by first-principles calculations
J Alloys Compd
Elastic properties of binary NiAl, NiCr and AlCr and ternary Ni 2AlCr alloys from molecular dynamic and Abinitio simulation
Comput Mater Sci
Elastic properties of ceramic-metal particulate composites
Mater Sci Eng, A
On the rule of mixtures for predicting the mechanical properties of composites with homogeneously distributed soft and hard particles
J Mater Process Technol
Three dimensional (3D) microstructure-based modeling of interfacial decohesion in particle reinforced metal matrix composites
Mater Sci Eng, A
Cohesive zone modeling of intergranular cracking in polycrystalline aggregates
Nucl Eng Des
Cohesive zone modeling of intergranular fatigue damage in rolling contacts
Tribol Int
A computational micromechanics study of the effect of interface decohesion on the mechanical behavior of composites
Acta Mater
Cited by (19)
Finite element analysis of dovetail joint fretting wear considering glaze layer at high temperature
2024, Tribology InternationalEffects of fretting wear on rolling contact fatigue
2024, Tribology InternationalRolling contact fatigue performance of M50 steel: A combined experimental and analytical approach to determine life
2023, International Journal of FatigueAn investigation into various failure criteria on rolling contact fatigue through an improved probabilistic model
2023, Tribology InternationalInvestigation into rolling contact fatigue performance of aerospace bearing steels
2023, International Journal of FatigueFinite element simulation of fretting wear behaviors under the ball-on-flat contact configuration
2023, Tribology InternationalCitation Excerpt :Fretting wear are mainly investigated through experimental and numerical methods. In experimental aspect, scholars not only conducted fretting researches under different modes including tangential [4], radial [5], torsional [6], rotational [7] and dual-motion [8], but also explored the effects of temperature [9], humidity [10], atmosphere [11], lubrication [12], frequency [13], coatings [14] and contact configuration [15], etc. Numerical models have long been of interest to scientists studying fretting wear as they can reduce the need for costly and time-consuming experimental tests and allow the underlying behavior of the fretting phenomena to be observed [16–18].