The primary target of modeling thin films has commonly been to increase understanding of the conditions where a coating can fulfill its functional requirement of preventing the activation of a mechanism inducing wear. Approaches have often emphasized fracture mechanical approaches, such as in the classic works presented in Holmberg et al. (2003), where a fracture mechanical model was developed based on the crack density of a thin hard film and the input based on a numerical contact model. Similar approaches employing fracture mechanics have been utilized by several researchers for different coating systems, such as Li et al. (1997) for DLC coatings on hard material substrates, Nastani et al.
(1999) for DLC coatings on a silicon substrate, and Diao et al. (1994) for TiN and Al2O3
coatings on hard material substrates. The latest developments in the fracture mechanical route can be stated to largely reside in a series of three papers: Holmberg et al. (2006a), Holmberg et al. (2006b), and Laukkanen et al. (2006). In these papers, the fracture mechanical methodology has been developed to include residual stresses as well as complex loadings and shapes and types of cracks in addition to considering the influence of material properties of the coating and the substrate.
3.1.1 Thin films (Publication I)
A common feature of the fracture mechanical route is the limitations of the underlying theory, i.e., the assumptions regarding the crack field type, size and shape that are
9
Figure 3.1: PSPP approach to ICME (Laukkanen et al. (2017a)).
required. Moreover, the treatment of multimaterial systems is somewhat limited in this kind of approach (see Laukkanen et al. (2006) for details). In Publication I, the previous work was revisited by exploiting the developments affiliated with CZM as well as the damage mechanical approaches to modeling failure initiation and propagation in coated systems, also taking advantage of the enhancements in the available HPC capabilities. The basis of CZM and its application in the microstructural scale still lies in the classic works of Dugdale (1960) and Barenblatt (1962). Consequently, the basis for the applicability of CZM to different types of cracking problems, including cohesive and adhesive crack problems, can be considered to exist. CZM is commonly applied over spatial scales although the underlying physics and basis for defining Traction Separation Law (TSL) behavior differ, and the atomistic scale arguments do not explicitly transform to larger scales. The present consensus, however, is that the principle is sound enough to be exploited. Similarly, mixed-mode loading conditions have been studied, for example by van den Bosch et al. (2006), which is a prerequisite for working with coated systems and having any possibility to track the relevant modes of failure.
The basic experimental problem setting is presented in Figure 3.2, i.e., a finite sliding and finite strain frictional contact with a plastically deforming substrate, utilizing an Augmented Lagrangian-Eulerian (ALE) formulation for better finite deformation perfor-mance. The cracking patterns as sketched in Figure 3.2 have been shown to be consistent (Holmberg et al. (2003), Holmberg et al. (2006a)) with experimental findings, as presented in Figure 3.3 for a TiN coating. The added feature of CZM is that it provides a more general modeling capability compared with the direct fracture mechanical approach, the
CZM tightly interacting with the solution of the contact problem and different material deformation behaviors.
(a) Schematic representation of the studied cracking pattern for thin hard films in scratch testing:
a) Angular cracks, b) parallel cracks, c) transverse (angled) cracks, d) coating chipping, e) coating spalling, and f) coating breakthrough.
(b) Schematic representation of the different crack types and affiliated deformation mechanisms in a coated system.
Figure 3.2: Description of the mechanistic background in the cracking of thin hard films (Holmberg et al. (2006a)).
The input to a CZM is a TSL, and as such calibration of the failure model was carried out. The methodology developed by Laukkanen et al. (2006), which is based on a weight-function methodology having its basis on a Boundary Element Method (BEM) founded derivation of the actual weight functions, was applied. In the methodology, the Stress Intensity Factor (SIF) being computed is presented as
K(2)= E0 2K(1)
Z
Γ
t(2)∂u(1)
∂a dΓ +Z
Ω
f(2)∂u(1)
∂a dΩ
, (3.1)
where E0 is the stress field dependent elastic modulus, (1) the weight function reference solution (and K(1) the respective SIF, generally under mixed mode conditions as in Laukkanen et al. (2006)), u the displacement vector, t the traction vector, f the body force vector, Ω the solution domain, Γ = ∂Ω, and a the crack length parameter. The
Figure 3.3: SEM image of crack patterns after scratch testing of a 2µm TiN coated surface, stylus movement from left to right (Holmberg et al. (2006a)).
weight function is given by
h= E0 2K(1)
∂u(1)
∂a (3.2)
which upon substitution to Equation 3.1 yields the weight function based expression for the evaluation of the SIF:
K(2) =Z
Γ
t(2)hdΓ +Z
Ω
f(2)hdΩ. (3.3)
Upon scratch testing and evaluation of the respective scratch test contacts by FE, the fracture toughnesses can be calculated for specific crack field types and for through coating cracks, which were utilized as a baseline for the fracture toughness in the current work (FE also introduces a substrate plasticity correction to the thin film stress state). The results are presented in Figure 3.4a. The FE modeling and the details are presented more thoroughly in Laukkanen et al. (2006) and Holmberg et al. (2009). The approach includes the effects of crack field orientation, crack density and crack location within the crack field, the loading conditions with respect to, for example, stress biaxiality and mode of loading. The calibration of the TSL was carried out based on the fracture toughness assessment, adapting an exponential TSL as a basis, where the damage is presented by
d= 1 − δ0m δmaxm ·
1 −1 − exp
−αδmaxm −δm0
δfm−δm0
1 − exp (α)
, (3.4)
where α is the rate parameter for the damage evolution and δfm− δ0mis the difference between the effective mixed-mode displacement at failure and at the initiation of the damage. The chosen calibration approach is presented in detail in Laukkanen et al. (2011), but in short, it relies on considering the coating failure as brittle (fast evolution of damage through the coating or within a critical stress-strain field, selecting the extreme from Figure 3.4) and ensuring that the effective fracture energy is identical to the measured
fracture toughness, i.e.,
Gf =Z δfm δm0
(1 − d)ti|d=0dδ. (3.5)
Since no direct information regarding the adhesive failure or fracture toughness was available, other than the likely occurrence of adhesive failure once the through coating crack field propagates with greater density through the coating, identical TSL properties were utilized at the film-to-substrate interface as well.
(a) Evaluation of through coating crack frac-ture toughnesses for a 2µm thick TiN coating from scratch tests.
(b) CZM model and its TSL relationship with different parameters influencing the rate of decrease of cohesive traction.
Figure 3.4: Fracture toughness evaluation and its exploitation in establishing the TSL parame-ters for modeling the film fracture (Laukkanen et al. (2011)).
The FE approach did not rely on remeshing but rather retained the hexahedral mesh throughout the solution, and as a result the CZM was carried out by populating the element interfaces from the contacting region with cohesive zone elements. Examples of typical meshes and resolution of the stress fields are presented in Figure 3.5.
3.1.2 Surface topography (Publication V)
Publication I focused on considering film damage, while Publications II-IV dealt mostly with various aspects of coating microstructure. As a natural progression, the aim of Publication V was to address the influence of surface roughness. In particular, the emphasis was on developing the analysis and modeling methodologies in line with the microstructure scale modeling and to approach the surface roughness explicitly rather than by utilizing effective models. The interactions between the film, the substrate microstructure, the bond layer, and the other structures and surface topography could be investigated during the design of new coating solutions or when assessing the tribological performance of the films under differing operating conditions.
The evaluation of the contact behavior of rough surfaces has traditionally been approached by the so-called “effective” models, largely due to the complexities in both the analytical and numerical incorporation of the behavior of a rough surface in the modeling of the behavior of the tribological contact. This has been primarily due to the difficulties in
(a) First principal stress contours.
(b) Equivalent von Mises stress contours.
Figure 3.5: FE mesh and contact response for CZM of thin film scratch tests (Laukkanen et al.
(2011)).
approaching the contact problem, and as such it is logical to approach it by way of numerical modeling. The present state-of-the-art is summarized in multiple sources, including for example Holmberg and Matthews (2009), where the complexities arising from the numerous parameters are acknowledged in making it difficult to outline a general theory or even methodology suited for coated surfaces. Although the significance of surface roughness has certainly been acknowledged, the simple models typically with an analytical origin have had difficulties in formulating a theory or model capable of merging the numerous parameters impacting the behavior of a coated system with those of surface roughness and topography. Such classic models, relying often on analytical simplifications of the rough contact problem to be able to approach the problem, have been presented for example by Greenwood and Williamson (1966), Halling (1975) and Halling et al. (1983).
Following the possibilities to utilize numerical modeling in the realm of thin films as well, the use of computation in deriving roughness models has increased. Works have taken the next steps over classic works, and clear influences of surface roughness have been demonstrated, for example, by Kalin and Pogacnik (2013), Kucharski and Starzynski (2014) and Reichert et al. (2016). DLC coated surfaces have been studied, for example, by Jiang and Arnell (2000) and Xiao et al. (2016). These works can be stated to have taken the first steps in applying modeling to rough surface problems, although the approaches in a computational sense have been limited to simple models of surface contact where the
roughness has been discretized for example to a single asperity contacting a flat surface or a similar modeling outline. Typically these earlier works do not or can not include the other aspects of the system when considering the design of the coating microstructure (such as the gradient or multilayer character of the coating, bond layer, microstructure of the substrate, defects, etc.). In Publication V, a toolset was developed to include surface roughness and topography alongside the other studied characteristics of the coated system, to introduce a methodology where all these features are present at the microstructural scale of the tribological system.
The experimental details related to Publication V are presented in Holmberg et al. (2015).
The details of the surface topography characterization technique and the fractal analysis procedures for surface characterization and its analysis are provided in Wolski et al. (2017).
In order to be able to produce different types of representations of coated surfaces, a toolset was developed and implemented to support different methods and types of rough surface topographies, as presented in Figure 3.6. The basis of the approach is to support various typical sources of characterization input, such as different types of profilometry and topography data, or to simply generate surfaces based on mean values or statistical data, such as the Ra and Rz values. Following interfacing to experimental data, different surface representations are available, arranged by the ascending complexity of the surface representation:
• stochastic random walk surfaces: generation of surfaces based on random walk methods
• isotropic and anisotropic fractal surfaces: representation of the topography as a fractal surface
• Fourier series and spectra: use of series developments to describe the surface topography
• direct use of experimental data: reproducing the experimentally measured surface directly to the model
Figure 3.6: Toolset for modeling rough surfaces (Laukkanen et al. (2016b)).
The objective of supporting different ways to represent the surface roughness was essentially to both enable direct transfer of experimental measurements to the model of the surface, and also to enable parametric and systematic studies of the effects arising from the variation of surface roughness characterization parameters and methods. In Publication V, the coating system under study is a DLC coated steel substrate, typical of, for example, automotive applications. The surfaces were prepared with three surface finishes, resulting in different levels of surface roughness and consisting of the DLC surface layer, a CrCx and Cr bond layer, and an AISI52100 bearing steel substrate, as shown in Figure 3.7.
(a) Three different DLC coating surface fin-ishes: smooth, average roughness, and rough
surface (b) FIB cross section of the coating
Figure 3.7: DLC coatings studied in Publication V (Laukkanen et al. (2017b)).
Examples of the generated surface roughnesses are presented in Figures 3.8 through 3.10. In Figure 3.8, a random walk surface prepared based on the analysis of surface topography measurement statistics is displayed, the surface being generated and merged with a representation of a Face Centered Cubic (FCC) like tessellated steel microstructure.
In Figure 3.9, a similar system and a typical microscratch test diamond tip are introduced.
The system studied in Publication V is presented in Figure 3.10 with respect to the material domain. In Figure 3.11, the FE mesh used for solving the contact problem is shown including the countersurface. The resolution of the microstructure of the bearing steel, the bond layer, and the DLC coating are visible in the figures.