Improving WC-Co coating adhesive strength on rough substrate: Finite element modeling and experiment

1. Introduction

Cemented tungsten carbide (WC-Co) is a well-known material that demonstrates exceptional fracture toughness and hardness. Accordingly, it is preferably suited for the high abrasion conditions. The tough tungsten monocarbide (WC) grains have a transfuse network of a soft and ductile binder metals such as cobalt (Co) which is mostly often used. The WC-Co composite with these properties is essential for various engineering applications, for instance fluid control valve trim, machining, oil and gas drilling and mining [[1], [2], [3], [4], [5], [6], [7]]. Current composite structural materials with minimum two phases have strong dissimilar mechanical properties, which makes the composite a complex core structure [[8], [9], [10], [11], [12], [13]]. Consequently, the spreading of stress and strain inside these composite materials is a complex process and depends on various characteristics of internal material structure, like mechanical properties of phases, particle size distributions or grain, volume fraction of phases, thickness of intergranular phase, contiguity and way of phases joining. Moreover, these characteristics are predominantly vital in our case of composite (WC-Co) which consists of brittle and plastic material components. As usually approved in literature, the hard metals display higher fatigue sensitivity and the effects of hard metals in addition to the ductile failure arise mostly in the binder phase [[14], [15], [16], [17], [18]]. In brief, the complex core structure makes the evaluation of the mechanical properties of the composite materials from its components actually a tough task.

On with the sliding of surfaces, the tangential force just not individually depends on the deformation component of friction but as well as depends heavily on shear strength of adhesion bonds between them [[1],[18], [19], [20]]. The contact surfaces of metallic bodies which are formed during the wear process are characterized by considerable roughness. Additionally, the contact surfaces having a poly-crystalline structure are inhomogeneous in its mechanical and physical properties. Accordingly, the deforming components of the tangential contact force in the friction are substantially significant. Yet, especially at increased contact temperatures, it is very difficult to govern the value of friction [[19],[21]], and it is intolerable to discrete it from the whole tangential forces for the understanding of adhesion component. These situations make it difficult to determine the adhesion bond strength straight from cutting. Thus, simulation method is the most hopeful direction for calculating the parameters of the adhesion interaction between hard bodies. On the other hand, a huge research on WC-Co coatings has been attentive towards the tribological and corrosion properties while a little research has been focused towards the estimation of bonding strength, which is very essential for the coating lifetime in service. The failure of the WC-Co coating system was originated mainly due to the adhesive fracture at the interface between the substrate and the WC-Co layer, where cracks generally begin from the boundaries of nonmelted particles and formerly spread along the substrate/coating interface. Despite the wide research being done on the wear of WC-Co [[1],[11],[22],[23]], unexpectedly slight advancements have been made for the modelling part of the material. So, primary modelling studies used available finite element modeling (FEM) to find majority of material properties from actual microstructures [[24],[25]], where 2D meshes representative of the real microstructure were modelled through separate WC and Co phases. These models provided decent estimates on the whole material response after linked with the analytical and experimental results created on the mixture approach.

In a coating/substrate system, imperative mechanical characteristics affecting coating performance is the strength of adhesion bonds. The works of Sigl et al. [[26],[27]] in the multiligament zone model is widely recognized as the key mechanism for the evolution and initiation of microcracks in WC-Co coatings on applying monotonic loads. Though, fatigue damage behavior in hard metals has not been entirely understood and inconsistent explanations for the damage effect in the binder content exist in literatures [[12],[28]]. It is known that the coating adhesion is not a constant in practical applications, but relatively a complex property that is determined by the process, loading conditions, interface roughness [29] and coating thickness [[30],[31]]. In this study, we investigated the effect of roughness degrees on the adhesion strength of WC-Co coatings on steel substrate. A comparative study of experiment and simulation was conducted to correlate the roughness and adhesion strength. The mechanism responsible for the effect of roughness on adhesion strength was discussed.

2. Framework of the model

2.1. Model development

The existing FEA software package ABAQUS [32] was used for all our simulation works. Quasi static loading was used, and viscous regularization was active to assist the convergence for all the solutions at individual integration time step. In ABAQUS, the viscous regularization is governed via the parameter damage stabilization. The further parameter tolerance controls the increment in the step time. The WC-Co system in this study involves of three layers, the 0.09 mm thick WC and Co phases, 0.11 mm thick of apparently homogeneous region WC-Co to limit the calculation time and 3.0 mm thick steel substrate. At the 0.09 mm thick layer, the area ratio of the WC phase to Co phase was set based on the experimental part in Section 4.1. Models built were Ra of 0 μm, 0.5 μm, 2.5 μm, 5 μm, 7.5 μm, 10 μm, and 12.5 μm. Fig. 1(a) shows the geometry model of Ra 10 μm which was implemented for finite element simulations.

The representative volume elements (RVE) [[33], [34], [35]] is the minimum volume in a unit cell of heterogeneous materials which permits appropriate detailed mapping of macroscopic properties. The complex structure of the composite materials with results from the eternal bonding of diverse material phases is a characteristic illustration of a mixed model typically examined by means of the RVE models, which produce the statistical response acceptable for a macroscopic model of the specified material. Right RVE models are an important problem to model microstructures, because they rightly control the simulation results. This method enables us to have quantitative and qualitative evaluation of the whole system’s response when external load is applied.

Incorporation of initial crack in the model was used for the study of crack spreading features as the cracks grow up to the steel sub/composite interphase, as shown in Fig. 1(c). Damage initiation is projected by the maximal principal stress (S_c) for the fulfilment of the initiation criterion, and these initiation stress values are shown in Table 1. Cohesive laws govern the crack growth while the fracture energy states the degree at which cohesive stiffness is degraded after the initiation criterion is encountered. The models for the WC-Co composite microstructures with RVE are developed on the two-dimensional (2D) modelling accordingly with the experiment. The composite structured is completed via the discretization process built in the 2D FEM, and plane strain is used.

In model development, the progression and initiation of microcracking at the interface of WC-Co and steel substrate was defined via the extended finite element method (XFEM) [[36],[38]]. XFEM enables, together with the quantitative and qualitative terms, the analysis on the separate stages for the material damage under load for our microstructure.

2.2. Extended finite element method for interface crack propagation

Created in the standard fracture mechanics, XFEM covers an estimated potential of the FEM aimed at simulations of central discontinuity short for the need of remesh again [[39],[40]]. So, the finite elements and nodes are improved with further degrees of freedom, and this scheme may be implemented to extend in the least predefined or progressing discontinuities from center within framework of the finite elements. In this method, we can approach by using especially designated approximation shape function in the discontinuous displacement area which are well-defined by elevating functions [41]. Displacement approximation and discontinuity edge can be well-defined by the independent degrees of freedom, so XFEM permits the simulations for the spreading of discontinuities autonomously for the finite element meshes. Displacement approximation function for the propagation of crack is well-defined and stated as below:

$u=\sum_{I=1}^{N}N_{I}(x)([u_{I}+H(x)a_{I}+\sum_{\alpha}^{4}F_{\alpha}(x)b_{I}^{\alpha}])$ (1)

whereas the right side term is the usual FEM displacement function, and the second term on the left is the improved displacement function for the nodes which supports when a crack forms. The discontinuous jump function H(x) is given below:

$H(x) =\begin{cases} 1, & if(x-x^{*}).n\ge 0 \\ -1, & otherwise \end{cases}$ (2)

where x is a gauss integration point, and x* is the closest point from the x by the crack surface and n is the unit vector normal form the crack next to point x*, as shown in Fig. 1(a). The mechanism involving failure between microstructure of WC-Co composite and steel interface is measured by the cohesive traction separation law (Fig. 1(b)) [[32],[42]], which defines the elastic behavior of material at O-A (point A is the damage initiation criterion), where it is calculated in our situation based on the stress criterion as shown below:

${\frac{\sigma_{n}}{N_{max}};\frac{\sigma_{t}}{T_{max}};\frac{\sigma_{ts}}{S_{max}}}=1$ (3)

Examples N_max and loss by the finite elements A-B in the evolution of inflexibility which resolute towards:

σ=1-dσ^* (4)

where d is a damage variable (As d = 1 material points have been entirely collapsed) and σ is stress owed to the undamaged response,

The resulting displacements of nodes, with mutually the normal interaction δn with the tangential interface in two reciprocally perpendicular directions δs and δt, are intended by equation as shown below:

$\delta=(\delta_{n}^{2}+\delta_{s}^{2}+\delta_{t}^{2})^{1/2}$ (5)

2.3. Boundary conditions

Strain is applied on the model through unvarying displacement used at the boundaries which are parallel to the primary crack, while the rest of the boundary conditions remain traction free. The periodic constraints are engaged on the right boundary, which could be achieved in multiple point constraint (MPC). Thus, all nodes on this boundary can move freely along the direction-3 and have a similar displacement along direction-1. All nodes on this boundary are constrained along the direction-1 by a symmetry constraint which is set on the left boundary. To avert the rigid displacement, the affected grid nodes lying on the bottom side of the structure have been constrained in the vertical direction.

3. Experimental procedure

3.1. Materials

A3 mild steel (ϕ25.4 mm × 3 mm) was used as substrate to support the coatings. WC-12Co (88 wt% WC and 12 wt% Co) was used as the feed powders. Morphology of the WC-12Co powders is shown in Fig. 2. The size distribution of the powders is 30-50 μm. It can be observed that the WC powders were surrounded by the matrix Co. Brown fused alumina was used as the grad blast materials. In order to achieve different roughness, four different sizes, namely 50 μm, 150 μm, 250 μm, 750 μm, were used to roughen the substrate surface.

3.2. Sample preparation

The substrate should be pretreated before depositing coatings. The preheating includes cleaning and roughening. To begin with, the surface of substrate was cleaned by acetone to remove the oil contamination. Subsequently, the substrate was roughened by sand blast. The brown fused alumina powders were perpendicularly sprayed on the surface of substrate at a distance of 100 mm. The compressed air was controlled to be 0.6 ± 0.1 MPa.

The WC-12Co coatings were sprayed by high velocity oxygen flame (HVOF, CH-2000, Xi’an Jiaotong University). The flame was formed by a propane and oxygen. Nitrogen was used to feed the powders into the flame. Table 2 shows the spraying parameters of HVOF.

3.3. Structural characterization and property determination

Cross-sectional morphology of coatings was observed by scanning electron microscopy (SEM). The cross-section images were also used to determine the area ratio of the two different phases using ImageJ software. The roughness of substrate was determined by using a laser microscopy. Firstly, a surface area of 640 μm × 480 μm was selected to form images. Subsequently, the Ra can be automatically determined by the system based on the rough surface. This method can also give the 3D image of cross-section, so that the rough morphology can be observed directly. The adhesion strength between coating and substrate was determined by using a tensile method (ASTMC663-79, Instron 1195, USA). The loading rate was controlled to be 1 mm/min. The adhesion strength can be obtained by dividing the load when fracture occurs by the cross section area of the sample. For each condition, at least 5 samples were used to minimize errors.

4. Results and discussion

4.1. Size effect of grad blast on the roughness and adhesion strength

Fig. 3 shows the cross-sectional morphology of coatings. It is observed that the microzone appears to be relatively dense. The very small fraction of closed pores observed in the cross-sections is generally regarded as the artificial pores during sample polishing. In addition, it is possible to find similarity between coatings and the powders, suggesting that the powders were impacted on the substrate in a solid-liquid state. The metal Co is melted, whereas the ceramic WC is still in solid state. This is consistent with previous reports [[4],[5],[16]]. The area ratio of WC and Co is approximately 80% and 20%, respectively.

Fig. 4 shows effect of the size of grad blast on the rough degree of substrate. A common phenomenon is that the substrate become roughening to some degree. However, the size effect of grad blast can be obviously observed. With the increase of the size of grad blast, the roughening becomes more significant. Fig. 5 shows the obtained roughness as a function of grit size. When the grit size is 750 μm, 250 μm, 150 μm, and 50 μm, the roughness of substrate is 9.2 μm, 4.4 μm, 2.7 μm, and 1.0 μm, respectively. It is obvious that a larger grit size leads to a larger roughness. This is consistent with the morphologies observed from Fig. 4.

Fig. 6 shows the adhesive strength as a function of roughness. It is observed that the adhesive strength is significantly affected by the roughness. In the case of the Ra<2 μm, the adhesive strength is approximately 35-46 MPa. When the Ra is 4 μm, the adhesive strength increases to nearly 60 MPa. And the adhesive strength seems to be unaffected by the Ra if it is larger than 4 μm.

4.2. Comparison between the model prediction and experimental results

Owing to the non-existent of comprehensive data for different WC-Co compositions, only one set of parameters were used. The mechanical properties of the particles (particularly yield strength and hardness) were anyway so different from those of the substrate materials. The numerical results allows us to compare the mechanical response of the WC-Co composite when being exposed to uniaxial tensile load. The interface between the substrate and coating was modelled as two contact surfaces that were originally bonded together and separated afterward, governed by a linear relationship.

4.2.1. The residual stress and interfacial crack in substrate/WC-Co

Determining residual stresses is hard which requires a blending of destructive and non-destructive approaches to evaluate precisely stress distribution [[43],[44]]. The stress states with differnet Ra values (Fig. 7) are firstly studied towards gaining data around the critical region that is most favorable for crack nucleation or growth. The normal stress component of S22 at interfacial region between substrate and WC-Co regions indicates stress regions just before start of crack. The maximum stress is at the center of interface region. The results allow us the qualitative and even quantitative analysis for assessment with degree of material effect at the interface regions.

Relating to the obtained distributions of stresses in the substrate/Co interface regions, we can see comparable regions measured in the peak values of these stresses in all the models. In all cases, a massive zone on the interface material experiences plasticization, from which we can deduce that the stresses at the interface regions have touched the values of critical stress (S_c). When failure criterion happens with the formation of plastic strains, principal towards the loss in the stability of the constituents wherever the principal damage variable was attained (i.e. d = 1). The influence of residual stresses on fracture behavior depends on the level of plasticity in an element. Under mainly elastic conditions, residual stresses can expressively minimize the load bearing capacity of the defective structures or we can say that the effects owning to the residual stresses can be minimized when the plasticity is widespread. The stress values have been changed considerably for the Ra 5 μm as shown in Fig. 7, as the values are not connected to the center but preferably spreaded in the upper part individually, which would assist in hindering the crack extension. This is the reason that the increase in Ra of the substrate enhances the adhesion strength of the WC-Co composite coating, as shown in Fig. 6.

4.2.2. Predicted adhesion strength compared with experimental results

The analysis is involved in determination of the Co interface and the damage processes related to the used material used, by means of the XFEM for failure modelling simulations. For example, to model cracking of substrate/coating system, XFEM was used based on the traction separation constitutive phenomena. As the stress concentrations are towards the tail ends of the adhesive layers, the damage initiation criterion is validated, and the degradation process starts from the adhesive edges to the center. Regarding the crack growth procedure, the cracks continue to spread lengthwise in the direction per minimize energy consumption. The crack formation impacts mechanical processes of the coating/substrate system. WC-Co coating with low fracture toughness can end up with the separate cracks in the coating, which tracks as of coating surface towards the interface of the coating/substrate with the diffusion depths being equivalent to the thickness of the whole coating [45]. Nevertheless, the comparatively high fracture toughness of this coating when related to interface is valuable towards the interfacial cracking phenomena. These cracks might similarly bend into the coating or the substrate and then yet again outspreads laterally along the interface, which propose the least resistance [46]. Moreover, the difference of stress states on the crack head in regard to the crack expansion also impacts the crack trial [47]. We have found that the crack starts in the interface from the center (Fig. 7), and grows to the loading direction in parallel.

Fig. 8 shows the stress versus displacement curves of high strength composite/steel under same force level. Stress increases monotonically followed by a brittle fracture for all the models. After loading is done, the stress curve primary increases linearly with the displacement, till failure occurs at critical stress (S_c). Critical stress has been significantly increased to nearly 60 MPa with the increase of roughness value till Ra = 4 μm and becomes steady with further increase in Ra values. Fig. 9 shows comparison between experimental and simulations values of adhesion as a function of roughness. The values for both experimental and simulation are consistent. The calculated values of WC-Co composite are higher than the experimental results. The results indicate that adhesion was strongly dependent on the roughness (Ra) of the substrate surface. Adhesive strength is increased drastically with increasing Ra of steel substrate. By increasing roughness (Ra), we are actually increasing the true surface area of substrate which improves the adhesion. From interface stress distribution, residual stresses are widespread with the increase in the Ra values which further improves adhesion strength. Adhesion strength is uniquely the most prominent factor in thermal spray coatings, in particular the plasma sprayed ceramic coatings with lots of pores [48], as it is straightly associated with the durability of the coating and it precisely impacts the fatigue life of the coating. Interfacial compressive residual stresses play an important role in performance. By increasing roughness, for example Ra>4 μm, the residual stress is reduced. In addition, the stress distribution changes from concentration at the center to wide spread all over the interface region. These would benefit the prevention of crack extension and improve the adhesion strength.

5. Conclusions

This study investigated the effect of roughness degrees on the adhesion strength of WC-Co coatings on steel substrate. A comparative study of experiment and simulation was conducted to correlate the roughness and adhesion strength. The mechanism responsible for the effect of roughness on adhesion strength was revealed. The detailed conclusions are:

(1)The experimental results show that the adhesive strength is significantly affected by the roughness. In the case of the Ra<2 μm, the adhesive strength is approximately 35-46 MPa. When the Ra is 4 μm, the adhesive strength increases to nearly 60 MPa. And the adhesive strength seems to be unaffected by the Ra if it is larger than 4 μm.

(2)The finite element simulation suggests that the predicted values are well consistent with the experimental data. Fracture toughness of WC on reaching critical stress (S_c) starts the crack at the interface which gradually grows from center towards the edges.

(3)The stress distribution on interface regions indicates that increasing roughness or the true surface area of substrate can change the distribution of residual stress from concentrated state to widespread state, which decreases the critical stress to result in crack extension. This is the main mechanism responsible for the fact that a larger roughness can cause a higher adhesive strength.

The deep understanding on the mechanism of adhesive strength affected by roughness would contribute to the parameter optimization of WC-Co coatings with better performance.

Acknowledgments

This work was supported financially by the China Scholarship Council (CSC, No. 2017GXZ020849), the Fundamental Research Funds for the Central Universities and the National Program for Support of Top-notch Young Professionals.

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