# Interfacial adhesion measurement of a ceramic coating on metal substrate.

Abstract The interfacial adhesion measurement of a ceramic coating on a metal substrate is studied by three-point bending (3PB) technique. In the measurement, interfacial cracks are induced during the 3PB test, and the interfacial energy release rate is calculated from the released energy per unit crack surface area during crack extension under the fixed displacement conditions. A finite element analysis (FEA) model encompassing the plastic behavior of the metal substrate is developed to simulate the 3PB test and extract the energy data. The inputs to the FEA model include the crack length, the maximum and critical loads corresponding to crack initiation, and the mechanical properties of the coating and substrate. A MoB/CoCr ceramic coating/stainless steel substrate system is investigated by the technique for demonstrating the utility of the technique.Keywords Interfacial adhesion, Coating, Three-point bending, Energy release rate, Finite element analysis

Introduction

Ceramic coatings have been widely used in the industry to improve the durability of engineering components under hostile working conditions. (1-5) As per usual practice, the coatings are formed on metal substrates by methods such as thermal spraying. (6) Unfortunately, interfacial cracks between coating and substrate may initiate at any time due to the residual stresses or other driving force to result in the debonding of the coating from the substrate. (7), (8) Consequently, the protection is lost and the lifetime of the components is reduced. Therefore, strong adhesion strength is critical to many engineering applications.

In order to improve the adhesion strength of the coating and predict the lifetime of the components, quantitative adhesion values and better understanding of the factors contributing to the adhesion strength are imperative. The interfacial adhesion can be defined either in terms of basic adhesion or in terms of practical adhesion. (9), (10) From a thermodynamic standpoint, basic adhesion is the amount of energy required to create free surfaces from the bonded materials. While practical adhesion is the total energy needed to separate the interface, including the elastic energy needed to create new surfaces and the energy dissipated in the plastic deformation or other sources. (9-11) In the past, a number of techniques such as four-point bending (4PB), (12-15) scratch, (16) indentation, (17-19) and pull-off tests (20), (21) were developed based on the practical adhesion definition and applied to different coating/substrate systems. Those methods usually evaluate the adhesion strength of the coating with the critical force or energy release rate (also named as crack driving force) needed to induce the interfacial crack. However, none of them can produce results under all conditions. The energy approaches are of special interest, as the energy release rate can characterize the system's resistance to crack propagation, to the well-known viewpoint of fracture mechanics.

In this study, we described a three-point bending (3PB) technology for measuring the interfacial adhesion of ceramic coating, with the advantages of the simple procedure, short testing time, and well-established fracture model. Controlled interfacial cracking mode and reasonable fracture mechanics model are required for interfacial adhesion measurement with the energy approach. The technology utilizes 3PB experiment to induce interfacial crack and finite element analysis (FEA) to study the fracture toughness of the interfacial crack. The utility of the technology was demonstrated in a MoB/CoCr ceramic coating/stainless steel substrate system.

Model

The fracture toughness of the interfacial crack is studied for evaluating the adhesion strength of the coating by this technology. Thus, an interfacial cracking in a controlled manner and a suitable fracture mechanics model are needed, which are presented in sections "Cracking configuration" and "Fracture mechanics model," respectively.

Cracking configuration

Because of bending, the tensile stress arises in the coating covered on the extended surface of the substrate via shear stress on the interface. If there are free edges in the coating, the stress concentration will arise near the edges and make the coating susceptible to delamination from the substrate. The free edges can be exposed by prefabricated notch in the coating (12-14) or surface cracking (8) that initiates from the surface of the coating and extends to the interface vertically under the action of tensile stress in the coating induced by bending (Fig. 1a-c). The moment the stress concentration is large enough, the crack extends along the interface and results in the delamination of the coating (Fig. 1d).

[FIGURE 1 OMITTED]

Fracture mechanics model

Energy release rate, [G.sub.ci], is the rate of change in potential energy with crack area (22) and can be used to quantify the interfacial adhesion strength of the coating. (10), (23) It is calculated by the energy per unit crack surface area available for crack extension, and expressed as (22):

[G.sub.ci] = [[DELTA][PI]]/[[DELTA]A], (1)

where [DELTA]A is the increment of crack area, and [DELTA][pi] is the release of potential energy during the crack extension. The potential energy includes the energy consumed by the deformation of the coating/substrate system, U, and the work done by external forces, F:

[PI] = U - F. (2)

Under fixed displacement of the loading indenter condition, no external work is done in the crack extension, that is, F = 0 and [pi] = U. Consequently, the equation (1) changes as:

[G.sub.ci] = [[[DELTA]U]/[[DELTA]A]]. (3)

From the standpoint of practical adhesion, the consumed energy, U, for separating the interface in an elastic-plastic system includes the elastic energy, [U.sub.e], and the dissipated energy by plastic deformation, [U.sub.p]. (24) Thus,

[G.sub.ci] = - [[[DELTA][U.sub.e] + [DELTA][U.sub.p]]/[[DELTA]A]]. (4)

The phase angle, [psi], which characterizes the relative strength of the normal to shear stress at the crack tip, is a complementary parameter to characterize the adhesion strength, since [G.sub.ci] varies with phase angle in general situations. (23) In 2-D problems, the phase angle is expressed as (22), (23):

[psi] = arctan ([[sigma].sub.12]/[[sigma].sub.22]), (5)

where [[sigma].sub.12] is the in-plane shear stress and [[sigma].sub.22] is the stress component applied normal to the crack plane.

Materials and experimental technology

In order to demonstrate the utility of the technique, a MoB/CoCr ceramic coating/stainless steel substrate system was investigated in this study. The coating (200 [micro]m thickness) was deposited by a TAFA JP-5000 HP/HVOF (high pressure/high velocity oxygen-fuel) system using commercially available MoB/CoCr cermet feedstock powders (Fujimi Incorporated, Japan) with particle sizes ranging from 15 to 53 [micro]m. The metallic substrate was sectioned into pieces of 60 mm x 3 mm x 3 mm in size. In the deposition, the oxygen flow rate was 870 L/min at 1.45 MPa, fuel flow rate was 0.38 L/min at 1.17 MPa, and spray distance was 355 mm. Five samples without pre-notch were prepared for testing.

3PB test was conducted using a Zwick T1-FR020.A50 instrument. The loading indenter with a radius of 5 mm was placed in the middle of the uncoated face of the substrate, and the two support indenters with 40 mm span between them were placed on the other side (Fig. 1). A loading rate of 0.2 mm/min was applied to control the loading process. During the bending process, the interfacial crack was investigated by observing the cross section of the sample using optical microscopy.

Experimental results and mechanical analysis

The interfacial crack was induced first in section "Interfacial crack and load vs deflection curve," and the elastic modulus of the coaling was calculated from the load vs deflection curve obtained in 3PB test. With the results in sections "Interfacial crack and load vs deflection curve" and "Elastic modulus of the coating," the interfacial toughness was analyzed by FEA simulation in section "Fracture toughness of the interfacial crack," based on the fracture mechanics model in section "Fracture mechanics model."

Interfacial crack and load vs deflection curve

The load and central deflection of the sample during the 3PB test were recorded by tensile tester and plotted as load vs deflection curve. The curve exhibits linear feature in the small loading region and nonlinear feature in the large loading region, as shown in Fig. 2. Interfacial crack was observed in the sample during the bending process. The inset of Fig. 2 is the interfacial crack corresponding to the maximum loading in one test. Although the cracking could result in the abrupt increase of the central deflection or decrease of the load, (12), (25) this cracking feature is not observed in the curve due to the limited resolution of the machine. The load increases continuously with respect to the central deflection in the curve. Hence, it is difficult to determine the critical load corresponding to the cracking initiation by the feature of the curve directly.

[FIGURE 2 OMITTED]

Elastic modulus of the coating

The linear behavior in the initial stage of the load vs deflection curve (Fig. 2) exhibits the elastic response of the sample to the external loading, and is governed by the elastic moduli of the coating and substrate. With the elastic modulus of the stainless steel substrate (200 GPa from a standard tensile test, not shown here), the modulus of the coating, [E.sub.coating], can be calculated from the initial slope of the curve using composite plate theory (26-29):

[E.sub.coating] = [[-A + [square root of ([A.sup.2] + C)]]/[2[R.sup.3]] [E.sub.substrate], (6)

where R = [h/H] with h and H are the thicknesses of the coating and substrate, respectively, and A = [4R.sup.2] + 6R + 4 - F; C = [4R.sup.2](F - 1). The constant F is:

F = [(1 + R).sup.3] [[E.composite]/[E.substrate]], (7)

where [E.sub.substrate] is the elastic modulus of the substrate and [E.sub.composite] is the composite modulus of coating/substrate structured sample:

[E.sub.composite] = [[L.sup.3]/[4[(H + h).sup.3] B]] [[[DELTA]P]/[[DELTA]w]], (8)

where L is the span, B is the width of the sample, P is the load, and w is the deflection in the middle of the sample.

The initial slopes [[DELTA]P/[DELTA]w] of the curves in five bending tests are listed in Table 1. The elastic moduli of the coatings were determined by substituting the slopes, the elastic moduli of the substrates, and geometry parameters of the samples into equations (6)-(8). The calculations were summarized in Table 1, which shows that the average elastic modulus of the coaling is 104 GPa.

Fracture toughness of the interfacial crack

For the cases in this study, the application of elastic analytical method for calculating [G.sub.ci] and [psi] is hindered by the difficulty in precisely controlling the interfacial fracture with desired crack length in elastic conditions. Therefore, numerical analysis was performed with an FEA model based on the fracture mechanics model.

The nonlinear feature in the load vs deflection curve (Fig. 2) is due to the combined action of the plastic behavior in the metallic substrate and the cracking in the interface. An FEA model was developed for studying the nonlinear behavior and calculating interfacial toughness. Only one half of the sample was analyzed because of the symmetry, and the structure consisted of a mesh with 2D 4-node elements (Fig. 3). In the FEA model, the loading indenter and two supporters were simulated by analytical rigid surfaces; the interface between the coating and substrate was modeled as two contact surfaces initially bonded together.

[FIGURE 3 OMITTED]

The bending process without cracking was studied first by the FEA simulation. The inputs in the model included the mechanical properties of the coating and substrate. The mechanical property of the substrate characterized by true stress-true strain curve was determined by a standard tensile test and simplified to be composed of three linear stages corresponding to the elastic, hardening, and perfect yielding stages, respectively (Fig. 4). The elastic modulus of the ceramic coating was determined by bending test in section "Elastic modulus of the coating" (Table 1). The Poisson's ratios of the substrate and the coating were set as 0.3.

[FIGURE 4 OMITTED]

Then, the load vs deflection curve in the assumed no-cracking condition was first calculated and compared with the experimental curve. Taking one 3PB test as example, the simulated and experimental curves in Fig. 5 correlate very well until the deflection reaches about 0.18 mm. Because the cracking weakens the stiffness of the sample, the load needed to deflect the sample in the assumed no-cracking condition should be larger than that in the cracking condition. Therefore, the load at the initial separation between those two curves should be the critical loading corresponding to the cracking onset. But the accurate separation point is difficult to be determined strictly due to the error in the experiment and simplicity in the analysis model. Only an approximate critical load can be determined by this way, e.g., 0.18 mm corresponding to the marked point in the inset of Fig. 5. The approximation does not weaken the accuracy of the energy release rate calculation in the following fracture mechanical analysis. The details will be discussed in section "Discussion."

[FIGURE 5 OMITTED]

After the critical load was determined, the cracking process in bending was further studied by a simulation of a debonding process of specified crack surfaces. (24), (30) The bonded surfaces of the coating and substrate in the interface were modeled as two contact surfaces, which were stuck together before the load exceeded the critical load. When the load reached the critical value, the crack propagation capability was activated and the initial bonded surfaces with a specified length (crack length) from the original location of the crack tip were separated. Then, the load vs deflection curve and energy consumed in the bending process were calculated. The results show that the simulated load vs deflection curve coincides with the experimental curve (Fig. 6). The energy increases continuously with the external loading during the bending and reaches the maximum when the displacement of the indenter also reaches the maximum (Fig. 7).

[FIGURE 6 OMITTED]

[FIGURE 7 OMITTED]

For aiding the calculation of the energy release rate, the interfacial crack was forced to spontaneously extend over a small length (0.2 mm) after the completion of the loading. (31), (32) In the spontaneous stage, the energy is released for creating new crack surfaces as illustrated by the decrease in the energy in the inset of Fig. 7. With the released energy and change in the crack area, the interfacial energy release rate was calculated by equation (3). In most cases, the resistance to interfacial crack of the coating/substrate system varies with respect to the load state at the crack tip. (23) Therefore, the load state corresponding to the measured critical energy release rate should be determined. The phase angle was obtained from the stress components ([[sigma].sub.12] and [[sigma].sub.22]) calculated at the node located at the crack tip by equation (5). The calculations from five tests (Table 1) show that the average critical energy release rate is 73 J/[m.sup.2] and the angle phase is 36.8[degrees].

Table 1: Mechanical property estimations of thermal spray coating/metal substrate system from 3PB tests No. dp/dw ([10.sup.6] N/m) [D.sub.0] (mm) D (mm) L (mm) 1 1.127 0.18 0.73 3.9 2 1.125 0.17 0.72 3.9 3 1.143 0.19 0.74 4.9 4 1.122 0.17 0.70 4.4 5 1.138 0.18 0.71 4.5 Average / / / / No. [E.sub.f] (GPa) [G.sub.ci] (J/[m.sup.2]) [psi] (degree) 1 100 86 37.7 2 98 68 37.7 3 115 83 35.6 4 95 62 36.8 5 110 68 36.4 Average 104 73 36.8 dP/dw is the slope of load vs deflection curve in initial elastic stage, [D.sub.0] is the critical deflection corresponding to crack initiation, D is the maximum deflection in the bending process, L is the crack length in one half of the sample, [E.sub.f] is the elastic modulus of the coating, [G.sub.ci] is the critical energy release rate, and [psi] is the phase angle

Discussion

The crack length, maximum load in bending, critical load corresponding to crack initiation, and mechanical properties of the coating and substrate are needed for the mechanical analysis. The accurate measurement of those parameters influences the calculation of the interfacial toughness. Among those parameters, the critical load and elastic modulus of the coating may be more difficult to be accurately determined. The error associated with those two parameters will be discussed below.

The critical load is determined approximately by comparing the load vs deflection curves obtained by FEA simulation under the assumed no-cracking condition with the experimental data in this study. The error associated with the uncertainty of the strict critical load can be ignored due to its infinitesimal influence on the energy release rate. Taking the first test in Table 1 as an example, the variation of the critical load from 0 to 0.35 mm (~50% maximum load) only results in less than 3% variation of the energy release rate (Table 2). According to fracture mechanics, (22) the critical energy release rate is determined by the transition state from stable to unstable behavior of the cracking when crack driving force (G) equals crack resistance force (R), and independent of the cracking process. Thus, the variation of the critical load has little effect on the energy release rate for the fixed transition state characterized by maximum crack length and central deflection in the FEA simulation. In fact, lots of analytical solutions of the critical energy release rates for interfacial cracking problems, e.g., the well-known blister test, (33), (34) are studied by the approximate model, which simplifies the cracking process as a bending process of plate with fixed length. For convenience, the cracking onset in the 3PB can be assumed to be the beginning of the bending without losing the accuracy on the energy release rate.

Table 2: Energy release rates with respect to different critical central deflections (E = 100 GPa, D = 0.73 mm, L = 3.9 mm) [D.sub.0] (mm) 0 0.10 0.15 0.25 0.30 0.35 G (J/[m.sup.2]) 86 86 85 86 87 87

Another parameter, the elastic modulus of the coating, is determined by initial slope of the load vs deflection curve using composite plate theory in this study. The porous nature of the thermal spraying coating brings uncertainty in the measurement of the coating's elastic modulus and influences the calculation of the energy release rate. However, the influence is negligible, because the energy needed for creating a new crack mainly comes from the released energy of the substrate, which possesses lager size compared to the coating. Similarly, in some approximate analyses on the interfacial toughness of coating/substrate system, such as four-point bending test with sandwich-structured sample, (10), (13) the elastic modulus of the coating is neglected in the close-form solutions of [G.sub.ci] due to the small contribution of the coating's deformation to the energy release of the system. Taking the first test in Table 1 as an example, the variation of energy release rate is less than 10% when the elastic modulus of the coating varies from 50 to 300 GPa (Table 3) with fixed elastic modulus of the substrate (200 GPa). This feature helps to evaluate the interfacial adhesion of the coating using an estimated elastic modulus of the coating without losing much accuracy. In addition, high loading rate should rather be avoided because of the unstable crack extension in high loading rate condition. (12)

Table 3: Energy release rates with respect to different elastic moduli of the coating ([D.sub.0] = 0.18 mm, D = 0.73 mm, L = 3.9 mm) E (GPa) 50 100 150 200 250 300 G (J/[m.sup.2]) 80 86 83 77 77 77

Controlled interfacial cracking mode is required for fracture analysis. In the bending test of this study, the crack initiates from the surface of the coating and extends to the interface vertically under the action of tensile stress in the coating induced by bending (Fig. 1). Similar cracking phenomenon was also observed in other bending tests. (7) However, the cracking configuration may not always be the case.

According to crack growth mechanism, the cracks always propagate along the direction with minimum energy consumption. The mechanical properties of the coating/substrate system influence the cracking configuration. Low fracture toughness of the coating can result in the segmentation cracks in the coating, which run from the surface of the coating toward the interface of the coating/substrate with the penetration depths comparable to the coating thickness. (8) However, the relatively higher fracture toughness of the coating compared to that of the interface is beneficial to the interfacial cracking. The crack may also kink into the substrate or the coating once again after it extends along the interface, (35) which offers the minimum resistibility. In addition, the variation of stress state at the crack tip with respect to the crack extension also influences the crack path. (23) Although the uncertainty of the crack path limits the application, the bending technique demonstrated here provides a selection with the advantages of the simple procedure, short testing time, and well-established fracture model.

Conclusion

An interfacial adhesion determination based on three-point bending (3PB) has been successfully applied to a thermally sprayed coating/metal substrate system. The method retains the advantages of simple testing procedures, short testing time, and well-understood fracture model similar to ordinary bending tests. Only the crack length, load (including the critical load corresponding to crack initiation and maximum load), and mechanical properties of the coating and substrate are required in the analysis model. The interfacial crack induced by bending can be observed directly from the sample's cross section. The analytical models developed to interpret the experimental data are based on the finite element analysis (FEA) and fracture mechanics analysis. By means of comparison of the load vs deflection curves of the FEA simulation results under the no-cracking conditions with the experimental results, the critical loads that induces cracking in the sample can be determined. Based on the maximum crack length and mechanical properties of the coating and substrate, the bending procedure including cracking can be simulated by the FEA model and the results agree well with experimental data. Hence, the interfacial energy release rate can be calculated based on the energy consumed in crack propagation crack under the fixed displacement conditions, and mode mixing can also be determined by the stress component in the crack tip. The error due to the uncertainty of the critical load and elastic modulus of the coating is small.

Acknowledgments The study was financially supported by Hong Kong Research Grants Council (RGC) through Competitive Earmarked Research Grant (CERG) No. CityU 112307.

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P. Nie (*), H. Lv, T. Zhou, X. Cai

Shanghai Key Laboratory of Materials Laser Processing and Modification, School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, People's Republic of China

e-mail: nplhxy@yahoo.com.cn

P.K. Chu

Department of Physics and Materials Science, City University of Hong Kong, China

J. Coat. Technol. Res., 7 (3) 391-398, 2010

DOI 10.1007/s11998-009-9192-2

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Author: | Nie, Pulin; Lv, Heping; Zhou, Tao; Cai, Xun; Chu, Paul K. |
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Publication: | JCT Research |

Date: | May 1, 2010 |

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