*Article* **Tensile Adhesion Strength of Atmospheric Plasma Sprayed MgAl2O4, Al2O<sup>3</sup> Coatings**

**Andrey Zayatzev 1,\*, Albina Lukianova <sup>2</sup> , Dmitry Demoretsky <sup>2</sup> and Yulia Alexandrova <sup>1</sup>**


**Abstract:** This study analyses the distribution of stress during the testing of glued cylindrical specimens with thermally sprayed MgAl2O<sup>4</sup> , Al2O<sup>3</sup> oxide coatings in order to evaluate the tensile adhesion strength. The set of studies that make up this work were conducted in order to evaluate the influence of the geometric parameters of cylindrical test specimens, 25 mm in diameter by 16–38.1 mm in height, on the measured tensile adhesion strength of the specimens. The stress and strain states inside the coating and at the coating-substrate interface were determined using the finite element modelling method. The debonding mechanisms, failure mode and influence of the coating microstructure on bond strength are also discussed. The finite element stress analysis shows a significant level of non-uniform stress distribution in the test specimens. The analysis of the results of the modelling stresses and strains using the finite element method for six types of cylindrical specimens, as well as the values obtained for the adhesion testing of MgAl2O<sup>4</sup> , Al2O<sup>3</sup> coatings, show a need to increase the height of the standard cylindrical specimen (according to ASTM C633-13 (2021), GOST 9.304-87). The height should be increased by no less than 1.5–2.0 times to reduce the level of a non-uniform stress distribution in the separation area.

**Keywords:** tensile adhesion strength; plasma spray coating; MgAl2O<sup>4</sup> ; Al2O<sup>3</sup> ; FEA

### **1. Introduction**

Thermally sprayed coatings of MgAl2O4, Al2O<sup>3</sup> are commonly used as a protective layer for parts that require strong insulating properties (<sup>ρ</sup> = 10−14−10−<sup>15</sup> Ohm cm, T = 20 ◦C) under the conditions of high temperature, vacuums and radiation. Magnesium aluminate spinel compositions using aluminium oxide MgAl2O<sup>4</sup> + 30%Al2O3, MgAl2O<sup>4</sup> + 50%Al2O3, with a coating thickness of between 0.35 and 0.50 mm, offers satisfactory electrical insulation via high intensity neutron and gamma fluxes in vacuum, at temperatures ranging between 20 and 700 ◦C. The MgAl2O4, Al2O<sup>3</sup> coatings are widely used as an electrical insulation layer for high-voltage electrical devices, channels and parts of magnetohydrodynamic (MHD) generators, sensors, the pads of reactors and International Thermonuclear Experimental Reactor (ITER) blanket modules. These types of coatings are predominantly deposited using atmospheric plasma spraying (APS) [1–3]. The performance of oxide ceramics that are applied to reactor facilities will be determined not only by a significant difference in the thermal expansion coefficients of the substrate and the coating material, but also by phase transformations at high temperatures and through exposure to radiation [4,5]. Compared to aluminium oxide, the cubic crystal lattice of spinel provides greater stability at high fluxes of gamma-neutron irradiation at high temperatures.

The problem of estimating the degree of a non-uniform stress-strain state at the interfacial debonding region of coating and over the thickness has practical applications that will allow us to better interpret the results and optimise the geometry parameters of standard cylindrical specimens, according to the international standards EN ISO 14916:2017,

**Citation:** Zayatzev, A.; Lukianova, A.; Demoretsky, D.; Alexandrova, Y. Tensile Adhesion Strength of Atmospheric Plasma Sprayed MgAl2O4, Al2O<sup>3</sup> Coatings. *Ceramics* **2022**, *5*, 1242–1254. https://doi.org/ 10.3390/ceramics5040088

Academic Editors: Amirhossein Pakseresht and Kamalan Kirubaharan Amirtharaj Mosas

Received: 14 November 2022 Accepted: 7 December 2022 Published: 9 December 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

ASTM C633-13 (2021) and GOST 9.304-87, JIS H 8666:1994 [6–9]. In practical terms, the standards and methods used to estimate the bond strength of thermal spray coatings are reduced to two main approaches for assessing cylindrical and conical specimens under tensile loads (uniaxial stress state). Most methods used to estimate the adhesion strength of a coating to a substrate can also be divided into two main groups; namely, qualitative testing methods and quantitative testing methods [10–15].

The tensile adhesion strength of thermal spray coatings will depend on different mechanical characteristics, including crack resistance (fracture toughness), Young's module, microhardness/hardness, compressive and tensile strength, types of residual stresses (quenching, peening, compressive [16,17]), differences in the coefficients of thermal expansion between the coating and the substrate as well as other features [10,11,18–20]. Parameters such as the roughness of the substrate after grit blasting, coating thickness, the composition of the coating, the tendency of the substrate/coating system to form chemical bonds and spraying methods (APS, HVOF, suspension-HVOF, DGS, LPCS [21–23], etc.) are critically important in terms of the adhesion strength. As such, there is no straightforward method for determining the adhesion strength of the part if it is operating under a complex stress state [24–27].

Meanwhile, test data obtained using different methods are often difficult to compare and are therefore rarely used for analytical description. There are some basic disadvantages that make it unfeasible to apply standard tensile strength test methods to a cylindrical specimen for high strength thermally sprayed ceramic coatings (bond strength more than 100 MPa). These are, firstly, the insufficient adhesive strength of glue at room and high temperatures, and secondly, the penetration of the adhesive to the substrate when the coatings are thin.

In cases where it impossible to perform the glue test, it is possible to apply an alternative pin method (Figure 1). However, this also has some drawbacks due to the lack of precise interpretation of the data due to the small diameter of the conical pin separation area (dpin = 2–2.5 mm) and the incomplete separation of the brittle and highly porous coating. *Ceramics* **2022**, *5,* FOR PEER REVIEW 3

**Figure 1.** A conical pin specimen and self-aligned test fixture for tensile adhesion test: (**1**) Conical pin; (**2**) Matrix; (**3**) Centring screw; (**4**) Coating; (**5**) Equipment for tensile testing machine: F ─ ultimate tensile force. **Figure 1.** A conical pin specimen and self-aligned test fixture for tensile adhesion test: (**1**) Conical pin; (**2**) Matrix; (**3**) Centring screw; (**4**) Coating; (**5**) Equipment for tensile testing machine: F—ultimate tensile force.

Comparative studies [10,14,24,28] show a significant impact on stress distribution at the bonding interface of the main geometric parameters based on the ratio of height (length)—hୱ୮ୣୡ to depth of the threaded closed hole—h୲୦୰.୦୭୪୪ and the nominal diameter—dୱ୮ୣୡ of a cylindrical specimen. The studies focus on investigating the influence of specimen height on tensile adhesion strength for both standard and elongated glued The application of a tensile adhesion test to a conical pin specimen may eliminate the influence of friction forces between the pin and the mating conical pair matrix (Figure 1). The end surfaces of the assembled pair must be carefully grounded before grit blasting and thermal spraying, and the absence of glue then makes it possible to investigate the adhesive strength of the thermally sprayed coatings at high temperatures.

specimens with thermal spray coatings assumed by ASTM C633-13 (2021), GOST 9.304-87. The effect of various specimen heights on the tensile adhesion test results and

Magnesium aluminum spinel (magnesium aluminate) and aluminium oxide powders (MgAl2O4 GTV 40.70.1, GTV GmbH, Luckenbach, Westerwald, Germany, particle size 20−45 µm; Al2O3 Amperit 740.001, H.C. Starck, particle size 22−45 µm) were deposited onto austenitic stainless steel 316L(N)-IG substrates using atmospheric plasma spraying, through the YPY-8M (JSC "Electromekhanika", Rzhev, Tver region, Russia [29]) technique, with a mounted low-capacity plasma torch. The spraying parameters for two types of oxide coatings and bond coatings are listed in Table 1. Argon-nitrogen was used as plasma-forming mixture, and the constant flow rates are also listed in Table 1. The standard plasma spray conditions of the oxide coating, such as MgAl2O4, Al2O3, are described in various articles [22,24,30,31]. Each set of specimens was deposited by specially designed equipment to set specimens at the same spray distance (Table 1). The spraying of ceramic electrically insulating MgAl2O4, Al2O3 oxide coatings on an austenitic steel substrate of a 316L(N)-IG alloy, standard EN 10088-1:2005 was performed using atmospheric plasma spraying equipment by feeding powdered material into the column of the compressed arc discharge (the anode spot of plasma torch between cathode and

For testing purposes, the coatings were deposited onto six cylindrical specimen types (dୱ୮ୣୡ = 25/25.4 mm in diameter; 3 standard and 3 elongated—heights hୱ୮ୣୡ = 28–38.1 mm) by thickness hୡ from 0.4 to 0.5 mm with a bond coating of NiAl (powder: Metco 40NS, Oerlicon Metco, Wohlen, Switzerland, particle size 45−90 µm) (Figure 2). In order to isolate

the following sections.

anode).

**2. Experimental Procedures**  *2.1. Plasma Spraying Conditions* 

Comparative studies [10,14,24,28] show a significant impact on stress distribution at the bonding interface of the main geometric parameters based on the ratio of height (length)—hspec to depth of the threaded closed hole—hthr.holl and the nominal diameter—dspec of a cylindrical specimen. The studies focus on investigating the influence of specimen height on tensile adhesion strength for both standard and elongated glued specimens with thermal spray coatings assumed by ASTM C633-13 (2021), GOST 9.304-87. The effect of various specimen heights on the tensile adhesion test results and the interface stress distribution at the debonding area will be presented and discussed in the following sections.

#### **2. Experimental Procedures**

### *2.1. Plasma Spraying Conditions*

Magnesium aluminum spinel (magnesium aluminate) and aluminium oxide powders (MgAl2O<sup>4</sup> GTV 40.70.1, GTV GmbH, Luckenbach, Westerwald, Germany, particle size 20−45 µm; Al2O<sup>3</sup> Amperit 740.001, H.C. Starck, particle size 22−45 µm) were deposited onto austenitic stainless steel 316L(N)-IG substrates using atmospheric plasma spraying, through the YPY-8M (JSC "Electromekhanika", Rzhev, Tver region, Russia [29]) technique, with a mounted low-capacity plasma torch. The spraying parameters for two types of oxide coatings and bond coatings are listed in Table 1. Argon-nitrogen was used as plasmaforming mixture, and the constant flow rates are also listed in Table 1. The standard plasma spray conditions of the oxide coating, such as MgAl2O4, Al2O3, are described in various articles [22,24,30,31]. Each set of specimens was deposited by specially designed equipment to set specimens at the same spray distance (Table 1). The spraying of ceramic electrically insulating MgAl2O4, Al2O<sup>3</sup> oxide coatings on an austenitic steel substrate of a 316L(N)-IG alloy, standard EN 10088-1:2005 was performed using atmospheric plasma spraying equipment by feeding powdered material into the column of the compressed arc discharge (the anode spot of plasma torch between cathode and anode).

**Table 1.** Plasma spraying operating parameters.


For testing purposes, the coatings were deposited onto six cylindrical specimen types (dspec = 25/25.4 mm in diameter; 3 standard and 3 elongated—heights hspec = 28–38.1 mm) by thickness h<sup>c</sup> from 0.4 to 0.5 mm with a bond coating of NiAl (powder: Metco 40NS, Oerlicon Metco, Wohlen, Switzerland, particle size 45−90 µm) (Figure 2). In order to isolate the uncoated surfaces of a cylindrical specimen from a stream of spray particles, a protective mask was applied. The first and third types of cylindrical specimen were manufactured in accordance with the standards ASTM C633-13 (2021), GOST 9.304-87, (Figure 2).

**Figure 2.** Six types of cylindrical specimens used to evaluate the bond strength of the thermal spray coating.

*Ceramics* **2022**, *5*, Firstpage–Lastpage. https://doi.org/10.3390/xxxxx www.mdpi.com/journal/ceramics The geometry of the second type of specimen (Figure 2) was altered to improve the ability of the process to remove the adhesive (glue) surge after curing and to save the possibility of further centring the specimen in the precision bushings (Figure 3). The design

of the elongated specimen was changed in accordance with the ratio of the specimen's height hspec to depth of the threaded closed hole hthr.holl using the following equation:

$$\alpha = \frac{\text{h}\_{\text{thr.holl}}}{\text{h}\_{\text{spec}}} = 0.4 \tag{1}$$

The coefficient ratio of the specimen heights α = 0.4 was chosen based on the results of similar studies [14]. *Ceramics* **2022**, *5,* FOR PEER REVIEW 6

**Figure 3.** The geometry of a cylindrical specimen (type 2) assembled by tensile force F = 14,000 N: (**1**) Specimen with coating; (**2**) Epoxy; (**3**) Specimen without coating; (**4**,**5**) Equipment for tensile testing machine; (**6**) Bushing. **Figure 3.** The geometry of a cylindrical specimen (type 2) assembled by tensile force F = 14,000 N: (**1**) Specimen with coating; (**2**) Epoxy; (**3**) Specimen without coating; (**4**,**5**) Equipment for tensile testing machine; (**6**) Bushing.

*2.2. Finite Element Analysis, Boundary Conditions*  Considerable research has been performed to investigate the stress-strain distribution in oxide coating and substrate interface to develop six finite element models using Before the substrates were coat-sprayed, they were grit-blasted with 1 mm alumina grit at an air pressure of up to 4–5 kg/cm<sup>2</sup> . The mean roughness of the substrate was approximately Rz 45 ± 5 µm.

#### the ANSYS R16.2 programme, (Ansys Inc., Canonsburg, Pennsylvania, USA). The axisymmetric models included two identical cylindrical halves, bonded together with a *2.2. Finite Element Analysis, Boundary Conditions*

ceramic coating. In order to facilitate calculations, the adhesive layer (glue) was excluded from the models, and the primary objective of this study was to estimate the level of uniformity in the interface stress distribution. It was therefore possible to simplify the finite element Considerable research has been performed to investigate the stress-strain distribution in oxide coating and substrate interface to develop six finite element models using the ANSYS R16.2 programme, (Ansys Inc., Canonsburg, PA, USA). The axisymmetric models included two identical cylindrical halves, bonded together with a ceramic coating.

models of the specimens. The following boundary conditions and assumptions were made for the finite-element models: In order to facilitate calculations, the adhesive layer (glue) was excluded from the models, and the primary objective of this study was to estimate the level of uniformity in the interface stress distribution. It was therefore possible to simplify the finite element models of the specimens.

• The contact between the substrate and coating was assumed as a rigid connection with a restriction on all degrees of freedom The following boundary conditions and assumptions were made for the finite-element models:

• Axial symmetry was provided by a cyclic region in the form of a 1/4 model by imposing boundary conditions to the symmetry regions along the XOY and YOZ planes • The contact between the substrate and coating was assumed as a rigid connection with a restriction on all degrees of freedom

ment analysis (FEA) of the models were compared with each other and with the results of the bond strength tests. The finite element models were loaded with a tensile load of F = 14,000 N to the threaded hole, as shown in Figure 4. The mechanical properties of the Al2O3 coating and substrate were taken from the material library of the ANSYS R16.2

The finite element grid near the coating-substrate interface was more refined than in

• The material of the substrate and oxide coating possessed only elastic strain.

programme.


The finite element grid near the coating-substrate interface was more refined than in other areas of the model—approximately 0.1 mm (Figure 4). The results of a finite element analysis (FEA) of the models were compared with each other and with the results of the bond strength tests. The finite element models were loaded with a tensile load of F = 14,000 N to the threaded hole, as shown in Figure 4. The mechanical properties of the Al2O<sup>3</sup> coating and substrate were taken from the material library of the ANSYS R16.2 programme. *Ceramics* **2022**, *5,* FOR PEER REVIEW 7 Previous tests [31–33] revealed very similar mechanical and physical properties for the MgAl2O4, Al2O3 oxide coatings, which made it possible to perform FEA only for the

**Figure 4.** The axisymmetric finite element model for the standard specimen (type 1): (**a**) the finite element of two identical cylindrical halves bonded together with ceramic coating, GOST 9.304-87; (**b**) the 3-D finite element model grid. **Figure 4.** The axisymmetric finite element model for the standard specimen (type 1): (**a**) the finite element of two identical cylindrical halves bonded together with ceramic coating, GOST 9.304-87; (**b**) the 3-D finite element model grid.

*2.3. Tensile Adhesion Strength Testing*  In this investigation, the test method of estimation tensile adhesion strength was based on the ASTM C633-13 (2021), GOST 9.304-87 [6,9] standards. Six specimens Previous tests [31–33] revealed very similar mechanical and physical properties for the MgAl2O4, Al2O<sup>3</sup> oxide coatings, which made it possible to perform FEA only for the Al2O<sup>3</sup> coating.

(standard and elongated) were bonded to the same uncoated specimens (counterparts)

#### using a single-part epoxy resin Permobond ES 550 (maximum tensile strength σ୲ୣ୬ = 60 ± *2.3. Tensile Adhesion Strength Testing*

3 GPa, maximum shear strength τୱ୦ = 41 ± 2 GPa by T = 20 °С). The alignment of the specimens was provided by centring bushings. The coatings produced were compared in terms of phase composition and microstructure, and the bond strength was also analysed at a temperature of T = 20 °С. After thermal curing and cooling, the specimens were loaded with axial breaking force until debonding occurred at a traverse speed of 0.5 mm/min in the IR5143-200-11 tensile testing machine (JSC "Tochpribor", Ivanovo, Russia [34]). The tensile adhesion In this investigation, the test method of estimation tensile adhesion strength was based on the ASTM C633-13 (2021), GOST 9.304-87 [6,9] standards. Six specimens (standard and elongated) were bonded to the same uncoated specimens (counterparts) using a single-part epoxy resin Permobond ES 550 (maximum tensile strength σten = 60 ± 3 GPa, maximum shear strength τsh = 41 ± 2 GPa by T = 20 ◦C). The alignment of the specimens was provided by centring bushings. The coatings produced were compared in terms of phase composition and microstructure, and the bond strength was also analysed at a temperature of T = 20 ◦C.

strength of σ୲ୣ୬ was calculated as the ratio between ultimate tensile force F divided by cross-sectional area A (A = 491 mm2 for all testing results). Three identical tests were performed under the same conditions for each type of cylindrical specimen, using the MgAl2O4, Al2O3 plasma spray coating. **3. Results and Discussion**  *3.1. Results of Tensile Bond Strength of Standard and Elongated Specimens*  After thermal curing and cooling, the specimens were loaded with axial breaking force until debonding occurred at a traverse speed of 0.5 mm/min in the IR5143-200-11 tensile testing machine (JSC "Tochpribor", Ivanovo, Russia [34]). The tensile adhesion strength of σten was calculated as the ratio between ultimate tensile force F divided by cross-sectional area A (A = 491 mm<sup>2</sup> for all testing results). Three identical tests were performed under the same conditions for each type of cylindrical specimen, using the MgAl2O4, Al2O<sup>3</sup> plasma spray coating.

Verification of the FEA data was performed by comparing them with the summary results of the tensile adhesion testing. The bond strengths of the APS ceramic coatings—MgAl2O4, Al2O3 for both standard and elongated specimens—are shown in Table 2.

estimated (Table 2). In the present investigation, the adhesive failure mode occurred at the bond coating-substrate interface [30] for all of the tensile tests of the MgAl2O4, Al2O3 coatings, without the visible penetration of epoxy resin into the coating-substrate inter-

#### **3. Results and Discussion**

#### *3.1. Results of Tensile Bond Strength of Standard and Elongated Specimens*

Verification of the FEA data was performed by comparing them with the summary results of the tensile adhesion testing. The bond strengths of the APS ceramic coatings–- MgAl2O4, Al2O<sup>3</sup> for both standard and elongated specimens—are shown in Table 2. Before testing the tensile strength of the coating thickness, the h<sup>c</sup> and roughness Ra were estimated (Table 2). In the present investigation, the adhesive failure mode occurred at the bond coating-substrate interface [30] for all of the tensile tests of the MgAl2O4, Al2O<sup>3</sup> coatings, without the visible penetration of epoxy resin into the coating-substrate interface. The trend of decreased adhesion strength for elongated specimens correlated well with the FEA results.

**Table 2.** Summary results of tensile bond strength measurements for APS—MgAl2O<sup>4</sup> , Al2O<sup>3</sup> and finite element surface stresses on standard and elongated specimens.


The results of the tensile adhesion strength tests showed a low level of bond strength for applied APS technology for MgAl2O4, Al2O<sup>3</sup> coatings [3,10,22,24]. This may be related to the spraying equipment used, the construction of the plasma torch, the residual stress distribution, the fatigue crack propagation, the pore size and distribution [35], or the rate of particle velocity and temperature.

The high level of stress discontinuity at the coating-substrate interface might help explain the increased value of the adhesion strength (Table 2). As the surface morphology images in Figure 5 show, the low level of bond strength conforms well to the results of the metallographic analysis of the scanning electron microscope (SEM) images of the cross sections and surface morphologies of the coatings (large, moulded agglomerates, a large number of pores and other defects).

#### *3.2. Assessment of Stress Distribution during Tensile Testing*

The equivalent stress distribution and total strain showed in the three standard and three elongated specimens are shown in Figures 6–8. A calculation of the stress distribution at the interface of three standard specimens showed a high level of nonuniformity over the debonding area. For example, the maximum value of equivalent stress came at the outer edge of the ASTM C633-13 (2021) standard specimen (type 3, Figure 2)—σ max eq = 71.5 MPa and the minimum value occurs at the centre—σ min eq = 14.5 MPa (Figure 8). The international standards procedure assumes that the stress is uniform based on testing a cylindrical specimen. The most uneven distribution of the equivalent stress

was found at the interface of the GOST 9.304-87 standard specimen (type 1, Figure 2)—the maximum σ max eq = 59.6 MPa occurs between the centre and the outer edge of the specimen, while the minimum σ min eq = 9 MPa occurs at the centre of the specimen (Figure 6). The maximum value of the equivalent stress can therefore be taken as the average equivalent of the interface for the standard specimen type 1—σ max eq = σeq. The high level of stress discontinuity at the coating-substrate interface might help explain the increased value of the adhesion strength (Table 2). As the surface morphology images in Figure 5 show, the low level of bond strength conforms well to the results of the metallographic analysis of the scanning electron microscope (SEM) images of the cross sections and surface morphologies of the coatings (large, moulded agglomerates, a large number of pores and other defects).

face. The trend of decreased adhesion strength for elongated specimens correlated well

The results of the tensile adhesion strength tests showed a low level of bond strength for applied APS technology for MgAl2O4, Al2O3 coatings [3,10,22,24]. This may be related to the spraying equipment used, the construction of the plasma torch, the residual stress distribution, the fatigue crack propagation, the pore size and distribution [35], or the rate

*Ceramics* **2022**, *5,* FOR PEER REVIEW 8

with the FEA results.

of particle velocity and temperature.

**Figure 5.** Cross-section SEM images of microstructures of the coating: (**a**) Al2O3; (**b**) MgAl2O4. For spray parameters, refer to Table 2. **Figure 5.** Cross-section SEM images of microstructures of the coating: (**a**) Al2O<sup>3</sup> ; (**b**) MgAl2O<sup>4</sup> . For spray parameters, refer to Table 2.

The average equivalent stress σeq = 43 MPa (Figure 8) showed by FEA is 155% higher than the average tensile adhesion strength σten = 27.8 ± 0.6 MPa for Al2O<sup>4</sup> (type 3, see Table 2) assumed by the ASTM C633-13 (2021) procedure.

The level of non-uniformity stress distribution in the test specimen was estimated using the following equation:

$$\beta \, \, = \frac{\sigma\_{\rm eq}^{\rm max}}{\sigma\_{\rm eq}^{\rm min}} \, \, \, \tag{2}$$

The non-uniform stress distribution will lead to the misinterpretation of the adhesion tensile testing results [14]. Significant excess of peak stress values at the outer edge, compared with average stress distribution, means that the inherent determination of high or low **Type of Specimen/Test** 

Type 1, standard/GOST 9.304-87 [9]

Type 4, elongated/GOST 9.304-87 [9]

Type 2, modified/an in-house test method

Type 5, elongated/an in-house test method

Type 3, standard/ASTM C633-13 (2021) [6]

Type 6, elongated/ASTM C633-13 (2021) [6]

**Method Type of Coating Thickness** 

Figure 2)—σୣ୯

values of adhesion strength can be assumed by the ASTM C633-13 (2021), GOST 9.304-87 test procedure. The result implies that the bond strength depends not only on the geometry of a specimen [14,16], but also on the degree of plasticity and brittleness of the coating (brittle or ductile fracture). 2)—the maximum σୣ୯ ୫ୟ୶ = 59.6 MPa occurs between the centre and the outer edge of the specimen, while the minimum σୣ୯ <sup>୫୧୬</sup> = 9 MPa occurs at the centre of the specimen (Figure 6). The maximum value of the equivalent stress can therefore be taken as the average equivalent of the interface for the standard specimen type 1—σୣ୯ ୫ୟ୶ = σതതത ୣ୯തത.

*Ceramics* **2022**, *5,* FOR PEER REVIEW 9

finite element surface stresses on standard and elongated specimens.

**Roughness [μm]** 

*3.2. Assessment of Stress Distribution During Tensile Testing* 

 **[μm]** 

**Table 2.** Summary results of tensile bond strength measurements for APS—MgAl2O4, Al2O3 and

**Relative Error of Tensile Bond Strength [%]** 

**Finite Element Average Equivalent Stress [MPa]** 

<sup>୫୧୬</sup> = 14.5

**Tensile Bond Strength**  തതതതതത േ  **[MPa]** 

Al2O3\_APS 420 ± 35 38 ± 10 30.1 ± 1.6 5 60 6.7 MgAl2O4\_APS 406 ± 27 33 ± 6 28.8 ± 1.9 7 - -

Al2O3\_APS 484 ± 21 29 ± 4 25.0 ± 2.6 10 45 1.4 MgAl2O4\_APS 446 ± 45 48 ± 5 22.0 ± 4.3 19 - -

Al2O3\_APS 424 ± 38 33 ± 8 23.2 ± 3.2 14 45 3.1 MgAl2O4\_APS 484 ± 18 31 ± 4 26.4 ± 1.6 6 - -

Al2O3\_APS 426 ± 36 31 ± 6 19.4 ± 0.5 2 44 1.8 MgAl2O4\_APS 440 ± 29 30 ± 2 20.8 ± 2.0 10 - -

Al2O3\_APS 460 ± 32 37 ± 8 27.8 ± 0.6 2 43 4.9 MgAl2O4\_APS 430 ± 30 38 ± 4 25.1 ± 3.2 13 - -

Al2O3\_APS 472 ± 12 33 ± 3 20.7 ± 1.7 8 44 1.7 MgAl2O4\_APS 450 ± 31 37 ± 3 18.4 ± 1.5 8 - -

The equivalent stress distribution and total strain showed in the three standard and three elongated specimens are shown in Figures 6, 7 and 8. A calculation of the stress distribution at the interface of three standard specimens showed a high level of non-uniformity over the debonding area. For example, the maximum value of equivalent stress came at the outer edge of the ASTM C633-13 (2021) standard specimen (type 3,

୫ୟ୶ = 71.5 MPa and the minimum value occurs at the centre—σୣ୯

MPa (Figure 8). The international standards procedure assumes that the stress is uniform based on testing a cylindrical specimen. The most uneven distribution of the equivalent stress was found at the interface of the GOST 9.304-87 standard specimen (type 1, Figure

**Figure 6.** Equivalent stress distribution at the debonding area of the Al2O3 coating with a tensile force of F = 14,000 N: (**a**) GOST 9.304-87 standard specimen, type 1; (**b**) Elongated specimen, type 4. For geometric parameters, see Figure 2. **Figure 6.** Equivalent stress distribution at the debonding area of the Al2O<sup>3</sup> coating with a tensile force of F = 14,000 N: (**a**) GOST 9.304-87 standard specimen, type 1; (**b**) Elongated specimen, type 4. For geometric parameters, see Figure 2.

higher than the average tensile adhesion strength σ୲ୣ୬ = 27.8 ± 0.6 MPa for Al2O4 (type 3,

ౣ౮ ౧

The non-uniform stress distribution will lead to the misinterpretation of the adhesion tensile testing results [14]. Significant excess of peak stress values at the outer edge, compared with average stress distribution, means that the inherent determination of high or low values of adhesion strength can be assumed by the ASTM C633-13 (2021), GOST 9.304-87 test procedure. The result implies that the bond strength depends not only on the geometry of a specimen [14,16], but also on the degree of plasticity and brittleness of

The main reasons for the appearance of significant non-uniform interface stress distribution should also be mentioned. These are the appearance of additional shear stress at the outer edge of the coating (the Edge effect), and the decrease in the stiffness of the specimen due to the close proximity of the threaded hole in relation to the detachment

β = ౧

ୣ୯തത = 43 MPa (Figure 8) showed by FEA is 155%

ౣ, (2)

The average equivalent stress തσതത

using the following equation:

the coating (brittle or ductile fracture).

surface of the coating.

**Figure 7.** The equivalent stress distribution and total strain at the debonding area of the coating Al2O3 with tensile force F = 14,000 N: (**a**) Modified specimen, type 2; (**b**) Elongated specimen, type 5. For geometric parameters, refer to Figure 2. **Figure 7.** The equivalent stress distribution and total strain at the debonding area of the coating Al2O<sup>3</sup> with tensile force F = 14,000 N: (**a**) Modified specimen, type 2; (**b**) Elongated specimen, type 5. For geometric parameters, refer to Figure 2.

The impact of the Edge effect can be minimized by increasing the diameter of the cylindrical specimen, up to dୱ୮ୣୡ = 40–60 mm, as well as the length of a cylindrical specimen. The distance from the threaded closed holes to the plane face of a cylindrical specimen with a diameter of dୱ୮ୣୡ = 25/25.4 mm should be enough to minimise the stiffness reduction. Applying elongated specimens with lengths of hୱ୮ୣୡ = 38–50 mm and The main reasons for the appearance of significant non-uniform interface stress distribution should also be mentioned. These are the appearance of additional shear stress at the outer edge of the coating (the Edge effect), and the decrease in the stiffness of the specimen due to the close proximity of the threaded hole in relation to the detachment surface of the coating.

more [9] will lead to more uniform stress distribution. The finite element analysis and laboratory testing of the elongated cylindrical specimens with a diameter of dୱ୮ୣୡ = 25/25.4 mm confirmed that the results of estimating bond strength using a standard cylindrical specimen assumed by ASTM C633-13 (2021), GOST 9.304-87 can be significantly higher than the actual tensile adhesion strength [2]. With the exception of the GOST 9.304-87 standard specimen, the equivalent stress peaks The impact of the Edge effect can be minimized by increasing the diameter of the cylindrical specimen, up to dspec = 40–60 mm, as well as the length of a cylindrical specimen. The distance from the threaded closed holes to the plane face of a cylindrical specimen with a diameter of dspec = 25/25.4 mm should be enough to minimise the stiffness reduction. Applying elongated specimens with lengths of hspec = 38–50 mm and more [9] will lead to more uniform stress distribution.

were not identified at the centre of the specimens, but rather, at the outer edge in all models. The finite element analysis and laboratory testing of the elongated cylindrical specimens with a diameter of dspec = 25/25.4 mm confirmed that the results of estimating bond strength using a standard cylindrical specimen assumed by ASTM C633-13 (2021), GOST 9.304-87 can be significantly higher than the actual tensile adhesion strength [2]. With the exception of the GOST 9.304-87 standard specimen, the equivalent stress peaks were not identified at the centre of the specimens, but rather, at the outer edge in all models.

**Figure 8.** Equivalent stress distribution and total strain at the debonding area of the Al2O3 coating with a tensile force of F = 14,000 N: (**a**) ASTM C633-79 (2021) standard specimen, type 3; (**b**) Elongated specimen, type 6. For geometric parameters, see Figure 2. **Figure 8.** Equivalent stress distribution and total strain at the debonding area of the Al2O<sup>3</sup> coating with a tensile force of F = 14,000 N: (**a**) ASTM C633-79 (2021) standard specimen, type 3; (**b**) Elongated specimen, type 6. For geometric parameters, see Figure 2.

#### **4. Conclusions 4. Conclusions**

According to the results of this scientific study and the analysis of the existing literature, we were able to make three conclusions. Firstly, the significant peak stress at the outer edge of the specimen, compared to the average stress calculated by tensile testing, implies that the bond strength should be estimated using elongated specimens, according to the ASTM C633-13 (2021), GOST 9.304-87 test procedure. Secondly, compared to conventional tests (EN ISO 14916:2017, ASTM C633-13 (2021), GOST 9.304-87), the accuracy of tensile bond strength estimation may be higher when the new geometry of a cylindrical specimen is applied. Thirdly, to provide a more accurate method, researchers should carry out finite element analysis and an epoxy tensile adhesion test using elongated cylindrical specimens using different diameters, dୱ୮ୣୡ = 20–60 mm (using the procedure defined in ASTM C633-13 (2021), GOST 9.304-87). According to the results of this scientific study and the analysis of the existing literature, we were able to make three conclusions. Firstly, the significant peak stress at the outer edge of the specimen, compared to the average stress calculated by tensile testing, implies that the bond strength should be estimated using elongated specimens, according to the ASTM C633-13 (2021), GOST 9.304-87 test procedure. Secondly, compared to conventional tests (EN ISO 14916:2017, ASTM C633-13 (2021), GOST 9.304-87), the accuracy of tensile bond strength estimation may be higher when the new geometry of a cylindrical specimen is applied. Thirdly, to provide a more accurate method, researchers should carry out finite element analysis and an epoxy tensile adhesion test using elongated cylindrical specimens using different diameters, dspec = 20–60 mm (using the procedure defined in ASTM C633-13 (2021), GOST 9.304-87).

**Author Contributions:** A.Z. developed and planned the concept and methodology for conducting and reporting this science work. A.L., D.D. and A.Z. carried out the simulations of stress-strain stated at the coating-substrate interface and analysed the data on the tensile tests. D.D. undertook the spraying of coatings on specimens. A.Z. wrote the draft document. Y.A. organised SEM analysis and contributed to the discussion and interpretation of the results. All authors have read and agreed to the published version of the manuscript. **Author Contributions:** A.Z. developed and planned the concept and methodology for conducting and reporting this science work. A.L., D.D. and A.Z. carried out the simulations of stress-strain stated at the coating-substrate interface and analysed the data on the tensile tests. D.D. undertook the spraying of coatings on specimens. A.Z. wrote the draft document. Y.A. organised SEM analysis and contributed to the discussion and interpretation of the results. All authors have read and agreed to the published version of the manuscript.

**Funding:** The study was carried out with the financial support of the Ministry of Science and Higher Education of the Russian Federation within the framework of the state task theme no. AAAAA12-2110800012-0. **Funding:** The study was carried out with the financial support of the Ministry of Science and Higher Education of the Russian Federation within the framework of the state task theme no. AAAAA12- 2110800012-0.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **References**

