Abstract
The mechanical properties of coatings are significantly influenced by their interfacial bonded status and interfacial stresses, which are quite difficult to measure by traditional testing techniques. In this study, a series of theoretical analyses regarding Young's modulus, interface shear stress and tension stress for coatings are successfully deduced based on an assumption of interfacial constraints and homogeneous strain. Three equations are derived to determine the Young's modulus, interface shear strength and cohesion strength for coatings. A tension method is used to test the mechanical properties of coatings and presented in detail. It concludes that this method is relatively simple to perform, and allows for a reliable determination of interface shear strength and cohesion strength for coatings. A corresponding theoretical analysis is logical and reasonable. The magnitude of the Young's modulus, interface shear strength and cohesion strength for yttria stabilised zirconia coatings was about 171–189, 6–24 and 175–238 MPa respectively.
Introduction
Thermal sprayed coatings are usually layered systems deposited on metallic components, for example, gas turbine engine blades or vanes, which allow higher operating temperatures. To this effect, thermal sprayed coatings can greatly increase the efficiency and durability of engineering materials.1,2 The demand for enhanced efficiency of engines has led to a significant increase in possible combustion temperatures. These requirements have been proven as a driving force for the study of thermal sprayed coatings.
Notably, it is very difficult to study interface theories about coatings. They are quite complex, diverse and interactive. It is necessary to thoroughly investigate these interface theories, and to further obtain the mechanical properties for thermal sprayed coatings. A wealth of literature concerning the interface stress of coatings has been published to date, including where Dolgov et al. 3 deduced a complex expression for tension stress in coatings via a series of Fourier transforms. Lyashenko et al. 4 subsequently introduced a mechanical model to calculate the maximal strain, Young's modulus, Poisson ratio or other important factors for coatings. Bai 5 established a mechanical model and deduced an equation for calculating the interface shear stress of coatings. Similarly, Morscher 6 found a mechanical model based on layered composite theories to calculate the Young's modulus of coatings. Zhang Xianchen 7 analysed the interior stress for functional gradient coatings based on the cantilever beam theories and solved the general solution of coatings’ interior stress. In surface engineering, the bonding strength for coatings is often defined by selecting the numbers of cyclic load.8–10 The critical forces are usually chosen to determine the adhesive strength for coatings,11,12 and using them as an evaluation index to evaluate the failure of coatings has gained widespread recognition in academia. 13
The primary objective of this work is to establish a theoretical model, based on an assumption of interface constraint and homogeneous strain, to deduce cohesion stress and interface shear stress, which can be used to evaluate the cohesion strength and the interface shear strength of coatings. A series of equations based the theoretical model of coatings are deduced, then used to calculate the mechanical properties of coatings. Considering the demand for measuring the mechanical properties of thermal sprayed coatings with different thicknesses, we improve the traditional testing method by introducing a special specimen. For verifying the reasonability of the theoretical model and the feasibility of the experimental method, we select the yttria stabilised zirconia coatings and the stainless steel 329 (329-SS) substrates system. The critical time and forces are obtained by analysing the load–time curve and stress–strain curve of coatings with different thicknesses. The cohesion strength and interface shear strength of coatings are then obtained. The Young's modulus, shear modulus and Poisson ratios of coatings are also calculated in order to complete an evaluation of strength. To conclude, the results are compared to other relevant literature.
Theories
Mechanical model
In order to deduce the interface shear stress and interior cohesion stress in coatings, the mechanical model of the coatings and substrate system is established, as shown in Fig. 1. Because the coatings are assumed to be closely deposited on the substrate and their strains are equal to each other, a theoretical model is found. As shown in this figure, the mechanical model possesses the following characteristics: the coatings and substrate are mutually constrained along their interfaces; the strain in every layer is homogeneous along the thickness direction of the coatings, when loading at both ends of the specimen along y direction within an elastic range.
Mechanical model reflecting the interfacial interaction of coatings and substrate
Interface stress analysis
The physical properties of most materials typically vary, the shearing stress τ(x,y,z) is induced from the interfaces between the coating and substrate when loading at both ends of specimen. Considering that the inherent magnitude of the compressive strength for most materials is greater than their tension strength, the interface shear stress at x direction can be ignored. The interface shear stress along z coordinate is likewise ignored, because of the coatings’ negligible thickness. The shear stress of coatings can then be simplified as an unary function τ(y), expressed as a dimensionless function in the following equation
14
Because the resultant forces along y direction amount to zero according to the balance condition, the following equation can be deduced
Young's modulus of coatings
The schematic of a tensile specimen is shown in Fig. 2. This specimen is symmetrically coated on both sides, and two types of coating with different thickness are deposited onto the substrate. The specimen contains three special zones (Zones I, II and III) among its gauge length, and the middle of the specimen (Zone II) is uncoated. Six strain foils, which are divided into three groups corresponding to the three zones, are glued on the upper surface of the specimen, and two strain foils are glued on every zone in the x direction and y direction, respectively. The two strain foils adhered to zone II are used to measure the strain data of the substrates, which are then used to calculate the Young's modulus and Poisson ratio of the substrate. Four other strain foils adhering to Zone I and Zone III are used to test the strain data of the coatings, which are likewise measured to obtain the Young's modulus and Poisson ratio of the coatings. Altogether, six groups of raw data are obtained, with three of these representing the strain data at the x direction, and the others describing the strain data at the y direction.
Schematic of tensile specimen: a frontal view; b profile view
In order to measure the interface shear strength or cohesion strength for coatings, it is crucial to first accurately obtain the Young's modulus of the coatings, (as described in detail in our previous work).
15
The Young's modulus of coatings in Zone I or Zone III can be calculated by the following equation
Experimental details
Specimens preparation
The stainless steel 329 (329-SS) plates (about 2·0 mm thick,) were designed with in-plane dimensions of 200×150 mm, then cut into strips by wire cut electrical discharge machining (WEDM). These strips were then further cut into a dog bone shape and sprayed with 6% Y2O3–ZrO2 coatings. To ensure the uniformity of all substrates, the first strip was cut at minimum 2 mm from the edge of the 329-SS plate. Additionally, to reduce the amount of edge defects (such as scratches, gaps or dents,) the strips were ground with 400–1200 grit SiC paper under flowing water, then polished using a 1 μm diamond abrasion paste. The finished substrates' surfaces were examined using a metallurgical microscope and their dimensions measured by a vernier caliper. The 6% Y2O3–ZrO2 TBCs were prepared on 329-SS substrates by plasma thermal spraying technology. The detailed deposition process are shown in Table 1.
Deposition process of coatings by plasma thermal spraying technology
Details regarding the processes are as follows. First, a special fixture composed of an upper cover plate and a lower cover plate were designed and manufactured, and a slot with in-plane dimensions of 120×60 mm was opened in these plates. Second, five predeposited specimens were tightly fixed in the fixture with 4–8 bolts after copper foils with 20 mm width were used to cover the middle (Zone II) in order to avoid spraying it. Lastly, 6% Y2O3–ZrO2 coatings were sprayed onto the front and back of the 329-SS substrates. Throughout the spraying process, we strictly controlled the spraying parameters under the same experimental conditions. Five specimens were prepared in one batch, and there were five batches to be sprayed altogether, so a total of 25 specimens were obtained. We only selected one specimen from every batch, thus the five specimens were tested in our study. A vernier caliper was used to measure the geometric size of five as deposited specimens. The detailed sizes of these specimens are shown in Table 2.
Detailed geometric sizes of five specimens
Experimental measurements
The mechanical properties of all specimens were determined by tensile machine (Electro-hydraulic Servo Static Dynamic Testing Machine, CSS-280S-100). The relationship between load and time was monitored by the force sensors. To ensure that the loading procedure was static, the loading speed was controlled at 5 N s−1. The loads ranged from 50 to 10 kN. The strain data were measured by standard strain foils (BE120-2AA). A strain gauge device (10-channel digital static strain gauge device, CM-1J-10) was simultaneously applied for recording the strain data of the coatings and substrate. The microstructure of the coatings was examined by scanning electron microscope (SEM, HITACHI S-570).
Results
Elastic constants of 6% Y2O3 ZrO2 TBCs
The tensile stress–strain curve of 329-SS substrate, obtained by testing specimen no. 3, is shown in Fig. 3. By linearly fitting, it becomes obvious that the stress versus strain plot (the small plot in Fig. 3,) is highly linear (with a linear correlation greater than 0·99949). Based on the slope of the stress–strain within the elastic range, the Young's modulus of 329-SS substrates was 205·11 GPa, and ranged from 199 to 238 GPa for the five specimens.
Stress–strain curve of 329-SS substrate by testing the no. 3 specimen
Figure 4a shows the load–time curve recorded by tensile machine and six strains-time curves recorded by the six strain foils. Three curves, I1, II1 and III1 respectively, show longitudinal strains marked
,
and
. The other three curves, I2, II2 and III2 respectively, describe the transverse strains marked
,
and
. For the 6% Y2O3–ZrO2 coatings and 329-SS substrate system, it is necessary to obtain steady and fit strain data. Fifty groups of strain data, marked as a dashed, orange circle in Fig. 4a, were selected to calculate the Young's modulus and Poisson ratio of 6% Y2O3–ZrO2 coatings, subsequently enlarged as shown in Fig. 4b.
Load, strain and time relationship curves of the no. 3 specimen: a load–time and strain–time curves; b six enlarged longitudinal and transverse strains in three zones
We then plugged the longitudinal strains at the y direction, including Zones I, II and III, into equation (10). The Young's modulus of the 6% Y2O3–ZrO2 coatings for Zones I and III were calculated to be 171·4–189·2 GPa, with the coatings’ thicknesses ranging from 63·22 to 320·54 μm. Their shear modulus changed from 68·4 to 75·7 GPa. The Poisson ratio remained relatively steady, only fluctuating between 0·249 and 0·252. The elastic constants of the thermal sprayed 6% Y2O3–ZrO2 coatings with different thicknesses for all specimens are shown in Table 3.
Elastic constants of thermal sprayed 6% Y2O3–ZrO2 coatings with different thicknesses
Failure analysis
The failure photos of the Zone I coating on the no. 3 specimen are shown in Fig. 5. The developing processes of the microcracks were recorded by the CCD and long focal lengths microscope (at a magnification of about ×8) in real time. As shown in Fig. 5a, there are no obvious microcracks on coating at 1800 s, then a small microcrack slowly begins at the right side at 2000 s, followed by two smaller microcracks emerging at the left side, as shown in Fig. 5b. These microcracks, as shown in Fig. 5c, further extend along the width alongside increasing tension forces. The microcrack at the right side extends nearly half the width of the coating by 2040 s. Compared to their previous states, the two small microcracks at the left side also grow significantly. Three wider cracks, as shown in Fig. 5d, form in the coating at 2060 s, further demonstrating the failure of the coating. Figure 5e shows a complete failure of the specimen after tensile testing. As shown in this figure, the coating in Zone III completely debonds from the substrate after tension. Meanwhile, three obvious microcracks corresponding to the cracks in Fig. 5d emerge in Zone I's coating, though this coating remains on the substrate. It has obviously debonded from the interface bewteen the coatings and substrate, however. Table 4 shows the failure phenomena and critical failure time of thermal spraying 6% Y2O3–ZrO2 coatings, recorded by CCD and long focal length microscope.
Failure photos of no. 3 specimen in Zone I after tension measured by CCD optical system: a 1800 s; b 2000 s; c 2040 s; d 2060 s e failure specimen after tension
Failure phenomena and critical failure time of thermal sprayed 6% Y2O3–ZrO2 coatings
As shown in Table 3, the testing time corresponding to the cracking phenomena of coatings decreases from 2040 to 1990 s, and the thickness of the coatings in turn increases from about 63 to 166 μm. The testing time corresponding to the debonding of the coatings' interface also decreases from 1970 to 1860 s; meanwhile, their thicknesses increase from about 215 to 320 μm. This indicates a gradual decrease of all critical loads corresponding to either interface debonding or cracks alongside an increasing thickness of coatings.
By further analysing the results, we found that cracks initially emerged in thermal spraying 6% Y2O3–ZrO2 coatings only when the coatings’ thickness was below 166 μm, and that the interface debonded when their thickness exceeded 215 μm. Results indicated that thicker coatings tended to debond from their substrate, and that thinner coatings in turn tended to crack. This is likely explained by the strain energy for crack propagation. As it is known, the thicker a coating is, the greater the strain energy for crack propagation is required, and vice versa. Where cracks in thinner coatings occur due to the small amount of strain energy required to form them, thicker coatings conversely debond more readily from their interface. As shown in above equations (8) and (9), the interface shear stress is related to seven parameters, Eco, Eo, W, L, H, h and Po. Moreover, cohesion stress is affected by the first five parameters. The testing results of the front five factors, however, are almost identical for all specimens via the above analysis. Only the last two factors altered for the five specimens, one is the coatings' thickness h, the other is the axial critical load Po corresponding to the failure of thermal spraying 6% Y2O3–ZrO2 coatings. It is obvious that the influence of critical load P0 on the interface shear stress is significantly smaller than that of the coatings’ thickness h. Therefore, as the coatings’ thickness increases, critical load P0 declines. To conclude, interface shear strength increased and cohesion strength decreased with the increasing thickness of coatings.
Strength analysis
One notable phenomena regarding the failure of thermal sprayed 6% Y2O3–ZrO2 coatings was that once the debonding was complete, no further cracking occurred. The different failure modes are very important to understand, because the different coatings' failure modes determine which type of strength properties for coatings can be calculated via different equations. Debonding failure due to the the maximum interface shear reaching the coatings’ interface shear strength, whereas cracks failure due to the maximum cohesion stress reaching the coatings’ cohesion strength. Using the no. 3 specimen as an example, we see where the interfacial debonding began at 1970 s near the end region in Zone III, and cracks began to form at 1990 s across the middle of Zone III. In this case, the interface shear stress at 1970 s had clearly reached maximum value corresponding to the coatings’ interface shear strength, and the cohesion stress at 1990 s increased to the maximum value corresponding to the coatings’ cohesion strength. Thus, critical force P0, corresponding to the different failure time, can be plugged into equations (8) and (9) to calculate the interface shear strength and the cohesion strength of coatings. For thermal spraying 6% Y2O3–ZrO2 coatings on the no. 3 specimen, the interface shear strength for Zone III was about 18·52 MPa, and because no debonding occurred prior to cracks forming in Zone I, we assume that the interface shear strength for Zone I was greater than 15·10 MPa. Similarly, the cohesion strength for Zone I was about 209·88 MPa. Because no cracks formed prior to the coating's debonding in Zone III, the interface shear strength was assumed to be greater than 198·68 MPa.
Table 5 lists two types of result for the interface shear strength and cohesion strength of thermal sprayed 6% Y2O3–ZrO2 coatings on five specimens. As shown, the interface shear strength changes gradually alongside an increase in the coatings’ thicknesses, ranging from 18·53 to 24·31 MPa for the thermal sprayed 6% Y2O3–ZrO2 coatings with 216–321 μm thicknesses. However, for the coatings of thicknesses below 216 μm, the interface shear strength was greater than 6·51 MPa, and because no microcracks emerged at the end regions of these coatings during the tension process, these results are semiquantitative.
Two kinds of strength properties for thermal sprayed 6% Y2O3–ZrO2 coatings with different thicknesses
Discussion
Table 6 shows the strength properties for Y2O3–ZrO2 coatings reported in both this study and other recent studies. In this study, the interface shear strength of thermal sprayed 6% Y2O3–ZrO2 coatings changed from 18·5 to 24·3 MPa when the coatings’ thicknesses ranged between 216 and 321 μm, but half-quantitatively changed from 6·5 to 18·5 MPa when the coatings’ thicknesses varied between 63 and 216 μm. Moreover, the cohesion strength of thermal sprayed 6% Y2O3–ZrO2 coatings were between 210 and 238 MPa, as corresponding to 63–216 μm thicknesses, altered to be 176–210 MPa for 63–216 μm thicknesses.
Comparison of strength properties for Y2O3–ZrO2 coatings
a is tension method, b is crack-opening displacement method, c is indentation method, d is scratch testing, e is micro-tension method, f is laser spallation technique and g is four-point bending method.
Recent literature has introduced other strength properties for thermal sprayed 6% Y2O3–ZrO2 coatings with different thicknesses. The interface adhesion strength (or bonding strength,) of yttria stabilised zirconia coatings was 6·1–9·5 MPa, corresponding to 300–400 μm thicknesses, 16 10·0–15·0 MPa for 50–250 μm thicknesses, 17 15·4–40·0 MPa for 1100–1300 μm thicknesses, 18 7·9–14·1 MPa for about 900 μm thicknesses 19 and about 26·6 MPa for about 270 μm thicknesses. 20 Unfortunately, few references specifically mention their interface shear strength or cohesion strength. Celik et al. 21 deposited Y2O3–ZrO2 coatings with 980–1500 μm thicknesses on a silver sheet by the sol–gel method, and measured the coatings’ interface shear strength to be about 2·4 MPa by micro-tensile method. Similarly, Schweitzer et al. 17 prepared thinner yttria stabilised zirconia coatings than the former, with the thickness of coatings ranging between 50–250 μm, possessing interface shear strengths between 11–30 MPa. The cohesion strength of Y2O3–ZrO2 coatings was introduced in recent studies,22–24 and ranged from 65–1500 MPa corresponding to 10–1000 μm thicknesses. Most notably, the magnitude of the cohesion strength for Y2O3–ZrO2 coatings with 60–360 μm thicknesses was found to be about 65–357 MPa, 23 which is in accordance with our results, showing cohesion strength to be 176–238 MPa corresponding to a thickness between 63–321 μm. We thus conclude that the results obtained in this paper are consistent with other studies. This also indicates that our mechanical model effectively and reasonably deduces the interface shear stress and the cohesion stress for coatings, and that the testing method is suitable for calculating interface shear strength and cohesion strength for coatings.
Conclusion
A reasonable mechanical model based on an assumption of interface constraint and homogeneous strain was established, and used to deduce the cohesion stress and interface shear stress of coatings. A series of equations based on this theoretical model were deduced for evaluating the cohesion strength and the interface shear strength of coatings. The elastic constants (Young's modulus, shear modulus and Poisson ratio) and strength properties (interface shear strength and cohesion strength) of thermal sprayed 6% Y2O3–ZrO2 coatings were calculated respectively. The interface shear strength increased slightly alongside increasing thickness of coatings, and the cohesion strength gradually decreased with increasing thickness of coatings. By further analysing the failure of certain coatings, it was found that thicker coatings tend to debond from their substrate, and thinner coatings in turn tend to crack. The reason for this is the strain energy required for the formation of cracks. The results obtained in this paper are consistent with other relevant literature. The major conclusions are as follows: the established mechanical model is reasonable; the theoretical analysis is accurate and logical; the deduced equations are correct; the method is relatively simple and allows for reliable determination of the strength properties of coatings; and the test results are successful and beneficial.
Footnotes
Acknowledgements
This paper was supported by the National Natural Science Foundation of China (61106124), Natural Science Foundation of Guangdong Province (S2013010013385), Science and Technology Projects of Zhanjiang City (2012D01, 2013D01) and Program for Innovative Research Team in Zhanjiang Normal University (ZSIT13006, 20131301109).