A method for measuring and calculating the fracture toughness of coating interfaces

Abstract

The present invention relates to a method for measuring and calculating the fracture toughness of a coating interface, comprising: measuring interface crack-related parameters of a test sample; wherein the interface crack-related parameters include: coating thickness, coating out-of-plane displacement, and crack radius under corresponding displacement; calculating the ratio of the crack radius to the coating thickness to determine the deformation type of the coating; and selecting a corresponding fracture toughness calculation model based on the deformation type to calculate the fracture toughness of the coating. In the measurement and calculation of the coating interface fracture toughness, the present invention considers the influence of the fracture mode and clarifies the separation mode of the coating. It also considers the influence of residual stress, making the interface fracture toughness more accurate.

Description

Technical Field

[0001] The present invention relates to the technical field of coating materials, in particular to a method for measuring and calculating the fracture toughness of a coating interface. Background Art

[0002] Coating technology is widely used in numerous industries. In the automotive sector, coatings enhance the wear and corrosion resistance of engine components while improving heat dissipation efficiency. In the machinery industry, coatings reduce friction and noise, improving the wear resistance of equipment. In the oil industry, coatings are used to reduce wear on drilling tools and extend their service life. In short, coating technology plays a key role in various industries by improving surface properties. However, during service, coating-substrate systems inevitably experience failures such as cracking and spalling, causing equipment to lose its normal operating capacity. Fracture toughness is one of the most important fundamental mechanical parameters of a material, characterizing its ability to resist fracture propagation. Therefore, studying the fracture toughness of coating interfaces is particularly important for assessing equipment reliability. Current research on the fracture properties of coating interfaces has primarily explored the relationship between the load acting between the coating and substrate and the fracture toughness of the coating interface, while ignoring the effects of residual stress between the coating and substrate, coating cracking patterns, and slip between the coating and substrate on fracture toughness.

[0003] Therefore, how to obtain a calculation method for the fracture toughness of the coating-substrate interface that takes into account the influence of residual stress between the coating and the substrate, as well as the slip problem at the coating-substrate interface and the coating cracking mode problem, as well as a testing method that matches the calculation method, has become a problem that needs to be solved urgently. Summary of the Invention

[0004] In response to the shortcomings of current research, the present invention aims to provide a method for measuring and calculating the fracture toughness of coating interfaces, which can accurately measure and calculate the fracture toughness of coating-substrate interfaces of different materials.

[0005] To achieve the above object, the present invention provides the following solutions:

[0006] A method for measuring and calculating the fracture toughness of a coating interface, comprising:

[0007] Measuring interface crack related parameters of the test sample; wherein the interface crack related parameters include: coating thickness, coating out-of-plane displacement, and crack radius under corresponding displacement;

[0008] Calculating the ratio of the crack radius to the coating thickness to determine the deformation type of the coating;

[0009] Based on the deformation type, a corresponding fracture toughness calculation model is selected to calculate the fracture toughness of the coating.

[0010] Optionally, measuring interface crack related parameters of the test sample includes:

[0011] Capturing an image of a coating cross section of the test sample, measuring the initial coating thickness at multiple locations from the image, and taking the average value as the coating thickness;

[0012] An indentation test is performed on the test sample to obtain the coating surface displacement and crack radius.

[0013] Optionally, performing an indentation test on the test sample includes:

[0014] S1.1. Place the test sample on the work surface with the substrate on the left and the coating on the right. Fix the test sample to the work surface with a clamp at the bottom.

[0015] S1.2. Select a conical diamond indenter with a preset tip radius and tip angle;

[0016] S1.3. Adjust the distance between the indentation point and the interface to be within the preset range;

[0017] S1.4. Perform an indentation test using the micro-loading module on the indenter. Set the load rate and remove the external load when the indentation depth reaches the preset value.

[0018] S1.5. When the penetration depth in step S1.4 is maximum, measuring the out-of-plane displacement of the coating;

[0019] S1.6. Remove the external load, observe the crack morphology, and extract the crack radius;

[0020] S1.7. Repeat S1.4 to S1.6 several times and take the average of the measured data.

[0021] Optionally, determining the deformation type of the coating includes:

[0022] When the ratio of crack radius to coating thickness is less than the preset ratio, the sample coating is in the linear deformation stage;

[0023] When the ratio of crack radius to coating thickness is greater than a preset ratio, the sample coating is in the nonlinear deformation stage.

[0024] Optionally, based on the deformation type, a corresponding fracture toughness calculation model is selected, and calculating the fracture toughness of the coating includes:

[0025] When the sample coating is in the linear deformation stage, the fracture toughness of mode I (Opening mode I) and mode II (shearing mode II) in the linear deformation stage are calculated using the fracture toughness linear model.

[0026] When the sample coating is in the nonlinear deformation stage, the fracture toughness nonlinear model is used to calculate the fracture toughness of mode I and mode II in the mixed mode and nonlinear deformation stage.

[0027] The fracture toughness of pure mode I and mode II is calculated using the fracture toughness results of the linear deformation stage and the nonlinear deformation stage.

[0028] Optionally, the fracture toughness of Modes I and II during the linear deformation stage can be calculated by:

[0029] When the sample coating is in the linear deformation stage, the expression of the relationship between the concentrated load P1 perpendicular to the coating-substrate interface and the residual stress is obtained;

[0030] The expression of the relationship between the concentrated load P1 and the residual stress is:

[0031]

[0032] Where P1 represents the concentrated load perpendicular to the cracking direction of the coating, h is the coating thickness, ν is the Poisson's ratio of the coating, E is the elastic modulus of the coating, w is the out-of-plane displacement after the coating is separated from the substrate, R is the half-length of the crack after the coating is separated from the substrate, and σ0 is the residual stress inside the coating;

[0033] The measured coating out-of-plane displacement w, the crack radius under the corresponding displacement, and the concentrated load P1 are introduced into the preset fracture toughness linear model to calculate the fracture toughness in the linear deformation stage;

[0034] The fracture toughness linear model includes:

[0035]

[0036] Substitute the expression of concentrated load P1 into G bI and G bII The expression of :

[0037]

[0038] G bc =G bI +G bII

[0039] Among them, G bI and G bII Indicates the energy release rate of mode I and mode II, G bc Represents the fracture toughness in the linear deformation stage.

[0040] Optionally, calculation of the mixed mode, nonlinear deformation stage, Mode I and Mode II fracture toughness includes:

[0041] When the sample coating is in the nonlinear deformation stage, the expression of the relationship between the concentrated load P2 perpendicular to the coating-substrate interface and the residual stress is obtained;

[0042] The expression of the relationship between the concentrated load P2 and the residual stress is:

[0043]

[0044] Where P2 represents the concentrated load perpendicular to the cracking direction of the coating, h is the coating thickness, ν is the Poisson's ratio of the coating, E is the elastic modulus of the coating, w is the out-of-plane displacement after the coating is separated from the substrate, R is the half-length of the crack after the coating is separated from the substrate, and σ0 is the residual stress inside the coating;

[0045] The measured coating out-of-plane displacement, the crack radius under the corresponding displacement, and the concentrated load P2 are introduced into the preset nonlinear deformation stage fracture toughness model to calculate the nonlinear deformation stage fracture toughness;

[0046] The fracture toughness in the nonlinear deformation stage includes:

[0047]

[0048] Substitute the expression of P2 into G mI and G mII The expression yields:

[0049]

[0050] G mc =G mI +G mII

[0051] in, and f(υ) represent parameters related only to Poisson's ratio, G mc represents the fracture toughness in the nonlinear deformation stage, G mI represents the energy release rate of mode I during the mixing phase of nonlinear deformation, G mII It represents the energy release rate of mode II in the nonlinear deformation stage.

[0052] The fracture toughness of pure mode I and pure mode II are calculated by combining the fracture toughness of linear stage and nonlinear stage and the distribution ratio of mode I and mode II.

[0053] The distribution ratio of Mode I and Mode II in the linear stage is:

[0054]

[0055] Among them, G bII Indicates the fracture toughness of mode II in the linear deformation stage and mixed mode, G bIrepresents the fracture toughness of mode I in the mixed mode during the linear deformation stage;

[0056] The distribution ratio of Mode I and Mode II in the nonlinear stage:

[0057]

[0058] Among them, G mII Indicates the fracture toughness of mode II in the nonlinear deformation stage and mixed mode, G mI Represents the fracture toughness of mode I in the nonlinear deformation stage and mixed mode.

[0059] Fracture toughness of the coating in pure mode I state:

[0060]

[0061] Fracture toughness of the coating in pure mode II state:

[0062]

[0063] Among them, G bc represents the linear deformation stage, the calculated fracture toughness, G mc Represents the calculated fracture toughness during the nonlinear deformation stage.

[0064] The beneficial effects of the present invention are:

[0065] The present invention obtains the crack radius R, coating displacement w and coating thickness h through cross-sectional indentation testing; constructs a calculation model for the fracture toughness of the coating-substrate interface based on Harvey's 2D elastic distribution theory and von Karman plate theory; and by bringing the test structure into the calculation model, the fracture toughness of the coating-substrate interface can be obtained under the influence of residual stress, fracture mode, and interface slip. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0067] Figure 1 This is a flow chart of a method for measuring and calculating the fracture toughness of a coating interface according to an embodiment of the present invention;

[0068] Figure 2 A flow chart of a cross-sectional indentation test according to an embodiment of the present invention;

[0069] Figure 3A schematic diagram of a cross-sectional indentation method according to an embodiment of the present invention;

[0070] Figure 4 Schematic diagram of crack morphology obtained by cross-sectional indentation method according to an embodiment of the present invention. DETAILED DESCRIPTION

[0071] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0072] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0073] like Figure 1 As shown, this embodiment proposes a method for measuring and calculating the fracture toughness of a coating interface, including:

[0074] Measuring interface crack related parameters of the test sample; wherein the interface crack related parameters include: coating thickness, coating out-of-plane displacement, and crack radius under corresponding displacement;

[0075] Calculating the ratio of the crack radius to the coating thickness to determine the deformation type of the coating;

[0076] Based on the deformation type, a corresponding fracture toughness calculation model is selected to calculate the fracture toughness of the coating.

[0077] Furthermore, the interface crack related parameters of the test sample are measured including:

[0078] Capturing an image of a coating cross section of the test sample, measuring the initial coating thickness at multiple locations from the image, and taking the average value as the coating thickness;

[0079] An indentation test is performed on the test sample to obtain the coating surface displacement and crack radius.

[0080] Specifically, in this embodiment, the cross-sectional indentation method is used to measure the interface crack related parameters of the test sample, such as Figure 2-Figure 4 The specific steps are as follows:

[0081] In step S1.1, the test sample is a cuboid, and the length and width of the sample coating are equal to the length and width of the sample substrate.

[0082] Step S1.2: Use a scanning electron microscope to photograph the coating cross section, select multiple locations, and use the image method to measure the coating thickness at multiple locations from the image, and take the average h as the coating thickness.

[0083] Step S1.3: Place the test sample on a work surface, with the substrate on the left and the coating on the right. Use a clamp to fix the sample to the surface to prevent it from tilting during testing.

[0084] Step S1.4: Select a conical diamond indenter with a tip radius of 0.2 mm and a tip angle of 90°.

[0085] Step S1.5: Use a long-distance microscope to precisely adjust the distance between the indentation point and the interface so that the indentation distance is between 150 and 220 μm.

[0086] Step S1.6: Perform an indentation test using the micro-loading module equipped on the indenter. Set the loading rate to 0.1 mm / min. When the indentation depth reaches 2 mm, remove the external load.

[0087] Step S1.7: When the indentation depth in step S1.6 is the maximum, the out-of-plane displacement of the coating is measured using a microscope equipped with an X-ray source, and is recorded as w.

[0088] Step S1.8: Remove the external load, observe the crack morphology using a scanning electron microscope, and extract the crack half-length, which is recorded as R.

[0089] Step S1.9: Repeat steps 1.6 to 1.8 multiple times and take the average of the measured data.

[0090] During the cracking process, there are generally three states: Type I - Opening mode I, i.e. mode I; Type II - shearing mode II, i.e. mode II; Type III - Tearing mode III; when the coating interface is cracking and deforming, it is linear deformation at the beginning, and gradually becomes nonlinear as the cracking becomes more serious. Regardless of the linear or nonlinear stage, generally Type I and Type II exist at the same time, but there are special cases. When the cracking just begins, the crack is pure Type I, and the crack gradually increases and tends to pure Type II in the end. Therefore, in general, this embodiment studies the fracture toughness of Type I and Type II under the mixed mode. In special cases, this embodiment calculates the fracture toughness of pure Type I and pure Type II.

[0091] Furthermore, the deformation type of the coating is determined to include:

[0092] When the ratio of crack radius to coating thickness is less than the preset ratio, the sample coating is in the linear deformation stage;

[0093] When the ratio of crack radius to coating thickness is greater than a preset ratio, the sample coating is in the nonlinear deformation stage.

[0094] Furthermore, based on the deformation type, a corresponding fracture toughness calculation model is selected, and the fracture toughness of the coating is calculated including:

[0095] When the sample coating is in the linear deformation stage, the fracture toughness linear model is used to calculate the linear deformation stage fracture toughness of mode I and mode II in the mixed mode.

[0096] When the sample coating is in the nonlinear deformation stage, the fracture toughness of the nonlinear deformation stage of mode I and mode II in the mixed mode is calculated using the nonlinear model of fracture toughness.

[0097] Specifically, in this embodiment, the specific steps of calculating the fracture toughness of the coating include:

[0098] Step S2.1: The outer displacement w, crack half-length R, and coating thickness h of the coating after separation are measured using the cross-sectional indentation method.

[0099] Step S2.2: Determine the coating elastic modulus E, Poisson's ratio υ, and residual stress σ0.

[0100] Step S2.2: Based on the von Karman plate theory and fracture theory, the coating deformation is divided into small deflection deformation in the linear stage and large deflection deformation in the nonlinear stage. According to previous studies, when the ratio of crack radius to coating thickness R / h is less than 15, small deflection deformation is dominant, and the force perpendicular to the coating-substrate interface is equivalent to the following expression (1) for calculation:

[0101]

[0102] When the ratio of crack radius to coating thickness R / h>15, the sample coating is mainly deformed by large deflection, and the equivalent force perpendicular to the coating-substrate interface is calculated as follows (2):

[0103]

[0104] In formula (1) and formula (2), P represents the force perpendicular to the cracking direction of the coating, in μN; h is the coating thickness, in μm; ν is the Poisson's ratio of the coating; E is the elastic modulus of the coating, in MPa; w is the out-of-plane displacement after the coating is separated from the substrate, in μm; R is the half-length of the crack after the coating is separated from the substrate, in μm; σ0 is the residual stress inside the coating, in MPa.

[0105] Step 2.3: Based on Harvey's 2D elastic distribution theory, the energy release rates of mode I and mode II in the mixed mode are used to obtain the energy release rate G of the coating in the linear stage under small deflection deformation state.bC , and the energy release rate G of mode I and mode II in the mixed mode bI and G bII :

[0106]

[0107] Substituting expression (1) into expression (3) and expression (4) yields:

[0108]

[0109] In formula (5), formula (6) and formula (7), G bI Indicates the energy release rate of mixing mode I during the linear deformation stage, in J / m 2 ; G bII Indicates the energy release rate of mode II in the linear deformation stage, in J / m 2 .

[0110] The fracture toughness expression in the linear deformation stage is calculated as:

[0111] G bc =G bI +G bII (8)

[0112] Under the large deflection deformation state, the energy release rate G of the coating in the nonlinear change stage can be obtained mC , and the energy release rate G of mode I and mode II in the mixed mode mI and G mII :

[0113]

[0114] Substituting expression (2) into expression (9) and expression (10) yields:

[0115]

[0116] In formula (11), formula (12) and formula (13), G mI Indicates the energy release rate of mixing mode I during the nonlinear deformation stage, in J / m 2 ; G mII Indicates the energy release rate of mode II during the nonlinear deformation stage, in J / m 2 ; and f(υ) are parameters related only to Poisson's ratio υ:

[0117]

[0118] The fracture toughness expression in the nonlinear deformation stage is calculated as:

[0119] G mc =G mI +G mII (14)

[0120] According to formula (7), formula (8), formula (13) and formula (14), the fracture toughness of the coating in pure mode I and pure mode II states can be calculated.

[0121]

[0122] In formula (15) and formula (16), G Ic Indicates the fracture toughness in pure mode I state, unit is J / m 2 ; G IIc Indicates the fracture toughness in pure mode II state, unit is J / m 2 .

[0123] In this embodiment, the crack half-length R, coating displacement w and coating thickness h are obtained through cross-sectional indentation testing; a calculation model for the fracture toughness of the coating-substrate interface is constructed based on the elastic distribution theory and the flat plate theory; by bringing the test structure into the calculation model, the fracture toughness of the coating-substrate interface under the influence of residual stress, fracture mode, and interface slip can be obtained.

[0124] The following example uses thermal barrier coating as an implementation case to measure and calculate fracture toughness.

[0125] Step S1. The sample used in this embodiment uses P92 steel as the base material, and the coating is sprayed on the base using atmospheric plasma spraying technology (APS). The top layer is a ceramic layer of yttria-partially stabilized zirconia (YSZ). In order to improve the bonding strength between the coating and the base and alleviate the difference in thermal expansion performance between the ceramic layer and the metal base, a layer of NiCoCrAlY is sprayed between the coating and the base as a bonding layer (BC). The overall size of the sample is 2 mm × 2 mm × 1.4 mm.

[0126] Step S2: Perform a cross-sectional indentation test to obtain interface crack related parameters.

[0127] The indenter uses a conical diamond indenter with a tip radius of 0.005 nm and a tip angle of 90°. Using a long-distance microscope, the distance (D CI ) is 220 μm, the loading rate is set to 0.1 mm / min, and the indentation depth is 0.2 mm.

[0128] Through the above operations, the crack half-length R = 456.87 μm, the coating displacement ω = 21.29 μm, and the coating thickness h = 75 μm were obtained.

[0129] The coating elastic modulus E = 49253.3 MPa, Poisson's ratio υ = 0.1 and residual stress σ0 = 248.9 MPa were obtained.

[0130] By calculating the ratio of crack radius to coating thickness R / h = 6.09 < 15, the current state is the linear stage. According to formula (1), the force perpendicular to the coating-substrate interface P = 4.72N can be calculated.

[0131] The energy release rate G under mode I is calculated according to formula (5) and formula (6): bI =82.43J / m 2 , energy release rate G of mode II bII =28.2J / m 2 , the total energy release rate G bc =111.24J / m 2 .

[0132] Because the test results for the thermal barrier coating in this example show the linear deformation phase, only the total energy release rate in the linear phase and the energy release rates for Mode I and Mode II under the mixed mode were calculated. The fracture toughness in the nonlinear phase was not demonstrated, and the energy release rates for pure Modes I and II were not calculated due to the lack of data for the nonlinear phase.

[0133] The embodiments described above are merely descriptions of preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by persons skilled in the art should fall within the scope of protection defined by the claims of the present invention.

Claims

1. A method for measuring and calculating the fracture toughness of a coating interface, characterized in that: include: Measuring interface crack related parameters of the test sample; wherein the interface crack related parameters include: coating thickness, coating out-of-plane displacement, and crack radius under corresponding displacement; Calculating the ratio of the crack radius to the coating thickness to determine the deformation type of the coating; Based on the deformation type, a corresponding fracture toughness calculation model is selected to calculate the fracture toughness of the coating; The interface crack related parameters measured on the test sample include: Capturing an image of a coating cross section of the test sample, measuring the initial coating thickness at multiple locations from the image, and taking the average value as the coating thickness; Performing an indentation test on the test sample to obtain the out-of-plane displacement and crack radius of the coating; The indentation test on the test sample includes: S1.

1. Fix the test sample; S1.

2. Select a conical diamond indenter with a preset tip radius and tip angle; S1.

3. Adjust the target distance between the indentation point and the interface; S1.

4. Perform an indentation test using the micro-loading module on the indenter. When the indentation depth reaches the preset value, remove the external load. S1.

5. When the penetration depth in S1.4 is maximum, measure the out-of-plane displacement of the coating; S1.

6. Remove the external load, scan the crack morphology, and extract the crack radius; S1.

7. Repeat S1.4 to S1.6 several times and take the average of the measured data. Determination of the type of deformation of the coating includes: When the ratio of crack radius to coating thickness is less than the preset ratio, the sample coating is in the linear deformation stage; When the ratio of crack radius to coating thickness is greater than the preset ratio, the sample coating is in the nonlinear deformation stage; Based on the deformation type, the corresponding fracture toughness calculation model is selected to calculate the fracture toughness of the coating, including: When the sample coating is in the linear deformation stage, the fracture toughness of mode I and mode II in the linear deformation stage is calculated using the fracture toughness linear model. When the sample coating is in the nonlinear deformation stage, the fracture toughness nonlinear model is used to calculate the fracture toughness of mode I and mode II in the mixed mode and nonlinear deformation stage. The fracture toughness of pure mode I and mode II is calculated using the fracture toughness results of the linear deformation stage and the nonlinear deformation stage.

2. The method for measuring and calculating the coating interface fracture toughness according to claim 1, characterized in that: Calculation of the fracture toughness of Mode I and Mode II during the linear deformation stage includes: When the sample coating is in the linear deformation stage, the expression of the relationship between the concentrated load P1 perpendicular to the coating-substrate interface and the residual stress is obtained; The expression for the relationship between the concentrated load P1 and the residual stress is: Where P1 represents the concentrated load perpendicular to the cracking direction of the coating, h is the coating thickness, ν is the Poisson's ratio of the coating, E is the elastic modulus of the coating, w is the out-of-plane displacement after the coating is separated from the substrate, R is the half-length of the crack after the coating is separated from the substrate, and σ0 is the residual stress inside the coating; The measured coating out-of-plane displacement w, the crack radius under the corresponding displacement, and the concentrated load P1 are introduced into the preset fracture toughness linear model to calculate the fracture toughness in the linear deformation stage; The fracture toughness linear model includes: Substitute the expression of P1 into G bI and G bII The expression of : G bc =G bI +G bII Among them, G bI and G bII Indicates the energy release rate of mode I and mode II, G bc Represents the fracture toughness in the linear deformation stage.

3. The method for measuring and calculating the coating interface fracture toughness according to claim 1, characterized in that: In the mixed mode, the fracture toughness of the nonlinear deformation stage of Mode I and Mode II includes: When the sample coating is in the nonlinear deformation stage, the expression of the relationship between the concentrated load P2 perpendicular to the coating-substrate interface and the residual stress is obtained; The expression for the relationship between the concentrated load P2 and the residual stress is: Where P2 represents the concentrated load perpendicular to the cracking direction of the coating, h is the coating thickness, ν is the Poisson's ratio of the coating, E is the elastic modulus of the coating, w is the out-of-plane displacement after the coating is separated from the substrate, R is the half-length of the crack after the coating is separated from the substrate, and σ0 is the residual stress inside the coating; The measured coating out-of-plane displacement, the crack radius under the corresponding displacement, and the concentrated load P2 are introduced into the preset non-fracture toughness linear model to calculate the fracture toughness in the nonlinear deformation stage. The fracture toughness nonlinear model includes: Substitute the expression of concentrated load P2 into G mI and G mII The expression yields: G mc =G mI +G mII in, and f(υ) represent parameters related only to Poisson's ratio, G mc represents the fracture toughness in the nonlinear deformation stage, G mI represents the energy release rate of mode I during the mixing phase of nonlinear deformation, G mII It represents the energy release rate of mode II in the nonlinear deformation stage.

4. The method for measuring and calculating the coating interface fracture toughness according to claim 1, characterized in that: Calculation of pure mode I and pure mode II fracture toughness includes: Combining the fracture toughness of the linear deformation stage and the nonlinear deformation stage, and the distribution ratio of mode I and mode II, the fracture toughness of pure mode I and pure mode II is calculated; The distribution ratio of Mode I and Mode II in the linear stage is: Among them, G bII Indicates the fracture toughness of mode II in the linear deformation stage and mixed mode, G bI represents the fracture toughness of mode I in the mixed mode during the linear deformation stage; The distribution ratio of Mode I and Mode II in the nonlinear stage: Among them, G mII Indicates the fracture toughness of mode II in the nonlinear deformation stage and mixed mode, G mI represents the fracture toughness of mode I in the nonlinear deformation stage and mixed mode; Fracture toughness of the coating in pure mode I state: Fracture toughness of the coating in pure mode II state: Among them, G bc represents the linear deformation stage, the calculated fracture toughness, G mc Represents the calculated fracture toughness during the nonlinear deformation stage.

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