Method for measuring and calculating fracture toughness of coating interface

Abstract

The invention relates to a method for measuring and calculating interface fracture toughness of a coating. The method comprises the following steps: measuring interface crack related parameters of a test sample; wherein the interface crack related parameters comprise the coating thickness, the coating out-of-plane displacement and the crack radius under the corresponding displacement; the ratio of the crack radius to the coating thickness is calculated, and the deformation type of the coating is determined; and based on the deformation type, selecting a corresponding fracture toughness calculation model, and calculating the fracture toughness of the coating. In the measurement and calculation of the interface fracture toughness of the coating, the influence of the fracture mode is considered, and the separation mode of the coating is defined. Meanwhile, the influence caused by residual stress is considered, so that the interface fracture toughness is more accurate.

Description

Technical Field

[0001] The invention relates to the technical field of coating materials, and 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 many industries. In the automotive field, coatings enhance the wear and corrosion resistance of engine parts and improve heat dissipation efficiency; in the machinery industry, coatings reduce friction and noise of parts and improve the wear resistance of equipment; in the petroleum industry, coatings are used to reduce the wear of drilling tools and extend their service life. In short, coating technology plays a key role in various industries by improving surface properties. However, during the service process, the coating-substrate system will inevitably fail due to cracking, peeling and other failure problems, causing the equipment to lose its normal working ability. Fracture toughness is one of the important basic mechanical parameters of materials, which characterizes the ability of materials to resist fracture propagation. Therefore, studying the fracture toughness of coating interfaces is particularly important for evaluating the reliability of equipment. At present, most of the research on the fracture performance of coating interfaces is to explore the relationship between the load acting between the coating and the substrate and the fracture toughness of the coating interface, while ignoring the residual stress between the coating and the substrate, the cracking mode of the coating, and the influence of slip between the coating substrate on the fracture toughness.

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

[0004] In view of the shortcomings in current research, the purpose of the present invention is to provide a method for measuring and calculating the fracture toughness of a coating interface, which can accurately measure and calculate the fracture toughness of the coating-substrate interface 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 an 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, an indentation test is performed on the test sample including:

[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 on the 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 within the preset range;

[0017] S1.4. Use the micro-loading module equipped on the indenter to perform the indentation test, set the fixed 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 the maximum, measuring the outer displacement of the coating surface;

[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 type of deformation of the coating comprises:

[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 a 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 linear model is used to calculate the fracture toughness of mode I (Opening mode I) and mode II (shearing mode II) in the linear deformation stage.

[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 in the linear deformation stage is 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] Wherein, 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 crack half-length after the coating is separated from the substrate, and σ0 is the residual stress inside the coating;

[0033] The measured coating surface 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 is:

[0037]

[0038] G bc =G bI +G bII

[0039] Among them, G bI and G bI represents 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] Wherein, 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 crack half-length after the coating is separated from the substrate, and σ0 is the residual stress inside the coating;

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

[0046] The nonlinear deformation stage fracture toughness includes:

[0047]

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

[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.

[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 represents the fracture toughness of mode II in the linear deformation stage and mixed mode, G m b I Represents the fracture toughness of mode I in the linear deformation stage and mixed mode.

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

[0057]

[0058] Among them, G mII represents 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 nonlinear deformation stage, the calculated fracture toughness

[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 coating-substrate interface fracture toughness calculation model based on Harvey's 2D elastic distribution theory and von Karman plate theory; and brings the test structure into the calculation model to obtain the coating-substrate interface fracture toughness considering 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 drawings required for use in the embodiments will be briefly introduced below. 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 creative labor.

[0067] Figure 1 A schematic 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 3 A schematic diagram of a cross-sectional indentation method according to an embodiment of the present invention;

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

[0071] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are 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 an 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 As shown, 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 positions, use the image method to measure the coating thickness at multiple positions 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, and fix the sample to the surface with a clamp at the bottom to prevent the sample from tilting during the test.

[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 accurately adjust the distance between the indentation point and the interface so that the indentation distance is between 150-220 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 coating surface displacement is measured using a microphotograph 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, 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] In 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 in 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 a 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 nonlinear model is used to calculate the fracture toughness of the nonlinear deformation stage of mode I and mode II in the mixed mode.

[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 by 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 deformation of the coating 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<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 by the following expression (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 obtained under the state of small deflection deformation, and the energy release rate G of the coating in the linear stage is obtained. 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 in 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 and mode I in 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 that are only related 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]

[0123] In formula (15) and formula (16), G Ic Indicates the fracture toughness in pure mode I state, unit J / m 2 ; G IIc Indicates the fracture toughness in pure mode II state, unit J / m 2 .

[0124] 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 plate theory; and the test structure is brought into the calculation model to obtain the fracture toughness of the coating-substrate interface under the influence of residual stress, fracture mode, and interface slip.

[0125] The following example uses thermal barrier coating as an implementation case to measure and calculate fracture toughness.

[0126] Step S1. The sample used in this embodiment uses P92 steel as the base material, and uses atmospheric plasma spraying technology (APS) to spray the coating on the base. The top layer is a ceramic layer of yttria-partially stabilized zirconia (YSZ) composition. In order to improve the bonding strength between the coating and the base and alleviate the difference in thermal expansion properties 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 2mm×2mm×1.4mm.

[0127] Step S2: Perform a cross-sectional indentation test to obtain interface crack related parameters.

[0128] 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.

[0129] 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.

[0130] The coating elastic modulus E = 49253.3 MPa, Poisson's ratio υ = 0.1 and residual stress σ0 = 248.9 MPa were obtained.

[0131] By calculating the ratio of crack radius to coating thickness R / h=6.09<15, the current state is a linear stage. According to formula (1), the force perpendicular to the coating-substrate interface P=4.72N can be calculated.

[0132] According to formula (5) and formula (6), the energy release rate G under mode I is calculated as bI =82.43J / m 2 , the energy release rate of mode II G bII =28.2J / m 2 , the total energy release rate G bc =111.24J / m 2 .

[0133] Since the test results of the thermal barrier coating in this embodiment are shown as the linear deformation stage, only the total energy release rate in the linear stage and the energy release rates of mode I and mode II in the mixed mode can be calculated. The fracture toughness in the nonlinear stage is not given as an example, and the energy release rates of pure mode I and pure mode II are not calculated because there is no data in the nonlinear stage.

[0134] The embodiments described above are only descriptions of the preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope determined 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.

2. The method for measuring and calculating the fracture toughness of the coating interface according to claim 1, characterized in that: The interface crack related parameters measured on the test samples 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 an average value as the coating thickness; An indentation test is performed on the test sample to obtain the coating surface displacement and crack radius.

3. The method for measuring and calculating the coating interface fracture toughness according to claim 2, characterized in that: 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 indentation instrument. When the indentation depth reaches the preset value, remove the external load. S1.5, when the penetration depth of S1.4 is the maximum, measuring the outer displacement of the coating surface; S1.6, removing the external load, scanning the crack morphology, and extracting the crack radius; S1.

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

4. The method for measuring and calculating the coating interface fracture toughness according to claim 1, characterized in that: 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 a preset ratio, the sample coating is in a nonlinear deformation stage.

5. The method for measuring and calculating the coating interface fracture toughness according to claim 4, characterized in that: 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 linear model is used to calculate the fracture toughness of mode I and mode II in the linear deformation stage; 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.

6. The method for measuring and calculating the coating interface fracture toughness according to claim 5, characterized in that: Calculation of the fracture toughness of mode I and mode II in 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: Wherein, 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 crack half-length after the coating is separated from the substrate, and σ0 is the residual stress inside the coating; The measured coating surface 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 is: G bc =G bI +G bII Among them, G bI and G bI represents the energy release rate of mode I and mode II, G bc Represents the fracture toughness in the linear deformation stage.

7. The method for measuring and calculating the coating interface fracture toughness according to claim 5, 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: Wherein, 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 crack half-length after the coating is separated from the substrate, and σ0 is the residual stress inside the coating; The measured coating surface displacement, crack radius under the corresponding displacement and 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 is: 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.

8. The method for measuring and calculating the coating interface fracture toughness according to claim 5, 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 represents the fracture toughness of mode II in the linear deformation stage and mixed mode, G m b I 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 is: Among them, G mII represents 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 mixed mode during the nonlinear deformation stage; Fracture toughness of the coating in pure mode I state: Fracture toughness of coating in pure mode II state: Among them, G bc represents the linear deformation stage, the calculated fracture toughness, G mc Represents the nonlinear deformation stage and the calculated fracture toughness.

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