Method for inverting equivalent elastic modulus of coating based on physical experiment and finite element simulation

Abstract

The invention discloses a method for inverting the equivalent elastic modulus of a coating based on a physical experiment and finite element simulation, and belongs to the technical field of material mechanics coating performance testing, and the method specifically comprises the following steps: S1, preparing to-be-tested samples of a matrix and the coating, and determining geometric and material parameters; s2, performing a physical three-point bending experiment at a to-be-measured temperature, and recording displacement and pressure data; s3, establishing a finite element model, endowing the coating with an elastic modulus initial assumed value, and performing simulation; s4, constructing and comparing displacement-pressure curves of a physical experiment and simulation; and S5, the elasticity modulus of the coating is adjusted through iteration until the two curves are consistent in the preset tolerance range, and the elasticity modulus at the moment is the equivalent elasticity modulus of the coating. Accurate measurement of the equivalent elastic modulus of the coating in normal-temperature and high-temperature environments is achieved, errors caused by direct measurement at high temperature are avoided, the experiment process is simple, and engineering application is easy.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of material mechanical property testing, in particular to a method for inversing the equivalent elastic modulus of a coating based on physical experiments and finite element simulation. BACKGROUND

[0002] The coating-substrate structure is constructed by attaching one or more layers of special material coating on the substrate material by spraying process, etc., wherein the mechanical properties of each layer of material are significantly different, which may cause different degrees of influence on each layer of material when the environment changes, and the coating-substrate structure is widely used in the fields of aerospace, energy power, etc. Since the coating material is difficult to be peeled off from the substrate without damage, and the thickness after peeling off is relatively thin, it is difficult to measure independently, and how to accurately measure the equivalent elastic modulus of the coating becomes a technical difficulty.

[0003] At present, the methods for measuring the elastic modulus of the coating mainly include nanoindentation method, bending method, etc. However, the above methods have some defects. The nanoindentation method is greatly affected by the size and substrate. When the coating is thin, the indenter will penetrate the coating and reach the substrate, resulting in that the measured value is actually the combined response of the coating and the substrate, rather than the real performance of the coating. Moreover, at high temperature, the oxidation and adhesion problems of the indenter tip and the sample surface are serious. The dynamic test method (such as the vibration beam method) has high requirements for sample preparation, and it is difficult to simulate static load, and the obtained result is the dynamic elastic modulus of the coating sample, rather than the static elastic modulus required. In addition, in the high temperature environment, the traditional sensors (high temperature extensometer, strain gauge) have problems such as signal drift and sensitivity decline, which leads to distortion of the measured data, and further makes the error of the elastic modulus calculated by inversion too large. Based on the above, a method for inversing the equivalent elastic modulus of the coating based on physical experiments and finite element simulation is proposed. SUMMARY

[0004] The purpose of the present application is to provide a method for inversing the equivalent elastic modulus of the coating based on physical experiments and finite element simulation, in order to solve the problems in the background art.

[0005] To achieve the above purpose, the present application provides a method for inversing the equivalent elastic modulus of the coating based on physical experiments and finite element simulation, comprising the following steps: S1, sample preparation and parameter determination: construct a sample to be tested of the upper substrate and lower coating structure and determine the geometric parameters and material parameters, the material parameters including the elastic modulus of the substrate at the measured temperature, the thermal expansion coefficient of the substrate at the measured temperature and the thermal expansion coefficient of the coating at the measured temperature, all of which are known quantities; the elastic modulus of the coating at the measured temperature is a quantity to be inverted; S2. Conduct a three-point bending test: At the test temperature, conduct a three-point bending test on the test sample in S1, and simultaneously collect the displacement data and corresponding pressure data of the test sample during the bending process. S3. Perform finite element simulation modeling and initial simulation: Based on the geometric and material parameters of the test sample determined in S1, establish the corresponding finite element model and assign an initial assumed value to the elastic modulus of the coating; perform a three-point bending simulation in the finite element analysis software that is consistent with the experimental conditions in S2, and obtain the displacement and pressure data obtained from the simulation. S4. Construct curves and perform comparative analysis: Construct the physical experiment displacement-pressure curve based on the data collected in S2, and construct the simulated displacement-pressure curve based on the simulation data in S3; compare the two curves. S5. Perform iterative inversion: Based on the results of S4, determine whether the simulated displacement-pressure curve and the physical experiment displacement-pressure curve are consistent within the preset tolerance range. If not, adjust the elastic modulus value of the coating in the finite element model according to the comparison difference, and repeat S3 to S5. If so, the coating elastic modulus used in the current finite element model is the equivalent elastic modulus of the coating at the temperature to be measured.

[0006] Preferably, in step S1, the upper substrate is a metallic material with high-temperature service characteristics, and its performance is sufficient to meet the service requirements at the temperature to be tested.

[0007] Preferably, in step S2, the displacement of the test sample is controlled by an actuator, the deflection of the middle part of the test sample is measured by an extensometer as displacement data, and the pressure data is measured by a force sensor.

[0008] Preferably, in S3, the finite element model only needs to simulate the thermal deformation of the sample during the heating process. In the three-point bending simulation process in the finite element analysis software, which is consistent with the experimental conditions in S2, the finite element model adopts the same geometric and mechanical parameters as the test sample in S2. That is, the elastic modulus and thermal expansion coefficient of the metal and the thermal expansion coefficient of the coating in the model are kept consistent with the values ​​at the ambient temperature of the S2 experiment, in order to simulate the material parameters consistent with those in the S2 experiment. Since it is necessary to calculate the elastic modulus of the coating under test at the set temperature, the experimental ambient temperature of S2 needs to be raised from room temperature to the set temperature. During this process, the elastic modulus and thermal expansion coefficient of the metal substrate and the coating material will change. According to S1, the curves of the elastic modulus and thermal expansion coefficient of the metal substrate with temperature are known, and the thermal expansion coefficient of the coating is similar. Therefore, the changes of the sample during the heating process can be simulated in the simulation model.

[0009] Preferably, in S3, the reaction force obtained from the simulation results is pressure data, and the downward displacement obtained is displacement data.

[0010] Preferably, in step S5, the adjustment rule in the process of adjusting the elastic modulus value of the coating in the finite element model according to the comparison difference is as follows: if the pressure value on the simulated displacement-pressure curve is greater than the pressure value on the physical experiment displacement-pressure curve under the same displacement, then the assumed value of the elastic modulus of the coating is reduced. Conversely, the assumed value of the coating's elastic modulus is increased.

[0011] Preferably, in step S5, the preset tolerance range is less than 5%.

[0012] Therefore, the method for inverting the equivalent elastic modulus of a coating based on physical experiments and finite element simulation of the present invention has the following beneficial effects: (1) This invention is applicable not only to room temperature but also to high temperature environments. It only requires inputting the material parameters at the corresponding temperature (the known elastic modulus and thermal expansion coefficient of the metal substrate at the measurement temperature, and the thermal expansion coefficient of the coating at the measurement temperature) into the simulation model to simulate the process of the real three-point bending experiment. Through one physical experiment and multiple simulation iterations, it avoids the difficulty of repeating physical experiments at high temperatures, reduces experimental costs and time, has strong versatility, and improves measurement accuracy.

[0013] (2) This invention avoids the influence of interference factors such as initial deformation of the sample and sensor drift caused by thermal expansion at high temperature on the measurement results by adopting the overall comparison of displacement-pressure curves. The thermal expansion coefficient has been considered in its simulation model. The two are compared under the same conditions, which cancels out the systematic error and makes the results more accurate.

[0014] (3) This invention constructs a complete parameter inversion closed-loop system with real experiments as anchor points, finite element models as digital twins, and curve matching as convergence criteria. It clearly establishes a finite element model that is completely consistent with the geometry and material parameters of the real sample, ensuring the consistency between the digital world and the physical world. It uses pressure-displacement curves and adjustment strategies to perform inversion calculations. In the simulation process, it simulates the deformation process of the sample from room temperature to high temperature. It only needs to consider the thermal deformation caused by temperature and does not need to consider other external forces. The equivalent elastic modulus obtained by inversion is the real modulus in the thermal deformation process, rather than the theoretical value under non-temperature or ideal conditions.

[0015] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of a three-point bending experiment according to an embodiment of the present invention; Figure 2The load-displacement curves are obtained from the physical experiments and simulation experiments in Embodiment 1 of the present invention; Figure 3 The load-displacement curves are from the physical experiment and the adjusted simulation experiment in Embodiment 1 of the present invention. Figure 4 The load-displacement curves are from the physical and simulation experiments in Embodiment 2 of this invention. Figure 5 The load-displacement curves are from the physical experiment and the adjusted simulation experiment in Embodiment 2 of the present invention. Detailed Implementation

[0017] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0018] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments.

[0019] Example 1 This embodiment takes the measurement of the equivalent elastic modulus of the thermal barrier coating on a high-temperature nickel-based alloy Haynes 230 substrate at 500°C as an example. The specific steps are as follows: S1. Sample Preparation and Parameter Determination: A rectangular beam sample with an upper layer of high-temperature alloy and a lower layer of thermal barrier coating was prepared. The sample dimensions were 40 mm in length and 4 mm in width, with a substrate thickness of 3 mm and a coating thickness of 0.3 mm. The elastic modulus of the substrate at 500℃ was known to be 199 GPa, and its coefficient of thermal expansion was 1.4 × 10⁻⁶. -5 ℃ -1 The coefficient of thermal expansion of the coating is 1.3 × 10⁻⁶. -5 ℃ -1 .

[0020] S2. Conduct a physical three-point bending test: The experiment uses a high-temperature environmental chamber, where the sample and the fixtures holding the sample are all subjected to the same high temperature, heated to 500℃ and held at that temperature. (The text then repeats itself, so the translation will only include the first instance.) Figure 1 The structure shown was subjected to a three-point bending test. The displacement of the indenter was controlled by an actuator, pressing it towards the center of the specimen. At the same time, a high-temperature extensometer was used to measure the deflection (displacement) at the center of the specimen, and a force sensor recorded the load (pressure). Displacement and pressure data were collected until the end of the experiment.

[0021] S3. Finite element simulation modeling and initial simulation: Using ABAQUS software, a finite element model with the same geometric dimensions as the sample is established. The elastic modulus of the matrix is ​​set to 199 GPa, and the initial assumed elastic modulus of the coating is 51 GPa. The thermal expansion coefficients of the matrix and coating are input, and the same boundary conditions and downward displacement values ​​as in the actual experiment are set. A three-point bending simulation is performed, and the reaction force and displacement data of the indenter reference point are extracted. The following process is given in this embodiment: A three-dimensional finite element model of the bending specimen was established using ABAQUS preprocessing, and a static general analysis step was implemented for simulation calculation. Currently, it is assumed that temperature changes only affect the mechanical properties of the material, and the simulation process does not involve thermo-mechanical coupling effects. The simulation process includes two analysis steps: the first step defines a uniform temperature field and simulates the heat preservation process (heating to the target temperature and during heat preservation); the second step implements indenter displacement loading, and finally outputs the simulation data of displacement and reaction force at the indenter reference point.

[0022] The boundary conditions are set as follows: (1) The support roller can expand freely at high temperature in the first step, and all degrees of freedom are constrained when mechanical load is applied in the second step; (2) The pressure head can expand freely at high temperature, and the reference point in the second step constrains three rotational degrees of freedom and translational degrees of freedom in the x and z directions, and applies vertical displacement load along the y axis; (3) In terms of setting the boundary conditions of the specimen, symmetrical boundary conditions are adopted to constrain the translational degree of freedom in the z direction (longitudinal direction) of the cross section of the specimen center and to constrain the translational degree of freedom in the x direction of the specimen center point.

[0023] S4. Curve Construction and Comparative Analysis: The data obtained from physical experiments and simulations are plotted as displacement-pressure curves, such as... Figure 2 As shown.

[0024] S5. Iterative Inversion: Comparing the two curves, it was found that there was a certain difference between the simulation curve and the physical experimental curve under the same displacement. According to the adjustment rules, the assumed value of the coating elastic modulus was adjusted to 52 GPa, and the simulation was run again to obtain a new simulation curve.

[0025] If the comparison is repeated and the result is still outside the tolerance range, adjustments are continued. After several iterations, when the coating's elastic modulus was adjusted to 53 GPa, the two curves were essentially identical, with an average error of approximately 5%, which is consistent with engineering practice. Figure 3 As shown. It should be noted that during the iteration process, it can be performed manually or automatically by training the simulation model using existing algorithms. The choice can be made according to the actual situation. In this embodiment, manual iteration can be used.

[0026] Therefore, 53 GPa is the equivalent elastic modulus of the thermal barrier coating at 500℃.

[0027] Example 2 This embodiment takes the measurement of the equivalent elastic modulus of the ceramic coating on the GH4099 alloy substrate at room temperature (25℃) as an example. The specific steps are as follows: S1. Sample Preparation and Parameter Determination: A rectangular beam sample with an alloy substrate as the upper layer and a ceramic coating as the lower layer was prepared. The sample dimensions were 40 mm in length and 4 mm in width, with a substrate thickness of 3 mm and a coating thickness of 0.3 mm. The elastic modulus of the substrate at 25℃ was known to be 223 GPa, and its coefficient of thermal expansion was 1.4 × 10⁻⁶. -5 ℃ -1 The coefficient of thermal expansion of the coating is 1.3 × 10⁻⁶. -5 ℃ -1 .

[0028] S2. Conduct a physical three-point bending test with a span of 30 mm. Control the displacement of the indenter using an actuator, while simultaneously measuring the deflection (displacement) at the center of the specimen using an extensometer, and recording the load (pressure) using a force sensor. Collect displacement and pressure data until the end of the experiment.

[0029] S3. Perform finite element simulation modeling and initial simulation: Use ABAQUS software to establish a finite element model with the same geometric dimensions as the sample, set the elastic modulus of the matrix to 223GP, and assume the initial elastic modulus of the coating to be 52GPa. Perform three-point bending simulation and extract the reaction force and displacement data of the indenter reference point.

[0030] S4. Curve Construction and Comparative Analysis: The data obtained from physical experiments and simulations are plotted as displacement-pressure curves, such as... Figure 4 As shown.

[0031] S5. Iterative Inversion: Comparing the two curves, it was found that there was a certain discrepancy between the simulated curve and the physical experimental curve under the same displacement. According to the adjustment rules, the assumed value of the coating's elastic modulus was reduced to 55 GPa, and the simulation was rerun. After several iterations, when the coating's elastic modulus was adjusted to 55 GPa, the two curves essentially overlapped, as shown below. Figure 5 As shown.

[0032] Therefore, 55 GPa is the equivalent elastic modulus of the ceramic coating at 25°C.

[0033] Therefore, this invention provides a method for inverting the equivalent elastic modulus of a coating based on physical experiments and finite element simulation. By considering temperature effects through finite element simulation, it achieves accurate measurement of the equivalent elastic modulus of the coating from room temperature to high temperature environments. It eliminates the need for numerical analysis and calculation of the pressure-displacement curves obtained from the three-point bending experiment. Instead, it directly compares the overall displacement-pressure curves and corrects the elastic modulus based on the results. This avoids the influence of interference factors such as thermal expansion deformation and sensor drift under high temperature environments on the measurement results, thus obtaining an accurate equivalent elastic modulus. In addition, the physical experiment only needs to be performed once, which greatly reduces the cost and difficulty of repeating experiments in extreme environments and is easy to apply in practical engineering.

[0034] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for inverting the equivalent elastic modulus of a coating based on physical experiments and finite element simulation, characterized in that, Includes the following steps: S1. Sample preparation and parameter determination: Construct the test sample with an upper substrate and a lower coating structure and determine the geometric and material parameters. The material parameters include the elastic modulus and thermal expansion coefficient of the substrate at the test temperature and the thermal expansion coefficient of the coating at the test temperature. S2. Conduct a three-point bending test: At the test temperature, conduct a three-point bending test on the test sample in S1, and simultaneously collect the displacement data and corresponding pressure data of the test sample during the bending process. S3. Perform finite element simulation modeling and initial simulation: Based on the geometric and material parameters of the test sample determined in S1, establish the corresponding finite element model and assign initial assumed values ​​to the elastic modulus of the coating. A three-point bending simulation was performed in finite element analysis software, consistent with the experimental conditions of S2, to obtain displacement and pressure data from the simulation. S4. Construct curves and perform comparative analysis: Construct the physical experiment displacement-pressure curve based on the data collected in S2, and construct the simulated displacement-pressure curve based on the simulation data in S3; compare the two curves. S5. Perform iterative inversion: Based on the results of S4, determine whether the simulated displacement-pressure curve and the physical experiment displacement-pressure curve are consistent within the preset tolerance range. If not, adjust the elastic modulus value of the coating in the finite element model according to the comparison difference, and repeat S3 to S5. If so, the coating elastic modulus used in the current finite element model is the equivalent elastic modulus of the coating at the temperature to be measured.

2. The method for inverting the equivalent elastic modulus of a coating based on physical experiments and finite element simulation according to claim 1, characterized in that: In S1, the upper substrate is a metallic material with high-temperature service characteristics.

3. The method for inverting the equivalent elastic modulus of a coating based on physical experiments and finite element simulation according to claim 2, characterized in that: In step S2, the displacement of the test sample is controlled by an actuator, the deflection of the middle part of the test sample is measured by an extensometer as displacement data, and the pressure data is measured by a force sensor.

4. The method for inverting the equivalent elastic modulus of a coating based on physical experiments and finite element simulation according to claim 1, characterized in that: In S3, the thermal expansion coefficients of the substrate and coating at the temperature to be measured are input into the finite element model.

5. The method for inverting the equivalent elastic modulus of a coating based on physical experiments and finite element simulation according to claim 1, characterized in that: In S3, the reaction force obtained from the simulation results is pressure data, and the downward displacement obtained is displacement data.

6. The method for inverting the equivalent elastic modulus of a coating based on physical experiments and finite element simulation according to claim 1, characterized in that: In S5, the adjustment rule in the process of adjusting the elastic modulus value of the coating in the finite element model according to the comparison difference is as follows: if the pressure value on the simulated displacement-pressure curve is greater than the pressure value on the physical experiment displacement-pressure curve under the same displacement, then the assumed value of the elastic modulus of the coating is reduced. Conversely, the assumed value of the coating's elastic modulus is increased.

7. The method for inverting the equivalent elastic modulus of a coating based on physical experiments and finite element simulation according to claim 1, characterized in that: In S5, the preset tolerance range is less than 5%.

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