High-temperature mechanical properties evaluation method of CMC structure based on in-situ intelligent sensing
Through the high-temperature mechanical performance evaluation method of CMC structure based on in-situ intelligent perception, the resistance response of CMC structure is collected and analyzed in real time, and the problem that the existing technology cannot realize the online mechanical performance evaluation of CMC structure is solved, and intelligent health monitoring of CMC structure bearing-perception integration is realized.
Patent Information
- Application Number
- CN202411378328.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-09-30
- Publication Date
- 2025-05-06
- Estimated Expiration
- 2044-09-30
AI Technical Summary
The existing technology cannot effectively realize online mechanical performance evaluation and intelligent health monitoring of CMC structures in high temperature environments, and cannot realize the integration of CMC structure bearing-perception.
The high-temperature mechanical performance evaluation method of CMC structure based on in-situ intelligent perception is adopted. By establishing a finite element model and resistive network model, the resistance response of the CMC structure is collected in real time, the resistivity is calculated, and the in-situ intelligent perception of structural damage is realized through resistance sensing signal increments.
It realizes online mechanical performance evaluation and intelligent health monitoring of CMC structures in high temperature environments, solves the intelligent problem of CMC high-temperature components of aircraft engines, and realizes the integrated bearing-perception of CMC structures.
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Figure CN119230028B_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of ceramic matrix composite material structure health monitoring, and in particular relates to a method for evaluating high temperature mechanical properties of a CMC structure based on in-situ intelligent sensing. Background Art
[0002] Fiber-reinforced ceramic matrix composites (Ceramic Matrix Composite, CMC for short) have good high-temperature stability, mechanical properties and electrical conductivity, and are ideal materials for high-temperature components of future advanced intelligent aircraft engines. However, the service environment of aircraft engine CMC structures is usually complex and harsh, which seriously affects the service life of the structure, and a reliable and durable intelligent health monitoring system is urgently needed. Therefore, the self-perception of the high-temperature mechanical properties of CMC structures is an important problem facing future intelligent aircraft engines. Realizing structural load-bearing-perception integration based on CMC sensing characteristics is an important support for the intelligence of aircraft engines.
[0003] The damage and mechanical properties sensing technologies currently developed for CMC include acoustic emission (CN106770677A), X-ray (CN108717727A), etc. However, the above methods either require large and complex equipment and cannot achieve online evaluation during service, or the structure needs to be disassembled and assembled during use, which is easy to cause additional damage and has a high application cost. Therefore, the existing technology has not yet been able to fully meet the intelligent needs of aero-engine CMC structures, and cannot achieve an important breakthrough in the integration of CMC structure load-bearing and perception. Since CMC has a low on-resistance and can still maintain its resistance characteristics in a high temperature environment, more importantly, the resistance change of CMC is very sensitive to damage such as fracture and delamination. Therefore, CMC itself can be used as a sensor to achieve in-situ intelligent perception of the structural load-bearing state based on the resistance response, and then evaluate its mechanical properties in a high temperature environment online and use it for failure warning.
[0004] However, the existing resistance-based sensing technology cannot describe the quantitative relationship between resistance increase and structural damage evolution, and the resistance response results cannot evaluate the high-temperature mechanical properties of the structure, and cannot yet achieve CMC structural load-bearing-sensing integration. Therefore, it is necessary to propose a CMC high-temperature mechanical performance evaluation method based on resistance in-situ intelligent sensing, to achieve CMC structural load-bearing-online sensing integration, and solve the problem of intelligentization of CMC high-temperature components of aircraft engines. Summary of the invention
[0005] The technical problem to be solved by the present invention is to provide a method for evaluating the high-temperature mechanical properties of CMC structures based on in-situ intelligent sensing in view of the above-mentioned existing deficiencies.
[0006] In order to achieve the above technical objectives, the technical solution adopted by the present invention is:
[0007] The high temperature mechanical properties evaluation method of CMC structure based on in-situ intelligent sensing includes the following steps:
[0008] Step 1: Set mechanical and temperature boundary conditions for the CMC structure and establish a finite element model of the CMC structure; establish a resistance network model of the CMC structure based on the geometric characteristics of the CMC structure; conduct high-temperature mechanical tests on the CMC structure whose mechanical properties are to be predicted, collect the resistance response of the CMC structure in real time through a resistance monitor, and calculate the resistivity of the CMC structure based on the initial resistance response of the CMC structure in a high-temperature environment;
[0009] Step 2: Discretize the resistance of the CMC structure into N layers of sensing unit groups connected in series, each layer of sensing unit group has a total of M sensing units connected in parallel, apply a load step to the CMC structure, calculate the finite element model of the CMC structure, obtain the force-displacement response of the CMC structure at the current load step, and count the area of the structural failure sensing unit; calculate the structural resistance sensing signal increment of the resistance network model based on the distribution of the CMC structural failure units;
[0010] Step 3: Analyze the damage distribution of the CMC structure under the current load step. If the damage distribution of the CMC structure under the current load step does not form a failure section, analyze whether a failure unit is formed in the current loading. If a failure unit is formed, go to step 4. If no failure unit is formed, go to step 5. If a failure section is formed, go to step 6.
[0011] Step 4: Reduce the failed unit modulus of the CMC structure, degrade the non-failed unit modulus according to the CMC material constitutive model, update the material parameters and go to step 2;
[0012] Step 5: Further apply the mechanical boundary conditions of the next load step and go to step 2;
[0013] Step 6: Count the sensing unit area forming the failure section and calculate the cumulative structural resistance sensing signal increment under each load step;
[0014] Step seven, according to the accumulated structural resistance sensing signal increment under each load step, and the CMC structure force-displacement response obtained by finite element calculation in the corresponding load step, the mechanical property-resistance increment response of the CMC structure is obtained; a resistance monitor is installed on the CMC structure whose mechanical property is to be predicted, and the resistance of the CMC structure whose mechanical property is to be predicted is collected in real time to obtain the resistance increment-time response of the CMC structure whose mechanical property is to be predicted; through the resistance increment of the CMC structure whose mechanical property is to be predicted, the force-displacement response at the corresponding moment is retrieved from the mechanical property-resistance increment response of the CMC structure; thereby realizing in-situ intelligent sensing of the high-temperature mechanical properties of the CMC structure whose mechanical property is to be predicted, and providing online real-time warning of the failure trend of the CMC structure whose mechanical property is to be predicted.
[0015] To optimize the above technical solutions, the specific measures taken also include:
[0016] In step 2, the specific method for calculating the structural resistance sensing signal increment of the resistance network model based on the distribution of the CMC structural failure unit is:
[0017] Total resistance of CMC structure R CMC for:
[0018]
[0019] Where R i is the resistance of the sensing unit at the i-th layer, R ij is the resistance of the jth sensing unit in the i-th layer, ρ is the material resistivity, l is the thickness of the sensing unit in this layer, and A ij is the area of the jth perceptual unit in the i-th layer;
[0020] After each load step finite element calculation is completed, the damage sensing unit area is counted and the CMC structural resistance R' after damage evolution is calculated CMC ,Right now:
[0021]
[0022] Where R i ' is the resistance of the i-th layer sensing unit after damage evolution, is the resistance of all damage-aware cells in the i-th layer, is the resistance of all undamaged sensing units in the i-th layer, S is the total number of damaged sensing units in the i-th layer, is the area of the jth damage sensing unit in the i-th layer, is the area of the kth undamaged sensing unit in the i-th layer, γ is the incremental factor of the damaged unit resistance sensing signal, which is the signal amplification factor when the unit fails. Thus, the structural resistance sensing signal increment ΔR caused by the damage of the CMC structure after each loading step is obtained:
[0023] ΔR=R'CMC -R CMC .
[0024] In step 3, the method for determining the CMC structural failure unit is as follows: if the strain component of the CMC structural unit is greater than the maximum material strain of the CMC structural unit, the unit is marked as failed, and the direction of the strain component of the CMC structural unit and the material parameters in the related directions are degraded.
[0025] In step 4, the specific method for degrading the modulus of the non-failed unit according to the CMC material constitutive model is:
[0026] The strain of the non-failed unit is extracted and brought into the modulus-strain degradation equation to obtain the material modulus after mechanical property degradation; where the modulus-strain degradation equation is:
[0027]
[0028] Where E is the material modulus, σ(ε) is the normal stress-strain constitutive model of the material, τ(ε) is the shear stress-strain constitutive model of the material, and ε is the strain component corresponding to the material.
[0029] The specific method for obtaining the damage unit resistance sensing signal increment factor γ is:
[0030] Step 1: Perform the first loading on the resistor network model to obtain the resistance response of the CMC structure loaded in this step. Since the damage unit resistance perception signal increment factor has not been determined in this process, the resistance increment obtained in the first finite element calculation is a resistance perception signal increment factor function, that is:
[0031] ΔR(γ)=R' CMC (γ)-R CMC
[0032] Where ΔR(γ) is the theoretical resistance increment of the first loading step, R' CMC (γ) is the resistance of the CMC structure after the first step of loading damage evolution;
[0033] Step 2: Load the resistor network model in the second step, set the theoretical resistance increment in the first step equal to the resistance increment response collected in the second load step, solve the equation to obtain the damage unit resistance sensing signal increment factor γ in this loading step, and directly apply it to all subsequent calculation steps, that is, solve the following equation:
[0034] ΔR(γ)=ΔR step1
[0035] Where ΔR step1 The incremental resistance response acquired for the first load step in the test.
[0036] The beneficial effects of the present invention are:
[0037] 1. The present invention proposes a method for evaluating the high-temperature mechanical properties of CMC structures, which couples the load-bearing function of CMC with its in-situ intelligent perception of damage, realizes the load-bearing-perception integration of the hot-end structure, and can solve the problem of online safety evaluation and efficient maintenance of key CMC components of aircraft engines;
[0038] 2. The in-situ intelligent sensing evaluation method proposed in the present invention is universal. By arranging appropriate resistance response sensing nodes, it can further obtain the damage distribution of CMC structures with complex spatial geometric structures, meeting the application requirements of online damage monitoring of various types of aviation hot end component structures;
[0039] 3. This method can be coupled with the intelligent design of aero-engine structures to solve the problem of CMC structural damage monitoring in high-temperature environments, break through the mechanical performance evaluation technology of intelligent aviation CMC high-temperature components, realize intelligent failure self-inspection of CMC components, and provide a reference for the service health self-perception technology of future intelligent aero-engines.
[0040] 4. Due to the differences in design, manufacturing and assembly of different CMC structures in engineering applications, the increment of resistance sensing signals when different CMC structures fail is also different. Therefore, it is necessary to additionally determine the increment factor γ of the damaged unit resistance sensing signal for the actual specific CMC structure. The present invention proposes to use a method of prior unified resistance increment to determine the unit resistance sensing signal increment factor of a specific type of CMC structure, which can more accurately measure the increment of resistance sensing signals when the CMC structure fails. BRIEF DESCRIPTION OF THE DRAWINGS
[0041] Figure 1 It is the specific analysis process of the embodiment;
[0042] Figure 2 It is the perception unit partitioning scheme of CMC pins;
[0043] Figure 3 It is the comparison between the simulation results and the test results of the mechanical response of the CMC pin connection structure;
[0044] Figure 4 It is the CMC pin resistance sensing signal increment monitoring result;
[0045] Figure 5 It is the relationship between the mechanical properties of the CMC pin connection structure and the increment of the resistance sensing signal;
[0046] Figure 6 It is the intelligent perception result of the mechanical properties of the CMC pin connection structure. DETAILED DESCRIPTION
[0047] In order to make the purpose, technical solutions and advantages of the present application clearer, the present application is described and illustrated below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not intended to limit the present application. Based on the embodiments provided in the present application, all other embodiments obtained by ordinary technicians in the field without making creative work are within the scope of protection of the present application.
[0048] Obviously, the drawings described below are only some examples or embodiments of the present application. For ordinary technicians in this field, the present application can also be applied to other similar scenarios based on these drawings without creative work. In addition, it can also be understood that although the efforts made in this development process may be complicated and lengthy, for ordinary technicians in this field related to the content disclosed in this application, some changes in design, manufacturing or production based on the technical content disclosed in this application are just conventional technical means, and should not be understood as insufficient content disclosed in this application.
[0049] Reference to "embodiments" in this application means that a particular feature, structure, or characteristic described in conjunction with the embodiments may be included in at least one embodiment of the present application. The appearance of the phrase in various locations in the specification does not necessarily refer to the same embodiment, nor is it an independent or alternative embodiment that is mutually exclusive with other embodiments. It is explicitly and implicitly understood by those of ordinary skill in the art that the embodiments described in this application may be combined with other embodiments without conflict.
[0050] Unless otherwise defined, the technical terms or scientific terms involved in this application should be understood by people with ordinary skills in the technical field to which this application belongs. The words "one", "a", "a", "the" and the like involved in this application do not indicate a quantitative limitation, and may represent the singular or plural. The terms "include", "comprise", "have" and any of their variations involved in this application are intended to cover non-exclusive inclusions; for example, a process, method, system, product or device that includes a series of steps or units (units) is not limited to the listed steps or units, but may also include steps or units that are not listed, or may also include other steps or units inherent to these processes, methods, products or devices. The words "connect", "connected", "coupled" and the like involved in this application are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. The "multiple" / "several" involved in this application refers to two or more. "And / or" describes the association relationship of associated objects, indicating that there can be three relationships, for example, "A and / or B" can mean: A exists alone, A and B exist at the same time, and B exists alone. The character " / " generally indicates that the objects before and after are in an "or" relationship. The terms "first", "second", "third", etc. involved in this application are only used to distinguish similar objects and do not represent a specific ordering of the objects.
[0051] This embodiment takes the CMC pin connection structure in the hot end component of an aircraft engine as an example, and the test and simulation environment temperature is 800° C. The present invention is further described in detail in conjunction with the accompanying drawings.
[0052] like Figure 1 The specific analysis process proposed in this embodiment is shown. Apply the displacement boundary condition L to the CMC connection structure, perform finite element calculation and obtain the force-displacement response of the structure. If the pin does not form a failed unit section, analyze whether a failed unit appears in this loading. If a failed unit appears, reduce the modulus of all failed units in the model, update the material parameters, calculate the increment of the pin structure resistance sensing signal, and re-perform the finite element calculation until no failed unit appears. Increase the structural displacement boundary condition L step by step, record the structural load and repeat the above process. When the pin failure unit forms a section, the structure is considered to have failed.
[0053] This embodiment combines Figure 2 This paper further describes how to calculate the increment of the pin structure resistance sensing signal based on the damage distribution. The pin resistance is regarded as N layers of sensing units connected in series, each layer has M sensing units, and the resistance of this layer is regarded as the resistance of all sensing units in this layer in parallel. Then the total resistance of the pin is:
[0054]
[0055] Where R i is the resistance of the sensing unit at the i-th layer, R ij is the resistance of the jth sensing unit in the i-th layer, ρ is the material resistivity, l is the thickness of the sensing unit in this layer, and A ij is the area of the jth perceptual unit in the i-th layer.
[0056] After each load step is calculated, the area of the damage-sensing unit is counted and the resistance of the pin after damage evolution is calculated, that is,
[0057]
[0058] in is the resistance of all damage-aware cells in the i-th layer, is the resistance of all undamaged sensing units in the i-th layer, S is the total number of damaged sensing units in the i-th layer, is the area of the jth damage sensing unit in the i-th layer, is the area of the kth undamaged sensing unit in the i-th layer. γ is the incremental factor of the damaged unit resistance sensing signal, which is the amplification factor of the signal when the unit fails. Thus, the increase in the resistance sensing signal of the CMC pin caused by damage after each loading step is obtained:
[0059]
[0060] This embodiment further describes how to degrade the mechanical properties of the CMC connection structure. The CMC material parameters used are shown in Table 1, and the maximum strain failure criterion is used to determine whether the CMC material unit fails. When the unit strain component is greater than the material failure strain, the material parameters in the direction and related directions are degraded (Table 2), and the unit is marked as failed.
[0061] Table 1 CMC material parameters
[0062]
[0063] Table 2 Failure mode and degradation method ('+' is tensile direction, '-' is compression direction)
[0064]
[0065] Among them, E is the elastic modulus of the material, G is the shear modulus of the material, and v is the Poisson's ratio of the material
[0066] If the unit in the model has not failed, the unit modulus needs to be degraded according to the CMC nonlinear constitutive relationship, that is, the modulus-strain degradation equation:
[0067]
[0068] By extracting the strain of the non-failed unit and substituting it into the modulus-strain degradation equation, the material modulus after mechanical property degradation is obtained. The modulus-strain degradation equation of the CMC in the 1 and 2 directions used in this embodiment is as follows:
[0069]
[0070] The CMC in-plane shear modulus-strain degradation equation used in this embodiment is as follows:
[0071] G (MPa) = 9.596 × 10 3 -1.091×10 4 ε+5.982×10 3 ε 2
[0072] +3.005×10 3 ε 3 -8.449×10 3 ε 5 (0<ε<6.3×10 -3 )
[0073] Based on the above method, this embodiment simulates the load-displacement response of the CMC connection structure in an 800°C environment. The calculation results are as follows: Figure 3 As shown in the figure, it can be seen that the simulation results of the mechanical response of the CMC connection structure are in good agreement with the test results, indicating that the method of the present invention can better realize the high-temperature mechanical performance evaluation of the CMC connection structure and obtain the damage extension process of the pin. The evaluation error of the failure displacement of the CMC connection structure test is 7.69%, the evaluation error of the failure load is 3.12%, and the evaluation error of the initial stiffness of the test is 14.62%.
[0074] Furthermore, this embodiment is based on Figure 4 The CMC pin resistance sensing signal increment obtained in the high temperature test at 800°C is shown to evaluate the high temperature mechanical properties of the structure. Based on the resistance increase of the first load step, the damage unit resistance sensing signal increment factor γ = 7.09 is calculated in this embodiment. The relationship between the resistance sensing signal increment of each load step and the mechanical properties of the CMC structure is calculated, as shown in Figure 5 As shown. Further, this embodiment normalizes the mechanical properties-resistance increment response and resistance increment-time response of the CMC connection structure. That is, given the test time point t at which the mechanical properties of the CMC structure need to be predicted, Figure 4 Retrieve the CMC structure resistance sensing signal increment response ΔR obtained during monitoring at this moment; through the resistance sensing signal increment response ΔR, it is possible to Figure 5 The mechanical properties of the CMC connection structure are obtained. Figure 6As shown, in this embodiment, the displacement-time response and force-time response of the CMC structure are obtained by the in-situ intelligent sensing method of resistance, and compared with the displacement data taken by DIC in the test and the data results of the force sensor in the test machine. The evaluation results of the displacement and force of the CMC connection structure based on the in-situ intelligent sensing characteristics are consistent with the test results. The maximum displacement perception error when the structure fails is 15.64%, and the structural failure load perception error is 7.43%. This shows that the high-temperature mechanical performance evaluation scheme of the CMC structure based on the in-situ intelligent sensing characteristics adopted in this embodiment is reliable.
[0075] The above are only preferred embodiments of the present invention, and the protection scope of the present invention is not limited to the above embodiments. All technical solutions under the concept of the present invention belong to the protection scope of the present invention. It should be pointed out that for ordinary technicians in this technical field, some improvements and modifications without departing from the principle of the present invention should be regarded as the protection scope of the present invention.
Claims
1. The high temperature mechanical properties evaluation method of CMC structure based on in-situ intelligent sensing is characterized by: The following steps are involved: Step 1: Set mechanical and temperature boundary conditions for the CMC structure and establish a finite element model of the CMC structure; establish a resistance network model of the CMC structure based on the geometric characteristics of the CMC structure; conduct high-temperature mechanical tests on the CMC structure whose mechanical properties are to be predicted, collect the resistance response of the CMC structure in real time through a resistance monitor, and calculate the resistivity of the CMC structure based on the initial resistance response of the CMC structure in a high-temperature environment; Step 2: Discretize the resistance of the CMC structure into N layers of sensing unit groups connected in series, each layer of sensing unit group has a total of M sensing units connected in parallel, apply a load step to the CMC structure, calculate the finite element model of the CMC structure, obtain the force-displacement response of the CMC structure at the current load step, and count the area of the structural failure sensing unit; calculate the structural resistance sensing signal increment of the resistance network model based on the distribution of the CMC structural failure units; Step 3: Analyze the damage distribution of the CMC structure under the current load step. If the damage distribution of the CMC structure under the current load step does not form a failure section, analyze whether a failure unit is formed in the current loading. If a failure unit is formed, go to step 4. If no failure unit is formed, go to step 5. If a failure section is formed, go to step 6. Step 4: Reduce the failed unit modulus of the CMC structure, degrade the non-failed unit modulus according to the CMC material constitutive model, update the material parameters and go to step 2; Step 5: Further apply the mechanical boundary conditions of the next load step and go to step 2; Step 6: Count the sensing unit area forming the failure section and calculate the cumulative structural resistance sensing signal increment under each load step; Step 7, according to the accumulated structural resistance sensing signal increment under each load step and the CMC structure force-displacement response obtained by finite element calculation in the corresponding load step, the mechanical property-resistance increment response of the CMC structure is obtained; A resistance monitor is installed on the CMC structure whose mechanical properties are to be predicted, and the resistance of the CMC structure whose mechanical properties are to be predicted is collected in real time to obtain the resistance increment-time response of the CMC structure whose mechanical properties are to be predicted; Through the resistance increment of the CMC structure whose mechanical properties are to be predicted, the force-displacement response at the corresponding moment is retrieved from the mechanical property-resistance increment response of the CMC structure; thereby, in-situ intelligent perception of the high-temperature mechanical properties of the CMC structure whose mechanical properties are to be predicted is achieved, and online real-time warning of the failure trend of the CMC structure whose mechanical properties are to be predicted is provided.
2. The method for evaluating high temperature mechanical properties of CMC structures based on in-situ intelligent sensing according to claim 1 is characterized by: In step 2, the specific method for calculating the structural resistance sensing signal increment of the resistance network model based on the distribution of the CMC structural failure unit is: Total resistance of CMC structure R CMC for: Where R i is the resistance of the sensing unit at the i-th layer, R ij is the resistance of the jth sensing unit in the i-th layer, ρ is the material resistivity, l is the thickness of the sensing unit in this layer, A ij is the area of the jth perceptual unit in the i-th layer; After each load step finite element calculation is completed, the damage sensing unit area is counted and the CMC structural resistance R' after damage evolution is calculated CMC ,Right now: Where R i ' is the resistance of the i-th layer sensing unit after damage evolution, is the resistance of all damage-aware cells in the i-th layer, is the resistance of all undamaged sensing units in the i-th layer, S is the total number of damaged sensing units in the i-th layer, is the area of the jth damage sensing unit in the i-th layer, is the area of the kth undamaged sensing unit in the i-th layer, γ is the incremental factor of the damaged unit resistance sensing signal, which is the signal amplification factor when the unit fails. Thus, the structural resistance sensing signal increment ΔR caused by the damage of the CMC structure after each loading step is obtained: ΔR=R' CMC -R CMC 。 3. The method for evaluating high temperature mechanical properties of CMC structures based on in-situ intelligent sensing according to claim 1 is characterized by: In step 3, the method for determining the CMC structural failure unit is as follows: if the strain component of the CMC structural unit is greater than the maximum material strain of the CMC structural unit, the unit is marked as failed, and the direction of the strain component of the CMC structural unit and the material parameters in the related directions are degraded.
4. The method for evaluating high temperature mechanical properties of CMC structures based on in-situ intelligent sensing according to claim 1 is characterized by: In step 4, the specific method for degrading the modulus of the non-failed unit according to the CMC material constitutive model is: The strain of the non-failed unit is extracted and brought into the modulus-strain degradation equation to obtain the material modulus after mechanical property degradation; where the modulus-strain degradation equation is: Where E is the material modulus, σ(ε) is the normal stress-strain constitutive model of the material, τ(ε) is the shear stress-strain constitutive model of the material, and ε is the strain component corresponding to the material.
5. The method for evaluating high temperature mechanical properties of CMC structures based on in-situ intelligent sensing according to claim 2 is characterized by: The specific method for obtaining the damage unit resistance sensing signal increment factor γ is: Step 1: Perform the first loading on the resistor network model to obtain the resistance response of the CMC structure loaded in this step. Since the damage unit resistance perception signal increment factor has not been determined in this process, the resistance increment obtained in the first finite element calculation is a resistance perception signal increment factor function, that is: ΔR(γ)=R' CMC (c)-R CMC Where ΔR(γ) is the theoretical resistance increment of the first loading step, R' CMC (γ) is the resistance of the CMC structure after the first step of loading damage evolution; Step 2: Load the resistor network model in the second step, set the theoretical resistance increment in the first step equal to the resistance increment response collected in the second load step, solve the equation to obtain the damage unit resistance sensing signal increment factor γ in this loading step, and directly apply it to all subsequent calculation steps, that is, solve the following equation: ΔR(γ)=ΔR step1 Where ΔR step1 The incremental resistance response acquired for the first load step in the test.
Citation Information
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