Ceramic matrix composite vibration simulation method comprehensively considering heat and damage

Abstract

The invention discloses a ceramic matrix composite vibration simulation method comprehensively considering heat and damage, which comprises the following steps of: performing kinetic analysis on a CMC (Carboxy Methylated Cellulose) material by using a finite element analysis method, and considering the damage on the basis of randomly loading and unloading a constitutive model of a woven ceramic matrix composite; a temperature field is discretized, the thermal strain of each point at each node temperature solving position is solved by using an interpolation method, a kinetic equation is solved by using a central difference method in a time domain, the response of a CMC material at each moment under different excitation frequencies can be calculated, and an amplitude-frequency curve is obtained, so that accurate and efficient simulation measurement of the CMC high-temperature nonlinear kinetic response is realized.

Description

Technical Field

[0001] The invention relates to the field of CMC material dynamics simulation, and in particular to a ceramic matrix composite material vibration simulation method that comprehensively considers heat and damage. Background Art

[0002] As one of the most important core components of aircraft, most of the parts of aircraft engines are subjected to huge thermal and force loads in harsh environments such as high temperature and high-frequency vibration for a long time. In the future, aerospace vehicles will fly at speeds exceeding Mach 5, and aerodynamic heating will quickly heat the fuselage to more than 1000°C, and the local operating temperature of the engine will exceed 1700°C, so new high-temperature resistant materials are urgently needed to meet the various requirements of the new generation of engines. Vibration exceeding the limit of composite materials means resonance, flutter and other adverse vibrations, which will cause engine structure failure. Therefore, under ultra-high temperature conditions, whether the vibration characteristics of new high-temperature resistant composite materials can meet the requirements of the new generation of aircraft engines is one of the key factors in judging whether the new high-temperature resistant composite materials are qualified. Therefore, it is very necessary to simulate the vibration performance of composite materials under ultra-high temperature conditions, which is of great significance to the further design of high-performance aircraft engines.

[0003] At present, most of the simulations of the vibration characteristics of CMC materials are based on linear theory to calculate the natural frequency and damping of CMC materials. There are few simulations of the nonlinear dynamic response of CMC materials. Due to the complexity of the weaving damage mechanism, the dynamic response of CMC materials lacks the calculation of damage, and there is little consideration of the influence of thermal strain on the dynamic characteristics of CMC materials under high temperature conditions.

[0004] Therefore, it is necessary to design a CMC vibration simulation method that takes thermal damage into consideration to fill the gap in the field of vibration simulation of CMC composite materials under ultra-high temperature conditions. Summary of the invention

[0005] The purpose of the present invention is to provide a vibration simulation method for ceramic matrix composites that comprehensively considers heat and damage. It can use the loading and unloading constitutive model of CMC materials to take damage into account in the dynamic calculation of CMC materials, change the different temperature fields at a finite number of moments provided by the user into a temperature field that satisfies the time interval Δt in the central difference method, and calculate the thermal strain caused by temperature at different times, thereby taking the thermal field and damage into account in the dynamic calculation at the same time.

[0006] In order to achieve the above technical objectives, the technical solution adopted by the present invention is:

[0007] A vibration simulation method for ceramic matrix composite materials taking into account heat and damage, the method comprising the following steps:

[0008] S1, using ANSYS software to establish a finite element model of ceramic matrix composites, output unit and node information; calculate the unit geometry matrix B, mass matrix M and damping matrix C that do not change with time;

[0009] S2, input the node temperature information, and use the quadratic difference method to average the provided temperature field into a temperature field that satisfies the time interval Δt;

[0010] S3, calculate the mass matrix M and the damping matrix C according to the unit geometry matrix B;

[0011] S4, calculate the stress load K at time t t ;

[0012] S5, input external load information and calculate the external load matrix Q t ;

[0013] S6, calculate the node displacement vector a at the next moment t+Δt ;

[0014] S7, calculate the total strain vector of the 8 Gaussian integration points in each element

[0015] S8, calculate the thermal strain vectors of 8 Gaussian integration points in each unit

[0016] S9, calculate the elastic strain vectors of 8 Gaussian integration points in each unit

[0017] S10, based on the CMCs constitutive model, calculate the stress vector σ of the 8 Gaussian integration points of each unit at the next moment t+Δt ;

[0018] S11, determine whether the number of calculations has been reached, if so, proceed to step S12, otherwise set t = t + Δt and proceed to step S4;

[0019] S12, calculate the displacement response of the CMC material at each moment under different excitation frequencies, obtain the amplitude-frequency curve, and write the displacement, strain and stress files at the corresponding moment.

[0020] Furthermore, the geometry matrix B, mass matrix M, damping matrix C, stress load matrix K t and the external load matrix Q t The expression is:

[0021]

[0022] In the formula, Ω e is the unit calculation domain, Γe is the unit external force domain, is the unit stress at the current moment, q tis the external force load at the current moment, c is the damping coefficient, N e The shape function of the i-th node of the unit, ρ is the material density, G e is the conversion matrix between unit node degrees of freedom and overall degrees of freedom, B e is the unit geometry matrix, the superscript T is the transpose symbol, the subscript t represents the current moment, and the superscript e represents the unit.

[0023] Further, in step S7, the total strain vector of the eight Gaussian integral points in each unit is calculated using the following formula:

[0024]

[0025] In the formula, is the shape function of the i-th node of the unit, is the displacement vector of the i-th node of the unit, B e is the unit geometry matrix, n is the total number of unit nodes, is the unit displacement vector, To find the derivative in the x direction, To find the derivative in the y direction, the superscript e represents the unit and the subscript t+Δt represents the next moment.

[0026] Further, in step S8, the following formula is used to calculate the thermal strain vectors of the eight Gaussian integral points in each unit:

[0027]

[0028] In the formula, is the instantaneous thermal expansion coefficient of the unit, is the unit change temperature, the superscript e represents the unit, and the subscript t+Δt represents the next moment.

[0029] Further, in step S9, the elastic strain vectors of the eight Gaussian integral points in each unit are calculated using the following formula:

[0030]

[0031] In the formula, B e is the unit geometry matrix, is the unit temperature change, is the thermal expansion coefficient of the unit in each direction, is the unit change temperature, the superscript e represents the unit, and the subscript t+Δt represents the next moment.

[0032] Furthermore, the CMCs constitutive model is:

[0033]

[0034] where p u1 、p u2 、p u3 、p u4 、p r1 、p r2 、p r3 and p r4 are all about the maximum strain ε max function; ε is the strain; is the strain rate, which is used to judge whether it is a loading or unloading process; σ uploud is the stress during loading, σ reloud is the stress during the unloading process.

[0035] Furthermore, the central difference method is used to calculate the node displacement vector a at the next moment. t+Δt :

[0036] a t+Δt =M -1 (K t -Q t )Δt 2 +2a t -a t-Δt

[0037] Where a is the displacement, M is the mass matrix, and K t is the stress load, Q t is the external load matrix, where the starting condition of the central difference method is:

[0038]

[0039] In the formula, a 0 is the initial displacement condition, is the initial velocity condition, is the initial acceleration condition, and the convergence conditions are as follows:

[0040]

[0041] Where Δt is the time step, Δt cr is the minimum time step, ω n is the highest order natural frequency of the vibration system, T n is the minimum period of the vibration system; T n The calculation formula is:

[0042]

[0043] In the formula, is the minimum unit size, E is the elastic modulus of the material, and ρ is the material density.

[0044] Compared with the prior art, the present invention has the following beneficial effects:

[0045] First, the ceramic matrix composite material vibration simulation method of the present invention comprehensively considers heat and damage, takes the damage of CMC material into consideration in the dynamic calculation, and substitutes the damage of CMC into the simulation calculation from the macroscopic phenomenological loading and unloading constitutive model, which is more in line with the experimental data. Compared with the previous method of quantifying the damage per unit time, the damage is considered using the fitted macroscopic phenomenological loading and unloading constitutive model, which is closer to reality and more in line with the experimental data.

[0046] Secondly, the ceramic matrix composite material vibration simulation method of the present invention which comprehensively considers heat and damage takes thermal strain into account in the dynamic response calculation of CMC materials. In order to cope with different temperature fields at different times provided by users, the temperature field is decomposed into temperature fields satisfying the time interval Δt by using the quadratic difference method, so as to analyze the dynamic response calculation considering the thermal field under transient conditions in each iteration. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 This is a flow chart of the vibration simulation method of ceramic matrix composite materials taking into account heat and damage of the present invention;

[0048] Figure 2 Schematic diagram of the constitutive model of ceramic matrix composites at room temperature;

[0049] Figure 3 Schematic diagram of time domain displacement obtained by dynamic frequency sweep experiment on ceramic matrix composites;

[0050] Figure 4 for Figure 3 A magnified image of the resonance peak in the mesodynamic sweep experiment;

[0051] Figure 5 This is a time domain diagram of the displacement solution for the simulation at 0.5s around the resonance peak;

[0052] Figure 6 Schematic diagram of the displacement time domain curve obtained by simulation when the frequency sweep starts at 0.1s (150Hz-150.1Hz);

[0053] Figure 7 Schematic diagram of the displacement time domain curve obtained by simulation when the frequency sweep ends at 0.1s (239.9Hz-240Hz). DETAILED DESCRIPTION

[0054] The embodiments of the present invention are further described in detail below in conjunction with the accompanying drawings.

[0055] The present invention discloses a vibration simulation method for ceramic matrix composite materials which comprehensively considers heat and damage. The finite element analysis method is used to perform dynamic analysis on CMC materials. Damage is considered based on an arbitrary loading and unloading constitutive model of woven ceramic matrix composite materials. The temperature field is discretized and the interpolation method is used to solve the thermal strain at each point at which the temperature of each node is solved. The central difference method is used in the time domain to solve the dynamic equation. The response of the CMC material at each moment under different excitation frequencies can be calculated, and the amplitude-frequency curve can be obtained, thereby realizing accurate and efficient simulation measurement of the high-temperature nonlinear dynamic response of the CMC.

[0056] The simulation calculation steps of the ceramic matrix composite material vibration simulation method of the present invention are as follows: Figure 1 The detailed description is as follows:

[0057] S1, using ANSYS software to establish a finite element model of ceramic matrix composites, output unit and node information; calculate the unit geometry matrix B, mass matrix M and damping matrix C that do not change with time;

[0058] S2, input the node temperature information, and use the quadratic difference method to average the provided temperature field into a temperature field that satisfies the time interval Δt;

[0059] S3, calculate the mass matrix M and the damping matrix C according to the unit geometry matrix B;

[0060] S4, calculate the stress load K at time t t ;

[0061] S5, input external load information and calculate the external load matrix Q t ;

[0062] As a preferred example, the geometry matrix B, the mass matrix M, the damping matrix C, the stress load matrix K t and the external load matrix Q t The expression is:

[0063]

[0064] In the formula, Ω e is the unit calculation domain, Γ e is the unit external force domain, is the unit stress, q t is the external load, c is the damping coefficient, N e The shape function of the i-th node of the unit, ρ is the material density, G e is the conversion matrix between unit node degrees of freedom and overall degrees of freedom, B e is the unit geometry matrix, the superscript T is the transpose symbol, the superscript e represents the unit, and the subscript t+Δt represents the next moment.

[0065] S6, calculate the node displacement vector a at the next moment t+Δt ;

[0066] S7, calculate the total strain vector of the 8 Gaussian integration points in each element

[0067] In step S7, the total strain vector of the eight Gaussian integration points in each unit is calculated using the following formula:

[0068]

[0069] In the formula, is the shape function of the i-th node of the unit, is the displacement vector of the i-th node of the unit, B e is the unit geometry matrix, n is the total number of unit nodes, is the unit displacement vector, To find the derivative in the x direction, To find the derivative in the y direction, the superscript e represents the unit and the subscript t+Δt represents the next moment.

[0070] S8, calculate the thermal strain vectors of 8 Gaussian integration points in each unit

[0071] In step S8, the thermal strain vectors of the eight Gaussian integral points in each unit are calculated using the following formula:

[0072]

[0073] In the formula, is the instantaneous thermal expansion coefficient of the unit, is the unit change temperature, the superscript e represents the unit, and the subscript t+Δt represents the next moment.

[0074] S9, calculate the elastic strain vectors of 8 Gaussian integration points in each unit

[0075] In step S9, the elastic strain vectors of the eight Gaussian integration points in each unit are calculated using the following formula:

[0076]

[0077] In the formula, B e is the unit geometry matrix, is the unit temperature change, is the thermal expansion coefficient of the unit in each direction, is the unit change temperature, the superscript e represents the unit, and the subscript t+Δt represents the next moment.

[0078] S10, based on the CMCs constitutive model, calculate the stress vector σ of the 8 Gaussian integration points of each unit at the next moment t+Δt ;

[0079] The constitutive model of CMCs is:

[0080]

[0081] where p u1 、p u2 、p u3 、p u4 、p r1 、p r2 、p r3 and p r4 are all about the maximum strain ε max function; ε is the strain; is the strain rate, which is used to judge whether it is a loading or unloading process; σ uploud is the stress during loading, σ reloud is the stress during the unloading process. Figure 2 Shown is the constitutive model of ceramic matrix composites at room temperature.

[0082] S11, determine whether the number of calculations has been reached, if so, proceed to step S12, otherwise set t = t + Δt and proceed to step S4;

[0083] S12, calculate the displacement response of the CMC material at each moment under different excitation frequencies, obtain the amplitude-frequency curve, and write the displacement, strain and stress files at the corresponding moment.

[0084] In the present invention, the method for CMC to calculate t=t+Δt, that is, the stress-strain vector at the next moment, is the central difference method, and its iterative formula is:

[0085] a t+Δt =M -1 (K t -Q t )Δt 2 +2a t -a t-Δt

[0086] The starting conditions for the central difference method above are:

[0087]

[0088] The time step Δt of the central difference method determines the stability of the calculation. When Δt is less than the critical Δt cr When , the calculation results converge, otherwise they diverge, so the convergence condition of the central difference method is as follows:

[0089]

[0090] In the formula, ω n is the highest order natural frequency of the vibration system, T n is the minimum period of the vibration system. n The calculation formula is:

[0091]

[0092] In the formula is the minimum unit size.

[0093] At a high temperature of 200°C, the ceramic matrix composite flat plate is subjected to an acceleration excitation of 10m / s 2 The dynamic sweep frequency experiment (150Hz-240Hz) was carried out to obtain the corresponding time domain displacement diagram, such as Figure 3 As shown, the peak part is enlarged to obtain Figure 4 .

[0094] According to the above theoretical calculation method, through C++ programming, it is calculated that the ceramic matrix composite material is excited by 10m / s at a high temperature of 200℃. 2 The time domain displacement diagram under the condition of transient dynamics is shown in Figure 1. Due to the large amount of transient dynamics calculation and limited calculation time, this calculation calculates the displacement time domain diagram around the resonance peak at 0.5s, as shown in Figure 1. Figure 5 At the same time, the displacement time domain curves at the beginning and end of the frequency sweep are calculated, which correspond to the sweep frequencies of 150-150.1Hz and 239.9-240Hz in the experiment, respectively. Figure 6 and Figure 7 shown.

[0095] Those skilled in the art will appreciate that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can adopt the form of complete hardware embodiments, complete software embodiments, or embodiments in combination with software and hardware. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code. The scheme in the embodiments of the present application can be implemented in various computer languages, for example, object-oriented programming language Java and literal scripting language JavaScript, etc.

[0096] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0097] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0098] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process in the computer or other programmable device. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0099] Although the preferred embodiments of the present application have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications falling within the scope of the present application.

[0100] Obviously, those skilled in the art can make various changes and modifications to the present application without departing from the spirit and scope of the present application. Thus, if these modifications and variations of the present application fall within the scope of the claims of the present application and their equivalents, the present application is also intended to include these modifications and variations.

Claims

1. A vibration simulation method for ceramic matrix composite materials taking into account heat and damage, characterized in that: The method The following steps are involved: S1, using ANSYS software to establish a finite element model of ceramic matrix composites, output unit and node information; calculate the unit geometry matrix B, mass matrix M and damping matrix C that do not change with time; S2, input the node temperature information, and use the quadratic difference method to average the provided temperature field into a temperature field that satisfies the time interval Δt; S3, calculate the mass matrix M and the damping matrix C according to the unit geometry matrix B; S4, calculate the stress load K at time t t ; S5, input external load information and calculate the external load matrix Q t ; S6, calculate the node displacement vector a at the next moment t+Δt ; S7, calculate the total strain vector of the 8 Gaussian integration points in each element S8, calculate the thermal strain vectors of 8 Gaussian integration points in each unit S9, calculate the elastic strain vectors of 8 Gaussian integration points in each unit S10, based on the CMCs constitutive model, calculate the stress vector σ of the 8 Gaussian integration points of each unit at the next moment t+Δt ; S11, determine whether the number of calculations has been reached, if so, proceed to step S12, otherwise set t = t + Δt and proceed to step S4; S12, calculate the displacement response of the CMC material at each moment under different excitation frequencies, obtain the amplitude-frequency curve, and write the displacement, strain and stress files at the corresponding moment.

2. The ceramic matrix composite material vibration simulation method considering heat and damage according to claim 1 is characterized in that: Geometry matrix B, mass matrix M, damping matrix C, stress load matrix K t and the external load matrix Q t The expression is: In the formula, Ω e is the unit calculation domain, Γ e is the unit external force domain, is the unit stress at the current moment, q t is the external force load at the current moment, c is the damping coefficient, N e The shape function of the i-th node of the unit, ρ is the material density, G e is the conversion matrix between unit node degrees of freedom and overall degrees of freedom, B e is the unit geometry matrix, the superscript T is the transpose symbol, the subscript t represents the current moment, and the superscript e represents the unit.

3. The ceramic matrix composite material vibration simulation method considering heat and damage according to claim 1, characterized in that: In step S7, the total strain vector of the eight Gaussian integration points in each unit is calculated using the following formula: In the formula, is the shape function of the i-th node of the unit, is the displacement vector of the i-th node of the unit, B e is the unit geometry matrix, n is the total number of unit nodes, is the unit displacement vector, To find the derivative in the x direction, To find the derivative in the y direction, the superscript e represents the unit and the subscript t+Δt represents the next moment.

4. The ceramic matrix composite material vibration simulation method considering heat and damage according to claim 1, characterized in that: In step S8, the thermal strain vectors of the eight Gaussian integral points in each unit are calculated using the following formula: In the formula, is the instantaneous thermal expansion coefficient of the unit, is the unit change temperature, the superscript e represents the unit, and the subscript t+Δt represents the next moment.

5. The ceramic matrix composite material vibration simulation method considering heat and damage according to claim 1, characterized in that: In step S9, the elastic strain vectors of the eight Gaussian integration points in each unit are calculated using the following formula: In the formula, B e is the unit geometry matrix, is the unit temperature change, is the thermal expansion coefficient of the unit in each direction, is the unit change temperature, the superscript e represents the unit, and the subscript t+Δt represents the next moment.

6. The ceramic matrix composite material vibration simulation method considering heat and damage according to claim 1, characterized in that: The constitutive model of CMCs is: where p u1 、p u2 、p u3 、p u4 、p r1 、p r2 、p r3 and p r4 are all about the maximum strain ε max function; ε is strain; is the strain rate, which is used to judge whether it is a loading or unloading process; σ uploud is the stress during loading, σ reloud is the stress during the unloading process.

7. The ceramic matrix composite material vibration simulation method considering heat and damage according to claim 1, characterized in that: The central difference method is used to calculate the node displacement vector a at the next moment. t+Δt : a t+Δt =M -1 (K t -Q t )Δt 2 +2a t -a t-Δt Where a is the displacement, M is the mass matrix, and K t is the stress load, Q t is the external load matrix, where the starting condition of the central difference method is: Where a0 is the initial displacement condition, is the initial velocity condition, is the initial acceleration condition, and the convergence conditions are as follows: Where Δt is the time step, Δt cr is the minimum time step, ω n is the highest order natural frequency of the vibration system, T n is the minimum period of the vibration system; T n The calculation formula is: In the formula, is the minimum unit size, E is the elastic modulus of the material, and ρ is the material density.

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