Composite material strength parameter inversion method considering in-situ effect in ultralow temperature environment

Abstract

The invention provides a composite material strength parameter inversion method considering an in-situ effect in an ultralow-temperature environment, and the method comprises the steps: obtaining the elastic section test data of a composite material one-way plate and a composite material laminated plate in the ultralow-temperature environment, and employing a composite material finite element model and a particle swarm optimization (PSO) algorithm, taking consistency of a response value of finite element simulation of the composite material and strain response of an elastic section measured by a test as a target, performing inversion to obtain constitutive parameters of the composite material, and establishing a progressive failure model of the composite material in combination with a failure criterion of the composite material and a rigidity degradation model; and finally, according to test data of the damaged sections of the composite unidirectional plate and the composite laminated plate, a composite progressive failure model and a PSO optimization algorithm are adopted, and composite strength parameters are obtained through inversion. The method solves the problem that the strength parameters of the composite material considering the in-situ effect are difficult to accurately obtain in the ultralow-temperature environment, is convenient to operate and accurate in parameter obtaining, can be repeatedly applied, and is used for simulation modeling, strength evaluation and the like of the composite material.

Description

Technical Field

[0001] This invention relates to the field of mechanical testing and strength assessment of composite materials, and specifically to a method for inverting the strength parameters of composite materials considering in-situ effects under ultra-low temperature conditions. Background Technology

[0002] With the increasing demands for lightweight spacecraft, composite materials are widely used in spacecraft structural components such as tanks and gas cylinders due to their numerous advantages, including high specific strength, light weight, high specific modulus, good fatigue resistance, and good vibration reduction performance. However, composite material tanks and gas cylinders account for a large proportion of the mass of the structural system and are used in extreme load environments. Therefore, their strength assessment and design optimization are important factors affecting the overall performance of the spacecraft.

[0003] Currently, only unidirectional plate strength test data are used to evaluate laminates in composite material strength assessment. Since composite material strength depends on its thickness and the angle between adjacent ply layers, i.e., there is an in-situ effect, the mechanical property results of the intermediate layers often have significant errors. Therefore, in ultra-low temperature environments, it is impossible to directly obtain the transverse tensile strength and shear strength parameters of composite materials considering in-situ effects through experimental methods alone. Summary of the Invention

[0004] To address the aforementioned problems, this invention provides a method for inverting composite material strength parameters considering in-situ effects under cryogenic conditions. Based on experimental data of composite one-way plates and laminates under cryogenic conditions, a composite material finite element model and particle swarm optimization (PSO) algorithm are used. The goal is to ensure consistency between the simulated response value of the composite material finite element model and the experimentally measured elastic segment strain response, thereby inverting the constitutive parameters of the composite material. Then, using these composite material constitutive parameters, combined with composite material failure criteria and stiffness degradation models, a progressive failure model of the composite material is established. Finally, based on experimental data of the failure segments of composite one-way plates and laminates under cryogenic conditions, the composite material progressive failure model and PSO optimization algorithm are used. The goal is to ensure consistency between the simulated response value of the progressive failure model and the experimentally measured failure segment strain response, thereby inverting the composite material strength parameters, including the transverse tensile strength and shear strength of the composite material considering in-situ effects. The specific steps are as follows:

[0005] S1: Obtain mechanical test data of composite materials under ultra-low temperature conditions

[0006] The composite material test data includes unidirectional plate test data and laminate test data, wherein the unidirectional plate test data includes longitudinal tensile and compression tests and transverse compression tests;

[0007] The laminate test data includes longitudinal tensile and compression tests, transverse compression tests, and shear tests. The composite material test data includes elastic segment test data and failure segment test data.

[0008] S2: Constitutive parameter inversion of composite materials

[0009] The material constitutive parameters are obtained by inverting the elastic segment test data of the composite unidirectional plate and laminate described in S1.

[0010] Establish a finite element model of the composite material test specimen. The finite element model has the same boundary and load conditions as the actual test specimen. Calculate the strain response value or data of the elastic segment.

[0011] With the goal of minimizing the strain deviation between the strain response calculated by finite element method and the strain at the measurement point, a PSO optimization algorithm is established. The particle position information is set as the constitutive parameters of the material to be inverted. Then, a matching degree analysis is performed to determine whether the PSO termination condition is met. The material constitutive parameter results are obtained through optimization iteration convergence.

[0012] S3: Establishment and Simulation Calculation of Progressive Failure Model for Composite Materials

[0013] Using the material constitutive parameters described in S2, a progressive failure model for composite materials is established by combining the improved Hashin failure criterion with a stiffness degradation model based on energy damage evolution. Based on stiffness degradation, the constitutive equation of the composite material is updated, and the strain response values ​​or data of the failure segment at each load step from the onset of stiffness degradation to complete failure are calculated.

[0014] S4: Inversion of composite material strength parameters

[0015] The particle position information in the PSO optimization algorithm described in S2 is set as the composite material strength parameters to be inverted. The elastic segment strain response data of the test specimen input by the PSO optimization algorithm and the elastic segment strain response data calculated by the finite element model of the composite material test specimen are changed to the failure segment test data under the ultra-low temperature environment described in S1 and the failure segment strain response calculated by the progressive failure model of the composite material described in S3. The composite material strength parameter results are obtained by inversion according to the PSO optimization algorithm implementation steps described in S2.

[0016] The beneficial effects achieved by this invention are as follows:

[0017] The composite material strength parameter inversion method based on finite element and PSO optimization algorithm provided by this invention is simple to develop, convenient to operate in the experimental process, accurate in parameter acquisition, and reproducible. It can provide a basic material parameter acquisition method for composite material simulation modeling, strength assessment and structural optimization design, and solves the problem of difficulty in accurately obtaining the strength parameters of composite materials considering in-situ effects under ultra-low temperature environment. Attached Figure Description

[0018] Figure 1 Schematic diagram of the composite material mechanical testing system under ultra-low temperature environment provided by the present invention

[0019] Figure 2 The present invention provides a flowchart for the inversion of constitutive parameters of composite materials based on finite element method and PSO optimization algorithm.

[0020] Figure 3 The present invention provides a flowchart for the simulation calculation of progressive failure of composite materials;

[0021] Figure 4 The present invention provides a flowchart for inverting the strength parameters of composite materials.

[0022] In the diagram, the markings are: 1 for a vertical mechanical testing machine; 2 for a liquid nitrogen environment chamber; 3 for a composite material test piece; 4 for a test fixture; 5 for a test fixture; and 6 for liquid nitrogen.

[0023] C 0 C represents the initial material constitutive parameters. j C represents the material constitutive parameters for the j-th iteration; * The constitutive parameters of the material for iterative convergence. Detailed Implementation

[0024] The following detailed description, in conjunction with the accompanying drawings and specific embodiments, provides a further explanation of the composite material strength parameter inversion method considering in-situ effects under cryogenic conditions proposed in this invention. It should be noted that the accompanying drawings are all in a very simplified form and use non-precise ratios, and are only used to facilitate and clarify the illustration of the embodiments of this invention.

[0025] Example 1:

[0026] S1, using Figure 1 The composite material mechanical testing system shown is used to obtain test data of composite unidirectional plates and laminates under ultra-low temperature conditions.

[0027] For the specific design methods of force loading and test fixtures, compression tests are conducted in accordance with ASTM D6641, and tensile and shear tests are conducted in accordance with ASTM D3039.

[0028] Before the test, two strain gauges in the 0° and 90° directions were first attached to the front and back of the composite material test specimen 3, respectively, and connected to the measurement line and the data acquisition and analysis computer.

[0029] Preferably, a vertical mechanical testing machine is used for loading. The lower test fixture 5 is fixedly connected to the liquid nitrogen environment chamber 2, and the liquid nitrogen environment chamber 2 is fixedly connected to the vertical mechanical testing machine 1. The composite material test specimen 3 is fixed using standard test fixtures 4 and 5 and placed into the liquid nitrogen environment chamber 4. Liquid nitrogen 6 is then added for heat preservation, so that the temperature of the composite material test specimen 3 is consistent with the test environment temperature. Then, after the temperature fluctuation causes the strain measurement data value to stabilize, the initial loading position of the testing machine is adjusted, and the test measurement system is zeroed. Finally, a force loading test is carried out, and the test force-displacement data and the strain data of each measuring point of the composite material test specimen 3 are recorded.

[0030] The test data include longitudinal tensile and compression tests and transverse compression tests of one-way slabs, and longitudinal tensile and compression tests, transverse compression tests, and shear tests of laminates.

[0031] The final test data obtained includes test data of the elastic segment and test data of the damaged segment.

[0032] S2, Constitutive parameter inversion of composite materials

[0033] The present invention provides a process for inverting constitutive parameters of composite materials based on finite element method and PSO optimization algorithm as follows: Figure 2 As shown.

[0034] Before performing the strength parameter inversion of composite materials, it is necessary to first obtain the material constitutive parameters using elastic segment test data. The specific process is as follows:

[0035] S2.1: Through the composite material mechanical tests conducted under the ultra-low temperature environment described in S1, the elastic segment data of the composite unidirectional plate and laminate test specimens are obtained, i.e., the strain response of each test specimen. (Elastic section);

[0036] S2.2: Establish a finite element model of the composite material specimen. The finite element model has the same boundary and load conditions as the actual test specimen, and calculate the strain response. (Elastic section);

[0037] S2.3: With the goal of minimizing the strain deviation between the strain response calculated by finite element method and the strain at the measurement point, a PSO optimization algorithm is established. The PSO optimization algorithm is initialized, the search space of the optimization objective is set, and the particle swarm, particle velocity, and position vector are initialized.

[0038] S2.4: Each particle searches for the target according to its initial position and velocity direction, and the position information of each particle is recorded. in, This represents the coordinates of the k-th particle in the search space after the j-th iteration;

[0039] S2.5: Using the optimal values ​​of the material constitutive parameters obtained in the current iteration step, calculate the response data using finite element simulation. Compare the simulated response values ​​with the experimentally measured response data to perform a matching degree analysis. Matching degree δ match The percentage-normalized root mean square error is defined as follows:

[0040]

[0041] Where, ε exp These are experimentally measured strain data. It is the average value of the measured strain data, ε sim These are the finite element simulation response values;

[0042] In equation (1), ||ε exp -ε sim || Specifically represented as (m is the number of data sequences, ε) i , (These represent experimentally measured strain data and finite element simulation responses in cryogenic tests on different test specimens, respectively.) Specifically represented as (m is the number of data sequences, ε) i , (These represent the experimentally measured strain data in different test specimens during cryogenic tests and the average value of the measured strain data, respectively).

[0043] With matching degree δ match Minimize the objective, identify the particle in the swarm that is in the optimal position, and denote the optimal value in the current iteration step as ...

[0044] S2.6: Perform PSO termination condition judgment and determine the matching degree δ match Is the value within the allowable error threshold range?

[0045] Preferably, the threshold is allowed to be adjusted according to the parameter inversion accuracy requirements, and is usually set to 99%;

[0046] S2.7: If not satisfied, calculate the inertia factor. This invention associates the value of the inertia factor with the number of iterations, expressed as:

[0047]

[0048] Where j is the current iteration number, J is the total number of iterations, and s j Let s be the inertia factor corresponding to the j-th iteration. max The initial maximum inertia factor is set. At the start of the iteration, j is relatively small, and s... j The value is relatively large, and as the number of iterations increases, j gradually approaches the total number of iterations J. jThis decreases accordingly, thus enabling the PSO optimization algorithm to achieve both fast convergence speed and high convergence accuracy.

[0049] Then, update the velocity and position information of each particle according to equation (3):

[0050]

[0051] in, and Let r1 and r2 be the velocity and position vectors of the particles, respectively, j = 1, 2, ..., J, r1 and r2 be random variables taking values ​​in the range [0, 1], and α1 and α2 be non-negative acceleration factors. Repeat steps S2.4 to S2.7 to continue optimizing the material parameters.

[0052] S2.8: When the above PSO termination criterion is met, stop the iteration and obtain the material constitutive parameter inversion results.

[0053] S3. Establishment and Simulation Calculation of Progressive Failure Model for Composite Materials

[0054] Using the material constitutive parameters obtained from S2, and combining the improved Hashin failure criterion with a stiffness degradation model based on energy damage evolution, a progressive failure model for composite materials is established. The simulation calculation process for progressive failure of composite materials in this invention is as follows: Figure 3 As shown, the specific process is as follows:

[0055] S3.1: Using the material constitutive parameters obtained in S2, establish the initial constitutive equation for the composite material. The constitutive equation expression for the composite laminate is:

[0056]

[0057] Where σ represents normal stress, ε represents normal strain, τ represents shear stress, γ represents shear strain, C represents stiffness coefficient, subscripts 1, 2, and 3 represent the directions of the rectangular coordinate axes, subscripts 11, 22, and 33 represent the positive directions of the three axes, subscripts 12, 13, 23, 21, 31, and 32 represent the shear directions of each pair of coordinate axes according to the right-hand screw rule, and subscripts 44, 55, and 66 correspond to the rotation directions between axes 12, 13, and 23 according to the right-hand screw rule, respectively.

[0058] The expression for the stiffness coefficient is:

[0059]

[0060] Where E represents the elastic modulus, G represents the shear modulus, ν represents Poisson's ratio, and κ is defined as a coefficient related to Poisson's ratio.

[0061] S3.2: Introduce an improved Hashin failure criterion.

[0062] Failure Mode 1 – Fiber Tensile Failure (σ 11 ≥0)

[0063]

[0064] Failure Mode 2 – Fiber Compression Failure (σ 11 <0)

[0065]

[0066] Failure Mode 3 – Matrix Tensile Failure (σ 22 ≥0)

[0067]

[0068] Failure Mode 4 – Matrix Compression Failure (σ 22 <0)

[0069]

[0070] Among them, F ft F is the fiber tensile failure factor. fc F is the fiber compression failure factor. mt F is the matrix tensile failure factor. mc The matrix compression failure factor; X represents the longitudinal (along the fiber direction) strength of the composite material, Y represents the transverse (perpendicular to the fiber direction) strength of the composite material, the subscript Te represents tension, Co represents compression, in represents in-plane shear, and out represents out-of-plane shear.

[0071] S3.3: Update the constitutive equations for composite materials.

[0072] According to one embodiment of the present invention, after damage initiation, continued application of load will cause material stiffness degradation, i.e., damage evolution, and a stiffness degradation model based on energy damage evolution is adopted:

[0073] When a material is damaged, its constitutive equation becomes:

[0074]

[0075] Where, d f This indicates that the stiffness degradation is affected by the longitudinal tensile / compressive degradation factor, d Δ This indicates that the stiffness degradation is caused by tension-compression and shear coupling or transverse tension-compression factor, d s This indicates that the stiffness degradation is affected by the pure shear degradation factor, d. f ,d Δ ,d s The expressions for the three degradation factors are as follows:

[0076] d f =1-(1-d) ft (1-d) fc (12)

[0077] d △ =(1-d) f (1-d) mt (1-d) mc (13)

[0078] d s =(1-d) f (1-S) mt d mt (1-S) mc d mc (14)

[0079] Among them, S mt S mc For the shear components of the matrix under tension and compression, the values ​​for carbon fiber resin matrix composites are 0.9 and 0.5, respectively. ft d fc d mt d mc The damage state variables for the four damage modes are represented by the following formula:

[0080]

[0081]

[0082] Wherein, the superscripts 0t and 0c represent the initial state of tensile and compressive damage, respectively. These represent the complete failure strain of tension and compression in the fiber direction, the complete failure strain of tension and compression perpendicular to the fiber direction, the damage initiation strain of tension and compression in the fiber direction, and the damage initiation strain of tension and compression perpendicular to the fiber direction, respectively.

[0083] S3.3: Calculation of Progressive Failure Model for Composite Materials

[0084] Based on the updated constitutive equations for composite materials, the strain response at each load step from the onset of stiffness degradation to complete failure was calculated. (Destruction section)

[0085] S4, Composite material strength parameter inversion

[0086] The composite material strength parameter inversion process of this invention is as follows: Figure 4 As shown in the figure, Γ 0 Let Γ be the initial vector of the composite material strength parameters. j Let be the value of the intensity parameter in the j-th iteration of the optimization process, expressed as: Γ * This represents the final value of the inversion parameter vector.

[0087] The particle position information in the PSO optimization algorithm described in S2 Set as The strain response of the specimen as input to the PSO optimization algorithm The strain response was obtained from the data of the (elastic segment) and the finite element model of the composite material specimen. (Elastic segment) data, change the input to the failure segment test data obtained in step one under ultra-low temperature environment. (Failure segment) Data and strain response calculated using the progressive failure model of composite materials in step three. (Damaged segment) data.

[0088] Then, following steps S2.4 to S2.8, the PSO optimization algorithm is implemented. Based on the test data of the failure segment of the longitudinal tensile and compressive tests of unidirectional plates measured in the mechanical tests of composite materials in ultra-low temperature environments, the longitudinal tensile strength is obtained by inversion. With longitudinal compressive strength Subsequently, the transverse compressive strength was obtained based on the transverse compression test. Finally, based on the transverse tensile and shear tests of the laminate, the transverse tensile strength considering the in-situ effect is obtained by inversion. and in-plane shear strength out-of-plane shear strength

[0089] The contents not described in detail in this specification are prior art known to those skilled in the art. It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, it is intended that all variations falling within the meaning and scope of equivalents of the claims be included within the present invention.

Claims

1. A method for inverting the strength parameters of composite materials considering in-situ effects under ultra-low temperature conditions, characterized in that, Based on experimental data of composite one-way plates and composite laminates under cryogenic conditions, this study employs a composite finite element model and particle swarm optimization (PSO) algorithm. The goal is to ensure that the response values ​​from the composite finite element simulation match the strain response of the experimentally measured elastic segment, thereby inverting the constitutive parameters of the composite material. Then, using these constitutive parameters, combined with composite failure criteria and stiffness degradation models, a progressive failure model for the composite material is established. Finally, based on experimental data of the failure segments of composite one-way plates and composite laminates under cryogenic conditions, the study uses the composite progressive failure model and PSO algorithm, aiming to ensure that the response values ​​from the progressive failure model simulation match the strain response of the experimentally measured failure segment, thereby inverting the strength parameters of the composite material.

2. The method for inverting composite material strength parameters considering in-situ effects under ultra-low temperature conditions according to claim 1, characterized in that, The specific steps of the method are as follows: S1: Obtain mechanical test data of composite materials under ultra-low temperature conditions The composite material test data includes composite unidirectional plate test data and composite laminate test data; S2: Constitutive parameter inversion of composite materials The material constitutive parameters are obtained by inverting the elastic segment test data of the composite unidirectional plate and composite laminate described in S1. First, a finite element model of the composite specimen is established. The finite element model has the same boundary and load conditions as the actual test specimen. The strain response value or data of the elastic segment is calculated. With the goal of minimizing the strain deviation between the strain response calculated by the finite element and the strain at the measurement point, a PSO optimization algorithm is established. The particle position information is set as the material constitutive parameters to be inverted. Then, a matching degree analysis is performed to determine whether the PSO termination condition is met. The composite constitutive parameters are obtained through optimization iteration convergence. S3: Establishment and Simulation Calculation of Progressive Failure Model for Composite Materials Using the composite material constitutive parameters described in S2, and combining the improved Hashin failure criterion with the stiffness degradation model based on energy damage evolution, a progressive failure model of composite materials is established. Based on stiffness degradation, the composite material constitutive equation is updated, and the strain response values ​​or data of each load step from the beginning of stiffness degradation to complete failure are calculated. S4: Inversion of composite material strength parameters The particle position information in the PSO optimization algorithm described in S2 is set as the composite material strength parameters to be inverted. The elastic segment strain response data of the test specimen input by the PSO optimization algorithm and the elastic segment strain response data calculated by the finite element model of the composite material test specimen are changed to the failure segment test data under the ultra-low temperature environment described in S1 and the failure segment strain response calculated by the progressive failure model of the composite material described in S3. The composite material strength parameter results are obtained by inversion according to the PSO optimization algorithm implementation steps described in S2.

3. The method for inverting composite material strength parameters considering in-situ effects under ultra-low temperature conditions according to claim 2, characterized in that, The test data for the composite unidirectional plate include longitudinal tensile and compression tests and transverse compression tests.

4. The method for inverting composite material strength parameters considering in-situ effects under ultra-low temperature conditions according to claim 2, characterized in that... The test data for the composite laminates include longitudinal tensile and compression tests, transverse compression tests, and shear tests.

5. The method for inverting composite material strength parameters considering in-situ effects under ultra-low temperature conditions according to claim 2, characterized in that, The composite material test data includes elastic segment test data and failure segment test data.

6. The method for inverting composite material strength parameters considering in-situ effects under cryogenic conditions according to claim 1, characterized in that, The specific method for inverting the constitutive parameters of the S2 composite material is as follows: S2.1: Through the composite material mechanical tests conducted under the ultra-low temperature environment described in S1, the elastic segment data of the composite unidirectional plate and laminate test specimens are obtained, i.e., the strain response of each test specimen. (Elastic section); S2.2: Establish a finite element model of the composite material specimen. The finite element model has the same boundary and load conditions as the actual test specimen, and calculate the strain response. (Elastic section); S2.3: With the goal of minimizing the strain deviation between the strain response calculated by finite element method and the strain at the measurement point, a PSO optimization algorithm is established. The PSO optimization algorithm is initialized, the search space of the optimization objective is set, and the particle swarm, particle velocity, and position vector are initialized. S2.4: Each particle searches for the target according to its initial position and velocity direction, and the position information of each particle is recorded. in, This represents the coordinates of the k-th particle in the search space after the j-th iteration; S2.5: Using the optimal values ​​of the material constitutive parameters obtained in the current iteration step, calculate the response data using finite element simulation; The simulated response values ​​are compared with the experimentally measured response data to perform a matching degree analysis; the matching degree δ match The percentage-normalized root mean square error is defined as follows: Where, ε exp These are experimentally measured strain data. It is the average value of the measured strain data, ε sim These are the finite element simulation response values; (value in the middle), Specifically represented as (m is the number of data sequences, ε) i , (These represent the experimentally measured strain data in different test specimens during cryogenic tests and the average value of the measured strain data, respectively). With matching degree δ match Minimize the objective, identify the particle in the swarm that is in the optimal position, and denote the optimal value in the current iteration step as ... S2.6: Perform PSO termination condition judgment and determine the matching degree δ match Is the value within the allowable error threshold range? S2.7: If not satisfied, calculate the inertia factor. This invention associates the value of the inertia factor with the number of iterations, expressed as: Where j is the current iteration number, J is the total number of iterations, and s j Let s be the inertia factor corresponding to the j-th iteration. max The initial maximum inertia factor is set. At the start of the iteration, j is relatively small, and s... j The value is relatively large, and as the number of iterations increases, j gradually approaches the total number of iterations J. j This decreases accordingly, thus enabling the PSO optimization algorithm to achieve both fast convergence speed and high convergence accuracy. Then, update the velocity and position information of each particle according to equation (3): in, and Let r1 and r2 be the velocity and position vectors of the particle, respectively, j = 1, 2, ..., J, r1 and r2 be random quantities taking values ​​in the range [0, 1], and α1 and α2 be non-negative acceleration factors; Repeat steps S2.4 to S2.7 to continue optimizing the material parameters; S2.8: When the above PSO termination criterion is met, stop the iteration and obtain the material constitutive parameter inversion results.

7. The method for inverting composite material strength parameters considering in-situ effects under ultra-low temperature conditions according to claim 6, characterized in that, The allowable threshold range is adjusted according to the parameter inversion accuracy requirements, and is usually set to 99%.

8. The method for inverting the strength parameters of composite materials considering in-situ effects under ultra-low temperature conditions according to claim 1 or 2, characterized in that, The strength parameters of the composite material include the transverse tensile strength and shear strength of the composite material considering in-situ effects.

9. The method for inverting composite material strength parameters considering in-situ effects under cryogenic conditions according to claim 1, characterized in that, The composite material test data were obtained using a vertical mechanical testing machine.

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