A numerical inversion method and system for constitutive damage parameters of brittle material JH-2

Abstract

The present invention discloses a numerical inversion method and system for the damage parameters of the JH-2 constitutive model of a brittle material, specifically comprising: obtaining a free surface particle velocity curve of a material to be fitted; determining all parameters except damage parameters D1 and D2 in the constitutive model of the material to be fitted; determining the value range of the damage parameter of the ceramic material; establishing an equivalent SPH model of a flying piece impact test in LS-PrePost, wherein some components unrelated to mechanical properties use a finite element mesh model; setting the calculation parameters of the equivalent SPH model and the finite element mesh model, and calculating the free surface particle velocity one by one according to the designed working conditions; comparing the calculated free surface particle velocity curve with the free surface particle velocity curve of the material to be fitted to determine the final damage parameter value. The present invention eliminates the interference of other parameters in the constitutive model, and the parameter determination process is more refined and accurate.

Description

Technical Field

[0001] The present invention relates to a technology for characterizing the mechanical properties of brittle materials, and in particular to a numerical inversion method and system for constitutive damage parameters of a brittle material JH-2. Background Art

[0002] With the rapid development of numerical simulation technology, its application in materials research and structural design is becoming increasingly widespread. To characterize the relationship between generalized stress and strain in materials and the mechanical response characteristics of materials under different external loads during calculations, it is necessary to define constitutive models that describe the mechanical properties of materials within simulation software. Brittle materials such as ceramics, rock, and glass exhibit damage accumulation and strain rate effects under impact loads, and above a certain pressure, they also exhibit plasticity. Currently, the JH-2 constitutive model is commonly used in dynamics software to describe these mechanical properties of brittle materials. However, the JH-2 constitutive model has a large number of parameters, some of which cannot be accurately determined through testing or calculation and must be obtained through indirect methods or numerical simulation.

[0003] The JH-2 constitutive model parameters can be divided into: (1) state equation parameters K1, K2, K3; (2) strength model parameter σ HEL 、P HEL 、T * , A, B, C, M, N; (3) damage model parameters D1, D2. The state equation parameters can be obtained by fitting the relationship between the pressure and density of the sample measured by the flying chip impact test. The σ in the strength equation parameters HEL 、P HEL The residual strength parameters can be calculated from the free-surface particle velocity measured in a flying-chip impact test. The existing patent, "A Method for Optimizing the Parameters of the JH-2 Constitutive Complete Strength Equation" (Application Number: 202110648185.7), provides a clear calculation method. The damage parameters D1 and D2 are primarily used in the constitutive equation to calculate the ultimate plastic strain. Since brittle materials such as ceramics break at low strains, these parameters are difficult to measure experimentally and are often obtained through iterative optimization using numerical simulation methods.

[0004] Currently, the numerical inversion method for determining D1 and D2 primarily relies on iterative optimization through comparison with residual penetration tests (DOP tests). This method, based on the knowledge of other parameters, continuously varies the values of D1 and D2 for numerical simulation. The D1 and D2 values corresponding to the residual penetration depths obtained from the numerical simulations and the closest match to the test results are used as the damage parameters in the constitutive model. Because the penetration depth is related to other parameters in the JH-2 constitutive model and is not solely controlled by the damage parameters D1 and D2, and because the finite element calculation results are intertwined with meshing, algorithms, boundary conditions, and other factors, determining damage values solely based on residual penetration depth is too crude, and the resulting parameter values may not be applicable in other models. Furthermore, it does not provide a decoupled solution for D1 and D2. Summary of the Invention

[0005] The purpose of the present invention is to provide a numerical inversion method and system for the damage parameters of the JH-2 constitutive model of brittle material, so as to make the fitting results of the JH-2 constitutive model more accurate and improve the reliability of the parameter fitting results.

[0006] The technical solutions for achieving the purpose of the present invention are:

[0007] A numerical inversion method for constitutive damage parameters of brittle material JH-2, comprising:

[0008] Step 1: Obtain the free surface particle velocity curve of the material to be fitted by using a flying chip impact test combined with a VISAR velocity measurement system;

[0009] Step 2: Determine all parameters of the constitutive model of the material to be simulated except for the damage parameters D1 and D2 through experimental testing and constitutive fitting methods;

[0010] Step 3: Determine the value range of the ceramic material damage parameter and design a series of numerical calculation conditions within the value range where D1 changes from the initial value, where D1 is preset to the initial value.

[0011] Step 4: Establish an equivalent SPH model for the flying chip impact test in LS-PrePost, where some parts not related to mechanical properties use finite element mesh models;

[0012] Step 5: Set the calculation parameters of the equivalent SPH model and the finite element mesh model, and calculate the free surface particle velocity one by one according to the working conditions designed in step 3;

[0013] Step 6: Extract the free surface particle velocity curves calculated for all working conditions in step 5, plot the calculated free surface particle velocity curves and the free surface particle velocity curves in step 1 on the same graph, select the simulation working condition value closest to the free surface particle velocity curve in step 1, and the D1 value therein will be used as the final value in the constitutive model;

[0014] Step 7: After determining the value of D1, repeat steps 2-6 to determine the value of D2.

[0015] Furthermore, a finite element mesh model is used for the target ring in the flying chip impact test.

[0016] Furthermore, in the finite element mesh model, automatic point-to-surface contact is adopted between the flyer particles and the target ring units, the same contact is adopted between the ceramic sample particles and the target ring, no contact is defined between the flyer particles and the sample particles, and full constraints are applied to the boundaries of the target ring in the finite element model.

[0017] Furthermore, the numerical calculation condition of D1 in step 3 is designed to change gradually from small to large.

[0018] Furthermore, the material to be fitted is AlMgB 14 For ceramics, the parameter D1 ranges from 0.001 to 0.009, and the parameter D2 ranges from 0.5 to 2.0.

[0019] Furthermore, the numerical calculation conditions for a single change of D1 starting from the initial value are: 0.001, 0.003, 0.005, 0.003, 0.003, 0.003, 0.003, 0.003, and the numerical calculation conditions for a single change of D2 starting from the initial value are: 0.5, 0.5, 0.5, 0.8, 1.1, 1.4, 1.7 and 2.0.

[0020] A numerical inversion system for the constitutive damage parameters of brittle material JH-2, including:

[0021] The fitting unit obtains the free surface particle velocity curve of the material to be fitted through the flying piece impact test combined with the VISAR velocity measurement system;

[0022] The first parameter determination unit determines all parameters except damage parameters D1 and D2 in the constitutive model of the material to be simulated through experimental testing and constitutive fitting methods;

[0023] The second parameter determination unit is used to determine the damage parameters D1 and D2, and includes a numerical calculation condition determination module, a model construction module, a calculation module and a parameter determination module. The numerical calculation condition determination module determines the value range of the damage parameters of the ceramic material, and designs a series of numerical calculation conditions in which D1 and D2 change from the initial value within the value range. The model construction module establishes an equivalent SPH model of the flying piece impact test in LS-PrePost, in which some components that are not related to mechanical properties use finite element mesh models. The calculation module calculates the free surface particle velocity one by one according to the conditions designed by the numerical calculation condition determination module. The parameter determination module extracts the free surface particle velocity curves of all conditions numerically calculated in the calculation module, plots the calculated free surface particle velocity curves and the free surface particle velocity curves of the fitting unit in the same graph, selects the simulation condition value closest to the free surface particle velocity curve of the fitting unit, and the corresponding damage parameters D1 and D2 are used as the final values in the constitutive model.

[0024] Compared with the prior art, the present invention has the following beneficial effects:

[0025] (1) Since the plastic strain value of brittle materials is very small, conventional test methods are difficult to measure the plastic strain value of samples under high pressure and high strain rate. Special tests need to be designed for measurement. The results obtained from the tests usually cannot meet the requirements. Numerical methods are also required to continuously iterate and optimize to determine the final damage parameters. The fitting process is extremely complicated. The present invention specifically compares the free surface particle velocity curve obtained by the finite element numerical calculation model of flying piece impact with the test results to determine the final damage parameter value, which is more convenient than the existing method.

[0026] (2) The free surface particle velocity curve obtained by numerical calculation using the numerical inversion method proposed in the present invention is compared with the experimental curve. Since the curve is determined by multiple factors such as slope, inflection point, and extreme value, the constraints on the numerical calculation are more sufficient and the fitting result is more accurate. At the same time, the present invention also proposes to use other numerical models to verify the entire set of constitutive parameters, further improving the reliability of the parameter fitting results.

[0027] (3) The present invention can decouple and solve the damage parameters D1 and D2. Previous experiments or numerical simulations all determined the damage parameter values simultaneously and could not decouple the two. The method proposed in the present invention can determine the damage parameter values separately during the fitting process because the two damage parameters control different characteristics of the curve respectively.

[0028] (4) Strong versatility. The method proposed in the present invention uses the flying piece impact test to obtain the dynamic mechanical parameters of the material as a numerical inversion model. The numerical calculation results are directly compared with the basic mechanical properties of the material. The damage parameter values finally determined can be directly extended to other models. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 Flowchart of numerical inversion of JH-2 constitutive damage parameters.

[0030] Figure 2 AlMgB 14 Particle velocity history curve on the free surface of ceramics.

[0031] Figure 3 This is a diagram of the numerical calculation model of flying fragment impact.

[0032] Figure 4 This is the numerical inversion result diagram of damage parameter D1.

[0033] Figure 5 This is the numerical inversion result of damage parameter D2.

[0034] Figure 6 Two loading waveforms for the Hopkinson test.

[0035] Figure 7 This is the numerical simulation result of the Hopkinson test. DETAILED DESCRIPTION

[0036] In order to make the purpose, content and advantages of the present invention more clear, the specific embodiments of the present invention are further described in detail below with reference to the accompanying drawings and examples.

[0037] Due to the difficulty in obtaining the damage parameters D1 and D2 in the current JH-2 constitutive model for brittle materials, the inaccurate damage parameters obtained through numerical simulation, and the poor versatility of the model, the inventors, while studying the failure mechanism of ceramic materials under impact loads, discovered that the particle velocity history of the sample's free surface during a flying chip impact test is closely related to the damage and fragmentation within the material, corresponding to the damage parameters D1 and D2 in the constitutive parameters. Therefore, the present invention proposes an inversion method to determine the damage parameter values by comparing the free surface particle velocity curve obtained from numerical simulation with the experimental results.

[0038] The present invention proposes a numerical inversion process for the constitutive damage parameters of the brittle material JH-2 as follows: Figure 1 As shown in Figure 3, before the damage parameters are fitted, other parameters in the constitutive model need to be determined through theoretical calculation and experimental methods. At the same time, a flying chip impact test is required to obtain the free surface particle velocity curve of the sample.

[0039] The numerical simulation method used in the present invention is smoothed particle hydrodynamics (Smoothed Particle Hydrodynamics, SPH), and the SPH method is to represent continuous matter as a set of movable discrete particles with speed. The particles comply with the mass, momentum and energy conservation theorem, and are solved in combination with the material constitutive equation to obtain the motion law of the material. The calculation result of this method is smooth and continuous, and can better simulate the damage and crack propagation of brittle materials. It is convenient to track the particle velocity of the sample free surface in post-processing, and the method avoids the mesh distortion problem in the traditional finite element method simulation of high-speed impact. In order to reduce the calculation amount of the model, the traditional finite element mesh (i.e., FEM algorithm) is adopted for the target ring component that does not pay attention to its mechanical properties.

[0040] In order to reduce the computational complexity of the numerical inversion process, the damage parameter range of the material to be simulated is determined by consulting public information before the numerical calculation begins, and the minimum value within the damage parameter range is used as the initial value to start the first numerical calculation.

[0041] Before numerical calculations, it is necessary to initially determine the ranges of the damage parameters D1 and D2 of the material to be tested. Because the damage parameters D1 and D2 control different characteristics of the free surface particle velocity curve, the D1 value is determined first and then the D2 value during the fitting process. Therefore, it is necessary to design a series of simulation calculation conditions in which the D1 value changes gradually from small to large, with D2 as the initial value. Based on the determined D1 value, a series of numerical calculation conditions with a gradient change of the D2 value are then designed.

[0042] Calculations are performed based on the pre-designed D1 and D2 numerical simulation conditions. The free surface particle velocity of each calculation condition is extracted in post-processing and compared with the experimental curve. Finally, the D1 and D2 values that best match the experimental curve are determined as constitutive parameters.

[0043] Finally, the entire set of JH-2 constitutive parameters needs to be verified. Other numerical calculation models need to be established based on the determined constitutive parameters. The numerical calculation results are compared with the experimental results to analyze whether the damage and failure process and mechanical properties of the material are consistent with the experiment. If the results are within the error range, the constitutive model passes the verification. If they are beyond the error range, the corresponding control parameters need to be analyzed and refitted.

[0044] This paper proposes a method for inverting the values of the damage parameters D1 and D2 in JH-2 using a finite element method based on smoothed particle hydrodynamics (SPH). Specifically, the free-surface particle velocity curves obtained from a finite element numerical calculation model of flying fragment impact are compared with experimental results to determine the final damage parameter values. This fitting method eliminates the interference of other parameters in the constitutive model, and the numerical simulation results must match the experimental curves, making the parameter determination process more precise and accurate. At the same time, the damage parameters D1 and D2 control different characteristics of the curves in the numerical calculation, and their mutual coupling is weak, allowing them to be decoupled and determined.

[0045] Example

[0046] To fit AlMgB 14 Taking the damage parameter value of ceramics as an example, the specific fitting process of this method and its key steps are explained in detail.

[0047] AlMgB 14 The specific steps of the numerical inversion method for ceramic damage parameters are as follows:

[0048] Step 1: Before numerical inversion, it is necessary to obtain the free surface particle velocity curve of the material to be fitted through a flying sheet impact test combined with a VISAR velocity measurement system. This will be used as a reference curve for numerical model debugging in steps 6 and 7.

[0049] Through some previous research work of the inventors, it was found that the free surface particle velocity curve of the sample in the flying piece impact test is related to the material damage, that is, the damage parameters D1 and D2 in the corresponding numerical calculation constitutive parameters, and D1 and D2 control different characteristics of the free surface particle velocity curve in the simulation model. Therefore, the free surface particle velocity curve is used as the basis for inverting the damage parameters.

[0050] Step 2: Determine all parameters of the constitutive model of the material to be simulated except for the damage parameters D1 and D2 through experimental testing and combining existing constitutive fitting methods;

[0051] Step 3: Before simulation calculation, consult relevant data to preliminarily determine the value range of ceramic material damage parameters. Within the value range, design a series of numerical calculation conditions in which D1 changes from the initial value, where D1 is preset to the initial value.

[0052] Step 4: Establish an equivalent SPH model for the flying chip impact test in LS-PrePost. To reduce the amount of model calculation, a finite element mesh model can be used for some unimportant components.

[0053] Step 5: Construct the simulation calculation model and perform calculations one by one in LS-DYNA according to the calculation conditions designed in step 3;

[0054] In the finite element model, automatic point-to-surface contact (AUTOMATIC_NODES_TO_SURFACE) is used between the flyer particles and the target ring elements. The ceramic sample particles and the target ring use identical contact, and no contact is required between the flyer particles and the sample particles. In the experiment, the target ring is fixed to the target chamber base with screws, so the target ring boundary is fully constrained in the finite element model.

[0055] Step 6: Extract the free surface particle velocity curves calculated numerically for all working conditions in step 5, plot the simulation curves and the test curves in the same graph, select the simulation condition that is closest to the test curve, and the D1 value in it will be used as the final value in the constitutive model;

[0056] Step 7: Based on the determined D1 value, design a series of numerical calculation conditions in which D2 changes from the initial value. These conditions are then incorporated into the model for calculation. The free surface particle velocity is extracted and compared with the experimental curve to determine the D2 value that best matches the experimental curve (this determination process is the same as the previous D1 determination process). This concludes the D1 and D2 inversion process.

[0057] AlMgB was measured experimentally before fitting 14 The particle velocity history curve of the ceramic free surface is as follows Figure 2 As shown, in this test, the size of the oxygen-free copper flying piece is φ23mm×1.7mm, the size of the ceramic sample is φ15mm×3.5mm, the size of the target ring is φ30mm×3.5mm, and the flying piece impact velocity is 580m / s.

[0058] The SPH numerical calculation model of flying fragment impact established according to the experiment is as follows: Figure 3 As shown, the flying pieces and AlMgB 14 The ceramic sample was modeled using the SPH algorithm, while the target ring was modeled using the FEM algorithm to reduce computational complexity. Contact was defined to achieve FEM-SPH coupling. Automatic point-to-surface contact (AUTOMATIC_NODES_TO_SURFACE) was used between the flyer particles and the target ring elements, while identical contact was used between the ceramic sample particles and the target ring. The target ring was fixed to the target chamber base with screws, so the finite element model applied full constraints to the target ring's boundaries.

[0059] According to the dynamic / static mechanical properties tests and theoretical calculations, the remaining parameters in the constitutive model have been determined before fitting the damage parameters, as shown in Table 1.

[0060] Table 1 AlMgB 14 JH-2 constitutive parameters table of ceramics

[0061]

[0062] By consulting relevant data, the damage factor range of the JH-2 model for ceramic materials was determined, D1∈[0.001,0.009], D2∈[0.5,2.0]. Based on the damage range, eight numerical calculation conditions in Table 2 were further designed.

[0063] Table 2 Numerical simulation conditions of different damage factors

[0064] serial number <![CDATA[D1]]> <![CDATA[D2]]> serial number <![CDATA[D1]]> <![CDATA[D2 <!-- 5 -->]]> S1 0.001 0.5 S5 0.003 1.1 S2 0.003 0.5 S6 0.003 1.4 S3 0.005 0.5 S7 0.003 1.7 S4 0.003 0.8 S8 0.003 2.0

[0065] First, D2 is fixed at 0.5, and D1 varies in the range of 0.001 to 0.009. Three simulation conditions S1 to S3 are designed. The simulation results are consistent with the test results. Figure 4 The calculation results show that as D1 increases, the particle velocity upon reaching the first platform increases, and the platform residence time also increases. The particle velocity at the first platform is positively correlated with the D1 value. When D1 is 0.003, the simulation results are in good agreement with the experimental results. Therefore, D1 is initially set to 0.003.

[0066] Based on the initial setting of D1=0.003, the value of D2 was changed and five working conditions S4~S8 were designed. The simulation results are as follows Figure 5 Comparing the simulation results for each operating condition, we find that as the D2 value increases, the particle velocity upon reaching the first plateau gradually decreases. Furthermore, as the D2 value increases, the slope of the second free-surface particle velocity curve increases. Observing the various curves in the figure, we find that operating condition S8 best matches the experimental results, so we ultimately selected the damage variable values for this condition: D1 = 0.003 and D2 = 2.

[0067] In order to verify the correctness of the damage parameters fitted by this invention, a finite element model of the Hopkinson test was established. The incident waveforms of the two strain rates in the test are as follows: Figure 6 As shown, numerical simulation shows that AlMgB 14 The damage evolution process of ceramics at different strain rates is as follows Figure 7 As shown in the figure, the numerical simulation results are consistent with the experimental results, indicating that the JH-2 constitutive model established by this method can accurately simulate the stress of AlMgB under shock compression. 14 Dynamic deformation and damage evolution behavior of ceramics.

[0068] A computer storage medium stores an executable program, wherein the executable program is executed by a processor to implement the steps of the numerical inversion method.

[0069] Although the preferred embodiments of the present invention have been described, those skilled in the art may make additional 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 that fall within the scope of the present invention.

[0070] Obviously, those skilled in the art may make various changes and modifications to the embodiments of the present invention without departing from the spirit and scope of the embodiments of the present invention. Thus, if such changes and modifications of the embodiments of the present invention fall within the scope of the claims and their equivalents, the present invention is intended to include such changes and modifications.

Claims

1. A numerical inversion method for constitutive damage parameters of brittle material JH-2, characterized in that: include: Step 1: Obtain the free surface particle velocity curve of the material to be fitted by using a flying chip impact test combined with a VISAR velocity measurement system; Step 2: Determine all parameters of the constitutive model of the material to be simulated except for the damage parameters D1 and D2 through experimental testing and constitutive fitting methods; Step 3: Determine the value range of the ceramic material damage parameter and design a series of numerical calculation conditions within the value range where D1 changes from the initial value, where D1 is preset to the initial value. Step 4: Establish an equivalent SPH model for the flying chip impact test in LS-PrePost, where some parts not related to mechanical properties use finite element mesh models; Step 5: Set the calculation parameters of the equivalent SPH model and the finite element mesh model, and calculate the free surface particle velocity one by one according to the working conditions designed in step 3; Step 6: Extract the free surface particle velocity curves calculated for all working conditions in step 5, plot the free surface particle velocity curves and the free surface particle velocity curves in step 1 on the same graph, and select the simulation working condition value closest to the free surface particle velocity curve in step 1. The D1 value in the curve will be used as the final value in the constitutive model. Step 7: After determining the value of D1, repeat steps 2-6 to determine the value of D2.

2. The numerical inversion method for constitutive damage parameters of a brittle material JH-2 according to claim 1, characterized in that: The target ring in the flying fragment impact test adopts a finite element mesh model.

3. The numerical inversion method for constitutive damage parameters of a brittle material JH-2 according to claim 2, characterized in that: In the finite element mesh model, automatic point-to-surface contact is adopted between the flyer particles and the target ring units, identical contact is adopted between the ceramic sample particles and the target ring, and no contact is defined between the flyer particles and the sample particles. Full constraints are applied to the boundaries of the target ring in the finite element model.

4. The numerical inversion method for constitutive damage parameters of a brittle material JH-2 according to claim 1, characterized in that: The numerical calculation condition of D1 in step 3 is designed to change gradually from small to large.

5. The numerical inversion method for constitutive damage parameters of a brittle material JH-2 according to claim 1, characterized in that: The material to be fitted is AlMgB 14 For ceramics, the parameter D1 ranges from 0.001 to 0.009, and the parameter D2 ranges from 0.5 to 2.

0.

6. The numerical inversion method for constitutive damage parameters of brittle material JH-2 according to claim 5, characterized in that: The numerical calculation conditions for a single change of D1 starting from the initial value are: 0.001, 0.003, 0.005, 0.003, 0.003, 0.003, 0.003, 0.003, and the numerical calculation conditions for a single change of D2 starting from the initial value are: 0.5, 0.5, 0.5, 0.8, 1.1, 1.4, 1.7 and 2.

0.

7. A numerical inversion system for constitutive damage parameters of brittle material JH-2, implementing the method according to any one of claims 1 to 6, characterized in that: include: The fitting unit obtains the free surface particle velocity curve of the material to be fitted through the flying piece impact test combined with the VISAR velocity measurement system; The first parameter determination unit determines all parameters except damage parameters D1 and D2 in the constitutive model of the material to be simulated through experimental testing and constitutive fitting methods; The second parameter determination unit is used to determine the damage parameters D1 and D2, and includes a numerical calculation condition determination module, a model construction module, a calculation module and a parameter determination module. The numerical calculation condition determination module determines the value range of the damage parameters of the ceramic material, and designs a series of numerical calculation conditions in which D1 and D2 change from the initial value within the value range. The model construction module establishes an equivalent SPH model of the flying piece impact test in LS-PrePost, in which some components that are not related to mechanical properties use finite element mesh models. The calculation module calculates the free surface particle velocity one by one according to the conditions designed by the numerical calculation condition determination module. The parameter determination module extracts the free surface particle velocity curves of all conditions numerically calculated in the calculation module, plots the calculated free surface particle velocity curves and the free surface particle velocity curves of the fitting unit in the same graph, selects the simulation condition value closest to the free surface particle velocity curve of the fitting unit, and the corresponding damage parameters D1 and D2 are used as the final values in the constitutive model.

8. A computer storage medium, characterized in that The computer storage medium stores an executable program, and the executable program is executed by a processor to implement the steps of the numerical inversion method according to any one of claims 1 to 6.

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