A brittle material jh-2 damage parameter calibration method based on fragment size effect

Abstract

The application discloses a brittle material JH2 damage parameter calibration method based on a fragment size effect, and belongs to the technical field of brittle material constitutive model parameter calibration. The method comprises the following steps: screening brittle material broken powder into a plurality of particle size groups, respectively performing constraint compression experiments on the particle size groups, and calibrating the broken strength coefficients and pressure indexes corresponding to the particle size groups; taking the parameters of the particle size group with the smallest particle size as a complete broken state benchmark, inversely solving the equivalent damage parameters corresponding to the particle size groups through a JH2 strength interpolation equation; taking the representative particle sizes of the particle size groups as independent variables and the equivalent damage parameters as dependent variables, fitting a size-dependent damage interpolation model, and outputting model parameters. The application overcomes the fundamental defect that all fragments are uniformly regarded as a complete broken state in the prior art, gives different particle size fragments their real damage degrees, and improves the physical rationality of damage parameter calibration.

Description

Technical Field

[0001] This invention relates to the field of constitutive model parameter calibration technology for brittle materials, specifically to a method for calibrating damage parameters of the JH-2 constitutive model for brittle materials based on fragment size effect. Background Technology

[0002] The JH-2 constitutive model describes the strength degradation process of brittle materials from an intact state to a completely fractured state through the damage variable D. Its strength interpolation equation uses the damage variable as weights to linearly interpolate the normalized strength of the intact state and the normalized strength of the completely fractured state. This model has been widely used in numerical simulations of impact dynamics for brittle materials such as ceramics, rocks, and glasses. Accurate calibration of damage parameters is a core prerequisite for the engineering application of the JH-2 model. Among them, damage parameters D1 and D2 are particularly sensitive to describing the cumulative damage process of materials under high strain rate impact. However, these parameters cannot be directly obtained through experiments and require fitting with a large amount of experimental data. Moreover, different fitting methods yield different results, reducing the reliability of parameter calibration. Currently, the calibration of JH-2 damage parameters mainly relies on numerical inversion methods. CN119580883A discloses a numerical inversion method for the JH-2 constitutive damage parameters of brittle materials, which inverts the damage parameters D1 and D2 through a fly-plate impact test combined with the SPH numerical model. Although this scheme involves the calibration of JH-2 damage parameters, its numerical inversion-based approach differs fundamentally from the method of inverse deduction based on fragment size effects experiments in this scheme. CN114550851B discloses a method for optimizing constitutive model parameters of brittle materials, which iteratively optimizes JH-2 model parameters through projectile penetration tests combined with chaotic global optimization algorithms. The parameter acquisition and optimization method proposed by Wang Yangwei et al. uses a chaotic global optimization algorithm combined with numerical simulations of dynamic compression and penetration tests to obtain damage-related parameters. However, the above methods generally overlook a key experimental fact: after dynamic fracture, materials produce fragments with a wide range of particle sizes, and fragments of different sizes exhibit significantly different residual strengths in constrained compression tests—the smaller the particle size, the lower the residual strength, and the higher the corresponding damage degree. Existing methods uniformly treat all fragments as completely fractured, leading to a systematic underestimation of the strength of large-diameter fragments. Studies on the influence of particle size on mechanical behavior have shown that the degree of damage intensifies with increasing impact velocity, and larger particle sizes promote crack propagation. However, the method of using the difference in residual strength of fragments with different particle sizes to calibrate equivalent damage parameters has not yet been proposed in the prior art.

[0003] Therefore, providing a JH-2 damage parameter calibration method that considers the fragment size effect and can assign the true damage degree to fragments of different sizes has become a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0004] This invention provides a method for calibrating damage parameters of brittle materials JH-2 based on fragment size effect, comprising the following steps: Step S100: The brittle material powder is sieved into multiple particle size groups, and a constrained compression test is conducted on each particle size group to calibrate the crushing strength coefficient corresponding to each particle size group. and stress index , where i=1,2,…,N, and N is the number of particle size groups; Step S200: The crushing strength parameter of the smallest particle size group is used as the reference parameter for the fully crushed state. and , where D represents the damage variable, with a value ranging from 0 to 1; Step S300, with and The complete fracture strength curve and the intact strength parameters are determined by independent experiments. The fracture strength-hydrostatic pressure data for each particle size group are substituted into the JH-2 strength interpolation equation, and the equivalent damage parameters for each particle size group are solved by the least squares method. The intensity interpolation equation for JH-2 is: ; in This represents the normalized equivalent force of the complete state. This represents the normalized equivalent stress in a completely fragmented state. Represents normalized hydrostatic pressure. For normalized equivalent effect; Step S400: Using the representative particle size of each particle size group As the independent variable, with equivalent damage parameters As the dependent variable, fit a size-dependent damage interpolation model. ; in This is the lower limit of damage saturation. is the characteristic transition diameter, and n is the transition steepness index; Step S500: Output the parameters of the size-dependent damage interpolation model. , , n and goodness of fit .

[0005] Further, step S100 includes: Step S110: After the brittle material is dynamically crushed and recycled, it is classified according to the particle size range using a standard square hole sieve to obtain crushed powder samples of at least three particle size groups. There is no overlap between adjacent particle size groups. The powder of each particle size group is weighed separately, and the mass of each particle size group is not less than 0.35 g. Step S120: Conduct constraint compression experiments on fragments of each particle size group, determine the crushing strength coefficient Bi and pressure index Mi corresponding to each particle size group according to the dual criterion effective window method, and the fitting linear correlation coefficient R2 is not less than 0.90.

[0006] Furthermore, in step S200, The crushing strength parameter of the smallest particle size group under experimental conditions was used as the benchmark parameter for the fully crushed state. and This corresponds to D=1.

[0007] Further, step S300 includes: Step S310, using reference parameters and Define the strength curve of the fully fractured state ; Complete state intensity curve Where A and N are the whole-state intensity parameters, determined by independent experiments. To normalize the maximum hydrostatic tensile strength, , The maximum hydrostatic tensile strength that the material can withstand. This represents the hydrostatic pressure component of the material at the Hugoniot elastic limit. Step S320: Compress the fragmentation strength-hydrostatic pressure dataset obtained from the constrained compression experiments for each particle size group. Substitute JH 2. Intensity interpolation equation: ; The optimal equivalent damage parameters for this particle size group were determined by least squares fitting. .

[0008] Furthermore, it is characterized in that, The equivalent damage parameters The lower limit of the value A value less than 1 corresponds to the damage saturation state of large-sized fragments.

[0009] Further, step S400 includes: Step S410, using the representative particle size of each particle size group The independent variable is the corresponding equivalent damage parameter determined in step S300. As the dependent variable, the representative particle size of each particle size group is taken as the geometric mean between the sieve sections. For intervals without a lower limit, take ; Step S420: Use the nonlinear least squares method to... Fitting a size-dependent damage interpolation model to the dataset: ; Goodness of fit A value of 0.95 or higher is considered a valid fit.

[0010] Furthermore, the size-dependent damage interpolation model is mathematically isomorphic to the JH-2 intensity interpolation equation. when hour ,when hour .

[0011] Furthermore, it also includes step S600: combining the size-dependent damage interpolation model with JH By combining the two strength interpolation equations, a continuous strength prediction formula with the representative particle size d as the independent variable is obtained, which can be used to directly predict the equivalent strength of fragments of any particle size under a given hydrostatic pressure.

[0012] Further, step S600 includes: Step S610: Fit the obtained SDDI model parameters , Substituting n into the size-dependent damage interpolation model, we obtain a continuous function of the damage parameters with respect to particle size: ; Step S620, will Substitute JH 2. Intensity interpolation equation: ; The values ​​of d and normalized hydrostatic pressure are obtained. The formula for predicting the continuous intensity of an independent variable is given.

[0013] Furthermore, the brittle material is one or more of metallic glass, ceramics, rock, or concrete.

[0014] Compared with the prior art, the present invention has the following beneficial effects: (1) By taking advantage of the experimental fact that fragments of different particle sizes exhibit different residual strengths in the constrained compression test, the minimum particle size group parameter is used as the benchmark for the completely broken state. The equivalent damage parameters corresponding to each particle size group are solved by the JH-2 strength interpolation equation, thus realizing the true damage degree of fragments of different particle sizes. This overcomes the fundamental defect of the existing technology that treats all fragments as completely broken, which leads to the systematic underestimation of the strength of large-particle-size fragments.

[0015] (2) By establishing a size-dependent damage interpolation model, with the representative particle size as the independent variable and the equivalent damage parameter as the dependent variable, a three-parameter nonlinear function is fitted. The three parameters of the model have clear physical meanings: the damage saturation lower limit reveals the asymptotic limit of material structure degradation under a specific dynamic loading mode, the characteristic transformation diameter gives the characteristic particle size at which the damage state undergoes the most rapid transformation, and the transformation steepness index reflects the step characteristics of damage transformation, which helps to deeply understand the microscopic mechanism of dynamic fracture.

[0016] (3) By using multi-size group constraint compression experiments, the damage information contained in the strength difference between fragments of different sizes is fully utilized, and a quantitative continuous relationship between fragment size and damage degree is established, which significantly improves the statistical reliability of parameter fitting.

[0017] (4) By combining the SDDI model with the JH-2 strength interpolation equation, a continuous strength prediction formula with the representative particle size as the independent variable is obtained. The strength calibration results of the discrete particle size group are extended to a continuous function with respect to the particle size. The equivalent strength of any particle size fragment under a given hydrostatic pressure can be directly predicted, which breaks through the limitations of the traditional discrete point calibration method.

[0018] The present invention will now be further described with reference to the accompanying drawings. Attached Figure Description

[0019] Figure 1 This is a flowchart illustrating the overall process of the method of the present invention.

[0020] Figure 2 A comparison of the fragmentation strength-hydrostatic pressure envelope of fragments with different particle sizes.

[0021] Figure 3 This is a schematic diagram showing the calibration results of the damage parameter D for each particle size group.

[0022] Figure 4 The image shows the fitting results of the SDDI model. Detailed Implementation

[0023] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0024] This invention provides a brittle material JH based on fragment size effect. 2. Damage Parameter Calibration Method: This method utilizes the experimental fact that fragments of different particle sizes exhibit different residual strengths in constrained compression experiments to deduce the equivalent damage parameters corresponding to each particle size group, and establishes a correlation with JH... A size-dependent damage interpolation model with a two-framework mathematical isomorphism enables a continuous description of the damage state of fragments of arbitrary size.

[0025] Reference Figure 1 This method includes the following steps performed in sequence.

[0026] Step S100 involves preparing multi-size fragment samples and calibrating the fracture strength parameters for each size group. This includes: Step S110: After the brittle material is dynamically crushed and recycled, it is classified according to the particle size range using a standard square hole sieve to obtain crushed powder samples of at least three particle size groups. There is no overlap between adjacent particle size groups. The powder of each particle size group is weighed separately, and the mass of each particle size group is not less than 0.35g to ensure the representativeness of the packing density. Step S120: Conduct constrained compression tests on fragments of each particle size group. The powder is loaded into a high-strength metal sleeve, and a quasi-static axial load is applied under the combined action of the axial indenter and the radial constraint of the sleeve. The axial stress time history and the circumferential strain time history of the outer wall of the sleeve are recorded simultaneously. The crushing strength coefficient corresponding to each particle size group is determined according to the dual-criteria effective window method. and stress index Where i = 1, 2, ..., N, and N is the number of particle size groups, the fitted linear correlation coefficient is... Not less than 0.90. The dual-criteria effective window method refers to axial stress. The data extraction method uses the moment when the second derivative of the strain curve changes from fluctuating to a sustained positive value as the lower limit of the effective window and the moment when the von Mises equivalent stress on the inner wall of the sleeve reaches the yield limit as the upper limit of the effective window. (Each particle size group...) and The calibration was performed using a log-linear regression method, and the calibration results were independent of the specific fitting algorithm chosen within a certain range.

[0027] Each particle size group and The calibration results serve as the basis for subsequent damage parameter back-calculation.

[0028] Step S200: The crushing strength parameter of the smallest particle size group under experimental conditions is used as the benchmark parameter for the fully crushed state. and The physical basis for this benchmark definition is that the interparticle bonding force and cohesive force of the extremely fine powder have been reduced to their minimum values ​​under experimental conditions. Therefore, its residual strength parameter is directly used as the engineering benchmark of D=1. If there are even finer fragments, their strength may be further lower than the measured value of the finest particle size in this experiment, and this benchmark has a certain degree of engineering conservatism. Here, D represents the damage variable, taking a value from 0 to 1, with D=0 corresponding to the intact state of the material and D=1 corresponding to the completely broken state of the material.

[0029] Step S300, via JH 2. Inverse solution of the strength interpolation equation: equivalent damage parameters corresponding to each particle size group .include: Step S310, using reference parameters and Define the strength curve of the fully fractured state Complete state intensity curve Where A and N are the whole-state strength parameters, determined independently by the MTS quasi-static compression experiment and the SHPB dynamic compression experiment. Normalized maximum hydrostatic tensile strength , The maximum hydrostatic tensile strength that the material can withstand. This represents the hydrostatic pressure component of the material at the Hugoniot elastic limit. Determined by the plate impact experiment, it is JH 2. Known input parameters of the model. This represents the normalized equivalent force of the complete state. This represents the normalized equivalent stress in a completely fragmented state. Represents normalized hydrostatic pressure. This experiment was conducted under quasi-static loading conditions, with the normalized experimental strain rate approaching 1. 2. The strain rate correction term in the strength equation approaches 1. For the sake of simplification, this term is omitted in the following formulas. Step S320, for the first The crushing strength obtained from constrained compression experiments for each particle size group hydrostatic pressure dataset Substitute JH 2. Intensity interpolation equation: ; The optimal equivalent damage parameters for this particle size group were determined by least squares fitting. This minimizes the mean square error between the model's predicted intensity and the experimental data. Different particle size groups... When the differences in values ​​are within the statistical error range, the benchmark shall be used uniformly. conduct Inverse calculation. Record the values ​​for each particle size group and the corresponding goodness of fit. .

[0030] JH 2. The primary damage variable D is defined based on the equivalent plastic strain accumulation, with parameters... and Control its evolution rate. In this method... It is an equivalent damage index determined by the fragment size effect. Both follow the normalized definition that D=0 corresponds to the intact state and D=1 corresponds to the completely fragmented state. They have the same mathematical function in the intensity interpolation equation, but different physical sources. Not a replacement for JH 2 native and parameter.

[0031] Step S400: Establish a size-dependent damage interpolation model. This includes: Step S410, using the representative particle size of each particle size group The independent variable is the corresponding equivalent damage parameter determined in step S300. The dependent variable is the representative particle size of each particle size group, which is the geometric mean between the sieve sections. For intervals without a lower limit, take ; Step S420: Fit the size-dependent damage interpolation model using the following formula: ; in The lower limit of damage saturation represents the asymptotic damage level corresponding to large-sized fragments; The characteristic transformation diameter is defined as follows: The corresponding particle size represents the characteristic scale of the transition from near-complete fragmentation to a saturation plateau; n is the steepness index of the transition, and the larger the value of n, the closer the transition is to step behavior.

[0032] Using nonlinear least squares method The dataset is fitted to the above three-parameter model, and the initial guess values ​​are... =0.8、 =100μm, n=5. The above initial values ​​are selected based on engineering experience and only affect the convergence speed, not the uniqueness of the final fitting result. Goodness of fit A fitting result is considered valid if it is not lower than 0.95. Record the fitted result. , , n, and confidence interval.

[0033] The functional form of the above SDDI model is derived from JH Inspired by the structure of the intensity interpolation equation: JH The two equations interpolate material strength using the damage variable D, while the SDDI model interpolates the damage state of fragments representing the particle size d. Both maintain inherent consistency in mathematical structure and physical logic.

[0034] Step S500: Output SDDI model parameters , , n and goodness of fit Damage parameter calibration considering fragment size effects was completed.

[0035] Step S600, connect the SDDI model with JH 2. By simultaneously solving the intensity interpolation equations, a continuous intensity prediction formula with the representative particle size d as the independent variable is obtained. This includes: Step S610: Fit the obtained SDDI model parameters , Substituting n into the size-dependent damage interpolation model, we obtain a continuous function of the damage parameters with respect to particle size: ; Step S620, will Substitute JH 2. Intensity interpolation equation: ; The values ​​of d and normalized hydrostatic pressure are obtained. The formula for predicting the continuous intensity of an independent variable is given.

[0036] Reference Figure 2 The fragmentation strength obtained by different particle size groups in constrained compression experiments The hydrostatic pressure envelope is linearly distributed on logarithmic coordinates. The smaller the particle size, the lower the overall position of the envelope. This indicates that under the same hydrostatic pressure, the residual strength of fine-particle fragments is significantly lower than that of coarse-particle fragments. This is the experimental basis for establishing a quantitative relationship between fragment size effect and damage state in this method.

[0037] Reference Figure 3 Equivalent damage parameters corresponding to each particle size group The value of D decreases non-linearly with increasing representative particle size d: the minimum particle size group D=1 is used as the defining benchmark, and the value of D tends to the lower limit of damage saturation after the particle size exceeds the characteristic transformation diameter. .

[0038] Reference Figure 4 The SDDI model fitting curves and the experimental calibration curves for each particle size group The values ​​match well.

[0039] The three fitting parameters in this method have clear physical meanings. It reveals the asymptotic limit of material structure degradation under specific dynamic loading modes. The characteristic particle size at which the damage state undergoes the most abrupt transition is given, where n reflects the step characteristics of the damage transition.

[0040] The method will be described below with reference to specific embodiments.

[0041] Example 1, this example uses The powder obtained from the high-speed impact crushing of bulk amorphous alloy was used as the test material. The ballistic impact velocity was approximately 1200 m / s, impacting a No. 45 steel target. Five particle size groups were obtained: <74 μm, 100~160 μm, 160~180 μm, 180~224 μm, and 355~600 μm. The intact state strength parameters were taken as A=0.96, N=0.68, and the normalized maximum hydrostatic tensile strength was used. .

[0042] Constrained compression experiments were conducted on each particle size group. Continuous datasets within the effective window of each particle size group were extracted, and log-linear regression was performed after strain rate correction to obtain the following fracture strength parameters for each particle size group: Defined as ; ; ; ; .

[0043] by Using particle size parameters as a baseline for D=1, the strength curve in the fully fractured state is determined. Complete state intensity curve .

[0044] Substitute the data for each particle size group into JH 2 Interpolation Equations The particle size groups were determined by minimizing the mean square error. value: : ; ; ; ; , The representative particle size of each particle size group is taken as the geometric mean: .

[0045] by Fitting the SDDI model to the dataset Fitting results: =0.824±0.004, =134.5 μm is the characteristic grain size at which the damage state undergoes the most abrupt transition. Fragments smaller than this size are in a highly damaged state, while fragments larger than this size show a rapid shift in damage. Convergence; n=14.0 indicates an extremely steep damage transition, with the D value rapidly decreasing from close to 1 to close to 1 within a narrow particle size range of approximately 100–170 μm. This exhibits characteristics similar to a step jump.

[0046] Example 2, based on Example 1, this example combines the SDDI model with JH 2. Combining the intensity interpolation equations, we obtain a continuous intensity prediction formula with the representative particle size d as the independent variable: ; in, .

[0047] With d=169.7 Substituting, we get , compared with the experimental calibration Completely identical; with d=200.8 Substituting, we get The residual from the experimental value of 0.83 is 0.005; with d=461.5 Substituting, we get The residual between the predicted value and the experimental value of 0.82 is 0.004. The maximum residual between the continuous predicted value and the discrete experimental calibration value is 0.006, which verifies the SDDI model's ability to accurately describe the damage state of fragments of various particle sizes.

Claims

1. A method for calibrating damage parameters of brittle materials JH-2 based on fragment size effect, characterized in that, Includes the following steps: Step S100: The brittle material powder is sieved into multiple particle size groups, and a constrained compression test is conducted on each particle size group to calibrate the crushing strength coefficient corresponding to each particle size group. and stress index , where i=1,2,…,N, and N is the number of particle size groups; Step S200: The crushing strength parameter of the smallest particle size group is used as the reference parameter for the fully crushed state. and , where D represents the damage variable, with a value ranging from 0 to 1; Step S300, with and The complete fracture strength curve and the intact strength parameters are determined by independent experiments. The fracture strength-hydrostatic pressure data for each particle size group are substituted into the JH-2 strength interpolation equation, and the equivalent damage parameters for each particle size group are solved by the least squares method. The intensity interpolation equation for JH-2 is: ； in This represents the normalized equivalent force of the complete state. This represents the normalized equivalent stress in a completely fragmented state. Represents normalized hydrostatic pressure. For normalized equivalent effect; Step S400: Using the representative particle size of each particle size group As the independent variable, with equivalent damage parameters As the dependent variable, fit a size-dependent damage interpolation model. ； in This is the lower limit of damage saturation. is the characteristic transition diameter, and n is the transition steepness index; Step S500: Output the parameters of the size-dependent damage interpolation model. , , n and goodness of fit .

2. The method according to claim 1, characterized in that, Step S100 includes: Step S110: After the brittle material is dynamically crushed and recycled, it is classified according to the particle size range using a standard square hole sieve to obtain crushed powder samples of at least three particle size groups. There is no overlap between adjacent particle size groups. The powder of each particle size group is weighed separately, and the mass of each particle size group is not less than 0.35 g. Step S120: Conduct constraint compression experiments on fragments of each particle size group, determine the crushing strength coefficient Bi and pressure index Mi corresponding to each particle size group according to the dual criterion effective window method, and the fitting linear correlation coefficient R2 is not less than 0.

90.

3. The method according to claim 1, characterized in that, In step S200, The crushing strength parameter of the smallest particle size group under experimental conditions was used as the benchmark parameter for the fully crushed state. and This corresponds to D=1.

4. The method according to claim 1, characterized in that, Step S300 includes: Step S310, using reference parameters and Define the strength curve of the fully fractured state ; Complete state intensity curve Where A and N are the whole-state intensity parameters, determined by independent experiments. To normalize the maximum hydrostatic tensile strength, , The maximum hydrostatic tensile strength that the material can withstand. This represents the hydrostatic pressure component of the material at the Hugoniot elastic limit. Step S320: Compress the fragmentation strength-hydrostatic pressure dataset obtained from the constrained compression experiments for each particle size group. Substitute JH 2. Intensity interpolation equation: ； The optimal equivalent damage parameters for this particle size group were determined by least squares fitting. .

5. The method according to claim 4, characterized in that, The equivalent damage parameters The lower limit of the value A value less than 1 corresponds to the damage saturation state of large-sized fragments.

6. The method according to claim 1, characterized in that, Step S400 includes: Step S410, using the representative particle size of each particle size group The independent variable is the corresponding equivalent damage parameter determined in step S300. As the dependent variable, the representative particle size of each particle size group is taken as the geometric mean between the sieve sections. For intervals without a lower limit, take ; Step S420: Use the nonlinear least squares method to... Fitting a size-dependent damage interpolation model to the dataset: ； Goodness of fit A value of 0.95 or higher is considered a valid fit.

7. The method according to claim 6, characterized in that, The size-dependent damage interpolation model is mathematically isomorphic to the JH-2 intensity interpolation equation. when hour ,when hour .

8. The method according to claim 1, characterized in that, It also includes step S600: combining the size-dependent damage interpolation model with JH By combining the two strength interpolation equations, a continuous strength prediction formula with the representative particle size d as the independent variable is obtained, which can be used to directly predict the equivalent strength of fragments of any particle size under a given hydrostatic pressure.

9. The method according to claim 8, characterized in that, Step S600 includes: Step S610: Fit the obtained SDDI model parameters , Substituting n into the size-dependent damage interpolation model, we obtain a continuous function of the damage parameters with respect to particle size: ； Step S620, will Substitute JH 2. Intensity interpolation equation: ； The values ​​of d and normalized hydrostatic pressure are obtained. The formula for predicting the continuous intensity of an independent variable is given.

10. The method according to claim 1, characterized in that, The brittle material is one or more of the following: metallic glass, ceramics, rock, or concrete.

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