Brittle material constrained compression experiment double-criterion effective window data extraction method

Abstract

The application discloses a brittle material constrained compression experiment double-criterion effective window data extraction method, which comprises the following steps: loading broken powder into a sleeve and pre-pressing; synchronously collecting an axial stress-strain curve and a sleeve hoop strain; performing second-order derivation on the curve fitting, taking the starting moment when the derivative changes from fluctuation to continuous positive value as the lower limit of the window, and taking the moment when the equivalent stress of the inner wall of the sleeve reaches the yield limit as the upper limit of the window; converting the hoop strain into radial constraint pressure in the window, calculating the crushing strength and hydrostatic pressure moment by moment, and obtaining a continuous paired data set; and performing logarithmic linear regression on the data set after strain rate correction, and obtaining the crushing strength coefficient and pressure index of the JH-2 constitutive model. The application defines the window by using double criteria, and improves the physical rationality and statistical reliability of parameter calibration.

Description

Technical Field

[0001] This invention relates to the field of dynamic mechanical parameter testing and constitutive model calibration of brittle materials, specifically to a method for extracting constrained compression experimental data of brittle fracture materials based on a dual-criteria effective window. Background Technology

[0002] Constrained compression testing is a standard method for directly measuring the pressure-related fracture strength of fractured materials. Its principle involves loading brittle material powder into a metal sleeve. Under the combined action of an axial indenter and the sleeve's radial constraint, the powder is subjected to an approximately axisymmetric triaxial compressive stress state. This allows for obtaining the relationship between fracture strength and hydrostatic pressure over a relatively wide pressure range, providing direct experimental evidence for calibrating the fractured strength parameters B and M of the JH-2 constitutive model. The complete constrained compression loading process comprises three distinct physical stages. The initial compaction stage is dominated by pore closure and particle rearrangement, with extremely low tangential stiffness. The load is primarily consumed by pore elimination rather than particle bearing; data from this stage do not reflect the material's true strength. The stable particle compression stage involves the complete establishment of the particle contact network, with the stress state conforming to the axisymmetric triaxial compression assumption. Tangential stiffness enters a stable growth phase, making this the only effective stage for extracting effective strength-pressure data. The sleeve yielding stage involves the inner wall of the sleeve entering a plastic state, the constraint boundary failing, and a pseudo-hardening effect occurring. Data from this stage no longer reflects the material's true strength. However, existing technologies for calibrating the JH-2 fracture strength parameters using constrained compression experiments generally directly take the maximum axial stress or maximum hydrostatic pressure during the experiment as a single characteristic data point. This approach has two fundamental flaws. First, it ignores the stage division of the loading process, and the data points often contain the pseudo-hardening effect of the sleeve yielding stage, resulting in the extracted strength data lacking a clear physical correspondence. Second, the calibration method based on a single data point discards the continuously changing strength-pressure information within the stable particle compression stage, and parameter fitting relies only on a very small number of discrete points, resulting in poor statistical reliability. In the related technical field, Chen Haoxiang, Li Jie, Deng Shuxin, Wang Derong, and Wang Mingyang, in their 2022 paper "Theoretical Correction Method for Stress Calculation of SHPB Radial Constrained Pressure Test Body in Bulk Media," published in *Explosion and Shock*, simplified the rigid sleeve into a cylindrical shell subjected to uniform banded internal pressure using classical plate and shell theory, and theoretically calculated the relationship between the sleeve's circumferential strain and internal pressure. While this scheme involves the elastic mechanical relationship between the strain of the outer wall of the sleeve and the internal pressure, it is applied to dynamic impact loading scenarios and does not involve the objective determination of the upper and lower limits of the effective data window based on sleeve yielding in quasi-static constrained compression experiments. Furthermore, using the second derivative of the stress-strain curve to determine the material state transition has been applied in rock mechanics, but this method does not involve defining the effective data window under sleeve constraint conditions, nor does it involve the calibration of the JH-2 constitutive model parameters.

[0003] Therefore, providing a systematic method that can objectively define the effective data window of the constraint compression experiment and extract continuous intensity data from the effective stage 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 extracting effective window data from dual criteria in constrained compression experiments of brittle materials, comprising the following steps:

[0005] Step S100: After the brittle material is crushed into powder and classified, it is loaded into a metal sleeve and a preload is applied. The inner diameter of the sleeve is a and the outer diameter is b.

[0006] Step S200: Apply an axial load to the powder inside the sleeve and simultaneously acquire the axial true stress-true strain curve and the circumferential strain of the outer wall of the sleeve.

[0007] Step S300: After polynomial fitting of the axial true stress-true strain curve, calculate the second derivative. Use the starting moment when the second derivative changes from a fluctuating state to a continuously positive value as the lower limit of the effective window. , The corresponding particle contact network is fully established;

[0008] Step S400: Utilizing the circumferential strain of the outer wall of the sleeve, the von Mises equivalent stress of the inner wall of the sleeve is inverted based on the Lamé elastic solution, and this equivalent stress is used to achieve the yield strength of the sleeve material. The time when the product of the safety factor SF is used as the upper limit of the effective window. , The corresponding sleeve elastic constraint failure occurs, where E represents the elastic modulus of the sleeve material;

[0009] Step S500, in Within the window, the circumferential strain of the outer wall of the sleeve is converted into radial constraint pressure using the Lamé solution. Calculate the crushing strength at each time step And hydrostatic pressure P, to obtain continuous Paired datasets, where , , Indicates the true axial stress;

[0010] Step S600, After strain rate correction, linear regression was performed on the dataset in logarithmic coordinates to obtain the fracture strength coefficient B and pressure index M of the JH-2 constitutive model.

[0011] Further, step S100 includes:

[0012] Step S110: After the brittle material is dynamically crushed and recycled, it is classified according to the particle size range using a standard sieve to obtain crushed powder samples of several particle size groups. The powder of each particle size group is weighed separately.

[0013] Step S120: The weighed powder is loaded into a high-strength metal sleeve with an inner diameter of a and an outer diameter of b, where b / a is not less than 1.5.

[0014] Step S130: Apply initial preload to ensure the powder is in a stable and compacted state, and use a new sleeve for each experiment.

[0015] Further, step S200 includes:

[0016] Step S210: Apply a quasi-static axial load to the specimen on the universal testing machine. Simultaneously record the axial force F(t) and axial displacement u(t) using force and displacement sensors. Calculate the true axial stress by combining the real-time cross-sectional area correction. Harmony and True Response ,get Curve; in which Indicates the true axial stress. t represents the true axial strain, and t represents time.

[0017] Step S220: At least two resistance strain gauges are evenly arranged circumferentially on the outer wall of the sleeve, and the arithmetic mean of the signals from each strain gauge is taken as the circumferential strain of the outer wall of the sleeve. Where b represents the outer diameter of the sleeve, This indicates circumferential strain.

[0018] Further, step S300 includes:

[0019] Step S310, for The curve is fitted with a high-order polynomial, and the root mean square of the fitting residual does not exceed 0.5% of the experimental range to obtain a smooth analytical expression.

[0020] Step S320: Calculate the second-order analytic derivative of the fitted polynomial;

[0021] Step S330, with The starting point when the fluctuation changes from a state of fluctuation to a sustained positive value and the fluctuation amplitude tends to stabilize is taken as the lower limit of the effective window. .

[0022] Furthermore, in step S330 The judgment criteria are:

[0023] Within a range of 100 consecutive data points, It remains positive and its fluctuation range is less than 10% of the mean of the interval.

[0024] Further, step S400 includes:

[0025] Step S410, utilizing the circumferential strain of the outer wall of the sleeve Calculate the circumferential stress of the outer wall. for:

[0026] ;

[0027] Where E represents the elastic modulus of the sleeve material;

[0028] Step S420, solve for the uniform internal pressure using the Lamé solution:

[0029] ;

[0030] Step S430: Calculate the radial stress at the inner wall of the sleeve using the Lamé solution.

[0031] ;

[0032] Step S440: Calculate the circumferential stress at the inner wall of the sleeve using the Lamé solution.

[0033] ;

[0034] Step S450, calculate the von Mises equivalent stress on the inner wall:

[0035] ;

[0036] Step S460, with The moment as ,in σ is the yield strength of the sleeve material, and SF is the safety factor.

[0037] Further, step S500 includes:

[0038] Step S510, in Extract axial stress within the window. and circumferential strain of the outer wall of the sleeve Time history data;

[0039] Step S520, will Converted to radial constraint pressure via Lamé solution , ;

[0040] Step S530, calculate crushing strength for:

[0041] ;

[0042] Step S540, calculate the hydrostatic pressure P as follows:

[0043] ;

[0044] Obtain a continuous fracture strength-hydrostatic pressure paired dataset. .

[0045] Further, step S600 includes:

[0046] Step S610, will Dimensionless data is obtained to achieve dimensionless fracture strength. and dimensionless hydrostatic pressure ,in , For reference pressure;

[0047] Step S620: The strain rate is corrected for the JH-2 fracture strength equation. The correction formula is as follows:

[0048] ;

[0049] Where C is the strain rate coefficient of the JH-2 model. To normalize the experimental strain rate, Static strength at the reference strain rate;

[0050] Step S630, in logarithmic coordinates... Linear regression is performed on the dataset, satisfying:

[0051] ;

[0052] The pressure index M is obtained from the slope of the linear regression, and the intercept is obtained from... Therefore, the crushing strength coefficient B is determined.

[0053] Furthermore, Derived from the axial mechanical response of the sample, The data sources for the two criteria are physically independent and do not have a circular dependency relationship, and they are derived from the circumferential deformation response of the sleeve.

[0054] Furthermore, the brittle material is an amorphous alloy, ceramic, rock, or concrete.

[0055] Compared with the prior art, the present invention has the following beneficial effects:

[0056] (1) Determine the lower limit of the effective window based on the axial mechanical response The effective window is determined based on the circumferential deformation response of the sleeve. The data sources for the two criteria are physically independent and there is no circular dependency, which ensures the objectivity and repeatability of the effective data window boundary. The critical moment when the particle contact network is fully established. At the critical moment when the elastic constraint condition of the sleeve fails, only the following is extracted: The continuous data within the window is used for parameter calibration, strictly satisfying the physical assumptions of the JH-2 crushing strength equation regarding the stable bearing state and elastic constraint conditions of the particles. This overcomes the fundamental defects of existing technologies, such as the pseudo-hardening effect of the sleeve yielding stage caused by taking the maximum axial stress as a single data point, and the lack of clear physical correspondence in the data.

[0057] (2) By upgrading the existing "taking a point" processing method to... Extracting continuous data time-by-time within the effective window The paired dataset fully utilizes all the effective experimental information during the stable particle compression stage, which significantly improves the statistical reliability of linear regression and overcomes the shortcomings of existing single-data-point methods, which rely on only a very small number of discrete points for parameter fitting, resulting in unstable and poor repeatability.

[0058] (3) By using the second derivative of the axial stress-strain curve The starting point when the fluctuation state changes to a sustained positive value and the fluctuation amplitude tends to stabilize is taken as The criterion enables an objective and quantitative determination of the moment when the particle contact network is fully established, avoiding the shortcomings of traditional experience-based judgment methods where different operators may obtain different results.

[0059] The present invention will now be further described with reference to the accompanying drawings. Attached Figure Description

[0060] Figure 1 This is a flowchart illustrating the overall process of the method of the present invention.

[0061] Figure 2 This is a schematic diagram of a typical constrained compression loading response curve and an effective data acquisition window.

[0062] Figure 3 This is a scatter plot of effective data points and the results of linear fitting in logarithmic coordinates. Detailed Implementation

[0063] 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.

[0064] This invention provides a method for extracting effective window data from dual criteria in constrained compression experiments of brittle materials, used to calibrate the fracture strength coefficient B and pressure exponent M of the JH-2 constitutive model. (Refer to...) Figure 1 This method includes the following steps performed in sequence.

[0065] Step S100: Prepare the test sample, insert it into the metal sleeve, and apply a preload. This includes:

[0066] Step S110: After the brittle material is dynamically crushed and recycled, it is classified according to the particle size range using a standard sieve to obtain crushed powder samples of several particle size groups. The powder of each particle size group is weighed separately.

[0067] Step S120: The weighed powder is loaded into a high-strength metal sleeve with an inner diameter of a and an outer diameter of b, where b / a is not less than 1.5.

[0068] Step S130: Apply an initial preload to ensure the powder is in a stable and compacted state before the test begins. Use a new sleeve for each experiment to avoid interference from residual plastic deformation in subsequent measurements.

[0069] Step S200: Simultaneously acquire axial mechanical data and sleeve circumferential deformation data. This includes:

[0070] Step S210: Apply a quasi-static axial load to the specimen on the universal testing machine. Simultaneously record the axial force F(t) and axial displacement u(t) using force and displacement sensors, and convert the acquired signals into true stress-true strain curves. The conversion method is: true strain... True stress ,in For engineering stress, To measure the load, This is the initial cross-sectional area of ​​the sample. The initial length of the sample. This is the remaining length after the compression process. Indicates the true axial stress. Indicates true axial strain. Indicate time, obtain curve;

[0071] Step S220: At least two resistance strain gauges are uniformly arranged circumferentially on the outer wall of the sleeve. The output signal of each strain gauge is synchronously acquired with the axial data through a data acquisition system. The arithmetic mean of the signals from each strain gauge is taken as the circumferential strain of the outer wall of the sleeve. Where b represents the outer diameter of the sleeve, This indicates circumferential strain.

[0072] Step S300: Determine the lower limit of the effective window based on the axial mechanical response. .include:

[0073] Step S310, for The curve is fitted with a high-order polynomial, and the root mean square of the fitting residual does not exceed 0.5% of the experimental range to obtain a smooth analytical expression.

[0074] Step S320: Calculate the second-order analytic derivative of the fitted polynomial to obtain... curve;

[0075] Step S330, with The starting point when the fluctuation changes from a state of fluctuation to a sustained positive value and the fluctuation amplitude tends to stabilize is taken as the lower limit of the effective window. . The critical moment when the particle contact network is fully established corresponds to the point where the tangential stiffness enters a steady increase, and the axisymmetric triaxial compressive stress state assumption holds true.

[0076] Reference Figure 2 ,exist On the curve, The boundary between the initial compaction stage and the stable particle compression stage was defined.

[0077] Step S400: Determine the upper limit of the effective window based on the circumferential deformation response of the sleeve. .include:

[0078] Step S410, utilizing the circumferential strain of the outer wall of the sleeve Let E represent the elastic modulus of the sleeve material, and calculate the circumferential stress on the outer wall. for:

[0079] ;

[0080] Step S420: Solve for the uniform internal pressure using the Lamé solution. and Relationship:

[0081] ;

[0082] Where a is the inner diameter of the sleeve and b is the outer diameter of the sleeve;

[0083] Step S430: Calculate the radial stress at the inner wall of the sleeve using the Lamé solution. for:

[0084] ;

[0085] Step S440: Calculate the circumferential stress at the inner wall of the sleeve using the Lamé solution. for:

[0086] ;

[0087] Step S450: Calculate the von Mises equivalent stress on the inner wall. for:

[0088] ;

[0089] Step S460, with The time as the effective window limit ,in Where is the yield strength of the sleeve material, and SF is the safety factor. Exceeding... Afterward, the inner wall of the sleeve enters a plastic state, the Lamé elastic solution is no longer applicable, the constraint boundary conditions fail, and the corresponding data does not meet the physical assumptions, so it is discarded.

[0090] Reference Figure 2 ,exist On the curve, The boundary between the stable particle compression stage and the sleeve yielding stage was defined.

[0091] Derived from the axial mechanical response of the sample, The data sources for the two criteria are physically independent and do not have a circular dependency relationship, and they are derived from the circumferential deformation response of the sleeve.

[0092] Step S500: Extract the continuous dataset within the valid window. This includes:

[0093] Step S510, in Extract axial stress within the window. and circumferential strain of the outer wall of the sleeve Time history data;

[0094] Step S520, will The Lamé solution converts the stress into radial constraint pressure at the sleeve-sample interface. , ;

[0095] Step S530, calculate crushing strength for:

[0096] ;

[0097] Step S540, calculate the hydrostatic pressure P as follows:

[0098] ;

[0099] Obtain a continuous fracture strength-hydrostatic pressure paired dataset. .

[0100] Step S600, strain rate correction and parameter fitting. This includes:

[0101] Step S610, will The data is dimensionless to obtain the dimensionless crushing strength. and dimensionless hydrostatic pressure ,in , The hydrostatic pressure of the material at its Hugoniot elastic limit;

[0102] Step S620: The JH-2 fracture strength equation is corrected by strain rate adjustment, from the experimental strain rate to the static strength under the reference strain rate. The corrected formula is:

[0103] ;

[0104] Where C is the strain rate coefficient of the JH-2 model. Normalized experimental strain rate;

[0105] Step S630, refer to Figure 3 Linear regression on the corrected dataset in logarithmic coordinates satisfies the following relationship:

[0106] ;

[0107] The pressure index M is obtained from the slope of the linear regression, and the intercept is obtained from... Therefore, the crushing strength coefficient B is determined.

[0108] The method will be described below with reference to specific embodiments.

[0109] Example 1

[0110] This embodiment uses The powder obtained from the high-speed impact crushing of bulk amorphous alloy was used as the test material, and five particle size groups were tested. The sleeve was made of 45# steel with an elastic modulus E=200 GPa and a yield strength of [missing information]. The inner diameter a = 4 mm and the outer diameter b = 8 mm. Four strain gauges are arranged at 90° intervals along the outer wall of the sleeve.

[0111] Taking the 160 to 180 μm particle size group as an example, for The curve was fitted using a fourth-order polynomial, and the root mean square of the fitting residuals was 0.3% of the maximum experimental stress. Taking the second derivative of the fitted polynomial yields... Curve, Determined correspond .

[0112] The circumferential strain of the outer wall of the sleeve was calculated using the Lamé solution: , , Let SF = 0.9, and let... Solving for ,correspond .from Find the first time reached in the timeline The moment, determine correspond .

[0113] exist Calculate time-by-time within the effective window Approximately 2200 sets of continuous data points were obtained by using P. After strain rate correction, linear regression was performed on logarithmic coordinates, yielding B=0.21, M=0.82, and R²=0.95 for this particle size group. The above operation was repeated for the remaining four particle size groups, and the R² for each group was not lower than 0.95.

Claims

1. A method for extracting effective window data from a dual-criteria confined compression experiment of brittle materials, characterized in that, Includes the following steps: Step S100: After the brittle material is crushed into powder and classified, it is loaded into a metal sleeve and a preload is applied. The inner diameter of the sleeve is a and the outer diameter is b. Step S200: Apply an axial load to the powder inside the sleeve and simultaneously acquire the axial true stress-true strain curve and the circumferential strain of the outer wall of the sleeve. Step S300: After polynomial fitting of the axial true stress-true strain curve, calculate the second derivative. Use the starting moment when the second derivative changes from a fluctuating state to a continuously positive value as the lower limit of the effective window. , The corresponding particle contact network is fully established; Step S400: Utilizing the circumferential strain of the outer wall of the sleeve, the von Mises equivalent stress of the inner wall of the sleeve is inverted based on the Lamé elastic solution, and this equivalent stress is used to achieve the yield strength of the sleeve material. The time when the product of the safety factor SF is used as the upper limit of the effective window. , The corresponding sleeve elastic constraint failure occurs, where E represents the elastic modulus of the sleeve material; Step S500, in Within the window, the circumferential strain of the outer wall of the sleeve is converted into radial constraint pressure using the Lamé solution. Calculate the crushing strength at each time step And hydrostatic pressure P, to obtain continuous Paired datasets, where , , Indicates the true axial stress; Step S600, After strain rate correction, linear regression was performed on the dataset in logarithmic coordinates to obtain the fracture strength coefficient B and pressure index M of the JH-2 constitutive model.

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 sieve to obtain crushed powder samples of several particle size groups. The powder of each particle size group is weighed separately. Step S120: The weighed powder is loaded into a high-strength metal sleeve with an inner diameter of a and an outer diameter of b, where b / a is not less than 1.

5. Step S130: Apply initial preload to ensure the powder is in a stable and compacted state, and use a new sleeve for each experiment.

3. The method according to claim 1, characterized in that, Step S200 includes: Step S210: Apply a quasi-static axial load to the specimen on the universal testing machine. Simultaneously record the axial force F(t) and axial displacement u(t) using force and displacement sensors. Calculate the true axial stress by combining the real-time cross-sectional area correction. Harmony and True Response ,get Curve; in which Indicates the true axial stress. t represents the true axial strain, and t represents time. Step S220: At least two resistance strain gauges are evenly arranged circumferentially on the outer wall of the sleeve, and the arithmetic mean of the signals from each strain gauge is taken as the circumferential strain of the outer wall of the sleeve. Where b represents the outer diameter of the sleeve, This indicates circumferential strain.

4. The method according to claim 1, characterized in that, Step S300 includes: Step S310, for The curve is fitted with a high-order polynomial, and the root mean square of the fitting residual does not exceed 0.5% of the experimental range to obtain a smooth analytical expression. Step S320: Calculate the second-order analytic derivative of the fitted polynomial; Step S330, with The starting point when the fluctuation changes from a state of fluctuation to a sustained positive value and the fluctuation amplitude tends to stabilize is taken as the lower limit of the effective window. .

5. The method according to claim 1, characterized in that, In step S330 The judgment criteria are: Within a range of 100 consecutive data points, It remains positive and its fluctuation range is less than 10% of the mean of the interval.

6. The method according to claim 1, characterized in that, Step S400 includes: Step S410, utilizing the circumferential strain of the outer wall of the sleeve Calculate the circumferential stress of the outer wall. for: ； Where E represents the elastic modulus of the sleeve material; Step S420, solve for the uniform internal pressure using the Lamé solution: ； Step S430: Calculate the radial stress at the inner wall of the sleeve using the Lamé solution. ； Step S440: Calculate the circumferential stress at the inner wall of the sleeve using the Lamé solution. ； Step S450, calculate the von Mises equivalent stress on the inner wall: ； Step S460, with The moment as ,in SF is the yield strength of the sleeve material, and SF is the safety factor, where the value of SF ranges from 0.8 to 0.

95.

7. The method according to claim 1, characterized in that, Step S500 includes: Step S510, in Extract axial stress within the window. and circumferential strain of the outer wall of the sleeve Time history data; Step S520, will Converted to radial constraint pressure via Lamé solution , ; Step S530, calculate crushing strength for: ； Step S540, calculate the hydrostatic pressure P as follows: ； Obtain a continuous fracture strength-hydrostatic pressure paired dataset. .

8. The method according to claim 1, characterized in that, Step S600 includes: Step S610, will The data is dimensionless to obtain the dimensionless crushing strength. and dimensionless hydrostatic pressure ,in , The hydrostatic pressure of the material at its Hugoniot elastic limit; Step S620: The strain rate is corrected for the JH-2 fracture strength equation. The correction formula is as follows: ； Where C is the strain rate coefficient of the JH-2 model. To normalize the experimental strain rate, Static strength at the reference strain rate; Step S630, in logarithmic coordinates... Linear regression is performed on the dataset, satisfying: ； The pressure index M is obtained from the slope of the linear regression, and the intercept is obtained from... Therefore, the crushing strength coefficient B is determined.

9. The method according to claim 1, characterized in that, Originating from the axial mechanical response of the sample, The data sources for the two criteria are physically independent and do not have a circular dependency relationship, and they are derived from the circumferential deformation response of the sleeve.

10. The method according to claim 1, characterized in that, The brittle material is an amorphous alloy, ceramic, rock, or concrete.

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