Method for obtaining material wide strain rate constitutive relationship by single taylor impact test
By combining single Taylor impact tests with full-time tracking, DIC processing, and Lagrange inversion, the problem of discontinuous strain rate coverage was solved, enabling the acquisition of constitutive relations of materials in the range of 10²-10⁵ s⁻¹. A quantitative correlation between macroscopic and microscopic synergy was established, improving the reliability and accuracy of constitutive relations.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- TAIYUAN UNIVERSITY OF TECHNOLOGY
- Filing Date
- 2026-03-09
- Publication Date
- 2026-06-09
Smart Images
Figure CN122171357A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of dynamic mechanical property testing and characterization technology of materials, specifically a method for obtaining the constitutive relationship of materials with a wide strain rate using a single Taylor impact test. Background Technology
[0002] Constitutive relations are mathematical equations describing the relationship between stress and strain, strain rate, temperature, time, and other parameters of a material; that is, the "stress-strain" law governing the material. In 10... 2 -10 5 s -1 Within the strain rate range, the mechanical response of the material is fundamentally different from that under quasi-static loading, mainly manifested in the following ways: (1) High strain rate sensitivity. The yield strength and flow stress of the material increase significantly with the increase of strain rate; (2) Under high-speed impact, the load does not have time to be transmitted to the whole object, and complex stress waves will be formed. The failure of the material is often caused by the interaction of these waves (such as reflection and superposition); (3) Most of the work done by plastic deformation will be converted into heat. Under such a high loading rate, the heat has no time to diffuse, which leads to a sharp increase in temperature in the local deformation area, which in turn leads to the softening of the material.
[0003] The material is suitable for a wide strain rate (10) 2 -10 5 s -1 The constitutive relationship under load is the core basis for the safety design of structures under extreme working conditions, but the existing testing technology has three major limitations: (1) discontinuous strain rate coverage. Traditional impact tests only obtain a single strain rate data in a single test, and multiple adjustments to the impact velocity are required to obtain different strain rates. In the existing technology, the upper limit of strain rate in the SHPB test is 10. 4 s -1 Unable to cover 10 4 -10 5 s -1 (2) Constitutive inversion depends on specific material assumptions. Existing methods, such as the DIC acceleration distribution method and the bilinear internal force assumption method, all require a pre-set constitutive model, which has poor universality and has not formed a standardized research paradigm. Some methods, such as the Lagrange analysis method combined with SHPB experiments, are limited by material properties and strain rate range. (3) Lack of correspondence between macroscopic mechanical behavior and microscopic deformation mechanism. Existing studies focus on the accuracy of macroscopic data and only focus on macroscopic mechanical response. They lack macro-micro collaborative analysis logic and have not constructed a quantitative correlation with microscopic organization evolution. At the same time, they have not revealed the physical essence of its mechanical response through microscopic characterization, resulting in insufficient physical credibility of constitutive relations and inaccurate description. Summary of the Invention
[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for obtaining a wide strain rate constitutive relation of a material using a single Taylor impact test. This method can overcome the limitation of strain rate coverage and achieve a single test coverage of 10... 2 -10 5 s -1 By using a wide strain rate gradient, a quantitative correlation between macroscopic mechanical response and microstructure evolution is established, ultimately leading to the establishment of a thermoviscoplastic constitutive relation based on the microscopic deformation mechanism.
[0005] To solve the above-mentioned technical problems, the present invention adopts the following technical solution: a method for obtaining a broad strain rate constitutive relation of a material using a single Taylor impact test, comprising the following steps: S1: Taylor impact test and full-time tracking: A speckled specimen is impacted onto a target plate at an impact velocity v0 using a light gas gun. An ultra-high-speed camera is used to capture images of the specimen impact process at a preset frame rate. The images cover the entire process from the start of the impact to the end of the deformation, forming a high-speed image sequence.
[0006] S2: Acquisition of high-precision velocity field: High-speed image sequences are processed using DIC software to obtain the axial displacement of each Lagrange position at different time points. The velocity at each Lagrange position is calculated using the central difference method to obtain the initial velocity dataset v. ’ (X,t); Using an extreme random tree model to complete and fit the initial velocity dataset v ’ (X,t) uses the Lagrange position X, time t, and impact velocity v0 as input features and the axial velocity v as the target variable to learn a machine learning model and output a complete and high-precision velocity field v(X,t).
[0007] S3: Lagrange inversion: Using the "nv+T0" Lagrange analysis method, with the velocity field v(X,t) in step S2 as input, the stress field σ(X,t) and strain field ε(X,t) are calculated based on the mass conservation equation and momentum conservation equation in one-dimensional stress wave theory, as well as a six-dimensional data matrix containing time-velocity-position-stress-strain-strain rate; S4: Local Strain Rate Calculation: Import the high-speed image sequence obtained in step S1 into ImageJ software, analyze the axial dimension changes at each Lagrange point under different strain rates, and calculate the strain rate at each Lagrange point using the local strain rate formula, constructing a 10... 2 -10 5 s -1 Continuous strain rate gradient The impacted specimen was sliced at the characteristic strain rate location, and the microstructure at the corresponding location was recorded.
[0008] S5: Obtain the inverted stress-strain curves: Using the stress field σ(X,t) and strain field ε(X,t) obtained in step S3, eliminate the time parameter t to obtain a stress-strain relationship over a wide strain rate range. Analyze the six-dimensional data matrix to obtain σ-ε- Relationship; S6: Macro-micro correlation: Microscopic mechanism analysis was performed on the sliced samples prepared in step S4 to construct the microscopic deformation mechanism under different strain rates; based on the stress-strain relationship with a wide strain rate range and the microscopic deformation mechanism that changes with the strain rate gradient obtained in step S5, a thermoviscoplastic constitutive model was established.
[0009] Preferably, in step S1, the trigger signal of the ultra-high-speed camera is issued by a timing synchronization and trigger control system, which includes a magnetic velocimeter coil and an oscilloscope. The magnetic velocimeter coil is electrically connected to the oscilloscope, the oscilloscope is connected to the ultra-high-speed camera, and the flash lamp. The sample passes through the magnetic velocimeter coil, cutting magnetic field lines and outputting a noisy analog voltage pulse signal. After the noisy analog voltage pulse signal is filtered and denoised by the oscilloscope, a purified analog voltage pulse is output. After the purified analog voltage pulse is identified and triggered by the oscilloscope, a standard digital TTL trigger pulse is output. The ultra-high-speed camera receives the trigger pulse, waits for a preset delay time, and then begins to acquire speckle images. The flash lamp receives the trigger pulse and provides supplementary lighting for the ultra-high-speed camera.
[0010] Preferably, the ultra-high-speed camera uses a Kirana 05M sensor with a resolution of 924×768 pixels and a frame rate of 1×10⁻⁶. 5 --5×10 6 The flash delay time is 300μs shorter than that of the camera, and it uses rising edge triggering. The fill light intensity is 1200lm. The oscilloscope has a bandwidth of ≥200 MHz, uses rising edge triggering mode, and is filtered by a 50 kHz low-pass filter. The accuracy of the magnetovelocity signal is ±0.3 m / s. No speckle is set at 2 / 5 of the position of the sample near the end of the sabot, and speckle is evenly set at other positions.
[0011] Preferably, in step S2, subpixel interpolation is used to improve displacement measurement accuracy; when completing and fitting the velocity field, Bayesian optimization is used to automatically tune hyperparameters, with the parameters set as follows: tree depth 20-40 layers, number of leaf nodes 8-15, random feature selection ratio 0.6-0.8, to predict and complete unmeasured data points, and the fitting accuracy determination coefficient R0 is used. 2 ≥0.9; SHAP visualization analysis is used to analyze the importance of features, so that the contribution of the initial impact velocity v0 to the fitting of the wide strain rate region is ≥30%.
[0012] Preferred Bayesian optimization parameters: tree depth 35 layers, leaf nodes 12, random feature ratio 0.7, completion of 20 sets of velocity data, SHAP analysis shows that the initial impact velocity v0 contributes 32% of the feature, and the fitting accuracy coefficient of determination R0 is [value missing]. 2 =0.9835.
[0013] Preferably, the local strain rate calculation in step S4 is as shown in formula (1). (1), in, For average strain rate, The length after the micro-segment deformation is completed. t1 is the initial length of the micro-segment, t2 is the deformation end time, and t1 is the initial deformation time.
[0014] Preferably, the characteristic strain rate locations in step S4 include low strain rate, medium strain rate, and high strain rate regions. The impacted specimen is sliced at the characteristic strain rate locations, and its microstructure characteristics are characterized using microscopic characterization techniques such as SEM, EBSD, and TEM to analyze the microscopic deformation mechanism under different strain rate loading.
[0015] Preferably, the verification method for step S6 is as follows: dual verification is achieved through both experimental cross-validation and numerical simulation verification via SHPB experimental comparison and FEA simulation comparison. The SHPB experiment uses a Hopkinson pressure bar apparatus to conduct dynamic compression tests on samples from the same batch. Stress-strain curves are obtained by processing the stress wave signals using the three-wave method and compared with the results of the strain rate inversion in step S5 to verify the accuracy of the results. The FEA simulation was based on a Taylor impact model built using Ansys 2022 R2. AISI 1010 steel was used as the verification carrier. Under the publicly available parameters, the simulation was run in the Johnson-Cook constitutive model in 1s-dyna software. The impact velocity was set to v0, and the stress-strain curve was obtained by inversion using the same method. The result was compared with the result of inversion in step S5 to verify the accuracy of the result.
[0016] The specific process of the Lagrange inversion in step S3 is as follows: the mass conservation equation and the momentum conservation equation are expressed as formula (2) and formula (3) respectively. (2), (3), in, , , , Let represent the initial density, velocity, stress, and Lagrange position of the sample, respectively, and let α and t represent strain and time, respectively.
[0017] Then, combining the propagation state of the elastic precursor wave as the initial condition, we obtain the simplified mass conservation law. Formula and The simplified equations for the conservation of momentum are shown in equations (4) and (5), respectively. (4), (5), in, , v, σ, and X represent the first path line, velocity, stress, and Lagrangian position of the specimen, respectively; ɛ and t represent strain and time, respectively; the path line p is a characteristic line on the Xt plane that satisfies a specific wave velocity relationship; the first path line... This corresponds to the propagation path of the elastic precursor wave.
[0018] Therefore, based on the derivation and calculation by Wang et al., the dynamic stress field and dynamic strain field are shown in equation (6) and equation (7), respectively. (6), (7), Then, along the first path line ( The differential form is used to update the stress, as shown in formula (8). (8), Where i is the spatial index, representing the discrete index of the Lagrange position X, and j is the time index, representing the discrete index of time t. Let represent the stress value at the i-th spatial point and the j-th time step. The stress value to be determined at the next time step (j+1) is... This indicates the initial density of the sample. The acceleration at the current time step j and position i is obtained from the velocity field v(X,t) in step S3 through time difference. The slope of the first path line (p0) is related to the slope of the material's stress-strain curve.
[0019] Then, the difference form along the remaining path lines is used to update the strain, as shown in equation (9). (9), in, Let the strain value be the value to be determined at the next time step. The strain value at the current time step is known.
[0020] Therefore, the initial stress equation is shown in formula (10). (10) in, coordinates Stress rate at the point, p is the path line.
[0021] Therefore, the difference form of the initial stress equation is shown in formula (11). (11), in, The stress to be determined is the stress at material point i in the second time step. Given the known stress at the first time step of material point i, Let i be the wave velocity at the material point i and the first time step. Let be the acceleration at point i in the first time step. For time step.
[0022] The beneficial effects of this invention are as follows: 1. This invention achieves true gradient constitutive relation acquisition by combining Taylor impact testing with full-length optical measurement, enabling the construction of 10 [structures / relationships] in a single experiment. 2 -10 5 s -1 The continuous strain rate gradient efficiently and completely reveals the continuous variation law of material properties with strain rate; through the strategy of "DIC + machine learning completion", the data loss problem caused by speckle occlusion and image blurring in high-speed deformation is solved, ensuring the integrity and high accuracy of input data, laying a solid foundation for reliable inversion; and the Lagrange inversion is based on the physical conservation law, without the need to pre-assume the material constitutive model, and the inversion results are more objective.
[0023] 2. A macro-micro synergistic mechanism explanation system was constructed, which quantitatively correlated macroscopic mechanical response with microscopic structural evolution under the same strain rate conditions, revealing the microscopic deformation mechanism as the strain rate gradient changes, and forming a complete cognitive loop from phenomenon to mechanism.
[0024] 3. A multi-level, cross-validation reliability guarantee was established. Through cross-validation in four dimensions, namely “experimental results vs. known constitutive models”, “inversion results vs. SHPB experiments”, “inversion results vs. finite element simulation”, and “macro-constitutive model vs. micro-mechanism”, the accuracy and reliability of the method described in this invention were jointly proved from different perspectives.
[0025] 4. An integrated research paradigm of "driving-measurement-analysis-expansion" has been formed, seamlessly integrating multiple advanced technology modules such as Taylor impact, ultra-high-speed photography, DIC technology, machine learning, Lagrange inversion, and macro- and micro-characterization to form a standardized and streamlined solution. This avoids the problems of fragmented methods and difficulty in data benchmarking in traditional research. Moreover, the core logic of this paradigm remains unchanged. When extended to new materials, only the sample needs to be changed, the basic physical parameters need to be input, and the parameters of the machine learning model need to be fine-tuned. It has extremely high versatility and promotional value. Attached Figure Description
[0026] Figure 1 This is a technical flowchart of the present invention; Figure 2 This is a structural diagram of the sample after speckle marking was completed; Figure 3 This is a diagram showing the actual results of machine learning; Figure 4 It is a velocity field map obtained through machine learning; Figure 5 It is a stress-strain graph with a wide strain rate range; Figure 6 These are dynamic stress-strain relationships and constitutive relation diagrams obtained by the Lagrange inversion method; Figure 7 This is a microstructure characterization diagram of EBSD. Detailed Implementation
[0027] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.
[0028] In this embodiment, AISI 1010 steel is used as the verification carrier, and the details are described in detail as follows. Figure 1 The implementation steps and methods of the present invention are shown.
[0029] This invention provides a method for obtaining a material's broad strain rate constitutive relationship using a single Taylor impact test. The first step is a Taylor impact test and full-time tracking: a speckled specimen is impacted onto a target plate at a known velocity using a light gas gun, and images of the specimen impact process are captured at a preset frame rate using an ultra-high-speed camera. The images cover the complete process from the start of the impact to the end of the deformation, forming a high-speed image sequence.
[0030] In this step, the first step is to prepare the sample. AISI 1010 steel bar is wire-cut into Φ10mm × 50mm cylinders, and both ends are precision ground (parallelism 0.01 mm). Then, using a speckle mold, black matte paint is applied to the sides of the sample. After drying, the speckles are pressed in, thus completing the preparation of the speckled sample. The total length of the sample is 50mm. No speckles are placed 0-20mm from the free end. At the Lagrange points 20-50mm from the free end, speckles with a diameter of 1.2mm and a spacing of 1.5mm are used, covering only half of the side surface, to prepare the sample as shown. Figure 2 As shown.
[0031] In this step, the trigger signal of the ultra-high speed camera is issued by the timing synchronization and trigger control system, which includes a magnetic velocimeter coil and an oscilloscope. The magnetic velocimeter coil is electrically connected to the oscilloscope, and the oscilloscope is electrically connected to the ultra-high speed camera and the flash lamp.
[0032] The sample is cut by a magnetic velocimetry coil, which outputs a noisy analog voltage pulse signal. After the noisy analog voltage pulse signal is denoised by an oscilloscope, a purified analog voltage pulse is output. After the purified analog voltage pulse is identified and triggered by the oscilloscope, a standard digital TTL trigger pulse is output. The ultra-high-speed camera receives the trigger pulse, waits for a preset delay time, and then begins to acquire speckle images. The flash receives the camera trigger signal and provides supplementary lighting for the ultra-high-speed camera.
[0033] The settings parameters for each device are as follows: Light air cannon air pressure: 0.75 MPa, inner diameter 25 mm, large air pressure adjustment range, corresponding to an impact velocity of 166 m / s; magnetic velocity measuring coil: trigger threshold 0.1 V; Oscilloscope: Filter frequency 50 kHz; Ultra-high-speed camera: Kirana 05M model, equipped with a 100mm telephoto lens, resolution 924×768 pixels, frame rate 1×10 6 fps, with a 2.0 ms delay for triggering, and using rising edge triggering; Flash: 1.7 ms delay (300 μs shorter than camera), 1200 lm light intensity; Target plate: 45# steel, quenched at 1153 K, coaxiality error ≤0.08 mm.
[0034] During operation, according to the target strain rate range (10) 2 -10 5 s -1The flight time was calculated by considering the velocity range and the distance the sample traveled from the ejector to the target plate (20-40 cm). The camera delay trigger time (2.0-3.0 ms, taking the smaller value) was determined by superimposing the magnetovelocity signal transmission delay (approximately 8 μs) and the oscilloscope filtering delay (approximately 5 μs). The sample was then placed in a polycarbonate sabot with a 0.05 mm gap and loaded into the light gas cannon's firing tube. The target chamber was evacuated to 8 Pa, and the gas valve was closed. A timing synchronization and trigger control system was set up, and the light gas cannon was started. After the sample left the barrel, the magnetovelocity system detected the velocity signal, which was then filtered by the oscilloscope before triggering the camera and flash. The camera acquired 180 images within a total duration of 300 μs, recording the deformation process of the sample from ejection to impact with the target plate. The speckle displacement was clearly discernible, forming a high-speed image sequence.
[0035] The second step is to obtain a high-precision velocity field: High-speed image sequences are processed using DIC software to obtain the axial displacement of each Lagrange position at different time points. The velocity at each Lagrange position is calculated using the central difference method to obtain the initial velocity dataset v. ’ (X,t); Using an extreme random tree model to complete and fit the initial velocity dataset v ’ (X,t) uses the Lagrange position X, time t, and impact velocity v0 as input features and the axial velocity v as the target variable to learn a machine learning model and output a complete and high-precision velocity field v(X,t).
[0036] In this embodiment, the high-speed image sequence obtained in the first step is loaded using Match ID Installer software. Sub-pixel interpolation is used to track the speckle center coordinates, and the axial displacement u(X, t) of each Lagrange position at different time points is calculated. This ensures that the tracking accuracy of the speckle center coordinates is higher than one pixel, which is the cornerstone for obtaining high-precision displacement data. The central difference method is a highly accurate numerical differentiation method. Taking the time derivative of the displacement data u(X, t) yields the initial dataset v. ’ (X,t).
[0037] Machine learning fitting with a wide strain rate adaptability addresses the problem of missing experimental data caused by speckle occlusion, image blurring, etc. It utilizes an extreme random tree model to complete and fit the velocity field, using Lagrange position X, time t, and impact velocity v0 as input features, and axial velocity v as the target variable. The machine learning model learns to obtain the mapping at a given impact velocity v0, a specified Lagrange position X, and a specified time t, thus outputting a complete and high-precision velocity field v(X,t).
[0038] In this embodiment, machine learning fitting constructs an extreme random tree model by calling the scikit-learn library in the Python environment. The inputs are X, t, and v0, where the impact velocity v0 is 166 m / s. The introduction of impact velocity v0 is the key to adapting to a wide strain rate. The target variable is the axial velocity v. The importance of features is analyzed by visualizing SHAP, so that the contribution of impact velocity v0 to the fitting of the wide strain rate region is ≥30%.
[0039] Bayesian optimization was used to automatically tune hyperparameters, with the following parameters set: tree depth 20-40 layers, number of leaf nodes 8-15, and random feature selection ratio 0.6-0.8. Predictive completion was performed for untested data points, and the coefficient of determination R for fitting accuracy was [value missing]. 2 ≥0.9. The optimal model parameters were obtained through Bayesian optimization: tree depth 35 layers, 12 leaf nodes, random feature ratio 0.7, and completion of 20 sets of velocity data. SHAP analysis showed that the v0 feature contributed 32%, and the fitting accuracy coefficient of determination R0 was ≥0.9. 2 =0.9835, machine learning performance is as follows Figure 3 As shown, the completed velocity field v(X,t) (velocities at different Lagrange positions and at different times) is as follows: Figure 4 As shown.
[0040] Among them, the feature importance analysis results obtained from regression analysis are as follows: Figure 3 As shown in (a), the importance weight of time information is 0.82, which is the core feature for achieving complete velocity-time curve fitting and plays a decisive role in the completeness of the velocity-time curve fitting; the importance weight of position information is 0.16, which is used to ensure the correlation between each Lagrangian position data and improve the data interpolation accuracy, providing support for the reliability of curve fitting; the importance weight of the outer surface path parameter is only 0.02, which indicates that the sample is basically in a positive state, its flight attitude remains stable, and the interference of the outer surface path parameter on the measurement accuracy is effectively avoided.
[0041] The prediction results of the regression model are as follows: Figure 3 As shown in (b), the coefficient of determination R between the predicted velocity value and the measured velocity value 2 =0.9835, root mean square error (RMSE) =0.021 m / s. The above data show that the predicted value output by the model is highly consistent with the actual measured value, and the prediction accuracy is excellent.
[0042] The residual distribution is as follows Figure 3As shown in (c), the residual values are concentrated in the range of -0.05 to 0.05 m / s, and the overall distribution is normal with the mean approaching 0. This characteristic indicates that the regression model has no obvious bias or abnormal clustering of errors, and the fitting effect is excellent. This proves that the accuracy of the velocity field data reconstructed by the model can meet the requirements of subsequent related calculations, and provides a strong guarantee for the reliability of subsequent experiments and calculations.
[0043] The third step is the Lagrange inversion: Code for the "nv+T0" Lagrange analysis method is written, using the velocity field v(X,t) from step S2 as input. Based on the mass and momentum conservation equations in one-dimensional stress wave theory, the stress field σ(X,t) and strain field ε(X,t), as well as a six-dimensional data matrix containing time, velocity, position, stress, strain, and strain rate, are calculated. The "nv+T0" Lagrange analysis method was proposed by Wang Lili using the dual information of initial stress and strain, and has been published in a paper; it is a technical term commonly understood by those skilled in the art.
[0044] The fourth step is the calculation of local strain rate: the high-speed image sequence obtained in the first step is imported into the software ImageJ, and the axial size variation at each Lagrange point at different strain rate locations is analyzed. The strain rate at each Lagrange point is calculated using the local strain rate formula, and a 10-fold local strain rate model is constructed. 2 -10 5 s -1 Continuous strain rate gradient The impacted specimen was sliced at the characteristic strain rate location, and the microstructure at the corresponding location was recorded. The local strain rate was calculated as shown in formula (1). (1), where, For average strain rate, The length after the micro-segment deformation is completed. t1 is the initial length of the micro-segment, t2 is the deformation end time, and t1 is the initial deformation time.
[0045] Step S5: Obtain the inverted stress-strain curves: Using the stress field σ(X,t) and strain field ε(X,t) obtained in step S3, eliminate the time parameter t to obtain a stress-strain relationship over a wide strain rate range. Analyze the six-dimensional data matrix to obtain σ-ε- The relationship.
[0046] In this embodiment, by inputting AISI 1010 steel parameters into the MATLAB program, the initial density ρ0 = 7.85 g / cm³. 3 The Young's modulus E = 205 GPa and the completed velocity field v(X,t) are substituted into the code edited using the Lagrange inverse analysis method to calculate 10. 2 -105 s -1 tvx-σ-ε- Data set. Constitutive relations of strain rate gradients are as follows: Figure 5 As shown, it comprehensively demonstrates the complex coupling relationship between stress, strain, and strain rate, and is the most direct data source for constructing and calibrating three-dimensional constitutive surfaces. The dynamic stress-strain relationship and local constitutive relation obtained by the Lagrange inversion method are shown below. Figure 6 As shown, this demonstrates the stress-strain response of a material over a specific wide range of strain rates. This method is directly based on physical conservation laws and does not require prior assumptions about the material's constitutive model.
[0047] The derivation process based on the one-dimensional stress wave theory is shown below: the mass conservation equation and the momentum conservation equation are expressed as formula (2) and formula (3) respectively. (2), (3), in, , , , Let represent the initial density, velocity, stress, and Lagrange position of the sample, respectively, and let α and t represent strain and time, respectively.
[0048] Then, combining the propagation state of the elastic precursor wave as the initial condition, we obtain the simplified mass conservation law. Formula and The simplified equations for the conservation of momentum are shown in equations (4) and (5), respectively. (4), (5), in, v, σ, and X represent the first path line, velocity, stress, and Lagrange position of the specimen, respectively, while ɛ and t represent strain and time, respectively.
[0049] Therefore, based on the derivation and calculation by Wang et al., the dynamic stress field and dynamic strain field are shown in equation (6) and equation (7), respectively. (6), (7).
[0050] Then, along the first path line ( The differential form is used to update the stress, as shown in formula (8). (8), Where i is the spatial index, representing the discrete index of the Lagrange position X, and j is the time index, representing the discrete index of time t. Let represent the stress value at the i-th spatial point and the j-th time step. The stress value to be determined at the next time step (j+1) is... This indicates the initial density of the sample. The acceleration at the current time step j and position i is obtained from the velocity field v(X,t) in step S3 through time difference. The slope of the first path line (p0) is related to the slope of the material's stress-strain curve.
[0051] Then, the difference form along the remaining path lines is used to update the strain, as shown in equation (9). (9), in, Let the strain value be the value to be determined at the next time step. The strain value at the current time step is known.
[0052] Therefore, the initial stress equation is shown in formula (10). (10) in, coordinates Stress rate at the point, p is the path line.
[0053] Therefore, the difference form of the initial stress equation is shown in formula (11). (11), in, The stress to be determined is the stress at material point i in the second time step. Given the known stress at the first time step of material point i, Let i be the wave velocity at the material point i and the first time step. Let be the acceleration at point i in the first time step. For time step.
[0054] Thus, this method integrates experimental mechanics, machine learning, and Lagrange inversion, representing the cutting-edge direction of current research on the dynamic properties of materials. From experimental observation to data completion and then to Lagrange inversion, each step is interconnected, forming a complete closed loop. Subpixel and central difference methods ensure data accuracy, machine learning completes data defects, and finally, high-confidence constitutive relations are obtained through first-principles Lagrange inversion.
[0055] To verify the reliability of the method, a material (such as AISI 1010 steel) can be selected as the verification carrier. The publicly available constitutive model parameters are used to run the model and output the theoretical dynamic stress-strain curve. The theoretical dynamic stress-strain curve is then compared with the inverted dynamic stress-strain curve obtained in step 5 to determine the accuracy and reliability. If the accuracy and reliability do not meet the requirements, the parameter settings in steps 1-3 are adjusted until the accuracy meets the requirements.
[0056] This step involves using a known benchmark to verify the reliability of the inversion method. Specifically, AISI 1010 steel is used, and the accuracy of the method is verified by comparing it with the known Johnson-Cook model through "experimental results - known constitutive model". The parameters are shown in Table 1. Table 1. Parameters of the AISI 1010 steel experimental Johnson-Cook model Once the reliability of the inversion method is verified, the sixth step, macro-micro correlation, is carried out. In this step, micro-characterization tests are conducted on the strain rate gradient distribution region of the AISI 1010 steel specimen after impact.
[0057] Step six involves macro-micro correlation: Microscopic mechanism analysis is performed on the sliced samples prepared in step four to construct micro-deformation mechanisms under different strain rates. Based on the stress-strain relationship over a wide strain rate range obtained in step S5 and the micro-deformation mechanism varying with the strain rate gradient, a thermoviscoplastic constitutive model is established. Characteristic strain rate locations include low strain rate, medium strain rate, and high strain rate regions. The impacted specimens are sliced at characteristic strain rate locations, and their microstructural characteristics are characterized using microscopic characterization techniques such as SEM, EBSD, and TEM to analyze the micro-deformation mechanisms under different strain rate loading.
[0058] The specific implementation method is as follows: First, complete the sample preparation: 10 along the axial direction of the sample. 2 s -1 (X=5 mm), 10 3 s -1 (X=25 mm), 10 5 s -1 (X=45 mm) Characteristic positions ensure a strict correspondence between microscopic analysis locations and macroscopic mechanical states. Thin-film samples of Ф3 mm × 1 mm were obtained using wire cutting technology. After mounting, progressive grinding with sandpaper (120#-2000#), and fine polishing with diamond polishing paste (1 μm), electropolishing (electrolyte: 10% perchloric acid + 90% ethanol, voltage: 20 V, temperature: 25 ℃) was performed to remove the surface stress layer. Electropolishing ensured the accuracy of EBSD observation results.
[0059] Secondly, analysis and characterization were performed: using the EBSD system (step size 0.2 μm) with the scanning electron microscope, the average grain size was calculated using software, and the orientation distribution and dislocation density were analyzed. Figure 7 This image shows a comparison of the microstructure characterization of AISI steel samples taken at three different characteristic strain rate locations after a single Taylor impact test. a1 is the inverse pole figure (IPF) of the microstructure in the low strain rate region, a2 is the kernel mean orientation difference (KAM) diagram of the microstructure in the low strain rate region, and a3 is the phase diagram of the microstructure in the low strain rate region. Similarly, b1, b2, b3 and c1, c2, c3 are the inverse pole figures (IPF), kernel mean orientation difference (KAM), and phase diagrams for the medium and high strain rate regions, respectively. The image shows that the alloy exhibits significant changes in crystallographic orientation characteristics with increasing strain rate. The grain orientation distribution shows a clear enhancement of preferred orientation, indicating an intensified tendency for grain rotation and orientation concentration during plastic deformation. Simultaneously, local orientation difference analysis shows an increased orientation gradient near grain boundaries and in localized areas within the grains, corresponding to significant micro-stress concentration, reflecting an intensified non-uniform strain distribution. Comparison of the phase diagrams reveals that no new phase formation was observed during this process, indicating that the material mainly relies on crystal slip for plastic deformation.
[0060] The comparison of KAM plots with increasing strain rate shows that the KAM value increases with increasing strain rate, confirming that the dislocation density of the entire sample and local regions increases with increasing strain rate. (where b is the Burgers vector and u is the unit length per point, i.e., the scan step size, which is 0.25 μm in this embodiment.) Calculations of the geometrically required dislocation density show that it increases with increasing strain rate. Increased dislocation density implies intensified lattice distortion and more pronounced non-uniformity and localization of strain distribution. At high strain rates, dislocation slip cannot be fully coordinated, leading to rapid dislocation pile-up near specific slip systems or grain boundaries, resulting in strong local stress concentrations. As the strain rate increases, the deformation time shortens, the rate of dislocation multiplication and movement accelerates, and the dislocation density increases significantly, thereby promoting more pronounced grain orientation and increased local stress. The continuously increasing dislocation density leads to greater lattice friction stress, and the local stress concentrations caused by dislocation entanglement and pile-up become more significant. This corresponds to the macroscopically observed yield stress and flow stress increasing with increasing strain rate.
[0061] These microscopic characterizations reveal the physical origin of macroscopic stress strengthening: across a wide strain rate range, the dislocation strengthening effect increases with the strain rate gradient, leading to a significant increase in the macroscopic flow stress of AISI 1010 steel. Finally, based on the stress-strain relationship obtained over a wide strain rate range through inversion and the microscopic deformation mechanism varying with the strain rate gradient, a thermoviscoplastic constitutive model is established.
[0062] To further verify the experimental results, AISI 1010 steel was used to conduct a special verification, which confirmed the accuracy and stability of the experimental technique. The verification was achieved through both experimental and numerical simulation comparisons using SHPB experiments and FEA simulations.
[0063] The specific operating steps are as follows: First, the quasi-static compression test was performed using an Instron universal testing machine, and the SHPB test was performed using a Φ14 mm Hopkinson bar device at 10... -4 -10 4 s -1 Dynamic compression tests were conducted on samples from the same batch within a strain rate range, and stress-strain curves were obtained using the one-dimensional stress wave principle. Compared with the inversion results of the same strain rate range in this invention, the average error was 4.2% (≤6%). The inversion results are highly consistent with those of a widely accepted standard dynamic testing method, strongly demonstrating the accuracy of the inversion results of this invention from an experimental perspective.
[0064] Then, a Taylor impact model was established based on Ansys 2022 R2 using finite element analysis. The specimen was given known JC model parameters (A=0.325 GPa, B=0.68 GPa, n=0.26, C=0.014, m=0.6), and an impact velocity of 166 m / s was set. The stress-strain curve was then calculated. (This is related to the present invention 10...) 5 s -1 The results show an error of 7.5%; this proves that the core inversion algorithm of this invention is correct in mathematics and physics and can reproduce the dynamic response of materials under known constitutive relations.
[0065] Both experimental and simulation verifications demonstrate that this technology possesses reliable measurement accuracy across a wide strain rate range, providing solid support for an integrated research paradigm. When extended to other materials, only the target material sample needs to be replaced, and the basic physical parameters of the material (initial density ρ0, elastic modulus E) need to be input. The number of leaf nodes in the extreme random tree model can be fine-tuned (±3) according to the material's plastic flow characteristics. No modification to the core logic and technical system of "synchronous acquisition-intelligent inversion-macro-micro verification" is required, enabling rapid migration and reuse of the research paradigm.
[0066] In this invention, a wide strain rate gradient deformation is achieved through a single Taylor impact experiment. The mechanical behavior curves under different strain rates are obtained by combining Lagrange inversion theory. The microstructure of the deformed structure under different strain rates is characterized, thereby establishing a quantitative correlation between the macroscopic mechanical behavior and microstructure evolution of the wide strain rate gradient. Furthermore, a thermoviscoplastic constitutive relation based on the microstructure deformation mechanism can be established, creating an integrated research paradigm of "mechanical behavior-microstructure-constitutive relation" that provides a standardized process for the study of wide strain rate properties of other materials.
[0067] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.
Claims
1. A method for obtaining a broad strain rate constitutive relation of a material using a single Taylor impact test, characterized in that: Includes the following steps: S1: Taylor shock test and full-time tracking: A speckled specimen is impacted onto a target plate at an impact velocity v0 using a light air gun. An ultra-high-speed camera is used to capture images of the specimen impact process at a preset frame rate. The images cover the entire process from the start of the impact to the end of the deformation, forming a high-speed image sequence. S2: Acquisition of high-precision velocity field: High-speed image sequences were processed using DIC software to obtain the axial displacement of each Lagrange position at different time points. The velocity at each Lagrange position was calculated using the central difference method to obtain the initial velocity dataset v. ’ (X,t); Using an extreme random tree model to complete and fit the initial velocity dataset v ’ (X,t), with Lagrange position X, time t, and impact velocity v0 as input features and axial velocity v as target variable, performs machine learning model learning and outputs a complete and high-precision velocity field v(X,t); S3: Lagrange inversion: Using the "nv+T0" Lagrange analysis method, with the velocity field v(X,t) in step S2 as input, the stress field σ(X,t) and strain field ε(X,t) are calculated based on the mass conservation equation and momentum conservation equation in the one-dimensional stress wave theory, as well as a six-dimensional data matrix containing time-velocity-position-stress-strain-strain rate. S4: Local Strain Rate Calculation and Microscopic Sample Preparation: The high-speed image sequence obtained in step S1 was imported into ImageJ software. The axial size variation at each Lagrange point under different strain rates was analyzed. The strain rate at each Lagrange point was calculated using the local strain rate formula, and a 10-dimensional microstructure was constructed. 2 -10 5 s -1 Continuous strain rate gradient , The impacted specimen was sliced at the characteristic strain rate location, and the microstructure at the corresponding location was recorded. S5: Obtain the inverted stress-strain curves: Using the stress field σ(X,t) and strain field ε(X,t) obtained in step S3, eliminate the time parameter t to obtain a stress-strain relationship over a wide strain rate range. Analyze the six-dimensional data matrix to obtain σ-ε- Relationship; S6: Macro-micro correlation: Microscopic mechanism analysis was performed on the sliced samples prepared in step S4 to construct the microscopic deformation mechanism under different strain rates; based on the stress-strain relationship with a wide strain rate range and the microscopic deformation mechanism that changes with the strain rate gradient obtained in step S5, a thermoviscoplastic constitutive model was established.
2. The method for obtaining a material's broad strain rate constitutive relation using a single Taylor impact test according to claim 1, characterized in that: In step S1, the trigger signal of the ultra-high speed camera is issued by the timing synchronization and trigger control system, which includes a magnetic speed measuring coil and an oscilloscope. The magnetic speed measuring coil is electrically connected to the oscilloscope, and the oscilloscope is electrically connected to the ultra-high speed camera and the flash lamp. The sample is cut by a magnetic velocimetry coil, which outputs a noisy analog voltage pulse signal. After the noisy analog voltage pulse signal is filtered and denoised by an oscilloscope, a purified analog voltage pulse is output. After the purified analog voltage pulse is identified and triggered by the oscilloscope, a standard digital TTL trigger pulse is output. The ultra-high-speed camera receives the trigger pulse, waits for a preset delay time, and then begins to acquire speckle images. The flash receives the trigger pulse and provides supplemental lighting for the high-speed camera.
3. The method for obtaining a material's broad strain rate constitutive relation using a single Taylor impact test according to claim 2, characterized in that: The ultra-high-speed camera used is a Kirana 05M, with a resolution of 924×768 pixels and a frame rate of 1×10. 5 --5×10 6 fps, the flash delay time is 300μs shorter than the camera, and the fill light intensity is 1200lm; The oscilloscope has a bandwidth of ≥200 MHz, adopts rising edge triggering mode, and is filtered by a 50 kHz low-pass filter. The accuracy of processing magnetic velocity measurement signals is ±0.3 m / s. No speckle pattern was set at the 2 / 5 position of the sample near the sabot end, and speckle patterns were evenly spaced at the remaining positions.
4. The method for obtaining a broad strain rate constitutive relation of a material using a single Taylor impact test according to claim 1, characterized in that: In step S2, subpixel interpolation is used to improve the accuracy of displacement measurement. When completing and fitting the velocity field, Bayesian optimization is used to automatically tune the hyperparameters. The parameters are set as follows: tree depth 20-40, number of leaf nodes 8-15, and random feature selection ratio 0.6-0.
8. Predictive completion is performed on unmeasured data points, and the fitting accuracy determination coefficient R0 is used. 2 ≥0.9; The importance of features was analyzed using SHAP visualization, ensuring that the contribution of the initial impact velocity v0 to the fitting of the wide strain rate region was ≥30%.
5. The method for obtaining a broad strain rate constitutive relation of a material using a single Taylor impact test according to claim 4, characterized in that: Bayesian optimization parameters: tree depth 35 layers, leaf nodes 12, random feature ratio 0.7, 20 sets of velocity data completed, SHAP analysis shows that the initial impact velocity v0 contributes 32% of the feature, and the fitting accuracy coefficient of determination R0 is [value missing]. 2 =0.9835.
6. The method for obtaining a broad strain rate constitutive relation of a material using a single Taylor impact test according to claim 1, characterized in that: The calculation of local strain rate in step S4 is shown in formula (1). （1）， in, For average strain rate, The length after the micro-segment deformation is completed. t1 is the initial length of the micro-segment, t2 is the deformation end time, and t1 is the initial deformation time.
7. The method for obtaining a broad strain rate constitutive relation of a material using a single Taylor impact test according to claim 1, characterized in that: The characteristic strain rate locations in step S4 include low strain rate, medium strain rate, and high strain rate regions. The impacted specimen is sliced at these characteristic strain rate locations, and its microstructure characteristics are characterized using microscopic characterization techniques such as SEM, EBSD, and TEM. The microscopic deformation mechanism under different strain rates was analyzed.
8. The method for obtaining a broad strain rate constitutive relation of a material using a single Taylor impact test according to claim 1, characterized in that: The macroscopic mechanical behavior under different strain rates constructed in step S6 was verified by means of dual verification: experimental cross-verification and numerical simulation verification through SHPB experimental comparison and FEA simulation comparison. The SHPB experiment uses a Hopkinson pressure bar apparatus to conduct dynamic compression tests on samples from the same batch. Stress-strain curves are obtained by processing the stress wave signals using the three-wave method and compared with the results of the strain rate inversion in step S5 to verify the accuracy of the results. The FEA simulation was based on a Taylor impact model built using Ansys 2022 R2. AISI 1010 steel was used as the verification carrier. Under the publicly available parameters, the simulation was run in the Johnson-Cook constitutive model in 1s-dyna software. The impact velocity was set to v0, and the stress-strain curve was obtained by inversion using the same method. The result was compared with the result of inversion in step S5 to verify the accuracy of the result.