Method and system for measuring material dynamic stress-strain relation of projectile impact indentation

Abstract

The invention provides a material dynamic stress-strain relation measuring method and system for bullet impact indentation, and the method comprises the steps: pre-processing a target material, and executing N times of hard spherical bullet impact target material tests; taking the indentation radius and residual depth of the pit as test data as input, and calculating and obtaining corresponding representative plastic strain according to the geometrical relationship that the spherical indenter of the hard spherical projectile generates the indentation on the target material; the bullet impact speed, the rebound speed and the pit geometric parameters which serve as test data serve as input, and representative stress is obtained through calculation; and performing data fitting on the representative plastic strain and the representative stress to obtain a dynamic stress-strain relationship of the target material. The technical bottleneck of direct measurement of the stress-strain relation under the ultrahigh strain rate is broken through, a representative stress-strain method in a quasi-static scene is innovatively expanded to the dynamic field, dependence on a preset constitutive model is not needed, and the dynamic stress-strain relation of the material is directly derived through test data.

Description

Technical Field

[0001] This invention belongs to the field of materials analysis and testing technology, specifically relating to a method and system for measuring the dynamic stress-strain relationship of materials based on projectile impact indentations. More specifically, it is a method for measuring the dynamic stress-strain relationship of materials based on projectile impact indentations. Background Technology

[0002] In aerospace, defense, and materials processing, engineering materials often face short-term, high-rate dynamic loads, such as those encountered in manufacturing processes like micro-peening, laser peening, and cold spraying, as well as in service scenarios like bullet impacts and space debris collisions, where strain rates typically exceed 10. 4 s -1 The dynamic stress-strain relationship of materials under ultra-high strain rates, i.e., the dynamic constitutive relationship, is the core basis for structural design, process optimization, and service safety assessment.

[0003] In traditional dynamic mechanical property testing techniques, split Hopkinson bars (SHPB), Taylor impact tests, and expansion ring tests are mature methods for measuring the dynamic constitutive relations of metals. However, these techniques have inherent limitations: on the one hand, they require relatively large specimens, and on the other hand, the upper limit of the strain rate is usually below 10. 4 s -1 It cannot cover scenarios with ultra-high strain rates.

[0004] Compared with traditional dynamic testing techniques, indentation technology has significant advantages such as low sample consumption and simple preparation, and has become an important means of measuring dynamic mechanical properties. According to the literature M. Rueda-Ruiz, BD Beake, JM Molina-Aldareguia, Materials & Design, 192 (2020) 108715., the nano-impact indentation technique developed by Beake et al. can achieve 10 4 s -1 Performance measurement under strain rate. Projectile impact indentation technology accelerates spherical projectiles using air gun-driven or laser-induced pressure, enabling measurements exceeding 10... 4 s -1 This provides the technical prerequisite for measuring the mechanical properties under ultra-high strain rates. According to the literature Y. Tirupataiah, G. Sundararajan, Materials Science and Engineering: A, 189 (1994) 117-127, Sundararajan et al.'s air gun-driven projectile impact indentation test measured the strain rate at 10... 4 s -1Dynamic hardness was determined using an energy-based method. According to the literature M. Hassani, D. Veysset, KA Nelson, et al., Scripta Materialia, 177 (2020) 198-202, Hassani et al. developed a laser-driven projectile impact indentation test. By calculating the ratio of the plastic work absorbed by the target material to the residual indentation volume, they evaluated the dynamic hardness at strain rates higher than 10⁻⁶. 5 s -1 Dynamic hardness using energy method.

[0005] However, existing projectile impact indentation technology still has fundamental shortcomings in measuring dynamic stress-strain relationships, making accurate characterization difficult. Firstly, mature stress-strain calculation methods for quasi-static scenarios have not been effectively extended to the dynamic domain. Quasi-static instrumented spherical indentation technology, such as patent documents CN109030259A and CN114935516B, can calculate the stress-strain relationship of materials using a strain-stress estimation formula through repeated loading and unloading of a spherical indenter. However, this method is currently limited to quasi-static scenarios and has not been systematically extended to the dynamic scenario of projectile impact indentation—the dynamic indentation constraint factor is directly related to the indentation's plastic state, and the definition and calculation of the representative indentation strain rate lack a standardized scheme, becoming a core bottleneck restricting the measurement of dynamic stress-strain relationships.

[0006] Secondly, existing dynamic measurement methods rely on empirical models or pre-defined constitutive models, lacking universality. As shown in I. Dowding, CA Schuh, Nature, 630 (2024) 91-95, Schuh et al. evaluated the average dynamic yield strength of materials based on a semi-empirical model of the coefficient of restitution. This model assumes the material is an ideal elastoplastic body, leading to inaccurate yield strength calculations and failing to reflect the true stress-strain relationship. As shown in X. Wang, M. Hassani, Journal of Applied Mechanics, 87 (2020) and Y. Song, Z. Gu, C. Huang, et al., International Journal of Impact Engineering, 202 (2025) 105318, Hassani and Wu et al. calibrated the parameters of known constitutive models such as Johnson-Cook and ZA through projectile impact tests combined with numerical simulations. However, such methods are only applicable to materials with existing, well-defined constitutive models and cannot meet the testing needs of novel materials or materials without established constitutive models.

[0007] Patent document CN121275538A discloses a method for measuring the dynamic hardness of materials based on projectile impact indentation, including: cleaning and polishing the surface of the target material; measuring the elastic modulus of the area to be tested; launching a hard spherical projectile to impact the area to be tested, forming an impact crater, and measuring the rebound velocity of the projectile in situ; measuring the geometric parameters of the impact crater; establishing a contact force model of the elastic unloading section of the projectile impact; using the rebound velocity and the geometric parameters of the crater as inputs, obtaining the maximum loading force through the contact force model, and finally calculating the dynamic hardness. This method does not solve the technical problem of measuring the stress-strain relationship at high strain rates.

[0008] In summary, the current ultra-high strain rate, i.e. ≥10 4 s -1 Under these conditions, the measurement of dynamic stress-strain relationships in materials by projectile impact indentation faces two major problems: First, the definitions of dynamic indentation constraint factor and representative strain rate are unclear, and there is a lack of an effective correlation path from indentation parameters to stress-strain relationships; second, existing methods rely on empirical assumptions or pre-set constitutive models, resulting in insufficient measurement accuracy and universality.

[0009] Therefore, there is an urgent need to develop an innovative method for measuring projectile impact indentation, which clarifies the calculation logic of representative strain, strain rate, and indentation constraint factor under dynamic scenarios. This method should not rely on a pre-set constitutive model and should directly derive the dynamic stress-strain relationship of materials from experimental data, filling the technological gap in the field of ultra-high strain rate stress-strain measurement. Summary of the Invention

[0010] To address the shortcomings of existing technologies, the purpose of this invention is to provide a method and system for measuring the dynamic stress-strain relationship of materials in projectile impact indentations.

[0011] A method for measuring the dynamic stress-strain relationship of a material indentation caused by a projectile impact, provided by the present invention, includes: Impact test procedure: Pre-treat the target material, perform N tests on the target material with hard spherical projectiles, and then record the test data; Calculation steps: Using the indentation radius and residual depth of the pit as input, the representative plastic strain is calculated and obtained based on the geometric relationship of the indentation produced by the spherical indenter of the hard spherical projectile on the target material; using the projectile impact velocity, rebound velocity and pit geometric parameters as input, the representative stress is calculated through the contact force model. Relationship fitting step: Fit the representative plastic strain and the representative stress to obtain the dynamic stress-strain relationship of the target material.

[0012] Preferably, the impact test step includes: Step S1: Clean and polish the target surface to form the test area on the target surface; Step S2: Launch a hard spherical projectile to impact the test area of ​​the target material to form an impact crater, and perform the test N times at different impact velocities; Step S3: Measure the first i The impact velocity and rebound velocity of the hard spherical projectile in this test are included in the test data, 1≤ i ≤ N; Measure the first i The indentation radius and residual depth of the pits from this test are included in the test data.

[0013] Preferably, in the calculation step, the expression for the representative plastic strain is:

[0014] in, Indicates the first i The representative plastic strain of this experiment, , Indicates the number of trials; Indicates the first i The residual depth of the pit in this test; Indicates the first i The indentation radius of the pit in this test; The representative stress is calculated using the projectile impact velocity, rebound velocity, and dent geometry parameters (as experimental data) as inputs through a contact force model, including: Step A1: Input the rebound velocity of the projectile and the geometric parameters of the dent into the contact force model, calculate and obtain the first... i The maximum loading force in the test, and then the target material in the first test is obtained based on the maximum loading force. i Dynamic hardness under this test; Step A2: Calculate and obtain the dimensionless number that reflects the plastic state of the indentation based on the impact velocity, rebound velocity, maximum loading force, and indentation geometry parameters of the projectile. Step A3: Based on the dimensionless number, calculate the first... i The indentation constraint factor under the test is used to calculate the representative stress based on the indentation constraint factor and the dynamic hardness.

[0015] Preferably, in step A1, the expression for the contact force model is:

[0016] in, The function representing the change of contact force over time in the elastic unloading section of the projectile impact; Indicates the effective radius; Indicates the effective elastic modulus; A function representing the difference between the indentation depth and the residual depth of the impact crater as a function of time; This represents Argatov's dimensionless constant; Indicates the transverse wave velocity of the target material; A function representing the change of projectile velocity over time; A function representing the change in indentation depth of an impact crater over time; Indicates the remaining depth of the pit; Indicates time; The dynamic hardness is expressed as: = / ( π ( a c (i ) ) 2 ) in, Indicates the first i The dynamic hardness of this test; Indicates the first i The maximum loading force obtained from the contact force model in this test; a c (i ) Indicates the first i The radius of the indentation from the impact dent in the second test; In step A2, the expression for the dimensionless number is:

[0017] in, Indicates the first i The dimensionless number of the experiment; Indicates the mass of the projectile; Indicates the first i The contact area of ​​the impact dent in the second test; Indicates the first i The maximum volume of the impact dent in the test; Indicates the first i Impact velocity of the projectile in the second test; In step A3, the first i The indentation constraint factor under this test is expressed as follows:

[0018] in, Indicates the first i Indentation constraint factor under this test; This indicates the calculation relationship of the indentation constraint factor; This represents the preset maximum indentation constraint factor; The representative stress is expressed as follows:

[0019] in, Indicates the first i The representative stress under this test.

[0020] Preferably, in step A3, the first i The indentation constraint factor under this test is expressed as follows:

[0021] in, This represents the logarithmic function with base e, or simply log; and All represent fitting constants; This represents the preset maximum indentation constraint factor, with a value range of 2.8 to 3; [symbol] Indicates product; In the relationship fitting step, the expression for the dynamic stress-strain relationship is:

[0022] in, It is the elastic limit; It is the strain hardening modulus; It is the strain hardening index.

[0023] A dynamic stress-strain relationship measurement system for projectile impact indentation provided by the present invention includes: Impact testing module: Pre-treat the target material, perform N tests on the target material with hard spherical projectiles, and then record the test data; The calculation module takes the indentation radius and residual depth of the pit as input, and calculates and obtains the corresponding representative plastic strain based on the geometric relationship of the indentation produced by the spherical indenter of the hard spherical projectile on the target material. It also takes the projectile impact velocity, rebound velocity and pit geometric parameters as input, and calculates the representative stress through the contact force model. Relationship Fitting Module: The representative plastic strain and the representative stress are fitted together to obtain the dynamic stress-strain relationship of the target material.

[0024] Preferably, the impact test module includes: Module M1: Cleans and polishes the target surface to form the test area on the target surface; Module M2: Launches a hard spherical projectile to impact the test area of ​​the target material to form an impact crater, and performs the test N times at different impact velocities; Module M3: Measurement of the first iThe impact velocity and rebound velocity of the hard spherical projectile in this test are included in the test data, 1≤ i ≤ N; Measure the first i The indentation radius and residual depth of the pits from this test are included in the test data.

[0025] Preferably, in the calculation module, the expression for the representative plastic strain is:

[0026] in, Indicates the first i The representative plastic strain of this experiment, , Indicates the number of trials; Indicates the first i The residual depth of the pit in this test; Indicates the first i The indentation radius of the pit in this test; The representative stress is calculated using the projectile impact velocity, rebound velocity, and dent geometry parameters (as experimental data) as inputs through a contact force model, including: Module A1: Input the rebound velocity of the projectile and the geometric parameters of the dent into the contact force model, calculate and obtain the first... i The maximum loading force in the test, and then the target material in the first test is obtained based on the maximum loading force. i Dynamic hardness under this test; Module A2: Calculate and obtain a dimensionless number that reflects the plastic state of the indentation based on the impact velocity, rebound velocity, maximum loading force, and indentation geometry parameters of the projectile; Module A3: Based on the dimensionless number, calculate the first... i The indentation constraint factor under the test is used to calculate the representative stress based on the indentation constraint factor and the dynamic hardness.

[0027] Preferably, in module A1, the expression for the contact force model is:

[0028] in, The function representing the change of contact force over time in the elastic unloading section of the projectile impact; Indicates the effective radius; Indicates the effective elastic modulus; A function representing the difference between the indentation depth and the residual depth of the impact crater as a function of time; This represents Argatov's dimensionless constant; Indicates the transverse wave velocity of the target material; A function representing the change of projectile velocity over time; A function representing the change in indentation depth of an impact crater over time; Indicates the remaining depth of the pit; Indicates time; The dynamic hardness is expressed as: = / ( π ( a c (i ) ) 2 ) in, Indicates the first i The dynamic hardness of this test; Indicates the first i The maximum loading force obtained from the contact force model in this test; a c (i ) Indicates the first i The radius of the indentation from the impact dent in the second test; In module A2, the expression for the dimensionless number is:

[0029] in, Indicates the first i The dimensionless number of the experiment; Indicates the mass of the projectile; Indicates the first i The contact area of ​​the impact dent in the second test; Indicates the first i The maximum volume of the impact dent in the test; Indicates the first i Impact velocity of the projectile in the second test; In module A3, the first i The indentation constraint factor under this test is expressed as follows:

[0030] in, Indicates the first i Indentation constraint factor under this test; This indicates the calculation relationship of the indentation constraint factor; This represents the preset maximum indentation constraint factor; The representative stress is expressed as follows:

[0031] in, Indicates the first i The representative stress under this test.

[0032] Preferably, in module A3, the first i The indentation constraint factor under this test is expressed as follows:

[0033] in, This represents the logarithmic function with base e, or simply log; and All represent fitting constants; This represents the preset maximum indentation constraint factor, with a value range of 2.8 to 3; [symbol] Indicates product; In the relationship fitting module, the expression for the dynamic stress-strain relationship is:

[0034] in, It is the elastic limit; It is the strain hardening modulus; It is the strain hardening index.

[0035] Compared with the prior art, the present invention has the following beneficial effects: 1. This invention breaks through the technical bottleneck of direct measurement of stress-strain relationship under ultra-high strain rate, and innovatively extends the representative stress-strain method in quasi-static scenarios to the dynamic domain. It does not rely on a preset constitutive model and can directly derive the dynamic stress-strain relationship of materials through experimental data.

[0036] 2. This invention utilizes projectile impact indentation testing, eliminating the need for real-time data acquisition from high-frequency force / displacement sensors. This overcomes the strain rate limitation imposed by traditional technologies due to hardware constraints, filling a gap in the measurement of dynamic stress-strain relationships at ultra-high strain rates; the ultra-high strain rate refers to a strain rate greater than 10. 4 / s, where s represents seconds.

[0037] 3. This invention establishes the correlation between dynamic indentation constraint factor and indentation plasticity by constructing a dimensionless number characterizing the plastic state of indentation, fully considering key influencing factors under high strain rates, and significantly reducing the high dynamic calculation error of representative stress.

[0038] 4. By using the projectile impact indentation test, there is no need to rely on a high-frequency contact force sensor. Only the projectile impact / rebound velocity and indentation parameters need to be measured. This solves the problem of strain rate upper limit caused by hardware limitations in traditional technology and fills the gap in dynamic stress-stress-strain measurement under high strain rate. Attached Figure Description

[0039] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings: Figure 1 A schematic diagram of the dynamic stress-strain relationship measurement process provided by the present invention; Figure 2 A schematic diagram illustrating the representative stress calculation process provided by this invention; Figure 3 This is a geometric schematic diagram of the spherical projectile being pressed into the target material according to the present invention; Figure 4 This is a schematic diagram of the dynamic stress-strain relationship of pure copper provided by the present invention. Detailed Implementation

[0040] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.

[0041] This invention provides a method for measuring the dynamic stress-strain relationship of materials based on projectile impact indentation, comprising: cleaning and polishing the surface of a target material; launching a hard spherical projectile to impact the area to be tested, forming an impact crater, and performing N tests at different impact velocities; measuring the impact and rebound velocities of the projectile in situ, and subsequently measuring the geometric parameters of the impact crater; calculating a representative plastic strain using the crater geometric parameters as input; calculating a representative stress using the impact velocity, rebound velocity, and crater parameters as input; and plotting a stress-strain scatter plot based on the representative plastic strain and representative stress to obtain the dynamic stress-strain relationship of the target material.

[0042] Specifically, according to the present invention, a method for measuring the dynamic stress-strain relationship of materials based on projectile impact indentation includes: S1: Pre-treat the target material to form the test area on the target surface; specifically, clean and polish the target surface to ensure that the test area is smooth and flat, without obvious scratches or impurities. S2: Launch radius R p ,density ρ p With modulus E p A known hard spherical projectile is used to impact the test area of ​​the target material to form an impact dent, and the test is repeated N times at different impact velocities. S3: In-situ measurement i Projectile impact velocity in this test With rebound speed , 1 ≤ i ≤ N; S4: Post-hoc measurement i The key geometric parameters of the impact dent formed in this test include the indentation radius. With residual depth , 1 ≤ i ≤ N; S5: with the first i The radius of the indentation formed by the impact crater in this test With residual depth For input, 1 ≤ i ≤N, calculate the first i The representative plastic strain corresponding to this experiment =f ε ( , ); f ε This represents the functional relationship between the indentation radius and the residual depth of the impact crater; S6: with the first i Projectile impact velocity in this test rebound speed Using the geometric parameters of the pit as input, calculate the first... i Representative stress corresponding to this test ;1 ≤ i ≤ N; S7: Representative plastic strain based on N tests With representative stress Stress-strain scatter plots were plotted, and the dynamic stress-strain relationship of the target material was obtained through data fitting.

[0043] Specifically, the representative plastic strain expression in S5 =f ε ( , Specifically:

[0044] Specifically, the calculation steps for the representative stress in S6 are as follows: S61: Based on the bullet's rebound speed Using the geometric parameters of the crater as input, a contact force model based on the elastic unloading segment during the projectile impact process is used, i.e., the contact force model. Calculate the first i Maximum loading force in this test According to the formula = / ( π ( ) 2 ), calculate the target material in the first iDynamic hardness under this test , 1 ≤ i ≤ N; S62: with projectile impact speed rebound speed Maximum loading force Using the geometric parameters of the indentation as input, calculate the dimensionless number that reflects the plastic state of the indentation. C H (i) ,

[0045] Among them, the function Based on maximum loading force Projectile velocity parameters, i.e., impact velocity rebound speed and the geometric parameters of the indentation, i.e., the radius of the indentation. Residual depth The constructed mapping relationship; S63: Based on dimensionless numbers Calculate the first i Indentation constraint factor under this test The expression is:

[0046] in, The function is the preset maximum indentation constraint factor. Based on and The established indentation constraint factor calculation relationship; S64: Based on dynamic hardness With indentation constraint factor Calculate representative stress The expression is:

[0047] Specifically, the contact force model in S61 The expression is as follows:

[0048] The numerical solution algorithm for the contact force model is the Runge-Kutta algorithm, with initial values ​​substituted. Calculation speed The contact force when it is zero is taken as the maximum loading force. ; In other words, the contact force model is solved numerically by substituting the initial values. Calculation speed The contact force when it is zero is taken as the maximum loading force. ; in, It is a function of the contact force in the elastic unloading section of the projectile impact as a function of time; Indicates time; The depth of the impact dent is a function of time. The transverse wave velocity of the target material. , G s The shear modulus of the target material. ρ s The density of the target material; For the effective radius, satisfying ,in, R p Let the radius be the projectile radius. R s The radius of curvature of the indentation after full rebound. ; For the effective elastic modulus, satisfying ,in, For the target material Poisson's ratio, Let be the elastic modulus of the target material. For the Poisson's ratio of a bullet, Let be the elastic modulus of the projectile; Argatov's dimensionless constant reflects the influence of the material's Poisson's ratio. It is a function of the projectile velocity as a function of time; The depth of the indentation and the residual depth of the impact dent h r The difference is a function of time.

[0049] Specifically, the dimensionless number in S62 C H (i) The specific expression is:

[0050] in, It is the mass of the bullet; , for the first i The contact area of ​​the secondary impact dent; For the first i The maximum volume of the secondary impact crater is determined by the indentation radius. With residual depth h r Calculated.

[0051] Specifically, the stress-strain relationship in S7 is fitted by the following expression:

[0052] in, It is the elastic limit; It is the strain hardening modulus; It is the strain hardening index.

[0053] Specifically, no. i The representative average strain rate of the impact is calculated as follows:

[0054] in, Indicates the first i The representative average strain rate of the impact. is the indentation strain rate coefficient, with a value of 0.21~0.28.

[0055] Specifically, in S2, the projectile is spherical and is launched by a projectile impact testing device to impact the target material vertically. When the projectile radius is >0.5mm, an air gun is used as the projectile impact testing device, and when the projectile radius is ≤0.5mm, a laser-driven projectile launcher is used as the projectile impact testing device.

[0056] In S1, the pretreatment includes cleaning and polishing the surface of the target material, and the area to be tested is smooth and free of scratches; When polishing the target surface, firstly, use 400-grit, 1200-grit, and 2400-grit sandpaper for rough polishing, and then use woolen cloth for fine polishing.

[0057] Indentation constraint factor in S63 The specific expression is:

[0058] in, and These are the fitting constants; It is the preset maximum indentation constraint factor, with a value of 2.8 to 3.

[0059] Example, Figure 1 This is a flowchart of the dynamic stress-strain measurement of the present invention; (Participants) Figure 1 A method for measuring the dynamic stress-strain relationship of a material indentation caused by a projectile impact, provided by the present invention, includes: Step 1: Clean and polish the surface of the target material to ensure that the surface of the area to be tested is smooth and flat, without obvious scratches or impurities. In this embodiment, the target material is pure copper, 5N, and a 5mm × 5mm × 2mm cube is cut from the material under test for performance testing. During surface polishing, the test surface is first coarsely polished sequentially using 400-grit, 1200-grit, and 2400-grit sandpaper. Next, a woolen cloth is used for further polishing. During polishing, a 2.5-micron diamond suspension is continuously used; these fine particles further smooth the surface. Simultaneously, the test surface is periodically rinsed with clean water to remove residual particles and suspension generated during polishing, preventing them from affecting surface quality. Finally, the test surface should exhibit a high-gloss mirror finish to significantly reduce the impact of surface roughness on subsequent performance testing.

[0060] Step 2: Launch radius R p ,density ρ p With modulus E p A known hard spherical projectile is used to impact the test area of ​​the target material to form an impact dent, and the test is repeated N times at different impact velocities. In this embodiment, the glass pellet has a diameter of 300 μm and a density of 2.5 g / cm³. 3 The modulus is 70 GPa. The projectile is launched by a laser-driven projectile impact testing device and impacts pure copper and pure aluminum targets vertically. The angle deviation is <2°. The projectile launch speed range is 1 ~ 100 m / s. The elastic modulus of the test area is 110 GPa. The elastic modulus of the test area is obtained by nanoindentation test.

[0061] Step 3: Utilize the principle of high-frequency flash combined with multiple exposures to measure the first... i Projectile impact velocity in this test With rebound speed , 1 ≤ i ≤ N; Step 4: Post-hoc measurement using confocal microscopy i The key geometric parameters of the impact dent formed in this test include the indentation radius. With residual depth , 1 ≤ i ≤ N, geometric features as follows Figure 3 As shown; Step 5: Using the first i The radius of the indentation formed by the impact crater in this test With residual depth For input, 1 ≤ i ≤ N, calculate the first i The representative plastic strain corresponding to this experiment The expression is specifically as follows:

[0062] Step 6: Using the first i Projectile impact velocity in this test v i (i) rebound speed v r (i) Using the geometric parameters of the pit as input, calculate the first... i Representative stress corresponding to this test σ (i) Specifically including Figure 2 The following steps are shown: Step 61: Using the bullet's rebound speed v r (i) Using the geometric parameters of the crater as input, a contact force model based on the elastic unloading segment during projectile impact is proposed. Calculate the first i Maximum loading force in this test P max (i) According to the formula H d (i) = P max (i) / ( π ( a c (i) ) 2 ), calculate the target material in the first i Dynamic hardness under this test H d (i) , 1 ≤ i ≤ N; Contact force model for,

[0063] The numerical solution algorithm for the contact force model is the Runge-Kutta algorithm, with initial values ​​substituted. Calculation speed The contact force when it is zero is taken as the maximum loading force. P max ; in, It is a function of the contact force in the elastic unloading section of the projectile impact as a function of time; Indicates time; The depth of the impact dent is a function of time. The transverse wave velocity of the target material. , G sThe shear modulus of the target material. ρ s The density of the target material; For the effective radius, satisfying ,in, R p Let the radius be the projectile radius. R s The radius of curvature of the indentation after full rebound. ; For the effective elastic modulus, satisfying ,in, For the target material Poisson's ratio, Let be the elastic modulus of the target material. For the Poisson's ratio of a bullet, Let be the elastic modulus of the projectile; Argatov's dimensionless constant reflects the influence of the material's Poisson's ratio. It is a function of the projectile velocity as a function of time; The depth of the indentation and the residual depth of the impact dent h r The difference is a function of time.

[0064] Step 62: At the impact velocity of the projectile rebound speed Maximum loading force Using the geometric parameters of the indentation as input, calculate the dimensionless number that reflects the plastic state of the indentation. The expression is as follows:

[0065] in, It is the mass of the bullet; , for the first i The contact area of ​​the secondary impact dent; For the first i The maximum volume of the secondary impact crater is determined by the indentation radius. a c With residual depth h r Calculated.

[0066] Step 63: Based on dimensionless numbers Calculate the indentation constraint factor under the i-th test. The specific expression is:

[0067] in, and These are the fitting constants; It is the preset maximum indentation constraint factor, which is generally 2.8~3.

[0068] Step 64: Based on dynamic hardness With indentation constraint factor Calculate representative stress The expression is:

[0069] Step 7: Representative plastic strain based on N tests ε (i) With representative stress Stress-strain scatter plots were plotted, and the dynamic stress-strain relationship of the target material was obtained through data fitting.

[0070] The stress-strain relationship of pure copper is fitted by the following expression:

[0071] The stress-strain relationship of ultra-high strain rate pure copper is as follows: Figure 4 As shown, due to its higher strain rate, the stress level is significantly higher than that of the SHPB with a lower strain rate and the results of dynamic compression tests.

[0072] The present invention also provides a material dynamic stress-strain relationship measurement system for projectile impact indentation. The material dynamic stress-strain relationship measurement system for projectile impact indentation can be implemented by executing the process steps of the material dynamic stress-strain relationship measurement method for projectile impact indentation. That is, those skilled in the art can understand the material dynamic stress-strain relationship measurement method for projectile impact indentation as a preferred embodiment of the material dynamic stress-strain relationship measurement system for projectile impact indentation.

[0073] A dynamic stress-strain relationship measurement system for projectile impact indentation provided by the present invention includes: Impact testing module: Pre-treat the target material, perform N tests on the target material with hard spherical projectiles, and then record the test data; The calculation module takes the indentation radius and residual depth of the pit as input, and calculates and obtains the corresponding representative plastic strain based on the geometric relationship of the indentation produced by the spherical indenter of the hard spherical projectile on the target material. It also takes the projectile impact velocity, rebound velocity and pit geometric parameters as input, and calculates the representative stress through the contact force model. Relationship Fitting Module: The representative plastic strain and the representative stress are fitted together to obtain the dynamic stress-strain relationship of the target material.

[0074] Those skilled in the art will understand that, besides implementing the system and its various devices, modules, and units provided by this invention in the form of purely computer-readable program code, the same functions can be achieved entirely through logical programming of the method steps, making the system and its various devices, modules, and units of this invention function in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers. Therefore, the system and its various devices, modules, and units provided by this invention can be considered as a hardware component, and the devices, modules, and units included therein for implementing various functions can also be considered as structures within the hardware component; alternatively, the devices, modules, and units for implementing various functions can be considered as both software modules implementing the method and structures within the hardware component.

[0075] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A method for measuring the dynamic stress-strain relationship of a material indented by a projectile impact, characterized in that, include: Impact test procedure: Pre-treat the target material, perform N tests on the target material with hard spherical projectiles, and then record the test data; Calculation steps: Using the indentation radius and residual depth of the pit as input, the representative plastic strain is calculated and obtained based on the geometric relationship of the indentation produced by the spherical indenter of the hard spherical projectile on the target material; using the projectile impact velocity, rebound velocity and pit geometric parameters as input, the representative stress is calculated through the contact force model. Relationship fitting step: Fit the representative plastic strain and the representative stress to obtain the dynamic stress-strain relationship of the target material.

2. The method for measuring the dynamic stress-strain relationship of material indentation from projectile impact according to claim 1, characterized in that, The impact test procedure includes: Step S1: Clean and polish the target surface to form the test area on the target surface; Step S2: Launch a hard spherical projectile to impact the test area of ​​the target material to form an impact crater, and perform the test N times at different impact velocities; Step S3: Measure the first i The impact velocity and rebound velocity of the hard spherical projectiles in this test are included in the test data, 1 ≤ i ≤ N; Measure the first i The indentation radius and residual depth of the pits from this test are included in the test data.

3. The method for measuring the dynamic stress-strain relationship of material indentation from projectile impact according to claim 1, characterized in that, In the calculation step, the expression for the representative plastic strain is: in, Indicates the first i The representative plastic strain of this experiment, , Indicates the number of trials; Indicates the first i The residual depth of the pit in this test; Indicates the first i The indentation radius of the pit in this test; The representative stress is calculated using the projectile impact velocity, rebound velocity, and dent geometry parameters (as experimental data) as inputs through a contact force model, including: Step A1: Input the rebound velocity of the projectile and the geometric parameters of the dent into the contact force model, calculate and obtain the first... i The maximum loading force in the test, and then the target material in the first test is obtained based on the maximum loading force. i Dynamic hardness under this test; Step A2: Calculate and obtain the dimensionless number that reflects the plastic state of the indentation based on the impact velocity, rebound velocity, maximum loading force, and indentation geometry parameters of the projectile. Step A3: Based on the dimensionless number, calculate the first... i The indentation constraint factor under the test is used to calculate the representative stress based on the indentation constraint factor and the dynamic hardness.

4. The method for measuring the dynamic stress-strain relationship of material indentation from projectile impact according to claim 3, characterized in that, In step A1, the expression for the contact force model is: in, The function representing the change of contact force over time in the elastic unloading section of the projectile impact; Indicates the effective radius; Indicates the effective elastic modulus; A function representing the difference between the indentation depth and the residual depth of the impact crater as a function of time; This represents Argatov's dimensionless constant; Indicates the transverse wave velocity of the target material; A function representing the change of projectile velocity over time; A function representing the change in indentation depth of an impact crater over time; Indicates the remaining depth of the pit; Indicates time; The dynamic hardness is expressed as: = / ( π ( ) 2 ) in, Indicates the first i The dynamic hardness of this test; Indicates the first i The maximum loading force obtained from the contact force model in this test; Indicates the first i The radius of the indentation from the impact dent in the second test; In step A2, the expression for the dimensionless number is: in, Indicates the first i The dimensionless number of the experiment; Indicates the mass of the projectile; Indicates the first i The contact area of ​​the impact dent in the second test; Indicates the first i The maximum volume of the impact dent in the test; Indicates the first i Impact velocity of the projectile in the second test; In step A3, the first i The indentation constraint factor under this test is expressed as follows: in, Indicates the first i Indentation constraint factor under this test; This indicates the calculation relationship of the indentation constraint factor; This indicates the preset maximum indentation constraint factor; The representative stress is expressed as follows: in, Indicates the first i The representative stress under this test.

5. The method for measuring the dynamic stress-strain relationship of material indentation from projectile impact according to claim 4, characterized in that, In step A3, the first i The indentation constraint factor under this test is expressed as follows: in, This represents a logarithmic function with the natural constant e as its base. and All represent fitting constants; This represents the preset maximum indentation constraint factor, with a value range of 2.8 to 3; [symbol] Indicates product; In the relationship fitting step, the expression for the dynamic stress-strain relationship is: in, It is the elastic limit; It is the strain hardening modulus; It is the strain hardening index.

6. A system for measuring the dynamic stress-strain relationship of a material indented by a projectile impact, characterized in that, include: Impact testing module: Pre-treat the target material, perform N tests on the target material with hard spherical projectiles, and then record the test data; The calculation module takes the indentation radius and residual depth of the pit as input, and calculates and obtains the corresponding representative plastic strain based on the geometric relationship of the indentation produced by the spherical indenter of the hard spherical projectile on the target material. It also takes the projectile impact velocity, rebound velocity and pit geometric parameters as input, and calculates the representative stress through the contact force model. Relationship Fitting Module: Fits the representative plastic strain and the representative stress to obtain the dynamic stress-strain relationship of the target material.

7. The dynamic stress-strain relationship measurement system for projectile impact indentations according to claim 6, characterized in that, The impact test module includes: Module M1: Cleans and polishes the target surface to form the test area on the target surface; Module M2: Launches a hard spherical projectile to impact the test area of ​​the target material to form an impact crater, and performs the test N times at different impact velocities; Module M3: Measurement of the first i The impact velocity and rebound velocity of the hard spherical projectiles in this test are included in the test data, 1 ≤ i ≤ N; Measure the first i The indentation radius and residual depth of the pits from this test are included in the test data.

8. The material dynamic stress-strain relationship measurement system for projectile impact indentation according to claim 6, characterized in that, In the calculation module, the expression for the representative plastic strain is: in, Indicates the first i The representative plastic strain of this experiment, , Indicates the number of trials; Indicates the first i The residual depth of the pit in this test; Indicates the first i The indentation radius of the pit in this test; The representative stress is calculated using the projectile impact velocity, rebound velocity, and dent geometry parameters (as experimental data) as inputs through a contact force model, including: Module A1: Input the rebound velocity of the projectile and the geometric parameters of the dent into the contact force model, calculate and obtain the first... i The maximum loading force in the test, and then the target material in the first test is obtained based on the maximum loading force. i Dynamic hardness under this test; Module A2: Calculate and obtain a dimensionless number that reflects the plastic state of the indentation based on the impact velocity, rebound velocity, maximum loading force, and indentation geometry parameters of the projectile; Module A3: Based on the dimensionless number, calculate the first... i The indentation constraint factor under the test is used to calculate the representative stress based on the indentation constraint factor and the dynamic hardness.

9. The material dynamic stress-strain relationship measurement system for projectile impact indentation according to claim 8, characterized in that, In module A1, the expression for the contact force model is: in, The function representing the change of contact force over time in the elastic unloading section of the projectile impact; Indicates the effective radius; Indicates the effective elastic modulus; A function representing the difference between the indentation depth and the residual depth of the impact crater as a function of time; This represents Argatov's dimensionless constant; Indicates the transverse wave velocity of the target material; A function representing the change of projectile velocity over time; A function representing the change in indentation depth of an impact crater over time; Indicates the remaining depth of the pit; Indicates time; The dynamic hardness is expressed as: = / ( π ( ) 2 ) in, Indicates the first i The dynamic hardness of this test; Indicates the first i The maximum loading force obtained from the contact force model in this test; Indicates the first i The radius of the indentation from the impact dent in the second test; In module A2, the expression for the dimensionless number is: in, Indicates the first i The dimensionless number of the experiment; Indicates the mass of the projectile; Indicates the first i The contact area of ​​the impact dent in the second test; Indicates the first i The maximum volume of the impact dent in the test; Indicates the first i Impact velocity of the projectile in the second test; In module A3, the first i The indentation constraint factor under this test is expressed as follows: in, Indicates the first i Indentation constraint factor under this test; This indicates the calculation relationship of the indentation constraint factor; This indicates the preset maximum indentation constraint factor; The representative stress is expressed as follows: in, Indicates the first i The representative stress under this test.

10. The dynamic stress-strain relationship measurement system for projectile impact indentations according to claim 9, characterized in that, In module A3, the first i The indentation constraint factor under this test is expressed as follows: in, This represents a logarithmic function with the natural constant e as its base. and All represent fitting constants; This represents the preset maximum indentation constraint factor, with a value range of 2.8 to 3; [symbol] Indicates product; In the relationship fitting module, the expression for the dynamic stress-strain relationship is: in, It is the elastic limit; It is the strain hardening modulus; It is the strain hardening index.

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