Method for estimating penetration UHPC depth of long-rod projectile based on empirical formula

Abstract

The invention discloses a method for estimating the penetration UHPC depth of a long-rod projectile based on an empirical formula, which comprises the following steps: firstly, according to a known test, carrying out numerical simulation by utilizing LS-Dyna finite element software, comparing a numerical simulation result with an experimental result, verifying the accuracy and correctness of a numerical simulation method, then designing 27 calculation working conditions according to 5 parameters, and calculating the penetration UHPC depth of the long-rod projectile according to the 27 calculation working conditions. Under the condition that other parameters are controlled to be unchanged, the influences of the parameters M, d, v, fc and phi on the penetration depth are analyzed in detail, and an empirical formula is given, so that the empirical formula is suitable for long-rod projectile penetration UHPC depth prediction. According to the method, a mathematical model is adopted to establish the relationship between the penetration depth and the projectile body speed, the projectile body mass, the bullet shape, the compressive strength and the projectile body diameter. And the penetration depth of the projectile body to the UHPC is predicted by inputting related parameters. The method is mainly used for evaluating the anti-penetration performance of the UHPC structural engineering, and is beneficial to improving the working efficiency and saving the cost.

Description

Technical Field

[0001] The invention belongs to the technical field of penetration research, and relates to a method for estimating the penetration depth of a projectile into concrete, and in particular to a method for estimating the penetration depth of a long-rod projectile into UHPC based on an empirical formula. Background Art

[0002] In recent years, regional conflicts and other incidents have occurred frequently, posing a certain degree of threat to civilian and military buildings. Therefore, research on the impact load resistance of new building materials is very important.

[0003] Ultra High Performance Concrete (UHPC) is a new type of building material that has attracted widespread attention. Compared with traditional concrete, UHPC has the characteristics of high compressive and tensile strength, high fracture toughness and excellent durability, which make it an ideal material in structural impact resistance design.

[0004] At present, the research on the anti-ballistic penetration performance of UHPC is still relatively limited. Most of the existing studies are only for UHPC of specific projectile type or specific strength, and the applicability of the research conclusions is limited. This study first verifies the correctness and accuracy of the numerical simulation method through experiments, and then uses LS-DYNA finite element software and the verified KC material constitutive model to simulate the process of projectile penetration of UHPC target plate. On this basis, the compressive strength f c The influence of penetration velocity v, CRH (ratio of the curvature radius of the projectile head to the projectile diameter) Φ, projectile mass M, and projectile diameter d on the penetration depth. Based on this, a formula suitable for predicting the penetration depth of UHPC is derived, which is of great significance for improving the efficiency of UHPC anti-penetration performance evaluation and saving costs. Summary of the invention

[0005] The present invention proposes a method for estimating the penetration depth of a long-rod projectile into UHPC based on an empirical formula, and uses a mathematical model to establish the relationship between the penetration depth and the velocity, mass, shape, compressive strength and diameter of the projectile. The penetration depth of the projectile into UHPC is predicted by inputting relevant parameters. This method is mainly used in the evaluation of the anti-penetration performance of UHPC structural engineering, which is conducive to improving work efficiency and saving costs.

[0006] In order to achieve the above object, the present invention provides a method for estimating the penetration depth of a long rod projectile into UHPC based on an empirical formula. Firstly, according to known experiments, numerical simulation is performed using LS-Dyna finite element software, and the numerical simulation results are compared with the experimental results to verify the accuracy and correctness of the numerical simulation method. Then, 27 calculation conditions are designed according to 5 parameters. Under the condition of keeping other parameters unchanged, the parameters M, d, v, and f are respectively calculated.c The influence of Φ on the penetration depth is analyzed in detail, and an empirical formula is given to make it suitable for predicting the penetration depth of long-rod projectiles into UHPC.

[0007] The specific implementation process of this method is as follows:

[0008] S1. Use KC constitutive method to perform numerical simulation on known experiments to verify the correctness and accuracy of numerical simulation method;

[0009] Known experiments: 35mm diameter 35CrMnSiA projectiles penetrated UHPC targets with a strength of 119MPa at speeds of 463m / s and 922m / s, with penetration depths of 325mm and 590mm respectively.

[0010] The LS-DYNA finite element software was used to numerically simulate the test process of projectile penetration into UHPC. To save calculation time, a 1 / 4 model was first established. Both the projectile and the UHPC target used SOLID164 three-dimensional solid units. The projectile and target meshes were hexahedral structured meshes. To ensure the calculation accuracy, mesh encryption was performed within 0.2 meters of the target center to ensure that the target center mesh size was close to the projectile mesh size. The target mesh size in the encrypted area was about 4 mm, the mesh size in the non-encrypted area was about 8 mm, and the projectile mesh size was 3 mm. The keyword *CONTACT_EROSION_SURFACE_TO_SURFACE was used in LS-DYNA to define the penetration process.

[0011] By comparison, it was found that in terms of penetration depth, the errors between the calculated results of the numerical model and the experimental results were only 4.01% and 5.76%, respectively, and the calculated results of the numerical model were in good agreement with the experimental results.

[0012] S2. Set the parameters M, d, v, f respectively. c , Φ is set as a variable and numerical simulation is performed;

[0013] For the problem of rigid projectile penetrating concrete, the penetration depth can generally be expressed as

[0014] h=f(M,d,v,Φ,ρ,E,f c , α, γ, μ)

[0015] Where: M, d, v are the mass, diameter and initial impact velocity of the projectile, respectively; Φ is the shape factor of the projectile, Φ = CRH (defined as the ratio of the radius of curvature of the projectile to the diameter of the projectile); ρ, E, are the density, elastic modulus and unconfined compressive strength of the concrete target plate, respectively; a is the characteristic length of the aggregate in the concrete; γ is the volume content of the steel bars in the target plate. In order to obtain higher compressive strength, coarse aggregates are usually removed from UHPC materials to improve the uniformity of the underlying material, so parameter a does not need to be considered; at the same time, there is no reinforcement in the UHPC target, and the influence of parameter γ can be ignored; when the impact velocity is less than 800 m / s, the sliding friction between the projectile and the target only has a second-order effect and can be ignored; the elastic modulus E is interdependent with the concrete strength, and the elastic modulus of different concretes varies little. At the same time, the elastic modulus of the target plate has only a second-order effect on the penetration depth. For concrete materials, the density ρ is mostly concentrated in 2300-2500 kg / m 3 , the change is small. The expression can be further simplified as:

[0016] h=f(M,d,v,f c , Φ)

[0017] Therefore, a total of 27 calculation conditions were designed. Under the condition of keeping other parameters unchanged, the parameters M, d, v, f c , and the influence of Φ on the penetration depth was analyzed in detail. Among them: Groups 1 to 5 carried out numerical simulations of the penetration of a UHPC target with a strength of 120MPa by a long rod projectile at a speed of 250 to 450m / s; Groups 6 to 11 simulated the penetration of a UHPC target with a mass of 0.5kg, 1.0kg, 1.5kg, 2.0kg, 2.5kg and 3.0kg at a penetration speed of 350m / s; Groups 12 to 16 simulated the penetration of a 120MPUHPC target with a projectile Φ of 2, 3, 4, 5, and 6 without changing the mass and diameter of the projectile. The penetration process of PC target; Groups 17-21 only changed the projectile diameter while controlling M and Φ unchanged, simulating the process of the long rod projectile penetrating the 120MPaUHPC target at a speed of 350m / s when the projectile diameter was 20mm, 25mm, 30mm, 35mm and 40mm; Groups 22 to 27 simulated the penetration process of the same projectile on UHPC targets with strengths of 60MPa, 100MPa, 120MPa, 150MPa, 180MPa and 200MPa respectively.

[0018] S3. According to the above 27 sets of numerical simulation results, curve fitting is performed to obtain the parameters (M, d, v, f c The influence of Φ on the penetration depth is expressed as a function.

[0019] The data obtained from numerical simulation was fitted nonlinearly using the data processing software Origin, and iterated until convergence to obtain the quantitative relationship between a single parameter and the penetration depth. The conclusions are as follows:

[0020] 1) When the projectile speed is 200-450m / s, the penetration depth is related to the projectile speed v 0.97 It has a linear relationship, and the function expression is h = 1.004v 0.97 -10.81;

[0021] 2) Penetration Depth and M 0.274 Linear correlation, which can be expressed as h = 824.4 M 0.274 -547.6

[0022] 3) Penetration depth and Φ 0.13 Linear correlation, which can be expressed as h = 400Φ 0.13 -171.5

[0023] 4) Penetration depth and bullet diameter d -1.35 It has a linear relationship, and the function expression is h = d + 2.56 × 10 4 d -1.35

[0024] 5) Penetration depth and Has a linear relationship, the function expression is

[0025] S4. Combine the above parameters (M, d, v, f c , Φ), and the calculation formula for the penetration depth of the long rod projectile into UHPC is derived;

[0026] Fit an empirical formula to represent the above five parameters (M, d, v, f c , Φ) and penetration depth, the formula is based on the NDRC formula, as follows:

[0027]

[0028] Compared with the prior art, the method of the present invention utilizes traditional numerical simulation and experimental verification to propose a new prediction formula. Compared with numerical simulation and experimental methods, it provides a cost-effective and easy-to-use solution to quickly evaluate the penetration depth of long-rod projectiles into UHPC targets. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 Effect of velocity on penetration depth.

[0030] Figure 2 The effect of projectile mass on penetration depth.

[0031] Figure 3 Effect of Φ on penetration depth.

[0032] Figure 4 Effect of projectile diameter on penetration depth.

[0033] Figure 5 Effect of compressive strength on penetration depth. DETAILED DESCRIPTION

[0034] The method of the present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0035] A method for estimating the penetration depth of a long rod projectile into UHPC based on an empirical formula, the implementation steps of the method are as follows:

[0036] S1. Use KC constitutive model to perform numerical simulation on known tests to verify the correctness and accuracy of numerical simulation method;

[0037] LS-DYNA finite element software was used to numerically simulate the test process of projectile penetration into UHPC. In order to save calculation time, a 1 / 4 model was first established. Both the projectile mesh and the UHPC target body adopted SOLID164 three-dimensional solid units, and the meshes were all hexahedral structured meshes. In order to ensure the calculation accuracy, the mesh was encrypted within 0.2 meters of the target center to ensure that the target center mesh size was close to the projectile mesh size. The target mesh size in the encrypted area was about 4 mm, the mesh size in the non-encrypted area was about 8 mm, and the projectile mesh size was 3 mm.

[0038] Table 1 shows the comparison between the test and numerical simulation results. The calculated results are in good agreement with the test results. In terms of penetration depth, the maximum error is 5.76%. Figure 1 The damage and destruction of the UHPC target surface are given, and it can be seen that the numerical simulation is in good agreement with the experimental results.

[0039] Table 1 Comparison of numerical simulation and experimental results

[0040] Test No. Projectile speed (m / s) Test penetration depth (mm) Numerical simulation penetration depth (mm) error% 1# 463 325 337 4.01 2# 922 590 624 5.76

[0041] S2. Set the parameters M, d, v, f respectively. c , Φ is set as a variable for numerical simulation;

[0042] Each parameter was set as a unique variable, and a total of 27 working conditions were set for numerical simulation. The penetration depth was measured by marking the deepest part of the crater;

[0043] The results are shown in Table 2.

[0044] Table 2 Numerical simulation penetration depth

[0045]

[0046]

[0047] S3. Perform curve fitting based on the corresponding 6 sets of numerical simulation results, so as to express the influence of this parameter on the penetration depth with a function.

[0048] The data obtained from numerical simulation were fitted using the data processing software Origin.

[0049] S3.1. Effect of projectile velocity on penetration depth;

[0050] Figure 1 The variation trend of the penetration depth of the 120MPaUHPC target plate with the projectile speed is given. It can be seen that when the projectile speed increases from 250m / s to 450m / s, the penetration depth increases from 206mm to 374mm. With the increase of speed, the penetration depth increases significantly. This study has drawn a conclusion by fitting the numerical simulation data, and believes that when the projectile speed is 200-450m / s, the penetration depth has a linear relationship with the projectile speed v.

[0051] S3.2. Effect of projectile mass on penetration depth;

[0052] Figure 2 The penetration depth results of projectiles with masses of 0.5kg, 1.0kg, 1.5kg, 2.0kg, 2.5kg, and 3.0kg at a penetration speed of 350m / s into 120MPaUHPC are given. When the mass of the projectile increases from 0.5kg to 3.0kg, the penetration depth increases from 129mm to 576mm. It can be seen that with the increase of the mass of the projectile, the penetration depth also increases significantly. This study fits the simulation results and believes that the penetration depth is related to M 0.274 Linear correlation.

[0053] S3.3. Effect of warhead shape (CRH) on penetration depth;

[0054] There are few studies on the effect of projectile shape on penetration depth. The larger the Φ, the sharper the projectile, the smaller the resistance during penetration, and the greater the penetration depth. This study studied the penetration performance of the projectile on a 120MPa UHPC target plate when the CHR of the projectile is 2, 3, 4, 5, and 6 without changing the mass and diameter of the projectile. Figure 3 As shown in the figure, when the penetration speed is 350m / s, φ increases from 2 to 6, and the penetration depth increases from 266mm to 332mm. This shows that as the projectile Φ increases, the penetration depth also increases significantly. Through the fitting calculation results, it is believed that the penetration depth is related to Φ 0.13 Has a linear correlation.

[0055] S3.4. Effect of projectile diameter on penetration depth;

[0056] Under the premise of keeping the mass and shape of the projectile unchanged, the larger the diameter of the projectile, the greater the resistance it encounters during penetration, and the corresponding penetration depth is lower. Under the premise of keeping the mass and CRH of the projectile the same as the test projectile, only the projectile diameter is changed, and the penetration depth of the projectile penetrating the 120MPaUHPC target at a speed of 350m / s is calculated when the projectile diameter is 20mm, 25mm, 30mm, 35mm, and 40mm. The calculation results are as follows: Figure 4 As shown in the figure, the bullet diameter increases from 20mm to 40mm, and the penetration depth decreases from 475mm to 222mm. After fitting, the penetration depth and bullet diameter d are obtained. -1.35 Has a linear relationship.

[0057] S3.5. Effect of compressive strength on penetration depth;

[0058] The compressive strength of concrete materials has an important influence on the penetration depth. A large number of scholars have found through research that the penetration depth generally decreases with the increase of compressive strength, but when the compressive strength increases to a certain level, the reduction in penetration depth will no longer be obvious. Figure 5 The penetration depths of 60MPa, 100MPa, 120MPa, 150MPa, 180MPa and 200MPa concrete at a speed of 350m / h obtained by numerical simulation in this paper are given. When the strength increases from 60MPa to 200MPa, the penetration depth decreases from 368mm to 255mm. It can be seen that with the increase of concrete strength, the penetration depth decreases significantly. By fitting the data, it is believed that the penetration depth is related to Has a linear relationship.

[0059] In the above five figures, R 2 is the correlation coefficient, indicating the accuracy of the fit, R 2 They are 0.999, 0.994, 0.997, 0.999 and 0.974 respectively, indicating that the fitting accuracy is high.

[0060] S4. Combining the above parameters, the calculation formula of the penetration depth of the long rod projectile into UHPC is derived;

[0061] An empirical formula is fitted to express the relationship between the above five parameters and the penetration depth. The formula form refers to the NDRC formula, as follows:

[0062]

[0063] Where: d is the diameter of the projectile, in m; M is the mass of the projectile, in kg; v is the initial penetration velocity of the projectile, in m / s; Φ is the ratio of the curvature radius of the projectile head to the projectile diameter; f c It is the unconfined compressive strength of concrete, in Pa.

Claims

1. A method for estimating the penetration depth of a long-rod projectile into UHPC based on an empirical formula, characterized in that: According to the known test, numerical simulation was carried out using LS-Dyna finite element software, and the numerical simulation results were compared with the experimental results to verify the accuracy and correctness of the numerical simulation method. Then, 27 calculation conditions were designed according to 5 parameters. Under the condition of keeping other parameters unchanged, the parameters M, d, v, and f were respectively c The influence of Φ on the penetration depth is analyzed and an empirical formula is given to make it suitable for predicting the penetration depth of long-rod projectiles into UHPC.

2. A method for estimating the penetration depth of a long rod projectile into UHPC based on an empirical formula according to claim 1, characterized in that: The KC constitutive model is used to perform numerical simulation on known experiments to verify the correctness and accuracy of the numerical simulation method.

3. The method for estimating the penetration depth of a long rod projectile into UHPC based on an empirical formula according to claim 2, characterized in that: Known test: 35mm diameter 35CrMnSiA projectile penetrated the UHPC target with a strength of 119MPa at a speed of 463m / s and 922m / s, and the penetration depth was 325mm and 590mm respectively; LS-DYNA finite element software was used to numerically simulate the test process of projectile penetration into UHPC. In order to save calculation time, a 1 / 4 model was first established. Both the projectile and the UHPC target used SOLID164 three-dimensional solid units. The meshes of the projectile and the target were hexahedral structured meshes. In order to ensure the calculation accuracy, the mesh was encrypted within 0.2 meters of the target center to ensure that the mesh size of the target center was close to that of the projectile. The mesh size of the target in the encrypted area was about 4 mm, the mesh size in the non-encrypted area was about 8 mm, and the mesh size of the projectile was 3 mm. The keyword *CONTACT_EROSION_SURFACE_TO_SURFACE was used in LS-DYNA to define the penetration process.

4. The method for estimating the penetration depth of a long rod projectile into UHPC based on an empirical formula according to claim 1, characterized in that: The parameters M, d, v, f are c , Φ is set as a variable and numerical simulation is performed; For the problem of rigid projectile penetrating concrete, the penetration depth is expressed as h=f(M,d,v,Φ,ρ,E,f c ,a,c,m) Where: M, d, v are the mass, diameter and initial impact velocity of the projectile, respectively; Φ is the projectile shape coefficient, Φ = CRH, which is defined as the ratio of the curvature radius of the bullet to the diameter of the projectile; ρ, E, are the density, elastic modulus and unconfined compressive strength of the concrete target plate, respectively; a is the characteristic length of the aggregate in the concrete; γ is the volume content of the steel bars in the target plate; in order to obtain higher compressive strength, coarse aggregate is removed from the UHPC material to improve the uniformity of the underlying material, so parameter a does not need to be considered; at the same time, there is no reinforcement in the UHPC target body, and the influence of parameter γ is ignored; when the impact velocity is less than 800m / s, the sliding friction between the projectile and the target only has a second-order effect and can be ignored; the elastic modulus E is interdependent with the concrete strength, and the elastic modulus of different concretes varies little; at the same time, the elastic modulus of the target plate has only a second-order effect on the penetration depth; and for concrete materials, the density ρ is mostly concentrated in 2300-2500kg / m 3 ; The expression simplifies to: h=f(M,d,v,f c ,Φ) 27 calculation conditions are designed. Under the condition of keeping other parameters unchanged, the parameters M, d, v, f are calculated respectively. c The influence of Φ on the penetration depth was analyzed in detail; among them: Groups 1 to 5 carried out numerical simulation of the penetration of a UHPC target with a strength of 120MPa by a long rod projectile at a speed of 250 to 450m / s; Groups 6 to 11 simulated the penetration of a UHPC target with a mass of 0.5kg, 1.0kg, 1.5kg, 2.0kg, 2.5kg and 3.0kg at a penetration speed of 350m / s; Groups 12 to 16 simulated the penetration of a UHPC target with a Φ of 2, 3, 4, 5 and 6 without changing the mass and diameter of the projectile. The penetration process of the 120MPa UHPC target; Groups 17-21 only changed the projectile diameter while controlling M and Φ unchanged, simulating the process of the long rod projectile penetrating the 120MPa UHPC target at a speed of 350m / s when the projectile diameter was 20mm, 25mm, 30mm, 35mm and 40mm; Groups 22 to 27 simulated the penetration process of the same projectile on UHPC targets with strengths of 60MPa, 100MPa, 120MPa, 150MPa, 180MPa and 200MPa, respectively.

5. The method for estimating the penetration depth of a long rod projectile into UHPC based on an empirical formula according to claim 1, characterized in that: According to the above 27 sets of numerical simulation results, curve fitting is performed to c , the influence of Φ) on the penetration depth is expressed by a function; The data obtained from the numerical simulation was fitted nonlinearly using the data processing software Origin, and iterated until convergence to obtain the quantitative relationship between a single parameter and the penetration depth. The following conclusions were drawn: 1) When the projectile speed is 200-450m / s, the penetration depth is related to the projectile speed v 0.97 It has a linear relationship, and the function expression is h = 1.004v 0.97 -10.81; 2) Penetration Depth and M 0.274 Linear correlation, expressed as a function of h = 824.4M 0.274 -547.6; 3) Penetration depth and Φ 0.13 Linear correlation, expressed as a function h = 400Φ 0.13 -171.5; 4) Penetration depth and bullet diameter d -1.35 It has a linear relationship, and the function expression is h = d + 2.56 × 10 4 d -1.35 ; 5) Penetration depth and Has a linear relationship, the function expression is 6. The method for estimating the penetration depth of a long rod projectile into UHPC based on an empirical formula according to claim 1, characterized in that: Combining the above parameters (M, d, v, f c , Φ), and the calculation formula for the penetration depth of the long rod projectile into UHPC is derived; Fit an empirical formula to represent the above five parameters (M, d, v, f c , Φ) and penetration depth, the formula is based on the NDRC formula, as follows:

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