A multi-field coupling strength analysis method suitable for high-speed water entry of cross-medium projectiles

Abstract

The application discloses a multi-field coupling strength analysis method suitable for the case of high-speed water entry of a cross-medium projectile, and comprises the following steps: a flow field model with water entry angle correction is established, and pressure field solving is completed; an improved JC constitutive equation is used for material setting, so as to accurately characterize the yield behavior of the material under high strain rate; a flow field pressure is transmitted from a fluid grid to a structure grid by using an inverse distance weighting method, and dynamic response analysis is carried out, so as to obtain the stress condition of the projectile; and a crystal plastic finite element submodel is embedded in the high-stress area of the projectile, so as to further accurately analyze the damage condition of the projectile material. The multi-field coupling strength analysis method can more accurately characterize the high-speed water entry of the cross-medium projectile, and improve the simulation accuracy.

Description

Technical Field

[0001] This invention belongs to the field of cross-medium projectile water entry strength analysis, specifically relating to a multi-field coupling strength analysis method applicable to cross-medium projectiles entering water at high speed. Background Technology

[0002] Projectiles face extremely complex multiphysics coupling problems during high-speed, cross-medium water entry. Under these conditions, projectiles must withstand enormous transient impact overloads. These extreme loads can cause structural deformation, surface failure, or even fracture, further leading to ballistic loss of control and preventing the projectile from reaching its target. Furthermore, the different entry angles significantly affect the forces acting on both sides of the projectile, resulting in uneven stress distribution and increased local stress and deformation. Therefore, it is necessary to analyze the stress characteristics and strength of projectiles in conjunction with the specific features of high-speed, cross-medium water entry.

[0003] Commonly used numerical simulation methods lack analytical methods for such high-speed cross-medium situations, which prevents them from performing detailed and targeted analysis of the high-speed water entry process of cross-medium projectiles. Therefore, an intensity analysis method that considers instantaneous high pressure is needed to accurately characterize the above process by coupling different physical fields. Summary of the Invention

[0004] The purpose of this invention is to provide a multi-field coupling strength analysis method applicable to the case of high-speed water entry of cross-medium projectiles, so as to more accurately simulate the complex multi-physics coupling problem in the process.

[0005] The technical solution to achieve the purpose of this invention is as follows:

[0006] A multi-field coupled strength analysis method applicable to high-speed water entry of cross-medium projectiles, using the total stress field σ total Analyze whether plastic deformation has occurred in the projectile material, and analyze whether grain boundary fracture has occurred in the projectile material through damage variable D;

[0007] The damage variable D is obtained by integrating the following equation:

[0008]

[0009] Total stress field σ total For the global stress σ global The local stress increment Δσ is superimposed on the nodes:

[0010] σ total =σ global +Δσ

[0011] Where: η and p are damage rate coefficients, calibrated through molecular dynamics simulations; R is the gas constant; T is the current temperature in S2; σ local For local stress tensor; σ th The grain boundary loss threshold, i.e., the critical strength, is determined by nanoindentation experiments; Q is the grain boundary failure activation energy.

[0012] If the total stress field σ total Exceeding the dynamic yield stress σ y If the damage variable D ≥ 1, then the projectile material is considered to have undergone plastic deformation; if the damage variable D ≥ 1, then the projectile material is considered to have undergone grain boundary fracture.

[0013] The significant advantages of this invention compared to existing technologies are:

[0014] (1) A modified Tait equation is proposed, which can more accurately describe the special working condition of projectile entering water. By introducing the water entry angle correction coefficient, the asymmetric pressure field caused by different water entry angles can be characterized in a targeted manner.

[0015] (2) An improved JC constitutive equation is proposed, which can more accurately describe the dynamic yielding behavior of materials under high strain rates. At the same time, it considers the transient coupling between the thermal conductivity of the material and the adiabatic temperature rise, and is more suitable for describing high-speed impact conditions than the traditional model.

[0016] (3) A multi-field coupling analysis method is proposed to perform synergistic analysis of the grain boundary damage model and the fluid-structure interaction process of projectile entering water, thereby improving the analysis accuracy. At the same time, the inverse distance weighting method is used to transfer the flow field load, which can improve the computational efficiency to a certain extent. Attached Figure Description

[0017] Figure 1 This is a flowchart illustrating the steps of the multi-field coupling strength analysis method for high-speed water entry of a cross-medium projectile according to the present invention.

[0018] Figure 2 This is a schematic diagram of the cavitation in the high-speed water flow field of a cross-medium projectile.

[0019] Figure 3 This is a pressure cloud map of the high-speed water flow field for a cross-medium projectile.

[0020] Figure 4 This is a stress cloud diagram of a cross-medium projectile entering water at high speed. Detailed Implementation

[0021] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0022] Figure 2A cavitation diagram is shown for a projectile with a slug-like fin entering water at an angle. During this process, the projectile enters the water at high speed and is subjected to a large impact load. Due to the entry angle, stress concentration zones appear on both sides of the projectile. A more refined numerical analysis method is needed to analyze this process.

[0023] This invention proposes a multi-field coupling strength analysis method applicable to high-speed water entry of cross-medium projectiles, such as... Figure 1 As shown, it mainly includes:

[0024] Step S1: Establish a flow field model with water inlet angle correction using the modified Tait equation, and solve for the fluid pressure field;

[0025] A three-dimensional projectile-in-water model was constructed, and the VOF method was used to track the evolution of the air-water interface, solving the continuity and momentum equations:

[0026]

[0027] Where α is the volume fraction of the water phase, ranging from 0 to 1; t is time; u is the flow velocity field; P is the fluid pressure field; and the fluid density ρ and viscosity μ can be obtained from a table based on the water temperature. This is the gradient operator.

[0028] To characterize the asymmetric pressure field upon oblique entry into water, the modified Tait equation is used to calculate the pressure distribution P on the projectile surface:

[0029]

[0030] In the formula, P0 is the standard atmospheric pressure, K is the bulk modulus of water, γ is an empirical constant, and ρ0 is the fluid reference density.

[0031] In the formula The kinetic energy term characterizes the effect of projectile kinetic energy on pressure; the projectile's normal velocity component V n It can be obtained from the decomposition of the measured projectile velocity V, and is expressed as:

[0032] V n =Vsinθ

[0033] The water entry angle correction coefficient β(θ) is a function of the projectile's water entry angle θ. The water entry angle θ is measured using high-speed camera images, and the time history curve of the water entry angle θ(t) is extracted through image processing. A parametric model is established in ANSYS Fluent, and the pressure distribution under different θ values ​​is compared to fit the model, resulting in an expression for the water entry angle correction coefficient β(θ). Depending on the computational requirements and accuracy, an exponential function or a polynomial function of different degrees can be used for fitting. For example, a quadratic polynomial form can be used:

[0034] β(θ)=a0+a1θ+a2θ 2

[0035] The coefficients a0, a1, and a2 were optimized using the least squares method, with the objective function being that the peak error between the simulation and the experiment is ≤5%.

[0036] The pressure gradient of the flow field can be calculated by analyzing the spatial distribution of the pressure field.

[0037]

[0038] Where x, y, and z correspond to the three coordinate directions in the three-dimensional model.

[0039] From this, we can obtain the following... Figure 3 The pressure cloud diagram shown can intuitively reflect the pressure situation of the projectile, and the results also provide data support for further analysis.

[0040] Step S2: Material setting is performed using the improved JC constitutive equation to accurately characterize the yield behavior of the material at high strain rates;

[0041] A finite element model of a tungsten alloy projectile core was established using hexahedral elements, and an improved Johnson-Cook constitutive equation was defined to characterize the dynamic yielding behavior of the projectile material under high strain rates.

[0042]

[0043] Where, σ y ε represents the dynamic yield stress, and ε represents the material strain.

[0044] Stress-strain curves were obtained through quasi-static tensile tests. The initial yield stress A, strain hardening coefficient B, and strain hardening exponent n were extracted from the elastic segment of the curve. These parameters reflect the plasticity of the material under static conditions.

[0045] Dynamic stress-strain curves were obtained through Hopkinson bar experiments. C is the strain rate sensitivity coefficient, which is fitted with a logarithmic relationship using the ratio of yield strength at different strain rates; m is the dynamic hardening exponent, determined by the slope of the hardening curve in the high strain rate range. For material strain rate, This is the material reference strain rate.

[0046] The formula innovatively introduces a strain rate threshold correction function. Defined as:

[0047]

[0048] in, The material strain rate threshold is determined through inflection point analysis of the dynamic hardening curve; 'a' is the post-threshold strengthening coefficient, determined through... The additional reinforcement slope of the segment is determined.

[0049] Among them, the normalized temperature T * The definition of is:

[0050]

[0051] Among them, T room The local room temperature (determined based on actual environmental conditions), T melt The normalized temperature T at each time step during the iterative calculation is the melting point of the material. * The formula is calculated from the current temperature T in the previous step:

[0052] T = T room +ΔT

[0053] The adiabatic temperature rise ΔT is calculated using the following integral formula:

[0054]

[0055] In the formula, β is the heat conversion coefficient of plastic work, which is calibrated by measuring the temperature rise using an infrared thermal imager; c p ρ is the specific heat capacity of the projectile material; m The density of the projectile material.

[0056] Step S3: The inverse distance weighting method is used to transfer the flow field pressure from the fluid grid to the structural grid, and dynamic response analysis is performed to obtain the projectile stress.

[0057] The inverse distance-weighted method is used to transfer flow field pressure from the fluid mesh to the structure mesh. Its core idea is that the influence of neighboring fluid cells on structure nodes decreases with increasing distance. The mapping formula is:

[0058]

[0059] In the formula: P i P is the mapped pressure value for structural node i; j The pressure value of the adjacent fluid element j is calculated using the pressure formula given in S1; r ij Let N be the distance between fluid element j and structural node i, and let N be the number of neighboring fluid elements. The selection of N requires a balance between efficiency and computational accuracy.

[0060] The mapped structural node pressure value P i The JC constitutive equation in S2, along with its coefficients, exponents, reference strain rate, strain rate threshold, and other parameters, are input into the dynamic solver. Additionally, the elastic modulus E of the projectile material needs to be initialized. By solving the dynamic equilibrium equations, the global stress σ of the structural field is obtained. global , which is the stress tensor at the node or integration point.

[0061] The local stress increment Δσ is determined by the pressure gradient in S1. Coupled calculation with model element size Δx:

[0062]

[0063] Total stress field σ total For the global stress σ global The local stress increments are superimposed on nodes:

[0064] σ total =σ global +Δσ

[0065] This allows us to obtain the stress distribution under fluid-structure interaction caused by macroscopic loads and local pressure gradient effects, such as... Figure 4 The stress contour plot shown.

[0066] Step S4: Embed a crystalline plastic finite element sub-model in the high-stress region of the projectile to further analyze the damage of the projectile material;

[0067] As the projectile enters the water, significant localized stress concentrations may occur at the projectile's head, tail fins, and sides, such as... Figure 4 The red areas in the stress cloud diagram of the projectile shown represent high-stress regions for further analysis at a fine scale. The displacement field of the high-stress region is extracted from the global model of S3 as the boundary conditions of the sub-model.

[0068] The stress loading condition is:

[0069]

[0070] Where: τα is the tangential component on the slip system; σ total The total stress tensor in S3; s α and n α These are the unit vectors representing the slip direction and the normal to the slip surface of the slip system, respectively. This represents the tensor product operation.

[0071] A grain boundary damage evolution equation is defined, which describes the damage accumulation rate through the relative relationship between the effective stress and the threshold at the grain boundary and the thermal activation mechanism. The derivative of the damage variable D with respect to time t is:

[0072]

[0073] In the formula: η and p are damage rate coefficients, calibrated through molecular dynamics simulations; R is the gas constant; T is the current temperature in S2; σ local For local stress tensor; σ this the grain boundary loss threshold, i.e., the critical strength, which is calibrated by nanoindentation experiments; Q is the grain boundary failure activation energy.

[0074] The temperature term in the JC model in S2 is corrected as follows:

[0075] T * =T * ·(1+0.5D)

[0076] Correct the material elastic modulus E required in the S3 solver:

[0077] E = E·(1-D)

[0078] By implementing the above steps and applying them to numerical simulations, a more accurate strength analysis can be achieved for high-speed water entry of projectiles: through the total stress field σ total Analyze whether plastic deformation has occurred in the projectile material. If the total stress field σ total The dynamic yield stress σ exceeds that defined in S2. y If the damage variable D is greater than or equal to 1, it is determined that the projectile material has undergone plastic deformation. The damage variable D is used to analyze whether grain boundary fracture has occurred in the high-stress area of ​​the projectile material. If the damage variable D ≥ 1, it is considered that grain boundary fracture has occurred in the high-stress area of ​​the projectile material.

[0079] Obviously, the above embodiments of the present invention are merely examples to clearly illustrate the present invention, and are not intended to limit the implementation of the present invention. For those skilled in the art, other variations or modifications can be made based on the above description. It is impossible to exhaustively list all the implementation methods here. All obvious variations or modifications derived from the technical solutions of the present invention are still within the protection scope of the present invention.

Claims

1. A multi-field coupling strength analysis method applicable to high-speed water entry of cross-medium projectiles, characterized in that, Through the total stress field Analyze whether plastic deformation has occurred in the projectile material, and analyze whether grain boundary fracture has occurred in the projectile material through damage variable D; The damage variable D is obtained by integrating the following equation: Total stress field For global stress With local stress increment Overlay by node: in: p is the damage rate coefficient, calibrated through molecular dynamics simulations; R is the gas constant; T is the current temperature in S2; For local stress tensor; The grain boundary loss threshold, i.e., the critical strength, is determined by nanoindentation experiments; Q is the grain boundary failure activation energy. If the total stress field Exceeding the dynamic yield stress If the damage variable is zero, it is determined that the projectile material has undergone plastic deformation; if the damage variable is zero, it is determined that the projectile material has undergone plastic deformation. If so, it is considered that grain boundary fracture has occurred in the projectile material; Global stress By mapping the structural node pressure values The JC constitutive equation and the corresponding parameters in the equation are input into the dynamic solver, and the elastic modulus E of the projectile material is initialized. The dynamic equilibrium equation is then solved to obtain the result. The JC constitutive equation employs a modified Johnson-Cook constitutive equation to characterize the dynamic yielding behavior of projectile materials at high strain rates: in, For dynamic yield stress, Let A be the material strain, B be the strain hardening coefficient, n be the strain hardening exponent, C be the strain rate sensitivity coefficient, and m be the dynamic hardening exponent. For material strain rate, For material reference strain rate, For normalized temperature, This is the strain rate threshold correction function. At room temperature T represents the melting point of the material, and T represents the current temperature. denoted as the material strain rate threshold, and 'a' as the post-threshold strengthening coefficient. Local stress increment Due to pressure gradient With model unit size Coupled computation: P represents the pressure distribution on the projectile surface, and x, y, and z correspond to the three coordinate directions in the three-dimensional model of the projectile entering the water. Where K is the standard atmospheric pressure and K is the bulk modulus of water. It is an empirical constant. For fluid reference density, For fluid density, This is the water entry angle correction factor, calculated based on the projectile's water entry angle. The fitting yielded the following results: This represents the normal velocity component of the projectile.

2. The multi-field coupling intensity analysis method applicable to high-speed water entry of cross-medium projectiles according to claim 1, characterized in that, Among them, the pressure value of structural nodes The flow field pressure is obtained by transferring it from the fluid mesh to the structured mesh using the inverse distance weighting method, as shown in the formula: In the formula: The mapped pressure value for structural node i; The pressure value of the neighboring fluid unit j. Let N be the distance between fluid element j and structural node i, and N be the number of neighboring fluid elements.

3. The multi-field coupling strength analysis method applicable to high-speed water entry of cross-medium projectiles according to claim 1, characterized in that, Normalized temperature The following formula is also used for correction: 。 4. The multi-field coupling strength analysis method applicable to high-speed water entry of cross-medium projectiles according to claim 1, characterized in that, The elastic modulus E of the projectile material is also corrected using the following formula: 。

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