Multi-field coupling strength analysis method suitable for high-speed water entry of cross-medium projectile

Abstract

The invention discloses a multi-field coupling strength analysis method suitable for a cross-medium projectile under a high-speed water entry condition, which comprises the following steps: establishing a flow field model with water entry angle correction, and completing pressure field solution; an improved JC constitutive equation is used for material setting, and the yield behavior of the material under the high strain rate is accurately represented; transferring the flow field pressure from the fluid grid to the structural grid by adopting an inverse distance weighting method, and performing dynamic response analysis to obtain a projectile stress condition; and a crystal plasticity finite element sub-model is embedded in a high-stress area of the projectile, and the damage condition of a projectile body material is further accurately analyzed. According to the multi-field coupling strength analysis method provided by the invention, high-speed water entry of the cross-medium projectile can be more accurately represented, and the simulation precision is improved.

Description

Technical Field

[0001] The present invention belongs to the field of cross-medium projectile entry into water strength analysis, and in particular relates to a multi-field coupling strength analysis method suitable for cross-medium projectile entry into water at high speed. Background Art

[0002] Projectiles face extremely complex multi-physics 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, leading to loss of trajectory control and preventing the projectile from reaching its intended target. Furthermore, varying angles of entry significantly impact the forces on both sides of the projectile, causing uneven forces and further increasing local stress and deformation. Therefore, it is necessary to analyze the force characteristics and strength of the projectile, taking into account the characteristics of high-speed cross-medium water entry.

[0003] Commonly used numerical simulation methods lack an analysis method for such high-speed cross-medium situations, resulting in the inability to conduct a detailed and targeted analysis of the high-speed water entry process of a cross-medium projectile. Therefore, a strength analysis method that considers instantaneous high-pressure conditions is needed to accurately characterize the above process by coupling different physical fields. Summary of the Invention

[0004] The purpose of the present invention is to provide a multi-field coupling strength analysis method suitable for the case of a cross-medium projectile entering water at high speed, so as to more accurately simulate the complex multi-physical field coupling problem in the process.

[0005] The technical solutions for achieving the purpose of the present invention are:

[0006] A multi-field coupling strength analysis method suitable for high-speed water entry of cross-medium projectiles is proposed. total Analyze whether the projectile material has undergone plastic deformation, and analyze whether the projectile material has undergone grain boundary fracture through the damage variable D;

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

[0008]

[0009] Total stress field σ total is the global stress σ global Superposition with local stress increment Δσ at each node:

[0010] σ total =σ global +Δσ

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

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

[0013] Compared with the prior art, the present invention has the following significant advantages:

[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 specifically characterized.

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

[0016] (3) A multi-field coupling analysis method is proposed to synergistically analyze the grain boundary damage model and the fluid-solid coupling process of the projectile entering the water, thereby improving the analysis accuracy. At the same time, the inverse distance weighted method is used to transfer the flow field load, which can improve the computational efficiency to a certain extent. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 This is a step diagram of the method for analyzing the multi-field coupling strength of a cross-medium projectile entering water at high speed according to the present invention.

[0018] Figure 2 Schematic diagram of the cavitation flow field of a high-speed water entry projectile across a medium.

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

[0020] Figure 4 This is the stress cloud diagram of the projectile body when it enters water at high speed through the medium. DETAILED DESCRIPTION

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

[0022] Figure 2This example shows a cavitation diagram of a projectile with a flap entering water at an oblique angle. During this process, the projectile enters the water at high speed, subjecting it to significant impact loads. Due to the angle of entry, stress concentration areas appear on both sides of the projectile. A more refined numerical analysis method is required for this process.

[0023] The present invention proposes a multi-field coupling strength analysis method suitable for the case of a cross-medium projectile entering water at high speed. Figure 1 As shown, it mainly includes:

[0024] Step S1: Using the modified Tait equation to establish a flow field model with water entry angle correction, and solve the fluid pressure field;

[0025] A three-dimensional projectile entry into water model was constructed, and the VOF method was used to track the evolution of the air-water interface and solve the continuity equation and momentum equation:

[0026]

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

[0028] In order to characterize the asymmetric pressure field of oblique water entry, the modified Tait equation is used to calculate the surface pressure distribution P of the projectile:

[0029]

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

[0031] In the formula is the kinetic energy term, which can characterize the effect of the projectile kinetic energy on the pressure. The normal velocity component V n It can be decomposed from the measured projectile velocity V and 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. This angle is measured using high-speed camera images, and the time history of the 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 obtain an expression for the water entry angle correction coefficient β(θ) through fitting. Depending on the computational requirements and accuracy, exponential functions or polynomial functions of varying degrees can be used for fitting. For example, a quadratic polynomial is used:

[0034] β(θ)=a0+a1θ+a2θ 2

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

[0036] The flow field pressure gradient can be calculated through the spatial distribution of the pressure field

[0037]

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

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

[0040] Step S2: Use the improved JC constitutive equation to set the material and accurately characterize the yield behavior of the material at high strain rates;

[0041] The finite element model of the tungsten alloy core is established using hexahedral elements, and the improved Johnson-Cook constitutive equation is defined to characterize the dynamic yield behavior of the projectile material at high strain rates:

[0042]

[0043] Among them, σ y is the dynamic yield stress and ε is the material strain.

[0044] The stress-strain curve is obtained through quasi-static tensile test, and the initial yield stress A, strain hardening coefficient B and strain hardening exponent n are extracted from the elastic section of the curve. The above parameters reflect the plastic properties of the material under static conditions.

[0045] Dynamic stress-strain curves were obtained from Hopkinson bar experiments. C is the strain rate sensitivity coefficient, which is obtained by fitting a logarithmic relationship between the yield strength ratios at different strain rates. m is the dynamic hardening exponent, which is determined by the slope of the hardening curve at high strain rates. is the material strain rate, is the material reference strain rate.

[0046] The strain rate threshold correction function is innovatively introduced in the formula Defined as:

[0047]

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

[0049] Among them, the normalized temperature T * is defined as:

[0050]

[0051] Among them, T room is the local room temperature (determined according to the actual environment), T melt is the melting point of the material. During the iterative calculation process, the normalized temperature T of each time step is * Calculated from the current temperature T in the previous step, the formula is:

[0052] T=T room +ΔT

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

[0054]

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

[0056] Step S3: using the inverse distance weighted method to transfer the flow field pressure from the fluid grid to the structural grid, and performing dynamic response analysis to obtain the projectile stress condition;

[0057] The inverse distance weighted method is used to transfer the flow field pressure from the fluid grid to the structural grid. The core idea is that the influence of adjacent fluid units on the structural nodes decays as the distance increases. The mapping formula is:

[0058]

[0059] Where: P i is the mapped pressure value of the structural node i; P j is the pressure value of the adjacent fluid unit j, which is calculated using the pressure formula given in S1; r ij is the distance between fluid unit j and structural node i, and N is the number of adjacent fluid units. Its selection needs to balance efficiency and calculation accuracy.

[0060] The mapped structural node pressure value P i The JC constitutive equation in S2 and the parameters such as coefficients, exponents, reference strain rate, strain rate threshold, etc. contained in the equation are input into the dynamic solver. In addition, the elastic modulus E of the projectile material needs to be initialized. By solving the dynamic equilibrium equation, the global stress σ of the structural field is obtained. global , which is the stress tensor at a 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 is the global stress σ global Superimposed with local stress increments per node:

[0064] σ total =σ global +Δσ

[0065] From this, we can obtain the stress distribution under the macro load and local pressure gradient effect of fluid-solid coupling, such as Figure 4 The stress cloud diagram is shown.

[0066] Step S4: embedding a crystal plasticity finite element sub-model in the high stress area of ​​the projectile to further accurately analyze the damage of the projectile material;

[0067] As the water entry process progresses, obvious local stress concentration may occur at the head, tail and sides of the projectile, such as Figure 4 The red part of the stress contour of the projectile is shown. These high stress areas can be further analyzed at the microscopic scale. The displacement field of the high stress area is extracted from the global model of S3 as the boundary condition of the sub-model.

[0068] The stress loading conditions are:

[0069]

[0070] Where: τα is the tangential component of the slip system; σ total is the total stress tensor in S3; s α and n α are the unit vectors of the slip direction of the slip system and the normal to the slip plane, respectively; Represents a tensor product operation.

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

[0072]

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

[0074] Correct the temperature term of the JC model in S2:

[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 of a projectile entering water at high speed can be achieved: total Analyze whether the elastic material has plastic deformation. If the total stress field σ total Exceeds the dynamic yield stress σ defined in S2 y , it is determined that plastic deformation has occurred in the projectile material; the damage variable D is used to analyze whether grain boundary fracture has occurred in the material of the high stress area of ​​the projectile. If the damage variable D ≥ 1, it is considered that grain boundary fracture has occurred in the material of the high stress area of ​​the projectile.

[0079] Obviously, the above embodiments of the present invention are only examples to clearly illustrate the present invention, and are not limitations on the implementation methods of the present invention. For ordinary technicians in the field, other different forms of changes or modifications can be made based on the above description. It is impossible to list all the implementation methods here. All obvious changes or modifications derived from the technical solution of the present invention are still within the scope of protection of the present invention.

Claims

1. A multi-field coupling strength analysis method suitable for the case of a cross-medium projectile entering water at high speed, characterized by: Through the total stress field σ total Analyze whether the projectile material has undergone plastic deformation, and analyze whether the projectile material has undergone grain boundary fracture through the damage variable D; The damage variable D is obtained by integrating the following formula: Total stress field σ total is the global stress σ global Superposition with local stress increment Δσ at each node: s total =s global +Ds Where: η and p are damage rate coefficients, calibrated by molecular dynamics simulation; R is the gas constant; T is the current temperature in S2; σ local is the local stress tensor; σ th is the grain boundary loss threshold, i.e., critical strength, calibrated by nanoindentation experiments; Q is the activation energy of grain boundary failure; If the total stress field σ total Exceeding the dynamic yield stress σ y , it is determined that the projectile material has undergone plastic deformation; if the damage variable D≥1, it is considered that the projectile material has undergone grain boundary fracture.

2. The multi-field coupling strength analysis method for a cross-medium projectile entering water at high speed according to claim 1 is characterized in that: Global stress σ global By mapping the structural node pressure value P i 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 to solve the dynamic equilibrium equation.

3. The multi-field coupling strength analysis method applicable to the case of a cross-medium projectile entering water at high speed according to claim 1, characterized in that: The structural node pressure value P i The flow field pressure is transferred from the fluid grid to the structure grid using the inverse distance weighted method. The formula is: Where: P i is the mapped pressure value of the structural node i; P j is the pressure value of the adjacent fluid unit j, r ij is the distance between fluid unit j and structural node i, and N is the number of adjacent fluid units.

4. The multi-field coupling strength analysis method applicable to the case of a cross-medium projectile entering water at high speed according to claim 2, characterized in that: The JC constitutive equation uses the modified Johnson-Cook constitutive equation to characterize the dynamic yield behavior of elastomeric materials at high strain rates: Among them, σ y is the dynamic yield stress, ε is the material strain, A is the initial yield stress, B is the strain hardening coefficient, n is the strain hardening exponent, C is the strain rate sensitivity coefficient, m is the dynamic hardening exponent, is the material strain rate, is the material reference strain rate, T * is the normalized temperature, is the strain rate threshold correction function, T room is room temperature, T melt is the melting point of the material, T is the current temperature, is the material strain rate threshold, and a is the strengthening coefficient after the threshold.

5. The multi-field coupling strength analysis method applicable to the case of a cross-medium projectile entering water at high speed according to claim 4, characterized in that: Normalized temperature T * The following correction is also used: T * =T * ·(1+0.5D).

6. The multi-field coupling strength analysis method applicable to the case of a cross-medium projectile entering water at high speed according to claim 2, characterized in that: The elastic modulus E of the elastomeric material is also corrected using the following formula: E=E·(1-D).

7. The multi-field coupling strength analysis method applicable to the case of a cross-medium projectile entering water at high speed according to claim 1, characterized in that: The local stress increment Δσ is determined by the pressure gradient Coupled calculation with model element size Δx: P is the surface pressure distribution of the projectile, x, y, and z correspond to the three coordinate directions in the three-dimensional model of the projectile entering the water, P0 is the standard atmospheric pressure, K is the bulk modulus of the water body, γ is the empirical constant, ρ0 is the fluid reference density, ρ is the fluid density, β(θ) is the water entry angle correction coefficient, which is obtained by fitting the projectile entry angle θ, and V n is the normal velocity component of the projectile.

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