CN111785331B - Multi-scale continuous calculation method for solving microscopic mechanical properties of energetic material - Google Patents
Multi-scale continuous calculation method for solving microscopic mechanical properties of energetic material Download PDFInfo
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Abstract
The invention discloses a multi-scale continuous calculation method for solving the microscopic mechanical property of an energetic material, which comprises the following steps: respectively carrying out molecular dynamics simulation and coarse graining molecular dynamics simulation on explosive crystal components and polymer binder components in the PBX; converting a real PBX structure into a random circular particle digital model by an effective approximation method; key parameters from microscopic scale to microscopic scale are linked; calculating the mechanical properties of the PBX particles under the microscopic scale, establishing a representative volume meta-model of the PBX by adopting an object point method on the microscopic scale, researching the mechanical behavior of the PBX under uniaxial compression to obtain the elastic modulus and state equation parameters of the PBX, and inputting the elastic modulus and state equation parameters as parameters into a macroscopic-scale continuum for calculation. The invention realizes a composite energetic material trans-scale continuous calculation method based on theoretical calculation completely from microcosmic scale to microscopic scale and from single component to compound, and has important guiding significance for the safety design of explosive.
Description
Technical Field
The invention belongs to the field of energetic materials and computer simulation, and particularly relates to a simulation method for solving microscopic-microscopic hierarchical multi-scale continuous calculation of the microscopic mechanical properties of an energetic material.
Background
With the development of computer technology and simulation methods, theoretical simulation has become an important means for understanding material properties. Because the structure and the property of the material on different scales are different, corresponding material calculation methods are corresponding to research objects with different time and space scale characteristics. However, these single-scale simulation methods have shortcomings in simulating materials with trans-scale properties, for example, microscopic simulation methods can well describe atomic or molecular properties of materials, but cannot accurately solve macroscopic properties of continuous materials; macroscopic simulation method algorithm and softwareThe method is simple and convenient for perfecting and solving, but the accuracy of the result depends on factors of grid division size to a great extent and interaction of material interfaces cannot be reflected. There is therefore a need to develop new simulation methods to solve the problem of cross-scale computation, i.e. multi-scale methods. The multi-scale simulation refers to comprehensive application of various theoretical models, comprehensive study is carried out on the properties of the system from microscopic to macroscopic, and the multi-scale simulation is widely applied to the fields of biology, materials, chemistry, engineering and the like until the proposal of the method [1-3] 。
Currently, polymer-bonded explosives (Polymer Bonded Explosive, PBX), which are widely used in the field of energetic materials, are a typical particle-highly filled composite material formed by processing high explosive particles and high molecular polymers, as well as other additives. The PBX has a complex microscopic structure, the macroscopic mechanical property of the PBX is influenced by the microscopic structure, and compared with a single-component material, the PBX has the characteristics of non-uniformity, discontinuity, anisotropy and the like, and the microscopic mechanical property of the PBX is extremely complex. In addition, the explosive relates to dangerous environments such as ignition, detonation and the like in the using process, the cost and risk of preparing experiment research on the PBX are high, and the experiment cost and risk are greatly reduced by using a computer to simulate and assist in designing and guiding the formula design and production process of the PBX. Therefore, the establishment of the cross-scale method for accurately predicting the mechanical properties of the PBX in the external loading environment has important significance.
As for research methods, the previous research on composite materials is mostly carried out under a single time and space scale, and limitations exist in terms of ensuring the calculation efficiency and the simulation accuracy; while microscale (mesoscale) simulation is not uncommon between the macroscopic and microscopic scales, for heterogeneous composites, the internal boundary effects caused by the microstructure cause differences in properties from those of the individual components, which are reflected on the microscale and are closely related to the particle characteristics and particle size distribution of the components in the composite, the mechanical, thermodynamic and chemical properties of the composite are directly related to the physical and chemical processes at the microscale [4,5] Thus, studying the structure and properties of a complex at a microscopic scale is of great importance for understanding its macroscopic properties.
Through analysis of domestic and foreign documents, the microscopic scale simulation aiming at the interface performance among different components of the energy-containing composite material is not found in the current multi-scale simulation method, and the prior patent is provided [6] A multi-scale calculation method for equivalent heat conduction coefficient of complex composite material structure is provided, the patent establishes a microscopic-macroscopic three-scale model to solve the equivalent performance of the material, but the patent establishes a single-cell model of the composite material on a microscopic scale, and interfacial interaction among components of the composite material is not involved, so that the model is not applicable to composites with larger component property differences. The composite material is PBX, wherein the mechanical properties of the explosive crystal material and the polymer have large differences, and the single component property and interface interaction of the explosive crystal material and the polymer must be considered. The accurate interface performance is guaranteed to obtain a reasonable macroscopic simulation result, so that the microscopic scale simulation taking the interface effect into consideration is required to be used as a connecting bridge, and the microscopic-microscopic hierarchical multi-scale simulation from microscopic scale single-component calculation to microscopic scale composite material calculation is realized, so that the calculation result of the microscopic scale composite material can provide reliable parameters for macroscopic scale continuum calculation.
Reference to the literature
[1]Sodhani D,Reese S,S,et al.Multi-scale modelling and simulation of a highly deformable embedded biomedical textile mesh composite[J].Composites Part B Engineering,2018,143:113-131.
[2]K,Geers M G D,Kouznetsova V G,et al.A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials[J].Journal of Computational Physics,2016,330(C):192-220.
[3]Amaro R E,Mulholland A J,et al.Multiscale methods in drug design bridge chemical and biological complexity in the search for cures[J].Nature Reviews Chemistry,2018,2(4):0148.
[4]Wehrkamp-Richter T,De Carvalho N V,Pinho S T.A meso-scale simulation framework for predicting the mechanical response of triaxial braided composites[J].Composites Part A:Applied Science and Manufacturing,2018,107:489-506.
[5]Dinh T D,Garoz D,Hajikazemi M,et al.Mesoscale analysis of ply-cracked composite laminates under in-plane and flexural thermo-mechanical loading[J].Composites Science and Technology,2019,175:111-121.
[6] Zhang Rui, wen Lihua, shang Ze, etc. A multi-scale calculation method for equivalent heat conductivity coefficient of complex composite material structure is described in China, CN 107451308[ B ].2020.06.16.
Disclosure of Invention
The present invention is directed to solving the above problems of the prior art. A multi-scale continuous calculation method for solving the microscopic mechanical property of an energetic material is provided. The technical scheme of the invention is as follows:
a multi-scale continuous calculation method for solving the microscopic mechanical property of an energetic material comprises the following steps:
step 1, performing molecular dynamics simulation on high-energy crystal explosive in PBX, wherein the molecular dynamics simulation comprises the following steps: constructing a super cell model of the explosive crystal by taking crystal data obtained by neutron diffraction as a basis, solving the mechanical property of the crystal by using molecular dynamics simulation software, and deducing state equation parameters of the crystal under the high pressure condition according to the pressure-volume relation;
step 2, carrying out coarse grain molecular dynamics simulation on the polymer binder in the PBX: establishing a state equation and mechanical properties of the fluoropolymer by adopting a coarse grain molecular dynamics method;
step 3, establishing a particle digital model of the microscale composite material: firstly, carrying out digital processing based on a real micro-structure of a PBX, wherein PBX particles in the micro-structure consist of high-energy explosive crystals and polymers in the steps 1 and 2; secondly, homogenizing and approximating the polymer bonding; finally, adopting an approximate method that random circles are not overlapped with each other, and generating a PBX particle filling model with random distribution of positions and particle sizes in a sealed mold;
step 4, key parameter linking from microscopic scale to microscopic scale: inputting mechanical modulus and state equation parameters of an explosive crystal and a polymer binder which are obtained through micro-scale MD simulation as single component property parameters into simulation calculation of a representative volume element model, establishing interface parameters and a multiphase material contact algorithm between different components, and considering interaction of particles, polymers and polymers;
step 5, calculating the mechanical properties of the PBX under the microscopic scale: and under the microscopic scale, adopting an object point method, taking RVE of the PBX as a calculation model, researching the microscopic mechanical behavior and deformation process of the PBX under the external loading condition, and fitting the constitutive relation and state equation of the PBX.
Further, the step 1 performs molecular dynamics simulation on the high-energy crystal explosive in the PBX, specifically: constructing a super cell model (see figure 1) of the explosive crystal by taking crystal data obtained by neutron diffraction as a basis, solving the mechanical property of the crystal by using molecular dynamics simulation software, and deducing state equation parameters of the crystal under high pressure according to the pressure-volume relationship;
and performing structural relaxation on a super cell model of the crystal by using LAMMPS software to obtain a stable structure, performing uniaxial tension deformation under the NPT ensemble at a constant strain rate, wherein the initial temperature is 300K, analyzing the elastic constant and stress-strain relation of the crystal in the compression process, and calculating other mechanical parameters such as the elastic modulus and the like through the elastic constant. Pseudo particle velocity (u) p ) And pseudo impact velocity (u) s ) The relationship with the pressure-volume data is as follows:
u p and u s There is a linear fit relationship between:
u s ＝su p +c (3)
the parameters c and s of the Mie-Groneisen equation of state (relation (4)) can be fitted by relation (3), whereGamma is the volume ratio 0 ≈2s-1。
Further, step 2 performs coarse grain molecular dynamics simulation on the polymer binder in the PBX: establishing a state equation and mechanical properties of the fluoropolymer by adopting a coarse grain molecular dynamics method;
and (3) establishing a total atom simulation system of the polymer chain, coarsening a plurality of unit structures of the polymer chain into different types of beads according to a coarsening mapping scheme (see figure 2), calculating radial distribution functions among the beads in coarse grain force field calculation software Magic, and expanding the radial distribution functions by adopting Boltzmann inversion iteration to obtain a coarse grain force field file of the polymer. Writing the force field file into a simulation input file, and performing isothermal compression simulation of the NPT ensemble in the LAMMPS software to obtain the relation between the elastic constant and the pressure-volume.
The pressure-volume data of the fluoropolymer was fitted using two state equations, tait and Sun, the relationship of which is as follows:
tait state equation:
sun state equation:
wherein C, m and n are constants for most polymer systems, so the parameters to be fitted are B 0 。
Further, the step 3 establishes a particle digital model of the fine-scale composite material: firstly, carrying out digital processing based on a real micro-structure of a PBX, namely after edge contour extraction is carried out on PBX particles, dividing an image of the PBX into a plurality of pixel small areas, and after the quantization processing, representing gray values of all areas by integers to form digital images with particles with different sizes; secondly, homogenizing approximation treatment of the polymer bond, namely, classifying crystal particles with extremely small size into a polymer matrix in calculation, and representing the polymer bond by using a homogenized viscoelasticity matrix; and finally, approximating the PBX particles into circular particles by adopting an approximation method that random circles are not overlapped with each other, and generating a PBX particle filling model with random distribution of particle sizes at the position of a sealed mould according to the principle that the particles are not intersected, are not overlapped with each other and are not included with each other.
Further, in the step 4, the mechanical modulus and the state equation parameters of the explosive crystal and the polymer binder obtained by the micro-scale MD simulation are input as single component property parameters into the simulation calculation of a representative volume meta-model, the representative volume meta-model is shown in fig. 4, the model is composed of a plurality of PBX particles and pores which are randomly distributed, and the PBX particles are represented by polymer coated crystal particles. Interfacial frictional interactions are also considered in the model and interface parameters between the different components are established, such as the coefficient of friction between the polymer-binder, etc.
Further, the step 4 of the multiphase material contact algorithm comprises the following steps: assuming two materials, a and b, respectively, the momentum change imposed on material a needs to be calculated first, as follows:
wherein Δp i,a Representing the change in momentum of material a, p i,a 、p i,b Representing the movements of material a and material b, respectivelyQuantity, m i,a And m i,b Representing the mass of material a and material b, respectively; centroid speed of grid node Is the sum of the masses of all grid nodes, and subscripts i and j respectively represent the grid nodes and the material types, p i,j 、m i,j 、v i,j Corresponding to the momentum, mass and velocity of the different material types at the grid nodes, respectively. For material b, its momentum changes Δp i,b ＝-Δp i,a 。
Relative sliding velocity Deltav between materials a and b i In connection with the change of momentum:
wherein m is i,red Mass reduced for node i, m i,red ＝m i,a m i,b /(m i,a +m i,b ) The momentum solving formula after the change is as follows:
where N is the normal pressure of the contact surface, S stick Is a traction force that resists frictional sliding of the interface,and->Direction vectors normal and tangential, respectively, A c And Deltat are respectively contactsArea and time variations. In this algorithm, the condition that the material has a contact interface is +.>
In order to achieve the friction effect of the interface, it is necessary to calculate the tangential traction of the sliding friction, namely:
S stick ＝f(N,A c ,Δv′ i ,....) (9)
wherein f (N, A) c ,Δv′ i ,..) may be any law of friction, which may depend on various parameters such as normal pressure, contact area, relative sliding speed, in point of matter calculations the background grid will calculate interactions between different materials according to the set law of material contact.
Further, the mechanical properties of the PBX under the microscopic scale in the step 5 are calculated: adopting an object point method under a microscopic scale, taking RVE of the PBX as a calculation model, researching microscopic mechanical behavior and deformation process of the PBX under external loading condition, and fitting constitutive relation and state equation of the PBX, wherein
The object point method (Material Point Method, MPM) is a particle-based grid-less computing method that is easier to handle in terms of intrinsic boundary conditions and deformation contacts, in which the sample is represented by a set of discrete "material points" and each particle is assigned mass, coordinates, velocity, etc. properties. The basic calculation principle of MPM is as follows: assuming that the state of the particles at the beginning is known, the mass (m) of the particles is calculated using equation (10), external force (f ext ) And speed (v) is transferred to the mesh node:
wherein subscript i represents a grid node and p represents a particle; s is S ip Is a deformation function of the grid node at particle p. Subsequently using grid node velocity v i Calculating a velocity gradient at each particle
Wherein G is ip Is the gradient of the deformation function of the mesh node at particle p.
Internal force of grid node (f i int ) The calculation formula is as follows:
middle sigma p And V p Stress and volume of the particle, respectively.
In each time step of the simulation, all particle information is mapped to the background grid node, the information of the mass, the speed, the force and the like of the node is updated by using a formula (10-15), and then the calculation results are returned to the particles through the mapping relation. At the beginning of the next time step, the above calculation process is repeated until the specified time or condition is completed, thereby completing the solution of the actual problem.
The mechanical properties of the PBX mainly calculate the elastic modulus: first, the Young's modulus (E) and Poisson's ratio (μ) of the PBX need to be calculated. E is the slope of the stress (sigma) -strain (epsilon) curve at the elastic stage, i.eMu is the transverse strain (. Epsilon.) of uniaxial compression xx ) And longitudinal strain (. Epsilon.) yy ) Ratio of (2), i.e.)>The shear modulus (G) and bulk modulus (K) of PBX are calculated as follows:
the pressure-volume relationship of the PBX is described by the Mie-Groneisen state equation, the formula is as follows:
the invention has the advantages and beneficial effects as follows:
(1) The composite material representative volume element model established under the microscopic scale can be used for researching the mechanism of complex processes such as hot spot and detonation impact of the PBX by observing the deformation process, stress and temperature distribution of the PBX under the microscopic scale.
(2) The microcosmic-mesoscopic multi-scale continuous calculation method for the mesoscopic mechanical property and the state equation of the PBX of the energetic material is provided, and has important guiding significance for researching the design of the mechanical property of the PBX under extreme environments such as ignition, explosion and the like in experiments.
(3) The interfacial interaction between different components is considered in the calculation of the microscale, so that the microscale boundary effect of the material can be reflected, and the calculation result of the microscale is more accurate.
(4) The system starts from the microstructure of the molecule, uses different mathematical models and time and space scales on different levels, and the parameters required by high-level mechanical property calculation in the calculation system can be determined by low-level simulation experiment, so that the macroscopic physical and mechanical properties of the energy are calculated step by step in a recursive manner.
(5) The micro-scale polymer calculation adopts system coarse-grained molecular dynamics simulation, so that the necessary chemical structure is reserved, the degree of freedom of the system is reduced, and the chemical structure of the composite material can be described in a wider time scale and a larger volume scale.
(6) By a multiscale method of microcosmic-mesoscopic continuous calculation, a research model of a trans-scale multiphase mixture from small scale (microcosmic) to large scale (mesoscopic) from single component to composite material is established, and the model has obvious advantages when processing the mechanical properties of the composite material with larger difference of multi-component mechanical properties.
Drawings
FIG. 1 is a schematic representation of a TATB supercell model built from molecular dynamics modeling in accordance with a preferred embodiment of the present invention.
FIG. 2 is a polymer binder F 2314 Is a coarse graining scheme of (a).
Fig. 3 is a representative volume metamodel of a microscale PBX.
Fig. 4 shows the change in temperature field during uniaxial compression of the PBX.
Fig. 5 is a graph showing the change in longitudinal stress field during PBX uniaxial compression.
Fig. 6 is a graph showing the stress-strain relationship of PBX under different porosity models.
FIG. 7 is a graph of pressure-to-volume ratio of PBX for different porosity models;
fig. 8 is a flow chart of a method of a preferred embodiment of the present invention.
Table 1 shows the elastic constants and elastic moduli of the TATB super cells
Table 2 shows the fitting parameters of the TATB state equation
Table 3 shows the polymer binder F 2314 Tait and Sun equation parameters simulating data fitting
Table 4 shows binder F 2314 Mechanical property parameter of (2)
Table 5 shows the mechanical properties of PBX at three different porosities
Table 6 shows the results of the parameter fitting of the PBX state equation at different porosities
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and specifically described below with reference to the drawings in the embodiments of the present invention. The described embodiments are only a few embodiments of the present invention.
The technical scheme for solving the technical problems is as follows:
referring to fig. 8, a simulation method for solving microscopic-microscopic hierarchical multiscale continuous calculation of the microscopic mechanical properties of an energetic material PBX according to the present invention comprises the following steps:
step 1, performing molecular dynamics simulation (Molecular Dynamics, MD) on the high-energy crystal explosive in the PBX: based on crystal data obtained by neutron diffraction, a super cell model of the explosive crystal is built, mechanical properties such as elastic modulus of the crystal are solved by using molecular dynamics simulation software, and state equation parameters of the crystal under high pressure conditions are deduced according to pressure-volume relations.
Step 2, carrying out coarse grain molecular dynamics simulation on the polymer binder in the PBX: because the problems that the complex space topological structure, the long-time relaxation behavior and the actual strain rate of the MD simulated mechanical behavior of the polymer are far higher than an experimental value are considered, a coarse grain molecular dynamics method is adopted, and a state equation and mechanical properties of the fluoropolymer are solved by establishing a coarse grain force field.
Step 3, establishing a particle digital model of the microscale composite material: firstly, based on a real micro-structure of a PBX, the particles of the explosive are in different shapes after being subjected to digital two-dimensional image processing, and in order to facilitate modeling and calculation, the particles with different sizes are represented by circles with different diameters by adopting a circular particle effective approximation method. Secondly, homogenizing treatment of the polymer, namely classifying explosive crystal particles with extremely small particle diameters in a system into the polymer to perform material property homogenization, and coating the surfaces of the explosive crystal particles after polymer homogenization approximation. And finally, approximating the PBX particles into circular particles by adopting an approximation method that random circles are not overlapped with each other, and generating a PBX particle filling model with random distribution of particle sizes at the position of a sealed mould according to the principle that the particles are not intersected, are not overlapped with each other and are not included with each other.
Step 4, key parameter linking from microscopic scale to microscopic scale: in the microscopic scale, component proportion, particle size distribution and the like of explosive crystals and binders are considered to establish a representative volume element (Representative Volume Element, RVE) capable of reflecting a real structure, mechanical modulus and state equation parameters of the explosive crystals and the polymer binders which are obtained through microscopic scale MD simulation are input into simulation calculation of a representative volume element model as single component property parameters, interface parameters and multiphase material contact algorithm among different components are established, and interaction of particles-particles, particles-polymers and polymers-polymers is considered.
Step 5, calculating the mechanical properties of the PBX under the microscopic scale: and under the microscopic scale, adopting a mass point method (Material Point Method, MPM), taking RVE of the PBX as a calculation model, researching the microscopic mechanical behavior and deformation process of the PBX under the external loading condition, fitting the constitutive relation and state equation of the PBX, and laying a foundation for calculating macroscopic properties.
The following description will take a polymer bonded explosive (PBX) as an example, which is prepared from crystalline explosive, trinitrobenzene (TATB) and binder F 2314 And (3) a composite explosive.
101. First, a super cell model is constructed based on neutron diffraction crystal data of TATB crystals, and the calculation model is shown in figure 1.
102. In a large-scale atomic molecular parallel simulator, LAMMPS package, a TATB supercell model is placed in a periodic box of periodic boundary conditions, and a COMPASS force field is used to minimize energy to the supercell model to obtain a stable conformation.
103. And carrying out uniaxial deformation MD simulation on the stable structure of the TATB super cell under the NPT ensemble, analyzing a simulation track file to obtain a stress-strain curve and an elastic constant of the TATB, and fitting the elastic modulus of the TATB according to the stress-strain curve, wherein the elastic modulus is shown in Table 1.
TABLE 1 MD simulation results of elastic constant and elastic modulus of TATB ultrasonic cell
104. And applying a series of pressures to the stable structure of the TATB super cell under the NPT ensemble, performing isothermal compression MD simulation, analyzing a simulation track file to obtain a pressure-volume relation curve of the TATB, deducing a Hugonot equation of impact according to the curve, and further fitting Mie-Groneisen equation of state parameters of the TATB, wherein the parameters are shown in Table 2.
TABLE 2 TATB state equation fitting parameters
201. According to the system coarse-grain mapping method, a plurality of atoms or atomic groups in a polymer all-atom system are regarded as coarse-grain beads, the degree of freedom of molecules is reduced, and the polymer F 2314 Is a random copolymer of vinylidene fluoride and chlorotrifluoroethylene mixed in a ratio of 1:4, and the coarse-grained mapping scheme of the polymer is shown in figure 2.
202. The target distribution function of the coarsening beads is obtained from a total atom simulation by means of a coarsening mapping scheme, whereby the bond formation (bond length, bond angle, dihedral angle) and non-bond formation potential between the coarsening beads are obtained.
203. Further correcting the coarse graining force field by adopting a Boltzmann inversion iterative method (Inverse Boltzmann Iteration, IBI) method in the system coarse graining method to ensure that the bead distribution of coarse graining simulation and full atomic simulation is the same, finally obtaining a particle radial distribution function of bond-forming and non-bond-forming action potentials, and constructing a coarse graining potential table (i.e. coarse graining force field).
204. Coarse grain molecular dynamics simulation (Coarse Grain Molecular Dynamics, CGMD) was performed in MD simulation software using a coarse grain mapping model and a coarse grain force field to calculate the state equation and elastic modulus of the polymeric binder, see tables 3 and 4.
TABLE 3 based on Polymer F 2314 Tait and Sun equation parameters simulating data fitting
Table 4F 2314 Mechanical property parameter
| Modulus parameter | F 2314 |
| Bulk modulus K/GPa | 3.952 |
| Shear modulus G/GPa | 1.756 |
| Young's modulus E/GPa | 4.588 |
301. According to the round particle approximation, polymer homogenization treatment, a random particle filling method is adopted to build a particle digital model of the micro-scale PBX, and a polymer F in the model 2314 Coating on the surface of TATB particles, TATB and F 2314 Wherein the mass ratio of TATB is 95:5, the particle size of TATB is 10-100 mu m, the particle size accords with normal distribution, and F 2314 The coating thickness is 0.3-3 mu m. FIG. 4 shows a representative volume metamodel of a microscale PBX with particles placed in a rigid mold with some voids between particles, TATB and F 2314 Taking into account interfacial interactions, in the simulation by the upper partThe ram of the boundary applies an external load.
401. Material property descriptions of PBX single components the components of the PBX are described in the model created at 301 using different state equations and constitutive relationships.
TATB particles were described using an elastoplastic model and Mie-Groneisen's equation of state. The stress of the elastoplastic material model is expressed as:
wherein sigma is stress, sigma 0 The initial yield stress is expressed in MPa;for strain rate, C and P are Cowper-Symond strain rate parameters, ε P eff Is effective plastic strain, E P Is the plastic hardening modulus, beta is the hardening parameter.
The Mie-Gruneisen state equation is:
wherein P is pressure;ρ 0 for bulk density, i.e. mass of particles per unit volume, V 0 Is the initial state volume; c is sound velocity at normal temperature and normal pressure; gamma ray 0 Is Grunessen constant; s is the slope of the shock wave velocity-particle velocity curve.
Polymer F 2314 The description of the viscoelastic constitutive model and Sun state equation is given in Prony series form. The constitutive model of the viscoelastic material in Prony series form is expressed as:
wherein σ is stress; g (t) is a shear relaxation function; k (t) is a volume relaxation function;is a shear strain offset,Is the volume strain offset; t is the current time, τ is the relaxation time, and I is the unit tensor.
Description F 2314 The Sun state equation of (2) is:
wherein V is 0 The initial state volume and V the equilibrium state volume. For polymer systems, the values of parameters n and m are typically 6.14 and 1.16, respectively. Parameter B 0 Representing the bulk modulus at zero pressure.
402. TATB and F 2314 The material property parameters of (2) are respectively from the micro-scale molecular dynamics simulation results of 104 and 204, and the result calculation is used as a key parameter to be input into the micro-scale simulation calculation.
403. The component ratio, particle size distribution, etc. have been considered in the case of the PBX-representing volume element model established at 301, but TATB and F 2314 The mechanical properties are greatly different, so that the interface effect between two materials needs to be considered in the mesoscopic simulation, and the invention considers TATB and F 2314 In the MPM multi-material contact algorithm, each material has a respective mapping speed field, whether the materials are in a contact state or not is judged through the speed field of the node, and if the materials are in the contact state, the momentum and the external force of the node are required to be modified to realize the modeling of the interface interaction, wherein the specific algorithm is as follows:
assuming two materials, a and b, respectively, the momentum change imposed on material a needs to be calculated first, as follows:
wherein Δp i,a Representing the change in momentum of material a, p i,a 、p i,b Respectively represent the momentum of material a and material b, m i,a And m i,b Representing the mass of material a and material b, respectively; centroid speed of grid node Is the sum of the masses of all grid nodes, and subscripts i and j respectively represent the grid nodes and the material types, p i,j 、m i,j 、v i,j Corresponding to the momentum, mass and velocity of the different material types at the grid nodes, respectively. For material b, its momentum changes Δp i,b ＝-Δp i,a 。
Relative sliding velocity Deltav between materials a and b i In connection with the change of momentum:
wherein m is i,red Mass reduced for node i, m i,red ＝m i,a m i,b /(m i,a +m i,b ) The momentum solving formula after the change is as follows:
/>
where N is the normal pressure of the contact surface, S stick Is a traction force that resists frictional sliding of the interface,and->Direction vectors normal and tangential, respectively, A c And Δt are the contact area and time variation, respectively. In this algorithm, the condition that the material has a contact interface is +.>
In order to achieve the friction effect of the interface, it is necessary to calculate the tangential traction of the sliding friction, namely:
S stick ＝f(N,A c ,Δv′ i ,....) (9)
wherein f (N, A) c ,Δv′ i ,..) may be any law of friction, which may depend on various parameters, such as normal pressure, contact area, relative sliding speed, etc. In MPM calculations the background grid will calculate the interactions between different materials according to the set material contact law.
501. Simulation of TATB/F at the mesoscale using MPM method 2314 And in the deformation process of the PBX under the uniaxial compression, observing the evolution of a temperature field and a stress field among particles in the deformation process through the visualization of an output result, and analyzing the microscopic mechanical behavior of the PBX under the compression load as shown in fig. 4 and 5.
502. Models with different initial porosities were created and the stress-strain curve and the pressure-volume curve of the PBX were calculated as shown in fig. 6 and 7. And fitting the elastic modulus and the state equation parameters of PBX with different densities under the microscopic scale according to the calculation result, wherein the elastic modulus and the state equation parameters are shown in tables 5 and 6, and reliable parameters are provided for macroscopic continuum calculation.
Table 5 mechanical properties of PBX at three different porosities
TABLE 6 parameter fitting results of PBX State equations at different porosities
The system, apparatus, module or unit set forth in the above embodiments may be implemented in particular by a computer chip or entity, or by a product having a certain function. One typical implementation is a computer. In particular, the computer may be, for example, a personal computer, a laptop computer, a cellular telephone, a camera phone, a smart phone, a personal digital assistant, a media player, a navigation device, an email device, a game console, a tablet computer, a wearable device, or a combination of any of these devices.
Computer readable media, including both non-transitory and non-transitory, removable and non-removable media, may implement information storage by any method or technology. The information may be computer readable instructions, data structures, modules of a program, or other data. Examples of storage media for a computer include, but are not limited to, phase change memory (PRAM), static Random Access Memory (SRAM), dynamic Random Access Memory (DRAM), other types of Random Access Memory (RAM), read Only Memory (ROM), electrically Erasable Programmable Read Only Memory (EEPROM), flash memory or other memory technology, compact disc read only memory (CD-ROM), digital Versatile Discs (DVD) or other optical storage, magnetic cassettes, magnetic tape magnetic disk storage or other magnetic storage devices, or any other non-transmission medium, which can be used to store information that can be accessed by a computing device. Computer-readable media, as defined herein, does not include transitory computer-readable media (transmission media), such as modulated data signals and carrier waves.
It should also be noted that the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one … …" does not exclude the presence of other like elements in a process, method, article or apparatus that comprises the element.
The above examples should be understood as illustrative only and not limiting the scope of the invention. Various changes and modifications to the present invention may be made by one skilled in the art after reading the teachings herein, and such equivalent changes and modifications are intended to fall within the scope of the invention as defined in the appended claims.
Claims (7)
1. A multi-scale continuous calculation method for solving the microscopic mechanical property of an energetic material is characterized by comprising the following steps:
step 1, performing molecular dynamics simulation MD on high-energy crystal explosive in an energetic material PBX, wherein the method specifically comprises the following steps: constructing a super cell model of the explosive crystal by taking crystal data obtained by neutron diffraction as a basis, solving the mechanical property of the crystal by using molecular dynamics simulation software, and deducing state equation parameters of the crystal under the high pressure condition according to the pressure-volume relation;
step 2, carrying out coarse grain molecular dynamics simulation on the polymer binder in the PBX: establishing a state equation and mechanical properties of the polymer by adopting a coarse grain molecular dynamics method;
step 3, establishing a particle digital model of the microscale composite material: firstly, carrying out digital processing based on a real micro-structure of a PBX, wherein PBX particles in the micro-structure consist of high-energy explosive crystals and polymers in the steps 1 and 2; secondly, homogenizing and approximating the polymer bonding; finally, adopting an approximate method that random circles are not overlapped with each other, and generating a PBX particle filling model with random distribution of positions and particle sizes in a sealed mold;
step 4, key parameter linking from microscopic scale to microscopic scale: inputting mechanical modulus and state equation parameters of an explosive crystal and a polymer binder which are obtained through micro-scale MD simulation as single component property parameters into simulation calculation of a representative volume element model, establishing interface parameters and a multiphase material contact algorithm between different components, and considering interaction of particles, polymers and polymers;
step 5, calculating the mechanical properties of the PBX under the microscopic scale: and under the microscopic scale, adopting an object point method, taking RVE of the PBX as a calculation model, researching the microscopic mechanical behavior and deformation process of the PBX under the external loading condition, and fitting the constitutive relation and state equation of the PBX.
2. The multi-scale continuous calculation method for solving the microscopic mechanical properties of the energetic material according to claim 1, wherein the step 1 is to perform molecular dynamics simulation on the high-energy crystal explosive in the PBX, specifically: constructing a super cell model of the explosive crystal by taking crystal data obtained by neutron diffraction as a basis, solving the mechanical property of the crystal by using molecular dynamics simulation software, and deducing state equation parameters of the crystal under the high pressure condition according to the pressure-volume relation;
performing structural relaxation on a super cell model of a crystal by using LAMMPS software to obtain a stable structure, performing uniaxial tension deformation under a constant strain rate under an NPT system, analyzing the elastic constant and stress-strain relation of the crystal in the compression process, calculating other mechanical parameters of the elastic modulus through the elastic constant, and obtaining the pseudo particle velocity u in a Hugonlot equation p And pseudo-impact velocity u s The relationship with the pressure-volume data is as follows:
u p and u s There is a linear fit relationship between:
u s ＝su p +c (3)
obtaining Mie-Gru by fitting the relation (3)Parameters c and s of the neisen state equation, whereGamma is the volume ratio 0 Is constant, gamma 0 ≈2s-1；
3. The multi-scale continuous computing method for solving the microscopic mechanical properties of energetic materials according to claim 2, wherein step 2 performs coarse-grained molecular dynamics simulation on the polymer binder in the PBX: establishing a state equation and mechanical properties of the fluoropolymer by adopting a coarse grain molecular dynamics method;
establishing a total atom simulation system of a polymer chain, coarsening a plurality of unit structures of the polymer into different types of beads according to a coarsening mapping scheme, calculating radial distribution functions among the beads in coarsening force field calculation software Magic, and expanding the radial distribution functions by adopting Boltzmann inversion iteration to obtain a coarsening force field file of the polymer; writing the force field file into a simulation input file, and performing isothermal compression simulation of the NPT ensemble in LAMMPS software to obtain an elastic constant and a pressure-volume relationship;
the pressure-volume data of the fluoropolymer was fitted using two state equations, tait and Sun, the relationship of which is as follows:
tait state equation:
sun state equation:
wherein C, m and n are constants for most polymer systems, so the parameters to be fitted are B 0 。
4. A multi-scale continuous computing method for solving the microscopic mechanical properties of energetic materials according to claim 3, wherein the step 3 is to build a particle digital model of the microscopic scale composite material: firstly, carrying out digital processing based on a real micro-structure of a PBX, namely after edge contour extraction is carried out on PBX particles, dividing an image of the PBX into a plurality of pixel small areas, and after the quantization processing, representing gray values of all areas by integers to form digital images with particles with different sizes; secondly, homogenizing approximation treatment of the polymer bond, namely, classifying crystal particles with extremely small size into a polymer matrix in calculation, and representing the polymer bond by using a homogenized viscoelasticity matrix; and finally, approximating the PBX particles into circular particles by adopting an approximation method that random circles are not overlapped with each other, and generating a PBX particle filling model with random distribution of particle sizes at the position of a sealed mould according to the principle that the particles are not intersected, are not overlapped with each other and are not included with each other.
5. The method for continuously calculating the microscale for solving the microscopic mechanical properties of energetic materials according to claim 4, wherein the step 4 is characterized in that the mechanical modulus and the equation of state parameters of the explosive crystal and the polymer binder obtained by the microscale MD simulation are input as single component property parameters into the simulation calculation of a representative volume metamodel, the representative volume metamodel is composed of a plurality of PBX particles and pores which are randomly distributed, and the PBX particles are represented by polymer-coated crystal particles; interfacial frictional interactions are also considered in the model and interface parameters between the different components, such as the coefficient of friction between the polymer-binder, are established.
6. The multi-scale continuous computing method for solving the microscopic mechanical properties of energetic materials according to claim 4, wherein the step 4 of the multi-phase material contact algorithm comprises the following steps: assuming two materials, a and b, respectively, the momentum change imposed on material a needs to be calculated first, as follows:
wherein Δp i,a Representing the change in momentum of material a, p i,a 、p i,b Respectively represent the momentum of material a and material b, m i,a And m i,b Representing the mass of material a and material b, respectively; centroid speed of grid nodeIs the sum of the masses of all grid nodes, and subscripts i and j respectively represent the grid nodes and the material types, p i,j 、m i,j 、v i,j Corresponding to the momentum, mass and speed of different material types on the grid nodes respectively; for material b, its momentum changes Δp i,b ＝-Δp i,a ；
Relative sliding velocity Deltav between materials a and b i In connection with the change of momentum:
wherein m is i,red Mass reduced for node i, m i,red ＝m i,a m i,b /(m i,a +m i,b ) The momentum solving formula after the change is as follows:
where N is the normal pressure of the contact surface, S stick Is a traction force that resists frictional sliding of the interface,and->Direction vectors normal and tangential, respectively, A c And Δt is the contact area and time variation, respectively; in this algorithm, the condition that the material has a contact interface is +.>
In order to achieve frictional interaction of the interface, it is necessary to calculate the sliding traction of the frictional sliding, namely:
S slide ＝f(N,A c ,Δv′ i ) (9)
wherein f (N, A) c ,Δv′ i ) Is an arbitrary law of friction that depends on various parameters such as normal pressure, contact area, relative sliding speed, and in point of matter calculations the background grid will calculate interactions between different materials according to the set law of material contact.
7. The multi-scale continuous calculation method for solving the microscopic mechanical properties of energetic materials according to claim 5, wherein the calculation of the mechanical properties of the PBX under the microscopic scale of step 5: adopting an object point method under a microscopic scale, taking RVE of the PBX as a calculation model, researching microscopic mechanical behavior and deformation process of the PBX under external loading condition, and fitting mechanical property and state equation of the PBX;
the mass point method (Material Point Method, MPM) is a particle-based gridless calculation method that is easier to handle in terms of intrinsic boundary conditions and deformation contacts, in which the sample is represented by a set of discrete "material points", each particle being assigned mass, coordinates, velocity properties; the basic calculation principle of MPM is as follows: assuming that the state of the particles at the beginning is known, the mass m of the particles, the external force f, is calculated using equation (10) ext And speed v is passed to the mesh node:
wherein subscript i represents a grid node and p represents a particle; s is S ip Is a deformation function of the grid node at particle p; subsequently using grid node velocity v i Calculating a velocity gradient at each particle
Wherein G is ip Is the gradient of the deformation function of the grid node at particle p;
internal force f of grid node i int The calculation formula is as follows:
middle sigma p And V p Stress and volume of the particle, respectively;
in each time step of simulation, mapping all particle information to background grid nodes, updating the quality, speed and force information of the nodes by using formulas (10) - (14), returning the calculation results to the particles through a mapping relation, and repeating the calculation process when the next time step is started until the appointed time or condition is completed, thereby completing the solution of the actual problem;
the mechanical properties of the PBX mainly calculate the modulus of elasticity: first, the Young's modulus E and Poisson's ratio mu of PBX need to be calculated, E is the slope of stress sigma-strain epsilon curve in the elastic phase, namelyMu is the transverse strain epsilon of uniaxial compression xx And longitudinal strain ε yy Ratio of (2), i.e.)>The shear modulus G and bulk modulus K of PBX are calculated as follows:
the pressure-volume relationship of the PBX is described by the Mie-Groneisen state equation, the formula is as follows:
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