Numerical Simulation Method for Brazilian Splitting Test of PBX Considering Non-uniform Material Properties

Abstract

The present invention provides a numerical simulation method for the Brazilian splitting test of PBX considering non-uniform material properties, aiming to establish a complete heterogeneous model of PBX explosive Brazilian splitting to accurately reproduce the crack propagation process and the final morphology during splitting, and provide practical theoretical guidance for the analysis of the actual cracking mechanism; the heterogeneous method is realized by modeling through the finite element software ABAQUS combined with self-written Python scripts: First, establish a two-dimensional Brazilian splitting complete matrix model of irregularly shaped explosive particles, then assign random linear elastic material parameters within a certain range to each explosive particle item by item, assign Cohesive bilinear constitutive parameters to the zero-thickness interface between the explosive particles, and finally set boundary conditions, mesh division and analysis steps to complete the establishment of the heterogeneous overall model of PBX Brazilian splitting; the beneficial effect of the present invention is that on the basis of the existing technology, the model further considers the material property differences of the explosive particles, fully reflects the material heterogeneity of PBX, and can reproduce the complete fracture process and the final morphology of PBX Brazilian splitting.

Description

Technical Field

[0001] The present invention belongs to the field of explosive product production, and particularly relates to a numerical simulation method for PBX Brazilian splitting test considering non-uniform material properties. Background Technique

[0002] The uniaxial tensile test is the most commonly used method for measuring the mechanical properties of materials. However, for brittle materials such as concrete and rock, it is difficult to prepare specimens according to the requirements of the uniaxial tensile test. Moreover, due to the very small fracture strain of the materials, it is also difficult to accurately measure the specimen deformation. The Brazilian Splitting Test, also known as the Brazilian test or indirect tensile test, is to make the specimen into a disc shape and apply a compressive load in the opposite direction along its diameter, so that induced transverse tensile forces occur inside the specimen and cause cracking failure, which can be used to indirectly measure the tensile strength of brittle materials such as concrete. And the specimen preparation is simple, the required materials are few, the experiment is fast, convenient and low-cost, so it has more applications in the fields of architecture, geology and manufacturing.

[0003] Polymer bonded explosive (PBX) is a solid high-energy explosive made mainly of single-component explosives and added with various additives that can improve its processing performance and service performance under the action of certain temperature and pressure. Under the action of external loads, macroscopic or mesoscopic damages such as debonding of explosive particles and microcrack evolution may occur inside the PBX, deteriorating its performance. Therefore, it is crucial to accurately control its damage and fracture performance. Since the process of preparing specimens for the uniaxial tensile test of PBX is complex, requires a large amount of explosive, and has a long cycle, the use of the Brazilian splitting test to study the mechanical properties of PBX has gradually received attention [Pang Haiyan, Li Ming, etc. Brazilian Tests of PBX Explosives with Different Loading Forms. Chinese Journal of Energetic Materials. 2012, 20(2): 205-209]. However, the internal deformation and fracture information of materials obtained through physical experiments is relatively limited, and it is also difficult to analyze its damage mechanism and cracking reasons based on the internal stress state of the specimens. Numerical simulation can obtain detailed information on the material deformation and cracking process, which is helpful for deeply understanding and recognizing the dynamic mechanical response and fracture behavior of materials. Therefore, some scholars have begun to analyze the damage and failure behavior of PBX through numerical simulation of the Brazilian test [Dai Kaida, Li Shengtao, Chen Pengwan. Research on Fracture Behavior of PBX Explosives in Brazilian Tests Based on XFEM. Transactions of Beijing Institute of Technology. 2018, 38(2): 111-117] etc.

[0004] At present, there are two methods for simulating the damage and fracture behavior of PBX Brazilian splitting experiments, namely macroscopic and microscopic approaches. Among them, numerical simulations at the macroscopic level include the extended finite element method, the meshless method, and the finite element method based on the cohesive crack model, etc., which can reproduce the crack initiation and propagation process of PBX disks to a certain extent. However, PBX materials are composed of randomly distributed explosive particles (usually with a content greater than 95%) and binders, so they have obvious heterogeneity. The above numerical simulation methods are difficult to reflect the heterogeneous characteristics at the microscopic level of PBX. The crack morphology obtained from the simulated Brazilian splitting experiment is nearly linear, which is quite different from the irregular cracks in actual experiments.

[0005] There are currently two main modeling methods to reflect the actual structure of materials and embody the heterogeneous characteristics through models at the mesoscopic level. One is the Discrete Element Method. For example, first randomly generate particles within a given size range and randomly overlap and aggregate them to embody the irregularity of explosive particles; then generate small particles and fill the void areas as binders; finally, assign corresponding material properties to the explosive particles and binders and set the contact relationships. Such models are close to the actual physical structure of PBX explosives, but the modeling process is cumbersome, the handling of particle contact relationships is difficult, and the computational efficiency is low. The other is to equivalent the explosive particles to randomly distributed irregular polygons, ignore the actual content of the binder (usually less than 5-10%), and regard the zero-thickness interface between the polygonal particles as the "binder"; then assign linear elastic or viscoelastic material properties to the explosive particles and Cohesive material properties to the "binder" to establish a finite element model of the Brazilian split specimen of PBX explosives with heterogeneous characteristics [H. Guo, J. R. Luo, P. A. Shi, et al. Research on the fracture behavior of PBX under static tension [J]. Defence Technology, 2014]. To consider the actual content of the binder, some studies have also shrunk the boundaries of the polygonal particles so that there is a certain gap between the particles, and used this gap area as the binder; then assign corresponding material properties to the irregular explosive particles and the binder respectively; finally, use the Numerical Manifold Method or the finite element method to simulate the fracture behavior of PBX under compression [A. Barua, M. Zhou. A Lagrangian framework for analyzing microstructural level response of polymer-bonded explosives. Modelling & Simulation in Materials Science & Engineering, 2011, 19(5):055001; K. Ge, Y. J. Ning, P. W. Chen. Meso-structure construction and effective modulus simulation of PBXs. Journal of Energetic Materials, 2020, 38(3):261-282]. This method can more accurately simulate the crack initiation and propagation of PBX under compression, especially reflecting the irregular morphology of the cracks. However, these models assign the same material properties to all PBX explosive particles and do not consider the heterogeneous characteristics of different particles.In addition, due to the high computational cost, a representative volume element (RVE) is generally used in these studies to conduct research, and the crack initiation and propagation process of the PBX Brazilian splitting experiment cannot be fully reproduced globally.

[0006] Generally speaking, the existing simulation methods for Brazilian splitting experiments cannot well consider the heterogeneous material properties of PBX, and there is a large deviation between the analysis results and the actual situation, so it is necessary to improve them. Summary of the Invention

[0007] Based on the above background, the present invention provides a numerical simulation method for PBX Brazilian splitting experiments considering non-uniform material properties to accurately reproduce the crack propagation process and final morphology during the experiment, and provide theoretical guidance for the analysis of cracking mechanisms. To achieve the above object, the present invention provides the following technical solutions:

[0008] A numerical simulation method for PBX Brazilian splitting experiments considering non-uniform material properties, and the implementation steps of the method are as follows:

[0009] Step 1): Establish a two-dimensional circular model in the CAE interface of ABAQUS, and the model represents the Brazilian splitting circular matrix.

[0010] Step 2): Use a Python script to construct a random Voronoi polygon in ABAQUS. The number of polygons is a positive integer N, and the circular matrix is cut by the sides of the polygons.

[0011] Step 3): Use a Python script to set the N polygons in Step 2) as N sets Set1, Set2,... Set N , and the N sets are described as "explosive particles" with irregular shapes in reality. All the sides of the polygons are set as set Set C , and the set Set C is described as the "adhesive" between the "explosive particles".

[0012] Step 4): Assign N linear elastic material properties Material1, Material2,... Material to the N "explosive particles" item by item; assign the "adhesive" the Cohesive material property. N ; Assign the Cohesive material property to the "adhesive".

[0013] Step 5): Set boundary conditions and analysis steps, conduct mesh division, and complete the construction of the PBX Brazilian splitting heterogeneous overall model.

[0014] Further, in Step 1), the two-dimensional Brazilian splitting circular matrix model is set to the plane stress mode.

[0015] Further, in the step 2), the average particle size of the Thiessen polygon is constructed according to the average particle size scale of the actual explosive particles. The specific construction method is as follows: combining the total area of the circular matrix, the number of polygons N is adjusted through a Python script.

[0016] Further, in the step 4), the elastic moduli E1, E2, …, E in the N linear elastic material properties N satisfy the normal distribution probability density function The Cohesive material property adopts a bilinear constitutive model.

[0017] Further, in the step 5), the boundary condition is pressed at a speed of 0.05 mm / s; the analysis step target time increment is scaled to 6×10 -8 , and the average mesh size is one-tenth of the average particle size of the polygon, and the mesh type is quadrilateral.

[0018] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0019] On the basis of the prior art, the simulation model further considers the differences in the material properties of explosive particles, fully reflects the material inhomogeneity of PBX, and can reproduce the complete fracture process and final morphology of the Brazilian splitting of PBX. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 is a flow chart for model construction;

[0021] Figure 2 is a two-dimensional Brazilian splitting circular matrix diagram;

[0022] Figure 3 is a Thiessen polygon cutting matrix diagram;

[0023] Figure 4 is a diagram of assigning material properties to "explosive particles" and "binder";

[0024] Figure 5 is a diagram of the inhomogeneous overall model of PBX Brazilian splitting;

[0025] Figure 6 is the cracking process of the PBX specimen measured by the DIC (Digital Image Correlation) method;

[0026] Figure 7 is the overall cracking process of the conventional (homogeneous) model of PBX Brazilian splitting;

[0027] Figure 8 is the overall cracking process of the inhomogeneous model of PBX Brazilian splitting;

[0028] Figure 9It is a PBX Brazilian split heterogeneous integral model randomly generated again according to the process;

[0029] Figure 10 It is the cracking result of the PBX Brazilian split heterogeneous integral model randomly generated again.

[0030] Among them:

[0031] 1 - Thiessen polygon 2 - Side of the polygon 3 - Explosive particle 4 - Adhesive 5 - Lower platform 6 - Upper pressing plate Specific implementation manner

[0032] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0033] Refer to Figures 1 - 10 , the present invention provides a numerical simulation method for PBX Brazilian split experiments considering non-uniform material properties. By establishing a complete PBX explosive Brazilian split heterogeneous model, the crack propagation process and the final morphology during the split process can be accurately reproduced. See Figure 1 , the implementation steps are as follows:

[0034] Step 1): Establish a two-dimensional Brazilian split circular matrix in the CAE interface of ABAQUS (see Figure 2 ); the diameter of the circular matrix is 10 mm; the two-dimensional model satisfies the plane stress condition;

[0035] Step 2): Use a Python script to construct a random Thiessen polygon 1 in ABAQUS, and cut the circular matrix through the sides 2 of the polygon (see Figure 3 ); the average particle size of the Thiessen polygon is constructed according to the average particle size of the actual explosive particles, which is 200 um; the specific construction method is: adjust the number of polygons N in the Python script in combination with the total area of the circular matrix. When N = 2500, the average particle size of the polygon meets the requirements;

[0036] Step 3): Describe all the irregular polygons in step 2) as "explosive particles" 3 with actual irregular shapes, and describe all the sides of the irregular polygons as "adhesives" 4 between the "explosive particles" (see Figure 4 ); the specific operation is: use a Python script to set all the polygons one by one as sets Set1, Set2,... Set N , and set all the sides of the polygons as set Set CConsidering that the actual adhesive content is extremely small, the model ignores the actual adhesive content, that is, the "adhesive" is a zero-thickness layer in the model;

[0037] Step 4): Assign N linear elastic material properties Material1, Material2, ...Material to each of the N “explosive particles” set. N , the elastic modulus E of the N linear elastic material properties takes random values within a certain range and satisfies the normal distribution probability density function The mean μ is 5000 MPa and the standard deviation σ is 300 MPa;

[0038] The "adhesive" set is assigned a cohesive material property, which uses a bilinear constitutive model suitable for describing the delamination of composite materials. The specific material parameters are: density ρ = 1.8 g / cm 3 , shear modulus G = 0.27GPa, Poisson's ratio v = 0.3, tensile strength F T =6MPa, fracture energy G f =0.324N / mm;

[0039] Step 5): Set boundary conditions, analysis steps, and perform meshing to complete the construction of the PBX explosive Brazilian splitting heterogeneous overall model (see Figure 5 ); the boundary conditions are as follows: the lower boundary is described as a fixed constraint of the lower platform 5, and the upper boundary is described as the upper platen 6 pressing down at a speed of 0.05 mm / s; the analysis step is set to 10 s, and the target time increment is scaled to 6x10 -8 ; The average grid size is 20um and the grid type is quadrilateral.

[0040] From the simulation results, the PBX Brazilian splitting conventional (homogeneous) model (see Figure 7 ) is uniformly distributed: when the upper platen 6 moves downward to 0.05mm, no cracks appear in sample result ①; when the upper platen 6 moves downward to 0.15mm, cracks initiate at the center of sample result ②; when the upper platen 6 moves downward to 0.35mm, cracks extend to the upper and lower ends of sample result ③; when the upper platen 6 moves downward to 0.5mm, cracks extend to the edges of sample result ④. The cracking mode is that the crack initiates from the center of the sample and extends linearly to the upper and lower ends; obviously, the simulation results of the conventional model are consistent with the experimental results (see Figure 6 [Cui Yunxiao, Chen Pengwan, Dai Kaida, et al. Numerical simulation of PBX explosive arc Brazilian experiment based on EFG method [J]. Journal of Explosives and Propellants, 2016, 39(1):5]) has obvious differences in the final crack morphology. The PBX Brazilian splitting heterogeneous model provided by the present invention (see Figure 8) The Mises stress distribution in it is uneven: when the upper platen 6 moves downward to 0.05 mm, no crack appears in the specimen result ①; when the upper platen 6 moves downward to 0.15 mm, a crack initiates at the center position of the specimen result ②; when the upper platen 6 moves downward to 0.35 mm, the crack in the specimen result ③ extends upward and downward; when the upper platen 6 moves downward to 0.5 mm, the crack in the specimen result ④ extends to the edge. The cracking mode is that the crack still initiates from the middle position of the specimen and extends upward and downward, but the crack propagation path is not linear, and the final crack morphology is irregular, which essentially coincides with the experimental cracking result. To further confirm the simulation results, we randomly generated the heterogeneous model of the complete Brazilian splitting of PBX again according to the described model construction process (see Figure 9 ), and the obtained simulation results (see Figure 10 ) also coincide with the experimental results. Therefore, the heterogeneous model proposed by the present invention can reflect the heterogeneous characteristics of the actual PBX material and can completely reproduce the crack propagation process and the final morphology during the splitting process of PBX, thereby providing a practical theoretical guidance for the analysis of the actual cracking mechanism.

[0041] Although the embodiments of the present invention have been shown and described, those of ordinary skill in the art can understand that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention. The scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A numerical simulation method for the Brazilian splitting test of PBX considering non-uniform material properties, characterized in that The implementation steps of the method are as follows: Step 1): Establish a two-dimensional circular model in the CAE interface of ABAQUS, and the model represents a Brazilian split circular matrix; Step 2): Use a Python script to construct random Thiessen polygons in ABAQUS. The number of polygons is a positive integer N, and the circular matrix is cut through the sides of the polygons; Step 3): Use a Python script to set the N polygons in step 2) as N sets Set1, Set2, … Set N , and the N sets are described as "explosive particles" with an actual irregular shape. The edges of all polygons are set as set Set C , and the set Set C is described as the "adhesive" between "explosive particles"; Step 4): Assign N linear elastic material properties Material1, Material2, to each of the N "explosive particles" item by item. … Material N ; Assign the "adhesive" the Cohesive material property. Step 5): Set boundary conditions and analysis steps, perform mesh division, and complete the construction of the PBX Brazilian split heterogeneous overall model.

2. The numerical simulation method for PBX Brazilian splitting experiment considering non-uniform material properties according to claim 1, characterized in that, In the above step 1), the two-dimensional Brazilian split circular matrix model is set to the plane stress mode.

3. The numerical simulation method for PBX Brazilian splitting test considering non-uniform material properties according to claim 1, characterized in that, In the above step 2), the average particle size of the Thiessen polygons is constructed according to the average particle size scale of the actual explosive particles. The specific construction method is: combined with the total area of the circular matrix, adjust the number of polygons N through a Python script.

4. The numerical simulation method for PBX Brazilian splitting experiment considering non-uniform material properties according to claim 1, characterized in that In step 4), the elastic moduli E1, E2, among the N linear elastic material properties … E N satisfy the normal distribution probability density function The Cohesive material property adopts a bilinear constitutive model.

5. The numerical simulation method for PBX Brazilian splitting test considering non-uniform material properties according to claim 1, characterized in that In step 5), the boundary condition is suppressed at a speed of 0.05 mm / s; the analysis step target time increment is scaled to 6x10 -8 , the average mesh size is one tenth of the average particle size of the polygon, and the mesh type is quadrilateral.

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