Method for simulating interface debonding of hollow particle reinforced composite material based on VCFEM model

Abstract

The invention relates to the technical field of composite material detection, in particular to a hollow particle reinforced composite material interface debonding simulation method based on a VCFEM model, and the method comprises the following steps: S1, creating a geometric model; s2, defining an interface between the matrix and the inclusion, and setting that no delamination is contained at the initial time; s3, simulating the deformation and damage evolution process of the composite material under the action of external force by gradually increasing the applied load or displacement; s4, adopting a grid re-division technology to ensure that the model can dynamically adjust a grid to adapt to a new crack propagation path and a delamination state when the stress of an interface node exceeds a critical value to cause interface debonding; s5, in a numerical simulation stage, generating a stress nephogram after each incremental loading step so as to visually display stress distribution and concentration phenomena in the composite material; according to the method, the interface delamination damage evolution process of a complex composite material structure is effectively simulated.

Description

Technical Field

[0001] The invention relates to the technical field of composite material detection, and in particular to a simulation method for interface debonding of hollow particle reinforced composite materials based on a VCFEM model. Background Art

[0002] Particle-reinforced composites are widely used in many industrial fields such as aviation, military, nuclear energy, and construction. Hollow glass microspheres (HGM) have the characteristics of being hollow, lightweight, wear-resistant, and corrosion-resistant. Studies have shown that adding HGM to composite materials is a way to improve mechanical properties. For example, Swetha and Kumar studied the effects of hollow sphere content and microsphere wall thickness on the mechanical response of foam materials through a series of quasi-static uniaxial compression tests. R. Scotta et al. explored the effects of glass microspheres on the mechanical properties of cement-based composites with weight-reducing characteristics and the compressive strength of glass microsphere-reinforced cement-based composites under quasi-static and high strain rate loading conditions. F Blanco et al. proved that the compressive strength of lightweight cement-based materials mixed with hollow microspheres is higher than that of traditional expanded perlite lightweight cement materials. Vikrant Tiwari et al.'s research shows that adding hollow glass microspheres to cement matrix can greatly improve the sound insulation performance of the material.

[0003] When selecting hollow glass microsphere reinforced matrix composites, many studies evaluate mechanical properties based on microstructure-property relationships. This homogenized analytical method based on the Eshelby solution of uniform strain in ellipsoidal uniform inclusions cannot accurately predict the elastic properties of the material. Subsequently, the inhomogeneity of the microstructure was considered to develop a more accurate analytical model. However, the aggregation of hollow microspheres, microsphere cracking, and interface debonding will reduce the mechanical properties and ultimately lead to failure of the composite material, limiting the model's ability to provide accurate predictions. Therefore, in the study of hollow glass microsphere reinforced matrix composites, it is also very important to clearly understand the effect of damage on the mechanical properties of the material. Due to the stress concentration at the damaged interface, it is difficult for traditional displacement-based finite elements to simulate complex composites. Because composites contain a large number of randomly distributed inclusions with arbitrary sizes and shapes, some special finite element methods have been developed to reduce computational costs.

[0004] VCFEM is an alternative method to improve computational efficiency. Compared with traditional finite element models, VCFEM greatly reduces the degrees of freedom, thereby greatly improving computational efficiency. Zhang and Katsube proposed a hybrid finite element method for calculating the mechanical response of two-dimensional heterogeneous materials with randomly dispersed rigid inclusions of arbitrary sizes. The Voronoi unit finite element method proposed by Ghosh and Moorthy has been used as an efficient and accurate tool to model non-uniform microstructures with arbitrary shapes, sizes or dispersed heterogeneities. Guo proposed a Voronoi unit to simulate the creep strain, thermal strain and plastic strain of two-dimensional particle reinforced composites. Zhang proposed a new finite element model MHSFEM, which simplified the mesh generation method. Its combination with VCFEM helps to analyze special microstructures and expand the application range of VCFEM. Zhang proposed a singular Voronoi unit model (SVCFEM) to simulate the stress concentration at the crack tip of homogeneous materials. Ghosh and Ling et al. used VCFEM to simulate the interfacial debonding of fiber-reinforced composites, in which the matrix and inclusions of the two-phase material were assumed to be connected by springs, while the present invention uses a pair of common node pairs to simulate the interfacial debonding. Li and Ghosh proposed an extended Voronoi unit finite element model (XVCFEM) to simulate multiple crack propagation in homogeneous materials. Zhang used the Voronoi unit finite element method to simulate the multiple crack problem of homogeneous materials. The above methods all simulate the crack propagation problem of homogeneous materials. The present invention proposes a new VCFEM to simulate the interface debonding of hollow particle composites. Zhang extended the Voronoi unit finite element method to include composite materials reinforced by arbitrary distribution of inclusions with uniform phases. In summary, VCFEM is suitable for the simulation of composite materials containing more inclusions. At present, VCFEM is mostly used for micromechanical damage analysis such as crack propagation of homogeneous materials, and does not consider the influence of hollow particle reinforced composite materials during crack propagation and delamination between phases.

[0005] The present invention proposes a new VCFEM based on a mixed stress model for hollow inclusion two-phase damage characterization. According to the principle of complementary energy, a special unit containing hollow inclusions is specified, and stress and displacement are regarded as independent fields. The stress field satisfies the equilibrium equation in advance and is expressed in the form of a combination of a polynomial stress function and a reciprocal stress function in a matrix. Lagrange multipliers are introduced into the function to construct a correction function. The present invention constructs a function that links the stress function and the displacement variable, converts the equation into a solvable form, and displays the obtained model in the form of a FEM standard solution. Using a new interface debonding mesh re-division strategy, the interface delamination problem of hollow particle reinforced composites is studied through numerical examples to verify the feasibility of this new VCFEM. Summary of the invention

[0006] The purpose of the present invention is to provide a simulation method for interface debonding of hollow particle reinforced composite materials based on VCFEM model. By adding nodes to simulate progressive interface debonding, a mesh re-division algorithm is proposed, which is applied to simulate the generation and expansion process of hollow particle reinforced composite material interlayer debonding. The effectiveness and high efficiency of the unit are verified by comparing the results with the corresponding commercial software MARC and ABAQUS. The method is further used to simulate the interface debonding damage evolution process of complex composite structures, and the influence of interface damage on horizontal displacement on constraint reaction force and hollow microsphere wall thickness on interface debonding is studied, showing the effectiveness and high efficiency of the method in dealing with complex problems.

[0007] In order to achieve the above technical objectives and the above technical effects, the present invention is implemented through the following technical solutions:

[0008] A method for simulating interfacial debonding of hollow particle reinforced composite materials based on a VCFEM model comprises the following steps:

[0009] S1: Create a geometric model, including the distribution of the matrix and hollow particle inclusions; use Voronoi cells to simulate the particle composite material, one Voronoi cell contains one inclusion to accurately describe the actual distribution and geometric characteristics of the particles; assign material properties to the matrix and inclusions, including physical parameters such as elastic modulus and Poisson's ratio, to ensure that the mechanical behavior of these materials is accurately reflected in the simulation.

[0010] S2: It is particularly important to define the interface between the matrix and the inclusion and set the interface to be perfectly bonded at the beginning. For the initial state of the simulation, the stress field state in the matrix and the inclusion should be described by the stress hybrid finite element method.

[0011] S3: In the incremental loading stage, the deformation and damage evolution of the composite material under the action of external forces is simulated by gradually increasing the applied load or displacement; the stress state of all nodes is calculated in each incremental step, and the nodes whose stress reaches or exceeds the critical value are identified. For these supercritical nodes, it indicates that interface debonding may occur.

[0012] S4: For the treatment of interface debonding, combined with the characteristics of the VCFEM model, the mesh re-division technology is used. When the stress of the interface node exceeds the critical value, the interface debonds. For each node debonding, a common node is added, such as Figure 2 The model can automatically adjust the mesh to adapt to the new crack propagation path and delamination state;

[0013] S5: During the numerical simulation stage, a stress cloud diagram is generated after each incremental loading step to intuitively display the stress distribution and concentration phenomenon inside the composite material. Stress concentration often indicates impending material damage or fracture, which can be clearly seen in the stress cloud diagram. Based on the stress state analysis, the results are checked in combination with MARC and ABAQUS, and the comparative analysis helps to verify the accuracy and effectiveness of VCFEM application.

[0014] S6: Based on the analysis results, a stress curve is drawn to show the mechanical response during the entire damage evolution process; by changing the particle thickness and interface bonding condition parameters in the simulation, the influence of different factors on the interface debonding behavior is studied.

[0015] Furthermore, the inclusion phase and matrix phase of the hollow particle delaminated Voronoi unit are denoted as Ω c ,Ω m .n e is the unit boundary The direction of the external normal. b It is the undebonded matrix-inclusion interface The direction of the external normal. i Hollow interface The direction of the external normal. m and n c Debonding matrix interface and debonding inclusion interface The direction of the external normal.

[0016] Undelaminated interface between inclusion and matrix The surface force continuity condition is satisfied

[0017]

[0018] At the delamination interface, the surface force is zero

[0019]

[0020]

[0021] Interface between inclusions and voids The surface force is zero

[0022]

[0023] Based on the stress hybrid element functional formula, the Lagrange multiplier is used to impose constraints and the modified complementary energy functional is obtained:

[0024]

[0025] Among them, u m and uc represents the debonding crack displacement, and the unit boundary displacement field is obtained by the linear interpolation function;

[0026] The functional expression of complementary energy after finite element discretization is:

[0027]

[0028] In the above formula, the matrix H m ,H c ,G e ,G mb ,G cc ,G cb ,G mm ,G ci Defined as:

[0029]

[0030] The identification of Gaussian points in the integral calculation is achieved by dividing the matrix of each phase into multiple quadrilaterals.

[0031] P m ,P c is the known stress function of the relative point positions of the matrix and inclusions.

[0032] By Stress function β m ,β c Derivation, get

[0033]

[0034] The weak expression of the motion relationship within the unit can be obtained

[0035] H m β m =G e q e -G mb q b +G mm q m

[0036] H c β c =G cb q b +G cc q c -G ci q i (12)

[0037]

[0038] By Q e ,q b,q m ,q m ,q i Derivation, get

[0039]

[0040] The weak expression of the surface force boundary condition can be obtained

[0041]

[0042] in,

[0043] The coefficient β can be written as

[0044] β=H -1 Gq (17)

[0045] Substituting (17) into (15) we obtain

[0046]

[0047] Furthermore, the step S4 specifically includes: simulating the gradually debonded matrix-inclusion interface by using a matrix-inclusion interface re-meshing method.

[0048] Assume that during a certain loading process of a particle reinforced composite material, at the beginning of an incremental step, a section of delamination has occurred between the matrix and inclusion interface of a certain unit. According to certain fracture mechanics principles, when the node stress reaches or exceeds the critical state, the original crack tip will extend forward along the interface between the matrix and the inclusion at the node. A sub-step of crack extension is the debonding of the interface where the node is located while other interfaces remain bonded together. In the first step, the stress state of all nodes of the interface is judged. If the node stress reaches or exceeds the critical stress, the interface will debond. In the second step, a new delamination is generated by connecting the two nodes of the debonding interface. Figure 2 Take the middle node A as an example. When A reaches the critical stress, the interface debonds. Before the new delamination occurs, the matrix and the inclusion share the same node at point A. This is not a problem in the bonding state. However, with the emergence of new delamination, the displacement of the matrix at point A and the inclusion at point A are no longer completely consistent. In order to ensure that the crack surface force is zero, the node pair A1 and A2 are used here to represent point A on the inclusion and point A on the matrix, respectively. The corresponding node variables satisfy the following relationship:

[0049] Δu A1 =Δu A2 =Δu A (20)

[0050] When the original crack tip A extends to point B, if the stress state of node B reaches or exceeds the critical state, point B continues to debond, resulting in new delamination, and proceeds to the next step to determine whether the stress state of other nodes has reached the critical state.

[0051] Beneficial effects of the present invention:

[0052] The present invention uses Voronoi units to represent hollow particles in reinforced composite materials. This modeling method can describe the actual geometric distribution and shape characteristics of particles with higher accuracy and fewer degrees of freedom, overcoming the limitations of describing irregular distribution of particles in traditional finite element simulation. With the help of stress hybrid finite element method, this method allows stress and displacement to be processed as independent fields, pre-satisfies the equilibrium equation, and helps to improve the simulation accuracy of complex stress states of materials. In addition, by introducing Lagrange multipliers, the model can accurately process stress distribution and its changes within the unit, improving the ability to predict interface debonding.

[0053] In the simulation of interface debonding, the present invention adopts dynamic mesh repartitioning technology. The core of this technology is that when it is detected that the node stress reaches or exceeds the critical value, the mesh can be automatically repartitioned to describe the new crack propagation path and delamination state, thereby ensuring the continuity and accuracy of the simulation results. This automatic adjustment capability stems from the flexibility of the VCFEM model itself. Compared with the traditional static mesh model, it not only improves the stability of the calculation, but also enables the model to more effectively capture the dynamic evolution process of the crack.

[0054] The VCFEM method excels in reducing degrees of freedom. This method assumes a high-order stress field inside the unit, so fewer units are used to capture the stress concentration phenomenon at the interface. Traditional displacement finite elements use low-order stress fields, so a large number of grids need to be divided at the interface. At the same time, since the hybrid stress finite element of the present invention does not need to assume a displacement field inside the unit, the displacement interpolation calculation of the traditional displacement finite element is avoided, which does not involve the calculation of shape functions. Therefore, it is not usually limited to three-node or four-node units like displacement finite elements. Since the hybrid stress finite element of the present invention is applicable to arbitrary polygonal units, it is suitable for combination with Voronoi grids. Such a unit contains only one inclusion, which greatly reduces the degrees of freedom compared to displacement finite elements. Therefore, it is particularly suitable for engineering problems that require efficient processing of a large number of microstructures and complex geometric shapes.

[0055] During the numerical simulation process, the stress cloud map generated by the present invention can not only intuitively display the stress concentration phenomenon inside the composite material, but also accurately predict the damage location and evolution path of the material. This result, combined with the stress curve, provides a deep insight into the response characteristics of the material at different damage stages. By adjusting the particle thickness and interface parameters, users can systematically study the effects of these variables on the interface debonding behavior, thereby providing a scientific basis and practical guidance for material design optimization. This flexible and in-depth analysis capability provides strong support for material selection and design in engineering applications.

[0056] Of course, any product implementing the present invention does not necessarily need to achieve all of the advantages described above at the same time. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for describing the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative work.

[0058] Figure 1 Schematic diagram of the Voronoi unit model with hollow inclusions considering interface debonding;

[0059] Figure 2 Schematic diagram of the mesh redrawing steps for matrix-inclusion interface debonding;

[0060] Figure 3 (a) is the structural condition modeling, (b) is the Voronoi unit cell and local enlargement, and (c) is the MARC grid schematic diagram;

[0061] Figure 4 Schematic diagram of horizontal stress contours of (a) VCFEM model and (b) MARC model;

[0062] Figure 5 (a) and (b) are respectively x , σ y Schematic diagram of stress distribution along the horizontal center line Figure 1 ;

[0063] Figure 6 (a) and (b) are respectively x , σ y Schematic diagram of stress distribution along the vertical center line Figure 1 ;

[0064] Figure 7 Schematic diagram of the comparison of horizontal stress contours between (a), (c), (e), (g) MARC model and (b), (d), (f), (h) VCFEM model;

[0065] Figure 8 is x Schematic diagram of the distributed stress along the horizontal center line and the vertical center line;

[0066] Fig. 9 Schematic diagram of (a) Voronoi grid and (b) MARC grid;

[0067] Fig.10 Schematic diagram of the comparison of horizontal stress cloud diagrams of (a) MARC model and (b) VCFEM model;

[0068] Fig.11 (a) and (b) are respectively x , σ y Schematic diagram of stress distribution along the horizontal center line Figure 2 ;

[0069] Fig.12 (a) and (b) are respectively σ x , σ y Schematic diagram of stress distribution along the vertical center line Figure 2 ;

[0070] Fig.13 (a) is the horizontal stress nephogram of the 1st incremental step, (b) is the horizontal stress nephogram of the 6th incremental step, (c) is the horizontal stress nephogram of the 11th incremental step, and (d) is the schematic diagram of the horizontal stress nephogram of the 16th incremental step;

[0071] Fig.14 It is a schematic diagram of the change of the right end restraint reaction force with the right end horizontal displacement during the damage generation process;

[0072] Fig.15 Schematic diagram of damage cross-section at the sixth incremental step for (a) 0.0055 mm thickness, (b) 0.00825 mm thickness, and (c) 0.011 mm thickness. DETAILED DESCRIPTION

[0073] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0074] Example 1

[0075] The present embodiment provides a method for simulating interfacial debonding of hollow particle reinforced composite materials based on a VCFEM model, comprising the following steps:

[0076] S1: Create a geometric model, including the distribution of the matrix and hollow particle inclusions; use Voronoi elements to divide the hollow particle composite material to accurately describe the actual distribution and geometric properties of the particles; assign material properties to the matrix and inclusions, including elastic modulus and Poisson's ratio and critical stress physical parameters to ensure that the mechanical behavior of these materials is accurately reflected in the simulation.

[0077] S2: It is particularly important to define the interface between the matrix and the inclusion and set the interface to be perfectly bonded at the beginning. For the initial state of the simulation, the stress field state in the matrix and the inclusion should be described by the stress hybrid finite element method.

[0078] S3: In the incremental loading stage, the deformation and damage evolution of the composite material under the action of external forces is simulated by gradually increasing the applied load or displacement; the stress state of all nodes is calculated in each incremental step, and those nodes whose stress reaches or exceeds the critical value are identified. For these supercritical nodes, it indicates that interface debonding may occur.

[0079] S4: For the treatment of interface debonding, combined with the characteristics of the VCFEM model, the mesh re-division technology is used to ensure that when the stress of the interface node exceeds the critical value and causes interface debonding, the model can automatically adjust the mesh to adapt to the new crack propagation path and delamination state;

[0080] S5: During the numerical simulation stage, a stress cloud diagram is generated after each incremental loading step to intuitively display the stress distribution and concentration phenomenon inside the composite material. Stress concentration often indicates impending material damage or fracture, which can be clearly seen in the stress cloud diagram. Based on the stress state analysis, the results are checked in combination with MARC and ABAQUS, and the comparative analysis helps to verify the accuracy and effectiveness of VCFEM application.

[0081] S6: Based on the analysis results, a stress curve is drawn to show the mechanical response during the entire damage evolution process; by changing the particle thickness and interface bonding condition parameters in the simulation, the influence of different factors on the interface debonding behavior is studied.

[0082] Example 2

[0083] Delamination Voronoi unit construction of hollow particles

[0084] In this example, a two-dimensional linear elastic problem is studied and a numerical example is performed under plane stress. In order to analyze the effect of delamination between inclusions and matrix on the microscopic evolution and macroscopic properties of the structure, consider Figure 1 The inclusion phase and matrix phase of the hollow particle delaminated Voronoi unit are denoted as Ω c Ω m .n e is the unit boundary The direction of the external normal. b It is the undebonded matrix-inclusion interface The direction of the external normal. i Hollow interface The direction of the external normal. m and n c Debonding matrix interface and debonding inclusion interface The direction of the external normal.

[0085] Undelaminated interface between inclusion and matrix The surface force continuity condition is satisfied

[0086]

[0087] At the delamination interface, the surface force is zero

[0088]

[0089] Interface between inclusions and voids The surface force is zero

[0090]

[0091] Based on the stress hybrid element functional formula, the Lagrange multiplier is used to impose constraints and the modified complementary energy functional is obtained:

[0092]

[0093] Among them, u m and u c represents the debonding crack displacement, and the unit boundary displacement field is obtained by the linear interpolation function.

[0094] The functional expression of complementary energy after finite element discretization is:

[0095]

[0096] In the above formula, the matrix H m ,H c ,G e ,G mb ,G cc ,G cb ,G mm ,G ci Defined as:

[0097]

[0098] The identification of Gaussian points in the integral calculation is achieved by dividing the matrix of each phase into multiple quadrilaterals.

[0099] P m ,P c is the known stress function of the matrix and inclusions relative to the point position.

[0100] By Stress function β m ,β c Derivation, get

[0101]

[0102] The weak expression of the motion relationship within the unit can be obtained

[0103] H m β m =G e q e -G mb q b +G mm q m

[0104] H c β c =G cb q b +G cc q c -G ci q i (12)

[0105]

[0106] By Q e ,q b ,q m ,q m ,q i Derivation, get

[0107]

[0108] The weak expression of the surface force boundary condition can be obtained

[0109]

[0110] in,

[0111] The coefficient β can be written as

[0112] β=H -1 Gq (17)

[0113] Substituting (17) into (15) we obtain

[0114]

[0115] Matrix-inclusion interface debonding remeshing technology

[0116] In order to realistically simulate the interfacial delamination process of particle reinforced composites, the corresponding grid structure must inevitably change as the delamination area changes. Therefore, the matrix-inclusion interface mesh re-division method is used to simulate the gradually debonded matrix-inclusion interface.

[0117] Assume that during a certain loading process of a particle reinforced composite material, at the beginning of an incremental step, a section of delamination has occurred between the matrix and inclusion interface of a certain unit. According to certain fracture mechanics principles, when the node stress reaches or exceeds the critical state, the original crack tip will extend forward along the interface between the matrix and the inclusion at the node. A sub-step of crack extension is the debonding of the interface where the node is located while other interfaces remain bonded together. In the first step, the stress state of all nodes of the interface is judged. If the node stress reaches or exceeds the critical stress, the interface will debond. In the second step, a new delamination is generated by connecting the two nodes of the debonding interface. Figure 2 Take the middle node A as an example. When A reaches the critical stress, the interface debonds. Before the new delamination occurs, the matrix and the inclusion share the same node at point A. This is not a problem in the bonding state. However, with the emergence of new delamination, the displacement of the matrix at point A and the inclusion at point A are no longer completely consistent. In order to ensure that the crack surface force is zero, the node pair A1 and A2 are used here to represent point A on the inclusion and point A on the matrix, respectively. The corresponding node variables satisfy the following relationship:

[0118] Δu A1 =Δu A2 =Δu A (20)

[0119] When the original crack tip A extends to point B, if the stress state of node B reaches or exceeds the critical state, point B continues to debond, resulting in new delamination, and proceeds to the next step to determine whether the stress state of other nodes has reached the critical state.

[0120] Example 3

[0121] Numerical Examples

[0122] This embodiment has two types of numerical examples: the first type of examples is to verify the effectiveness of this VCFEM. Its effectiveness is verified by comparing the results with the commercial computing software MRAC and ABAQUS. The second type of examples uses this unit to simulate a composite material containing a large number of randomly distributed hollow inclusions, and calculates the gradual cracking process between the matrix and the hollow inclusion interface under the action of load. Its effectiveness is also verified by comparing certain states of the cracking process with the MARC software. All examples use the same number of polynomials and stress function terms.

[0123] A matrix-hollow inclusion element

[0124] In this example, the VCFEM model consists of a simple Voronoi cell, while the MARC model and the ABQAQUS model consist of a fine finite element mesh containing a large number of cells. The effectiveness of VCFEM is verified by comparing the results with those of MARC. The model to be simulated is a 2×2 mm 2 The square matrix contains a hollow inclusion with a radius of 0.2 mm and a radius of 0.15 mm for the hollow part of the inclusion. The inclusion is located at the center of the square matrix. The inclusion is represented by an octagonal structure with cracks on the two right sides. For the convenience of comparative analysis, the boundary conditions and displacement loads of the VCFEM model, MARC model and ABAQUS model are exactly the same, such as Figure 3 As shown in (a), the displacements of the top and bottom boundaries are 0, and the horizontal displacement of the left boundary is 0. The horizontal displacement on the right boundary is 0.0002 mm.

[0125] The MARC model consists of 9856 second-order isoparametric plane stress triangular elements, which contain 5107 nodes such as Figure 3 As shown in (c), the VCFEM model consists of a Voronoi unit. Figure 3 As shown in (b), the stress functions of the matrix and inclusion parts in the Voronoi unit contain 99 items, which are composed of 63 polynomial stress functions and 33 interaction stress function items. The material properties used in the model analysis are as follows:

[0126] Inclusion E c =80000MPa,υ c =0.25,r c =0.2mm

[0127] Base Base E m =40000MPa,υ c =0.2

[0128] The above results show that the three models can be well matched with each other. Figure 5 σ of VCFEM, MARC, and ABAQUS at the midline position x , σ yBy comparison, it can be seen that different peaks appear at the interface between the matrix and the crack, different degrees of stress concentration appear in the hollow part of the inclusion, and the stress drops rapidly to the minimum value at the crack. Except at the interface between the matrix and the inclusion, the stress components of the three models are more or less different, mainly due to the following two reasons: (I) In VCFEM, the matrix and the inclusion in each unit are assumed to be stress functions. It is difficult to describe the stress field with two continuous functions and to satisfy perfect continuity at all interfaces between the matrix and the inclusion; (II) In the MARC model, there is only one node at the same position on the interface between the matrix and the inclusion, and the interface node stress component value obtained by the software is only one, which cannot reflect the stress discontinuity applied on the interface. In the VCFEM model and ABAQUS, there are two stress values ​​at the interface point.

[0129] Progressive debonding with a hollow inclusion

[0130] In this example, the VCFEM model contains a simple Voronoi unit, and the MARC model is composed of a large number of fine mesh units. The effectiveness of VCFEM is verified by comparing the results with those of MARC. 2 The square matrix contains a hollow inclusion with a radius of 0.2mm and a radius of 0.15mm for the hollow part of the inclusion. The inclusion is located at the center of the square matrix and is represented by a hexagonal structure. For the convenience of comparative analysis, the boundary conditions and displacement loads of the VCFEM model, MARC model and ABAQUS model are exactly the same, with the displacements of the top and bottom boundaries being 0 and the horizontal displacement of the left boundary being 0. The horizontal displacement on the right boundary is 0.0002mm. Initially, there is no delamination on each edge. As the load increases, delamination of different numbers of edges occurs when the stress state of each node of the inclusion reaches or exceeds the critical stress state.

[0131] To correspond to the delamination process, four MARC models for comparative analysis were established, which consisted of 13424 second-order isoparametric plane stress triangular elements and 6970 nodes. The VCFEM consisted of a Voronoi element. The stress functions of the matrix and the inclusion part in the Voronoi element contained 99 items each, consisting of 63 polynomial stress functions and 33 interaction stress function terms. The material properties of the model were the same as above.

[0132] Figure 7 The σ values ​​of MARC and VCFEM for no debonding, 2×2 edge debonding, 2×4 edge debonding, and 2×6 edge debonding are given. x Stress cloud diagram. Figure 8 The midline position of MARC, VCFEM, and ABAQUS is given xIt can be seen from the two figures that for each delamination form, the stress cloud diagrams calculated by the two models are consistent, and the stress distribution has different peaks only at the interface between the inclusion and the matrix. The stress concentration in the hollow part is more obvious in MARC and ABAQUS.

[0133] Debonding extension of large hollow inclusions

[0134] In this example, we mainly simulate complex hollow particle reinforced composite materials, such as Fig. 9 As shown in (a), the target model is 1×1mm 2 20 elliptical hollow inclusions of arbitrary size and direction are randomly distributed on the square plate, and the radius of the hollow part of the inclusion is about 0.0049mm. The material properties are the same as above, the horizontal displacement of the left boundary is fixed, the vertical displacement of the upper and lower boundaries is fixed, and the load is applied on the right side.

[0135] Initially, all inclusion interfaces have no delamination, and each inclusion interface consists of 16 straight edges. As the load increases, the normal stress at some interface nodes is greater than the given critical stress, resulting in delamination of some interface segments. The nodes with normal stress greater than the given critical stress are replaced by a node pair after meshing. The stress functions of the matrix and inclusion parts in the unit in the VCFEM model contain 99 items.

[0136] The VCFEM model simulates the process of gradual damage to the entire structure under load as follows: the given displacement on the right side of the initial load is 0.0003 mm; then, for each incremental step, the displacement increment is 0.00001 mm, and the total load step is 50 steps.

[0137] To verify the effectiveness of VCFEM, a MARC model with the same damage condition is established based on the damage condition calculated by VCFEM in the fourth incremental step (delamination occurs at both ends of units 5 and 16). Fig. 9 As shown in (b), the MARC model consists of 30,027 units, including 15,974 nodes. Fig.10 (a) and (b) are the stress σ of MARC and VCFEM respectively. x Stress cloud diagram. Fig.11 and Fig.12 The stress distribution of the VCFEM model and the MARC model on the horizontal and vertical midlines. From these figures, it can be seen that the stress distribution of the two methods is well matched. The displacement of the internal nodes is related to the displacement of the external nodes of the unit itself, and the internal nodes are compressed in the unit. Therefore, if no new cracks are generated in the unit, the stiffness calculation of the unit only needs to be the first step in the entire calculation process.

[0138] The simulation results of the structural damage process by the VCFEM model are as follows: The horizontal stress cloud diagrams of step 1 (0.00031mm), step 6 (0.00036mm), step 11 (0.00041mm), and step 16 (0.00046mm) are as follows: Fig.13 As shown. For step 1, the interface between the matrix and the hollow inclusions was perfectly bonded. In step 6, six inclusions debonded at the interface. In step 11, fourteen inclusions debonded at the interface. In step 16, except for the interface of one inclusion, the other nineteen inclusions debonded at the interface.

[0139] In order to further understand the impact of interface delamination damage on the overall structure, the change of the right end constraint force with the horizontal displacement of the right end is obtained, as shown in Fig.14 As shown. The change of the curve can be roughly divided into three stages: (a) the initial linear stage, in which the displacement is less than 0.00033mm, almost no delamination occurs, and the constraint reaction force and displacement are basically in a linear change relationship; (b) the large damage stage, when the right end displacement increases in the range of 0.00033mm to 0.00048mm, due to the large amount of delamination, the increase in the constraint reaction force has slight fluctuations. (c) the linear rising stage, when the right end displacement is greater than 0.00048mm, although there is still a small amount of delamination, the impact on the overall structure is very small, and the constraint reaction force and displacement become a linear change relationship again.

[0140] Fig.15 is the debonding of the unit with different inclusion thicknesses in the sixth incremental step. Fig.15 (a) Six inclusion debonding occurred. Fig.15 (b) Debonding of sixteen inclusions occurred. Fig.15 (c) Debonding of eighteen inclusions occurred. It can be seen that under the same displacement load, the larger the inclusion thickness of the hollow inclusion unit, the easier it is to cause delamination damage.

[0141] The preferred embodiments of the present invention disclosed above are only used to help illustrate the present invention. The preferred embodiments do not describe all the details in detail, nor do they limit the invention to the specific implementation methods described. Obviously, many modifications and changes can be made according to the content of this specification. This specification selects and specifically describes these embodiments in order to better explain the principles and practical applications of the present invention, so that those skilled in the art can understand and use the present invention well. The present invention is limited only by the claims and their full scope and equivalents.

Claims

1. A simulation method for interface debonding of hollow particle reinforced composite materials based on VCFEM model, characterized in that: The following steps are involved: S1: Create a geometric model, including the distribution of matrix and hollow particle inclusions; use Voronoi cells to simulate particle composites, one Voronoi cell contains one inclusion to accurately describe the actual distribution and geometric characteristics of particles; assign material properties to the matrix and inclusions, including physical parameters such as elastic modulus and Poisson's ratio, to ensure that the mechanical behavior of these materials is accurately reflected in the simulation; S2: Define the interface between the matrix and the inclusion, and set the interface to be perfectly bonded at the initial stage; for the initial state of the simulation, the stress field state in the matrix and the inclusion should be described by the stress hybrid finite element method; S3: In the incremental loading stage, the deformation and damage evolution of the composite material under the action of external forces is simulated by gradually increasing the applied load or displacement; the stress state of all nodes is calculated in each incremental step, and the nodes whose stress reaches or exceeds the critical value are identified; Supercritical nodes indicate a high risk of interface debonding; S4: For the treatment of interface debonding, combined with the characteristics of the VCFEM model, the mesh re-division technology is used. When the stress of the interface node exceeds the critical value, the interface debonds; the model automatically adjusts the mesh to adapt to the new crack propagation path and delamination state; S5: During the numerical simulation stage, a stress cloud diagram is generated after each incremental loading step to visually display the stress distribution and concentration phenomenon inside the composite material; On the basis of stress state analysis, MARC and ABAQUS were combined to check the results, and comparative analysis was performed to verify the accuracy and effectiveness of VCFEM application. S6: Draw a stress curve based on the analysis results to show the force during the entire damage evolution process By changing the particle thickness and interface bonding condition parameters in the simulation, the influence of different factors on the interface debonding behavior is studied.

2. The method for simulating interfacial debonding of hollow particle reinforced composite materials based on the VCFEM model according to claim 1, characterized in that: The inclusion phase and matrix phase of the Voronoi unit are denoted as Ω c ,Ω m ;n e is the unit boundary The direction of the external normal; n b It is the undebonded matrix-inclusion interface The direction of the external normal; n i Hollow interface The direction of the external normal; n m and n c Debonding matrix interface and debonding inclusion interface The direction of the external normal of Undelaminated interface between inclusion and matrix The surface force continuity condition is satisfied n b ·(σ m -σ c )=0 (on ) (1) At the delamination interface, the surface force is zero n m ·σ m =0(in (2) n c ·σ c =0(in (3) Interface between inclusions and voids The surface force is zero n i ·σ c =0(in (4) Based on the stress hybrid element functional formula, the Lagrange multiplier is used to impose constraints and the modified complementary energy functional is obtained: Among them, u m and u c represents the debonding crack displacement, and the unit boundary displacement field is obtained by the linear interpolation function; The functional expression of the complementary energy after finite element discretization is: In the above formula, the matrix H m ,H c ,G e ,G mb ,G cc ,G cb ,G mm ,G ci Defined as: The identification of Gaussian points in the integral calculation is achieved by dividing the matrix of each phase into multiple quadrilaterals; P m ,P c is the known stress function of the relative point positions of the matrix and inclusions; By Stress function β m ,β c Derivation, get The weak expression of the motion relationship within the unit can be obtained By Q e ,q b ,q m ,q m ,q i Derivation, get The weak expression of the surface force boundary condition can be obtained in, The coefficient β can be written as β=H -1 Gq (17) Substituting (17) into (15) we obtain 3. The method for simulating interfacial debonding of hollow particle reinforced composite materials based on the VCFEM model according to claim 1, characterized in that: The step S4 uses a matrix-inclusion interface re-meshing method to simulate the gradually debonded matrix-inclusion interface; specifically, it includes the following sub-steps: S4.1: Determine the stress state of all nodes on the interface. If the node stress reaches or exceeds the critical stress, the interface will debond; S4.2: New delamination occurs at the two nodes connecting the debonding interface; Set the node as A. When A reaches the critical stress, the interface debonds. To ensure that the crack surface force is zero, A1 and A2 are used to represent point A on the inclusion and point A on the matrix, respectively. The corresponding node variables satisfy the following relationship: When the original crack tip A extends to a new node set as point B, if the stress state of node B reaches or exceeds the critical state, point B continues to debond and produce new delamination, and then proceeds to the next step to determine whether the stress state of other nodes reaches the critical state.

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