A tensile strength theoretical prediction method of polymer adhesive material considering mesoscopic components

Abstract

The application discloses a tensile strength theoretical prediction method of polymer bonding material considering micro components, and comprises the following steps: step 1: obtaining interface strength σ 界面 , polymer tensile strength σ 聚合物 , additive tensile strength σ 添加物 , additive particle size d and characteristic size h0 according to test calibration / direct test; step 2: calculating cross section equivalent inclination angle α 等效 and interface failure proportion ζ according to additive particle geometric morphology and lattice parameters; step 3: calculating effective bonding area proportion; and step 4: calculating polymer bonding material tensile strength.

Description

Technical Field

[0001] This invention belongs to the field of composite material technology, and more specifically relates to a theoretical prediction method for the tensile strength of polymer adhesive materials that takes into account microstructure components. Background Technology

[0002] Polymer-bonded composites have been widely used in aerospace, biomedicine and other fields due to their excellent mechanical properties. Accurately predicting the tensile strength of polymer-bonded composites is a prerequisite for composite material design and evaluation.

[0003] Currently, the tensile strength of polymer-bonded composites is commonly predicted using theoretical and simulation methods. In terms of simulation, finite element method (FEA) software is often used to establish a cell model (RVE) that includes the polymer and additives and considers the microstructure and composition to obtain the tensile strength of the composite material by cell stretching. However, simulation methods have problems such as low efficiency and indirectness in the iterative design process. Theoretical prediction methods are efficient and convenient, but due to the complex microstructure of polymer composites, such as the local weak adhesion between the polymer and additives and the large differences in the shape / size of the additives, the tensile strength of the composite material is not guaranteed.

[0004] Currently available methods for predicting the tensile strength of polymer composites are based on the failure mechanism of microcrack propagation, and assume that the maximum crack length is equal to the maximum additive size. However, these methods consider limited factors, such as polymer content, polymer / additive ratio, and interfacial tensile strength, thus limiting their application. Therefore, a method for predicting the tensile strength of polymer composites that simultaneously considers the shape and size of additives, as well as the tensile strength between the polymer, additives, and their interfaces, is still lacking. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention proposes a theoretical prediction method for the tensile strength of polymer composites that considers microstructure components. This method solves the problem of accurately predicting the tensile strength of polymer composites considering the shape and size of additive particles, as well as the tensile strength between the polymer, the additive, and their interfaces. This method is applicable to the tensile strength prediction of PBX explosives and concrete polymer composites.

[0006] To achieve the above-mentioned objectives, this invention adopts the following technical solution:

[0007] A theoretical prediction method for the tensile strength of polymer adhesives considering microstructures includes the following steps:

[0008] Step 1: Obtain the interface strength based on experimental calibration / direct testing Polymer tensile strength Tensile strength between additives Additive particle size and feature dimensions ;

[0009] Step 2: Calculate the equivalent dip angle of the cross section based on the particle geometry and lattice parameters of the additive. and the percentage of interface failures ;

[0010] Step 3: Calculate the percentage of effective bonded area;

[0011] Step 4: Calculate the tensile strength of the polymer adhesive material.

[0012] In step 1, Measured from a pure additive granule molded sample.

[0013] Step 2: Calculate the equivalent tilt angle of the cross section based on the geometric morphology and lattice parameters of the additive particles. and the percentage of interface failures ;include:

[0014] Step 21: Obtain particle lattice parameters by querying / experimenting / calculating ;

[0015] Step 22: Calculate the surface area of ​​each additive particle based on its morphology and lattice parameters. ;

[0016] (1);

[0017] Step 23: Calculate the normal direction of the surface of each additive particle based on geometric relationships. ;

[0018] (2);

[0019] In the formula: , , ;

[0020] Step 24: Calculate the equivalent inclination angle ;

[0021] (3);

[0022] Step 25: Calculate the proportion of interface failures based on lattice parameters ;

[0023] (4).

[0024] Step 3: Calculating the effective bonding area percentage; including:

[0025] Step 31: Calculate the volume of the additive particles based on the lattice parameters ,

[0026] (5);

[0027] Step 32: Calculate the surface area of ​​the additive particles based on the lattice parameters. ,

[0028] (6);

[0029] Step 33: Calculate the volume-to-surface ratio of the additive particles based on the volume and surface area of ​​the additive. ,

[0030] (7);

[0031] In the formula, For the dimensions of the added item.

[0032] Step 34: Calculate the average polymer layer thickness based on the particle surface area ratio of the additives and the polymer percentage.

[0033] (8);

[0034] Step 35: Calculate the effective bonding area percentage based on the average polymer layer thickness and characteristic thickness.

[0035] (9).

[0036] The calculation of the tensile strength of the polymer adhesive material includes:

[0037] (10).

[0038] The beneficial effects of this invention compared to the prior art are:

[0039] 1) This invention provides a theoretical prediction method for the tensile strength of polymer-bonded composite materials that takes into account microstructure components;

[0040] 2) This prediction method takes into account the proportion of micro-components, micro-structure (structure and size of additives), and micro-material parameters (such as additives, polymer tensile strength, and interfacial strength), and has high prediction accuracy and wide applicability.

[0041] 3) This prediction method does not require simulation and the prediction process is convenient. Attached Figure Description

[0042] Figure 1 Schematic diagram of the tensile fracture path of polymer adhesive materials;

[0043] Figure 2Schematic diagram of interface tension-shear composite;

[0044] Figure 3 Schematic diagram for determining the equivalent tilt angle using the projection rotation method;

[0045] Figure 4 Schematic diagram of crystal grain lattice parameters. Detailed Implementation

[0046] The present invention will be further described below with reference to embodiments. These embodiments are merely some, not all, of the embodiments of the present invention. Other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are all within the protection scope of the present invention.

[0047] The objective of this invention is to provide a theoretical prediction method for the tensile strength of polymer composites that takes into account the shape and size of additive particles and the tensile strength between the polymer, the additive, and their interfaces. This method can be applied to polymer composite materials such as PBX explosives and concrete.

[0048] To achieve the above prediction method, the basic idea of ​​this invention is as follows:

[0049] Typical microstructure of tensile failure of polymer adhesive materials, such as Figure 1 As shown, during tensile testing, the load is jointly borne by the additives, the polymer, and the interface between the additives and the polymer. The tensile failure mechanism generally consists of three components: interfacial debonding, polymer fracture, and defect propagation. Interfacial debonding is mainly dominated by the interfacial strength between the additives and the polymer, polymer fracture is mainly dominated by the tensile-shear strength of the polymer, and defect propagation is mainly dominated by the tensile strength between additive particles in areas not covered by the polymer. Therefore, the tensile strength of polymer adhesives is assumed to be a weighted sum of these three factors.

[0050] (11);

[0051] In the formula, For the macroscopic tensile strength of the material, For additive / polymer interface strength, For the tensile strength of the polymer, The tensile strength between additive particles. This represents the percentage of the effective adhesive area of ​​the polymer. This part considers interfacial debonding or polymer breakage as failure modes. The percentage of unbonded area is the failure mode, which is the separation of particles between additives. The percentage of interfaces that failed to effectively bond.

[0052] Preferably, This implies that the pure additive particle assembly has no tensile strength; or This indicates that the pure additive particle assembly still has a certain tensile strength.

[0053] Polymer effective adhesion ratio :

[0054] Theoretically, the effective bonding area ratio It is related to the polymer ratio and the size (gradation) of the additives, and further to the average polymer layer thickness, and is positively correlated, that is,

[0055] (12);

[0056] In the formula: The average polymer layer thickness, The particle size distribution of the additives is as follows: This represents the polymer volume percentage.

[0057] The above formula means that the higher the polymer content, the thicker the average polymer layer, and the larger the effective bonding area ratio; the larger the particle size and the smaller the surface area, the thicker the average polymer layer, and the larger the effective bonding area ratio. Therefore, the effective bonding area ratio is a function of the average polymer layer thickness.

[0058] (13);

[0059] The above equation satisfies:

[0060] (14);

[0061] Therefore, its functional form may be,

[0062] (15);

[0063] In the formula: is the feature size, and is a parameter to be determined.

[0064] Interface strength Correction:

[0065] Since the interface normal direction generally forms a certain angle with the tensile direction, meaning the interface is in a combined tensile-shear failure mode, such as... Figure 2 As shown. When at the tilt angle During loading, the interface is under a combined tensile and shear stress state, and its tensile stress and shear stress are decomposed into,

[0066] (16);

[0067] In the formula: The angle of inclination is Normal stress at time, The angle of inclination is The shear stress at that time.

[0068] Its composite failure criterion is,

[0069] (17);

[0070] In the formula: The tensile strength at the interface. This represents the interfacial shear failure strength.

[0071] Therefore, the angle of inclination The equivalent interface strength is,

[0072] (18);

[0073] In previous studies, Therefore, for simplicity, the equivalent interface strength can be approximately ,

[0074] (19);

[0075] Interface failure rate Determination:

[0076] Through equation (19), when the inclination angle When it approaches 90°, Approaching infinity, It tends towards infinity, which does not conform to reality. That is, when the angle of inclination... Beyond a certain angle, the equivalent interfacial strength will exceed the tensile strength of the polymer bulk, at which point the PBX will fail as a polymer tensile failure mode. This indicates the existence of a critical cross-sectional inclination angle. ,

[0077] (20);

[0078] When the angle At that time, the failure mode is interface debonding, when the tilt angle is... At that time, the failure mode was polymer fracture. Considering the tilt angle in the microstructure of the polymer adhesive material... It exhibits a certain distribution, meaning that both interfacial failure and polymer failure exist simultaneously. This refers to the percentage of interface failures, used to distinguish between interface failures and polymer failures.

[0079] Due to the random orientation of the additive particles, the interface failure rate is relatively low. This is an important but computationally difficult parameter. This invention proposes a method for determining the proportion of interface failures—the projection rotation integral averaging method, such as... Figure 3As shown, the main idea is as follows: Projecting the additive particles along any plane, the relationship between the projected surface area of ​​the i-th additive particle and the surface area of ​​the i-th additive particle can be obtained geometrically as follows:

[0080] (twenty one);

[0081] In the formula: Let i be the surface area of ​​the i-th additive particle. For spatial angle The tilt angle of the surface of the i-th additive particle during projection. For spatial angle The projected area of ​​the surface of the i-th additive particle during projection. It is the projection angle in three-dimensional space, and , .

[0082] Based on the spatial vector relationship, the surface inclination angle of the i-th additive particle is .

[0083] (twenty two);

[0084] in, Let be the unit vector of the outward normal to the surface of the i-th additive particle. For spatial angle The unit vector of the normal to the lower projection plane.

[0085] Therefore, the failure rate of the computing interface That is, to find a section with a dip angle less than the critical dip angle. The proportion, that is, finding all spatial angles. Down The proportion of [amount]. Therefore, its calculation formula is as follows:

[0086] (twenty three);

[0087] Equivalent section dip angle Determination:

[0088] Because the particle orientation of the additives is random, the equivalent dip angle of the cross section is... This is an important but computationally difficult parameter. This invention calculates the equivalent tilt angle based on the projection rotation integral averaging method, such as... Figure 3-4 As shown, the main idea is as follows: by projecting the additive particles along any plane, the projected area can be obtained. The corresponding inclination angle is Then, the projection plane is rotated to obtain the changes in the projected area and tilt angle with the rotation angle. The equivalent tilt angle is then obtained by averaging the weighted integrals. The expression is as follows:

[0089] (twenty four);

[0090] In the formula: This is the equivalent cross-sectional dip angle. For spatial angle The tilt angle of the surface of the i-th additive particle during projection. For spatial angle The projected area of ​​the surface of the i-th additive particle during projection. It is the projection angle in three-dimensional space, and , .

[0091] Detailed Implementation Plan

[0092] Step 1: Obtain the interface strength based on experimental calibration / direct testing Polymer tensile strength Tensile strength between additives Additive particle size and feature dimensions ,in It can be measured from a pure additive granule molded sample;

[0093] Step 2: Calculate the equivalent dip angle of the cross section based on the particle geometry and lattice parameters of the additive. and the percentage of interface failures ;

[0094] Step 21: Obtain particle lattice parameters by querying / experimenting / calculating ;

[0095] Step 22: Calculate the surface area of ​​each additive particle based on its morphology and lattice parameters. ;

[0096] (25);

[0097] Step 23: Calculate the normal direction of the surface of each additive particle based on geometric relationships. ;

[0098] (26);

[0099] In the formula: , , .

[0100] Step 24: Calculate the equivalent inclination angle ;

[0101] (27)

[0102] Step 25: Calculate the proportion of interface failures based on lattice parameters ;

[0103] (28);

[0104] Step 3: Calculate the percentage of effective bonded area;

[0105] Step 31: Calculate the volume of the additive particles based on the lattice parameters ,

[0106] (29);

[0107] Step 32: Calculate the surface area of ​​the additive particles based on the lattice parameters. ,

[0108] (30);

[0109] Step 33: Calculate the volume-to-surface ratio of the additive particles based on the volume and surface area of ​​the additive. ,

[0110] (31);

[0111] In the formula, For the dimensions of the added item.

[0112] Step 34: Calculate the average polymer layer thickness based on the particle surface area ratio of the additives and the polymer percentage.

[0113] (32);

[0114] Step 35: Calculate the effective bonding area percentage based on the average polymer layer thickness and characteristic thickness.

[0115] (32);

[0116] Step 4: Calculate the tensile strength of the polymer adhesive material;

[0117] (34).

[0118] Example 1

[0119] This invention has been successfully applied to PBX materials at the Institute of Chemical Materials, China Academy of Engineering Physics, enabling accurate testing of the tensile strength of PBX materials and achieving excellent application results.

[0120] Step 1: The selected PBX polymer adhesive material contains HMX crystals as additives, with a size of [missing information]. The tensile strength of pure additives after compression molding is The polymer tensile strength is The additive / polymer interface strength is Feature size (Feature dimensions are obtained through calibration).

[0121] Step 2: Calculate the equivalent dip angle of the cross section and the percentage of interface failures ;

[0122] Step 21: Query / experiment / calculate to obtain TATB lattice parameters;

[0123] ;

[0124] Step 22: Calculate the number of additive particles on the surface and the surface area of ​​each additive particle ;

[0125] (35);

[0126] Step 23: Calculate the normal direction of the surface of each additive particle. ;

[0127] ,

[0128] ,

[0129] .

[0130] (36);

[0131] Step 24: Calculate the equivalent inclination angle using the following formula. :

[0132] (37);

[0133] Note: Spatial angles in spherical coordinates The normal direction of the projection plane below is

[0134] Therefore, the equivalent tilt angle .

[0135] Step 25: Calculate the percentage of interface failures ;

[0136] (38);

[0137] Step 3: Calculate the percentage of effective bonded area ;

[0138] Step 31: Calculate the volume of the additive particles based on the lattice parameters.

[0139] (39);

[0140] Step 32: Calculate the surface area of ​​the additive particles based on the lattice parameters.

[0141] (40);

[0142] Step 33: Calculate the volume-to-surface ratio of the additive particles based on the volume and surface area of ​​the additive (considering the size of the additive).

[0143] (41);

[0144] Step 34: Calculate the average polymer layer thickness based on the added object surface area and polymer percentage.

[0145] (42);

[0146] Step 35: Calculate the effective bonding area percentage based on the average polymer layer thickness and characteristic thickness.

[0147] (43);

[0148] Step 36: Calculate the tensile strength of the polymer adhesive material PBX;

[0149] (44).

[0150] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A theoretical prediction method for the tensile strength of polymer adhesive materials considering microstructure, characterized in that, Includes the following steps: Step 1: Obtain the interface strength based on experimental calibration / direct testing Polymer tensile strength Tensile strength between additives Additive particle size and feature dimensions ; Step 2: Calculate the equivalent dip angle of the cross section based on the particle geometry and lattice parameters of the additive. and the percentage of interface failures ; Step 3: Calculate the percentage of effective bonded area; Step 4: Calculate the tensile strength of the polymer adhesive material; Step 2: Calculate the equivalent tilt angle of the cross section based on the geometric morphology and lattice parameters of the additive particles. and the percentage of interface failures ;include: Step 21: Obtain particle lattice parameters by querying / experimenting / calculating ,in, Let the lengths of the three edges of the unit cell be denoted as _____. Let be the angle between edge b and edge c of the unit cell. Let be the angle between edge a and edge c of the unit cell. Let be the angle between edge a and edge b of the unit cell; Step 22: Calculate the surface area of ​​each additive particle based on its morphology and lattice parameters. ; （1）； Step 23: Calculate the normal direction of the surface of each additive particle based on geometric relationships. ; （2）； In the formula: , , ; Step 24: Calculate the equivalent tilt angle ; ； （3）； in, The tensile strength at the interface; Let be the surface area of ​​the i-th additive particle; For the three-dimensional spatial projection angle, , It is a spatial angle variable, and , ; For spatial angle Unit vector of the normal to the lower projection plane; Step 25: Calculate the proportion of interface failures based on lattice parameters. ; （4）； Step 3: Calculating the effective bonding area percentage; including: Step 31: Calculate the volume of the additive particles based on the lattice parameters , （5）； Step 32: Calculate the surface area of ​​the additive particles based on the lattice parameters. , （6）； Step 33: Calculate the volume-to-surface ratio of the additive particles based on the volume and surface area of ​​the additive. , （7）； In the formula, For the dimensions of the additive; Step 34: Calculate the average polymer layer thickness based on the particle surface area ratio of the additives and the polymer percentage. （8）； Where β is the particle surface area ratio of the additive, and ω is the volume percentage of the polymer; Step 35: Calculate the effective bonding area percentage based on the average polymer layer thickness and characteristic thickness. （9）； The calculation of the tensile strength of the polymer adhesive material includes: （10）； in, The tensile strength at the interface; The percentage of effective bonding area; The equivalent dip angle of the tensile fracture surface The cosine value.

2. The theoretical prediction method for the tensile strength of polymer adhesive materials considering microstructure components according to claim 1, characterized in that, In step 1, The results were obtained from a sample formed from pure additive particles.

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