A simulation prediction method and system for tensile strength of aramid paper

Abstract

The present invention provides a simulation prediction method and system for the tensile strength of aramid paper, which relates to a composite material of aramid paper and uses a finite element method, and belongs to the technical field of electrical digital data processing. The present invention can generate an equivalent material field representing three material phases by constructing an interface phase field model, so that the phase field model can be used to analyze the crack extension problem of sudden changes in material properties. The present invention provides a basic equation of a dynamic phase field model including an interface phase field and a crack phase field, and the tensile strength of the aramid paper composite material can be obtained by combining finite element analysis. When predicting the tensile strength of aramid paper, the present invention fully considers the real microstructural characteristics of aramid paper, including the diameter and length of fibers, the random distribution of fibers, the volume fraction of fibers, and the porosity. When predicting the tensile strength, the volume fraction of fiber-reinforced materials, the volume fraction of pores, the strength and critical energy release rate of the interface, the strength and critical energy release rate of the matrix, etc. can be used as input characteristics.

Description

Technical Field

[0001] The invention belongs to the technical field of electrical digital data processing, relates to a composite material of aramid paper and a finite element method, and specifically relates to a simulation prediction method and system for the tensile strength of aramid paper. Background Art

[0002] As a kind of artificial synthetic fiber, aramid fiber has excellent properties such as high strength, high modulus, low density, high temperature resistance and corrosion resistance. Short fiber reinforced composite paper based on aramid fiber can be used to make honeycombs with excellent mechanical properties. In modern industries such as aerospace, national defense, and communications, honeycombs are widely used in various structures. Therefore, short-cut aramid reinforced paper with higher performance is needed, which plays a key role in the performance of honeycombs. At the same time, establishing a model that can accurately predict the performance of aramid paper is of great significance for the engineering application of this material. The progressive failure model of composite materials provides an important tool in safety and stability design.

[0003] However, the complex microstructure of aramid fiber composite paper may lead to multiple failure mechanisms such as fiber breakage, matrix cracking, and fiber debonding. At the same time, there are many interactions between so many failure modes, which poses a challenge to existing numerical analysis methods. Another challenge of modeling and analyzing progressive failure at the microscale is the need for huge computing resources. So far, many classic damage models are limited to small-scale models, and when considering large-scale models, the modeling time is too long. Summary of the invention

[0004] The present invention is made to solve the above-mentioned problem, and its purpose is to provide a method and system for simulating and predicting the tensile strength of aramid paper.

[0005] The present invention provides a method for simulating and predicting the tensile strength of aramid paper, which has the following characteristics: S10, the microstructure of the aramid paper whose tensile strength is to be predicted contains an interface set and a crack set, the aramid paper is regarded as consisting of a fiber region and a transition region, the boundary of a given load and the boundary of a displacement, the total potential energy of the aramid paper system W = W mix + W f - W ext ,in, W ext represents the total potential energy of the load, W mix represents the elastic potential energy in the transition region, W frepresents the elastic potential energy of the fiber area; S20, the structural failure of aramid paper under a given load is considered to occur only in the transition area, without considering the material damage of aramid paper, and the elastic potential energy of the transition area W mix Split into the tensile part and the compressive part, only the tensile part contributes to the phase field evolution of the crack set, and we can get: , where Ω mix represents the transition region, F represents the crack phase field corresponding to the crack set, ω ( F ) represents the attenuation function of the crack phase field, represents the tensile part, Indicates the compressed part. G c represents the critical elastic potential energy release rate, ▽ F represents the gradient of the crack phase field, γ ( F ,▽ F ) represents the crack surface density functional; S30, after introducing the viscous energy into the crack phase field model, the Lagrangian functional of the system of the aramid paper to be predicted tensile strength can be obtained: , where the system kinetic energy , Ω represents the analysis area, ρ Indicates the material density of aramid paper, represents the system velocity, viscous energy , T is the total time span, represents the model viscosity of the constructed crack phase field, u represents the system displacement, ; S40, order , The Lagrangian equation of the system of the tensile strength of aramid paper to be predicted can be obtained as follows: ; S50, obtain the phase field model of dynamic asymptotic damage failure containing the interface phase field and crack phase field corresponding to the interface set: ,in, represents the tensile stress part of the load, represents the compressive stress part of the load, represents the gradient of compressive stress, represents the acceleration of the system, , , represents the change of crack phase field, represents the pressure gradient corresponding to the load, n The external normal vector of the boundary representing the displacement, represents a given load, represents the boundary of a given load, represents the boundary of the analysis area, Ω f represents the fiber area, H Represents the introduced historical variables, H Used to replace the tensile part of the elastic potential energy in the transition area; S60, the phase field model of dynamic asymptotic damage failure is discretized by the corresponding finite element, and the asymptotic damage analysis of the phase field model is completed by the finite element method, so as to obtain the longitudinal and transverse tensile strengths of the aramid paper.

[0006] The method for simulating and predicting the tensile strength of aramid paper provided by the present invention may also have the following features: wherein step S20 includes the following sub-steps: S21, the structural failure of the aramid paper under a given load is regarded as occurring only in the transition region, then , where Γ c represents the crack set, Ω mix \Γ c represents the transition region that does not contain cracks, represents the elastic potential energy density without considering the material damage of aramid paper; S22, using the regularized format to represent the crack and the related fracture energy, is obtained ; S23, in order to ensure that cracking only occurs under tensile stress, the elastic potential energy of the transition region W mix Split into the tensile part and the compressive part, only the tensile part contributes to the phase field evolution of the crack set, and we can get: .

[0007] The method for simulating and predicting the tensile strength of aramid paper provided by the present invention may also have the following characteristics: wherein, in step S22, , α ( F )=2 F - F 2 , α ( F ) represents the variables of the crack phase field, , c 0 are the model parameters of the crack phase field, l 0 represents the regularization length.

[0008] The method for simulating and predicting the tensile strength of aramid paper provided by the present invention may also have the following characteristics: wherein, in step S50, , τ Indicates time, Indicate point x In time τ The strain of time.

[0009] The method for simulating and predicting the tensile strength of aramid paper provided by the present invention may also have the following feature: the composite material of aramid paper for which the tensile strength is to be predicted adopts standard hexahedral grid units.

[0010] The present invention also provides an aramid paper tensile strength simulation prediction system, which has the following characteristics: it uses any of the aforementioned aramid paper tensile strength simulation prediction methods, including: a data input part, used to input the number of grids of the composite material of the aramid paper whose tensile strength is to be predicted and the material properties of the aramid paper and establish a finite element model of the corresponding composite material; a simulation stretching part, which applies uniform tensile displacement to the aramid paper in the longitudinal and transverse directions; a prediction part, which has a phase field model of dynamic asymptotic damage failure inside, and is used to perform asymptotic damage finite element analysis on the aramid paper during the loading process of the simulation stretching part, thereby obtaining the damage cloud map and displacement stress curve of the aramid paper during the loading process, and calculating the tensile strength of the aramid paper.

[0011] The beneficial effects of the present invention are:

[0012] (1) The present invention can generate an equivalent material field representing three material phases by constructing an interface phase field model, so that the phase field model can be used to analyze crack propagation problems with sudden changes in material properties, further expanding the application scenarios of the phase field model.

[0013] (2) The present invention provides the basic equations of the dynamic phase field model including the interface phase field and the crack phase field, and the tensile strength of the aramid paper composite material can be obtained by combining with finite element analysis.

[0014] (3) When predicting the tensile strength of aramid paper, the present invention fully considers the real microstructure characteristics of aramid paper, including: fiber diameter and length, fiber random distribution, fiber volume fraction and porosity, etc. When predicting the tensile strength, the volume fraction of fiber reinforcement, the volume fraction of pores, the strength and critical energy release rate of the interface, the strength and critical energy release rate of the matrix, etc. can be used as input characteristics.

[0015] (4) The present invention uses the interface phase field model to replace the commonly used cohesive force unit and adopts the standard hexahedral unit, which reduces the number of node degrees of freedom, saves computing resources, and provides an efficient numerical analysis method for the performance prediction of aramid paper. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 Schematic diagram of the microstructure of aramid paper according to an embodiment of the present invention.

[0017] Figure 2 It is a schematic diagram of the connection relationship of an aramid paper tensile strength simulation prediction system according to an embodiment of the present invention.

[0018] Figure 3is a schematic diagram of a finite element model of a composite material established in a test example of the present invention.

[0019] Figure 4 It is the uniform stretching of the composite material of aramid paper in the test example of the present invention in the longitudinal and transverse directions.

[0020] Figure 5 It is a destruction cloud diagram of the aramid paper during the loading process in the test example of the present invention.

[0021] Figure 6 It is the displacement stress curve of the aramid paper during the loading process in the test example of the present invention. DETAILED DESCRIPTION

[0022] In order to make the technical means, creative features, objectives and effects of the present invention easy to understand, the following embodiments and drawings specifically describe a method and system for simulating and predicting the tensile strength of aramid paper of the present invention.

[0023] <Example>

[0024] This embodiment provides a method for aramid paper tensile strength simulation prediction, including the following steps S10-S60:

[0025] Figure 1 Schematic diagram of the microstructure of aramid paper according to an embodiment of the present invention.

[0026] S10, such as Figure 1 As shown, the microstructure of the aramid paper whose tensile strength is to be predicted contains an interface set Γ i and the crack set Γ c , consider the aramid paper as a fiber area Ω f and the transition region Ω mix Composition, the boundary of the given load and displacement boundaries , the total potential energy of the aramid paper system: W = W mix + W f - W ext .

[0027] in, W ext represents the total potential energy of the load, W mix represents the elastic potential energy in the transition region, W f represents the elastic potential energy of the fiber region.

[0028] Figure 1 middle, η represents the phase field function defined, η = 0 represents the matrix area, η =1 represents the interface region, Ω represents the analysis region, F represents the crack phase field corresponding to the crack set, and t* represents the given load.

[0029] S20, gives the elastic potential energy of the transition region W mix The specific expression includes the following sub-steps S21 to S23:

[0030] S21, since the fiber has higher stiffness and toughness than the interface and matrix, the structural failure of aramid paper under a given load is considered to occur only in the transition region. The total potential energy in the transition region consists of two parts, and equation 1 is obtained:

[0031] .

[0032] Among them, Ω mix represents the transition region, Γ c represents the crack set, Ω mix \Γ c represents the transition region that does not contain cracks, represents the elastic potential energy density without considering the material damage of aramid paper, G c represents the critical elastic potential energy release rate.

[0033] S22, according to phase field theory, cracks and related fracture energies can be expressed in a regularized format, rewriting Equation 1 to obtain Equation 2:

[0034] .

[0035] in, ω ( F ) represents the attenuation function of the crack phase field, ▽ F represents the gradient of the crack phase field, γ ( F ,▽ F ) represents the crack surface density functional, , α ( F )=2 F - F 2 , α ( F ) represents the variables of the crack phase field, , c 0 are the model parameters of the crack phase field, l 0 represents the regularization length.

[0036] S23, in order to ensure that cracking occurs only under tensile stress, the elastic potential energy of the transition region W mix Split into the tensile part and the compressive part, only the tensile part contributes to the phase field evolution of the crack set, so Equation 2 is rewritten to obtain Equation 3:

[0037] .

[0038] in, represents the tensile part, Indicates the compressed part.

[0039] S30, similar to dynamic mechanics, introduces viscous energy into the crack phase field model to obtain the Lagrangian functional of the system for the tensile strength of aramid paper to be predicted:

[0040] .

[0041] Among them, the system kinetic energy , ρ Indicates the material density of aramid paper, represents the system velocity, viscous energy , T is the total time span, represents the model viscosity of the constructed crack phase field, u represents the system displacement, .

[0042] S40, order , The Lagrangian equation of the system of the tensile strength of aramid paper to be predicted can be obtained as follows:

[0043] .

[0044] S50, the phase field model of dynamic asymptotic damage failure containing the interface phase field and crack phase field corresponding to the interface set is obtained:

[0045] .

[0046] in, represents the tensile stress part of the load, represents the compressive stress part of the load, represents the gradient of compressive stress, represents the acceleration of the system, , , represents the change of crack phase field, represents the pressure gradient corresponding to the load, n The external normal vector of the boundary representing the displacement, represents the boundary of a given load, represents the boundary of the analysis area, Ω f represents the fiber area, H Represents the introduced historical variables, H The tensile part used to replace the elastic potential energy in the transition region, , τ Indicates time, Indicate point x In time τ The strain of time.

[0047] S60, the phase field model of dynamic asymptotic damage failure is discretized by finite element, and the asymptotic damage analysis of the phase field model is completed by finite element method, so as to obtain the longitudinal and transverse tensile strength of aramid paper.

[0048] Figure 2 It is a schematic diagram of the connection relationship of an aramid paper tensile strength simulation prediction system according to an embodiment of the present invention.

[0049] like Figure 2 As shown, this embodiment also provides an aramid paper tensile strength simulation prediction system, which uses the aramid paper tensile strength simulation prediction method of this embodiment.

[0050] The aramid paper tensile strength simulation prediction system 100 in this embodiment includes a data input unit 10 , a simulation stretching unit 20 and a prediction unit 30 .

[0051] The data input unit 10 is used to input the number of grids of the composite material of aramid paper whose tensile strength is to be predicted and the material properties of the aramid paper and to establish a finite element model of the corresponding composite material.

[0052] The simulated stretching part 20 applies uniform stretching displacement to the aramid paper in the longitudinal and transverse directions.

[0053] The prediction unit 30 contains the phase field model of dynamic asymptotic damage failure obtained in step S50 of the aforementioned aramid paper tensile strength simulation prediction method, which is used to perform finite element analysis of asymptotic damage on the aramid paper during the loading process of the simulated stretching unit 20, thereby obtaining the damage cloud map and displacement stress curve of the aramid paper during the loading process, and calculating the tensile strength of the aramid paper.

[0054] <Test example>

[0055] This test example uses an aramid paper tensile strength simulation prediction method and system in the embodiment to perform a simulation test, and demonstrates by calculating the tensile strength of a 1 mm×3 mm×6 mm aramid paper composite material.

[0056] First, the data input unit 10 is used to input the number of grids of the composite material of aramid paper and the material properties of the aramid paper whose tensile strength is to be predicted, and a finite element model of the corresponding composite material is established.

[0057] Figure 3 Schematic diagram of the finite element model of the composite material established in the test example of the present invention. Figure 3 As shown, in this test example, the composite material structure of aramid paper adopts a uniform hexahedral grid, in which the number of fiber grids is 19835, the number of matrix grids is 48819, the elastic modulus of aramid fiber is 40 GPa, and the Poisson's ratio is 0.33; the elastic modulus of the matrix is ​​4 GPa, the Poisson's ratio is 0.4, the matrix strength is 30 MPa, and the critical energy release rate of the matrix is ​​0.25 N / m 2 ; The strength of the interface is 10MPa, and the critical energy release rate of the interface is 0.0135 N / m 2 .

[0058] Subsequently, the composite material of the aramid paper is subjected to uniform stretching displacement in the longitudinal and transverse directions by the simulated stretching unit 20. The uniform stretching in the longitudinal and transverse directions is as follows: Figure 4 As shown, Figure 4 It is the uniform stretching of the composite material of aramid paper in the test example of the present invention in the longitudinal and transverse directions.

[0059] Finally, by using the phase field model of dynamic asymptotic damage failure contained in the prediction part 30, a finite element analysis of asymptotic damage is performed on the aramid paper during the loading process of the simulated tensile part 20, thereby obtaining the damage cloud map and displacement stress curve of the aramid paper during the loading process, and calculating the tensile strength of the aramid paper.

[0060] Figure 5 is a destruction cloud diagram of aramid paper during loading in a test example of the present invention; Figure 6 It is the displacement stress curve of the aramid paper during the loading process in the test example of the present invention.

[0061] like Figure 5 and Figure 6 As shown, the longitudinal tensile strength and transverse tensile strength of the aramid paper in the test example of the present invention are 68.1 MPa and 30.6 MPa, respectively.

[0062] Those skilled in the art should understand that the present invention is not limited to the above embodiments, and the above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, and these changes and improvements fall within the scope of the present invention to be protected. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A simulation prediction method for tensile strength of aramid paper, characterized in that: The following steps are involved: S10, the microstructure of the aramid paper for which the tensile strength is to be predicted contains an interface set and a crack set. The aramid paper is considered to be composed of a fiber region and a transition region. Given the boundary of the load and the boundary of the displacement, the total potential energy of the aramid paper system W=W mix +W f -W ext , Among them, W ext represents the total potential energy of the load, W mix represents the elastic potential energy of the transition region, W f represents the elastic potential energy of the fiber region; S20, the structural failure of the aramid paper under a given load is considered to occur only in the transition region, without considering the material damage of the aramid paper, and the elastic potential energy W of the transition region is mix Split into a tensile part and a compressive part, only the tensile part contributes to the phase field evolution of the crack set, and we can get: Among them, Ω mix represents the transition region, F represents the crack phase field corresponding to the crack set, ω(F) represents the attenuation function of the crack phase field, represents the tension part, Indicates the compressed part, G c represents the critical elastic potential energy release rate, ▽F represents the gradient of the crack phase field, and γ(F,▽F) represents the crack surface density functional; S30, after introducing the viscous energy into the crack phase field model, the Lagrangian functional of the system of the part of the aramid paper to be predicted in terms of tensile strength can be obtained: Among them, the system kinetic energy Ω represents the analysis area, ρ represents the material density of the aramid paper, represents the system velocity, viscous energy T is the total time span, represents the model viscosity of the constructed crack phase field, u represents the system displacement, S40, let q = [u, F], The Lagrangian equation of the system of the aramid paper to be predicted tensile strength part can be obtained by the following formula: S50, obtaining a phase field model of dynamic asymptotic damage failure containing the interface phase field corresponding to the interface set and the crack phase field: Among them, σ + represents the tensile stress part of the load, σ - represents the compressive stress part of the load, represents the gradient of the compressive stress, ü represents the acceleration of the system, ΔF represents the change of the crack phase field, represents the pressure gradient corresponding to the load, n represents the external normal vector of the displacement boundary, t * represents the given load, represents the boundaries of the given load, represents the boundary of the analysis area, Ω f represents the fiber region, H represents the introduced historical variable, and H is used to replace the tensile part of the elastic potential energy of the transition region; S60, performing corresponding finite element discretization processing on the phase field model of dynamic asymptotic damage failure, and using finite element method to complete asymptotic damage analysis of the phase field model, so as to obtain the longitudinal and transverse tensile strengths of the aramid paper, Wherein, step S20 includes the following sub-steps: S21, the structural failure of the aramid paper under a given load is considered to occur only in the transition region, then Among them, Γ c represents the crack set, Ω mix \Γ c represents the transition region without cracks, ψ ε represents the elastic potential energy density without considering the material damage of the aramid paper; S22, using the regularized format to represent the crack and the associated fracture energy, we obtain α(F)=2F-F 2 , α(F) represents the variables of the crack phase field, c0 is the model parameter of the crack phase field, l0 represents the regularization length; S23, in order to ensure that cracking only occurs under tensile stress, the elastic potential energy W of the transition region is mix Split into a tensile part and a compressive part, only the tensile part contributes to the phase field evolution of the crack set, and we can get:

2. The method for simulating and predicting the tensile strength of aramid paper according to claim 1, characterized in that: in, In step S50, τ represents time, and ε(x, τ) represents the strain at point x at time τ.

3. The method for simulating and predicting the tensile strength of aramid paper according to any one of claims 1 to 2, characterized in that: in, The composite material of aramid paper whose tensile strength is to be predicted uses standard hexahedral grid elements.

4. A simulation prediction system for tensile strength of aramid paper, characterized in that: The method for simulating and predicting the tensile strength of aramid paper according to any one of claims 1 to 3 is used, comprising: A data input unit, used to input the number of grids of the composite material of the aramid paper whose tensile strength is to be predicted and the material properties of the aramid paper and to establish a finite element model of the corresponding composite material; A simulation stretching part, applying uniform stretching displacement to the aramid paper in the longitudinal and transverse directions; The prediction part has the phase field model of dynamic asymptotic damage failure loaded therein, and is used to perform finite element analysis of asymptotic damage on the aramid paper during the loading process of the simulated tensile part, thereby obtaining the damage cloud map and displacement stress curve of the aramid paper during the loading process, and calculating the tensile strength of the aramid paper.

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