Finite element-based composite material heat conduction coefficient analysis method

Abstract

The invention relates to the field of composite material performance characterization, in particular to a finite element-based composite material heat conduction coefficient analysis method, which comprises the following steps of: establishing a finite element model of a composite material unit cell; periodic boundary conditions are applied to the unit cells; using a user subprogram of commercial finite element software to define a heat conduction constitutive of the material; heat flow distribution under various working conditions is obtained through finite element calculation; and post-processing the calculation result to obtain the equivalent heat conduction coefficient of the composite material. According to the method, the load item at the right end of the fine-scale control equation is regarded as a constituent part of the heat conduction constitutive structure of the material, the heat conduction constitutive structure of the material is self-defined through a user subprogram of commercial finite element software, the problem of load item processing is ingeniously solved, and the method has the advantages of being simple in implementation process and small in calculation amount.

Description

Technical Field

[0001] The present invention relates to the field of composite material performance characterization, and in particular to a finite element-based composite material thermal conductivity analysis method. Background Art

[0002] Thermal conductivity is an important indicator of a material's thermal conductivity, directly impacting the thermal stability and thermal management capabilities of composite materials in high-temperature environments. Accurately predicting the equivalent thermal conductivity of composite materials provides a deeper understanding of the heat transfer mechanisms within the material, enabling optimized structural design and improved thermal performance.

[0003] The prediction methods of the equivalent thermal conductivity of composite materials can be divided into two categories: theoretical analytical methods and numerical methods. Commonly used theoretical analytical methods include the Mori-Tanaka method, the self-consistent method, and the generalized self-consistent method. However, in order to obtain relatively simple analytical expressions, theoretical methods usually use overly simplified microstructures, resulting in large errors between the predicted results and the experimental results. Numerical methods include conventional finite element methods, lattice models, lattice Boltzmann methods, and homogenization methods. Among them, the homogenization method has been used to predict material properties such as the elastic constants and thermal conductivity of composite materials. Although the asymptotic homogenization theory is relatively mature, the load term on the right side of its governing equation is special and cannot be directly applied in general finite element software. This requires integrating the load term on each unit to obtain the equivalent nodal load, which makes the implementation process of the homogenization calculation complex and difficult, limiting the promotion and application of this method. For example, in the “Simple Implementation Method for Progressive Homogenization Prediction of Thermal Conductivity Coefficient of Periodic Composite Materials (CN105574255B)” disclosed in Chinese Patent Publication No. CN105574255B, a special temperature field is applied according to the coordinate values ​​of the finite element grid nodes to construct a unit concentration gradient, and then the equivalent node load is obtained through finite element calculation. Although this method avoids the difficulty of manually solving the equivalent node load, it requires an additional finite element calculation, resulting in a doubling of the amount of calculation and a cumbersome implementation process. In the “Multi-scale Calculation Method for Equivalent Thermal Conductivity Coefficient of Complex Composite Structures” disclosed in Chinese Patent Publication No. CN107451308B, the heat conduction problem is converted into a thermoelastic mechanics problem, and then the calculation of the equivalent thermal conductivity coefficient is indirectly realized through the thermal strain method. However, the conversion process in this method is relatively complicated, and the number of load conditions after conversion increases, and the amount of finite element calculation increases, which seriously limits the engineering application of the homogenization method. Summary of the Invention

[0004] To this end, the present invention provides a finite element-based analysis method for thermal conductivity of composite materials, which is used to overcome the problems of complex homogenization analysis process and large amount of calculation in the prior art for thermal conductivity of composite materials.

[0005] To achieve the above object, the present invention provides a finite element-based method for analyzing the thermal conductivity of composite materials, comprising:

[0006] Step S1: Using finite element software to complete the thermal conductivity finite element modeling of the composite unit cell, including geometric structure establishment, mesh division, and assignment of thermal conductivity coefficients of each phase material;

[0007] Step S2: Apply periodic boundary conditions to the unit cell, where the boundary conditions are expressed by the following formula:

[0008]

[0009] Where, χ k is the temperature of the fine-scale problem, k is the index of the loading condition, y is the fine-scale coordinate, Y is the vector of the unit cell size, is the unit cell boundary, are vertices on the boundary of the unit cell;

[0010] Step S3: Define the thermal conductivity constitutive model of the material through the user subroutine of the finite element software, wherein the thermal conductivity constitutive model is expressed by the following formula:

[0011]

[0012] Where, f i k is the heat flow component, K ij is the thermal conductivity coefficient of each component in the unit cell, Indicates temperature gradient, subscripts i and j are the indexes of the coordinate axis, I jk is a 2nd-order unit tensor;

[0013] Step S4: Call the user subroutine of the thermal conductivity constitutive function of the material in step 3 to perform finite element calculation to obtain the temperature field χ under each working condition. k and heat flux distribution f i k ;

[0014] Step S5: Perform post-processing to obtain the equivalent thermal conductivity of the composite material, which is calculated as follows:

[0015]

[0016] Where, is the equivalent thermal conductivity of the composite material, and |Θ| represents the volume of the unit cell.

[0017] The beneficial effects of the present invention are as follows: for solving the uniformization of the thermal conductivity coefficient of composite materials, the present invention regards the load term on the right side of the control equation as a component of the thermal conductivity constitutive law of the material, cleverly solving the problem of load term processing. Compared with the existing technology, the numerical calculation results of the present invention are in good agreement with the theoretical analytical values, the implementation process is simple, and the calculation amount is small. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 This is a flow chart of a method for analyzing thermal conductivity of composite materials based on finite element method according to an embodiment of the present invention;

[0019] Figure 2 Schematic diagram of the microstructure of a unidirectional fiber composite material according to an embodiment of the present invention;

[0020] Figure 3 Schematic diagram of a unit cell of a unidirectional fiber composite material according to an embodiment of the present invention;

[0021] Figure 4 This is a verification diagram of the calculation results of the equivalent thermal conductivity of the embodiment of the present invention. DETAILED DESCRIPTION

[0022] In order to make the objects and advantages of the present invention more clearly understood, the present invention is further described below in conjunction with embodiments; it should be understood that the specific embodiments described herein are merely used to explain the present invention and are not intended to limit the present invention.

[0023] The preferred embodiments of the present invention are described below with reference to the accompanying drawings. It should be understood by those skilled in the art that these embodiments are only used to explain the technical principles of the present invention and are not intended to limit the scope of protection of the present invention.

[0024] See also Figure 1 、 Figure 2 、 Figure 3 and Figure 4 As shown, they are respectively a flow chart of the composite material thermal conductivity analysis method based on finite element according to an embodiment of the present invention; a schematic diagram of the microstructure of the unidirectional fiber composite material according to an embodiment of the present invention; a schematic diagram of the unit cell of the unidirectional fiber composite material according to an embodiment of the present invention; and a verification diagram of the calculation result of the equivalent thermal conductivity according to an embodiment of the present invention.

[0025] The finite element method for analyzing the thermal conductivity of composite materials according to an embodiment of the present invention includes:

[0026] Step S1: Use the commercial finite element software ABAQUS to establish a thermal conductivity finite element model of the composite unit cell, including geometric structure establishment, mesh division, and assignment of thermal conductivity coefficients of each phase material.

[0027] The microstructure of the fiber reinforced composite material in this embodiment is as follows Figure 2As shown, the unit cell diagram of unidirectional fiber composite material is as follows Figure 3 As shown, the unit cell consists of two phases of materials: fiber and matrix, where fiber is represented by A and matrix is ​​represented by B. Assuming that the fiber is transversely isotropic, its in-plane thermal conductivity is represented by K f Indicates that the matrix is ​​an isotropic material and its thermal conductivity is expressed as K m express.

[0028] Step S2: According to the formula Apply periodic boundary strips to the unit cell

[0029] Where, χ k is the temperature of the fine-scale problem, k is the index of the loading condition, y is the fine-scale coordinate, Y is the vector of the unit cell size, is the unit cell boundary, In ABAQUS, the temperature of the corner points of the unit cell is set to zero, and the temperature degrees of freedom of the boundary surface nodes are bounded using Tie constraints.

[0030] Step S3: Define the formula using the UMATHT subroutine of ABAQUS The heat conduction constitutive model described by i k is the heat flow component, K ij is the thermal conductivity coefficient of each component in the unit cell, Indicates temperature gradient, subscripts i and j are the indexes of the coordinate axis, I jk is a 2nd-order unit tensor;

[0031] In this embodiment, a linear perturbation analysis step is created for each working condition, and then the index of the current working condition is obtained through the interface parameter KSTEP in the UMATHT subroutine, and then according to the formula Define the heat flux-temperature gradient relationship under this operating condition. This example uses a two-dimensional unit cell, including two operating conditions (k=1, 2). To facilitate post-processing calculations, set the integration point volume IVOL as the field output variable in the analysis step.

[0032] Step S4: Call the UMATHT subroutine written in step 3 to perform finite element calculation to obtain the temperature field χ under all working conditions k and heat flux distribution f i k .

[0033] Step S5: Write the post-processing Python program according to the formula Calculate the equivalent thermal conductivity of unidirectional fiber reinforced composite materials, where: is the equivalent thermal conductivity of the composite material, and |Θ| represents the volume of the unit cell.

[0034] In this example, the changes in fiber volume fraction and fiber thermal conductivity are considered, and the equivalent thermal conductivity of the composite material predicted by the homogenization method is compared with the analytical solution. Figure 4 As shown, it can be seen that the numerical calculation results are in good agreement with the theoretical analytical values, verifying the effectiveness of the simple implementation method proposed in the present invention.

[0035] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that the present invention is susceptible to various modifications and variations. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention.

Claims

1. A finite element-based analysis method for thermal conductivity of composite materials, characterized in that: include: Step S1: using finite element software to complete the thermal conductivity finite element modeling of the composite unit cell, including geometric structure establishment, mesh division, and assignment of thermal conductivity coefficients of each phase material; Step S2: Apply periodic boundary conditions to the unit cell, where the boundary conditions are expressed by the following formula: In the formula, χ k is the temperature of the fine-scale problem, k is the index of the loading condition, y is the fine-scale coordinate, Y is the vector of the unit cell size, is the unit cell boundary, are vertices on the boundary of the unit cell; Step S3: Define the thermal conduction constitutive model of the material through the user subroutine of the finite element software, wherein the thermal conduction constitutive model is expressed by the following formula: In the formula, f i k is the heat flow component, K ij is the thermal conductivity of each component in the unit cell, Indicates temperature gradient, subscripts i and j are indexes of coordinate axes, I jk is a 2nd-order unit tensor; Step S4: Call the user subroutine of the thermal conductivity constitutive model of the material in step 3 to perform finite element calculation to obtain the temperature field x under each working condition. k and heat flux distribution f i k ; Step S5: Perform post-processing to obtain the equivalent thermal conductivity of the composite material, which is calculated as follows: In the formula, is the equivalent thermal conductivity of the composite material, and |Θ| represents the volume of the unit cell.

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