A method for fast predicting anisotropic thermal conductivity of in-plane random oriented MWCNTs composites

Abstract

The application provides a fast prediction method for anisotropic thermal conductivity of in-plane random orientation MWCNTs composite, relates to the field of thermal performance design of hot-pressing formed plates, and comprises the following steps: obtaining MWCNTs matrix material parameters and geometric parameters of MWCNTs; calculating a shape factor of cylindrical MWCNTs; calculating an equivalent thermal conductivity of an interface layer and a volume fraction of the interface layer; calculating an equivalent fiber thermal conductivity after considering an interface thermal resistance; respectively calculating thermal conductivities along an orientation direction and perpendicular to the orientation direction in uniaxial alignment MWCNTs; calculating in-plane thermal conductivities and thickness direction thermal conductivities of the in-plane random orientation MWCNTs composite and outputting. The method of the application is highly matched with the in-plane random orientation characteristics of the hot-pressing plate, directly outputs the main value of thermal conductivity which is approximately isotropic in the plane and significantly different in the thickness direction, and realizes fast prediction of the anisotropic thermal conductivity of the in-plane random orientation MWCNTs composite.

Description

Technical Field

[0001] This invention relates to the field of composite material thermal conductivity modeling and hot-pressed sheet thermal performance design technology, specifically to a rapid prediction method for the anisotropic thermal conductivity of in-plane randomly oriented MWCNTs composite materials for hot-pressed sheets. Background Technology

[0002] Hot pressing is a common process for preparing carbon nanotube-reinforced polymer composite sheets. During hot pressing, under the shear force of melt flow and the constraint of the mold, multi-walled carbon nanotubes (MWCNTs) tend to disperse and randomly orient themselves within the sheet surface, forming a macroscopic thermal conductivity characteristic of "approximate isotropic in-plane and significantly lower thermal conductivity in the thickness direction," i.e., k1≈k2. k3. This type of sheet material has important applications in engineering scenarios such as thermal management structures and integrated thermal conductive / insulating layers.

[0003] In existing technologies, obtaining the aforementioned anisotropic thermal conductivity mainly relies on experimental measurements or numerical simulations, which suffers from problems such as high cost, long cycle time, and difficulty in characterizing the statistical averaging effect of in-plane random orientation. In addition, existing calculation methods cannot simultaneously consider the aspect ratio, finite volume fraction effect, and interfacial thermal resistance (ITR) of MWCNTs on the reduction of thermal conductivity.

[0004] Therefore, there is a need for an analytical closed-loop method that matches the actual orientation distribution of hot-pressed sheets, has low computational cost, and can explicitly incorporate interfacial thermal resistance, in order to quickly output the dominant thermal parameters of the sheet (in-plane k1, k2 and thickness direction k3) to support material formulation design, process window selection, and thermal simulation input. Summary of the Invention

[0005] In view of this, embodiments of the present invention provide a rapid prediction method for the anisotropic thermal conductivity of in-plane randomly oriented MWCNTs composite materials for hot-pressed sheets, in order to solve the technical problems of high cost, long cycle and difficulty in taking into account the influence of multiple factors in existing methods.

[0006] This invention provides the following technical solution: a method for rapid prediction of the anisotropic thermal conductivity of in-plane randomly oriented MWCNTs composite materials, comprising the following steps:

[0007] S1: Obtain the material parameters of the MWCNTs composite matrix and the geometric parameters of the MWCNTs; the material parameters include: the thermal conductivity k of the matrix. m MWCNTs intrinsic thermal conductivity k f The geometric parameters include: MWCNTs volume fraction φ fThe transverse half-axis length a1 and axial half-axis length a3 of MWCNTs, and the length-to-diameter ratio λ; S2: Calculate the shape factor γ of the cylindrical MWCNTs based on the aspect ratio λ; S3: Obtain the interfacial thermal resistance R between the MWCNTs and the substrate. if and the equivalent thickness h of the interface layer, based on the interface thermal resistance R if Given the equivalent thickness h of the interface layer, calculate the equivalent thermal conductivity of the interface layer. Based on the lateral half-axis a1 of the MWCNTs and the equivalent thickness h of the interface layer, the volume fraction of the interface layer is calculated. ; S4: Based on the geometric parameters and the equivalent thermal conductivity of the interface layer Interface layer volume fraction And the shape factor γ, calculate the equivalent fiber thermal conductivity considering interfacial thermal resistance. ; S5: Based on the geometric parameters and the equivalent fiber thermal conductivity Using shape factor γ, calculate the thermal conductivity along the MWCNT axis in uniaxially aligned MWCNT composites. And the lateral thermal conductivity perpendicular to the MWCNTs axis ; S6: Based on the aforementioned thermal conductivity and transverse thermal conductivity The thermal conductivity tensor of the uniaxially aligned MWCNTs composite material is averaged by orientation to obtain the in-plane thermal conductivity of the in-plane randomly oriented MWCNTs composite material. and thermal conductivity in the thickness direction ;in, =( + ) / 2; = ; S7: The in-plane thermal conductivity of the board is... As the thermal conductivity k1 and k2 in the two principal directions (X and Y directions) of the MWCNTs composite material, the thermal conductivity in the thickness direction is... Output as the thermal conductivity k3 of the MWCNTs composite material along the thickness direction (Z direction).

[0008] According to one embodiment of the present invention, in step S2, the shape factor γ is calculated using the following formula:

[0009] In the formula, γ is the shape factor, λ is the aspect ratio, λ=a3 / a1, a1 is the lateral half-axis length of MWCNTs, and a3 is the axial half-axis length of MWCNTs.

[0010] According to one embodiment of the present invention, in step S3, the equivalent thermal conductivity of the interface layer is... The following formula is used to calculate:

[0011] In the formula, R is the equivalent thermal conductivity of the interface layer. if denoted as , and h as , where h is the equivalent thickness of the interface layer.

[0012] According to one embodiment of the present invention, in step S3, the volume fraction of the interface layer... The following formula is used to calculate:

[0013] In the formula, denoted as the volume fraction of the interface layer, h as the equivalent thickness of the interface layer, and a1 as the length of the lateral half-axis of MWCNTs.

[0014] According to one embodiment of the present invention, in step S4, the equivalent fiber thermal conductivity is... The following formula is used to calculate:

[0015] In the formula, This is the equivalent fiber thermal conductivity. φ is the equivalent thermal conductivity of the interface layer. f For the volume fraction of MWCNTs, k f The intrinsic thermal conductivity of MWCNTs is... γ represents the volume fraction of the interface layer, and γ is the shape factor.

[0016] According to one embodiment of the present invention, in step S5, the thermal conductivity along the MWCNTs axis is... The following formula is used to calculate:

[0017] In the formula, k is the thermal conductivity along the axial direction of MWCNTs. m φ is the thermal conductivity of the matrix. f For MWCNTs volume fraction, γ is the equivalent fiber thermal conductivity, and γ is the shape factor.

[0018] According to one embodiment of the present invention, in step S5, the transverse thermal conductivity perpendicular to the MWCNTs axis is... The following formula is used to calculate:

[0019] In the formula, k is the transverse thermal conductivity perpendicular to the axial direction of MWCNTs. m φ is the thermal conductivity of the matrix. f For MWCNTs volume fraction, γ is the equivalent fiber thermal conductivity, and γ is the shape factor.

[0020] According to one embodiment of the present invention, step S6, averaging the thermal conductivity tensor of the uniaxially aligned MWCNTs composite material by orientation, includes: The thermal conductivity tensor of the uniaxially aligned MWCNTs composite material for: Where n is the axial unit vector of MWCNTs, and I is the third-order unit tensor, I = diag(1,1,1). This represents the baseline thermal conductivity contribution in each lateral direction. This represents the projection term along the axial direction n of the MWCNTs; when randomly oriented in-plane, the axial direction of the MWCNTs lies within the x–y plane of the plate and the azimuth angle is uniformly distributed, affecting the thermal conductivity tensor. Perform orientation averaging, < The average result is a diagonal matrix with in-plane components of 1 / 2 and a thickness component of 0, thus yielding... =( + ) / 2 and = .

[0021] According to one embodiment of the present invention, in step S2, when the aspect ratio λ=1, the shape factor γ takes the value of 1 / 3; in step S3, the equivalent thickness h of the interface layer is determined according to the actual physical thickness of the interface layer.

[0022] According to one embodiment of the present invention, the method further includes the following steps: using the output thermal conductivity k1, k2, and k3 as input parameters to perform three-dimensional steady-state or transient heat conduction simulation of hot-pressed sheet metal, and to optimize hot-pressing process parameters or material formulation.

[0023] Compared with the prior art, the beneficial effects that at least one technical solution adopted in the embodiments of this specification can achieve include at least: (1) Matching with hot-pressing orientation characteristics: The method of this embodiment directly faces k1≈k2 K3 plates commonly exhibit anisotropy, eliminating the need for complex orientation statistical modeling.

[0024] (2) Closed-loop analytical calculation, suitable for optimization: can quickly scan the volume fraction φ of MWCNTs. f Aspect ratio λ, interfacial thermal resistance R if Key parameters such as these assist in optimizing the hot pressing process and material formulation.

[0025] (3) Explicitly incorporated interfacial thermal resistance: through equivalent fiber thermal conductivity Introducing the influence of interfacial thermal resistance into the model improves the consistency between the predicted results and the actual materials.

[0026] (4) Facilitates simulation implementation: The embodiments of this invention output clear thermal conductivity principal values ​​(k1, k2, k3), which can be directly used in anisotropic heat conduction or conjugate heat transfer simulation models. Attached Figure Description

[0027] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0028] Figure 1 This is a schematic diagram of the equivalent fiber model composed of MWCNTs and the interface layer in an embodiment of the present invention; Figure 2 This is a schematic diagram of the in-plane random orientation of MWCNTs in the hot-pressed composite material sheet of an embodiment of the present invention. Detailed Implementation

[0029] The embodiments of this application will now be described in detail with reference to the accompanying drawings.

[0030] The following specific examples illustrate the implementation of this application. Those skilled in the art can easily understand other advantages and effects of this application from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. This application can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this application. It should be noted that, in the absence of conflict, the following embodiments and features in the embodiments can be combined with each other. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0031] This invention provides a method for rapid prediction of the anisotropic thermal conductivity of in-plane randomly oriented MWCNTs composite materials, comprising the following steps: S1: Obtain the material parameters of the MWCNTs composite matrix and the geometric parameters of the MWCNTs; the material parameters include: the thermal conductivity k of the matrix. m MWCNTs intrinsic thermal conductivity k f The geometric parameters include: MWCNTs volume fraction φ f The transverse half-axis length a1 and axial half-axis length a3 of MWCNTs, and the length-to-diameter ratio λ.

[0032] Wherein, the intrinsic thermal conductivity k of the MWCNTs f The equivalent scalar thermal conductivity of the MWCNTs filler phase in the model is given. To facilitate obtaining a closed-form analytical solution within the Mori–Tanaka framework, this invention treats MWCNTs as isotropic cylindrical inclusions, without distinguishing between their bulk axial and radial thermal conductivity. The difference in thermal conductivity between the composite material along the orientation direction (axial) and perpendicular to the orientation direction (transverse) is mainly determined by the aspect ratio λ, shape factor γ, and orientation distribution of the cylindrical inclusions.

[0033] In practice, the material and geometric parameters are the input parameters of the model, which can be obtained through material handbooks, supplier data, microscopic statistics, literature data, experimental measurements, or inversion calibration based on a small amount of experimental data. Specifically, the thermal conductivity k of the matrix... m The intrinsic thermal conductivity k of MWCNTs can be obtained from actual measurements of the matrix material or from literature. f Literature values, supplier parameters, or experimentally calibrated equivalent values ​​of MWCNTs can be used; MWCNT volume fraction φ f It can be obtained from the mass fraction and the density of each component; the transverse half-axis length a1 and axial half-axis length a3 of MWCNTs can be determined from the supplier's nominal dimensions, SEM / TEM statistics or literature dimensions; λ = a3 / a1 is calculated from the geometric dimensions.

[0034] S2: Calculate the shape factor γ of the cylindrical MWCNTs based on the aspect ratio λ; The shape factor γ is calculated using the following formula:

[0035] In the formula, γ is the shape factor, λ is the aspect ratio, λ = a3 / a1, a1 is the lateral semi-axis length of MWCNTs, and a3 is the axial semi-axis length of MWCNTs. When the aspect ratio λ = 1, the shape factor γ is 1 / 3.

[0036] The shape factor γ is derived from the Eshelby tensor of cylindrical or elongated ellipsoidal inclusions in the Mori–Tanaka homogenization model. For cylindrical MWCNTs with an aspect ratio λ = a3 / a1, the inclusion geometry affects the distribution of the temperature gradient in the axial and lateral directions; therefore, the shape factor γ is used to describe this aspect ratio effect. When λ = 1, it degenerates into the case of spherical inclusions, where γ = 1 / 3.

[0037] S3: Obtain the interfacial thermal resistance R between the MWCNTs and the substrate. if And the equivalent thickness h of the interface layer, the interface thermal resistance is equivalent to an interface layer of thickness h, according to the interface thermal resistance R if Given the equivalent thickness h of the interface layer, calculate the equivalent thermal conductivity of the interface layer. Based on the lateral half-axis a1 of the MWCNTs and the equivalent thickness h of the interface layer, the volume fraction of the interface layer is calculated. ; Wherein, the equivalent thermal conductivity of the interface layer The following formula is used to calculate:

[0038] In the formula, R is the equivalent thermal conductivity of the interface layer. if Interfacial thermal resistance (unit: m) 2 ·K / W), h is the equivalent thickness of the interface layer. The equivalent thickness h of the interface layer is determined based on the actual physical thickness of the interface layer, and the value of h ranges from 0.5 nm to 10 nm. Specifically, the equivalent thermal conductivity of the interface layer is... The calculation formula is based on the relationship between the interface temperature drop (ΔT) and thermal resistance: ΔT = q·R if The equation is derived from the assumption of an equivalent continuous medium at the interface layer, where q is the heat flux density.

[0039] The volume fraction of the interface layer The following formula is used to calculate:

[0040] In the formula, denoted as the volume fraction of the interface layer, h as the equivalent thickness of the interface layer, and a1 as the length of the lateral half-axis of MWCNTs.

[0041] Among them, the interfacial thermal resistance R ifThe thermal resistance parameter at the interface between MWCNTs and the polymer matrix can be obtained through literature references, molecular dynamics simulations, interfacial thermal conductivity tests, or by inversion calibration using a small amount of composite material thermal conductivity experimental data. The equivalent thickness h of the interfacial layer is the equivalent thickness introduced when the interfacial thermal resistance is equivalent to a finite-thickness interfacial layer. It can be estimated based on the actual physical thickness of the interfacial layer, the thickness of the surface modification layer, molecular scale, or determined as a fitting parameter. The volume fraction of the interfacial layer... The geometric volume fraction calculation from the interface layer after the MWCNTs are overlaid is essentially "interface layer volume / equivalent total fiber volume".

[0042] S4: Based on the geometric parameters and the equivalent thermal conductivity of the interface layer Interface layer volume fraction And the shape factor γ, calculate the equivalent fiber thermal conductivity considering interfacial thermal resistance. ; The equivalent fiber thermal conductivity was obtained by using the aligned cylindrical inclusion MT closed form, which was used to replace the original intrinsic thermal conductivity k of MWCNTs. f Wherein, the equivalent fiber thermal conductivity The following formula is used to calculate:

[0043] In the formula, This is the equivalent fiber thermal conductivity. φ is the equivalent thermal conductivity of the interface layer. f For the volume fraction of MWCNTs, k f The intrinsic thermal conductivity of MWCNTs is... γ represents the volume fraction of the interface layer, and γ is the shape factor.

[0044] Among them, the equivalent fiber thermal conductivity The calculation is based on a two-step equivalent approach: first, the MWCNT core layer and its surrounding interface layer are considered as a whole, defined as an equivalent fiber; then, the thermal conductivity of this equivalent fiber is calculated using the closed form of aligned cylindrical inclusions in the MT model. The equivalent fiber thermal conductivity is then obtained. Subsequently, the equivalent fiber thermal conductivity was used in the macroscopic composite material calculations. The intrinsic thermal conductivity k of the original MWCNTs is replaced f This allows the influence of interfacial thermal resistance to be explicitly incorporated into the model.

[0045] S5: Based on the geometric parameters and the equivalent fiber thermal conductivity Using shape factor γ, calculate the thermal conductivity along the MWCNT axis in uniaxially aligned MWCNT composites. And the lateral thermal conductivity perpendicular to the MWCNTs axis ; Wherein, the thermal conductivity The following formula is used to calculate:

[0046] The transverse thermal conductivity The following formula is used to calculate:

[0047] In the formula, The thermal conductivity is along the axial direction of MWCNTs. k is the transverse thermal conductivity perpendicular to the axial direction of MWCNTs. m φ is the thermal conductivity of the matrix. f For MWCNTs volume fraction, γ is the equivalent fiber thermal conductivity, and γ is the shape factor.

[0048] The Mori–Tanaka homogenization model establishes the relationship between the microstructure of MWCNTs and the macroscopic thermal conductivity of the composite material using the concentration tensor and the Eshelby tensor. The concentration tensor describes the difference between the mean temperature gradient within the matrix and filler phases and the macroscopic temperature gradient, while the Eshelby tensor characterizes the influence of the aspect ratio and geometry of the cylindrical MWCNT inclusions on the heat conduction path. Based on this model, the equivalent thermal conductivity of the uniaxially aligned MWCNT composite material along the orientation direction can be obtained first. Equivalent transverse thermal conductivity in the vertical orientation direction Furthermore, the equivalent fiber thermal conductivity after considering interfacial thermal resistance will be... The thermal conductivity k of the original filler is replaced f This allows us to obtain the thermal conductivity calculation results after introducing the interfacial thermal resistance correction.

[0049] S6: Based on the aforementioned thermal conductivity and transverse thermal conductivity The thermal conductivity tensor of the uniaxially aligned MWCNTs composite material is averaged by orientation to obtain the in-plane thermal conductivity of the in-plane randomly oriented MWCNTs composite material. and thermal conductivity in the thickness direction ;in, =( + ) / 2; = ; For thermoformed sheets, the axial direction of MWCNTs is always located within the xy plane of the sheet, and the azimuth angle θ is uniformly distributed between 0 and 2π. The in-plane thermal conductivity of the sheet along the plane direction is obtained by averaging the orientation. and thermal conductivity in the thickness direction .

[0050] S7: The in-plane thermal conductivity of the board is... As the thermal conductivity k1 and k2 in the two principal directions (X and Y directions) of the MWCNTs composite material, the thermal conductivity in the thickness direction is... Output as the thermal conductivity k3 of the MWCNTs composite material along the thickness direction (Z direction).

[0051] like Figure 1 As shown, MWCNTs are equivalent to cylindrical inclusions, and the interfacial thermal resistance is equivalent to the interfacial layer covering the outside of the MWCNTs. In the figure, a3 represents the axial semi-axis length of the cylindrical inclusion of MWCNTs along the axial direction; a1 represents the transverse semi-axis length of the core layer of MWCNTs; a2 = a1; h represents the equivalent thickness of the interfacial layer. Based on the above geometric parameters, the aspect ratio λ of MWCNTs can be calculated, and the shape factor γ and the volume fraction of the interfacial layer can be further calculated. And the equivalent fiber thermal conductivity after considering interfacial thermal resistance. .

[0052] like Figure 2 As shown, MWCNTs are mainly distributed within the x–y plane of the composite material sheet, exhibiting random orientation within the plane. The z-direction corresponds to the thickness direction of the sheet. In the figure, the x and y directions correspond to the two principal in-plane thermal conductivity directions of the composite material sheet, denoted as k1 and k2, respectively; the z-direction corresponds to the thickness direction, denoted as k3. This figure illustrates the structural characteristics of MWCNTs during the hot pressing process of the composite material, where their in-plane orientation and thickness-direction orientation are restricted, resulting in anisotropic thermal conductivity where k1≈k2 and k3 differs from the in-plane direction.

[0053] To characterize the anisotropic thermal conductivity of hot-pressed MWCNTs composites on a macroscopic scale, this invention introduces an equivalent thermal conductivity model based on in-plane random orientation of hot-pressed sheets. This model describes how, during hot pressing, due to melt flow shear and mold constraints, MWCNTs within the sheet sample tend to disperse and orient themselves more within the sheet surface, while their orientation is restricted in the thickness direction. This results in typical in-plane approximately isotropic heat transfer characteristics with significantly different orientations in the thickness direction, i.e., k1≈k2. k3.

[0054] Introducing two dominant thermal parameters k1=k2= in the case of uniaxial alignment with k3= Assuming the axial direction of MWCNTs is the only characteristic direction, uniaxially aligned materials can be considered as transversely isotropic axisymmetric media. Let n be the unit direction vector of MWCNTs, then the equivalent thermal conductivity tensor of the uniaxially aligned composite material can be expressed as:

[0055] Where n is the axial unit vector of MWCNTs, and I is the third-order unit tensor, I = diag(1,1,1). This represents the baseline thermal conductivity contribution in each lateral direction. Let n represent the projection term along the axial direction n of MWCNTs; when randomly oriented in-plane, the axial direction of MWCNTs lies within the x–y plane of the plate and the azimuth angle θ is uniformly distributed over 0…2π. Then, the random in-plane orientation is uniformly averaged. > = diag(1 / 2, 1 / 2, 0); < The average result is a diagonal matrix with 1 / 2 components in the two in-plane directions (x and y) and 0 components in the thickness direction (z), thus obtaining... =( + ) / 2 and = .

[0056] Based on the MT mean field homogenization, this invention first obtains two dominant thermal parameters for the case of uniaxially aligned cylindrical inclusions. (Along the MWCNT axis) and (Perpendicular to the MWCNTs axis), and then establish an in-plane random average based on the orientation characteristics of the hot-pressed sheet: the MWCNTs axis is always located in the x–y plane of the sheet, and the azimuth angle θ is uniformly distributed in 0…2π, thus obtaining a closed-form result that is approximately isotropic in the plane and significantly different in the thickness direction. Simultaneously, the interfacial thermal resistance R is reduced through an equivalent fiber step. if Explicitly introduced. Under typical orientation distribution conditions of in-plane randomness and thickness constraint, embodiments of the present invention can quickly predict the principal values ​​(k1, k2, k3) of their equivalent thermal conductivity. This type of sheet material is commonly used in thermal management structures, integrated thermally conductive / insulating layers, and engineering scenarios requiring differences between in-plane diffusion and thickness insulation.

[0057] In some embodiments of the present invention, the method further includes the following steps: using the output thermal conductivity k1, k2, and k3 as input parameters to perform three-dimensional steady-state or transient heat conduction simulation of hot-pressed sheet metal, and to optimize hot-pressing process parameters or material formulations.

[0058] In some embodiments of the present invention, the method of the present invention is integrated into the design process of aerospace heat dissipation structures: taking a MWCNTs-reinforced polymer sheet as a heat diffusion layer through hot pressing as an example: by changing the volume fraction φ of MWCNTs... fThe aspect ratio λ and interfacial thermal resistance parameters (which can be calibrated by experimental inversion) can be used to quickly obtain a dataset of in-plane thermal conductivity and thickness thermal conductivity. Based on this, under the constraints of quality, strength and molding, a better formula and hot pressing process (temperature, pressure, holding time, cooling rate, etc.) can be selected to achieve the target thermal performance.

[0059] In some embodiments of the present invention, the random orientation of MWCNTs in the plane caused by hot pressing can be used as a model application condition: when the thickness direction of the sheet is constrained by the mold and the MWCNTs are statistically uniformly distributed in the plane, the output (k1, k2, k3) of this scheme can better conform to the actual anisotropic characteristics.

[0060] This invention employs the Mori–Tanaka homogenization model to establish the relationship between the microstructural parameters and the macroscopic equivalent thermal conductivity of MWCNTs composite materials. This model treats the polymer matrix as an isotropic continuous medium, equating MWCNTs to isotropic cylindrical inclusions dispersed within the matrix. The concentration tensor describes the relationship between the average temperature gradient within the matrix and filler phases and the macroscopic temperature gradient. The aspect ratio λ and shape factor γ of the cylindrical MWCNTs are used to characterize the influence of the inclusion geometry on the heat conduction path, thus obtaining the equivalent thermal conductivity along the orientation direction and perpendicular to the orientation direction of MWCNTs under uniaxial alignment conditions. Based on this, considering the random in-plane orientation and restricted thickness orientation of MWCNTs in hot-pressed sheets, the in-plane orientation averaging of the uniaxial alignment thermal conductivity tensor is performed to obtain the in-plane thermal conductivity k1, k2 and the thickness thermal conductivity k3 of the sheet. Simultaneously, this invention uses an equivalent fiber model to represent the interfacial thermal resistance R between MWCNTs and the matrix. if By incorporating the Mori–Tanaka model, we can achieve rapid prediction of the anisotropic thermal conductivity of in-plane randomly oriented MWCNTs composites.

[0061] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A rapid method for predicting the anisotropic thermal conductivity of in-plane randomly oriented MWCNTs composite materials, characterized in that, Includes the following steps: S1: Obtain the material parameters of the MWCNTs composite matrix and the geometric parameters of the MWCNTs; The material parameters include: thermal conductivity of the matrix, k. m MWCNTs intrinsic thermal conductivity k f The geometric parameters include: MWCNTs volume fraction φ f The transverse half-axis length a1 and axial half-axis length a3 of MWCNTs, and the length-to-diameter ratio λ; S2: Calculate the shape factor γ of the cylindrical MWCNTs based on the aspect ratio λ; S3: Obtain the interfacial thermal resistance R between the MWCNTs and the substrate. if and the equivalent thickness h of the interface layer, based on the interface thermal resistance R if Given the equivalent thickness h of the interface layer, calculate the equivalent thermal conductivity of the interface layer. Based on the lateral half-axis a1 of the MWCNTs and the equivalent thickness h of the interface layer, the volume fraction of the interface layer is calculated. ; S4: Based on the geometric parameters and the equivalent thermal conductivity of the interface layer Interface layer volume fraction And the shape factor γ, calculate the equivalent fiber thermal conductivity considering interfacial thermal resistance. ; S5: Based on the geometric parameters and the equivalent fiber thermal conductivity Using shape factor γ, calculate the thermal conductivity along the MWCNT axis in uniaxially aligned MWCNT composites. And the lateral thermal conductivity perpendicular to the MWCNTs axis ; S6: Based on the aforementioned thermal conductivity and transverse thermal conductivity The thermal conductivity tensor of the uniaxially aligned MWCNTs composite material is averaged by orientation to obtain the in-plane thermal conductivity of the in-plane randomly oriented MWCNTs composite material. and thermal conductivity in the thickness direction ;in, =( + ) / 2; = ; S7: The in-plane thermal conductivity of the board... As the in-plane thermal conductivity k1 and k2 in the X and Y directions of the MWCNTs composite material, the thermal conductivity in the thickness direction is... Output as the thermal conductivity k3 in the Z direction of the MWCNTs composite material.

2. The method according to claim 1, characterized in that, In step S2, the shape factor γ is calculated using the following formula: In the formula, γ is the shape factor, λ is the aspect ratio, λ=a3 / a1, a1 is the lateral half-axis length of MWCNTs, and a3 is the axial half-axis length of MWCNTs.

3. The method according to claim 1, characterized in that, In step S3, the equivalent thermal conductivity of the interface layer is... The following formula is used to calculate: In the formula, R is the equivalent thermal conductivity of the interface layer. if denoted as , and h as , where h is the equivalent thickness of the interface layer.

4. The method according to claim 1, characterized in that, In step S3, the volume fraction of the interface layer The following formula is used to calculate: In the formula, denoted as the volume fraction of the interface layer, h as the equivalent thickness of the interface layer, and a1 as the length of the lateral half-axis of MWCNTs.

5. The method according to claim 1, characterized in that, In step S4, the equivalent fiber thermal conductivity The following formula is used to calculate: In the formula, This is the equivalent fiber thermal conductivity. φ is the equivalent thermal conductivity of the interface layer. f For the volume fraction of MWCNTs, k f The intrinsic thermal conductivity of MWCNTs is... γ represents the volume fraction of the interface layer, and γ is the shape factor.

6. The method according to claim 1, characterized in that, In step S5, the thermal conductivity along the MWCNTs axis The following formula is used to calculate: In the formula, k is the thermal conductivity along the axial direction of MWCNTs. m φ is the thermal conductivity of the matrix. f For MWCNTs volume fraction, γ is the equivalent fiber thermal conductivity, and γ is the shape factor.

7. The method according to claim 1, characterized in that, In step S5, the transverse thermal conductivity perpendicular to the MWCNTs axis The following formula is used to calculate: In the formula, k is the transverse thermal conductivity perpendicular to the axial direction of MWCNTs. m φ is the thermal conductivity of the matrix. f For MWCNTs volume fraction, γ is the equivalent fiber thermal conductivity, and γ is the shape factor.

8. The method according to claim 1, characterized in that, In step S6, the thermal conductivity tensor of the uniaxially aligned MWCNTs composite material is oriented and averaged, including: The thermal conductivity tensor of the uniaxially aligned MWCNTs composite material for: Where n is the axial unit vector of MWCNTs, and I is the third-order unit tensor, I = diag(1,1,1). This represents the baseline thermal conductivity contribution in each lateral direction. This represents the projection term along the axial direction n of the MWCNTs; when randomly oriented in-plane, the axial direction of the MWCNTs lies within the x–y plane of the plate and the azimuth angle is uniformly distributed, affecting the thermal conductivity tensor. Perform orientation averaging, < The average result is a diagonal matrix with in-plane components of 1 / 2 and a thickness component of 0, thus yielding... =( + ) / 2 and = .

9. The method according to claim 1, characterized in that, In step S2, when the aspect ratio λ=1, the shape factor γ is 1 / 3; in step S3, the equivalent thickness h of the interface layer is determined according to the actual physical thickness of the interface layer.

10. The method according to claim 1, characterized in that, The method further includes the following steps: using the output thermal conductivity k1, k2, and k3 as input parameters to perform three-dimensional steady-state or transient heat conduction simulation of hot-pressed sheet metal, and to optimize hot-pressing process parameters or material formulations.

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