CN110348054A - A kind of particle reinforced material conductivity calculation method of the body containing hard core-soft core structure - Google Patents
A kind of particle reinforced material conductivity calculation method of the body containing hard core-soft core structure Download PDFInfo
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- CN110348054A CN110348054A CN201910500152.0A CN201910500152A CN110348054A CN 110348054 A CN110348054 A CN 110348054A CN 201910500152 A CN201910500152 A CN 201910500152A CN 110348054 A CN110348054 A CN 110348054A
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Abstract
The invention discloses a kind of particle reinforced material conductivity calculation method of body containing hard core-soft core structure, steps are as follows: determine the geometric parameter of stone；Calculate the exclusion volume of soft-shell；Calculate the volume fraction of soft-shell；Calculate the percolation threshold of soft-shell；Calculate the particle reinforced material conductivity of hard core-soft core structure body.The present invention overcomes the prior art cannot describe to exceed due to middle layer seep caused by particle reinforced material conductivity mutation process constraint, and the technical bottleneck that numerical simulation low efficiency, precision are difficult to ensure, so that the calculation method of particle reinforced material conductivity has more generality and representativeness.
Description
Technical field
The invention belongs to composite micromechanics and field of material engineering technology, in particular to hard core-soft core structure
Body technique.
Background technique
In recent years, the materials such as carbon fiber, carbon nanotubes, nano-silver thread are because of its excellent stiffness and strength, higher thermally conductive
Property and electric conductivity receive more and more concerns.Researchers are added in matrix using these particles as reinforcing agent, as long as adding
Add seldom amount that the conductive performance of material entirety can be allowed to obtain huge promotion.This material is electronics, sensor, aviation
Ideal material in the engineering fields such as space flight and shielding.The electric conductivity of research and prediction particle reinforced material, which is one, extremely to be had
The problem in science of challenge has great importance for the research and development of material science.Disclose material microstructure and macroscopic view
The quantitative correlation mechanism of performance is to realize particle reinforced material " customization " design by regulating microstructure material macro property
Important channel.Existing research points out that due to processing technology and material property etc., there is be both different from particle around particle
It is different from the middle layer of basis material performance again, this system is typical nucleocapsid structure body, as shown in Figure 1.
In recent years, researcher has passed through scanning electron microscope and x-ray tomography it has been observed that in circumgranular
Interbed, which is mutually communicated, constitutes a complicated network, this complex network is that the media such as electric current, heat, magnetic current are passed in material internal
One of defeated predominating path, especially when mid-level network exceedes infiltration, special change can occur for the conductive performance of material.In current
Between the prediction technique of layer network percolation threshold have ignored the influence of eclipsing effects and particle geometric feature between middle layer, and
And none clearly method obtain aspherical particle surrounding interlayer network percolation threshold, limit them in practice
Application.In terms of particle reinforced material effective performance prediction, recent decades rise the effectively approximate reason of composite micromechanics
By method, such as: Mori-Tanaka mechanism, differential effective medium approximation, generalized self-consistent method cannot all describe middle layer and exceed
Particle reinforced material conductivity Evolution Mechanism under the conditions of infiltration.Based on this, establishes a kind of clear concept, operates conveniently, the scope of application
The calculation method of the wide particle reinforced material conductivity containing hard core-soft core structure body is the task of top priority.
Summary of the invention
Technical problem is mentioned in order to solve above-mentioned background technique, the invention proposes a kind of bodies containing hard core-soft core structure
Particle reinforced material conductivity calculation method.
In order to achieve the above technical purposes, the technical solution of the present invention is as follows:
A kind of particle reinforced material conductivity calculation method of the body containing hard core-soft core structure, comprising the following steps:
(1) geometric parameter of stone is determined；
(2) according to the geometric parameter of stone, the exclusion volume of soft-shell is calculated；
(3) according to the volume fraction of the geometric parameter of stone and particle, the volume fraction of soft-shell is calculated；
(4) using Particles at Critical volume fraction as the token state of the percolation threshold of soft-shell, the Particles at Critical volume point
Number is obtained according to the geometric parameter of the exclusion volume of soft-shell, the critical volume fraction of soft-shell and stone, the soft-shell
Critical volume fraction is obtained by the volume fraction of soft-shell；
(5) according to the volume fraction of the volume fraction of soft-shell and particle, the conductivity of hard core-soft core structure body is calculated；
The percolation threshold of conductivity and soft-shell further according to hard core-soft core structure body calculates the particle enhancing of hard core-soft core structure body
Materials conductive rate.
Further, in step (1), consider stone as spherocylinder, remember its a height of H, diameter D, then draw ratio α
=H/D, equivalent diameter Deq=D (1+1.5 α)1/3。
Further, in step (2), it is calculate by the following formula the exclusion volume of soft-shell:
In above formula, Sc=(1+ α) π Deq 2A-23,A=1+1.5 α, B=1+0.5 α,For soft-shell
Exclusion volume, t are the thickness of soft-shell.
Further, in step (3), it is calculate by the following formula the volume fraction of soft-shell:
In above formula, φsIt is the volume fraction of soft-shell, φcFor the volume fraction of particle, λ=t/Deq, s is the ball of particle
Like degree, s=(1+1.5 α)2/3/(1+α)。
Further, in step (4), it is calculate by the following formula the percolation threshold of soft-shell:
In above formula, φc cFor Particles at Critical volume fraction, the i.e. percolation threshold of soft-shell, φc sFor the critical body of soft-shell
Fraction,For the exclusion volume of soft-shell, gcs(φc c)=(1- φc c/2)/(1-φc c)3。
Further, in step (5), the conductivity of hard core-soft core structure body is calculated according to the following formula:
In above formula, σcsIt is the conductivity of hard core-soft core structure body, σsIt is the conductivity of middle layer, σcIt is particle in axial direction
Conductivity on direction, F (α) is depolarizing factor,
The particle reinforced material conductivity of hard core-soft core structure body is calculated further according to following formula:
In above formula, σeffIt is the conductivity of particle reinforced material, σmIt is the conductivity of matrix, P is that soft-shell exceedes infiltration
Percolation probability, LpeFor representative body
The side length of product unit.
By adopting the above technical scheme bring the utility model has the advantages that
The present invention can predict that geometric parameter based on aspherical particle, middle layer exceed infiltration and act on lower particle reinforced material
Conductivity, particle reinforced material conductivity mutated caused by overcoming the prior art and cannot describing to exceed due to middle layer infiltration
The technical bottleneck that the constraint of journey and numerical simulation low efficiency, precision are difficult to ensure, so that the meter of particle reinforced material conductivity
Calculation method has more generality and representativeness.It is clear concept of the present invention, easy to operate, for its field of compound material application
It promotes significant.
Detailed description of the invention
Fig. 1 is the particle reinforced material representative volume unit conductivity principle figure containing hard core-soft core structure body；
Fig. 2 is flow chart of the method for the present invention；
Fig. 3 is the comparison diagram of conductivity calculation method and experimental result proposed by the present invention, is included (a), (b) two width
Figure.
Specific embodiment
Below with reference to attached drawing, technical solution of the present invention is described in detail.
The present invention devises a kind of particle reinforced material conductivity calculation method of body containing hard core-soft core structure, such as Fig. 2 institute
Show, comprising the following steps:
Step 1: determining the geometric parameter of stone；
Step 2: according to the geometric parameter of stone, calculating the exclusion volume of soft-shell；
Step 3: according to the volume fraction of the geometric parameter of stone and particle, calculating the volume fraction of soft-shell；
Step 4: using Particles at Critical volume fraction as the token state of the percolation threshold of soft-shell, the Particles at Critical volume
Score is obtained according to the geometric parameter of the exclusion volume of soft-shell, the critical volume fraction of soft-shell and stone, the soft-shell
Critical volume fraction obtained by the volume fraction of soft-shell；
Step 5: according to the volume fraction of the volume fraction of soft-shell and particle, calculating the conduction of hard core-soft core structure body
Rate；The percolation threshold of conductivity and soft-shell further according to hard core-soft core structure body calculates the particle of hard core-soft core structure body
Reinforcing material conductivity.
In the present embodiment, above-mentioned steps 1 are realized using following preferred embodiment:
Consider stone as spherocylinder, remembers its a height of H, diameter D, then draw ratio α=H/D, equivalent diameter Deq=D (1
+1.5α)1/3。
In the present embodiment, above-mentioned steps 2 are realized using following preferred embodiment:
It is calculate by the following formula the exclusion volume of soft-shell:
In above formula, Sc=(1+ α) π Deq 2A-23,A=1+1.5 α, B=1+0.5 α,For soft-shell
Exclusion volume, t are the thickness of soft-shell.
In the present embodiment, above-mentioned steps 3 are realized using following preferred embodiment:
It is calculate by the following formula the volume fraction of soft-shell:
In above formula, φsIt is the volume fraction of soft-shell, φcFor the volume fraction of particle, λ=t/Deq, s is the ball of particle
Like degree, s=(1+1.5 α)2/3/(1+α)。
In the present embodiment, above-mentioned steps 4 are realized using following preferred embodiment:
It is calculate by the following formula the percolation threshold of soft-shell:
In above formula, φc cFor Particles at Critical volume fraction, the i.e. percolation threshold of soft-shell, φc sFor the critical body of soft-shell
Fraction,For the exclusion volume of soft-shell, gcs(φc c)=(1- φc c/2)/(1-φc c)3。
In the present embodiment, above-mentioned steps 5 are realized using following preferred embodiment:
The conductivity of hard core-soft core structure body is calculated according to the following formula:
In above formula, σcsIt is the conductivity of hard core-soft core structure body, σsIt is the conductivity of middle layer, σcIt is particle in axial direction
Conductivity on direction, F (α) is depolarizing factor,
The particle reinforced material conductivity of hard core-soft core structure body is calculated further according to following formula:
In above formula, σeffIt is the conductivity of particle reinforced material, σmIt is the conductivity of matrix, P is that soft-shell exceedes infiltration
Percolation probability, LpeFor representative body
The side length of product unit.
According to above-mentioned conductivity calculation method, actual experimental data can be brought into and be verified, with multi wall nano-sized carbon
For pipe enhances alumina composite material, the conductivity of deoxidation aluminum substrate is σm=10-12S/m, the conduction of multi-walled carbon nanotube
Rate takes σc=6 × 102S/m, the conductivity of middle layer are taken as the 10 of matrix conductive rate14Times, i.e. σs=1014σm, carbon nanotubes
Draw ratio is α=100, and taking the diameter of carbon nanotubes is D=20nm.Intermediate layer thickness t=0.6nm is taken, is led based on of the invention
Shown in (a) in electric rate theory prediction result and experimental result such as Fig. 3, the two has very high consistency.
In addition by taking single-wall carbon nanotubes enhances composite polyimide material as an example, choosing CP2 polyimides, it is led for matrix
Electric rate is σm=6.3 × 10-16S/m, the diameter of single-wall carbon nanotubes are D=1.4nm, and length is H=3 μm, take its conductivity to be
σc=0.6S/m, intermediate layer thickness take t=0.35nm, and mid layer conductive rate is taken as the 10 of matrix conductive rate13Times, i.e. σs=1013
σm, based on shown in (b) in conductivity theoretical prediction result of the invention and experimental result such as Fig. 3, the two has very high one
Cause property.
Embodiment is merely illustrative of the invention's technical idea, and this does not limit the scope of protection of the present invention, it is all according to
Technical idea proposed by the present invention, any changes made on the basis of the technical scheme are fallen within the scope of the present invention.
Claims (6)
1. a kind of particle reinforced material conductivity calculation method of body containing hard core-soft core structure, which is characterized in that including following step
It is rapid:
(1) geometric parameter of stone is determined；
(2) according to the geometric parameter of stone, the exclusion volume of soft-shell is calculated；
(3) according to the volume fraction of the geometric parameter of stone and particle, the volume fraction of soft-shell is calculated；
(4) using Particles at Critical volume fraction as the token state of the percolation threshold of soft-shell, the Particles at Critical volume fraction root
Obtained according to the geometric parameter of the exclusion volume of soft-shell, the critical volume fraction of soft-shell and stone, the soft-shell it is critical
Volume fraction is obtained by the volume fraction of soft-shell；
(5) according to the volume fraction of the volume fraction of soft-shell and particle, the conductivity of hard core-soft core structure body is calculated；Root again
According to the conductivity of hard core-soft core structure body and the percolation threshold of soft-shell, the particle reinforced material of hard core-soft core structure body is calculated
Conductivity.
2. the particle reinforced material conductivity calculation method of the body containing hard core-soft core structure, feature exist according to claim 1
In, in step (1), using stone as spherocylinder consider, remember its a height of H, diameter D, then draw ratio α=H/D, equivalent diameter
Deq=D (1+1.5 α)1/3。
3. the particle reinforced material conductivity calculation method of the body containing hard core-soft core structure, feature exist according to claim 2
In being calculate by the following formula the exclusion volume of soft-shell in step (2):
In above formula, Sc=(1+ α) π Deq 2A-2/3,A=1+1.5 α, B=1+0.5 α,For the repulsion of soft-shell
Volume, t are the thickness of soft-shell.
4. the particle reinforced material conductivity calculation method of the body containing hard core-soft core structure, feature exist according to claim 2
In being calculate by the following formula the volume fraction of soft-shell in step (3):
In above formula, φsIt is the volume fraction of soft-shell, φcFor the volume fraction of particle, λ=t/Deq, s is the ball of particle like degree, s
=(1+1.5 α)2/3/(1+α)。
5. the particle reinforced material conductivity calculation method of the body containing hard core-soft core structure, feature exist according to claim 4
In being calculate by the following formula the percolation threshold of soft-shell in step (4):
In above formula, φc cFor Particles at Critical volume fraction, the i.e. percolation threshold of soft-shell, φc sFor the critical size point of soft-shell
Number,For the exclusion volume of soft-shell, gcs(φc c)=(1- φc c/2)/(1-φc c)3。
6. the particle reinforced material conductivity calculation method of the body containing hard core-soft core structure, feature exist according to claim 5
In, in step (5), according to the following formula calculate hard core-soft core structure body conductivity:
In above formula, σcsIt is the conductivity of hard core-soft core structure body, σsIt is the conductivity of middle layer, σcBe particle in the axial direction
Conductivity, F (α) is depolarizing factor,
The particle reinforced material conductivity of hard core-soft core structure body is calculated further according to following formula:
In above formula, σeffIt is the conductivity of particle reinforced material, σmThe conductivity of matrix, P be soft-shell exceed infiltration exceed infiltration
Probability, LpeFor representative body
The side length of product unit.
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Citations (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101602929A (en) * | 2008-05-27 | 2009-12-16 | 香港科技大学 | A kind of conduction that improves conductive resin exceedes the method for oozing usefulness |
| WO2014209476A1 (en) * | 2013-06-24 | 2014-12-31 | International Business Machines Corporation | Injection of a filler material through implosion |
| US20160104882A1 (en) * | 2014-10-14 | 2016-04-14 | Sila Nanotechnologies Inc. | Nanocomposite battery electrode particles with changing properties |
| CN106164142A (en) * | 2014-03-11 | 2016-11-23 | 香港科技大学 | Conductive and heat-conductive paste composition and utilize said composition to reduce percolation threshold raising to exceed the method oozing conductive performance |
| CN106777822A (en) * | 2017-01-22 | 2017-05-31 | 河海大学 | Two-dimentional high-content particle strengthens composite three-phase meso-mechanical model and method for building up |
| US20170286588A1 (en) * | 2016-03-29 | 2017-10-05 | Mentor Graphics Corporation | Full-Chip Assessment Of Time-Dependent Dielectric Breakdown |
| US20190005172A1 (en) * | 2017-06-16 | 2019-01-03 | University Of Cincinnati | Methods, Software, and Apparatus for Porous Material or Medium Characterization, Flow Simulation and Design |
| CN109370155A (en) * | 2018-10-17 | 2019-02-22 | 中国人民解放军陆军工程大学 | Field causes non-linear conducing composite material preparation method, obtained composite material and application |
-
2019
- 2019-06-11 CN CN201910500152.0A patent/CN110348054B/en active Active
Patent Citations (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101602929A (en) * | 2008-05-27 | 2009-12-16 | 香港科技大学 | A kind of conduction that improves conductive resin exceedes the method for oozing usefulness |
| WO2014209476A1 (en) * | 2013-06-24 | 2014-12-31 | International Business Machines Corporation | Injection of a filler material through implosion |
| CN106164142A (en) * | 2014-03-11 | 2016-11-23 | 香港科技大学 | Conductive and heat-conductive paste composition and utilize said composition to reduce percolation threshold raising to exceed the method oozing conductive performance |
| US20160104882A1 (en) * | 2014-10-14 | 2016-04-14 | Sila Nanotechnologies Inc. | Nanocomposite battery electrode particles with changing properties |
| US20170286588A1 (en) * | 2016-03-29 | 2017-10-05 | Mentor Graphics Corporation | Full-Chip Assessment Of Time-Dependent Dielectric Breakdown |
| CN106777822A (en) * | 2017-01-22 | 2017-05-31 | 河海大学 | Two-dimentional high-content particle strengthens composite three-phase meso-mechanical model and method for building up |
| US20190005172A1 (en) * | 2017-06-16 | 2019-01-03 | University Of Cincinnati | Methods, Software, and Apparatus for Porous Material or Medium Characterization, Flow Simulation and Design |
| CN109370155A (en) * | 2018-10-17 | 2019-02-22 | 中国人民解放军陆军工程大学 | Field causes non-linear conducing composite material preparation method, obtained composite material and application |
Non-Patent Citations (3)
| Title |
|---|
| WENXIANG XU 等: "Excluded volumes of anisotropic convex particles in heterogeneous media: Theoretical and numerical studies", 《COMPUTERS, MATERIALS AND CONTINUA》 * |
| 胡圣飞 等: "石墨烯表面改性及其在聚合物导电复合材料中的应用研究", 《高分子材料科学与工程》 * |
| 许文祥 等: "软物质系颗粒材料组成、微结构与传输性能之间关联建模综述", 《物理学报》 * |
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