CN111079334A - Mesomechanics-based short fiber composite material effective elastic modulus prediction method - Google Patents
Mesomechanics-based short fiber composite material effective elastic modulus prediction method Download PDFInfo
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Abstract
The invention discloses a mesomechanics-based method for predicting the effective elastic modulus of a short fiber composite material, and belongs to the technical field of material performance prediction. The implementation method of the invention comprises the following steps: based on Mori-tanaka equivalent inclusion theory, a three-dimensional finite element model based on mesomechanics is established, input parameters are matrix material performance and fiber material performance to obtain a strain field, the average strain relation of each phase of the composite material and the effective rigidity of the short fiber composite material are combined to calculate to obtain the effective elastic coefficient of the composite material, and the prediction of the effective elastic modulus of the short fiber composite material is realized according to the relation between the effective elastic coefficient and the effective elastic modulus of the composite material. The invention can be applied to the field of the optimized design numerical simulation of the short fiber composite material and solves the related engineering problems, and the application fields of the optimized design numerical simulation engineering of the short fiber composite material comprise ship propeller performance prediction, injection molding short fiber composite material performance prediction and short fiber composite material fan blade design application.
Description
Technical Field
The invention relates to a prediction method of effective elastic modulus of a short fiber reinforced composite material, which is suitable for a prediction method for predicting mechanical property of the composite material based on mesomechanics and belongs to the technical field of material property prediction.
Background
The short fiber composite material is a polymer composite material with resin as a matrix and various short fibers as disperse phases. The short fiber reinforced resin matrix composite material has no characteristics of a continuous fiber reinforced composite material in the aspects of strength, rigidity and fatigue resistance, but has obvious advantages in the aspects of processability and production efficiency, and has the characteristics of effectively reducing self weight, improving earthquake resistance and being attractive in forming, so that the short fiber reinforced resin matrix composite material is widely applied in the fields of new energy automobiles, aerospace, marine ships, buildings, sports equipment and the like, and has wide development prospect and the possibility of replacing traditional metal and non-metal materials such as steel and the like. The effective elastic properties of the composite material are diverse due to the differences in the composition of the composite material, the variety of phases, the variety of internal structures, and the complex mesoscopic structure. It is very difficult to accurately predict the mechanical properties of the composite material, but the mechanical properties of the composite material are a key item of product indexes. The effective elastic property of the composite material can be measured by an experimental method, but the period is long, the efficiency is low and the production cost is high. Therefore, the method has important engineering significance for predicting the mechanical property of the composite material by establishing a mesoscopic mechanical model and combining a theoretical method and a finite element principle.
At present, aiming at the prediction of the elastic constant of the composite material, under the research of scholars at home and abroad for many years, a plurality of different calculation formulas for predicting the effective elastic constant of the composite material are provided, and comparison experiments show that the axial modulus and the axial Poisson ratio calculated according to the formulas have enough precision and are quite good in accordance with test values, but the prediction of the transverse elastic modulus and the shear modulus still has difficulty. Mori and Tanaka solve the basic theoretical problem of using Eshelby equivalent inclusion principle under the condition of limited volume fraction, and the Mori-Tanaka method has mathematical logicality and integrity, but the Mori-Tanaka method is only suitable for composite materials with inclusions in an ellipsoidal shape, cannot meet most engineering requirements and has strong limitation. Therefore, numerical solution is carried out based on a finite element principle, and the establishment of the short fiber composite material effective elastic constant prediction method which is simple and convenient to calculate, can obtain the transverse elastic modulus and the shear modulus, and is suitable for different shapes of inclusions and has stronger universality is of great significance.
Disclosure of Invention
The invention discloses a mesomechanics-based short fiber composite material effective elastic modulus prediction method, which aims to solve the technical problems that: a universal method for predicting the effective elastic modulus of the short fiber composite material is established, a three-dimensional finite element model based on mesomechanics is established based on a Mori-tanak equivalent inclusion theory, input parameters are the performance of a base material and the material performance of fibers, a strain field is obtained through numerical simulation, prediction of the effective elastic modulus of the short fiber composite material is achieved by using a finite element method, deep analysis and prediction of effective mechanical behaviors, physical behaviors and damage mechanisms of the composite material are facilitated, and the method can be applied to the field of optimization design numerical simulation of the short fiber composite material and solves related engineering problems. The application fields of the optimized design numerical simulation engineering of the short fiber composite material comprise ship propeller performance prediction, injection molding short fiber composite material performance prediction and short fiber composite material fan blade design application. The method can effectively predict the transverse elastic modulus and the shear modulus, and has the advantages of high prediction efficiency and high precision.
The purpose of the invention is realized by the following technical scheme.
The invention discloses a mesomechanics-based prediction method for effective elastic modulus of a short fiber composite material, which is characterized in that an effective rigidity calculation formula of the short fiber composite material is deduced based on a Mori-tanaka equivalent inclusion principle and an average stress principle, and a material constitutive model is established. The material constitutive model comprises an anisotropic material constitutive relation model, an isotropic material constitutive relation model and a transverse isotropic material constitutive relation model. And respectively outputting effective elastic coefficient matrixes of the matrix and the fibers by taking the performances of each phase of the short fiber reinforced resin matrix composite material as input parameters, wherein the performances of each phase comprise the elastic modulus and the Poisson ratio of the matrix and the fibers. And establishing a finite element theoretical model of the short fiber composite material based on the mesomechanics representative volume unit. And calculating the structural response of each phase of the short fiber composite material by using a finite element method. And establishing a relation between the strain fields of the fibers and the matrix and the average strain based on an average strain theory to obtain the average strain of each phase of the short fiber composite material. And calculating to obtain the effective elastic coefficient of the composite material by combining the average strain relationship of each phase of the composite material and the effective rigidity of the short fiber composite material, and predicting the effective elastic modulus of the short fiber composite material according to the relationship between the effective elastic coefficient and the effective elastic modulus of the composite material.
The invention discloses a mesomechanics-based method for predicting the effective elastic modulus of a short fiber composite material, which comprises the following steps of:
the method comprises the following steps: and deducing an effective rigidity calculation formula of the short fiber composite material based on a Mori-tanaka equivalent inclusion principle and an average stress principle, and establishing a material constitutive model. The material constitutive model comprises an anisotropic material constitutive relation model, an isotropic material constitutive relation model and a transverse isotropic material constitutive relation model.
A calculation formula for deducing the effective rigidity of the short fiber composite material based on the Mori-tanaka equivalent inclusion principle and the average stress principle is shown as a formula (1), wherein L0Is the effective modulus of elasticity of the matrix; l is1Is the effective elastic coefficient of the fiber; a is the strain concentration factor in the sparse inclusion state, v1Is the volume ratio of the short fiber to the material.
L＝L0+v1(L1-L0)A (1)
The anisotropic material stress-strain constitutive relation is shown as formula (2), and formula (3) is a matrix form of formula (2). If the material is isotropic, equation (3) reduces to the isotropic material constitutive relation as shown in equation (4), where k is the bulk modulus and μ is the shear modulus.
σ＝Lε (2)
The relationship between the shear modulus and the bulk modulus and the Young modulus and the Poisson ratio are respectively expressed by a formula (5) and a formula (6), wherein E is the Young modulus, and v is the Poisson ratio.
If the material is in transverse isotropy, the constitutive relation of stress and strain is shown in formula (3), and the conversion relation of the stiffness coefficient and the engineering constant is shown in formula (7).
Step two: and respectively outputting effective elastic coefficient matrixes of the matrix and the fibers by taking the performances of each phase of the short fiber reinforced resin matrix composite material as input parameters, wherein the performances of each phase comprise the elastic modulus and the Poisson ratio of the matrix and the fibers.
And respectively outputting effective elastic coefficient matrixes of the matrix and the fiber as shown in a formula (4) by taking the performance of each phase of the short fiber reinforced resin-based composite material as an input parameter, wherein the performance of each phase comprises the elastic modulus and the Poisson ratio of the matrix and the fiber, and the input parameter of the performance of each phase is input into the effective elastic coefficient matrix as shown in the formula (4).
Step three: and establishing a mesomechanics geometric model of the fiber and the matrix according to the distribution orientation and the arrangement mode of the short fibers and the volume ratio of the short fibers in the composite material.
Based on the Morit-anaka equivalent inclusion theory, the inclusions are embedded into an infinite base material bearing uniform strain or uniform stress, and the infinite base material is replaced by a base material with the inclusion size being 5-10 times. And establishing a mesomechanics geometric model of the fiber and the matrix according to the distribution orientation and the arrangement mode of the short fibers and the volume ratio of the short fibers in the composite material. And selecting and establishing a three-phase three-dimensional mesomechanics geometric model or a two-phase three-dimensional mesomechanics geometric model according to whether the interface factors are considered.
Step four: and establishing a finite element theoretical model of the short fiber composite material based on the mesomechanics representative volume unit.
Importing the built mesoscopic mechanical geometric models of the fibers and the matrix in the third step by using mesh division software, dividing meshes respectively, and setting elastic performance parameters of the fibers and the matrix, wherein the elastic performance parameters comprise: elastic modulus and Poisson ratio, and realizes the establishment of a finite element theoretical model of the short fiber composite material based on a mesomechanics representative volume unit.
In order to simplify the numerical simulation process, the mesh partitioning software in the fourth step preferably includes a Mechanical Model module and Ansys ICEM in a WorkBench platform.
Step five: and calculating the structural response of each phase of the short fiber composite material by using a finite element method.
And D, importing the finite element model of the representative volume unit of the short fiber composite material built in the step four into finite element analysis software to calculate the structural response of each phase of the short fiber composite material, adding uniform stress boundary conditions, building boundary value problems, and respectively obtaining a fiber strain field, a matrix strain field and a stress field by utilizing finite element post-processing analysis.
For consistency of the numerical simulation process, the finite element analysis software in step five preferably comprises a Workbench Static Structure, and Ansys APDL.
Step six: and establishing a relation between the strain fields of the fibers and the matrix and the average strain based on an average strain theory to obtain the average strain of each phase of the short fiber composite material.
Respectively extracting fiber and matrix strain fieldsAnd a stress field, based on the Morit-anaka equivalent inclusion theory, when the intrinsic strain is uniform (for intrinsic strain inclusion) or the external load is uniform (for heterogeneous inclusion), the elastic field in the inclusion is uniform and can be expressed by an integral form, the average strain calculation formula of the fiber and the matrix is shown as a formula (8), the average strain calculation formula in a representative form volume of the composite material is obtained according to the average strain theory and is shown as a formula (9), the relation between the effective strain of the composite material and the effective strain in each phase is established as a formula (10), wherein epsilon(1)Is the average strain of the fibres,. epsilon(0)As the average strain of the matrix, the average strain,
is the average of the strain at one point of the composite over the entire volume.
The average strain of the fiber and the matrix is obtained by the average strain equations (8), (9).
Step seven: and calculating to obtain the effective elastic coefficient of the composite material by combining the average strain relationship of each phase of the composite material and the effective rigidity of the short fiber composite material, and predicting the effective elastic modulus of the short fiber composite material according to the relationship between the effective elastic coefficient and the effective elastic modulus of the composite material.
And (3) calculating to obtain a strain concentration factor A required by the formula (1) according to the average strain relation of the fiber and the composite material representative volume unit in the step six as shown in the formula (10), and substituting the strain concentration factor A into the short fiber composite material effective rigidity calculation formula (7) in the step one, so that an effective elastic coefficient matrix of the short fiber composite material is obtained, and the prediction of the effective elastic modulus of the short fiber composite material is realized.
Further comprises the following steps: the method of the first step to the seventh step is applied to the field of the optimized design numerical simulation of the short fiber composite material, the predictability of the mechanical property of the short fiber composite material is realized, the deep analysis of the effective mechanical behavior, the physical behavior and the damage mechanism of the composite material is facilitated, and the related engineering problems can be solved.
And eighthly, the optimization design numerical simulation engineering application fields of the short fiber composite material comprise ship propeller performance prediction, injection molding short fiber composite material performance prediction and short fiber composite material fan blade design application.
When the method in the first step to the seventh step is applied to the optimization design numerical simulation of the short fiber composite material, the influence of the volume content of the short fibers and the arrangement mode of the short fibers on the effective elastic performance of the short fiber composite material is obtained, and a basis is provided for designing and optimizing the short fiber composite material in practical application.
Has the advantages that:
1. the invention discloses a mesomechanics-based short fiber composite material effective elastic modulus prediction method, which utilizes a Mori-Tanaka method and is a calculation method for predicting the mechanical property of a composite material with a strict derivation process and mathematical integrity.
2. The prior art utilizes the Mori-Tanaka method to solve the basic theoretical problem of using the Eshelby equivalent inclusion principle under the condition of limited volume fraction, but the Mori-Tanaka method is only suitable for composite materials with inclusions in an ellipsoidal shape, cannot meet most engineering requirements and has strong limitation. The invention discloses a method for predicting the effective elastic modulus of a short fiber composite material based on mesomechanics, which is based on a Mori-Tanaka method and combines a finite element theory to remove the restriction that the Mori-Tanaka method can only calculate the mechanical property of the composite material which is mixed with an ellipsoid, and improves the calculation precision and the calculation efficiency by establishing a three-dimensional finite element model.
3. The invention discloses a method for predicting effective elastic modulus of short fiber composite material based on mesomechanics, which can establish different three-dimensional finite element models according to short fiber reinforced composite materials with different arrangement modes and orientations, is suitable for short fiber composite materials with different inclusion arrangement modes, and improves the practical value of the conventional Mori-Tanaka method.
4. The method for predicting the effective elastic modulus of the conventional composite material is time-consuming in calculation, low in efficiency and low in calculation precision aiming at the transverse elastic modulus and the shear modulus.
Drawings
FIG. 1 is a flow chart of a method for predicting mechanical effective elastic modulus of a short fiber composite material based on mesomechanics, provided by the invention;
FIG. 2 is a schematic diagram of a two-phase three-dimensional mesomechanics geometric model of one eighth of a representative volume unit of a unidirectional fiber-reinforced composite material provided by an embodiment of the present invention;
FIG. 3 is a schematic diagram of boundary conditions imposed by a two-phase three-dimensional finite element model of one-eighth representative volume element of a unidirectional fiber-reinforced composite material according to an embodiment of the present invention;
FIG. 4 is a strain field response cloud for one-eighth representative volume element fibers and matrices of a unidirectional fiber-reinforced composite material according to an embodiment of the present invention. Wherein: fig. 4(a) is a carbon fiber strain field response cloud chart, and fig. 4(b) is a polyphenylene sulfide strain field response cloud chart.
Detailed Description
The prediction of the effective elastic modulus of a micron chopped carbon fiber reinforced polyphenylene sulfide resin matrix composite (PPS/CF) is taken as an example in combination with the attached drawings, and is shown in figures 1-4. The method for predicting the mechanical property of the short fiber composite material disclosed by the embodiment comprises the following concrete implementation steps of:
the method comprises the following steps: and deducing an effective rigidity calculation formula of the short fiber composite material based on a Mori-tanaka equivalent inclusion principle and an average stress principle, and establishing a material constitutive model. The material constitutive model comprises an anisotropic material constitutive relation model, an isotropic material constitutive relation model and a transverse isotropic material constitutive relation model.
A calculation formula for deducing the effective rigidity of the short fiber composite material based on the Mori-tanaka equivalent inclusion principle and the average stress principle is shown as a formula (1), wherein L0Is the effective modulus of elasticity of the matrix; l is1Is the effective elastic coefficient of the fiber; a is the strain concentration factor in the sparse inclusion state, v1Is the volume ratio of the short fiber to the material.
L＝L0+v1(L1-L0)A (1)
The anisotropic material stress-strain constitutive relation is as in formula (2), and formula (3) is in a matrix form. If the material is isotropic, equation (3) can be simplified to equation (4), where k is the bulk modulus and μ is the shear modulus.
σ＝Lε (2)
The relationship between the shear modulus and the bulk modulus and the Young's modulus and the Poisson's ratio can be expressed by formula (5) and formula (6), respectively, where E is the Young's modulus and v is the Poisson's ratio.
If the material is in transverse isotropy and the stress-strain constitutive relation is shown in formula (3), the conversion relation between the stiffness coefficient and the engineering constant can be shown in formula (7).
Step two: and respectively outputting effective elastic coefficient matrixes of the matrix and the fibers by taking the performances of each phase of the short fiber reinforced resin matrix composite material as input parameters, wherein the performances of each phase comprise the elastic modulus and the Poisson ratio of the matrix and the fibers.
And respectively outputting effective elastic coefficient matrixes of the matrix and the fiber as shown in a formula (4) by taking the performance of each phase of the short fiber reinforced resin-based composite material as an input parameter, wherein the performance of each phase comprises the elastic modulus and the Poisson ratio of the matrix and the fiber, and the input parameter of the performance of each phase is input into the effective elastic coefficient matrix as shown in the formula (4). The main performance parameters of the selected carbon fibers and polyphenylene sulfide (PPS) are shown in table 1. The carbon fiber was 2.35% by volume, and had a cross section of 2 μm and an aspect ratio (L/D) of 30.
TABLE 1 elastic Properties of carbon fiber and polyphenylene sulfide resin matrices
Step three: and establishing a mesomechanics geometric model of the fiber and the matrix according to the distribution orientation and the arrangement mode of the short fibers and the volume ratio of the short fibers in the composite material.
Based on the Morit-anaka equivalent inclusion theory, the inclusions are embedded into an infinite base material bearing uniform strain or uniform stress, and the infinite base material is replaced by a base material with the inclusion size being 5-10 times. And establishing a mesomechanics geometric model of the fiber and the matrix according to the distribution orientation and the arrangement mode of the short fibers and the volume ratio of the short fibers in the composite material. And selecting and establishing a three-phase three-dimensional mesomechanics geometric model or a two-phase three-dimensional mesomechanics geometric model according to whether the interface factors are considered. As shown in fig. 2. The effective elastic constant of the PPS/CF composite material is predicted without considering interface influence, so that a three-dimensional two-phase mesomechanics geometric model is established.
Step four: and establishing a finite element theoretical model of the short fiber composite material based on the mesomechanics representative volume unit.
Importing the built mesoscopic mechanical geometric models of the fibers and the matrix in the third step by using mesh division software, dividing meshes respectively, and setting elastic performance parameters of the fibers and the matrix, wherein the elastic performance parameters comprise: elastic modulus and Poisson ratio, and realizes the establishment of a finite element theoretical model of the short fiber composite material based on a mesomechanics representative volume unit.
In order to simplify the numerical simulation process, the mesh partitioning software in the step four is a Mechanical Model module in a WorkBench platform.
Step five: and calculating the structural response of each phase of the short fiber composite material by using a finite element method.
Leading the finite element model of the representative volume unit of the short fiber composite material built in the step four into finite element analysis software to calculate the response of each phase structure of the short fiber composite material, and adding a uniform stress boundary condition ux＝uy＝uz＝0，σ11＝σ22＝σ33And (3) establishing an edge value problem under 10000Mpa, and finally obtaining a fiber and matrix strain field by finite element post-processing analysis after finite element calculation and boundary conditions shown in figure 3, wherein the fiber and matrix strain fields are obtained respectively by the finite element post-processing analysis, and shown in figure 4.
For consistency of the numerical simulation process, the finite element analysis software in the fifth step is Workbench static Structure.
Step six: and establishing a relation between the strain fields of the fibers and the matrix and the average strain based on an average strain theory to obtain the average strain of each phase of the short fiber composite material.
Respectively extracting strain fields and stress fields of the fiber and the matrix, based on the Morit-anaka equivalent inclusion theory, when the intrinsic strain is uniform (for intrinsic strain inclusions) or the external load is uniform (for heterogeneous inclusions), the elastic field in the inclusions is uniform and can be expressed in an integral form, the calculation formula of the average strain of the fiber and the matrix is shown in a formula (8), and the calculation formula is based on the average strain of the fiber and the matrixThe average strain theory is obtained, the calculation formula of the average strain in the representative single volume of the composite material is obtained as shown in formula (9), the relation between the effective strain of the composite material and the effective strain in each phase is established as shown in formula (10), wherein epsilon(1)Is the average strain of the fibres,. epsilon(0)As the average strain of the matrix, the average strain,
is the average of the strain at one point of the composite over the entire volume.
The average strain of the fiber and the matrix is obtained by the average strain equations (8), (9).
Step seven: and calculating to obtain the effective elastic coefficient of the composite material by combining the average strain relationship of each phase of the composite material and the effective rigidity of the short fiber composite material, and predicting the effective elastic modulus of the short fiber composite material according to the relationship between the effective elastic coefficient and the effective elastic modulus of the composite material.
And (3) calculating to obtain a strain concentration factor A required by the formula (1) according to the average strain relation of the fiber and the composite material representative volume unit in the step six as shown in the formula (10), and substituting the strain concentration factor A into the short fiber composite material effective rigidity calculation formula (7) in the step one, so that an effective elastic coefficient matrix of the short fiber composite material is obtained, and the prediction of the effective elastic modulus of the short fiber composite material is realized.
And (3) calculating to obtain a strain concentration factor A required by the formula (1) in the step I according to the average strain relation of the fiber and the composite material representative volume unit in the step six as shown in the formula (10), substituting the strain concentration factor A into the short fiber composite material effective rigidity calculation formula (7) in the step I to obtain effective performance parameters of the PPS/CF composite material, and realizing prediction of the effective elastic modulus of the short fiber composite material as shown in the table 2.
TABLE 2 effective modulus of elasticity of PPS/CF composites
Further comprises the following steps: the method of the first step to the seventh step is applied to the field of the optimized design numerical simulation of the short fiber composite material, the predictability of the mechanical property of the short fiber composite material is realized, the deep research on the effective mechanical behavior, the physical behavior and the damage mechanism of the composite material is facilitated, and the related engineering problems can be solved.
In the embodiment, the method for predicting the effective elastic modulus of the short fiber composite material based on mesomechanics is applied to predict the effective elastic modulus of the short fiber composite material, and the three-dimensional finite element theoretical model based on the mesomechanics representative volume unit is established, so that the accurate prediction of the effective elastic performance of the composite material mixed with non-ellipses is realized, the application range of the Mori-Tanaka method can be widened, the prediction efficiency is improved, and the transverse elastic modulus and the shear modulus can be accurately predicted. Therefore, the method for predicting the mechanical property of the short fiber composite material based on the mesomechanics model has practical application value.
Finally, it should be noted that the above is only for illustrating the technical solutions of the present invention, and those skilled in the art can modify or substitute the technical solutions of the present invention equally. All changes, equivalents, modifications and the like which come within the spirit and principle of the invention are desired to be protected.
Claims (10)
1. The method for predicting the effective elastic modulus of the short fiber composite material based on mesomechanics is characterized by comprising the following steps of: comprises the following steps of (a) carrying out,
the method comprises the following steps: deducing an effective rigidity calculation formula of the short fiber composite material based on a Mori-tanaka equivalent inclusion principle and an average stress principle, and establishing a material constitutive model; the material constitutive model comprises an anisotropic material constitutive relation model, an isotropic material constitutive relation model and a transverse isotropic material constitutive relation model;
step two: taking the performance of each phase of the short fiber reinforced resin matrix composite material as an input parameter, wherein the performance of each phase comprises the elastic modulus and the Poisson ratio of a matrix and a fiber, and respectively outputting effective elastic coefficient matrixes of the matrix and the fiber;
step three: establishing a mesomechanics geometric model of the fiber and the matrix according to the distribution orientation and the arrangement mode of the short fibers and the volume ratio of the short fibers in the composite material;
step four: establishing a finite element theoretical model of the short fiber composite material based on the mesomechanics representative volume unit;
step five: calculating structural response of each phase of the short fiber composite material by using a finite element method;
step six: establishing a relation between strain fields of the fibers and the matrix and average strain based on an average strain theory to obtain the average strain of each phase of the short fiber composite material;
step seven: and calculating to obtain the effective elastic coefficient of the composite material by combining the average strain relationship of each phase of the composite material and the effective rigidity of the short fiber composite material, and predicting the effective elastic modulus of the short fiber composite material according to the relationship between the effective elastic coefficient and the effective elastic modulus of the composite material.
2. A mesomechanics-based short fiber composite effective elastic modulus prediction method as claimed in claim 1, characterized by: step eight, applying the method in the steps one to seven to the field of the optimized design numerical simulation of the short fiber composite material, realizing the predictability of the mechanical property of the short fiber composite material, being beneficial to the deep analysis of the effective mechanical behavior, the physical behavior and the damage mechanism of the composite material, and being capable of solving the related engineering problems;
and eighthly, the optimization design numerical simulation engineering application fields of the short fiber composite material comprise ship propeller performance prediction, injection molding short fiber composite material performance prediction and short fiber composite material fan blade design application.
3. A mesomechanics-based short fiber composite effective elastic modulus prediction method as claimed in claim 2, characterized by: when the method in the first step to the seventh step is applied to the optimization design numerical simulation of the short fiber composite material, the influence of the volume content of the short fibers and the arrangement mode of the short fibers on the effective elastic performance of the short fiber composite material is obtained, and a basis is provided for designing and optimizing the short fiber composite material in practical application.
4. A mesoscopic based short fiber composite useful elastic modulus prediction method as claimed in claim 1, 2 or 3, characterized in that: the first implementation method comprises the following steps of,
a calculation formula for deducing the effective rigidity of the short fiber composite material based on the Mori-tanaka equivalent inclusion principle and the average stress principle is shown as a formula (1), wherein L0Is the effective modulus of elasticity of the matrix; l is1Is the effective elastic coefficient of the fiber; a is the strain concentration factor in the sparse inclusion state, v1The volume ratio of short fiber to material is;
L＝L0+v1(L1-L0)A (1)
the anisotropic material stress strain constitutive relation is shown as a formula (2), and a formula (3) is a matrix form of the formula (2); if the material is isotropic, equation (3) reduces to the isotropic material constitutive relation as shown in equation (4), where k is the bulk modulus and μ is the shear modulus;
σ＝Lε (2)
the relations between the shear modulus and the bulk modulus and between the Young modulus and the Poisson ratio are respectively represented by a formula (5) and a formula (6), wherein E is the Young modulus, and v is the Poisson ratio;
if the material is in transverse isotropy, the constitutive relation of stress and strain is shown as a formula (3), and the conversion relation of the rigidity coefficient and the engineering constant is shown as a formula (7);
5. the mesomechanics-based short fiber composite effective modulus of elasticity prediction method of claim 4, wherein: the second step is realized by the method that,
and respectively outputting effective elastic coefficient matrixes of the matrix and the fiber as shown in a formula (4) by taking the performance of each phase of the short fiber reinforced resin-based composite material as an input parameter, wherein the performance of each phase comprises the elastic modulus and the Poisson ratio of the matrix and the fiber, and the input parameter of the performance of each phase is input into the effective elastic coefficient matrix as shown in the formula (4).
6. A mesomechanics-based short fiber composite effective elastic modulus prediction method as claimed in claim 5, characterized by: the third step is to realize the method as follows,
embedding the inclusion into an infinite base material bearing uniform strain or uniform stress based on the Morit-anaka equivalent inclusion theory, and replacing the infinite base material with a base material with the inclusion size of 5-10 times; establishing a mesomechanics geometric model of the fiber and the matrix according to the distribution orientation and the arrangement mode of the short fibers and the volume ratio of the short fibers in the composite material; and selecting and establishing a three-phase three-dimensional mesomechanics geometric model or a two-phase three-dimensional mesomechanics geometric model according to whether the interface factors are considered.
7. The mesomechanics-based short fiber composite effective modulus of elasticity prediction method of claim 6, wherein: the implementation method of the fourth step is that,
importing the built mesoscopic mechanical geometric models of the fibers and the matrix in the third step by using mesh division software, dividing meshes respectively, and setting elastic performance parameters of the fibers and the matrix, wherein the elastic performance parameters comprise: elastic modulus and Poisson ratio, and realizes the establishment of a finite element theoretical model of the short fiber composite material based on a mesomechanics representative volume unit.
8. A mesomechanics-based short fiber composite effective elastic modulus prediction method as claimed in claim 7, characterized by: the fifth step is to realize that the method is that,
and D, importing the finite element model of the representative volume unit of the short fiber composite material built in the step four into finite element analysis software to calculate the structural response of each phase of the short fiber composite material, adding uniform stress boundary conditions, building boundary value problems, and respectively obtaining a fiber strain field, a matrix strain field and a stress field by utilizing finite element post-processing analysis.
9. The mesomechanics-based short fiber composite effective modulus of elasticity prediction method of claim 6, wherein: the sixth realization method comprises the following steps of,
respectively extracting strain fields and stress fields of fibers and a matrix, based on the Morit-anaka equivalent inclusion theory, when intrinsic strain is uniform or external load is uniform, an elastic field in the inclusion is uniform and can be expressed in an integral form, an average strain calculation formula of the fibers and the matrix is shown as a formula (8), according to the average strain theory, an average strain calculation formula in a composite material representative table volume is obtained and is shown as a formula (9), and a relation between effective strain of the composite material and effective strain in each phase is establishedAs in equation (10), where ε(1)Is the average strain of the fibres,. epsilon(0)As the average strain of the matrix, the average strain,
is the average of the strain at one point of the composite over the entire volume;
obtaining average strain of the fiber and the matrix through average strain formulas (8) and (9);
the seventh implementation method comprises the following steps of,
and (3) calculating to obtain a strain concentration factor A required by the formula (1) according to the average strain relation of the fiber and the composite material representative volume unit in the step six as shown in the formula (10), and substituting the strain concentration factor A into the short fiber composite material effective rigidity calculation formula (7) in the step one, so that an effective elastic coefficient matrix of the short fiber composite material is obtained, and the prediction of the effective elastic modulus of the short fiber composite material is realized.
10. A mesomechanics-based short fiber composite effective elastic modulus prediction method as claimed in claim 9, characterized by:
in order to simplify the numerical simulation process, the grid division software in the fourth step comprises a Mechanical Model module and an Ansys ICEM in a WorkBench platform;
for consistency of the numerical simulation process, the finite element analysis software in step five includes Workbech static Structure, Ansys APDL.
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| CN111723433A (en) * | 2020-05-25 | 2020-09-29 | 电子科技大学 | Calculation design method for composite material deformation wing |
| CN111951970A (en) * | 2020-08-07 | 2020-11-17 | 山东大学 | Dentin material biological tissue mechanical property calibration method, system and device |
| CN111985140A (en) * | 2020-08-31 | 2020-11-24 | 武汉大学 | Method for calculating equivalent modulus of nickel-based single crystal superalloy |
| CN112052614A (en) * | 2020-08-31 | 2020-12-08 | 暨南大学 | Method for establishing transverse isotropic material finite element model of palm fiber mattress |
| CN112084616A (en) * | 2020-05-19 | 2020-12-15 | 北京航空航天大学 | Method for predicting compressive stiffness and compressive strength of composite material helical structure by considering geometric nonlinearity |
| CN112329297A (en) * | 2020-10-30 | 2021-02-05 | 西北工业大学 | Composite material strength detection method and system considering curing residual stress |
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| CN113312858A (en) * | 2021-06-07 | 2021-08-27 | 北京理工大学 | Two-dimensional composite material hydrofoil fluid-solid coupling characteristic prediction method based on plate theory |
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| CN113420481A (en) * | 2021-06-23 | 2021-09-21 | 江苏理工学院 | Method for calculating material characteristics of back field magnet winding |
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