Construction method of viscoelastic damage constitutive model for particle reinforced polymer matrix composites
By constructing a viscoelastic damage constitutive model for particle-reinforced polymer matrix composites, the problem that existing models are unable to describe various damage modes is solved, and a comprehensive description of the mechanical behavior of composite materials and efficient parameter acquisition are achieved, which is applicable to the engineering applications of various composite materials.
Patent Information
- Application Number
- CN202411384629.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-09-30
- Publication Date
- 2025-10-17
- Estimated Expiration
- 2044-09-30
AI Technical Summary
Existing viscoelastic damage models for particle-reinforced polymer matrix composites are insufficient to describe the influence of various damage modes on the mechanical response of materials, and some model parameters lack physical meaning and are difficult to measure experimentally.
Using genetic integrals, combined with physicochemical experiments and the Cauchy-Green deformation tensor B, the distortion free energy, volumetric free energy, and volume expansion ratio of particle-reinforced polymer matrix composites were calculated to construct a viscoelastic damage constitutive model, considering the influence of multiple damage modes, and the model parameters were determined through physical experiments.
The constructed model is applicable to composite materials with different matrix and reinforcing particle compositions. It can accurately describe the stress-strain response of materials over a wide loading rate and deformation range, reducing experimental costs and improving the applicability and accuracy of the model.
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Figure CN119274716B_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The application belongs to the technical field of material mechanics, and more particularly relates to a method for constructing a viscoelastic damage constitutive model of a particle-reinforced polymer matrix composite material. BACKGROUND
[0002] The particle-reinforced polymer matrix composite material refers to a series of multi-phase materials composed of particles as a dispersed reinforcing phase and a polymer polymer as a continuous matrix phase. The particle reinforcing phase can be metal, inorganic compound, explosive, etc., and the diameter ranges from nanoscale to millimeter scale. The continuous matrix phase can be polyethylene glycol, hydroxyl-terminated random copolyether, etc. Due to the characteristics of high specific strength, specific modulus and isotropy, the particle-reinforced polymer matrix composite material is widely used in many engineering fields such as automobiles, aerospace, propulsion technology, etc.
[0003] In the above material, the particles as the reinforcing phase mainly bear external load, and the polymer polymer as the continuous phase bonds the particles into a whole and plays a role in transmitting stress. An interface is formed between the well-bonded particles and the matrix, which ensures the load transmission between the particles and the matrix. The presence of the polymer matrix makes the particle-reinforced polymer matrix composite material generally viscoelastic, that is, the mechanical properties of the composite material are significantly different under different loading rates, and have time dependence; with the increase of external load, various forms of damage may occur in the composite material, including hole-type damage in the polymer matrix, fracture of the particles, debonding of the particle / matrix interface, etc., and the occurrence and evolution of the damage significantly reduce the ability of the material to bear external load, which brings great risk to the safety of the structure. The complex viscoelasticity and damage characteristics are the main difficulties in constructing a constitutive model to capture the stress-strain relationship of the material under different loading rates, which greatly restricts the application and further development of the material in engineering.
[0004] At present, the characterization of the viscoelastic damage behavior of the above material mainly exists in two types of models: one is a viscoelastic damage model based on phenomenological theory, and the other is a viscoelastic damage model based on particle dewetting. The viscoelastic damage model based on phenomenological theory does not contain the mechanism and details of the damage evolution in the material, so its application range is limited; the viscoelastic damage model based on particle dewetting contains the particle dewetting damage process, but does not consider the influence of other forms of damage on the mechanical behavior of the material. In addition, the above two types of models are usually established based on phenomenological or statistical mechanics viscoelastic constitutive models, and some model parameters also lack physical meaning and are difficult to obtain through physical and chemical experiments. SUMMARY
[0005] In view of the above defects or improvement needs of the prior art, the present application provides a granular reinforced polymer matrix composite viscoelastic damage constitutive model construction method, which aims to calculate the distortion free energy W of the material by using the constitutive parameters with clear physical meaning and the left Cauchy-Green deformation tensor B, calculate the volume change free energy U of the material by using the Poisson's ratio μ of the material, calculate the overall volume expansion ratio θ of the material by using the granular de-wetting damage parameter of the material and the left Cauchy-Green deformation tensor B, and further calculate the mechanical response D(θ) and μ(θ) of the material after damage. On this basis, the integral function is calculated in the form of genetic integral, so as to obtain the mapping relationship between the Cauchy stress σ of the material and the left Cauchy-Green deformation tensor B and time t, so as to represent the viscoelastic damage constitutive model of the material, thereby solving the technical problems that the existing viscoelastic damage constitutive model is difficult to describe the influence of multiple damage forms on the mechanical response of the granular reinforced polymer matrix composite and that part of the constitutive model parameters are difficult to measure by experimental means.
[0006] To achieve the above-mentioned purpose, according to one aspect of the present application, a granular reinforced polymer matrix composite viscoelastic damage constitutive model construction method is provided, which comprises the following steps:
[0007] Step S1, obtaining the constitutive parameters of the polymer matrix through physicochemical experiments, the constitutive parameters comprising: crosslinked molecular chain modulus free molecular chain modulus crosslinked molecular chain Kuhn monomer number N and free molecular chain movement hardening coefficient α;
[0008] Step S2, combining the matrix volume fraction V m , the elastic modulus of i kinds of reinforcing particles and the volume fraction to calculate the overall crosslinked modulus G c and the overall entanglement modulus G e ;
[0009] Step S3, obtaining the initial modulus E0 and relaxation parameters of the granular reinforced polymer matrix composite through stress relaxation experiments, the relaxation parameters comprising: normalized infinite modulus j normalized relaxation modulus and relaxation time τ l (l=1,…,j);
[0010] Step S4, obtaining the initial Poisson's ratio μ0 and granular de-wetting parameters of the granular reinforced polymer matrix composite through uniaxial tensile volume expansion experiments, the granular de-wetting parameters comprising: the elongation ratio mathematical expectation λ s of the granular de-wetting probability density function, the standard deviation s, and the maximum value V fm of the first derivative of the volume expansion ratio with respect to the elongation ratio caused by the granular de-wetting;
[0011] Step S5, using the overall crosslinking modulus G c , overall entanglement modulus G e The distortion free energy W is calculated using the Kuhn monomer number N of the cross-linked molecular chain and the hardening coefficient α of the free molecular chain motion. The volume free energy U is calculated using the initial Poisson's ratio μ0 and the material volume expansion J caused by deformation. The normalized infinite modulus j normalized relaxation moduli and relaxation time τ l Calculate the relaxation functions g(t) and k(t) related to time t, and use the mathematical expectation λ of the elongation ratio of the particle dewetting probability density function s , standard deviation s, maximum value of volume expansion rate V fm Calculate the material volume expansion ratio θ caused by particle dehumidification p , the left Cauchy-Green deformation tensor B is used to calculate the material volume expansion ratio θ caused by the matrix hole damage evolution m , using θ p and θ m Calculate the overall volume expansion ratio θ of the material, and use the overall volume expansion ratio θ to calculate the material modulus damage function D(θ) and the post-damage Poisson's ratio μ(θ);
[0012] Step S6, calculating the integral function using a genetic integration form, thereby obtaining a mapping relationship between the Cauchy stress σ of the particle reinforced polymer matrix composite material and the left Cauchy-Green deformation tensor B and time t, so as to characterize the viscoelastic damage constitutive model of the composite material.
[0013] Preferably, in step S1,
[0014] The cross-linked molecular chain modulus is obtained by nuclear magnetic resonance spectroscopy.
[0015] The free molecular chain modulus is obtained by swelling method test
[0016] Through molecular dynamics simulation or curve fitting of material tensile test, the cross-linked molecular chain Kuhn monomer number N and the free molecular chain motion hardening coefficient α are obtained.
[0017] Preferably, step S2 includes the following steps:
[0018] S21, by formula Calculate the overall crosslinking modulus G c ,in
[0019] S22, using the formula Calculate the overall entanglement modulus G e .
[0020] Preferably, in the step S3, the normalized initial modulus j normalized relaxation modulus satisfies Generally, j should satisfy j≥3.
[0021] Preferably, the step S4 comprises the following steps:
[0022] S41, calculating the positive square roots λ1, λ2, λ3 of the three principal eigenvalues of the left Cauchy-Green deformation tensor B, and taking the maximum value as the elongation ratio λ = max(λ1, λ2, λ3);
[0023] S42, obtaining the first derivative V of the volume expansion ratio θ caused by particle dehumidification with respect to the elongation ratio λ f Formula The mapping of the left Cauchy-Green deformation tensor B to the first derivative V of the volume expansion ratio θ caused by particle dehumidification with respect to the elongation ratio λ f , wherein
[0024] S43, obtaining the mapping of the left Cauchy-Green deformation tensor B to the volume expansion ratio θ caused by particle dehumidification p Formula
[0025] The mapping of the left Cauchy-Green deformation tensor B to the volume expansion ratio θ caused by particle dehumidification p , wherein
[0026] S44, obtaining the initial Poisson's ratio μ0 of the particle-reinforced polymer matrix composite material and the evolution curve of the volume expansion ratio of the composite material with deformation through uniaxial tensile volume expansion experiments , wherein V0 is the initial volume of the experimental sample, and V(λ) is the instantaneous volume of the experimental sample during the stretching process;
[0027] S45, determining the appropriate dehumidification parameters λ s , s, V fm by using parameter fitting methods such as bisection method, least squares method, etc., so that the root mean square error of the experimental test value of the volume expansion ratio and the calculation result of the formula is minimized.
[0028] Preferably, the step S5 comprises the following steps:
[0029] S51, calculating the distortion free energy by the formula , wherein tan -1 is the arctangent function, the distortion part of the left Cauchy-Green deformation tensor B the first invariant of the left Cauchy-Green deformation tensor distortion part J is the material volume expansion ratio caused by deformation;
[0030] S52, the free energy of volume change is calculated by the formula where the initial shear modulus E0 is the initial elastic modulus, and μ0 is the initial Poisson's ratio;
[0031] S53, the relaxation functions g(t), k(t) are calculated respectively by the formula
[0032] S54, the positive square roots λ1, λ2, λ3 of the three principal eigenvalues of the left Cauchy-Green deformation tensor B are calculated, and the maximum value is taken as the elongation ratio λ = max(λ1, λ2, λ3);
[0033] S55, the mapping relationship from the left Cauchy-Green deformation tensor B to the material volume expansion ratio θ p caused by particle dewetting is calculated by the formula dxdx;
[0034] S56, the material volume expansion ratio θ m caused by the evolution of matrix hole type damage is calculated by the formula
[0035] S57, the overall material volume expansion ratio θ is calculated by the formula θ = θ p θ m
[0036] S58, the material modulus damage function D(θ) is calculated by the formula where d1 and d2 are undetermined damage parameters;
[0037] S59, the damage Poisson's ratio μ(θ) is calculated by the formula
[0038] Preferably, the step S6 comprises the following steps:
[0039] S61, the stress tensor Q G caused by the distortion deformation energy W is calculated by the formula where C is the right Cauchy-Green deformation tensor, which has a certain relationship with the Cauchy-Green deformation tensor B C = F T BF -T , F T is the transpose of the deformation gradient F, F -T is the inverse of F T , C -1 is the inverse of C;
[0040] S62, the stress Q caused by the distortion deformation energy U is calculated by the formula K ;
[0041] S63, the mapping relationship between the second Piola-Kirchhoff stress S and the left Cauchy-Green deformation tensor B and the time t is calculated by the formula
[0042] S64, the integral function is solved by using genetic integral method, and the mapping relationship between the Cauchy stress sigma and the left Cauchy-Green deformation tensor B and the time t is calculated by the formula sigma = J -1 FSF T .
[0043] According to another aspect of the present application, an electronic device is provided, comprising a memory and a processor, the memory storing a computer program, and the processor implementing the steps of the method according to any one of the preceding aspects when executing the computer program.
[0044] According to another aspect of the present application, a computer readable storage medium is provided, storing a computer program, the computer program being executed by a processor to implement the steps of the method according to any one of the preceding aspects.
[0045] In general, the above technical solutions conceived by the present application can achieve the following beneficial effects compared with the prior art:
[0046] 1. The method for constructing the viscoelastic damage constitutive model of the particle reinforced polymer matrix composite material considers the influence of the structure and component factors such as the polymer matrix, different kinds of reinforcing particles, and different particle volume fractions on the overall mechanical behavior of the particle reinforced polymer matrix composite material, so that the described constitutive model can be applied to a series of composite materials containing different matrices, multiple reinforcing particles, and different particle filling ratios, and has a wider application range.
[0047] 2. The method for constructing the viscoelastic damage constitutive model of the particle reinforced polymer matrix composite material calculates the distortion free energy W by using the cross-linking modulus G c , the entanglement modulus G e , the cross-linking molecular chain Knudsen monomer number N, and the free molecular chain movement hardening coefficient alpha, calculates the volume change free energy U by using the initial Poisson's ratio mu0 and the material volume expansion J caused by deformation, calculates the relaxation functions g(t), k(t) by using the normalized modulus and the relaxation time, calculates the modulus damage function D(theta) and the Poisson's ratio mu(theta) after damage by using the dewetting parameter and the left Cauchy-Green deformation tensor B, and calculates the Cauchy stress sigma by taking the partial derivative and genetic integral, which has low calculation complexity, high precision, and can describe the stress-strain response of the composite material in a wide loading rate and a wide deformation range.
[0048] 3. The method for constructing the viscoelastic damage constitutive model of the particle-reinforced polymer matrix composite material, which considers the contribution of the crosslinked molecular chains to the crosslinking modulus G c crosslinking molecular chain library and the crosslinking molecular chain number N, and uses the entanglement modulus G e and the hardening coefficient α of the free molecular chain movement to consider the contribution of the entangled molecular chains, so that the interaction of various molecular chains in the matrix and the reinforcing effect of the particles on the interaction can be described, and the free energy of the composite material can be calculated efficiently and accurately.
[0049] 4. The method for constructing the viscoelastic damage constitutive model of the particle-reinforced polymer matrix composite material, which considers the volume expansion caused by particle dewetting, the volume expansion caused by the evolution of the hole-type defects in the polymer volume and the influence of various damage forms on the mechanical properties such as the overall modulus and Poisson's ratio of the composite material, and simply and effectively includes various damage evolution processes in the composite material and the performance degradation caused by the processes, so that the overall description of the damage mechanical behavior of the composite material can be realized.
[0050] 5. The method for constructing the viscoelastic damage constitutive model of the particle-reinforced polymer matrix composite material, which only includes two to-be-determined damage parameters, and the remaining parameters all have clear physical meanings and can be determined through physical, chemical or mechanical experiments, so that the model parameters are more convenient and fast to obtain, the time and economic cost of the experiments are reduced, and the direction for regulating the components and structure of the composite material to obtain better mechanical properties is indicated. BRIEF DESCRIPTION OF DRAWINGS
[0051] Figure 1 is the uniaxial tensile test data of the NEPE propellant at different rates in an embodiment of the present application and the prediction curve based on the viscoelastic damage model;
[0052] Figure 2 is a prediction curve based on a classical model and a prediction curve based on the viscoelastic damage model in an embodiment of the present application. DETAILED DESCRIPTION
[0053] In order to make the purpose, technical scheme and advantages of the present application clearer, the present application is further described in detail below with reference to the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application, and are not used to limit the present application. In addition, the technical features involved in each embodiment of the present application described below can be combined with each other as long as they do not conflict with each other.
[0054] The present application provides a method for constructing a viscoelastic damage constitutive model of a particle-reinforced polymer matrix composite material, which comprises:
[0055] The constitutive parameters of the polymer matrix are obtained by physical and chemical experiments, and the constitutive parameters include: crosslinked molecular chain modulus Free molecular chain modulus Crosslinked molecular chain Kuhn monomer number N and free molecular chain motion hardening coefficient α.
[0056] Specifically, the crosslinked molecular chain modulus is obtained by nuclear magnetic resonance spectroscopy
[0057] The free molecular chain modulus is obtained by swelling method
[0058] The crosslinked molecular chain Kuhn monomer number N and the free molecular chain motion hardening coefficient α are obtained by molecular dynamics simulation or fitting the material tensile mechanical test curve.
[0059] Further explanation, combined with matrix volume fraction V m , the elastic modulus of i kinds of reinforcing particles (n=1,…,i) and volume fraction The overall crosslinking modulus G c and the overall entanglement modulus G e .
[0060] Specifically, the overall crosslinking modulus G c is calculated by the formula , wherein The overall entanglement modulus G e is calculated by the formula .
[0061] Further explanation, the initial modulus E0 and relaxation parameters of the particle reinforced polymer matrix composite material are obtained by stress relaxation experiment, and the relaxation parameters include: normalized infinite modulus j normalized relaxation modulus and relaxation time τ l (l=1,...,j).
[0062] Specifically, the normalized initial modulus j normalized relaxation modulus satisfies In general, j should satisfy j≥3.
[0063] Further explanation, the initial Poisson's ratio μ0 and particle dewetting parameters of the particle reinforced polymer matrix composite material are obtained by uniaxial tensile volume expansion experiment, and the particle dewetting parameters include: the elongation ratio mathematical expectation λ s , standard deviation s, the maximum value V fm.
[0064] Specifically, the positive square roots λ1, λ2, and λ3 of the three main eigenvalues of the left Cauchy-Green deformation tensor B are calculated, and the maximum value is taken as the elongation ratio λ = max(λ1,λ2,λ3); the first derivative V of the volume expansion ratio caused by particle dehumidification with respect to the elongation ratio λ is used. f formula Obtain the first derivative V of the left Cauchy-Green deformation tensor B to the volume expansion ratio caused by particle dehumidification with respect to the stretch ratio λ f The mapping of The volume expansion ratio θ caused by particle dehumidification p formula
[0065] Calculate the left Cauchy-Green deformation tensor B to the volume expansion ratio θ caused by particle dehumidification p The mapping of The evolution curve of the initial Poisson's ratio μ0 and the volume expansion ratio of the composite material with deformation is obtained through uniaxial tensile volume expansion experiments. Where V0 is the initial volume of the experimental sample, V(λ) is the instantaneous volume of the experimental sample during the stretching process; the appropriate dewetting parameter λ is determined using parameter fitting methods such as bisection method and least squares method. s ,s,V fm The experimental test value and formula of volume expansion ratio The root mean square error of the calculation results is the smallest.
[0066] Further explanation, using the overall cross-linking modulus G c , overall entanglement modulus G e The distortion free energy W is calculated using the Kuhn monomer number N of the cross-linked molecular chain and the hardening coefficient α of the free molecular chain motion. The volume free energy U is calculated using the initial Poisson's ratio μ0 and the material volume expansion J caused by deformation. The normalized infinite modulus j normalized relaxation moduli and relaxation time τ l Calculate the relaxation functions g(t) and k(t) related to time t, and use the mathematical expectation λ of the elongation ratio of the particle dewetting probability density function s , standard deviation s, maximum value of volume expansion rate V fm Calculate the material volume expansion ratio θ caused by particle dehumidification p , the left Cauchy-Green deformation tensor B is used to calculate the material volume expansion ratio θ caused by the matrix hole damage evolution m , using θ p and θ m The overall volume expansion ratio θ of the material is calculated, and the material modulus damage function D(θ) and the post-damage Poisson's ratio μ(θ) are calculated using the overall volume expansion ratio θ of the material.
[0067] Specifically through the formula Calculate the distortion free energy, where tan -1 is the inverse tangent function, The distorted part of the left Cauchy-Green deformation tensor B is the distortion part of the left Cauchy-Green deformation tensor The first invariant, J is the volume expansion ratio of the material caused by deformation; through the formula Calculate the volume free energy, where the initial shear modulus E0 is the initial elastic modulus, μ0 is the initial Poisson's ratio; through the formula
[0068] Calculate the relaxation functions g(t) and k(t) respectively; calculate the positive square roots λ1, λ2, and λ3 of the three main eigenvalues of the left Cauchy-Green deformation tensor B, and take the maximum value as the stretch ratio λ=max(λ1,λ2,λ3); by formula Calculate the material volume expansion ratio θ from the left Cauchy-Green deformation tensor B to the particle dewetting p The mapping relationship; through the formula Calculate the material volume expansion ratio θ caused by matrix void damage evolution m For common composite materials, By the formula θ=θ p θ m Calculate the overall volume expansion ratio θ of the material; by the formula Calculate the material modulus damage function D(θ), where d1 and d2 are the undetermined damage parameters; by the formula Calculate the post-injury Poisson's ratio μ(θ).
[0069] To further illustrate, the integral function is calculated using a genetic integration form to obtain a mapping relationship between the Cauchy stress σ of the particle reinforced polymer matrix composite material and the left Cauchy-Green deformation tensor B and time t to characterize the viscoelastic damage constitutive model of the composite material.
[0070] Specifically, through the formula Calculate the stress tensor Q caused by the distortion energy W G , where C is the right Cauchy-Green deformation tensor, which has a definite relationship with the Cauchy-Green deformation tensor B C = F T BF -T , F T is the transpose of the deformation gradient F, F -T F T The inverse of C -1 is the inverse of C; by the formula Calculate the stress Q caused by the distortion deformation energy U K ; by the formula
[0071] Calculate the mapping relationship between the second Piola-Kirchhoff stress S and the left Cauchy-Green deformation tensor B and time t; adopt genetic integral method to solve integral function, and utilize the formula σ = J -1 FSF T Calculate the mapping relationship between the Cauchy stress σ and the left Cauchy-Green deformation tensor B and time t.
[0072] The technical solutions of the present application are further illustrated below through specific embodiments.
[0073] Embodiment 1
[0074] The undetermined damage parameters d1 = 0.55, d2 = 1.45 of the viscoelastic damage constitutive model are calibrated by using the uniaxial tension experiment data of NEPE propellant with a stretching rate of 420 mm / min, the related parameters are obtained by using the relaxation experiment data of NEPE propellant, and the relaxation functions g(t), k(t) are calculated, G c = 0.5035, G e = 0.0506, N = 10, α = 1.813, and the uniaxial tension stress-strain curves of NEPE propellant at different stretching rates are calculated according to the above parameters. The uniaxial tension experiment data of NEPE propellant at different rates and the prediction curves based on the viscoelastic damage model are plotted in Figure 1 At different stretching rates, the maximum relative error between the prediction based on the viscoelastic damage model and the corresponding experiment data is not more than 7.5%, and it can be seen that for the uniaxial tension experiment data, the viscoelastic damage model can give accurate prediction results for the mechanical response of composite materials in a wide strain rate range under the premise of using only two calibration parameters, and well reflects the influence of various forms of damage in the composite material on its mechanical response.
[0075] Embodiment 2
[0076] The constitutive parameters of the viscoelastic damage constitutive model and the parameters of the classical viscoelastic damage constitutive model considering only particle desorption damage are calibrated by using the uniaxial tension experiment data of particle reinforced composite material with a stretching rate of 500 mm / min. The experiment data, the prediction curve based on the classical model and the prediction curve based on the viscoelastic damage model are plotted in Figure 2The maximum relative error between the prediction based on the viscoelastic damage model and the experimental data is 2.1%, while the maximum relative error between the prediction based on the classical viscoelastic damage model and the experimental data is 10.7%. It can be seen that by introducing multiple damage forms, the viscoelastic damage model can give a prediction closer to the real experimental data, which helps to ensure the safe use of the composite material in engineering, avoid the waste of material redundancy, and reduce the economic cost.
[0077] Those skilled in the art will easily understand that the above description is only a preferred embodiment of the present application, and is not intended to limit the present application. Any modification, equivalent replacement and improvement made within the spirit and principle of the present application shall be included in the protection scope of the present application.
Claims
1. A method for constructing a viscoelastic damage constitutive model of a particle-reinforced polymer-based composite material, characterized in that: The method comprises the following steps: Step S1, obtaining the constitutive parameters of the polymer matrix through physical and chemical experiments, the constitutive parameters include: cross-linked molecular chain modulus , free molecular chain modulus , cross-linked molecular chain Kuhn monomer number and the free molecular chain motion hardening coefficient ; Step S2, combined with the matrix volume fraction , Elastic modulus of the reinforced particles , and volume fraction , Calculation of overall crosslink modulus and overall entanglement modulus ; Step S3, obtaining the initial modulus of the particle reinforced polymer matrix composite material through stress relaxation experiment and relaxation parameters, the relaxation parameters including: normalized infinite modulus , Normalized relaxation modulus , and relaxation time , ; Step S4, obtaining the initial Poisson's ratio of the particle reinforced polymer matrix composite material through uniaxial tensile volume expansion experiment and particle dewetting parameters, the particle dewetting parameters including: the mathematical expectation of the elongation ratio of the particle dewetting probability density function , standard deviation , the maximum value of the first derivative of the volume expansion ratio to the elongation ratio caused by particle dehumidification ; The step S4 comprises the following steps: S41, calculate the left Cauchy-Green deformation tensor The positive square roots of the three main eigenvalues of 、 、 , take the maximum value as the elongation ratio ; S42, using the volume expansion ratio and elongation ratio caused by particle dehumidification The first derivative of formula Get the left Cauchy-Green deformation tensor Volume expansion ratio to elongation ratio due to particle dehumidification The first derivative of The mapping of ; S43, using the volume expansion ratio caused by particle dehumidification formula Compute the left Cauchy-Green deformation tensor The volume expansion ratio of the particles due to dehumidification The mapping of ; S44, Obtaining the Initial Poisson's Ratio of Particle-Reinforced Polymer Composites by Uniaxial Tensile Volume Expansion Experiments Evolution curve of the volume expansion ratio of the composite material with deformation ,in is the initial volume of the experimental sample, is the instantaneous volume of the experimental sample during the stretching process; S45, using the dichotomy method and the least squares parameter fitting method to determine the dehumidification parameters 、 、 The experimental test value and formula of volume expansion ratio The root mean square error of the calculation results is the smallest; Step S5, using the overall crosslinking modulus , overall entanglement modulus , cross-linked molecular chain Kuhn monomer number and the free molecular chain motion hardening coefficient Calculation of distortion free energy , using the initial Poisson's ratio Volume expansion of the material due to deformation Calculation of volumetric free energy , using the normalized infinite modulus , j normalized relaxation moduli and relaxation time Computation and Time The relaxation function 、 , using the mathematical expectation of the elongation ratio of the particle dewetting probability density function , standard deviation , the maximum volume expansion rate Calculate the volume expansion ratio of the material caused by particle dehumidification , using the left Cauchy-Green deformation tensor Calculate the material volume expansion ratio caused by matrix void damage evolution ,use and Calculate the overall volume expansion ratio of the material , using the overall volume expansion ratio of the material Calculate the material modulus damage function separately Poisson's ratio after injury ; The step S5 comprises the following steps: S51, by formula Calculate the distortion free energy, where , is the inverse tangent function, , the left Cauchy-Green deformation tensor The distortion part , is the distortion part of the left Cauchy-Green deformation tensor The first invariant of is the volume expansion ratio of the material caused by deformation; S52, by formula Calculate the volume free energy, where the initial shear modulus , is the initial elastic modulus, is the initial Poisson's ratio; S53, by formula 、 Calculate the relaxation function separately 、 ; S54, Calculate the left Cauchy-Green deformation tensor The positive square roots of the three main eigenvalues of 、 、 , take the maximum value as the elongation ratio ; S55, by formula Compute the left Cauchy-Green deformation tensor The volume expansion ratio of the material caused by particle dehumidification The mapping relationship; S56, by formula Calculate the material volume expansion ratio caused by matrix void damage evolution For common composite materials 、 ; S57, by formula Calculate the overall volume expansion ratio of the material ; S58, by formula Calculating the material modulus damage function ,in and is the undetermined damage parameter; S59, by formula Calculate the Poisson's ratio after injury ; Step S6, using genetic integration to calculate the integral function, thereby obtaining the Cauchy stress of the particle reinforced polymer matrix composite material With the left Cauchy-Green deformation tensor and time , to characterize the viscoelastic damage constitutive model of the composite material; The step S6 comprises the following steps: S61, by formula Calculation of distortion energy The induced stress tensor ,in is the right Cauchy-Green deformation tensor, which is the same as the Cauchy-Green deformation tensor There is a definite relationship , is the deformation gradient The transpose of for The inverse, for The inverse of S62, by formula Calculation of distortion energy Stress caused ; S63, by formula Calculation of the second Piola-Kirchhoff stress With the left Cauchy-Green deformation tensor and time The mapping relationship; S64, the genetic integration method is used to solve the integral function, and the formula Calculate Cauchy stress With the left Cauchy-Green deformation tensor and time The mapping relationship.
2. The method for constructing a viscoelastic damage constitutive model of a particle reinforced polymer matrix composite material according to claim 1, characterized in that: In the step S1, The cross-linked molecular chain modulus is obtained by nuclear magnetic resonance spectroscopy. ; The free molecular chain modulus is obtained by swelling method test ; The Kuhn number of cross-linked molecular chains is obtained by molecular dynamics simulation or curve fitting of material tensile test. Hardening coefficient with free molecular chain motion .
3. The method for constructing a viscoelastic damage constitutive model of a particle reinforced polymer matrix composite material according to claim 1, characterized in that: The step S2 comprises the following steps: S21, by formula Calculation of overall crosslink modulus ,in ; S22, using the formula Calculate the overall tangle modulus .
4. The method for constructing a viscoelastic damage constitutive model of a particle reinforced polymer matrix composite material according to claim 1, characterized in that: In step S3, the normalized initial modulus obtained by the stress relaxation experiment , Normalized relaxation modulus satisfy , Should meet .
5. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 4 are implemented.
6. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 4 are implemented.
Citation Information
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