Method for constructing viscoelastic damage constitutive model of particle reinforced polymer-based composite material
Through the Left Cauchy-Green deformation tensor and genetic integral form, combined with physical and chemical experimental parameters, a viscoelastic damage constitutive model of particle-enhanced polymer-based composites was constructed, solving the problem that existing models are difficult to describe multiple damage forms. The accuracy of description of the mechanical response of composite materials and the convenience of obtaining parameters is achieved.
Patent Information
- Application Number
- CN202411384629.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-09-30
- Publication Date
- 2025-01-07
- Estimated Expiration
- 2044-09-30
AI Technical Summary
The viscoelastic damage constitutive models of existing particle-reinforced polymer-based composites are difficult to describe the impact of multiple damage forms on the mechanical response of materials, and some model parameters lack physical significance and are difficult to measure experimentally.
The mechanical response after damage is calculated using the Left Cauchy-Green deformation tensor B and genetic integral form, combined with the constitutive parameters obtained from the physical and chemical experiments. Changes in loose ratios to construct a constitutive model of viscoelastic damage.
The accurate description of the stress-strain response of the composite material in different loading rates and deformation ranges is achieved, which expands the scope of application of the model, reduces experimental costs, and simplifies the parameter acquisition process.
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Figure CN119274716A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of material mechanics, and more specifically, relates to a method for constructing a viscoelastic damage constitutive model of a particle-reinforced polymer-based composite material. Background Art
[0002] Particle-reinforced polymer matrix composites refer to a series of multiphase materials composed of particles as dispersed reinforcement phase and polymer as continuous matrix phase. Among them, the particle reinforcement phase can be metal, inorganic compound, explosive, etc., with diameters ranging from nanometer to millimeter; the continuous matrix phase can be polyethylene glycol, terminal hydroxyl random copolyether and other polymers. Due to its high specific strength, specific modulus, isotropy and other characteristics, particle-reinforced polymer matrix composites are widely used in many engineering fields such as automobiles, aerospace, propulsion technology, etc.
[0003] In the above materials, the particles as the reinforcing phase mainly bear the external load, while the polymer as the continuous phase bonds the particles as a whole and plays a role in transferring stress. An interface is formed between the well-bonded particles and the matrix, which ensures the load transfer between the particles and the matrix. The presence of the polymer matrix makes particle-reinforced polymer-based composites usually viscoelastic, that is, at different loading rates, the mechanical properties of the composites are significantly different and time-dependent; with the increase of external loads, various forms of damage may occur in the composite material, including pore-type damage in the polymer matrix, particle fracture, and debonding of the particle / matrix interface. The appearance and evolution of damage significantly reduce the ability of the material to bear external loads, posing a huge risk to the safety of the structure. The complex viscoelastic and damage properties are the main difficulties in constructing constitutive models to capture the stress-strain relationship of such materials at different loading rates, which greatly restricts the application and further development of such materials in engineering.
[0004] At present, there are mainly two types of models for characterizing the viscoelastic damage behavior of the above materials: one is the viscoelastic damage model based on phenomenological theory, and the other is the viscoelastic damage model based on particle dewetting. The viscoelastic damage model based on phenomenological theory does not include the mechanism and details of the damage evolution in the material, so its scope of application is greatly limited; the viscoelastic damage model based on particle dewetting includes 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 of their model parameters also lack physical meaning and are difficult to obtain through physical and chemical experiments. Summary of the invention
[0005] In view of the above defects or improvement needs of the prior art, the present invention provides a method for constructing a viscoelastic damage constitutive model of a particle-reinforced polymer-based composite material, the purpose of which is to use constitutive parameters with clear physical meanings and the left Cauchy-Green deformation tensor B to calculate the distortion free energy W of the material, and use the Poisson's ratio μ of the material to calculate the volume free energy U of the material; use the particle dewetting damage parameter of the material and the left Cauchy-Green deformation tensor B to calculate the overall volume expansion ratio θ of the material, and then 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 integration 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 characterize 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 various damage forms on the mechanical response of particle-reinforced polymer-based composite materials and some of its constitutive model parameters are difficult to measure by experimental means.
[0006] To achieve the above object, according to one aspect of the present invention, a method for constructing a viscoelastic damage constitutive model of a particle reinforced polymer matrix composite material is provided, the method comprising the following steps:
[0007] Step S1, obtaining the constitutive parameters of the polymer matrix through physical and chemical experiments, wherein the constitutive parameters include: cross-linked molecular chain modulus Free molecular chain modulus The Kuhn monomer number N of the cross-linked molecular chain and the hardening coefficient α of the free molecular chain motion;
[0008] Step S2, combining the matrix volume fraction V m , the elastic modulus of the i-th reinforcing particle With volume fraction Calculate the overall crosslink modulus G c and the overall entanglement modulus G e ;
[0009] Step S3, obtaining the initial modulus E0 and relaxation parameters of the particle-reinforced polymer matrix composite material through a stress relaxation experiment, wherein the relaxation parameters include: normalized infinite modulus j normalized relaxation moduli and relaxation time τ l (l=1,…,j);
[0010] Step S4, obtaining the initial Poisson's ratio μ0 and particle dewetting parameters of the particle-reinforced polymer matrix composite material through a uniaxial tensile volume expansion experiment, wherein the particle dewetting parameters include: the mathematical expectation λ of the elongation ratio of the particle dewetting probability density function s , standard deviation s, the maximum value V of the first derivative of the volume expansion ratio to the elongation ratio caused by particle dehumidification fm ;
[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 dehumidification 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 type 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 of the material to calculate the material modulus damage function D(θ) and the Poisson's ratio μ(θ) after damage;
[0012] Step S6, calculating the integral function using a genetic integral 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 fitting of the material tensile test curve, the cross-linked molecular chain Kuhn monomer number N and the free molecular chain motion hardening coefficient α are obtained.
[0017] Preferably, step S2 comprises the following steps:
[0018] S21, by formula Calculate the overall crosslink modulus G c ,in
[0019] S22, using the formula Calculate the overall entanglement modulus G e .
[0020] Preferably, in step S3, the normalized initial modulus obtained by the stress relaxation experiment is j normalized relaxation moduli satisfy Generally speaking, j should satisfy j≥3.
[0021] Preferably, step S4 comprises the following steps:
[0022] S41, calculate the positive square roots λ1, λ2, 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);
[0023] S42, using the first derivative V of the volume expansion ratio caused by particle dehumidification to the elongation ratio λ 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 elongation ratio λ f The mapping of
[0024] S43, using the volume expansion ratio θ caused by particle dehumidification p formula
[0025] Calculate the left Cauchy-Green deformation tensor B to the volume expansion ratio θ caused by particle dehumidification p The mapping of
[0026] S44, 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 test Where V0 is the initial volume of the experimental sample, V(λ) is the instantaneous volume of the experimental sample during the stretching process;
[0027] S45, using parameter fitting methods such as dichotomy and least squares method to determine the appropriate dehumidification parameter λ s ,s,V fm The experimental test value and formula of volume expansion ratio The root mean square error of the calculated results is the smallest.
[0028] Preferably, step S5 comprises the following steps:
[0029] S51, by 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;
[0030] S52, by formula Calculate the volume free energy, where the initial shear modulus E0 is the initial elastic modulus, μ0 is the initial Poisson’s ratio;
[0031] S53, by formula Calculate the relaxation functions g(t) and k(t) respectively;
[0032] S54, calculating the positive square roots λ1, λ2, λ3 of the three main eigenvalues of the left Cauchy-Green deformation tensor B, and taking the maximum value thereof as the stretch ratio λ=max(λ1,λ2,λ3);
[0033] S55, by formula dxdx calculates the material volume expansion ratio θ from the left Cauchy-Green deformation tensor B to the particle dewetting p The mapping relationship of
[0034] S56, by formula Calculate the material volume expansion ratio θ caused by matrix hole damage evolution m For common composite materials,
[0035] S57, by the formula θ=θ p θ m Calculate the overall volume expansion ratio θ of the material;
[0036] S58, by formula Calculate the material modulus damage function D(θ), where d1 and d2 are the damage parameters to be determined;
[0037] S59, by formula Calculate the post-damage Poisson's ratio μ(θ).
[0038] Preferably, step S6 comprises the following steps:
[0039] S61, by 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;
[0040] S62, by formula Calculate the stress Q caused by the distortion energy U K ;
[0041] S63, by formula Calculate the mapping relationship between the second Piola-Kirchhoff stress S and the left Cauchy-Green deformation tensor B and time t;
[0042] S64, using genetic integration method to solve the integral function, and using the formula σ = J -1 FSF T The mapping relationship between the Cauchy stress σ and the left Cauchy-Green deformation tensor B and time t is calculated.
[0043] According to another aspect of the present invention, an electronic device is provided, comprising a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of any one of the methods described above when executing the computer program.
[0044] According to another aspect of the present invention, a computer-readable storage medium is provided, on which a computer program is stored, and when the computer program is executed by a processor, the steps of any one of the methods described above are implemented.
[0045] In general, the above technical solutions conceived by the present invention can achieve the following beneficial effects compared with the prior art:
[0046] 1. The method for constructing the viscoelastic damage constitutive model of particle-reinforced polymer-based composite materials proposed in the present invention takes into account the influence of structural and component factors such as polymer matrix, different types of reinforcing particles, and different particle volume fractions on the overall mechanical behavior of particle-reinforced polymer-based composite materials, so that the constitutive model described can be applied to a series of composite materials containing different matrices, multiple reinforcing particles, and different particle filling ratios, and has a wider range of application.
[0047] 2. The viscoelastic damage constitutive model construction method of particle reinforced polymer matrix composites proposed in the present invention uses the crosslinking modulus G c , entanglement modulus G e The distortion free energy W is calculated by the cross-linked molecular chain Kuhn monomer number N and the free molecular chain motion hardening coefficient α. The volume free energy U is calculated using the initial Poisson's ratio μ0 and the material volume expansion J caused by deformation. The relaxation functions g(t) and k(t) are calculated using the normalized modulus and relaxation time. The modulus damage function D(θ) and the Poisson's ratio μ(θ) after damage are calculated using the dewetting parameter and the left Cauchy-Green deformation tensor B. The Cauchy stress σ is calculated by taking partial derivatives and genetic integration. The calculation has low complexity and high accuracy, and can describe the stress-strain response of composite materials over a wide loading rate and deformation range.
[0048] 3. The viscoelastic damage constitutive model construction method of particle-reinforced polymer-based composite materials proposed in the present invention utilizes the crosslinking modulus G in the distortion free energy W of the composite material. c The contribution of cross-linked molecular chains is taken into account by the Kuhn monomer number N, and the entanglement modulus G is used e Taking into account the contribution of entangled molecular chains and the free molecular chain motion hardening coefficient α, the interactions between various molecular chains in the composite matrix and the enhancement effect of particles on these interactions can be described, thus achieving efficient and accurate calculation of the free energy of the composite material.
[0049] 4. The method for constructing the viscoelastic damage constitutive model of particle-reinforced polymer-based composite materials proposed in the present invention takes into account the influence of various damage forms such as volume expansion caused by dehumidification of particles and volume expansion caused by the evolution of pore-type defects in the polymer volume on the overall modulus, Poisson's ratio and other mechanical properties of the composite materials. It simply and effectively includes various damage evolution processes in the composite materials and the performance degradation caused by them, and realizes a comprehensive description of the damage mechanical behavior of the composite materials.
[0050] 5. The method for constructing the viscoelastic damage constitutive model of particle-reinforced polymer-based composite materials proposed in the present invention only includes two pending damage parameters, and the remaining parameters have clear physical meanings and can be determined through physical, chemical or mechanical experiments, reflecting the components or structural characteristics of the composite materials, making it more convenient and faster to obtain model parameters, reducing the time and economic cost of the experiment, and pointing out the direction for regulating the components and structure of the composite materials to obtain better mechanical properties. BRIEF DESCRIPTION OF THE DRAWINGS
[0051] Figure 1 1 is the uniaxial tensile test data of NEPE propellant at different speeds and the prediction curve based on the viscoelastic damage model in one embodiment of the present invention;
[0052] Figure 2 It is a prediction curve based on a classical model and a prediction curve diagram based on the viscoelastic damage model in an embodiment of the present invention. DETAILED DESCRIPTION
[0053] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.
[0054] The present invention provides a method for constructing a viscoelastic damage constitutive model of a particle-reinforced polymer-based composite material, the method comprising:
[0055] The constitutive parameters of the polymer matrix are obtained through physical and chemical experiments, and the constitutive parameters include: cross-linked molecular chain modulus Free molecular chain modulus The cross-linked molecular chain Kuhn monomer number N and the free molecular chain motion hardening coefficient α.
[0056] Specifically, the cross-linked molecular chain modulus is obtained by nuclear magnetic resonance spectroscopy.
[0057] The free molecular chain modulus is obtained by swelling method test
[0058] Through molecular dynamics simulation or fitting of the material tensile test curve, the cross-linked molecular chain Kuhn monomer number N and the free molecular chain motion hardening coefficient α are obtained.
[0059] Further explanation, combined with the matrix volume fraction V m , the elastic modulus of the i-th reinforcing particle (n=1,…,i) and volume fraction Calculate the overall crosslink modulus G c and the overall entanglement modulus G e .
[0060] Specifically, through the formula Calculate the overall crosslink modulus G c ,in Using the formula Calculate the overall entanglement modulus G e .
[0061] Further explanation: the initial modulus E0 and relaxation parameters of the particle reinforced polymer matrix composite material are obtained by stress relaxation experiment. The relaxation parameters include: normalized infinite modulus j normalized relaxation moduli and relaxation time τ l (l=1,...,j).
[0062] Specifically, the normalized initial modulus obtained by stress relaxation experiment is j normalized relaxation moduli satisfy Generally speaking, 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 test. The particle dewetting parameters include: the mathematical expectation of the elongation ratio of the particle dewetting probability density function λ s , standard deviation s, the maximum value V of the first derivative of the volume expansion ratio to the elongation ratio caused by particle dehumidification 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 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 elongation 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 by uniaxial tensile volume expansion test 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 dehumidification parameter λ is determined by 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 calculated results is the smallest.
[0066] Further explanation, using the overall crosslink 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 dehumidification 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 type 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 Poisson's ratio μ(θ) after damage 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 is J, which is the volume expansion ratio of the material caused by deformation; 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 of Calculate the material volume expansion ratio θ caused by matrix hole 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 damage parameters to be determined; by the formula Calculate the post-damage Poisson's ratio μ(θ).
[0069] To further illustrate, the integral function is calculated using genetic integration to obtain the 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 energy U K ; Through 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; solve the integral function using the genetic integration method, and use the formula σ=J -1 FSF T The mapping relationship between the Cauchy stress σ and the left Cauchy-Green deformation tensor B and time t is calculated.
[0072] The technical solution of the present invention is further illustrated by specific embodiments below.
[0073] Example 1
[0074] The damage parameters d1=0.55 and d2=1.45 of the viscoelastic damage constitutive model were calibrated using the uniaxial tensile test data of NEPE propellant at a tensile rate of 420 mm / min. The relevant parameters were obtained using the relaxation test data of NEPE propellant, and the relaxation functions g(t) and k(t) were calculated. G was obtained based on the physicochemical test results of the polymer matrix and its particle filling volume ratio. c =0.5035, G e =0.0506, N=10, α=1.813, the uniaxial tensile stress-strain curves of NEPE propellant at different tensile rates are calculated based on the above parameters. The uniaxial tensile test data of NEPE propellant at different rates are plotted against the predicted curves based on the viscoelastic damage model. Figure 1 At different stretching rates, the maximum relative error between the prediction based on the viscoelastic damage model and the corresponding experimental data does not exceed 7.5%. It can be seen that for uniaxial tensile experimental 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] Example 2
[0076] The constitutive parameters of the viscoelastic damage constitutive model and the parameters of the classical viscoelastic damage constitutive model that only considers particle dewetting damage are calibrated using the uniaxial tensile test data of particle-reinforced composite materials at a tensile rate of 500 mm / min. The experimental data, the prediction curve based on the classical model, and the prediction curve based on the viscoelastic damage model are plotted on 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 that is closer to the actual experimental data. This advantage helps to ensure the safe use of the composite material in engineering, avoid redundant waste of materials, and reduce economic costs.
[0077] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.
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, wherein the constitutive parameters include: cross-linked molecular chain modulus Free molecular chain modulus The Kuhn monomer number N of the cross-linked molecular chain and the hardening coefficient α of the free molecular chain motion; Step S2, combining the matrix volume fraction V m , the elastic modulus of the i-th reinforcing particle (n=1,...,i) and volume fraction (n=1,...,i) Calculate the overall crosslinking modulus G c and the overall entanglement modulus G e ; Step S3, obtaining the initial modulus E0 and relaxation parameters of the particle-reinforced polymer matrix composite material through a stress relaxation experiment, wherein the relaxation parameters include: normalized infinite modulus j normalized relaxation moduli (l=1,...,j) and relaxation time τ l (l=1,...,j); Step S4, obtaining the initial Poisson's ratio μ0 and particle dewetting parameters of the particle-reinforced polymer matrix composite material through a uniaxial tensile volume expansion experiment, wherein the particle dewetting parameters include: the mathematical expectation λ of the elongation ratio of the particle dewetting probability density function s , standard deviation s, the maximum value V of the first derivative of the volume expansion ratio to the elongation ratio caused by particle dehumidification fm ; 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 dehumidification 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 of the material to calculate the material modulus damage function D(θ) and the Poisson's ratio μ(θ) after damage; Step S6, calculating the integral function using a genetic integral 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.
2. The method for constructing a viscoelastic damage constitutive model of a particle-reinforced polymer-based 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 Through molecular dynamics simulation or fitting of the material tensile test curve, the cross-linked molecular chain Kuhn monomer number N and the free molecular chain motion hardening coefficient α are obtained.
3. The method for constructing a viscoelastic damage constitutive model of a particle-reinforced polymer-based composite material according to claim 1, characterized in that: The step S2 comprises the following steps: S21, by formula Calculate the overall crosslink modulus G c ,in S22, using the formula Calculate the overall entanglement modulus G e .
4. The method for constructing a viscoelastic damage constitutive model of a particle-reinforced polymer-based composite material according to claim 1, characterized in that: In step S3, the normalized initial modulus obtained by the stress relaxation experiment is j normalized relaxation moduli satisfy Generally speaking, j should satisfy j≥3.
5. The method for constructing a viscoelastic damage constitutive model of a particle-reinforced polymer-based composite material according to claim 1, characterized in that: The step S4 comprises the following steps: S41, calculate the positive square roots λ1, λ2, 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); S42, using the first derivative V of the volume expansion ratio caused by particle dehumidification to the elongation ratio λ 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 elongation ratio λ f The mapping of S43, using the volume expansion ratio θ caused by particle dehumidification p formula Calculate the left Cauchy-Green deformation tensor B to the volume expansion ratio θ caused by particle dehumidification p The mapping of S44, 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 test Where V0 is the initial volume of the experimental sample, V(λ) is the instantaneous volume of the experimental sample during the stretching process; S45, using parameter fitting methods such as dichotomy and least squares method to determine the appropriate dehumidification parameter λ s ,s,V fm The experimental test value and formula of volume expansion ratio The root mean square error of the calculated results is the smallest.
6. The method for constructing a viscoelastic damage constitutive model of a particle-reinforced polymer-based composite material according to claim 1, characterized in that: The step S5 comprises the following steps: S51, by 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; S52, by formula Calculate the volume free energy, where the initial shear modulus E0 is the initial elastic modulus, μ0 is the initial Poisson’s ratio; S53, by formula Calculate the relaxation functions g(t) and k(t) respectively; S54, calculating the positive square roots λ1, λ2, λ3 of the three main eigenvalues of the left Cauchy-Green deformation tensor B, and taking the maximum value thereof as the stretch ratio λ=max(λ1,λ2,λ3); S55, 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; S56, by formula Calculate the material volume expansion ratio θ caused by matrix hole damage evolution m For common composite materials, S57, by the formula θ=θ p θ m Calculate the overall volume expansion ratio θ of the material; S58, by formula Calculate the material modulus damage function D(θ), where d1 and d2 are the damage parameters to be determined; S59, by formula Calculate the post-damage Poisson's ratio μ(θ).
7. The method for constructing a viscoelastic damage constitutive model of a particle-reinforced polymer-based composite material according to claim 1, characterized in that: The step S6 comprises the following steps: S61, by 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; S62, by formula Calculate the stress Q caused by the distortion energy U K ; S63, by formula Calculate the mapping relationship between the second Piola-Kirchhoff stress S and the left Cauchy-Green deformation tensor B and time t; S64, using genetic integration method to solve the integral function, and using the formula σ = J -1 FSF T The mapping relationship between the Cauchy stress σ and the left Cauchy-Green deformation tensor B and time t is calculated.
8. 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 7 are implemented.
9. 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 7 are implemented.
Citation Information
Patent Citations
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CN117497069A
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