Liquid oxygen compatible epoxy resin composite material flow compaction curing forming multi-physical field coupling model based on viscoelastic constitutive model and defect prediction method and system based on the model

Abstract

The application provides a liquid-oxygen-compatible epoxy resin composite material flow compaction curing forming multi-physical field coupling model based on a viscoelastic constitutive model, and a defect prediction method and system based on the model. The viscoelastic constitutive model is based on an analysis framework of full coupling of heat-chemistry-flow-solid, breaks the limitation of independent or one-way calculation of each physical field in the traditional method, and can more truly reflect complex physical phenomena in the curing process, especially for high-performance resins such as liquid-oxygen-compatible epoxy resins.

Description

Technical Field

[0001] This invention relates to the field of composite material manufacturing processes and numerical simulation technology. Specifically, it relates to a multiphysics modeling, simulation, and defect prediction method for liquid oxygen compatible epoxy resin composite materials during autoclave curing. Background Technology

[0002] Liquid oxygen-compatible epoxy resin composites have broad application prospects in the aerospace field, especially in the manufacture of launch vehicle fuel tanks, due to their excellent mechanical properties and low-temperature / oxidation resistance. However, the curing process of this type of resin in an autoclave involves complex thermo-chemical-fluid-solid multi-physics coupling effects. The exothermic curing reaction, drastic changes in resin viscosity, fiber bed compaction, residual stress accumulation, and pore evolution interact with each other, easily leading to manufacturing defects such as delamination, porosity, resin-rich areas, and curing deformation.

[0003] In existing technologies, simulations of composite material curing processes often employ decoupling or simplification. For example, temperature and degree-of-curing fields are calculated separately, or the flow compaction process is separated from stress-deformation analysis. These simplifications fail to adequately consider the strong coupling between physical fields, especially when dealing with high-performance, high-viscosity resins with complex curing behaviors, such as those with liquid oxygen compatibility. This results in insufficient accuracy and an inability to accurately predict pore formation and final deformation. Furthermore, existing viscoelastic constitutive models often fail to deeply correlate degree-of-curing, temperature, and the viscoelastic properties and defect evolution (such as pore pressure) of the resin, making it impossible to effectively simulate the diffusion control effects in the later stages of curing and the resulting micropore defects.

[0004] Therefore, there is an urgent need for a numerical simulation method that can accurately describe the coupling behavior of multi-physics field strengths of liquid oxygen compatible epoxy resin during the curing process in an autoclave and effectively predict curing deformation and porosity defects. Summary of the Invention

[0005] This invention aims to address the aforementioned problems in the prior art by providing a method and system for flow compaction curing and defect prediction of liquid oxygen-compatible epoxy resin composites based on a viscoelastic constitutive model. This model constructs a strongly coupled framework of thermo-chemical-fluid-solid multiphysics fields and introduces a diffusion-controlled curing kinetics and dynamic viscosity model based on free volume theory. This enables accurate simulation of the entire curing process and prediction of curing deformation, residual stress fields, and the generation and evolution of pore defects.

[0006] Therefore, some embodiments of this application provide a multi-physics coupling model for the flow, compaction, and curing of liquid oxygen-compatible epoxy resin composite materials based on a viscoelastic constitutive model. In some embodiments, the model can be built on a finite element software platform and implemented through a series of user subroutines, the core of which includes the following framework components: The heat transfer framework is constructed based on thermochemical coupling equations, including three-dimensional transient heat transfer control equations, taking into account anisotropic heat conduction, internal heat sources of resin reaction, and dynamic updates of material thermophysical parameters with temperature and degree of curing. The framework of the viscoelastic constitutive model for liquid oxygen-compatible epoxy resin is constructed using a modified generalized Maxwell model, with total stress... The total stress is the sum of instantaneous elastic stress and viscoelastic relaxation stress. The modulus and relaxation time are coupled with temperature and degree of cure, and the influence of the glass transition temperature is corrected using the WLF equation. Defined as: Among them, elastic modulus ;in Uncured modulus (The modulus of complete curing is given; k and c are fitting constants); relaxation time. d is the curing degree influence coefficient. The relaxation activation energy; The curing kinetics framework is based on the Kamal-Sourour model and free volume diffusion theory. The curing reaction rate includes autocatalytic form and diffusion control factor, and takes into account the change of glass transition temperature with degree of curing and the limiting degree of curing. The resin viscosity update framework is constructed based on the Cross-Castro-Macosko model and WLF correction. The zero-shear viscosity is dynamically updated with temperature and degree of curing, including the dramatic viscosity changes near the gel point and during the glass transition. The framework of the coupling governing equations for resin flow and fiber compaction is based on Darcy's law, the Kozeny-Carman permeability model, and the Gutowski compaction model, and includes the evolution of flow rate, permeability, compaction pressure, strain, and pore pressure.

[0007] In some embodiments, the multiphysics coupling model is integrated into the finite element software ABAQUS solver, and the data flow and calculation of each framework part are realized through user subroutines, including: The USDFLD subroutine corresponds to the curing kinetics framework, calculates the degree of curing at each integration point, and passes it as a field variable. The HETVAL subroutine calculates the internal heat source in the heat transfer frame section and calculates the heat release of the curing reaction based on the curing rate. The UMAT subroutine corresponds to the framework of the viscoelastic constitutive model of liquid oxygen compatible epoxy resin, the framework of resin viscosity update, and the framework of the coupled control equations of resin flow and fiber compaction. It updates the stiffness matrix, relaxation time, internal variables, viscosity, and calculates stress and flow compaction process. The UEXPAN subroutine corresponds to the calculation of thermal strain and chemical shrinkage in part E of the coupled control equation framework for resin flow and fiber compaction. The DISP subroutine defines temperature and pressure boundary conditions; The FILM subroutine defines the convective heat transfer coefficient and ambient temperature to simulate the heat exchange boundary.

[0008] In some embodiments, the internal heat source term in the heat transfer frame portion is directly related to the curing rate and takes into account the nonlinear changes in heat conduction behavior at low temperatures; the elastic modulus and relaxation time in the viscoelastic constitutive model frame portion of the liquid oxygen compatible epoxy resin are related to the glass transition temperature through the WLF equation.

[0009] In some embodiments, the diffusion control factor in the curing kinetics framework is derived based on the WLF equation, and the critical degree of cure increases linearly with temperature; the zero-shear viscosity in the resin viscosity update framework adopts a modified Arrhenius equation, including the drastic viscosity changes near the gel point and during the glass transition.

[0010] In some embodiments, the permeability in the framework of the coupling control equations for resin flow and fiber compaction is dynamically updated based on the fiber volume fraction using a modified Kozeny-Carman equation. The relationship between compaction pressure and strain is expressed in a modified form of the Gutowski model and includes pore pressure evolution based on the effective stress principle.

[0011] In some embodiments, the multiphysics coupling model further includes an input module for inputting material parameters, which include curing kinetic parameters, non-isothermal and isothermal exothermic curve data obtained by differential scanning calorimetry experiments, relaxation modulus master curve parameters obtained by dynamic mechanical analysis experiments, viscosity model parameters obtained by rheological experiments, and Gutowski model parameters obtained by compaction experiments.

[0012] In some embodiments, the multiphysics coupling model further includes a defect prediction module, configured to determine the changes in the pores inside the composite material based on the pore pressure and resin viscosity calculated by the flow-compaction-pore coupling model, combined with the critical pore pressure criterion or the bubble equilibrium radius model, and predict the initial porosity after complete curing.

[0013] In some embodiments, the defect prediction module is further configured to use the total stress calculated by the viscoelastic constitutive model, combined with failure criteria, to assess whether the interlaminar shear stress exceeds the interlaminar strength, and to predict the springback deformation and interlaminar delamination risk of the cured part.

[0014] Other embodiments of this application propose a defect prediction method based on this model, including: extracting pore pressure, resin viscosity, and total stress based on the calculation results of any of the above models; judging the changes in pores inside the composite material based on the pore pressure and resin viscosity calculated by the flow-compaction-pore coupling model, combined with the critical pore pressure criterion or the bubble equilibrium radius model, and predicting the initial porosity after complete curing; evaluating whether the interlaminar shear stress exceeds the interlaminar strength using the total stress calculated by the viscoelastic constitutive model, combined with the failure criterion, and predicting the rebound deformation and interlaminar delamination risk of the cured part; and outputting the displacement and deformation of the composite material during the curing process through simulation results to perform the defect prediction steps.

[0015] Other embodiments of this application propose a defect prediction system based on this model, which includes a processor and a memory, the memory storing a computer program that, when executed by the processor, implements the defect prediction method.

[0016] The beneficial effects of this application include: A fully coupled thermo-chemical-fluid-solid analysis framework was established, breaking the limitations of independent or unidirectional calculation of each physical field in traditional methods. Especially for high-performance resins such as liquid oxygen-compatible epoxy resins, it can more realistically reflect the complex physical phenomena in the curing process.

[0017] By introducing a diffusion control factor based on free volume theory, the transformation of the late-stage curing reaction from chemical control to diffusion control is accurately described, and the physical reality that complete curing cannot be achieved under low-temperature curing conditions is reasonably predicted, providing an accurate degree of curing input for subsequent mechanical property prediction.

[0018] The viscosity model, through the WLF equation, is directly related to the dynamically changing glass transition temperature. It can accurately capture the drastic changes in viscosity near the gel point and during the glass transition, which is key to controlling resin flow and pore discharge.

[0019] For the first time, a flow compaction model based on the effective stress principle and the pore pressure evolution equation are coupled in a multiphysics model, which can predict the generation, compression or growth of pores from a mechanistic perspective, providing a theoretical tool for process optimization to suppress pore defects. Attached image description:

[0020] Figure 1This is a schematic diagram of an L-shaped composite material model in the liquid oxygen compatible epoxy resin composite material flow compaction curing molding and defect prediction method according to an embodiment of this application.

[0021] Figure 2 for Figure 1 Curing displacement cloud map of the L-shaped composite material model.

[0022] Figure 3 for Figure 1 Curing degree distribution diagram of the L-shaped composite material model.

[0023] Figure 4 for Figure 1 The curing degree curve of the L-shaped composite material model.

[0024] Figure 5 for Figure 1 Temperature curves of the L-shaped composite material model.

[0025] Figure 6 for Figure 1 Porosity distribution diagram of the L-shaped composite material model.

[0026] Figure 7 This is a framework diagram of the multiphysics coupling model for the flow, compaction, curing, and molding of liquid oxygen compatible epoxy resin composite materials based on a viscoelastic constitutive model integrated into the ABAQUS solver according to this application. Detailed Implementation

[0027] Some embodiments of this application provide a multi-physics coupling model for the flow, compaction, and curing of liquid oxygen-compatible epoxy resin composite materials based on a viscoelastic constitutive model, the principle of which is shown in the following diagram. Figure 7 The multiphysics coupling model framework shown includes thermal, chemical, fluid, and solid components: This multiphysics coupling model framework treats the curing process as a whole, including bidirectional data transfer of heat transfer, curing reaction, resin flow, fiber compaction, and stress-strain evolution.

[0028] Specifically, the multiphysics coupling model framework includes a heat transfer framework section A, a liquid oxygen compatible epoxy resin viscoelastic constitutive model framework section B, a curing kinetics framework section C, a resin viscosity framework section D, and a resin flow and fiber compaction model framework section E.

[0029] The heat transfer frame A provides information on temperature field changes, which are input into the curing kinetics frame C to update the degree of cure, and into the resin viscosity frame D to update the resin viscosity. The degree of cure is fed back to the heat transfer frame A as an internal heat source, and also affects the material's viscoelastic parameters and other mechanical properties. The resin viscosity is input into the resin flow and compaction model frame E to control the flow of resin in the fiber bed. Fiber volume fraction, pore pressure, and the results of flow and compaction are used as state variables, directly affecting the stiffness matrix and stress calculation of the composite material. Finally, the curing deformation and total stress of the composite material are calculated using the liquid oxygen compatible epoxy resin viscoelastic constitutive model frame B, where the total stress is also referred to as the residual stress field.

[0030] The construction methods of each framework component in the multiphysics coupling model framework are as follows: Part A of the heat transfer framework is constructed based on thermochemical coupling equations.

[0031] The curing process of the composite material satisfies the three-dimensional transient heat transfer control equation, considering anisotropic heat conduction and internal heat sources of the resin reaction:

[0032] Among them: internal heat source intensity With curing rate Directly related, expressed as: , Total heat of reaction; The internal heat source intensity is the intensity of the heat of chemical reaction during the curing process. Throughout the curing process, the thermophysical parameters of the material, such as density, specific heat capacity and thermal conductivity, are dynamically updated with temperature and degree of curing. Furthermore, the thermal conduction behavior of the composite material changes significantly at low temperatures. These nonlinear characteristics are all considered in this model.

[0033] As an example, the HETVAL subroutine of ABAQUS software can be used to calculate the internal heat source of the curing reaction, the FILM subroutine to define the convective heat transfer coefficient and ambient temperature, simulate the heat exchange boundary, and the UMAT subroutine can be combined to calculate the changes of thermophysical parameters such as the specific heat capacity and thermal conductivity of the material with temperature T.

[0034] The HETVAL subroutine directly corresponds to the internal heat source term Q in frame A, which is related to the curing rate and is loaded into the heat transfer equation to ensure thermochemical coupling; the FILM subroutine handles the external heat exchange boundary conditions of frame A, such as surface heat exchange with the environment; and the UMAT subroutine supplements the dynamic updates of thermophysical parameters, such as specific heat / thermal conductivity, because the heat transfer frame requires real-time calculation of these parameters.

[0035] Unless otherwise defined below, all subroutines are subroutines of the ABAQUS software.

[0036] Part B of the viscoelastic constitutive model framework for liquid oxygen-compatible epoxy resin provides a viscoelastic constitutive model constructed using a modified generalized Maxwell model, with coupling temperature (0℃~200℃) and degree of cure (0~1) as dynamically updated parameters. The total stress σ(t) is the sum of the instantaneous elastic stress and the viscoelastic relaxation stress, and its core expression framework is as follows:

[0037] The instantaneous elastic stress is borne by six elastic elements connected in parallel. According to Hooke's Law, the stress in a single elastic element is... (i=1~6), the total instantaneous elastic stress is the sum of the stresses of each element:

[0038] in, In response, The dynamic elastic modulus of the i-th elastic element requires simultaneous coupling of curing α and temperature T. Its expression is as follows:

[0039] in: Let be the uncured modulus of the i-th elastic element; The fully cured modulus of the i-th elastic element; k is the fitting constant for the effect of degree of cure; c is the temperature-sensitive fitting constant; T is the reference temperature; T is the current curing temperature.

[0040] The viscoelastic relaxation stress is borne by eight parallel viscoelastic elements. The stress response of each viscoelastic element follows linear viscoelastic theory and is characterized by a relaxation function. For the j-th viscoelastic element, its stress relaxation process satisfies:

[0041] In the formula: Let be the dynamic elastic modulus of the spring in the j-th viscoelastic element; its derivation is consistent with the dynamic elastic modulus formula. Let be the dynamic relaxation time of the j-th viscoelastic unit; Traditional models often use empirical formulas in the form of Arrhenius:

[0042] In the formula: d represents the initial relaxation time of the j-th viscoelastic unit; d is the curing degree influence coefficient. Let f be the relaxation activation energy. R is the gas constant. This form is applicable in the high-temperature region, but it cannot accurately describe the dramatic increase in relaxation time near the glass transition. To more accurately characterize the entire process, this invention introduces the WLF (Williams-Landel-Ferry) equation based on free volume theory. According to the Doolittle equation, the relationship between relaxation time and free volume fraction f is:

[0043] In the formula , Let f be a material constant. The free volume fraction f increases linearly with increasing temperature and decreases with increasing degree of cure. When the temperature equals the glass transition temperature... When the free volume fraction approaches the universal constant, From this, we can derive:

[0044] in Let be the coefficient of thermal expansion of the free volume. Further simplification yields a form equivalent to the WLF equation:

[0045] In the formula The relaxation time at the glass transition temperature, which varies with the degree of cure, reflects the influence of the crosslinked network topology on the relaxation spectrum and can be described exponentially.

[0046] in This is the curing degree sensitivity coefficient. Further, a complete expression of the relaxation time is obtained.

[0047] In the formula To take into account the relaxation time, the complete expression for the total stress is further derived from the above:

[0048] As an example of this framework, UMAT is Abacus's standard interface for defining nonlinear material behavior, ensuring temperature / curing coupling, and allowing the use of UMAT subroutines to define the viscoelastic constitutive behavior of materials, update the stiffness matrix, relaxation time, and internal variables of the generalized Maxwell model, and calculate stress. UMAT is directly responsible for the entire constitutive calculation of frame B, including the dynamic elastic modulus E. i (α,T) and relaxation time τ j The update of (α,T) and the stress integral.

[0049] III. Construction of the solidification kinetic framework part C.

[0050] The solidification kinetics framework, part C, is constructed based on the Kamal-Sourour model and free volume diffusion theory.

[0051] This invention uses the Kamal-Sourour autocatalytic model to describe the curing reaction kinetics of epoxy resin, and introduces a diffusion control factor from the free volume theory to describe the diffusion control effect in the later stage of curing.

[0052] In the Kamal-Sourour autocatalytic model, the curing reaction rate adopts a two-parameter autocatalytic form:

[0053] The reaction rate constant follows the Arrhenius equation:

[0054] Where k1 is the catalytic reaction rate constant, k2 is the autocatalytic reaction rate constant, and m and n are the reaction orders. This model can accurately describe the entire process of the epoxy resin curing reaction, including the induction period, acceleration period, and decay period.

[0055] In the later stages of curing, as the crosslinking network density increases, the glass transition temperature (Tg) of the system rises. When Tg approaches or exceeds the curing temperature (T), the reaction changes from chemically controlled to diffusion-controlled. This invention uses a diffusion control factor based on free volume theory to modify the Kamal model:

[0056] diffusion control factor Derived from the WLF (Williams-Landel-Ferry) equation, this describes the inhibitory effect of diffusion confinement on the reaction rate:

[0057] Where C is the diffusion control parameter, The initial critical degree of curing is determined by the free volume theory to control diffusion.

[0058] Diffusion control of initial critical degree of cure Related to the free volume fraction of the system. When the glass transition temperature of the system... At a curing temperature T, diffusion restriction begins to become significant. This invention uses the following relationship to determine... :

[0059] The simplified form can be expressed as:

[0060] The critical degree of cure increases linearly with increasing curing temperature. The higher the temperature, the later diffusion control occurs, which is consistent with the prediction of free volume theory.

[0061] The glass transition temperature (Tg) as a function of degree of cure is described by the Gordon-Taylor equation, which is based on copolymer theory and takes into account the mixed contribution of uncured and cured resins:

[0062] in The glass transition temperature of the uncured resin. Let be the glass transition temperature of the fully cured resin, and k be the Gordon-Taylor constant. This model can accurately predict the glass transition temperature of the resin at different degrees of cure, providing a basis for calculating the diffusion control factor.

[0063] During the diffusion control stage, the curing reaction may not achieve complete curing (α=1) due to the glass transition. This invention introduces a temperature-dependent limit of curing. : ; This model ensures that when the curing temperature is below At that time, the ultimate degree of curing was less than 1, which is consistent with the physical reality.

[0064] As a partial implementation of this framework, it can employ the USDFLD subroutine to calculate the solidification degree α at each integration point, and pass α as a field variable to other subroutines. The USDFLD subroutine directly calls the solidification kinetic model of framework C to calculate α and outputs it to the HETVAL / UMAT subroutines, etc. This is because the core of the solidification framework is the dynamic evolution of α, and USDFLD is a user-defined field variable subroutine of Abacus, specifically used to calculate and pass state variables, such as α, for use by other modules, thus achieving coupling.

[0065] IV. Resin viscosity update framework section D.

[0066] This invention employs the Cross-Castro-Macosko model to describe the dynamic evolution of resin viscosity with temperature and degree of cure, and introduces the glass transition temperature to correct for the WLF of zero shear viscosity to construct part D of the resin viscosity update framework:

[0067] Zero shear viscosity The modified Arrhenius equation is adopted, and the glass transition temperature is introduced through the WLF equation. Impact:

[0068] in The viscosity at extreme high temperatures, The activation energy for viscous flow. , is a constant in the WLF equation. This expression comprehensively considers the excitation effect of temperature on molecular thermal motion and the surge in viscosity caused by the sudden drop in free volume near the glass transition. Gel point Rheological experiments determined that the typical value for liquid oxygen-compatible epoxy resin is 0.3~0.5.

[0069] As an example, this framework can be implemented using the UMAT subroutine. By integrating viscosity updates, η is calculated in the flow module for the Darcy flow rate. The UMAT subroutine includes viscosity calculations for framework D, which serve as input parameters for the flow compaction module. This is because the viscosity framework serves the flow simulation, and UMAT is the core subroutine of the multiphysics coupling, capable of updating η in real time and integrating it into the stress / flow calculations, ensuring coupling with framework E.

[0070] V. Framework of Coupled Control Equations for Resin Flow and Fiber Compaction (Part E)

[0071] Based on multi-media theory and effective stress principle, this invention establishes a coupling control equation for resin flow and fiber compaction to construct the framework part E of the coupling control equation for resin flow and fiber compaction, namely the flow-compactment-pore coupling model.

[0072] During the curing process of liquid oxygen compatible resin, the flow of resin in the fiber interstices follows Darcy's law, and the flow rate is driven by the gradient:

[0073] Where v is the resin flow rate, K is the permeability tensor, η is the resin viscosity, and ∇P is the pressure gradient.

[0074] During the curing process of the composite material, the resin flows and air is expelled from the overall structure, causing a change in the fiber volume fraction. The resin permeability as a function of the fiber volume fraction is described using a modified Kozeny-Carman equation.

[0075] in This represents the current fiber volume fraction. β is the initial fiber volume fraction, and β is the fitting exponent (usually taken as 2~3). This is for reference penetration rate.

[0076] The pressure on the fiber bed during fiber compaction, i.e., compaction pressure. Strain in the thickness direction The relationship is expressed in an improved form of the Gutowski model:

[0077] in This is the compaction coefficient. The maximum fiber volume fraction, This represents the compressive strain in the thickness direction.

[0078] During compaction, pore pressure Determined by both the gas law and volume constraints:

[0079] in The initial pore pressure, This represents the initial fiber volume fraction. For reference temperature, The external pressure is used. Based on the critical pore pressure criterion derived from the bubble equilibrium radius model, the evolution trend of pores within the composite material is determined. Critical pore pressure. Defined as the minimum pressure required to maintain the stability of a bubble at its current radius, applied externally. The capillary force, determined by both the surface tension of the resin and the capillary force, is expressed as follows:

[0080] in, R is the surface tension coefficient of the resin, and R is the current bubble radius.

[0081] Viscosity modulus (VISCMOD) characterizes the contribution of resin flow to stiffness, and is calculated using the following formula:

[0082] in Δt represents the characteristic size of the pores, and Δt represents the time step.

[0083] Furthermore, the fiber volume fraction and porosity change in real time during the process, with the fiber volume fraction and porosity updated based on strain in the thickness direction as follows:

[0084]

[0085] in The initial porosity is given. This model can simulate the dynamic process of fiber enrichment and pore closure / growth under the combined effects of compaction and resin flow.

[0086] As an example, this framework can use the UMAT subroutine to calculate flow and compaction based on Darcy's law, update fiber volume fraction / pore pressure, combine with the UEXPAN subroutine to calculate thermal strain and chemical shrinkage strain, and then combine with the DISP subroutine to define temperature / pressure boundary conditions. UMAT handles the core flow-compaction coupling and defect prediction of framework E, such as updating Vf and pore pressure; the UEXPAN subroutine calculates strain in framework E, such as thermal / chemical shrinkage; and the DISP subroutine sets external boundaries, such as temperature T(t) and pressure P. ext (t).

[0087] In some embodiments, a material parameter input module may also be provided for the model, configured to input material parameters obtained through differential scanning calorimetry (DSC) experiments, dynamic mechanical analysis (DMA) experiments, rheological experiments, and compaction experiments into the heat transfer frame part A. For example, the material parameters include curing kinetic parameters, non-isothermal and isothermal exothermic curve data obtained through DSC experiments, relaxation modulus master curve parameters obtained through DMA experiments, viscosity model parameters obtained through rheological experiments, and Gutowski model parameters obtained through compaction experiments. An autoclave curing process curve input module may also be provided for the model, configured to input curing process curves into the curing kinetics frame part. In some embodiments, a defect prediction module may also be provided for the model, configured to predict defects in the composite material based on the calculation results of the aforementioned multiphysics coupling model.

[0088] The defect prediction module is configured to calculate the pore pressure based on the flow-compaction-pore coupling model. The current resin viscosity η is obtained from the resin viscosity model, and combined with the critical pore pressure criterion or bubble equilibrium radius model, the change in internal porosity of the composite material is determined. By combining the results from the framework section, the initial porosity of the composite material after complete curing can be predicted, which makes it possible to optimize the curing process and reduce initial defects in the composite material during manufacturing.

[0089] The residual stress field calculated using a viscoelastic constitutive model, combined with failure criteria such as Tsai-Wu or Quads, is used to assess whether the interlaminar shear stress exceeds the interlaminar strength, thereby predicting the springback deformation and potential delamination risk of the cured part. Furthermore, based on the distribution of curing stress, the mold structure is adjusted to reduce the stress magnitude in stress concentration areas.

[0090] The simulation results output the displacement and deformation of the composite material during the curing process, especially improving the prediction ability of the curing deformation of L-shaped composite materials.

[0091] Defect prediction of liquid oxygen compatible epoxy resin composites can be performed based on the multi-physics coupling model of flow compaction curing molding of liquid oxygen compatible epoxy resin composites based on the viscoelastic constitutive model. Therefore, this application also proposes a method and system for predicting defects of liquid oxygen compatible epoxy resin composites based on the multi-physics coupling model of flow compaction curing molding of liquid oxygen compatible epoxy resin composites based on the viscoelastic constitutive model.

[0092] The method for predicting defects in liquid oxygen-compatible epoxy resin composite materials may include the following steps: Based on the calculation results of the multiphysics coupling model, pore pressure, resin viscosity and residual stress field are extracted; Based on the pore pressure and resin viscosity calculated by the flow-compaction-pore coupling model, combined with the critical pore pressure criterion or bubble equilibrium radius model, the changes in the pores inside the composite material are judged, and the initial porosity after complete curing is predicted. The residual stress field calculated using the viscoelastic constitutive model is combined with failure criteria to assess whether the interlaminar shear stress exceeds the interlaminar strength, and to predict the springback deformation and delamination risk of the cured part. The simulation results output the displacement and deformation of the composite material during the curing process, and the defect prediction is performed.

[0093] Other embodiments of this application also provide a defect prediction system for liquid oxygen compatible epoxy resin composite materials, which includes any hardware system having a processor and a memory, the memory storing a computer program that, when executed by the processor, implements the defect prediction method. Experimental example:

[0094] This experimental example uses a T700 grade carbon fiber reinforced liquid oxygen compatible epoxy resin composite L-shaped laminate as the object to verify the curing deformation prediction capability of the model and method of this invention.

[0095] Step 1: Obtain material parameters and input model.

[0096] Obtaining material parameters may include:

[0097] Differential scanning calorimetry (DSC) experiments were conducted, heating the samples from 30℃ to 300℃ at heating rates of 5, 10, 15, and 20℃ / min, performing non-isothermal tests, and recording the curing exothermic curves. Isothermal curing was performed at 100℃, 130℃, and 160℃ for 2 hours, and isothermal exothermic curves were obtained. The initial glass transition temperature of the uncured resin was determined using a "heat-cool-reheat" program (10℃ / min). and the final glass transition temperature of the fully cured resin. Finally, the curing kinetic parameters of the liquid oxygen-compatible epoxy resin were obtained: , , , , , And fit the parameters of the Gordon-Taylor equation. , , .

[0098] Dynamic mechanical analysis (DMA) experiments were conducted to obtain the master curves of relaxation modulus at different temperatures and degrees of cure, and the parameters of the generalized Maxwell model were fitted. , , , , , , The viscosity was measured as a function of temperature by scanning from 30℃ to 200℃ at heating rates of 2℃ / min, 3℃ / min, 5℃ / min, and 10℃ / min. The viscosity was then measured as a function of time (i.e., degree of cure) by scanning at isothermal temperatures of 60℃, 70℃, 80℃, 90℃, 100℃, and 110℃ for 60–120 minutes.

[0099] And obtain viscosity model parameters through rheological experiments: , , , , wait.

[0100] Gutowski model parameters were obtained through compaction experiments. , These parameters are then written as input to the user subroutine.

[0101] Step 2: Finite element modeling and simulation.

[0102] Based on the simulated real structural characteristics of the composite material, a geometric model of an L-shaped laminate was established in ABAQUS. The model dimensions are: arm length 50 mm, width 150 mm, thickness 3 mm, and inner corner radius 5 mm. An orthogonal layup of [0 / +45 / -45 / 90]²S was used to generate a mesh, and eight layers of mesh elements were arranged in the thickness direction to observe gradient changes. Coupled temperature-displacement solid elements of type C3D8T were selected.

[0103] Next, material properties are defined, relevant parameters are filled in according to the subroutine interface requirements, and state variables are set. After completing the material definition, material properties are assigned and the material orientation is specified. The autoclave curing process curve is defined in the subroutine, including the heating rate, holding plateau, curing temperature, and cooling rate, all represented by T(t), and the applied pressure, represented by P. ext (t) represents the analysis step. Appropriate physical boundary conditions are applied to the structural surface, and a predefined field consistent with the experimental conditions is set. Finally, the user-defined subroutine is called to perform calculations, updating material properties in real time, calculating the exothermic curing reaction, simulating the resin flow and compaction process, and stress accumulation.

[0104] The user framework and corresponding software modules in the subroutine mainly include: USDFLD in the Abacus software: calculating the degree of solidification at each integration point. It calls the curing kinetics model and... It is passed to other subroutines as a field variable. In Abacus software, HETVAL represents the curing rate calculated based on USDFLD. Calculate the internal heat source of the curing reaction. This is then loaded into the heat transfer equation. In the Abacus software, UMAT: defines the viscoelastic constitutive behavior of the material. It receives data from USDFLD. and current temperature It updates the stiffness matrix, relaxation time, and internal variables of the generalized Maxwell model and calculates the stress. Simultaneously, it calculates the thermophysical parameters of the material, such as specific heat capacity and thermal conductivity, as they change. and The changes. The flow compaction module is also coupled in the UMAT subroutine, based on Darcy's law and the effective stress principle, according to the current resin viscosity. The pressure gradient was used to calculate the resin flow and fiber compaction process, and the fiber volume fraction and pore pressure were updated. Simultaneously, permeability was... According to the Kozeny-Carman equation Real-time updates. UEXPAN in Abacus software: calculates thermal strain and chemical shrinkage strain. The coefficient of thermal expansion is based on... and Switching between glassy and rubbery states. Chemical shrinkage and degree of cure increment. Proportional. In Abacus software, DISP defines the temperature and pressure boundary conditions for the autoclave curing process. FILM defines the non-uniform convective heat transfer coefficient and ambient temperature, simulating the heat exchange between the component surface and its surroundings.

[0105] Step 3: Result Analysis and Verification

[0106] After the simulation, the displacement field of the flange portion of the L-shaped component was extracted, and the final springback angle after demolding was calculated to evaluate the curing deformation of the composite material. The consistency between the simulation results and the actual results was verified. A porosity distribution cloud map was extracted from the simulation results, focusing on the porosity in resin-rich areas and the inner corners, areas prone to porosity formation. The simulation results for the case study are shown below. Figure 1 , Figure 2 , Figure 3 , Figure 4 , Figure 5 and Figure 6 As shown, the diagram illustrates an L-shaped composite material model used in the liquid oxygen compatible epoxy resin composite material flow compaction curing and defect prediction method according to an embodiment of this application. Figure 2 for Figure 1 Curing displacement cloud map of the L-shaped composite material model. Figure 3 for Figure 1 Curing degree distribution diagram of the L-shaped composite material model. Figure 4 for Figure 1 The curing degree curve of the L-shaped composite material model. Figure 5 for Figure 1 Temperature curves of the L-shaped composite material model. Figure 6 for Figure 1 Porosity distribution diagram of the L-shaped composite material model.

[0107] from Figure 2 The springback deformation distribution demonstrates that the model optimizes the calculation of residual stress. By combining failure criteria to assess interlaminar shear stress, predicting deformation, and adjusting the process, actual springback deformation can be reduced, thereby keeping deformation at a low level, reducing the risk of delamination, and improving part accuracy.

[0108] Figure 3 This demonstrates that optimizing the curing kinetics framework C can prevent defects caused by uneven curing. By correcting late-stage diffusion using the WLF equation, the curing rate can be dynamically adjusted, reducing porosity formation and improving material consistency.

[0109] Figure 4 The smooth upward curve demonstrates that the model optimizes the curing process control (induction period - acceleration period - decay period). Through parameter calibration, such as obtaining k1, k2, and Ea through DSC experiments, the heating rate is adjusted to avoid stress caused by excessively rapid curing. This optimizes the curing time, shortens the cycle, and reduces energy consumption.

[0110] Figure 5 This reflects stable temperature control, such as a uniform insulation platform, and optimizes the heat transfer framework A. By dynamically updating thermophysical parameters, such as k varying with T / α, it prevents overheating / uniformity, thereby reducing cracks caused by thermal gradients.

[0111] Figure 6The color L-shaped porosity cloud map reflects low and uniform porosity, demonstrating the final optimization effect of the flow compaction frame E, which can improve material strength and reduce manufacturing failure rate.

[0112] This application describes the above embodiments. It should be understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Any changes, modifications, substitutions and variations made to the above embodiments by those skilled in the art are within the protection scope of the present invention.

Claims

1. A multi-physics coupling model for the flow, compaction, curing, and molding of liquid oxygen-compatible epoxy resin composite materials based on a viscoelastic constitutive model, characterized in that, Includes the following framework components: The heat transfer framework (A) is constructed based on the thermochemical coupling equation, including the three-dimensional transient heat transfer control equation, which takes into account anisotropic heat conduction, internal heat sources of resin reaction, and dynamic updates of material thermophysical parameters with temperature and degree of curing. The framework (B) of the viscoelastic constitutive model for liquid oxygen-compatible epoxy resin is constructed using a modified generalized Maxwell model, with a total stress... The total stress is the sum of instantaneous elastic stress and viscoelastic relaxation stress. The modulus and relaxation time are coupled with temperature and degree of cure, and the influence of the glass transition temperature is corrected using the WLF equation. Defined as: Among them, elastic modulus ;in Uncured modulus (The modulus of complete curing is given; k and c are fitting constants); relaxation time. d is the curing degree influence coefficient. The relaxation activation energy; The curing kinetics framework (C) is constructed based on the Kamal-Sourour model and free volume diffusion theory. The curing reaction rate includes autocatalytic form and diffusion control factor, and considers the change of glass transition temperature with degree of curing and the limiting degree of curing. The resin viscosity update framework (D) is constructed based on the Cross-Castro-Macosko model and WLF correction. The zero-shear viscosity is dynamically updated with temperature and degree of curing, including the viscosity changes near the gel point and during the glass transition. The framework (E) of the coupling governing equations for resin flow and fiber compaction is constructed based on Darcy's law, the Kozeny-Carman permeability model, and the Gutowski compaction model, including the evolution of flow rate, permeability, compaction pressure, strain, and pore pressure.

2. The multiphysics coupling model according to claim 1, characterized in that: The multiphysics coupling model is integrated into the finite element software ABAQUS solver, and the data flow and calculation of each framework part are realized through user subroutines, including: The USDFLD subroutine corresponds to the solidification kinetics framework (C), which calculates the degree of solidification at each integration point and passes it as a field variable. The HETVAL subroutine corresponds to the internal heat source calculation in the heat transfer frame part (A), and calculates the heat release of the curing reaction based on the curing rate; The UMAT subroutine corresponds to the framework of the liquid oxygen compatible epoxy resin viscoelastic constitutive model (B), the resin viscosity update framework (D), and the framework of the coupled control equations of resin flow and fiber compaction (E). It updates the stiffness matrix, relaxation time, internal variables, viscosity, and calculates stress and flow compaction process. The UEXPAN subroutine corresponds to the calculation of thermal strain and chemical shrinkage in the framework (E) of the coupled control equations for resin flow and fiber compaction. The DISP subroutine defines temperature and pressure boundary conditions; The FILM subroutine defines the convective heat transfer coefficient and ambient temperature, and simulates the heat exchange boundary.

3. The multiphysics coupling model according to claim 1, characterized in that: The internal heat source term in the heat transfer framework section (A) is directly related to the curing rate and takes into account the nonlinear changes in heat conduction behavior under low temperature conditions; the elastic modulus and relaxation time in the viscoelastic constitutive model framework section (B) of the liquid oxygen compatible epoxy resin are related to the glass transition temperature through the WLF equation.

4. The multiphysics coupling model according to claim 1, characterized in that: The diffusion control factor in the curing kinetics framework (C) is derived based on the WLF equation, and the critical degree of curing increases linearly with temperature; the zero-shear viscosity in the resin viscosity update framework (D) adopts the modified Arrhenius equation, including the drastic viscosity changes near the gel point and during the glass transition.

5. The multiphysics coupling model according to claim 1, characterized in that: The permeability in the framework (E) of the coupling control equations for resin flow and fiber compaction is dynamically updated based on the fiber volume fraction using the improved Kozeny-Carman equation. The relationship between compaction pressure and strain is expressed in an improved form of the Gutowski model and includes pore pressure evolution based on the effective stress principle.

6. The multiphysics coupling model according to claim 1, characterized in that: The multiphysics coupling model further includes an input module for inputting material parameters, which include solidification kinetic parameters, non-isothermal and isothermal exothermic curve data obtained by differential scanning calorimetry experiments, relaxation modulus master curve parameters obtained by dynamic mechanical analysis experiments, viscosity model parameters obtained by rheological experiments, and Gutowski model parameters obtained by compaction experiments.

7. The multiphysics coupling model according to claim 1, characterized in that: The multiphysics coupling model further includes a defect prediction module, which is configured to determine the changes in the pores of the composite material based on the pore pressure and resin viscosity calculated by the flow-compaction-pore coupling model, combined with the critical pore pressure criterion or the bubble equilibrium radius model, and predict the initial porosity after complete curing.

8. The multiphysics coupling model according to claim 7, characterized in that: The defect prediction module is further configured to use the total stress calculated by the viscoelastic constitutive model, combined with the failure criteria, to assess whether the interlaminar shear stress exceeds the interlaminar strength, and to predict the springback deformation and interlaminar delamination risk of the cured part.

9. A method for predicting defects in liquid oxygen-compatible epoxy resin composites based on a multi-physics coupling model of flow compaction curing molding of liquid oxygen-compatible epoxy resin composites according to claims 1 to 8, characterized in that, include: Based on the calculation results of the multi-physics field coupling model of the liquid oxygen compatible epoxy resin composite material flow compaction curing molding based on the viscoelastic constitutive model of any one of claims 1 to 8, pore pressure, resin viscosity and total stress are extracted. Based on the pore pressure and resin viscosity calculated by the flow-compaction-pore coupling model, combined with the critical pore pressure criterion or bubble equilibrium radius model, the changes in the pores inside the composite material are judged, and the initial porosity after complete curing is predicted. The total stress calculated using the viscoelastic constitutive model is combined with failure criteria to assess whether the interlaminar shear stress exceeds the interlaminar strength, and to predict the springback deformation and interlaminar delamination risk of the cured part. The simulation results output the displacement and deformation of the composite material during the curing process, and the defect prediction is performed.

10. A defect prediction system for liquid oxygen-compatible epoxy resin composite materials, characterized in that, include: A processor and a memory, the memory storing a computer program that, when executed by the processor, implements the defect prediction method of claim 9.

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