A polymer material life prediction method and system considering bidirectional coupling

Abstract

The application provides a polymer material life prediction method and system considering bidirectional coupling, and aims to solve the problem that the permeability of the polymer material suddenly increases due to hydrogen-induced damage accumulation under a high-pressure hydrogen environment. The method obtains material parameters and service boundary conditions, converts pressure into surface concentration, alternately performs mechanical and diffusion-damage evolution solving in a finite element increment step, modifies the stiffness by using the damage variable of the last step to calculate the hydrostatic stress of the current step, modifies the effective diffusion coefficient by using the stress and the damage variable of the last step, solves the hydrogen diffusion equation and updates the damage variable of the current step, and constructs a bidirectional positive feedback coupling closed loop. Finally, the residual life is output based on the permeation threshold or the damage critical value. The application is mainly used for life evaluation of polymer materials in high-pressure hydrogen storage and transportation equipment.

Description

Technical Field

[0001] This invention relates to the field of numerical simulation and material lifetime prediction technology, and in particular to a method and system for predicting the lifetime of polymer materials that considers the bidirectional coupling of hydrogen permeation and hydrogen-induced damage. Background Technology

[0002] Polymer linings or reinforcing layers in high-pressure hydrogen storage and transportation equipment are exposed to a high-pressure hydrogen environment for extended periods during service. Hydrogen molecules penetrate the polymer, causing plasticization, microcrack initiation, blistering damage, and even hydrogen embrittlement. This hydrogen-induced damage significantly increases the hydrogen permeability coefficient, leading to excessive hydrogen leakage and ultimately equipment failure.

[0003] In current engineering practice, polymer life assessment often relies on empirical formulas or accelerated aging experiments. This involves placing samples in a high-pressure hydrogen environment for different durations, then testing their mechanical properties and permeability, and finally extrapolating the lifespan from the curves. However, this experimental method struggles to reproduce the complex load history encountered during service and has limited extrapolation capabilities.

[0004] In terms of numerical simulation, the closest existing technology to this invention is a hydrogen diffusion-stress coupling model based on chemical potential. This model is implemented in finite element software through a user-defined subroutine, using the chemical potential gradient as the diffusion driving force. It expresses the flux as the sum of concentration and stress gradient terms, considers the relationship between the diffusion coefficient and pressure and concentration, introduces the hindering effect of the crystallinity of the semi-crystalline polymer on the diffusion coefficient, and extracts the diffusion coefficient and permeability coefficient from the flux-time curve using the time lag method. This model can calculate the steady-state permeability coefficient of polymer materials under different hydrogen pressures.

[0005] However, this existing technology has the following shortcomings: it assumes that the polymer material remains intact throughout the service process and does not introduce any damage variables that can describe the hydrogen-induced microstructural degradation. Therefore, it can only calculate the initial permeability coefficient of the intact material and cannot simulate the phenomenon that the permeability coefficient gradually increases over time; it is only applicable to isothermal conditions and does not provide a specific implementation method for temperature dependence; its parameter calibration depends on experimental data at multiple pressure points, while multiple sets of experimental conditions are often lacking in actual engineering.

[0006] Furthermore, while traditional progressive failure models for composite materials can be used to simulate mechanical damage, they primarily address pure mechanical loads, failing to consider the degrading effects of the hydrogen environment on material properties, and typically assuming no change in permeability before failure. Although artificial intelligence methods have been attempted for fitting hydrogen permeability data, they heavily rely on large amounts of high-quality training data, and their "black box" nature makes it difficult to embed physical mechanisms, resulting in poor predictive ability for operating conditions beyond the scope of the training data.

[0007] Therefore, there is an urgent need for a method and system for predicting the lifetime of polymer materials that considers the bidirectional coupling of hydrogen permeation and hydrogen-induced damage, in order to solve the problems existing in the prior art. Summary of the Invention

[0008] This invention provides a method and system for predicting the lifetime of polymer materials that considers the bidirectional coupling of hydrogen permeation and hydrogen-induced damage. It addresses the problem that existing macroscopic finite element numerical simulation methods do not introduce hydrogen-induced damage variables, cannot describe the positive feedback coupling effect between damage accumulation and increased permeability coefficient, and therefore cannot predict the finite lifetime of polymer materials under high-pressure hydrogen environments, which are caused by damage accumulation leading to a sudden increase in permeability and eventual failure.

[0009] The core technology of this invention is to introduce hydrogen-induced damage variables that characterize the degradation of microstructures into multiphysics finite element simulations, and to alternately solve the mutually coupled mechanical constitutive, hydrogen diffusion and damage evolution control equations in each time increment step, thereby constructing a damage-penetration bidirectional positive feedback coupling closed loop composed of stress-induced damage, damage-accelerated penetration, high-concentration hydrogen reverse-accelerated damage, and stiffness degradation changing stress distribution.

[0010] In a first aspect, the present invention provides a method for predicting the lifetime of polymer materials considering the bidirectional coupling of hydrogen permeation and hydrogen-induced damage, the method comprising the following steps:

[0011] S1: Obtain the initial mechanical parameters, hydrogen permeation parameters, damage evolution parameters, and service boundary conditions of the polymer material to be predicted, and convert the gas phase pressure in the service boundary conditions into the hydrogen concentration boundary of the polymer surface based on the solubility model. S2: Construct a multiphysics coupled numerical simulation framework, which includes a mechanical constitutive solution model with effective material stiffness and a diffusion-damage evolution solution model with effective diffusion coefficient. S3: Time-progression solution within each time increment step: Using the mechanical constitutive solution model, the effective stiffness is corrected using the hydrogen-induced damage variable from the previous increment step to calculate the hydrostatic stress of the current increment step; using the diffusion-damage evolution solution model, the effective diffusion coefficient is corrected using the hydrostatic stress of the current increment step and the hydrogen-induced damage variable from the previous increment step, and then the hydrogen diffusion equation coupled with the stress gradient is solved to obtain the internal hydrogen concentration of the current increment step, and the hydrogen-induced damage variable of the current increment step is updated; whereby the increase of the hydrogen-induced damage variable promotes the increase of the effective diffusion coefficient, which in turn leads to the increase of the infiltrated internal hydrogen concentration and inversely accelerates the evolution of the hydrogen-induced damage variable, forming a two-way coupled closed loop of damage-permeation; S4: As the time increment step progresses, extract the permeability performance index and hydrogen-induced damage variable at each time node. When the permeability performance index reaches the preset permeability threshold or the hydrogen-induced damage variable reaches the preset damage critical value, output the corresponding time node as the predicted remaining lifetime of the polymer material.

[0012] Further, in step S3, the hydrogen flux of the hydrogen diffusion equation coupled with the stress gradient is composed of the superposition of the concentration gradient driving term and the hydrostatic stress gradient driving term; the effective diffusion coefficient is corrected using the hydrostatic stress of the current increment step and the hydrogen-induced damage variable of the previous increment step, including: characterizing the effective diffusion coefficient as the product of the intrinsic diffusion coefficient of the undamaged material and the damage amplification factor, wherein the damage amplification factor increases positively with the increase of the hydrogen-induced damage variable.

[0013] Furthermore, in step S3, a power-law damage evolution model driven by multiple factors is used to update the hydrogen-induced damage variable in the current incremental step. In the power-law damage evolution model, the evolution rate of the hydrogen-induced damage variable is proportional to the power of the hydrostatic stress with positive compressive stress, the power of the internal hydrogen concentration, and the power of the current damage margin.

[0014] Further, in step S3, the effective stiffness correction includes: defining the effective elastic modulus of the polymer material as the product of the initial elastic modulus and the stiffness degradation factor, wherein the stiffness degradation factor decreases as the hydrogen-induced damage variable increases.

[0015] Furthermore, in step S3, an explicit staggered coupling strategy is adopted for time-progression solution, including the following sub-steps that are executed independently and sequentially within the same increment step without inter-field iteration: Sub-step S31: Update the hydrostatic stress of the current incremental step based on the mechanical constitutive solution model, and write the hydrostatic stress into the state variable storage area; Sub-step S32: The diffusion-damage evolution solution model reads the updated hydrostatic stress from the state variable storage area, calculates the internal hydrogen concentration and hydrogen-induced damage variables of the current increment step, and overwrites the updated data to the state variable storage area for use in the next increment step.

[0016] Furthermore, an adaptive time step strategy is introduced in step S3: after the calculation of sub-step S32 of an increment step is completed, the maximum increment of the hydrogen-induced damage variable is extracted from all integration points in the increment step; it is determined whether the maximum increment is greater than the preset damage increment threshold. If it is greater, the current time step is reduced by the preset step reduction coefficient and the current increment step is recalculated; if it is not greater, the calculation result of the current increment step is accepted and the next time increment step is entered.

[0017] Furthermore, in step S1, the damage evolution parameters are pre-calibrated based on a single working condition using a reverse numerical optimization method. The specific calibration steps include: Experimental curves were obtained showing the standard hydrogen permeation flux of polymer samples as a function of time under a single constant operating condition. Set initial guess values ​​for the damage evolution parameters to be calibrated, and substitute the initial guess values ​​into the forward coupled calculation model to obtain the predicted permeation curve; Calculate the objective function error between the experimental curve and the predicted permeation curve, call the optimization algorithm to iteratively update the damage evolution parameters until the objective function error meets the convergence condition, and output the converged parameters as the damage evolution parameters.

[0018] In a second aspect, the present invention provides a polymer material lifetime prediction device considering the bidirectional coupling of hydrogen permeation and hydrogen-induced damage, comprising: The boundary and parameter configuration module is used to obtain the initial mechanical parameters, hydrogen permeation parameters, damage evolution parameters and service boundary conditions of the polymer material to be predicted, and to convert the gas phase pressure in the service boundary conditions into the hydrogen concentration boundary of the polymer surface based on the solubility model. The coupled simulation module is used to construct a multiphysics coupled numerical simulation framework and perform time-progressive solutions within each time increment step: Using a mechanical constitutive model, the effective stiffness of the material is corrected using the hydrogen-induced damage variable from the previous increment step to calculate the hydrostatic stress in the current increment step; using a diffusion-damage evolution model, the effective diffusion coefficient is corrected using the hydrostatic stress in the current increment step and the hydrogen-induced damage variable from the previous increment step, and then the hydrogen diffusion equation of the coupled stress gradient is solved to obtain the internal hydrogen concentration in the current increment step, and the hydrogen-induced damage variable in the current increment step is updated; the increase in the hydrogen-induced damage variable leads to an increase in the effective diffusion coefficient, which in turn leads to an increase in the internal hydrogen concentration and, in turn, accelerates the evolution of the hydrogen-induced damage variable, forming a two-way coupled closed loop of damage-permeation; The lifetime determination output module is used to output the predicted remaining lifetime of the polymer material at the corresponding time point when the permeability performance index reaches the preset permeation threshold or the hydrogen-induced damage variable reaches the preset damage critical value during the time process.

[0019] Thirdly, the present invention provides an electronic device including a memory and a processor, wherein the memory stores a computer program and the processor is configured to run the computer program to perform the above-described method for predicting the lifetime of polymer materials considering the bidirectional coupling of hydrogen permeation and hydrogen-induced damage.

[0020] Fourthly, the present invention provides a readable storage medium storing a computer program, the computer program including program code for controlling a process to execute the process, the process including the polymer material lifetime prediction method considering the bidirectional coupling of hydrogen permeation and hydrogen-induced damage as described above.

[0021] The main contributions and innovations of this invention are as follows: 1. This invention establishes a bidirectional positive feedback coupling closed loop between hydrogen-induced damage variables and effective diffusion coefficients, which fully describes the progressive failure process of "stress-induced damage → damage-accelerated permeation → higher concentration of hydrogen-accelerated damage → stiffness decrease and stress distribution change". It overcomes the technical bottleneck of existing technologies that can only calculate the initial permeability coefficient of intact materials and cannot predict the finite life, and can output a remaining life prediction value with clear physical meaning.

[0022] 2. The power-law damage evolution equation proposed in this invention adopts a product coupling form of hydrostatic stress, hydrogen concentration and current damage margin, which can reflect the "stress-concentration-time" synergistic effect of polymer damage under high pressure hydrogen environment. Compared with the traditional linear superposition form of independent terms, it is more in line with the physical mechanism.

[0023] 3. This invention employs an explicit staggered coupling strategy for three-field coupling solution. Data transfer between the two solution modules is achieved through a state variable storage area, which is simple to implement and has low computational cost. Combined with an adaptive time step strategy that uses the damage variable increment as the control criterion, it effectively ensures the numerical stability and computational accuracy during the damage acceleration phase.

[0024] 4. This invention requires only a set of standard hydrogen permeation experimental data under a single operating condition. All material constants in the damage evolution equation can be simultaneously calibrated through a reverse numerical optimization method. There is no need to conduct multi-condition experiments, which has strong engineering applicability.

[0025] 5. This invention provides two failure determination methods, namely, the permeation threshold criterion and the damage criticality criterion, which can be used independently or in combination. Engineers can flexibly choose the appropriate method according to different application scenarios where sealing performance or structural integrity is of concern, making it widely applicable.

[0026] Details of one or more embodiments of the present invention are set forth in the following drawings and description, so that other features, objects and advantages of the invention will be more readily understood. Attached Figure Description

[0027] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this invention, illustrate exemplary embodiments of the invention and are used to explain the invention, but do not constitute an undue limitation of the invention. In the drawings: Figure 1 This is a flowchart of a polymer material lifetime prediction method considering the bidirectional coupling of hydrogen permeation and hydrogen-induced damage according to an embodiment of the present invention. Figure 2 It is a material constant according to an embodiment of the present invention ( A , p , q , r ) Flowchart of the reverse calibration algorithm; Figure 3This is a schematic diagram of the hardware structure of an electronic device according to an embodiment of the present invention. Detailed Implementation

[0028] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numerals in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with one or more embodiments of this specification. Rather, they are merely examples of apparatuses and methods consistent with some aspects of one or more embodiments of this specification as detailed in the appended claims.

[0029] It should be noted that the steps of the corresponding methods are not necessarily performed in the order shown and described in this specification in other embodiments. In some other embodiments, the methods may include more or fewer steps than described in this specification. Furthermore, a single step described in this specification may be broken down into multiple steps in other embodiments; and multiple steps described in this specification may be combined into a single step in other embodiments.

[0030] Example 1 This embodiment provides a method for predicting the lifetime of polymer materials considering the bidirectional coupling of hydrogen permeation and hydrogen-induced damage. This method is based on a multiphysics coupled numerical simulation framework and predicts the remaining lifetime of polymer materials under high-pressure hydrogen conditions by establishing a bidirectional positive feedback coupling model between hydrogen-induced damage variables and hydrogen permeation. Figure 1 As shown, the specific implementation method of this method is described below.

[0031] Step 1: Parameter Acquisition and Gas Phase Pressure Conversion After establishing a finite element mesh for the polymer structure to be predicted, the initial mechanical parameters, hydrogen permeation parameters, damage evolution parameters, and service boundary conditions of the polymer material to be predicted are first obtained. The specific parameters are obtained as follows: 1. Basic mechanical parameters: Initial elastic modulus of polymer materials Poisson's ratio and shear modulus For polymers exhibiting large deformation behavior, it is also necessary to specify the type and parameters of the hyperelastic constitutive model.

[0032] 2. Hydrogen permeation parameter: intrinsic diffusion coefficient of the undamaged material. (Unit: m) 2 / s) and the solubility coefficient S of hydrogen in the polymer (unit: mol·m -3 ·Pa -1 ). S can be determined by standard hydrogen permeation experiments or obtained from literature. It reflects the ability of hydrogen to dissolve in polymers at a certain temperature and pressure.

[0033] 3. Damage evolution parameters: damage evolution rate constant A, stress sensitivity index p, concentration sensitivity index q, damage saturation index r, damage amplification factor. and stiffness degradation coefficient These parameters are unique to the model of this invention and can be pre-calibrated using subsequent inverse numerical optimization methods.

[0034] In high-pressure storage and transportation engineering, the physical load applied to the surface of the structure is gas phase pressure. This embodiment uses a solubility model (preferably Henry's law) to convert the gas phase pressure into hydrogen concentration boundary conditions on the polymer surface:

[0035] In the formula, C is the hydrogen concentration on the polymer surface, S is the solubility coefficient, and P is the hydrogen pressure applied to the polymer surface (in Pa). The calculated surface hydrogen concentration C is used as the concentration boundary condition input for the subsequent hydrogen diffusion equation.

[0036] Step 2: Construction of a Multiphysics Coupled Numerical Simulation Framework The numerical simulation framework constructed by this method includes a mechanical constitutive solution model configured with the effective stiffness of the material, and a diffusion-damage evolution solution model configured with the effective diffusion coefficient.

[0037] 2.1 Solution Model for Diffusion-Damage Evolution of Coupled Stress Gradients Hydrogen transport in polymers follows a modified Fick's diffusion law. The hydrogen diffusion equation of this invention considers the contributions of both the concentration gradient and the hydrostatic stress gradient to the diffusion flux:

[0038] In the formula, Hydrogen flux (unit: C represents the internal hydrogen concentration (unit: ). ), Effective diffusion coefficient (unit: ) R is the ideal gas constant ( T represents absolute temperature (unit: ). ), Hydrostatic stress (unit: ), is the partial derivative of the chemical potential with respect to the force.

[0039] The flux expression above is composed of the superposition of the concentration gradient driving term (first term) and the hydrostatic stress gradient driving term (second term). The concentration gradient driving term reflects the diffusion of hydrogen from a high-concentration region to a low-concentration region; the hydrostatic stress gradient driving term introduces the driving effect of the stress field on hydrogen diffusion through the partial derivative of the chemical potential with respect to the stress, making hydrogen tend to accumulate in regions with higher compressive stress (larger hydrostatic compressive stress).

[0040] The corresponding mass conservation equation is:

[0041] In the formula, t represents time.

[0042] The known inputs include the intrinsic diffusion coefficient of the material. Solubility coefficient ,temperature The hydrostatic stress field obtained by mechanical calculation The surface hydrogen concentration boundary conditions obtained from the above transformation are also included. The unknown quantity to be solved is the hydrogen concentration at various points in space as a function of time. .

[0043] In this embodiment, the effective diffusion coefficient No longer a constant, but a variable that varies with hydrogen-induced damage. The effective diffusion coefficient increases with increasing [the amount of hydrogen]. To characterize the loosening of the microstructure and the increase in diffusion channels caused by hydrogen-induced damage, [the effective diffusion coefficient is...]. Characterized as the product of the intrinsic diffusion coefficient and the damage amplification factor:

[0044] In the formula, The intrinsic diffusion coefficient of the undamaged material. Damage amplification factor ( ), indicating complete damage ( The maximum magnification of the effective diffusion coefficient relative to the intrinsic diffusion coefficient at that time. Hydrogen-induced damage variable (dimensionless, range of values) Damage amplification factor characterizes the degree of accumulation of micro-defects within polymer materials. Hydrogen-induced damage variables The increase in hydrogen concentration is positive. This means that the development of damage morphologies such as microcracks and micropores within the polymer increases hydrogen diffusion channels, allowing more hydrogen to penetrate into the material more quickly, leading to an increase in internal hydrogen concentration. Increase.

[0045] Simultaneously, a power-law equation driven by multiple factors is used to update the hydrogen-induced damage variable in the current increment step:

[0046] In the formula, t is the service time, and A is the damage evolution rate constant (unit: t). This reflects the inherent sensitivity of materials to hydrogen-induced damage. The stress sensitivity index (dimensionless) characterizes the nonlinear effect of hydrostatic stress on damage driving. The concentration-sensitivity index (dimensionless) characterizes the nonlinear effect of hydrogen concentration on damage-driving processes. The damage saturation index (dimensionless) is used to describe the damage when it is close to complete ( The physical phenomenon that the rate of evolution slows down over time. The item represents the current damage margin, which... The power of this term constitutes a boundedness constraint term, ensuring that the damage variable remains within a predetermined physical range. Internal evolution does not result in unbounded, non-physical outcomes. The equation reflects the synergistic nonlinear control of the evolution rate by hydrostatic stress (mechanically driven) with positive compressive stress, internal hydrogen concentration (chemically driven), and remaining damage margin.

[0047] 2.2 Mechanical Constitutive Solution Model Polymer materials undergo hydrostatic pressure and deformation during service; their mechanical behavior is described by both equilibrium equations and constitutive relations involving damage. The equilibrium equations are:

[0048] in, For Cauchy stress tensor, This is a volume force vector.

[0049] For the large deformation behavior of polymer materials, a hyperelastic constitutive framework with damage correction is adopted. Taking the Neo-Hookean model as an example, its strain energy density function... Revised to:

[0050] In the formula, Shear modulus (unit: ) ), is the stiffness degradation coefficient (dimensionless). Hydrogen-induced damage variable (dimensionless, range of values) ), For the right Cauchy-Green deformation tensor, Represents the trace of a tensor.

[0051] Effective elastic modulus of polymer materials Defined as a variable with damage Degeneration occurs with the increase of [something], and the evolutionary formula is as follows:

[0052] In the formula, For effective elastic modulus, Initial elastic modulus (unit: ).when When it increases, The stiffness gradually decreases, reflecting the material's stiffness degradation caused by hydrogen-induced damage.

[0053] This invention defines the effective elastic modulus of a polymer material as the sum of its initial elastic modulus and the stiffness degradation factor. The product of the two factors. Stiffness degradation factor as a function of hydrogen-induced damage variable. It decreases monotonically with the increase of , and its range is . .

[0054] When damage variables (Without damage) the effective elastic modulus is equal to the initial elastic modulus. ; When damage variables As the effective elastic modulus gradually increases, it gradually decreases, reflecting the stiffness degradation of the material due to hydrogen-induced damage. It should be noted that the stiffness degradation coefficient... Must meet Constraints to ensure that even in complete failure ( When ), the effective elastic modulus is still a non-negative value.

[0055] In this embodiment, the known inputs include the initial elastic modulus of the material. shear modulus Poisson's ratio Stiffness degradation coefficient The external loads and displacement boundary conditions acting on the structure are also considered. The unknowns to be solved are the displacement fields at various points in space. and stress tensor hydrostatic stress This feedback further feeds back to the aforementioned hydrogen diffusion equation and damage evolution equation, forming a coupled closed loop of mechanics-diffusion-damage.

[0056] Stiffness degradation coefficient Experimental calibration is required. This can be achieved by measuring the degradation of the elastic modulus or shear modulus of polymer materials under different degrees of hydrogen-induced damage, and then performing an inversion fitting based on the previously mentioned evolution formula. .

[0057] Step 3: Time-progression solution and bidirectional coupling closed loop This method performs time-progression solutions within each time increment step, employing an explicit staggered coupling strategy. Within the same increment step, the following solution models are executed independently and sequentially, without inter-field iterations: 3.1 (i.e., sub-step S31): The mechanical constitutive solution model reads the damage variables from the previous incremental step. The current stress field is updated based on the effective elastic modulus to extract hydrostatic stress. And write it to the state variable storage area. Specifically: At the start of each increment step, the mechanical constitutive calculation module reads the damage variables from the state variable storage area at the end of the previous increment step. and hydrogen concentration ; Calculate the effective elastic modulus based on the constitutive relation (evolutionary formula) with damage correction. Based on this, update the stress field of the current increment step and calculate the hydrostatic stress. The updated hydrostatic stress Write it to a specified location in the state variable storage area for subsequent use by the diffusion-damage evolution module.

[0058] 3.2 (i.e., sub-step S32): Read the updated diffusion-damage evolution solution model. as well as The effective diffusion coefficient is corrected according to the formula. Solve the hydrogen diffusion equation to obtain the current internal hydrogen concentration. And update the damage variable at this time based on the concentration. This is then overwritten to the state variable storage area. Specifically: The diffusion-damage evolution calculation module reads the hydrostatic stress updated in substep S31 from the state variable storage area. and the damage variable from the previous increment step. and hydrogen concentration ; Calculate the effective diffusion coefficient Solving the hydrogen diffusion equation with coupled stress gradients yields the hydrogen concentration field for the current increment step. Solving the damage evolution equation yields the damage variables for the current increment step. The updated version and Overwrite to the state variable storage area for use in the next increment step.

[0059] In the above deduction, a damage-penetration bidirectional coupling closed loop is formed: Enlargement promotes A positive increase in hydrogen permeation flux raises the internal carbon concentration (C); this increased C, in turn, greatly accelerates the process through the power-law term. The rate of evolution.

[0060] In addition, to ensure the numerical stability and computational accuracy of nonlinear coupling analysis during the damage acceleration phase, this invention introduces an adaptive time step control strategy, using the damage variable increment as the key criterion for step adjustment.

[0061] The specific implementation process is as follows: After the calculation in sub-step S32 is completed, extract the maximum increment of the hydrogen-induced damage variable among all integration points within this increment step. . judge Is it greater than the preset damage increment threshold? ( The typical range of values ​​is The default value can be... (This can be adjusted according to the degree of material nonlinearity and the required calculation accuracy). Then, the preset step size reduction factor (usually taken as...) is used. Reduce the current time step and re-execute sub-steps S31-32 until... Meet the threshold requirement or reduce the time step to the preset minimum value. ( The specific value depends on the total simulation duration and the grid scale, and is usually set to a fraction of the total simulation time. (times); if If the result of the current increment step is accepted, the calculation will proceed to the next time increment step. When multiple consecutive increment steps... much smaller In such cases, the time step can be appropriately increased to improve computational efficiency.

[0062] The adaptive time step strategy, combined with the explicit staggered coupling strategy, effectively controls the numerical error in the rapid damage evolution stage without introducing inter-field iterations, thus ensuring the numerical stability and computational accuracy of the coupled analysis.

[0063] Step 4: Lifespan Determination and Output By solving the above coupled model using the finite element method, the damage variables can be obtained. and effective diffusion coefficient The evolution over time. As time progresses, internal damage variables are extracted at each time point. and permeability performance indicators (such as permeability coefficient) ).in:

[0064] In the formula, Let be the permeability coefficient at time t. Reaching a preset penetration threshold (e.g., 5 times the initial value), or When a preset damage threshold (e.g., 0.8) is reached, material failure is determined, and the corresponding time point is output as the predicted remaining lifetime. When the solubility coefficient... When the result is unknown or to simplify calculations, it can be used directly. The relative change (e.g.) () as a measure of the evolution of permeability performance.

[0065] This invention provides two lifetime criteria that can be used independently or in combination.

[0066] One is the permeability threshold criterion: when the permeability coefficient... Reaching the initial permeability coefficient Preset multiples (such as) times, that is When the specific multiple is determined experimentally based on the polymer material and engineering requirements, the polymer material is considered to have failed. This criterion is applicable to engineering scenarios where sealing performance is a concern.

[0067] The second is the critical criterion for damage: when the damage variable Reaching the preset critical value (like When the specific value is determined experimentally based on the polymer material and engineering requirements, the polymer material is considered to have failed. This criterion is applicable to engineering scenarios where structural integrity is a concern.

[0068] After the simulation, the results are output, including the permeability coefficient-time curve and damage variable distribution cloud map. When the permeability performance index reaches the preset permeability threshold or the hydrogen-induced damage variable reaches the preset damage critical value, the corresponding time point is output as the predicted remaining lifetime of the polymer material. Engineers can use this to assess the impact of design parameters on lifetime.

[0069] Step 5: Exemplary Calculation Case To fully demonstrate the implementation process and output format of this invention, a complete calculation example is given using polyamide 12 (PA12), a material commonly used in high-pressure hydrogen storage and transportation equipment. In this example, the basic mechanical parameters and hydrogen permeation parameters are set based on publicly available literature data, and the damage evolution-related parameters are theoretical demonstration values. All values ​​are used only to illustrate the output format and criterion application of this method and do not represent the actual measured lifetime prediction results for this material.

[0070] 5.1 Material Parameter Input PA12 at room temperature (approximately) ), The basic parameters under hydrogen pressure conditions are as follows.

[0071] (1) Basic mechanical parameters: initial elastic modulus Poisson's ratio .

[0072] (2) Basic parameters of hydrogen permeation: initial diffusion coefficient solubility coefficient .

[0073] (3) Model-specific parameters: The following parameters are theoretical assumptions based on the model framework of this invention and are only used for demonstrating the output format. In practical applications, the above parameters need to be obtained through experimental calibration for specific materials and working conditions. Damage amplification factor (Amplification factor of effective diffusion coefficient at complete damage), stiffness degradation coefficient (Proportion of effective elastic modulus degradation at complete damage), damage evolution constant Stress sensitivity index Concentration sensitivity index Damage saturation index .

[0074] 5.2 Simulation Boundary Conditions Pressure conditions are constant hydrogen pressure (about The temperature condition is constant. (At room temperature). The load condition is constant hydrostatic stress. The initial conditions are: At that time, calculate the initial hydrogen concentration. .

[0075] 5.3 Calculation Results An explicit staggered coupling and adaptive time step strategy were employed to solve the aforementioned coupled model using time-progression. The calculation results for some time points, given the input parameters, are shown in Table 1. Table 1 Calculation Results

[0076] The above results demonstrate the complete progressive failure process: in the early stages of service ( Hydrogen-induced damage accumulates slowly, and the permeability coefficient increases slowly; as the damage accumulates to a certain extent, a bidirectional positive feedback coupling effect emerges, and the damage develops rapidly. The rate of increase in permeability is significantly accelerated; in the final stage nearing failure ( The penetration coefficient quickly exceeds the safety threshold.

[0077] 5.4 Lifespan Determination Permeability threshold criterion: Set the engineering safety threshold to the initial permeability coefficient. times (i.e.) Based on the calculation results in Table 1, in hour, First time exceeding The predicted remaining lifespan is approximately Hour.

[0078] Using critical damage criteria: setting critical damage variables At the same time point ( ), damage variables Reaching the critical value further verifies the self-consistency of the failure determination. The consistency between the two determinations indicates that the proposed method has good consistency and reliability under a multi-criteria system.

[0079] 5.5 Comparison with the traditional unidirectional coupling model In contrast, if the traditional one-way coupling model is used, that is, the feedback effect of damage on the diffusion coefficient is not considered and no damage evolution equation is introduced, then the hydrogen diffusion coefficient always remains at its initial value. The permeability coefficient also remains constant. The previous method could not predict the increase in permeability and material failure caused by damage accumulation, meaning the theoretically predicted lifetime was infinite. This method, by constructing a two-way positive feedback coupling closed loop between hydrogen-induced damage and hydrogen permeation, successfully captures the complete evolution process of the permeability increasing with service time and eventually exceeding the failure threshold, and can output finite lifetime prediction values ​​with clear physical meaning.

[0080] The above values ​​are calculated based solely on the aforementioned input parameters. In practical engineering applications, different material grades (such as different grades of PA12), different manufacturing processes (such as injection molding and laser sintering), and different service temperatures will all have a significant impact on the above evolution curves, and need to be calibrated separately according to specific operating conditions.

[0081] Step Six: Reverse Calibration Method for Damage Evolution Parameters like Figure 2 As shown, this embodiment supplements the acquisition of damage evolution parameters (A, p, q, r) in Example 1 with a reverse numerical optimization calibration method, which can be completed with only a single working condition experiment: 6.1 Obtaining Experimental Data: Under standard hydrogen permeation experimental conditions of constant temperature, constant hydrogen partial pressure, and constant external load (or no external mechanical load), the experimental curves of hydrogen permeation flux of polymer samples versus time were measured using the Devanathan-Stachurski double electrolytic cell method or other equivalent standard methods. This experiment only needs to be conducted once under a single operating condition.

[0082] 6.2 Setting initial parameter values: Based on experience or literature, set initial guess values ​​for material constants. Substituting into the forward coupled calculation model, the predicted permeability curve is obtained. .

[0083] 6.3 Error Assessment: Construct the objective function between the experimental curve and the predicted curve, calculate the objective function error F between the experimental curve and the predicted curve, and optimize the root mean square error.

[0084] In the formula, F is the objective function error, and N is the total number of sampled data points. For the i-th time node, In order to be in Standard hydrogen permeation flux measured at real time In order to be in The predicted permeation flux is obtained by forward modeling at time step.

[0085] 6.4 The optimization algorithm is invoked to iteratively update the damage evolution parameters until the objective function error meets the convergence condition. The converged parameter set is then output for use in full lifecycle prediction. Specifically, when the relative change in the objective function between two adjacent iterations is less than a preset threshold... (For example (), or the current iteration step Reaching the maximum number of iterations (For example If the condition is met, terminate the iteration and output the calibrated parameters; otherwise, proceed to step 6.5.

[0086] 6.5 Parameter Optimization: Call an optimization algorithm (such as genetic algorithm, particle swarm optimization, Levenberg-Marquardt algorithm or simplex method, etc.) to iteratively update the parameters, so that the objective function value decreases, and then return to step 6.3 to continue the next round of iteration.

[0087] The above calibration method only requires a set of experimental data under a single working condition to simultaneously calibrate four material constants, without the need to conduct multi-working-condition experiments, and has strong engineering applicability.

[0088] Example 2 This embodiment provides a polymer material lifetime prediction device that considers the bidirectional coupling of hydrogen permeation and hydrogen-induced damage, to implement the method of Embodiment 1. The device includes: The boundary and parameter configuration module is used to obtain the initial mechanical parameters, hydrogen permeation parameters, damage evolution parameters, and service boundary conditions of the polymer material to be predicted, and to convert the gas phase pressure in the service boundary conditions into the hydrogen concentration boundary of the polymer surface based on the solubility model.

[0089] The coupled-driven simulation module is used to construct mechanical constitutive and diffusion-damage evolution solution models. This module achieves efficient alternation of physical fields within incremental steps through a state variable storage area, runs a bidirectional positive feedback closed loop, and incorporates an adaptive time-step reduction strategy based on the maximum damage increment to prevent numerical instability.

[0090] The lifetime determination output module is used to extract status data during the time progression and output the predicted remaining lifetime when the permeability performance index or damage variable reaches a preset threshold.

[0091] Example 3 This embodiment also provides an electronic device, see reference. Figure 3 It includes a memory 404 and a processor 402, the memory 404 storing a computer program and the processor 402 being configured to run the computer program to perform the steps in any of the above method embodiments.

[0092] Specifically, the processor 402 may include a central processing unit (CPU), or an application-specific integrated circuit (ASIC), or one or more integrated circuits that can be configured to implement embodiments of the present invention.

[0093] Memory 404 may include a mass storage device for data or instructions. For example, and not limitingly, memory 404 may include a hard disk drive (HDD), a floppy disk drive, a solid-state drive (SSD), flash memory, an optical disk drive, a magneto-optical disk drive, magnetic tape, or a Universal Serial Bus (USB) drive, or a combination of two or more of these. Where appropriate, memory 404 may include removable or non-removable (or fixed) media. Where appropriate, memory 404 may be internal or external to a data processing device. In a particular embodiment, memory 404 is non-volatile memory. In a particular embodiment, memory 404 includes read-only memory (ROM) and random access memory (RAM). Where appropriate, the ROM may be a mask-programmed ROM, a programmable read-only memory (PROM), an erasable read-only memory (EPROM), an electrically erasable read-only memory (EEPROM), an electrically alterable read-only memory (EAROM), or flash memory, or a combination of two or more of these. Where appropriate, the RAM can be Static Random-Access Memory (SRAM) or Dynamic Random-Access Memory (DRAM). DRAM can be Fast Page Mode Dynamic Random-Access Memory (FPMDRAM), Extended Data Out Dynamic Random-Access Memory (EDODRAM), Synchronous Dynamic Random-Access Memory (SDRAM), etc.

[0094] The memory 404 can be used to store or cache various data files that need to be processed and / or communicated, as well as possible computer program instructions executed by the processor 402.

[0095] The processor 402 reads and executes computer program instructions stored in the memory 404 to implement any of the polymer material lifetime prediction methods considering the bidirectional coupling of hydrogen permeation and hydrogen-induced damage in the above embodiments.

[0096] Optionally, the electronic device may further include a transmission device 406 and an input / output device 408, wherein the transmission device 406 is connected to the processor 402, and the input / output device 408 is connected to the processor 402.

[0097] The transmission device 406 can be used to receive or send data via a network. Specific examples of the network described above may include wired or wireless networks provided by the communication provider of the electronic device. In one example, the transmission device includes a Network Interface Controller (NIC), which can connect to other network devices via a base station to communicate with the Internet. In another example, the transmission device 406 may be a Radio Frequency (RF) module used for wireless communication with the Internet.

[0098] Input / output device 408 is used to input or output information.

[0099] Example 4 This embodiment also provides a readable storage medium storing a computer program, the computer program including program code for controlling a process to execute the process, the process including a polymer material lifetime prediction method considering the bidirectional coupling of hydrogen permeation and hydrogen-induced damage according to Embodiment 1.

[0100] It should be noted that the specific examples in this embodiment can refer to the examples described in the above embodiments and optional implementations, and will not be repeated here.

[0101] Generally, various embodiments can be implemented in hardware or dedicated circuitry, software, logic, or any combination thereof. Some aspects of the invention can be implemented in hardware, while others can be implemented by firmware or software executed by a controller, microprocessor, or other computing device, but the invention is not limited thereto. Although various aspects of the invention may be shown and described as block diagrams, flowcharts, or using some other graphical representation, it should be understood that, by way of non-limiting example, these blocks, apparatuses, systems, techniques, or methods described herein can be implemented in hardware, software, firmware, dedicated circuitry or logic, general-purpose hardware or controllers or other computing devices, or some combination thereof.

[0102] Embodiments of the present invention can be implemented by computer software, which may be executable by a data processor of a mobile device, such as a processor entity, or by hardware, or by a combination of software and hardware. Computer software or programs (also referred to as program products), including software routines, applets, and / or macros, can be stored in any device-readable data storage medium, and they include program instructions for performing specific tasks. A computer program product may include one or more computer-executable components configured to perform embodiments when the program is run. One or more computer-executable components may be at least one piece of software code or a portion thereof. Additionally, it should be noted that any block in the logical flow of the figures may represent a program step, or interconnected logical circuitry, blocks and functions, or a combination of program steps and logical circuitry, blocks and functions. The software may be stored on physical media such as memory chips or blocks of storage implemented within a processor, magnetic media such as hard disks or floppy disks, and optical media such as, for example, DVDs and their data variants, CDs, etc. The physical medium is a non-transient medium.

[0103] Those skilled in the art should understand that the technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments have been described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0104] The core of this invention lies in the bidirectional coupling mechanism between the damage variable and the diffusion coefficient. Under this concept, the damage evolution equation can adopt other functional forms (such as exponential, hyperbolic tangent, etc.), as long as they can describe the asymptotic damage behavior driven by hydrostatic stress and hydrogen concentration, which are all equivalent alternatives. Furthermore, the method of this invention does not rely on specific finite element analysis software; other commercial or open-source software (such as ANSYS, COMSOL, etc.) can achieve similar three-field coupling solutions through their own secondary development interfaces, which are also equivalent alternatives.

[0105] The above embodiments are merely illustrative of several implementations of the present invention, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of the present invention should be determined by the appended claims.

Claims

1. A method for predicting the lifetime of polymer materials considering bidirectional coupling, characterized in that, Includes the following steps: S1: Obtain the initial mechanical parameters, hydrogen permeation parameters, damage evolution parameters, and service boundary conditions of the polymer material to be predicted, and convert the gas phase pressure in the service boundary conditions into the hydrogen concentration boundary of the polymer surface based on the solubility model. S2: Construct a multiphysics coupled numerical simulation framework, which includes a mechanical constitutive solution model configured with effective material stiffness and a diffusion-damage evolution solution model configured with effective diffusion coefficient. S3: Perform time-progression solution within each time increment step: Using the aforementioned mechanical constitutive solution model, correct the effective stiffness using the hydrogen-induced damage variable from the previous increment step to calculate the hydrostatic stress in the current increment step; The diffusion-damage evolution solution model uses the hydrostatic stress of the current increment step and the hydrogen-induced damage variable of the previous increment step to correct the effective diffusion coefficient, and then solves the hydrogen diffusion equation coupled with the stress gradient to obtain the internal hydrogen concentration of the current increment step, and updates the hydrogen-induced damage variable of the current increment step; wherein, the increase of the hydrogen-induced damage variable causes the effective diffusion coefficient to increase, which in turn leads to an increase in the infiltrated internal hydrogen concentration and in turn accelerates the evolution of the hydrogen-induced damage variable, forming a two-way coupled closed loop of damage-permeation. S4: As the time increment step progresses, the permeation performance index and the hydrogen-induced damage variable are extracted at each time node. When the permeation performance index reaches the preset permeation threshold or the hydrogen-induced damage variable reaches the preset damage critical value, the corresponding time node is output as the predicted remaining lifetime of the polymer material.

2. The polymer material lifetime prediction method as described in claim 1, characterized in that, In step S3, the hydrogen flux of the hydrogen diffusion equation coupled with stress gradient is composed of the superposition of the concentration gradient driving term and the hydrostatic stress gradient driving term. The step of correcting the effective diffusion coefficient using the hydrostatic stress of the current increment step and the hydrogen-induced damage variable of the previous increment step includes: characterizing the effective diffusion coefficient as the product of the intrinsic diffusion coefficient of the undamaged material and the damage amplification factor, wherein the damage amplification factor increases positively with the increase of the hydrogen-induced damage variable.

3. The polymer material lifetime prediction method as described in claim 1, characterized in that, In step S3, the hydrogen-induced damage variable in the current incremental step is updated using a power-law damage evolution model driven by multiple factors. In the power-law damage evolution model, the evolution rate of the hydrogen-induced damage variable is proportional to the power of the hydrostatic stress with positive compressive stress, the power of the internal hydrogen concentration, and the power of the current damage margin.

4. The polymer material lifetime prediction method as described in claim 1, characterized in that, In step S3, the modification of the effective stiffness includes: defining the effective elastic modulus of the polymer material as the product of the initial elastic modulus and the stiffness degradation factor, wherein the stiffness degradation factor decreases as the hydrogen-induced damage variable increases.

5. The polymer material lifetime prediction method as described in claim 1, characterized in that, In step S3, an explicit staggered coupling strategy is used to perform the time-progression solution, which includes executing the following sub-steps independently and sequentially within the same increment step without inter-field iterations: Sub-step S31: Update the hydrostatic stress of the current incremental step based on the mechanical constitutive solution model, and write the hydrostatic stress into the state variable storage area; Sub-step S32: The diffusion-damage evolution solution model reads the updated hydrostatic stress from the state variable storage area, calculates the internal hydrogen concentration and hydrogen-induced damage variables of the current increment step, and overwrites the updated data to the state variable storage area for use in the next increment step.

6. The polymer material lifetime prediction method as described in claim 5, characterized in that, In step S3, an adaptive time step strategy is also introduced: after the calculation of sub-step S32 of an increment step is completed, the maximum increment of the hydrogen-induced damage variable among all integration points in the increment step is extracted; it is determined whether the maximum increment is greater than a preset damage increment threshold. If it is greater, the current time step is reduced by a preset step reduction coefficient and the current increment step is recalculated. If it is not greater than, then accept the result of the current increment step and proceed to the next time increment step.

7. The polymer material lifetime prediction method as described in claim 1, characterized in that, The damage evolution parameters mentioned in step S1 are pre-calibrated based on a single working condition using a reverse numerical optimization method. The specific calibration steps include: Experimental curves were obtained showing the standard hydrogen permeation flux of polymer samples as a function of time under a single constant operating condition. Set initial guess values ​​for the damage evolution parameters to be calibrated, and substitute the initial guess values ​​into the forward coupling calculation model to obtain the predicted permeation curve; Calculate the objective function error between the experimental curve and the predicted permeation curve, call the optimization algorithm to iteratively update the damage evolution parameters until the objective function error meets the convergence condition, and output the converged parameters as the damage evolution parameters.

8. A polymer material lifetime prediction device considering bidirectional coupling, characterized in that, include: The boundary and parameter configuration module is used to obtain the initial mechanical parameters, hydrogen permeation parameters, damage evolution parameters and service boundary conditions of the polymer material to be predicted, and to convert the gas phase pressure in the service boundary conditions into the hydrogen concentration boundary of the polymer surface based on the solubility model. The coupled simulation module is used to construct a multiphysics coupled numerical simulation framework and perform time-progressive solutions within each time increment step: Using a mechanical constitutive model, the effective stiffness of the material is corrected using the hydrogen-induced damage variable from the previous increment step to calculate the hydrostatic stress in the current increment step; using a diffusion-damage evolution model, the effective diffusion coefficient is corrected using the hydrostatic stress in the current increment step and the hydrogen-induced damage variable from the previous increment step, and then the hydrogen diffusion equation of the coupled stress gradient is solved to obtain the internal hydrogen concentration in the current increment step, and the hydrogen-induced damage variable in the current increment step is updated; the increase in the hydrogen-induced damage variable leads to an increase in the effective diffusion coefficient, which in turn leads to an increase in the internal hydrogen concentration and, in turn, accelerates the evolution of the hydrogen-induced damage variable, forming a damage-permeation bidirectional coupled closed loop; The lifetime determination output module is used to output the predicted remaining lifetime of the polymer material at the corresponding time point when the permeation performance index reaches a preset permeation threshold or the hydrogen-induced damage variable reaches a preset damage threshold during the time process.

9. An electronic device comprising a memory and a processor, characterized in that, The memory stores a computer program, and the processor is configured to run the computer program to perform the polymer material lifetime prediction method according to any one of claims 1 to 7.

10. A readable storage medium, characterized in that, The readable storage medium stores a computer program, the computer program including program code for controlling a process to execute the process, the process including the polymer material lifetime prediction method according to any one of claims 1 to 7.

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