CN113053473A

CN113053473A - Method for constructing full-stage creep model of polymer bonded composite material

Info

Publication number: CN113053473A
Application number: CN202110384553.1A
Authority: CN
Inventors: 关雪飞; 段晓畅; 袁洪魏; 唐维; 何晶靖
Original assignee: Graduate School Of Chinese Academy Of Engineering Physics; Beihang University; Institute of Chemical Material of CAEP
Current assignee: Graduate School Of Chinese Academy Of Engineering Physics; Beihang University; Institute of Chemical Material of CAEP
Priority date: 2021-04-09
Filing date: 2021-04-09
Publication date: 2021-06-29
Anticipated expiration: 2041-04-09
Also published as: CN113053473B

Abstract

The invention provides a method for constructing a full-stage creep model of a polymer bonded composite material with consideration of temperature and holding stress effects, which comprises the following steps of: acquiring strain time data of a sample of the polymer bonded composite material at different test temperatures and holding stresses as test data; processing the data into strain rate time data; using a bathtub curve model as a basic model, establishing a strain rate time model in a logarithmic domain, and obtaining a strain time curve by adopting a Runge Kutta method; the relation between the model parameters and the temperature and the holding stress is obtained through fitting, and the relation between the fracture time and the temperature and the holding stress is obtained, namely the full-stage creep model of the polymer bonding composite material considering the temperature and holding stress effect can be obtained. The model combines the full-stage creep relation of the material with temperature and holding stress, and can obtain a creep model of the polymer bonding composite material on the basis of using a small amount of model parameters, and can be used for predicting the service life of the material.

Description

Method for constructing full-stage creep model of polymer bonded composite material

Technical Field

The invention relates to the field of materials, in particular to a universal full-stage creep model construction method of a polymer bonded composite material, which considers the change of temperature and holding stress.

Background

Polymer-bonded composites have been widely used in engineering components that are subjected to thermomechanical loads due to their corrosion resistance, high tensile strength, light weight and ease of handling. To assess the durability of these components, understanding the creep behavior of the material is a key issue.

Numerous experiments have shown that the creep properties of polymer-bonded composites depend on material properties such as additive content, particle size, and external parameters such as temperature, humidity. The creep behavior of the polymer material comprises at least an initial creep stage and a stable creep stage. The initial creep phase is characterized by a decrease in strain rate with time and the steady creep phase is characterized by a steady state in which the strain rate is maintained with time. The third creep stage occurs when the holding stress is greater than the long term strength. This third creep stage strain rate increases rapidly with time until the material fractures. However, the filler material can greatly change the time to failure and the external conditions under which creep in the third creep stage occurs. Typical polymer-bonded composite full-stage creep responses are shown in fig. 1(a) and 1 (b).

In several experimental studies carried out on a variety of materials, having established the necessity to incorporate the effects of temperature and holding stress into the creep behavior of PBMs, F.J. Gagliardi et al measured the creep response of PBX 9502 materials between 24 ℃ and 70 ℃ and between 1.724MPa and 5.378MPa, and found that the increase in strain per unit time of the material increases with increasing temperature and stress to be heldThere is an increase. Raghavan et al have a creep response between 22 ℃ and 160 ℃ for AS 4/3501-6 composites with stress levels between 10% and 80%. Marina et al tested Nextel^TMCreep behavior of the 610/monazite/aluminum composite material when maintaining stress of 32MPa to 72MPa and temperature of 1 ℃ and 100 ℃. Lv et al measured the creep response of polypropylene/clay nanocomposites at 24 ℃ to 60 ℃, 28MPa to 31 MPa. Yang et al performed creep tests on PA66 in a temperature range of 23 ℃ to 80 ℃ and a holding stress range of 20MPa to 40 MPa. Abdel et al tested the creep behavior of the E-glass/polymer composites at 50 ℃ between 436MPa and 811 MPa.

Several models have been reported to describe the creep response of polymer-bonded composites under varying temperature, holding stress, including creep models based on the material stiffness and elastic-viscoelastic mapping principles. Based on the time-temperature equivalent principle, a Burgers model related to the temperature effect and a phenomenological visco-elastic model related to the retention stress effect can be established.

Research has found that the full-phase creep behavior of PBMs can be clearly divided into three phases, and the existing model describes the creep response of a primary creep phase and a stable creep phase, but ignores an accelerated creep phase. The accelerated creep stage represents the failure process of the material and is very important for researching the service life of the material. The model proposed by Sudduth et al can describe the material response for full-phase creep with three parameters, but does not account for changes in temperature and holding stress. Therefore, it is necessary to establish a full-phase creep model that takes into account temperature and holding stress.

Disclosure of Invention

In order to overcome the defects of the prior art, the invention constructs a full-stage creep model of the polymer bonded composite material considering the temperature and holding stress effect based on the strain rate accumulation principle.

The invention provides a method for constructing a full-stage creep model of a polymer bonded composite, which considers the change of temperature and holding stress and comprises the following steps:

step 1, acquiring creep data of a sample of the polymer bonded composite material at different testing temperatures and holding stresses;

step 2, using a bathtub curve equation as a basic model to obtain fitting parameters and the relation between the fitting parameters and the temperature and the holding stress;

step 2.1, processing the creep data obtained in the step 1 into strain rate time data;

step 2.2, fitting the test data of each sample by using a bathtub curve model to obtain fitting values of fitting parameters a, b and c of a bathtub curve equation of each sample; the bathtub curve model is represented as follows:

wherein d ε/dt is the strain rate, t is the time, t_iniInitial creep time, set to 0, t_rupA, b and c are model parameters for creep rupture time;

step 2.3, dividing the sample into a plurality of fitting parameter value sequences according to the temperature and the holding stress respectively according to the fitting values of all the sample model parameters a, b and c obtained in the step 2.2;

step 2.4, according to a scatter diagram of the model parameters a, b and c and the temperature and holding stress and the variation trend of the parameters along with the temperature and the holding stress, selecting a corresponding function to perform parameter fitting to obtain the functional relation between the model parameters a, b and c and the temperature T and the holding stress sigma;

step 2.5, fitting to obtain a function of the relation between the model parameters and the temperature and the stress according to the function relation between the fitting parameters selected in the step 2.4 and the temperature;

step 3, establishing a relation between creep rupture time and temperature and holding stress based on Larsen-Miller parameters;

step 3.1, obtaining creep rupture time under different test conditions from step 1;

step 3.2, fitting to obtain the relationship between the parameter value and the temperature and holding stress by adopting Larson-Miller parameters according to creep rupture time at different temperatures and different holding stresses;

step 4, combining the function of the relation between the model parameters and the temperature and the holding stress obtained according to the sample in the step 2.5 and the function of the relation between the Larson-Miller parameters and the temperature and the holding stress in the step 3.2, obtaining a creep model of the polymer bonding material, which is shown in the formula (2), for the sample and takes the temperature and holding stress effects into consideration;

in which ε is the strain ε₀Represents the initial value of creep strain.

Preferably, the method further comprises the following steps:

step 3.1, extracting creep rupture time under different test conditions obtained from the step 1;

3.2, obtaining parameter values in Lason-Miller parameters by adopting Lason-Miller parameters based on a linear regression method according to creep rupture time under different temperatures and different holding stresses, and establishing the relation between the creep rupture time and the temperature and the holding stress; the LMP equation is as follows:

P(σ)＝p₁+p₂·σ＝(T+273.15)[p₃+log₁₀t] (3)

in the formula, p₁，p₂，p₃As fitting parameters, σ is the holding stress, T is the temperature, and T is the time.

Further, in order to obtain a full-stage creep model of the polymer bonded composite material considering the effects of temperature and holding stress for the test sample, the method specifically comprises the following sub-steps,

step 4, combining the function of the relation between the model parameters and the temperature and the holding stress obtained according to the sample in the step 2.5 and the function of the relation between the Larson-Miller parameters and the temperature and the holding stress in the step 3.2, and obtaining a strain rate-time model of the polymer bonding material, which considers the temperature and the holding stress effect, for the sample;

and integrating the strain rate with respect to the obtained strain rate-time model, and obtaining the polymer bonded composite material full-stage creep model considering the temperature and the holding stress effect.

Preferably, the method further comprises the following steps: and 5, performing data verification on the full-stage creep model of the polymer bonded composite material, which is obtained in the step 4 and takes the temperature and the holding stress effect into consideration.

Preferably, step 2.3 is preceded by a step of checking whether the test conditions are accurate by determining coefficients, specifically: for the creep data for one of the samples, fitting was performed using the bathtub curve model set forth in step 2.2, and the coefficient of determination R was calculated from the predicted data and the experimental data using equations (6) and (7)²Determining the coefficient R²If the quantity meeting the requirements exceeds the specified threshold value, executing the step 2.3, otherwise, acquiring the test parameters again, and executing the step 2.1 and the step 2.2 again;

where SSE is the sum of the squares of the residuals, SST is the sum of the squares of the sums, N is the total number of test data per sample, y_iFor the prediction data based on the bathtub curve equation,

for the test data of each of the samples,

average of test data, R, for each sample²To determine the coefficients.

Further, in said step 2.4, the model parameters a, b, c are represented as a function of the temperature T and the holding stress σ using multivariate linear functions; the functional form is shown in equation (8):

in the formula, alpha_i，β_iAnd gamma_iAre parameter coefficients.

Preferably, the step 2.5 is specifically:

fitting the coefficients in the formula (8) by using a linear regression method according to the relationship between the screened model parameter value sequence and the temperature T and the holding stress sigma to obtain a fitting coefficient matrix under the stretching condition as shown in the formula (9):

substituting the fitting coefficient matrix (9) into equation (1):

thus obtaining the relationship of the model parameters a, b, c with temperature and holding stress.

Compared with the prior art, the invention has the following beneficial effects:

1. on the basis of the model, the full-stage creep model of the polymer adhesive composite material can be uniformly constructed by using reasonable parameters, the model structure is optimized, and the model can be constructed by only 2 groups of test results at least.

2. The creep rupture time of the polymer bonded composite material is predicted by utilizing an LMP equation, and the creep rupture time is matched with the constructed creep model, so that the creep life of the material under unknown conditions and the corresponding full-stage creep mechanical response can be predicted.

3. Collecting uniaxial tension and compression data only by a material testing machine; the complexity of experimental data acquisition is reduced, and the experimental data acquisition is simple, easy and feasible.

Drawings

FIG. 1a is a graphical representation of a typical polymer-bonded composite full-stage creep curve;

FIG. 1b is a schematic representation of a typical polymer matrix composite strain rate time curve;

FIG. 2 is a graph of the full-phase creep of a PBX test piece;

FIG. 3 is a graph of bathtub curve predicted results versus actual data under certain conditions;

FIG. 4 is a graph showing the relationship of model parameters to temperature and holding stress;

FIG. 5a is a graph of the parameter a versus temperature, holding stress as a function of actual data;

FIG. 5b is a graph of the parameter b versus temperature, holding stress as a function of actual data;

FIG. 5c is a plot of the parameter c versus temperature, holding stress as a function of actual data;

FIG. 6 is a schematic diagram of the residual error between the predicted result and the actual value of the bathtub curve model;

FIG. 7a is a graph comparing the predicted results of the bathtub curve model with actual values;

FIG. 7b is a graph comparing creep model prediction results to test data;

FIG. 8 is a third party data creep curve;

FIG. 9a is a graph of predicted versus actual values for a bathtub curve model for third party data;

FIG. 9b is a graph comparing predicted results to actual values for a creep model for third party data;

FIG. 10 is a flow chart of the present invention.

Detailed Description

In order to better understand the technical solution of the present invention, the following detailed description is made with reference to the accompanying drawings and examples. In the drawings, like reference numbers can indicate functionally identical or similar elements. While the various aspects of the embodiments are presented in drawings, the drawings are not necessarily drawn to scale unless specifically indicated.

Detailed description of the preferred embodiment 1

The invention discloses a method for constructing a full-stage creep model of a polymer bonded composite, which considers the effects of temperature and holding stress and comprises the following specific implementation steps as shown in figures 1 to 7:

step 1, obtaining creep data of a sample of the polymer bonded composite material at different testing temperatures as test data.

The test data can be obtained by directly using historical test data or by actual tests. The experimental data obtained by the actual test are specifically as follows: selecting a test temperature and a holding stress range according to actual engineering requirements, research requirements and the number of stocked samples, determining test conditions in the temperature and holding stress ranges, setting the number of samples in each test condition, carrying out a compression creep test on the samples of the polymer bonding composite material after heat preservation in a temperature box, acquiring stress, strain and corresponding time data of the samples under different test conditions, and selecting data with the holding stress deviation within a range of 1% based on the existing test data to determine the data as creep data.

For subsequent validation of the established model, the test data may be divided into modeling data and validation data. Wherein, the modeling data should account for 80% of the total data volume, and the verification data should account for 20% of the total data volume. The modeling data is used to construct a model, and the validation data is used to verify the accuracy of the model. If the test quantity is less than 5 groups, all data are generally used as modeling data, and the accuracy of the established model is improved; the minimum number of tests was 2 groups.

Test data selection range: in the present application, the test data range is from loading to material creep rupture.

The polymer adhesive material used in this example was a TATB (1,3, 5-triamino-2, 4, 6-trinitrobenzene) based PBX (hereinafter abbreviated as PBX) made of TATB crystals in a mass ratio of more than 94% to fluororubber in a mass ratio of less than 6%. A cold pressing method is adopted to prepare cylindrical samples with phi of 20mm multiplied by 20 mm.

Single axle pullTensile and compressive tests were performed on an Instron materials testing machine. The samples were stretched and compressed in a temperature cabinet. Before testing, each sample was equilibrated at the test temperature for 120 minutes to ensure that the sample reached the desired test temperature. The experiment was first loaded at a loading rate of 0.5mm/min (reduced strain rate of 4.16X 10)^-4Within the quasi-static range) and then constant stress loading until creep rupture of the material occurs, and recording all stress, strain and time data from the beginning of loading to the rupture of the material.

In this application, the temperature and holding stresses for a particular test in the modeling data are shown in table 1:

TABLE 1

Serial number	Temperature/. degree.C	Holding stress/MPa
			1	20	22.5
2	20	25
			3	30	20
4	40	15
			5	50	15

The temperature and holding stress for the specific tests in the validation data are shown in table 2:

TABLE 2

Serial number	Temperature/. degree.C	Holding stress/MPa
			1	40	17.5

In order to facilitate the understanding of the subsequent steps, the creep curve is explained below. In the present application, stress and strain are engineering stress and engineering strain in units of MPa and mm/mm, respectively, and time in units of seconds, written as s. When other units are used, unit conversion is required.

In this example, as shown in fig. 2, the creep curve with the abscissa as time and the ordinate as strain shows that the creep life of the material decreases with the increase of temperature and holding stress from 46900s at 40 ℃ and 15MPa to 918s at 50 ℃ and 15 MPa; the temperature was reduced from 9292s at 20 ℃ and 22.5MPa to 916s at 20 ℃ and 25 MPa.

As depicted in fig. 1, the strain time curve of the creep process shows clearly 3 different phases. The first stage A is a primary creep stage or initial creep stage with the strain rate decreasing along with the increase of time, and the rate of the strain increasing along with the time is gradually decreased; the following is a dominant stable creep stage B, in which a creep curve has a quasi-constant slope, i.e. the strain rate is basically unchanged; with further loading, a phase C of accelerated creep is entered which evolves rapidly, eventually leading to the material breaking at point P. At the same time, the greater the temperature and holding stress, the shorter the time required for the accelerated creep phase to occur.

And 2, obtaining fitting parameters by using a bathtub curve equation as a basic model.

Step 2.1, processing creep data into strain rate time data

Using the creep data obtained in step 1, the data is processed into strain rate time data using equations (28) and (29).

And 2.2, obtaining model parameters by using a bathtub curve equation.

The bathtub curve equation is used for the first time to describe the law of the reliability change of a product in the whole life cycle from input to rejection. The curve has the characteristics of high at both ends and low in the middle, and is matched with the change of the strain rate in the creep process shown in FIG. 1(b), so that the bathtub curve is proposed to describe the change of the strain rate time in the creep process.

The creep curve equation is expressed as follows:

wherein d ε/dt is the strain rate, t is the time, t_iniInitial creep time, set to 0, t_rupA, b and c are model parameters respectively for creep rupture time;

and respectively fitting the strain rate time data of each sample by using a bathtub curve model, wherein the fitting method can adopt various nonlinear fitting methods, such as a method of derivative-free for searching the minimum value of the sum of squares of residual errors, a nonlinear regression method or a least square method and the like. After fitting, fitting values of model parameters a, b and c of the bathtub curve equation of each sample, which are referred to as model parameter values for short, can be obtained.

And 2.3, dividing the sample into a plurality of model parameter value sequences according to the temperature and the holding stress according to the fitting values of all the sample model parameters a, b and c obtained in the step 2. A sequence refers to a plurality of sets of parameter values under different test conditions, which are referred to as a sequence.

In this step, a bathtub curve is used for fitting the creep data under one of the conditions, the prediction result is evaluated by using a decision coefficient, and whether the creep model of the material can be built by using the method is judged. The calculation method of the decision coefficient comprises the following steps: calculating the Sum of Squares (SSE) of the residual error sum of squares and the Sum of Squares (SST) of the total sum of squares based on the values of the fitting parameters, and subtracting the ratio of SSE to SST from 1 to obtain the corresponding determination coefficient (R)²) The calculation is shown in the formula (31) and the formula (32).

Where SSE is the sum of the squares of the residuals, SST is the sum of the squares of the sums, N is the total number of test data per sample, y_iFor the prediction data obtained by the Ramberg-Osgood equation,

for the test data of each of the samples,

average of test data, R, for each sample²To ensureAnd (5) fixing the coefficient.

In the present embodiment, the coefficient R is determined²It is required to be greater than 0.8 when R²And (3) when the value is more than 0.8, performing the next step 2.4, and if not, returning to the step 1 to obtain the test number again or replacing the creep model construction method. The step ensures the relative accuracy of the test data and provides the most basic guarantee for the establishment of the subsequent model.

In this example, creep data at T ═ 20 ℃ and σ ═ 22.5MPa will be described. Based on the bathtub curve model shown in the formula (30), the parameters are estimated by using the least square method, and the parameters a-5.763, b-0.6108, c-0.04702 are obtained, the goodness of fit is 0.999, the set standard is met, and the comparison between the fitted curve and the actual result can be shown in fig. 3.

And 2.4, selecting a corresponding functional relation between the model parameters and the temperature and the holding stress according to the scatter diagram of the model parameters and the temperature and the holding stress.

And obtaining a scatter diagram of the model parameters a, b and c and the temperature and the holding stress according to the screened model parameter value sequence, obtaining the variation trend of the parameters along with the temperature and the holding stress, and respectively selecting the functional relations of the parameters a, b and c and the temperature T and the holding stress sigma. In actual operation, different functions are selected to describe the relationship between the model parameters and the temperature and the stress retention according to different trends, and linear increasing is a linear function; taking logarithm when the exponent rises, and then expressing the logarithm linearly; a piecewise function may also be used for representation. According to the actual situation, the relation between the model parameters and the temperature and the holding stress can be described in a plurality of function coupling modes.

The temperature is merely taken as an independent variable for example, and the influence of the holding stress is not considered. The functional relationship between the model parameters and the temperature mainly comprises the following types:

(1) first function, first order function

(2) A second function, piecewise linear

(3) Third, quadratic function

(4) A fourth function, exponential function

Wherein a, b and c are coefficients of a function, and the fitting coefficient matrix is formed by the a, b and c. For formulas (33) and (36), a ═ α₁,α₂]，b＝[β₁,β₂]，c＝[γ₁,γ₂]For formulas (34) and (35), a ═ α₁,α₂,α₃]，b＝[β₁,β₂,β₃]，c＝[γ₁,γ₂,γ₃]T is temperature, T_kiRepresents the temperature of the segment point, i ═ 1, 2, 3, T_k1、T_k2、T_k3The temperatures of the segment points of the model parameters a, b and c can be the same or different. H (x) represents a step function, and when the value of x is less than 0, the result is 0; otherwise, the result is 1.

In the present embodiment, the scatter diagram of the model parameters a, b, and c with respect to temperature and holding stress is shown in fig. 4, and it can be found that the value of the parameter a monotonically decreases with the increase of temperature and holding stress, and the values of the parameters b and c monotonically increases with the increase of temperature and holding stress. Thus, the correspondence of the parameters a, b, c to temperature and holding stress is described in the 2-element form of a first function, such as:

and 2.5, obtaining a value of a model coefficient matrix according to the functional relation between the fitting parameters and the temperature selected in the step 3.4 by using the parameter value sequence of the model, the temperature and the holding stress, and substituting the value of the model coefficient matrix into the functional relation between the fitting parameters and the temperature selected in the step 3.4 to obtain a specific function of the relation between the model parameters and the temperature and the holding stress.

In this embodiment, a linear regression method is used to obtain a model coefficient matrix as shown in formula (38).

Substituting the model coefficient matrix (38) into the formula (37) to obtain the relationship between the model parameters and the temperature and the holding stress:

as shown in fig. 5(a) -5(c), where the scatter represents the value of a, b, or c under holding stress corresponding to temperature, the curved surface represents the mean of the fit. The fitted curve can reflect the variation trend of the parameter with the temperature.

And 3, obtaining the relation between creep rupture time and temperature and holding stress by using an improved Larsen-Miller parameter equation.

And 3.1, acquiring creep rupture time under each test condition. And (3) adopting the creep data obtained in the step (1), wherein the time value in the last group of data is the creep rupture time under the condition. By adopting the screening method for all the group data, creep rupture time data under different temperatures and holding stress can be obtained;

step 3.2, describing the relation between creep rupture time and temperature and holding stress by using an improved Larsen-Miller parameter equation; the original representation of the larsen-miller parameter is:

LMP＝(T+273.15)·(C+log₁₀t) (40)

in the formula, LMP represents Larson-Miller parameter, T is temperature, T is time, and C is constant; to add consideration to the holding stress, an extrapolation of creep rupture time is achieved. In this embodiment, the LMP is modified to a first order polynomial related to the holding stress, such as:

LMP(σ)＝p₁+p₂·log₁₀(σ)＝(T+273.15)·(C+log₁₀t_rup) (41)

where σ is holding stress, p₁、p₂Is a constant value of t_rupCreep rupture time; thus, the creep rupture time can be expressed as:

step 3.3, fitting by using a least square method according to the functional relation between creep rupture time and temperature and holding stress obtained in the step 3.2 to obtain the functional relation between corresponding fitting parameter values and creep rupture time and temperature and holding stress;

in this embodiment, a model coefficient matrix shown in formula (43) can be obtained by using the least square method.

And 4, obtaining a full-stage creep model of the polymer bonded composite material, which is based on the sample and takes the temperature and the holding stress effect into consideration.

For the bathtub curve model proposed in step 2.2, in combination with the functional relationship between the model parameters obtained in step 2.5 and the temperature and holding stress, a strain rate time model considering the temperature and holding stress can be obtained as follows:

in this embodiment, a residual map of the prediction result of the strain rate time model constructed based on the formula (44) and the actual data in the logarithmic domain is shown in fig. 6, the sum of squares of the residuals calculated by using the formula is 3934, and the standard deviation of the residuals is 0.6382. The residual sum of squares calculation method used is as follows:

and (4) combining the creep rupture time obtained in the step (44) and the creep rupture time obtained in the step 3.3 with the temperature and the holding stress, and finally obtaining a full-stage creep model of the polymer bonded composite material considering the temperature and the holding stress effect aiming at the sample.

Integrating (using the Runge-Kutta method) in the interval from the initial creep time to the creep rupture time to obtain the corresponding strain time relationship, such as:

in this embodiment, the joint model (39), formula (43) and formula (46) can be used to obtain a full-stage creep model of the PBX material in consideration of the effects of temperature and holding stress.

And 5, model verification based on independent test data.

In order to verify whether the constitutive model of the polymer-bonded composite material considering the temperature effect established in the step 4 can predict the stress-strain response before the ultimate strength is reached, the verification data in the step 1 is compared with the stress-strain model obtained in the step 4.

In model validation, MAE (mean absolute error) and RMSE (root mean square error) are used to quantify the error between the model and the validation data. The calculation method of each error mentioned in the present embodiment is as follows:

in the formula (I), the compound is shown in the specification,SSE is the sum of the squares of the residuals, N is the total number of verification data, y_iIn order to predict the data, it is,

in order to verify the data, the data is,

to verify the average of the data at a certain temperature.

FIGS. 7(a) and 7(b) show the comparison of the model strain rate time prediction results and creep curve prediction results with actual data for the validation data, respectively, which shows good agreement of the prediction results with the validation data. MAE and RMSE are 0.002805 and 0.003048, respectively.

Notably, these validation data are not used to determine parameters of the creep model. Therefore, the creep model established by the full-stage creep model establishing method for the polymer bonded composite material considering the temperature and holding stress effect provided by the invention can be proved to be reliable.

Specific example 2

By adopting creep data, the universality of the model constructed by the method for constructing the full-stage creep model of the polymer bonding composite material can be further verified, and the specific test temperature and holding stress are shown in table 3.

The corresponding creep data is shown in figure 8.

TABLE 3

Using the data in the literature, based on the creep model of embodiment 1, on the premise of not adjusting the model structure and only using new data to re-correct the model parameters, the creep model parameters can be obtained by using the operation methods of step 2.1 to step 2.5, as shown in formula (49).

As shown in fig. 9(a) -9(b), the predicted results of the proposed model are compared with the reference data, wherein the scatter is the third party data, the curve is the result of modeling using the third party data, the stress-strain response described by the model of this embodiment is very consistent with the measured data, and the maximum MAE is 0.0041 when it occurs at 45 ℃ and 28.69 MPa. The maximum RMSE was 0.0059, which occurred at 50 ℃ and 39.03 MPa. Therefore, the model constructed by the model construction method provided by the invention can be considered to be well fitted with third-party data, and shows good applicability.

As shown in fig. 10, the method for constructing a full-stage creep model of a polymer-bonded composite material provided by the present invention specifically includes the following steps:

step 1, obtaining stress time-varying data of a sample of the polymer-bonded composite material at different test temperatures and holding stresses, and screening out data in a creep stage based on stress indexes; testing of the polymer bonded composite material should meet the standards of the corresponding industry;

based on the existing test data, data with the deviation of the holding stress within 1% is selected as creep data based on the holding stress.

Step 2, using a bathtub curve equation as a basic model to obtain fitting parameters;

step 2.1, processing creep data into strain rate time data

And (3) processing the strain time data obtained in the step (1) into strain rate time data by adopting a formula (11).

In which i represents the time number ε_i+1Represents the strain value, ε, at i +1_iRepresents the strain value at i, t_i+1And t_iThe meaning of i in (a) is similar to that in (e), representing time.

Step 2.2, fitting the test data of each sample by using a bathtub curve model to obtain fitting values of fitting parameters a, b and c of a bathtub curve equation of each sample;

the bathtub curve model is represented as follows:

step 2.3, dividing the sample into a plurality of model parameter value sequences according to the fitting values of all sample model parameters a, b and c obtained in the step 2.2 and the temperature and the holding stress respectively;

and 2.4, selecting a corresponding function form to describe the relation between the model parameters and the temperature and the holding stress according to the three-dimensional scatter diagram of the model parameters and the temperature and holding stress:

based on the parameter value sequence of each model parameter, obtaining a scatter diagram of the model parameters a, b and c, the temperature T and the holding stress sigma respectively, and selecting proper functions according to the variation trend of the parameters along with the temperature; then, performing parameter fitting by adopting a corresponding function to obtain the functional relation between the model parameters a, b and c and the temperature and the holding stress; the functional relationship between the model parameters and the temperature is only explained here, and the functional relationship mainly comprises the following four functional types; if the relation between the parameters and the holding stress is considered, the additive processing can be adopted;

(1) function of the first kind

Wherein a, b and c are parameters of a function, a ═ α₁,α₂]，b＝[β₁,β₂]，c＝[γ₁,γ₂]T is temperature, groups a, b and cForming a fitting coefficient matrix;

(2) function of the second kind

Wherein a ═ α₁,α₂,α₃]，b＝[β₁,β₂,β₃]，c＝[γ₁,γ₂,γ₃]，T_kiRepresents the temperature of the segment point, i ═ 1, 2, 3, T_k1、T_k2、T_k3The segment point temperatures of the fitting parameters ln (K), n and E function are respectively the same or different, H (x) represents a step function, and when the value of x is less than 0, the result is 0; otherwise, the result is 1;

(3) third function

Wherein a ═ α₁,α₂,α₃]，b＝[β₁,β₂,β₃]，c＝[γ₁,γ₂,γ₃]；

(4) Fourth function

Wherein a ═ α₁,α₂]，b＝[β₁,β₂]，c＝[γ₁,γ₂]；

Step 2.5, obtaining a specific value of a fitting coefficient matrix by using a model parameter value sequence and temperature and holding stress numerical values according to the functional relation between the fitting parameters and the temperature selected in the step 2.4 and by using a linear regression method, and substituting the fitting coefficient matrix into the functional relation between the fitting parameters and the temperature selected in the step 2.4 to obtain a function of the relation between the model parameters and the temperature and holding stress;

step 3, obtaining the relation between creep rupture time and temperature and holding stress by using an improved Larsen-Miller parameter equation;

step 3.1, determining the time in the last group of data as creep rupture time by adopting the creep data obtained in the step 1; by adopting the screening method for all the group data, creep rupture time data under different temperatures and holding stress can be obtained;

LMP＝(T+273.15)·(C+log₁₀t) (17)

in the formula, LMP represents Larson-Miller parameter, T is temperature, T is time, and C is constant; to incorporate the consideration of holding stress, and to achieve an extrapolation of creep rupture time, the LMP can be corrected to a polynomial related to holding stress, such as:

LMP(σ)＝p₁+p₂·log₁₀(σ)＝(T+273.15)·(C+log₁₀t_rup) (18)

in addition, the polynomial form of the LMP may be modified according to the relationship between creep rupture time and holding stress, such as modifying the relationship between LMP and holding stress to a second order polynomial:

3.3, fitting by using a least square method according to the functional relation between creep rupture time and temperature and holding stress obtained in the step 3.2 to obtain the functional relation between corresponding fitting parameter values and creep rupture time and temperature and holding stress;

step 4, obtaining a creep model considering temperature and holding stress effect aiming at the polymer bonding composite material;

in the formula, the meanings of the parameters can be referred to formula (12); integrating (by using the Runge Kutta method) the equation (12) from the initial creep time to the creep rupture time to obtain the corresponding strain time relationship, for example:

and (3) simultaneously obtaining the relation between the strain time and the creep rupture time obtained in the step (3.3) and the temperature and the holding stress, and finally obtaining the full-stage creep model of the polymer bonded composite material considering the temperature and the holding stress effect aiming at the sample.

Preferably, the method further comprises a step 5 of performing data verification on the full-stage creep model of the polymer bonded composite material obtained in the step 4 by considering the temperature and holding stress effect.

Preferably, step 1 obtains creep curves of the samples of the polymer-bonded composite material at different test temperatures and holding stresses as test data, and the creep curves are obtained through tests, specifically:

selecting a test temperature and a holding stress range according to engineering or research requirements and the number of stocked samples, determining a test temperature and a holding stress value in the test range, setting the number of samples under each test condition, carrying out creep test on the samples of the polymer-bonded composite material after heat preservation in a temperature box, firstly loading the material to the set holding stress value under quasi-static state, and then keeping loading under the set holding stress until the material is broken. And acquiring creep curves of the sample under different test conditions after the test as test data, and dividing the test data into modeling data and verification data for subsequently verifying the effectiveness of the established model, wherein the modeling data accounts for about 80% of the total data amount, and the verification data accounts for about 20% of the total data amount.

Preferably, before the step 3.1, a step of checking whether the model is applicable by determining a coefficient is further included, specifically:

for the obtained creep data, the process described in step 2.1 and step 2.2 should be applied first, the creep data is fitted with a bathtub curve, and the predicted data and the experimental data are calculated using formula (23) and formula (24) to obtain the determination coefficient R²Determining the coefficient R²If the number of the intermediate satisfaction requirements exceeds the specified threshold, executing step 2.3, otherwise returning to step 1 to obtain the trial number again, wherein the equations (23) and (24) are as follows:

where SSE is the sum of the squares of the residuals, SST is the sum of the squares of the sums, N is the total number of test data per sample, y_iFor the prediction data obtained by the bathtub curve equation,

for the test data of each of the samples,

average of test data, R, for each sample²To determine the coefficients.

Preferably, in the step of checking whether the test condition is accurate by determining a coefficient, the specified threshold and the requirement to be met are specifically:

the threshold is set to 0.8, and the requirement to be satisfied is to determine the coefficient R²Greater than 0.8.

Preferably, in step 2.4, the function of the relationship between the model parameters and the temperature and holding stress is selected as a first function, which can be expressed as:

preferably, step 2.5 is specifically:

according to the relationship between the screened fitting parameter value sequence and the temperature and holding stress, a model coefficient matrix shown as a formula (26) can be obtained by utilizing a linear regression method:

substituting the fitting coefficient matrix type (26) into a formula (21) to obtain the functional relation between the model parameters and the temperature and the holding stress:

preferably, step 3.3 is specifically:

selecting LMP equation shown in formula (19) according to the relation between creep rupture time, temperature and holding stress after screening, and obtaining p by least square method₁＝22329，p₂＝-65081，C＝-42.17。

In summary, by comparing with the test data, the creep model constructed by the method for constructing the full-stage creep model of the polymer bonded composite material provided by the application is suitable for describing the full-stage creep behavior of the polymer bonded composite material.

The constructed creep model is a basic model of the material and is the primary task for predicting the service life of the material in a long-term service state, and the constructed model can be used for maintaining the structure and researching the cause of the structural damage.

Finally, it should be noted that: the above-mentioned embodiments are only used for illustrating the technical solution of the present invention, and not for limiting the same; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method of full-stage creep model construction for polymer-bonded composites, said method taking into account changes in temperature and holding stress, characterized by: which comprises the following steps:

step 4, combining the function of the relation between the model parameters and the temperature and the holding stress obtained according to the sample in the step 2.5 and the function of the relation between the Larsen-Miller parameters and the temperature and the holding stress in the step 3.2, obtaining a full-stage creep model of the polymer bonding material, which is shown as the formula (2) and aims at the sample and considers the temperature and the holding stress effect;

in which ε is the strain ε₀Represents the initial value of creep strain.

2. The method of claim 1 for constructing a full-stage creep model of a polymer-bonded composite, wherein: further comprising:

3.2, according to creep rupture time at different temperatures and different holding stresses, acquiring parameter values in Lason-Miller parameters by adopting Lason-Miller parameters based on a minimum two-pass method, and establishing the relation between the creep rupture time and the temperature and the holding stresses; the LMP equation is as follows:

P(σ)＝p₁+p₂·σ＝(T+273.15)[p₃+log₁₀t] (3)

3. The method of claim 1 for constructing a full-stage creep model of a polymer-bonded composite, wherein the method comprises the steps of: in order to obtain a full-stage creep model of the polymer bonded composite material considering the effects of temperature and holding stress for the test specimen, the method specifically comprises the following sub-steps,

4. The method of claim 3, wherein the full-stage creep model is constructed by: further comprising:

and 5, performing data verification on the full-stage creep model of the polymer bonded composite material, which is obtained in the step 4 and takes the temperature and the holding stress effect into consideration.

5. The method of claim 1 for constructing a full-stage creep model of a polymer-bonded composite, wherein: before the step 2.3, the method further comprises a step of checking whether the test condition is accurate by determining a coefficient, specifically:

for the creep data for one of the samples, fitting was performed using the bathtub curve model set forth in step 2.2, and the coefficient of determination R was calculated from the predicted data and the experimental data using equations (6) and (7)²Determining the coefficient R²If the quantity meeting the requirements exceeds the specified threshold value, executing the step 2.3, otherwise, acquiring the test parameters again, and executing the step 2.1 and the step 2.2 again;

for the test data of each of the samples,

average of test data, R, for each sample²To determine the coefficients.

6. The method of claim 5, wherein the full-stage creep model is constructed by: in said step 2.4, the model parameters a, b, c are represented as a function of the temperature T and the holding stress σ using multivariate linear functions; the functional form is shown in equation (8):

in the formula, alpha_i，β_iAnd gamma_iAre parameter coefficients.

7. The method of constructing a full-stage creep model of a polymer-bonded composite of claim 1 or 6, wherein: the step 2.5 is specifically as follows:

substituting the fitting coefficient matrix (9) into equation (1):