Method for predicting mechanical properties of pbt elastomer curing process
By measuring and fitting the tensile mechanical property parameters of PBT elastomers, a predictive model was established, which solved the problem of unclear mechanical properties during the curing process of PBT elastomers, realized rapid and economical prediction of mechanical properties, and reduced research risks.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- EAST CHINA UNIV OF SCI & TECH
- Filing Date
- 2022-11-29
- Publication Date
- 2026-05-29
AI Technical Summary
The mechanical properties of PBT elastomers during the curing process are unclear in the existing technology, and traditional testing methods are time-consuming, costly, and pose safety risks.
By measuring the tensile mechanical properties of PBT elastomer at different curing temperatures and times, a predictive model was established using a linear fitting method. The curing process was processed in segments to obtain the linear relationship between tensile mechanical properties and curing temperature and time, and the mechanical properties at room temperature were predicted.
It effectively shortens the test cycle and cost, provides rapid prediction of mechanical properties, reduces research risks, and obtains room temperature mechanical property data of PBT elastomers at arbitrary curing temperatures and times.
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Figure CN116008070B_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of solid propellant matrix technology, specifically to a method for predicting the mechanical properties of PBT elastomers during the curing process. Background Technology
[0002] Solid propellants are the power source for modern aerospace and military systems, playing a crucial role in the development of missiles and space technology. The mechanical properties of the propellant determine its performance and whether its energy performance can be truly realized. Propellants are subjected to significant loads during solidification, storage, and service; insufficient mechanical properties can lead to internal cracks, and in severe cases, even engine disintegration.
[0003] From a materials perspective, PBT propellant mainly consists of a dispersed phase composed of solid fillers such as oxidants and metallic fuels, a dispersed phase of an elastic matrix composed of binders and plasticizers, and phase interfaces composed of multiple interfaces between the fillers and the matrix, and between the matrix network. Its internal structure is complex, with chemical properties and physical properties influencing and interacting with each other. As a matrix material for PBT composite solid propellants, PBT elastomers are the most important factor determining the performance and processing technology of solid propellants, since their mechanical properties mainly depend on the curing process of the binder system to form a cross-linked network and connect the solid particles. Therefore, studying the mechanical properties of PBT elastomers and analyzing their curing mechanism to improve the overall performance of propellants is of great significance.
[0004] In scientific research and production practice, uniaxial tensile testing methods are generally used to characterize the mechanical properties of elastomeric matrix materials. This method offers the advantage of reliable results, but it involves a long testing cycle, high time and economic costs, and carries certain risks for subsequent research on propellants. Summary of the Invention
[0005] This application provides a method for predicting the mechanical properties of PBT elastomers during the curing process, which solves the problems that the mechanical properties of elastomers during the curing process are not yet clear and that existing test methods have long test cycles.
[0006] The method for predicting the mechanical properties of PBT elastomers during the curing process according to the first embodiment of this application includes:
[0007] Step S1: Determine the tensile mechanical properties of PBT elastomer under the influence of curing temperature and curing time.
[0008] Step S2: Plot the evolution curves of tensile mechanical property parameters with the vertical axis and the horizontal axis with the curing time at different curing temperatures, and perform linear fitting to obtain the linear fitting coefficient K and the linear fitting coefficient b between the tensile mechanical property parameters and the curing time.
[0009] Step S3: Plot the evolution curve with the linear fitting coefficients K and b as the vertical axis and the curing temperature as the horizontal axis, and perform linear fitting to obtain the linear fitting coefficient A between the linear fitting coefficient K and the curing temperature. K and linear fitting coefficient B K And the linear fitting coefficient b and the linear fitting coefficient A of curing temperature. b and linear fitting coefficient B b Thus, a predictive model for the mechanical properties of PBT elastomers during the curing process is obtained.
[0010] Optionally, in other embodiments of this application, the prediction model is: tensile mechanical property parameter = (A K T+B K )t+A b T+B b .
[0011] Optionally, in other embodiments of this application, the tensile mechanical property parameters include the tensile strength of the PBT elastomer and the elongation at break of the PBT elastomer.
[0012] Optionally, in other embodiments of this application, in step S2, based on the reaction rate difference analysis of the curing process, the curing process is segmented to obtain the linear fitting coefficient K and linear fitting coefficient b of the tensile mechanical property parameters and curing time in each segment of the curing process.
[0013] Optionally, in other embodiments of this application, in step S3, evolution curves are plotted for each segment of the curing process, with linear fitting coefficients K and b as the vertical axis and curing temperature as the horizontal axis, and linear fitting is performed to obtain the linear fitting coefficient A between the linear fitting coefficient K and the curing temperature for each segment. K and linear fitting coefficient B K And the linear fitting coefficient b of each segment and the linear fitting coefficient A of the curing temperature. b and linear fitting coefficient B b .
[0014] Optionally, in other embodiments of this application, the prediction model is:
[0015] When the curing time is 40h~96h, σ b1 = (-3.35×10 -4 T+0.02646)t+0.03485T-1.567;
[0016] ε b1 =(0.24T-22.41)t-51.86T+4879.41;
[0017] When the curing time is 96h~220h, σb2 = (-6.253×10 -5 T+0.00305)t+9.45×10 -3 T+0.644;
[0018] ε b2 =(0.12T-9.53)t-33.21T+3228.88;
[0019] Where T is the curing temperature in °C, t is the curing time in hours, and σ is the curing temperature in degrees Celsius. b1 The tensile strength of PBT elastomer with a curing time of 40–96 h is expressed in MPa and σ. b2 The tensile strength of PBT elastomer with a curing time of 96–220 h is expressed in MPa and ε. b1 Elongation at break of PBT elastomer with curing time of 40–96 h, expressed as %, ε b2 Elongation at break of PBT elastomer with a curing time of 96–220 h, in percentage.
[0020] Optionally, in other embodiments of this application, the PBT elastomer is formed by the curing reaction of 3,3-bis(azidomethyloxetane)tetrahydrofuran copolyether and toluene 2,4-diisocyanate.
[0021] Optionally, in other embodiments of this application, the molar ratio of the isocyanate group in 2,4-diisocyanate toluene and the hydroxyl group in 3,3-bis(azidomethyloxetane)tetrahydrofuran coether is 1.4:1.
[0022] Optionally, in other embodiments of this application, the curing temperature can be 50℃~70℃, 55℃~65℃, or 60℃.
[0023] Optionally, in other embodiments of this application, the curing time can be 40h to 220h, 72h to 200h, or 96h to 170h.
[0024] Optionally, in other embodiments of this application, in step S1, the tensile mechanical properties of the PBT elastomer are measured every 24 hours.
[0025] The method for predicting the mechanical properties of PBT elastomers during the curing process according to the embodiments of this application has at least the following technical effects:
[0026] (1) This application uses curing temperature and curing time as input parameters to estimate the mechanical properties (i.e., tensile strength σ) at room temperature. b With elongation at break ε bThis application can effectively shorten the test cycle and cost, and can obtain room temperature mechanical property data of PBT elastomer at any curing temperature and curing time;
[0027] (2) This application can realize the rapid prediction of the room temperature mechanical properties of PBT elastomer during the curing process, provide a lot of data support for the study of mechanical properties of PBT propellant matrix materials, and also provide a reference for the study of mechanical properties of PBT propellant. Attached Figure Description
[0028] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0029] Figure 1 This is a flowchart of a method for predicting the mechanical properties of PBT elastomers during the curing process, provided in an embodiment of this application.
[0030] Figure 2 These are the experimental points and piecewise linear fitting curves showing the change in tensile strength of PBT elastomer with curing time at different temperatures provided in the embodiments of this application;
[0031] Figure 3 These are the experimental points and piecewise linear fitting curves of the change in elongation at break of PBT elastomer with curing time at different temperatures provided in the embodiments of this application;
[0032] Figure 4A This application provides a linear relationship between the coefficients K and b of the tensile strength coefficients and the curing temperature when the curing time is between 40h and 96h.
[0033] Figure 4B This application provides a linear relationship between the coefficients K and b of the tensile strength coefficients and the curing temperature when the curing time is between 96h and 220h, as shown in the embodiments of this application.
[0034] Figure 5A This application provides a linear relationship between the coefficients K and b of the elongation at break and the curing temperature when the curing time is between 40h and 96h.
[0035] Figure 5B This describes the relationship between the coefficients K and b of the linear relationship between elongation at break and curing temperature when the curing time is between 96h and 220h, as provided in the embodiments of this application. Detailed Implementation
[0036] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.
[0037] This application provides a method for predicting the mechanical properties of PBT elastomers during the curing process. Detailed descriptions follow. It should be noted that the order of description of the following embodiments is not intended to limit the preferred order of the embodiments.
[0038] This application provides a method for predicting the mechanical properties of PBT elastomers during the curing process, including:
[0039] Step S1: Determine the tensile mechanical properties of PBT elastomer under the influence of curing temperature and curing time.
[0040] Step S2: Plot the evolution curves of tensile mechanical property parameters with the vertical axis and the horizontal axis with the curing time at different curing temperatures, and perform linear fitting to obtain the linear fitting coefficient K and the linear fitting coefficient b between the tensile mechanical property parameters and the curing time.
[0041] Step S3: Plot the evolution curve with the linear fitting coefficients K and b as the vertical axis and the curing temperature as the horizontal axis, and perform linear fitting to obtain the linear fitting coefficient A between the linear fitting coefficient K and the curing temperature. K and linear fitting coefficient B K And the linear fitting coefficient b and the linear fitting coefficient A of curing temperature. b and linear fitting coefficient B b Thus, a prediction model is obtained.
[0042] This application tests the room-temperature mechanical properties of PBT elastomers under a fixed formulation at different curing temperatures and times. A linear fitting method is used to obtain a prediction model for the room-temperature mechanical properties based on two parameters: curing temperature and curing time. Using curing temperature and curing time as input parameters, the mechanical properties at room temperature are predicted.
[0043] In some embodiments of this application, the prediction model is: tensile mechanical property parameter = (A K T+B K )t+A b T+B b .
[0044] In some embodiments of this application, tensile mechanical property parameters include tensile strength and elongation at break.
[0045] In some embodiments of this application, in step S2, based on the reaction rate difference analysis of the curing process, the curing process is segmented, and the linear fitting coefficients K and b of the tensile mechanical property parameters and curing time in each segment are obtained respectively. Figure 2 It is known that the tensile strength gradually increases with the curing process, and the rate of increase differs before and after the curing time t = 96 h: the linear increase rate is large before t = 96 h; after t = 96 h, the linear increase rate decreases and tends to stabilize. The curing process is divided into curing process ① (40 h ~ 96 h) and curing process ② (96 h ~ 220 h) with curing time t = 96 h as the node. Piecewise linear fitting using Origin yields the coefficients K and b of the two linear equations for tensile strength at different temperatures. Based on limited experimental data, this application uses piecewise linear fitting to obtain the quantitative relationship between curing temperature, curing time, and mechanical property parameters. Using curing temperature and curing time as input parameters, the tensile strength σ of PBT elastomer at room temperature during the curing process is predicted. b With elongation at break ε b This effectively shortened the experimental cycle.
[0046] In some embodiments of this application, in step S3, evolution curves are plotted for each segment of the curing process, with linear fitting coefficients K and b as the vertical axis and curing temperature as the horizontal axis. Linear fitting is then performed to obtain the linear fitting coefficient A between the linear fitting coefficient K and the curing temperature for each segment. K and linear fitting coefficient B K And the linear fitting coefficient b of each segment and the linear fitting coefficient A of the curing temperature. b and linear fitting coefficient B b .Depend on Figure 4A and Figure 4B It can be seen that the coefficients K and b have a good linear relationship with the curing temperature. Using Origin for linear fitting, the coefficients A of the linear relationship between K, b and temperature are obtained. K B K A b B b In some embodiments of this application, the prediction model is as follows:
[0047] When the curing time is 40h~96h, σ b1 = (-3.35×10 -4 T+0.02646)t+0.03485T-1.567;
[0048] ε b1 =(0.24T-22.41)t-51.86T+4879.41;
[0049] When the curing time is 96h~220h, σ b2 = (-6.253×10 -5 T+0.00305)t+9.45×10 -3 T+0.644;
[0050] ε b2 =(0.12T-9.53)t-33.21T+3228.88;
[0051] Where T is the curing temperature in °C, t is the curing time in hours, and σ is the curing temperature in degrees Celsius. b1 The tensile strength of PBT elastomer with a curing time of 40–96 h is expressed in MPa and σ. b2 The tensile strength of PBT elastomer with a curing time of 96–220 h is expressed in MPa and ε. b1 Elongation at break of PBT elastomer with curing time of 40–96 h, expressed as %, ε b2 The elongation at break of PBT elastomers with curing times of 96–220 h is expressed as a percentage. The predictive model for the mechanical properties of PBT elastomers during the curing process in this application uses curing temperature and curing time as input parameters to predict the mechanical properties (i.e., tensile strength σ) at room temperature. b With elongation at break ε b This application can effectively shorten the test cycle and cost, and can obtain room temperature mechanical property data of PBT elastomer under any curing temperature and curing time.
[0052] In some embodiments of this application, the PBT elastomer is formed by the curing reaction of 3,3-bis(azidomethyloxetane)tetrahydrofuran copolyether (PBT) and toluene diisocyanate (TDI).
[0053] In some embodiments of this application, the molar ratio of the isocyanate group in toluene 2,4-diisocyanate to the hydroxyl group in 3,3-bis(azidomethyloxetane)tetrahydrofuran coether is 1.4:1.
[0054] In some embodiments of this application, the curing temperature can be 50℃~70℃, 55℃~65℃, or 60℃.
[0055] In some embodiments of this application, the curing time can be 40h to 220h, 72h to 200h, or 96h to 170h.
[0056] In some embodiments of this application, in step S1, the tensile mechanical properties of the PBT elastomer are measured every 24 hours. The curing temperature can be any of several temperatures selected from 50℃ to 70℃ for testing; for example, 50℃, 60℃, and 70℃ can be selected. Considering the influence of curing temperature on the curing rate, when curing at 50℃, the range of curing cycles extracted at the time point is 72–220 hours; when curing at 60℃ or 70℃, the range of curing cycles extracted at the time point is 40–200 hours.
[0057] The following description is based on specific embodiments.
[0058] Example 1
[0059] This embodiment provides a method for establishing a predictive model for the mechanical properties of PBT elastomers during the curing process, including the following steps:
[0060] S1: Determine the mechanical properties of samples under a fixed ratio at different curing temperatures and times. Curing temperatures of 50℃, 60℃, and 70℃ were selected sequentially. Additionally, cured samples were extracted every 24 hours and dried in a desiccator for 7 days. The mechanical properties (tensile strength σ) at room temperature were then tested. b With elongation at break ε b ).
[0061] S2: Based on the test results of the mechanical performance parameters obtained in step S1, obtain the mechanical performance evolution curve, such as... Figure 2 and Figure 3 As shown, based on the differences in the rate of change of performance parameters during the reaction process, the curing process was divided into curing process ① (40h~96h) and curing process ② (96h~220h) with curing time t=96h as the node. The coefficients K and b of the linear equation for tensile strength at the three temperatures were obtained by piecewise linear fitting, as shown in Table 1, and the coefficients K and b of the linear equation for elongation at break at the three temperatures are shown in Table 2.
[0062] Table 1. Linear fitting equations for tensile strength at different temperatures, K and b coefficients.
[0063]
[0064] Table 2. Linear fitting equations for elongation at break at different temperatures, K and b coefficients.
[0065]
[0066] Where K1 and b1 are the coefficients of curing process ①, and K2 and b2 are the coefficients of curing process ②.
[0067] S3: Plot a scatter plot of the curing temperature versus the linear coefficients K and b of the tensile strength at that temperature, as shown below. Figure 4A and 4B As shown, the scatter plot of the curing temperature versus the linear coefficients K and b of the elongation at break at that temperature is as follows. Figure 5A and 5B As shown in Table 3, the coefficients A and B of the linear relationship between tensile strength K and b and temperature were obtained by linear fitting of their respective curves, and the coefficients A and B of the linear relationship between elongation at break K and b and temperature are shown in Table 4.
[0068] Table 3. Coefficients A and B of the linear relationship between tensile strength K and b coefficients and temperature.
[0069]
[0070] Table 4. Coefficients A and B of the linear relationship between elongation at break K, b coefficients and temperature.
[0071]
[0072] Where A k B k Let A be the coefficient relating K to temperature. b B b This is the coefficient of relationship between coefficient b and temperature.
[0073] Using curing temperature and curing time as independent variables, the tensile strength σ at 50–70℃ is calculated. b With elongation at break ε b Using the curing temperature and curing time as the dependent variable, piecewise linear fitting analysis was used to obtain the relationship between curing temperature, curing time, and σ. b ε b The quantitative relationship between them is expressed by the following formula:
[0074] Curing temperature, curing time and σ b Quantitative relationship:
[0075] Curing process ① (40h~96h):
[0076] σ b1 = (-3.35×10 -4 T+0.02646)t+0.03485T-1.567
[0077] Curing process ② (96h~220h):
[0078] (-6.253×10 -5 T+0.00305)t+9.45×10 -3 T+0.644
[0079] Curing temperature, curing time and ε b Quantitative relationship:
[0080] Curing process ① (40h~96h):
[0081] ε b1 =(0.24T-22.41)t-51.86T+4879.41
[0082] Curing process ② (96h~220h):
[0083] ε b2 =(0.12T-9.53)t-33.21T+3228.88
[0084] Where σ b1 σ b2 The tensile strengths of curing processes ① and ② are respectively; ε b1 With ε b2 These are the elongation at break of curing processes ① and ②, respectively. The subscripts 1 and 2 represent the two stages of the curing process; T is any curing temperature within the range of 50 to 60℃; and t is any curing time within the range of 40 to 220 hours.
[0085] Based on limited experimental data, this application uses a piecewise linear fitting method to obtain a quantitative relationship between curing temperature, curing time, and mechanical property parameters. Using curing temperature and curing time as input parameters, it estimates the tensile strength σ of PBT elastomer at room temperature during the curing process. b With elongation at break ε b This effectively shortened the experimental cycle.
[0086] The above provides a detailed description of the predictive model and its establishment method for the mechanical properties of PBT elastomer during the curing process. Specific examples have been used to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of this application. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this application. Therefore, the content of this specification should not be construed as a limitation of this application.
Claims
1. A method for predicting the mechanical properties of PBT elastomers during the curing process, characterized in that, include: Step S1: Determine the tensile mechanical properties of PBT elastomer under the influence of curing temperature and curing time. Step S2: Plot the evolution curves at different curing temperatures with the tensile mechanical property parameters as the vertical axis and the curing time as the horizontal axis, and perform linear fitting to obtain the linear fitting coefficient K and the linear fitting coefficient b between the tensile mechanical property parameters and the curing time. Step S3: Plot the evolution curve with the linear fitting coefficient K and the linear fitting coefficient b as the vertical axis and the curing temperature as the horizontal axis, and perform linear fitting to obtain the linear fitting coefficient A between the linear fitting coefficient K and the curing temperature. K and linear fitting coefficient B K And the linear fitting coefficient b and the linear fitting coefficient A of the curing temperature b and linear fitting coefficient B b Thus, a predictive model for the mechanical properties of the PBT elastomer during the curing process is obtained; the predictive model is: tensile mechanical property parameters. Where T is the curing temperature and t is the curing time.
2. The method for predicting the mechanical properties of PBT elastomers during the curing process according to claim 1, characterized in that, The tensile mechanical properties include the tensile strength and elongation at break of the PBT elastomer.
3. The method for predicting the mechanical properties of PBT elastomers during the curing process according to claim 1, characterized in that, In step S2, based on the reaction rate difference analysis of the curing process, the curing process is segmented, and the linear fitting coefficients K and b of the tensile mechanical property parameters and the curing time in each segment of the curing process are obtained respectively.
4. The method for predicting the mechanical properties of PBT elastomers during the curing process according to claim 1, characterized in that, In step S3, the evolution curves of each segment of the curing process are plotted with the linear fitting coefficients K and b as the vertical axis and the curing temperature as the horizontal axis, and linear fitting is performed to obtain the linear fitting coefficient A between the linear fitting coefficient K and the curing temperature for each segment. K and linear fitting coefficient B K And the linear fitting coefficient b of each segment and the linear fitting coefficient A of the curing temperature. b and linear fitting coefficient B b .
5. The method for predicting the mechanical properties of PBT elastomers during the curing process according to claim 3 or claim 4, characterized in that, The prediction model is as follows: When the curing time is 40h~96h ; ; When the curing time is 96h~220h ; ; Where T is the curing temperature in °C, t is the curing time in hours, and σ is the curing temperature in degrees Celsius. b1 The tensile strength of PBT elastomer with a curing time of 40~96h is expressed in MPa. Excluding a curing time of 96h, σ b2 The tensile strength of PBT elastomer with a curing time of 96~220h is expressed in MPa and ε. b1 Elongation at break of PBT elastomer with curing time of 40~96h, in % ε b2 Elongation at break of PBT elastomer with a curing time of 96~220h, in units of .
6. The method for predicting the mechanical properties of PBT elastomers during the curing process according to claim 5, characterized in that, The PBT elastomer is formed by the curing reaction of 3,3-bis(azidomethyloxetane)tetrahydrofuran copolyether and toluene 2,4-diisocyanate.
7. The method for predicting the mechanical properties of PBT elastomers during the curing process according to claim 6, characterized in that, The molar ratio of the isocyanate group in the toluene 2,4-diisocyanate to the hydroxyl group in the 3,3-bis(azidomethyloxetane)tetrahydrofuran coether is 1.4:
1.
8. The method for predicting the mechanical properties of PBT elastomers during the curing process according to claim 1, characterized in that, The curing temperature is 50℃~70℃.
9. The method for predicting the mechanical properties of PBT elastomers during the curing process according to claim 1, characterized in that, The curing time is 40h~220h.
10. The method for predicting the mechanical properties of PBT elastomers during the curing process according to claim 1, characterized in that, In step S1, the tensile mechanical properties of the PBT elastomer are measured every 24 hours.