A method for predicting the flexural strength of fiber-reinforced composite FDM samples

Abstract

This invention provides a method for predicting the flexural strength of fiber-reinforced composite FDM samples, comprising: Step S1, preparing and drying the polymer material filament for printing, leveling the printing base plate, and generating the G-Code of the printed sample; Step S2, setting up a temperature measurement platform device, fixing thermocouples at the starting position of the filling path of the first layer of printing, directly contacting the printed surface during the printing process to measure the temperature, acquiring the thermocouple information through a dynamic signal acquisition and analysis instrument, and converting the digital signal into a real-time temperature curve graph for real-time output on a computer; Step S3, performing FDM printing on the fiber-reinforced composite material, and calculating the flexural strength of the sample based on the acquired temperature according to a formula. The prediction error of this invention is an average relative error rate of 4.4%, which is a significant improvement in accuracy compared to the prediction results of existing technology models.

Description

Technical Field

[0001] This invention relates to the field of additive manufacturing technology, and in particular to a method for predicting the flexural strength of fiber-reinforced composite (FDM) samples. Background Technology

[0002] Fused deposition modeling (FDM) is widely used in the manufacturing and processing field due to its advantages such as low cost, easy maintenance, and simple operation. Its processing principle is to inject thermoplastic filaments into a heated, melted, or liquefied nozzle, and then extrude and deposit them onto a substrate. Because of this processing method, the structure of FDM printed parts is printed and bonded layer by layer. Each layer interface is formed by the diffusion and bonding of polymer molecules. During the bonding process, the polymer filaments may experience problems such as high porosity and poor adhesion due to insufficient melting and insufficient polymer diffusion, which may result in mechanical properties that do not meet the expected requirements.

[0003] To improve the poor strength of FDM printed parts and increase strength accuracy, quantitative prediction of FDM printed part performance has become crucial to meeting these requirements. This has led many scholars to dedicate themselves to establishing an accurate FDM strength prediction model. Some researchers have proposed a coupled model of interface evolution and molecular diffusion, introducing thermally driven molecular diffusion to describe bonding strength at the microscale. This model establishes a precise relationship between process parameters and adhesion strength parallel / perpendicular to the deposition direction. However, this study only tested PLA as a printing material, and its applicability to other printing materials remains uncertain. Other researchers have constructed a mathematical model for neck growth in ABS-P430 printing material, indicating that the strength of the FDM portion mainly depends on intralayer adhesion, interlayer adhesion, and neck growth between filaments. However, this mathematical model does not delve into the specific temperature changes over time during printing, thus failing to determine the specific adhesion degree between adjacent filaments and resulting in an inaccurate prediction. Researchers have also developed an interlayer strength model for FDM parts as a function of printing settings and material properties. This model can be used to predict the interlayer bond strength of FDM in the Z-axis direction, and then extended to predict the strength in the X and Y axes. This work can better optimize the anisotropy of the strength and stiffness of FDM parts. However, the coefficient of determination for the prediction is 0.795, which means the error rate is 21.5%. Therefore, the error with the actual results is relatively large and cannot achieve accurate strength prediction. Summary of the Invention

[0004] To address the above technical problems, this invention discloses a method for predicting the flexural strength of fiber-reinforced composite FDM samples. By monitoring the temperature history during the FDM process, the mechanical properties of FDM printed parts can be predicted online, in real time, and accurately. This solves the problem that current fiber-reinforced composite materials have complex matrix and reinforcing material properties and even more complex interface properties, making it impossible to accurately establish temperature models.

[0005] The technical solution adopted by this invention is as follows:

[0006] A method for predicting the flexural strength of fiber-reinforced composite (FDM) samples includes the following steps:

[0007] Step S1: Prepare and dry the fiber-reinforced composite material filaments for printing, level the printing base plate, and generate the G-Code of the printed sample.

[0008] Step S2: Set up a temperature measurement platform device, fix the thermocouple at the starting position of the filling path of the first layer of printing, and directly contact the printing surface of the printing process to measure the temperature. Use a dynamic signal acquisition and analysis instrument to collect the thermocouple information at a set temperature acquisition time interval, and convert the digital signal into a real-time temperature curve graph and output it on the computer in real time.

[0009] Step S2: Perform FDM printing and collect temperature data during the printing process;

[0010] Step S3: Perform FDM printing on the fiber-reinforced composite material. Calculate the temperature t at different times using the following formula based on the collected data. i Bending strength value:

[0011]

[0012] Among them, T g The glass transition temperature of the printed fiber-reinforced composite material; t i T(t) represents the temperature measurement time. i ) represents different times t i The temperature; the time interval between different temperatures is 1 / N, where N is the temperature sampling frequency, t r The time it takes for the molecules of the printed fiber-reinforced composite material to reach the maximum interlayer bonding strength is the time during which the material is above the glass transition temperature in the measurement. A and B are constants.

[0013] Step S4, calculate the strength value of the sample according to the following formula (2):

[0014]

[0015] Wherein F(t) i ,T(t iThe value represents the bending strength of the printed part. For each time t i The bending strength value will be calculated for each printing time t. i The final bending strength value is obtained by summing the strength values.

[0016] Furthermore, in step S3, the intensity values ​​at different times... It is obtained in the following way:

[0017] Step S31, according to previous research by Yin et al., the strength value of polymer healing depends on the interfacial temperature change T(t) i ) and time t i The intensity value can be expressed as F(t) i ,T(t i )). Calculate each printing time t according to formula (3). i Intensity value for:

[0018]

[0019] Step S32: Determine the time t for the polymer molecules to reach maximum interlayer adhesive strength using the Arrhenius relation. r for:

[0020]

[0021] Where C1 and C2 are constants; and 3C² / 4 = B;

[0022] Step S33, in which formula (4) is substituted into formula (3), and t is extracted from the denominator. r From the power of 3 / 4, we can obtain formula (1).

[0023] Furthermore, in step S3, constants A and B are obtained using the following steps:

[0024] 1) Substituting further into formula (1) into formula (2), we can obtain the predicted bending strength value F(t). i ,T(t i )) and interface temperature distribution T(t i ) and time t i The relationship is shown in formula (5):

[0025]

[0026] 2) Three-point bending measurements of a set of bent samples of the printing material and the polymer material's temperature change T(t) were selected. i ) and time t iThe case was fitted with constants A and B until the temperature change T(t) was substituted. i ) and time t i Intensity prediction result F(t) i ,T(t i The predicted result of the three-point bending strength F Exp When the error is less than 2%, the fitting ends, and the obtained A and B results are substituted into formula (5).

[0027] Furthermore, the specific fitting steps for A and B are as follows:

[0028] ① First, fix the value of B and extract the value of A. Temporarily take B = 1 and substitute it into the printing time t. i and at each time t i Temperature T(t) i Solve Then F Exp and Solve for A by calculating the quotient;

[0029] ② Substitute value A and change The value of B in the middle until The result is consistent with F. Exp The fitting process ends when the error is less than 2%.

[0030] This technical solution selects temperature change as an important parameter in the printing process, establishes the temperature history of the FDM printing process and the functional relationship between the predicted intensity of the FDM print at each printing moment (Formula (5)), and names it OTTP-S. F (Online time and temperature flexural strength prediction). After comparison with experimental measurements, the prediction method, validated by CF-PEEK and CF-PLA, has an average relative error rate of 4.4%, demonstrating higher prediction accuracy.

[0031] This method is not limited to fiber-reinforced composite materials; it is applicable to any FDM printing process where the filling path is periodic for each layer or every few layers. Preferably, the fiber-reinforced composite material is a carbon fiber polyetheretherketone composite material or a carbon fiber reinforced polylactic acid (CF-PLA) composite material.

[0032] As a further improvement of the present invention, in step S1, the printed fiber-reinforced composite material wire is placed in a vacuum drying oven for vacuum drying.

[0033] As a further improvement of the present invention, in step S1, a linear filling pattern with the required grating angle is set, and the gap between the nozzle and the printing bed is leveled multiple times before the experiment begins until a standard A4 sheet of paper can be moved. At the same time, glue is applied to the base plate to ensure successful adhesion of the bottom layer.

[0034] As a further improvement of the present invention, in step S2, the thermocouple is fixed at multiple points during the temperature measurement process, and a gap of 0.1 to 0.2 mm is reserved on the basis of leveling the printing base plate.

[0035] As a further improvement of the present invention, in step S2, the temperature signal sampling frequency of the dynamic signal acquisition and analysis instrument is 25.6Hz.

[0036] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0037] The prediction error of the technical solution of the present invention is an average relative error rate of 4.4%, which is a significant improvement in accuracy compared with the prediction results of the existing technology model. Attached Figure Description

[0038] Figure 1 This is a schematic diagram of the experimental apparatus of the present invention.

[0039] Figure 2 The temperature of the CF-PEEK material at different nozzle temperatures and the OTTP-S in Example 1 of this invention are related. F Curve showing how it changes over time.

[0040] Figure 3 The three-point bending test strength of CF-PEEK material under different nozzle temperatures in Example 1 of this invention is compared with that of OTTP-S. F Comparison chart.

[0041] Figure 4 This relates to the temperature of CF-PEEK material and OTTP-S at different printing speeds in Example 1 of the present invention. F Curve showing how it changes over time.

[0042] Figure 5 This relates to the three-point bending test strength of CF-PEEK material at different printing speeds and the OTTP-S ratio in Example 1 of this invention. F Comparison chart.

[0043] Figure 6 This relates to the relationship between different grating angles, CF-PEEK material temperature, and OTTP-S in Embodiment 1 of the present invention. F Curve showing how it changes over time.

[0044] Figure 7 The three-point bending test strength of CF-PEEK materials with different grating angles in Embodiment 1 of the present invention is compared with that of OTTP-S. F Comparison chart.

[0045] Figure 8 The temperature and OTTP-S of the CF-PLA material in Embodiment 2 of the present invention FCurve showing how it changes over time.

[0046] Figure 9 The three-point bending test strength of the CF-PLA material in Example 2 of this invention is compared with that of OTTP-S. F Comparison chart.

[0047] The reference numerals in the figures include:

[0048] 1-Printer, 2-Test point, 3-Thermocouple, 4-Printing base plate, 5-First layer fill path, 6-Dynamic signal acquisition and analysis instrument, 7-Computer. Detailed Implementation

[0049] The preferred embodiments of the present invention will be described in further detail below.

[0050] A method for predicting the flexural strength of fiber-reinforced composite (FDM) samples includes the following steps:

[0051] Step S1: Prepare and dry the fiber-reinforced composite material filaments for printing, level the printing base plate, and generate the G-Code of the printed sample.

[0052] Step S2: Set up a temperature measurement platform device, fix the thermocouple at the starting position of the filling path of the first layer of printing, and directly contact the printing surface of the printing process to measure the temperature. Use a dynamic signal acquisition and analysis instrument to collect the thermocouple information at a set temperature acquisition time interval, and convert the digital signal into a real-time temperature curve graph and output it on the computer in real time.

[0053] Step S2: Perform FDM printing and collect temperature data during the printing process;

[0054] Step S3: Perform FDM printing on the fiber-reinforced composite material. Calculate the temperature t at different times using the following formula based on the collected data. i Bending strength value:

[0055]

[0056] Among them, T g The glass transition temperature of the printed fiber-reinforced composite material, in degrees Celsius; t i T(t) represents the temperature measurement time in seconds. i ) represents different times t i Temperature, in degrees Celsius; the time interval between different temperatures is 1 / N, where N is the temperature sampling frequency, in Hz, t r The time it takes for the molecules of the printed fiber-reinforced composite material to reach maximum interlayer bonding strength, in seconds, is the time during which the material is above the glass transition temperature. A and B are constants.

[0057] Step S4, calculate the strength value of the sample according to the following formula (2):

[0058]

[0059] Wherein F(t) i ,T(t i The value represents the bending strength of the printed part. For each time t i The bending strength value will be calculated for each printing time t. i The final bending strength value is obtained by summing the strength values.

[0060] In step S3, intensity values ​​at different times It is obtained in the following way:

[0061] Step S31, according to previous research by Yin et al., the strength value of polymer healing depends on the interfacial temperature change T(t) i ) and time t i The intensity value can be expressed as F(t) i ,T(t i )). Calculate each printing time t according to formula (3). i Intensity value for:

[0062]

[0063] Step S32: Determine the time t for the polymer molecules to reach maximum interlayer adhesive strength using the Arrhenius relation. r for:

[0064]

[0065] Where C1 and C2 are constants, and 3C² / 4 = B;

[0066] Step S33, in which formula (4) is substituted into formula (3), and t is extracted from the denominator. r From the power of 3 / 4, we can obtain formula (1).

[0067] In step S3, constants A and B are obtained using the following steps:

[0068] 1) Substituting further into formula (1) into formula (2), we can obtain the predicted bending strength value F(t). i ,T(t i )) and interface temperature distribution T(t i ) and time t i The relationship is shown in formula (5):

[0069]

[0070] 2) Three-point bending measurements of a set of bent samples of the printing material and the polymer material's temperature change T(t) were selected. i ) and time t i The case was fitted with constants A and B until the temperature change T(t) was substituted. i ) and time t i Intensity prediction result F(t) i ,T(t i The predicted result of the three-point bending strength F Exp When the error is less than 2%, the fitting ends, and the obtained A and B results are substituted into formula (5).

[0071] The specific fitting steps for A and B are as follows:

[0072] ① First, fix the value of B and extract the value of A. Temporarily take B = 1 and substitute it into the printing time t. i and at each time t i Temperature T(t) i Solve Then F Exp and Solve for A by calculating the quotient;

[0073] ② Substitute value A and change The value of B in the middle until The result is consistent with F. Exp Fitting ends when the error is below 2%. Example 1

[0074] The steps for predicting and verifying the flexural strength of carbon fiber reinforced polyetheretherketone (CF-PEEK) composites are as follows:

[0075] Step 1: Preparation of Experimental Materials

[0076] After placing the CF-PEEK printing filament in a vacuum drying oven and drying it at a constant temperature of 120℃ for 12 hours, the CF-PEEK printed sample was modeled and generated in STL format. This model was then imported into Simplify-3D slicing software for G-code generation. A linear fill pattern with a 0° raster angle was set. Before the experiment, the gap between the nozzle and the printing bed was leveled several times until a standard A4 sheet of paper could be moved. Glue was applied to the substrate to ensure successful adhesion of the bottom layer.

[0077] Step 2: Set up a temperature measurement platform device, such as... Figure 1 As shown, the device includes an FDM printer 1, a K-type thermocouple 3, a dynamic signal acquisition and analysis instrument 6, and a computer 7.

[0078] The thermocouple 3 is fixed at the starting position of the first layer filling path 5 on the printing base plate 4, i.e. Figure 1 Test point 2 in the process measures the temperature by directly contacting the printing surface during the printing process. The collected temperature analog signal is collected using a dynamic signal test and analysis system, and the digital signal is converted into a real-time temperature curve by dynamic signal analysis software and output in real time on computer 7.

[0079] Step 3: Perform FDM printing, collect temperature data, and obtain temperature data.

[0080] Import the G-code with pre-set process parameters into the fused deposition modeling 3D printer. The process parameters are in... Figure 2 , Figure 4 , Figure 6 The table below illustrates this process. After the printhead and substrate have successfully heated up, printing begins. When the printhead reaches the first layer of the infill path, the thermocouple is placed at the measurement point. Once the thermocouple is secured, temperature data acquisition begins. The acquisition time is the infill time of the first layer, which is determined by the printing speed and the printed path, typically around 30-50 seconds. During this process, the temperature curve in the dynamic signal acquisition and analysis system is monitored in real time, paying attention to the stability of the signal output. If the signal stability is too poor to be recognized, the temperature measurement is immediately stopped, and step three is repeated until a clear temperature curve is output, completing this temperature acquisition task. Each temperature acquisition needs to be repeated 3-4 times, and the clearest curve is selected as preparation for the next step.

[0081] Step 4: Derivation of temperature data formulas to predict CF-PEEK flexural strength

[0082] 1) Analysis of the CF-PEEK extrusion process: When CF-PEEK filament is extruded through a nozzle, the temperature is between 350 and 400°C. At this temperature, the polymer is in a viscous flow state. When it comes into contact with a base plate close to the glass transition temperature (Tg) of CF-PEEK (approximately 147°C), it wets the existing layer at the interface, forming an initial bonding strength. Under the excitation of thermal energy, the polymer's microscopic macromolecular chains diffuse at the interface. This phenomenon continues until the temperature drops to the glass transition temperature, at which point the molecular chains are in a frozen glassy state, ending the diffusion process. At this point, 147°C is the dividing line for strength formation. Therefore, CF-PEEK at each time t... i The calculated strength value is as follows, see formula (7):

[0083]

[0084] 4) Substituting into formula (7) into formula (2), we can obtain the predicted bending strength value and the interface temperature distribution T(t). i ) and time ti The relationship is shown in formula (8):

[0085]

[0086] 5) Three-point bending measurements of a set of CF-PEEK bending samples and the polymer material's temperature change T(t) were selected. i ) and time t i The fit was performed on the case, and it was found that when A≈3, B≈1, the fit was 99.83% and the fit error was within 1%, which met the prediction accuracy requirements. Therefore, the values ​​of A and B can be substituted to obtain formula (9).

[0087]

[0088] Wherein, F CF-PEEK (t i ,T(t i The value is the predicted flexural strength of the CF-PEEK printed part, in MPa. The calculated result here has been experimentally verified to be applicable to the prediction of flexural strength of fiber-reinforced composite materials.

[0089] In Example 1, the temperature of CF-PEEK (445℃, 485℃, 525℃) during the printing process and OTTP-S under different printhead temperatures were compared. F Results that change over time, such as Figure 2 As shown, the test specimens were compared with those measured under three-point bending conditions using OTTP-S. F The results showed that the relative average error rates of the predictions were 1.3%, 0.2%, and 1.8%, respectively. Figure 3 As shown.

[0090] Temperature and OTTP-S during printing of CF-PEEK (20mm / s, 30mm / s, 40mm / s) at different printing speeds F Results that change over time, such as Figure 4 As shown, the test specimens under three-point bending measurements and OTTP-S were compared. F The results showed that the relative average errors of the predictions were 1.8%, 2.8%, and 8.3%, respectively. Figure 5 As shown.

[0091] Temperature and OTTP-S during printing process for CF-PEEK with different grating angles (0°, 30°) F Results that change over time, such as Figure 6 As shown, the test specimens were compared in the three-point bending measurement experiment and the OTTP-S experiment. F The results showed that the relative average errors in the predictions were 3.9% and 9.1%, respectively. Figure 7 As shown.

[0092] Example 2

[0093] The steps for predicting and verifying the flexural strength of carbon fiber reinforced polylactic acid (CF-PLA) composites are as follows:

[0094] Step 1: Preparation of Experimental Materials

[0095] After the CF-PLA printing filament was placed in a vacuum drying oven and vacuum dried at a constant temperature of 60°C for 6 hours, a bent sample model was created in SolidWorks and exported as an STL file to UP Studio slicing software. A straight fill pattern and a 0° / 90° raster angle cross printing mode were set. Due to the limitations of the printing machine itself, the nozzle temperature was fixed at 210°C, the fill speed was 40mm / s, and the printing layer thickness was 0.2mm.

[0096] Step 2: Set up a temperature measurement platform, as in Example 1.

[0097] Step 3: Temperature Data Acquisition

[0098] Level the printing plate, start the printing slicing software, and begin printing after the nozzle and plate have successfully heated up. When the nozzle reaches the first layer of the fill path, place the thermocouple at the measurement point and secure it. Begin temperature acquisition during this process, monitoring the temperature curve in the dynamic signal acquisition and analysis system in real time, paying attention to the stability of the signal output. If the signal stability is too poor and cannot be recognized, immediately stop the temperature measurement and repeat step three until a clear temperature curve is output, completing this temperature acquisition task. Each temperature acquisition needs to be repeated 3-4 times, and the clearest one should be selected as preparation for the next step.

[0099] Step 4: Derivation of temperature data formulas to predict the flexural strength of CF-PLA

[0100] 1) Analysis of the CF-PLA extrusion process: When CF-PLA filament is extruded through the nozzle, the temperature is around 120℃. At this temperature, the polymer is in a viscous flow state. When it comes into contact with the glass transition temperature T of CF-PLA... g When the base plate is around 58℃, it will wet the original layer at the contact interface, forming an initial bonding strength. Under the excitation of thermal energy, the microscopic macromolecular chains of the polymer diffuse at the interface. This phenomenon continues until the temperature drops to the glass transition temperature. At this time, the molecular chains are in a frozen glassy state, and the diffusion state ends. At this time, 58℃ is the dividing line for the formation of strength, as shown in formula (10):

[0101]

[0102] 4) Substituting into formula (10) into formula (2), we can obtain the predicted bending strength value and the interface temperature distribution T(t). i ) and time t i The relationship is shown in formula (11):

[0103]

[0104] 5) Three-point bending measurements of a set of CF-PLA bending samples and the polymer material's temperature change T(t) were selected. i ) and time t i The fit was performed on the case, and it was found that when A≈5 / 16 and B≈1, the fit was 98.82% and the fit error was within 2%, which met the prediction accuracy requirements. Therefore, the values ​​of A and B can be substituted to obtain formula (12).

[0105]

[0106] In Example 2, the temperature during the printing process of CF-PLA at different printing speeds and OTTP-S F The results over time are as follows: Figure 8 As shown, due to temperature limitations, test samples printed at different speeds were compared under three-point bending measurements with OTTP-S. F The results showed that the relative average error rates for prediction were 1.18% and 3.92%, respectively. Figure 9 As shown.

[0107] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A method for predicting the flexural strength of fiber-reinforced composite (FDM) samples, characterized in that: Includes the following steps: Step S1: Prepare and dry the fiber-reinforced composite material filaments for printing, level the printing base plate, and generate the G-Code of the printed sample. Step S2: Set up a temperature measurement platform device, fix the thermocouple at the starting position of the filling path of the first layer of printing, and directly contact the printing surface of the printing process to measure the temperature. Use a dynamic signal acquisition and analysis instrument to collect the thermocouple information at a set temperature acquisition time interval, and convert the digital signal into a real-time temperature curve graph and output it on the computer in real time. Step S2: Perform FDM printing and collect temperature data during the printing process; Step S3: Perform FDM printing on the fiber-reinforced composite material. Calculate the temperature t at different times using the following formula (1) based on the collected temperature data. i Bending strength value: Among them, T g The glass transition temperature of the printed fiber-reinforced composite material; t i T(t) represents the temperature measurement time. i ) represents different times t i The temperature; the time interval between different temperatures is 1 / N, where N is the temperature sampling frequency, t r The time it takes for the molecules of the printed fiber-reinforced composite material to reach the maximum interlayer adhesive strength is the time during which the material is above the glass transition temperature in the measurement. A and B are constants. Step S4, calculate the bending strength of the sample according to the following formula (2): Wherein F(t) i ,T(t i The value represents the bending strength of the printed part. For each time t i The bending strength value will be calculated for each printing time t. i The final bending strength value is obtained by summing the strength values.

2. The method for predicting the flexural strength of fiber-reinforced composite FDM samples according to claim 1, characterized in that: The fiber-reinforced composite material is a carbon fiber polyether ether ketone composite material or a carbon fiber reinforced polylactic acid composite material.

3. The method for predicting the flexural strength of fiber-reinforced composite FDM samples according to claim 1, characterized in that: In step S1, the printed fiber-reinforced composite material wire is placed in a vacuum drying oven for vacuum drying.

4. The method for predicting the flexural strength of fiber-reinforced composite FDM samples according to claim 3, characterized in that: In step S1, set the linear fill pattern with the required grating angle. Before the experiment begins, level the gap between the nozzle and the printing bed multiple times until a standard A4 sheet of paper can be moved. At the same time, apply glue to the base plate to ensure successful adhesion of the bottom layer.

5. The method for predicting the flexural strength of fiber-reinforced composite FDM samples according to claim 1, characterized in that: In step S2, during the temperature measurement process, the thermocouple is fixed at multiple points, and a gap of 0.1 to 0.2 mm is reserved after the printing base plate is leveled.

6. The method for predicting the flexural strength of fiber-reinforced composite FDM samples according to claim 1, characterized in that: In step S2, the temperature signal sampling frequency of the dynamic signal acquisition and analysis instrument is 25.6Hz.

7. The method for predicting the flexural strength of fiber-reinforced composite FDM samples according to any one of claims 1 to 6, characterized in that: In step S3, the bending strength values ​​at different times It is obtained through the following steps: Step S31, calculate the printing time t according to formula (3). i Intensity value Step S32: Determine the time t for the polymer molecules to reach maximum interlayer adhesive strength using the Arrhenius relation. r for: Where C1 and C2 are constants, and 3C24 = B; Step S33: Substitute formula (4) into formula (3) and extract t from the denominator. r From the power of 3 / 4, we can obtain formula (1).

8. The method for predicting the flexural strength of fiber-reinforced composite FDM samples according to claim 7, characterized in that: In step S3, constants A and B are obtained as follows: 1) Substituting into formula (1) into formula (2), we can obtain the predicted bending strength value F(t). i ,T(t i )) and interface temperature distribution T(t i ) and time t i The relationship is shown in formula (5): 2) Three-point bending measurements of a set of bent samples of the printing material and the polymer material's temperature change T(t) were selected. i ) and time t i The case was fitted with constants A and B until the temperature change T(t) was substituted. i ) and time t i Intensity prediction result F(t) i ,T(t i The predicted result of the three-point bending strength F Exp When the error is reduced to less than 2%, the fitting ends, and the obtained A and B results are substituted into formula (5).

9. The method for predicting the flexural strength of fiber-reinforced composite FDM samples according to claim 8, characterized in that: The specific fitting steps for constants A and B are as follows: ① First, fix the value of B and extract the value of A. Temporarily take B = 1 and substitute it into the printing time t. i and at each time t i Temperature T(t) i Solve Then F Exp and Solve for A by calculating the quotient; ② Substitute value A and change The value of B in the middle until The result is consistent with F. Exp The fitting process ends when the error is less than 2%.

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