A method for predicting fatigue life of asphalt mixture

Abstract

The application discloses a kind of asphalt mixture fatigue life prediction methods, comprising the following steps: S1, making the standard test piece of asphalt mixture;S2, the three-point bending fatigue test of asphalt mixture under different stress levels is carried out to the standard test piece made under the setting parameter;S3, according to the stress-strain hysteresis curve of asphalt mixture is fitted to test data;S4, the accuracy of the stress-strain hysteresis curve obtained is verified;S5, based on the hysteresis curve, the fatigue damage variable of asphalt mixture is constructed;S6, the fatigue life prediction model of asphalt mixture is constructed.The method of the application avoids the defect that the relative change rate of dissipation energy is the discrete index data of prediction fatigue life, so as to improve the prediction accuracy of asphalt mixture fatigue life, the model construction step is less, form is simple, and has higher practical value.

Description

Technical Field

[0001] This invention relates to the field of asphalt life prediction technology, specifically a method for predicting the fatigue life of asphalt mixtures. Background Technology

[0002] Fatigue failure or fatigue cracking of asphalt mixtures is one of the major defects of asphalt pavements. Researching the fatigue damage characteristics of asphalt mixtures and establishing methods for predicting their fatigue life can help predict the fatigue life of asphalt mixtures, further optimize material design, and improve their fatigue resistance. Asphalt mixtures are viscoelastic materials. Under repeated loading and unloading, the stress-strain curves cannot completely coincide, forming hysteresis loops and continuously generating energy dissipation. Eventually, fatigue failure occurs when the accumulated dissipated energy reaches a certain level. Currently, when analyzing the fatigue performance of asphalt mixtures from an energy perspective, most studies use the area enclosed by the stress-strain curves to represent the rate of change of dissipated energy as an index to evaluate and predict the fatigue life of asphalt mixtures. However, this approach suffers from drawbacks such as discrete data on the rate of change of dissipated energy and low accuracy in fatigue life prediction.

[0003] Currently, when analyzing the fatigue performance of asphalt mixtures from an energy perspective, most studies use the area enclosed by the stress-strain curve to represent the rate of change of dissipated energy as an index to evaluate and predict the fatigue life of asphalt mixtures. However, this approach suffers from drawbacks such as discrete data on the rate of change of dissipated energy and low accuracy in fatigue life prediction. Summary of the Invention

[0004] The purpose of this invention is to address the above shortcomings by providing a method for predicting the fatigue life of asphalt mixtures based on the rate of change of hysteresis curve morphology parameters, thereby solving the defects of data dispersion of dissipation energy change rate index and low accuracy of fatigue life prediction.

[0005] The technical solution adopted in this invention is:

[0006] A method for predicting the fatigue life of asphalt mixtures includes the following steps:

[0007] S1. Prepare standard specimens for asphalt mixtures;

[0008] S2. Under the set parameters, conduct three-point bending fatigue tests on the prepared standard specimens of asphalt mixtures under different stress levels.

[0009] S3. Fit the stress-strain hysteresis curve of the asphalt mixture based on the test data;

[0010] S4. Verify the accuracy of the obtained stress-strain hysteresis curve;

[0011] S5. Construct fatigue damage variables for asphalt mixtures based on the hysteresis curves;

[0012] S6. Construct a fatigue life prediction model for asphalt mixtures.

[0013] As a further optimization, in step S1 of the present invention, the standard specimen is required to be a prism beam with a length of 250mm±2.0mm, a width of 30mm±2mm, and a height of 35mm±2mm, cut after being formed by roller rolling, and its span is 200mm±5mm.

[0014] As a further optimization, in step S2 of the present invention, the set parameters are a single loading frequency of 10Hz and a single test temperature of 15℃.

[0015] As a further optimization, in step S2 of the present invention, when conducting the three-point bending fatigue test of the asphalt mixture, the load, displacement at the mid-span position of the specimen and the number of times the load is applied when the specimen breaks are recorded in each test, and the number of times the load is applied when the specimen breaks is taken as the fatigue life of the asphalt mixture.

[0016] The conversion formula for the recorded measured bending tensile stress is as follows:

[0017]

[0018] The recorded displacement parameters are converted into bending tensile strain using the following formula:

[0019]

[0020] Where: σ m —Measured bending tensile stress (MPa);

[0021] ε m —Measured bending tensile strain;

[0022] d—Specimen span (mm);

[0023] F — Measured load (N);

[0024] b — Width of the cross-interruption interview piece (mm);

[0025] h — Height of the inter-interruption interview piece (mm);

[0026] l — Mid-span displacement of the specimen (mm).

[0027] As a further optimization, in step S3 of the present invention, curve fitting is performed using Matlab software based on flexural stress and flexural strain to obtain the stress-strain hysteresis curve of the asphalt mixture, and the morphological parameters of the hysteresis curve are obtained: major axis, minor axis, center point coordinates, and the angle between the major axis and the x-axis of the coordinate system.

[0028] As a further optimization, step S4 of the present invention, the process of verifying the accuracy of the obtained stress-strain hysteresis curve, includes the following steps:

[0029] S41. Calculate the relationship between the abscissa of the center point of the hysteresis curve and the theoretical bending tensile strain. The calculation formula is as follows:

[0030]

[0031]

[0032]

[0033]

[0034] Where: A, B, C — process parameters;

[0035] a—the major axis of the hysteresis curve;

[0036] b—the minor axis of the hysteresis curve;

[0037] θ — the angle (in radians) between the major axis a and the x-axis;

[0038] x0 — x-coordinate of the center point of the hysteresis curve;

[0039] ε t —Theoretical bending strain;

[0040] S42. The error between the theoretical bending tensile strain and the measured bending tensile strain is calculated using the following formula:

[0041]

[0042] Where: ε t —Theoretical bending strain;

[0043] ε m —Measured bending tensile strain;

[0044] V err ors——ε t With ε m The error value;

[0045] S43. When the curve showing the relationship between theoretical bending tensile strain and measured bending tensile strain is distributed near the 45° contour line, it indicates the accuracy of the fitted hysteresis curve.

[0046] As a further optimization, in step S56 of the present invention, the fatigue damage variable of asphalt mixture fatigue is constructed based on the abscissa of the center point of the hysteresis curve, and its calculation formula is as follows:

[0047]

[0048] Where: D—fatigue damage variable;

[0049] x 0-n —The x-coordinate of the center point of the hysteresis curve in the nth period;

[0050] x 0-n+1 — The x-coordinate of the center point of the hysteresis curve in the (n+1)th period.

[0051] As a further optimization, in step S6 of the present invention, the relationship curve between fatigue damage variable and loading period is first constructed: the ratio of load period to fatigue life is used as the abscissa and the fatigue life variable is used as the ordinate to construct the relationship curve between fatigue damage variable and loading period, and the relationship curve between fatigue damage variable and loading period is divided into three stages in sequence.

[0052] As a further optimization, the present invention divides the relationship curve between fatigue damage variables and loading cycles into three stages: The relationship curve between fatigue damage variables and loading cycles is established, and the fatigue life variable value for adjacent cycles is calculated using the following formula:

[0053]

[0054] Where: D n — Fatigue damage variables in the nth period;

[0055] D n+1 — Fatigue damage variables in the (n+1)th cycle;

[0056] V errors —The error value between the fatigue damage variable in the (n+1)th cycle and the fatigue damage variable in the nth cycle; when V errors If the ratio is less than 15%, the ratio of the load cycle to the fatigue life at this point is taken as the dividing point of the three stages, and the point value of the intermediate smooth stage is taken as the effective value.

[0057] As a further optimization, this invention obtains the fatigue damage variable values ​​at points during the smoothing phase, calculates the average value of these fatigue damage variable values, and constructs a relationship model between the average fatigue damage variable value and fatigue life. This relationship model is the fatigue life prediction model for asphalt-hybrid beams, and its expression is:

[0058] D average =f(N) f )

[0059] Where: D average —The average value of fatigue injury variable

[0060] N f — Fatigue lifespan.

[0061] The present invention has the following advantages:

[0062] The method of this invention avoids the defect of discrete data in predicting fatigue life index when the relative change rate of dissipated energy is not high, thereby improving the prediction accuracy of fatigue life of asphalt mixtures. The model construction steps are fewer and the form is simple, which has high practical value. Attached Figure Description

[0063] To more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0064] The present invention will be further described below with reference to the accompanying drawings:

[0065] Figure 1 Theoretical bending tensile strain ε t Compared with the measured bending tensile strain ε m Relationship curve;

[0066] Figure 2 The fatigue damage variable D and the loading period N / N f Relationship curve;

[0067] Figure 3 The mean D of the fatigue damage variable average With fatigue life N f Relationship curve;

[0068] Figure 4 P is the mean rate of change of dissipated energy. average With fatigue life N f Relationship curve;

[0069] Figure 5 The error values ​​are the fatigue damage variable D and the rate of change of dissipated energy P between adjacent cycles. Detailed Implementation

[0070] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments are not intended to limit the present invention. In the absence of conflict, the embodiments of the present invention and the technical features in the embodiments can be combined with each other.

[0071] It should be understood that in the description of the embodiments of the present invention, terms such as "first" and "second" are used only for descriptive purposes and should not be construed as indicating or implying relative importance, nor as indicating or implying order. In the embodiments of the present invention, "multiple" refers to two or more.

[0072] In this embodiment of the invention, "and / or" is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, B existing alone, or both A and B existing simultaneously. Furthermore, in this document, the character " / " generally indicates that the preceding and following related objects have an "or" relationship.

[0073] This embodiment provides a method for predicting the fatigue life of asphalt mixtures, including the following steps:

[0074] S1. Prepare standard specimens for asphalt mixtures;

[0075] The test procedure in this embodiment mainly refers to the requirements of the bending test of asphalt mixture in T0715-2011 of the "Test Procedure for Asphalt and Asphalt Mixtures in Highway Engineering" (JTGE20—2011). Therefore, the required standard specimen of asphalt mixture is a prism beam with a length of 250mm±2.0mm, a width of 30mm±2mm, and a height of 35mm±2mm, cut after being formed by roller rolling, and its span is 200mm±5mm.

[0076] S2. Under the set parameters, conduct three-point bending fatigue tests on the prepared standard specimens of asphalt mixtures under different stress levels.

[0077] According to the conventional settings, the setting parameters are a single loading frequency of 10Hz and a single test temperature of 15℃. Setting the loading frequency to 10Hz is closer to the actual use of the road surface. At this temperature value, the state of the asphalt mixture is more stable and it is more suitable for most use environments. The stress level is preferentially set to level four, that is, four sets of tests are conducted.

[0078] When conducting a three-point bending fatigue test on asphalt mixtures, record the load F, displacement l at the mid-span of the specimen, and the number of load applications at the time of specimen fracture in each test. The number of load applications at the time of specimen fracture is taken as the fatigue life N of the asphalt mixture. f ;

[0079] The recorded measured load F-parameters are converted into bending tensile stress using the following formula:

[0080]

[0081] The recorded displacement l parameter is converted into bending tensile strain using the following formula:

[0082]

[0083] Where: σ m —Measured bending tensile stress (MPa);

[0084] ε m —Measured bending tensile strain;

[0085] d—Specimen span (mm);

[0086] F — Measured load (N);

[0087] b — Width of the cross-interruption interview piece (mm);

[0088] h — Height of the inter-interruption interview piece (mm);

[0089] l — Mid-span displacement of the specimen (mm).

[0090] S3. Fit the stress-strain hysteresis curve of the asphalt mixture based on the test data;

[0091] In this process, an algorithm was developed using Matlab software. Based on the bending tensile stress and bending tensile strain, curve fitting was performed to obtain the stress-strain hysteresis curve of the asphalt mixture. The morphological parameters of the hysteresis curve were also obtained: major axis a, minor axis b, center point coordinates, and the angle θ between major axis a and the x-axis of the coordinate system.

[0092] S4. Verify the accuracy of the obtained stress-strain hysteresis curve;

[0093] The process of verifying the accuracy of the obtained stress-strain hysteresis curves in this project includes the following steps:

[0094] S41. Calculate the relationship between the abscissa of the center point of the hysteresis curve and the theoretical bending tensile strain. The calculation formula is as follows:

[0095]

[0096]

[0097]

[0098]

[0099] Where: A, B, C — process parameters;

[0100] a—the major axis of the hysteresis curve;

[0101] b—the minor axis of the hysteresis curve;

[0102] θ — the angle (in radians) between the major axis a and the x-axis;

[0103] x0 — x-coordinate of the center point of the hysteresis curve;

[0104] ε t —Theoretical bending strain;

[0105] S42. Calculate the error between the theoretical bending tensile strain and the measured bending tensile strain. The calculation formula is as follows:

[0106]

[0107] Where: ε t —Theoretical bending strain;

[0108] ε m —Measured bending tensile strain;

[0109] V errors ——ε t With ε m The error value;

[0110] S43, when the theoretical bending strain ε t Compared with the measured bending tensile strain ε m When the relationship curve is distributed near the 45° contour line, it indicates that the fitted hysteresis curve is accurate.

[0111] S5. Construct the fatigue damage variable D of the asphalt mixture based on the hysteresis curve;

[0112] In this process, the fatigue damage variable of asphalt mixture fatigue is constructed based on the abscissa of the center point of the hysteresis curve, and its calculation formula is as follows:

[0113]

[0114] Where: D—fatigue damage variable;

[0115] x 0-n —The x-coordinate of the center point of the hysteresis curve in the nth period;

[0116] x 0-n+1 —The x-coordinate of the center point of the hysteresis curve in the (n+1)th period;

[0117] S6. Construct a fatigue life prediction model for asphalt mixtures;

[0118] In this process, the relationship curve between fatigue damage variables and loading period is first constructed: the ratio of load period to fatigue life is used as the horizontal axis and the fatigue life variable is used as the vertical axis to construct the relationship curve between fatigue damage variables and loading period, and the relationship curve between fatigue damage variables and loading period is divided into three stages in sequence.

[0119] The relationship curve between fatigue damage variables and loading cycles is divided into three stages: The fatigue life variable value for adjacent cycles is calculated using the established relationship curve between fatigue damage variables and loading cycles. The calculation formula is as follows:

[0120]

[0121] Where: D n — Fatigue damage variables in the nth period;

[0122] D n+1 — Fatigue damage variables in the (n+1)th cycle;

[0123] V errors —The error value between the fatigue damage variable in the (n+1)th cycle and the fatigue damage variable in the nth cycle;

[0124] When V errors If the value is less than 15%, the ratio of the load cycle to the fatigue life at this point is taken as the dividing point of the three stages. The three stages represent the changes in the entire loading process of the specimen. Since the first stage and the third stage correspond to the initial and final stages of loading, the changes in the specimen are quite different in these two stages. The changes in the second stage are more uniform. Therefore, the point value of the second stage is taken as the effective value.

[0125] Obtain the fatigue damage variable values ​​D at points during the smoothing phase, and calculate the average value D of these fatigue damage variable values. average Construct the average value D of fatigue damage variable average With fatigue life N f The relationship model, that is, the average value D of fatigue damage variables from multiple sets of experiments. average With fatigue life N f The point values ​​are sequentially marked in the coordinate system, and a fitting curve is plotted based on these point values. This forms the fatigue life prediction model for asphalt-mixed beams, and its expression is:

[0126] D average =f(N) f )

[0127] Where: D average —The average value of fatigue injury variable

[0128] N f — Fatigue lifespan.

[0129] The following specific example will further illustrate this embodiment:

[0130] S1. Conduct three-point bending fatigue tests on epoxy asphalt mixture beams;

[0131] In this experiment, the stress ratios used were 0.3, 0.4, 0.5, and 0.6, the test temperature was 15℃, and the loading frequency was 10Hz. The number of load cycles at which the specimen fractured was taken as the fatigue life N of the asphalt mixture. fThe results are summarized in Table 1 (where P represents the rate of change of dissipated energy, used to compare the technical effects of this embodiment). During the experiment, the load F and displacement l parameters at the mid-span of the small beam specimen were collected, and according to the aforementioned formula, the load F and displacement l parameters were converted into the measured bending tensile stress σ. m and bending tensile strain ε m .

[0132] Stress ratio <![CDATA[N f ]]> <![CDATA[D average ]]> <![CDATA[P average ]]> 0.6 586 0.0311 0.0063 0.5 1227 0.0207 0.0035 0.4 2523 0.0140 0.0044 0.3 5390 0.0095 0.0020

[0133] Table 1

[0134] S2. Based on the above experimental data, use Matlab to develop an algorithm to fit the stress-strain hysteresis curve and obtain the x-coordinate of the center point of the hysteresis curve x0.

[0135] S3. Verify the accuracy of the obtained stress-strain hysteresis curve using the aforementioned formula;

[0136] Plot the measured bending tensile strain ε m Calculation of bending tensile strain ε t Relationship curves as follows Figure 1 As shown in the figure, the data points of both algorithms are evenly and closely distributed near the 45° contour line, indicating that the Matlab algorithm is reliable and accurate.

[0137] S4. Construct fatigue damage variables;

[0138] Using the aforementioned calculation formula, the rate of change D of the coordinates x0 of the hysteresis curve center point is calculated as the damage variable of the asphalt mixture, and D ~ N / N is plotted. f Relationship curves as follows Figure 2 As shown, calculate the D value for adjacent periods using the aforementioned formula. Then, assign D to N / N. f The curve is divided into three phases: Phase I, Phase II, and Phase III. When D n+1 and D n Error value V at time errors When it is less than 15%, change the N / N ratio at this point. f Using these as the dividing points for Phase I to Phase II and Phase II to Phase III respectively, the average value of D in Phase II was obtained. average The results are summarized in Table 1 (see step S1).

[0139] S5. Construct a fatigue life prediction model for asphalt mixtures. Using N... f D is the x-axis. average Plot D with the vertical axis as the ordinate. average ~N f Relationship curves as follows Figure 3 As shown, D is constructed. average ~N fThe relational model, i.e., the fatigue life prediction model for asphalt mixtures, has its fitting parameters and accuracy summarized in Table 2. R 2 =0.94735, proving that the model has high accuracy and reliability.

[0140] D average ~N f The fitting parameters for the relational model are shown below:

[0141] D average =KLn(N f )+M

[0142] Where: K and M are both setting parameters;

[0143] Ln is the logarithm with the constant e as the base.

[0144] <![CDATA[D average ]]> <![CDATA[P average ]]> A -0.00968 -0.00164 B 0.09119 -0.00164 <![CDATA[R 2 ]]> 0.94735 0.63524

[0145] Table 2

[0146] To compare with the rate of change of dissipated energy P average To account for the differences in fatigue prediction models, the area under the hysteresis curve under each repeated load is obtained, which represents the dissipated energy S for each fatigue life cycle. The rate of change of dissipated energy P is calculated using the following formula.

[0147]

[0148] According to the above determination, D average Method to obtain P average D average ~N f Relationship curves as follows Figure 4 As shown, the fatigue life N is constructed. f The relationship model, i.e., the fatigue life prediction model of asphalt mixture, is obtained. The fitting parameters and accuracy are summarized in Table 2. R 2 =0.63524. A comparison shows that in this embodiment, D... average The reliability of the fatigue prediction model based on the index is significantly higher than that of the dissipation energy change rate P. average To assess the reliability of fatigue prediction models for indicators.

[0149] P average =KLn(N f )+M

[0150] To compare the dispersion of D and P values ​​in Phase II, the relative error values ​​of D and P in adjacent periods were calculated and plotted. Figure 5 As can be seen from the figure, the data dispersion of P is significantly greater than that of D, which gives rise to the P of Phase II. averageThe selection of these values ​​introduces significant uncertainty, thereby reducing the accuracy of fatigue life prediction for asphalt mixtures. In summary, the fatigue life prediction method for asphalt mixtures based on the rate of change of hysteresis curve morphology parameters proposed in this invention is more reliable and accurate.

Claims

1. A method for predicting the fatigue life of asphalt mixtures, characterized in that: Includes the following steps: S1. Prepare standard specimens for asphalt mixtures; S2. Under the set parameters, conduct three-point bending fatigue tests on the prepared standard specimens of asphalt mixtures under different stress levels. S3. Fit the stress-strain hysteresis curve of the asphalt mixture based on the test data; S4. Verify the accuracy of the obtained stress-strain hysteresis curve; S5. Construct fatigue damage variables for asphalt mixtures based on the hysteresis curves; S6. Construct a fatigue life prediction model for asphalt mixtures; In step S5, the fatigue damage variable of asphalt mixture fatigue is constructed based on the abscissa of the center point of the hysteresis curve, and its calculation formula is as follows: D = ； in: D —Fatigue injury variables; x 0-n —The x-coordinate of the center point of the hysteresis curve in the nth period; x 0-n+1 —The x-coordinate of the center point of the hysteresis curve in the (n+1)th period; In step S6, the relationship curve between fatigue damage variables and loading period is first constructed: the ratio of load period to fatigue life is used as the horizontal axis and the fatigue life variable is used as the vertical axis to construct the relationship curve between fatigue damage variables and loading period, and the relationship curve between fatigue damage variables and loading period is divided into three stages in sequence. The relationship curve between fatigue damage variables and loading cycles is divided into three stages: The fatigue life variable value for adjacent cycles is calculated using the established relationship curve between fatigue damage variables and loading cycles. The calculation formula is as follows: V errors = 100% ； Where: D n — Fatigue damage variable in the nth period; D n+1 — Fatigue damage variables in the (n+1)th cycle; V errors —The error value between the fatigue damage variable in the (n+1)th cycle and the fatigue damage variable in the nth cycle; when V errors If it is less than 15%, the ratio of the load cycle to the fatigue life at this point is taken as the dividing point of the three stages, and the point value of the intermediate smoothing stage is taken as the effective value. Obtain the fatigue damage variable values ​​at points during the smoothing phase, calculate the average of these fatigue damage variable values, and construct a relationship model between the average fatigue damage variable value and fatigue life. This relationship model is the fatigue life prediction model for asphalt-hybrid beams, and its expression is: D average =f(N f ) ； in: D average —The average value of fatigue injury variable N f — Fatigue lifespan.

2. The method for predicting the fatigue life of asphalt mixtures according to claim 1, characterized in that: In step S1, the standard specimen is required to be a prism beam with a length of 250mm±2.0mm, a width of 30mm±2mm, and a height of 35mm±2mm, cut after being formed by roller rolling, and its span is 200mm±5mm.

3. The method for predicting the fatigue life of asphalt mixtures according to claim 1, characterized in that: In step S2, the set parameters are a single loading frequency of 10Hz and a single test temperature of 15℃.

4. The method for predicting the fatigue life of asphalt mixtures according to claim 1, characterized in that: In step S2, when conducting the three-point bending fatigue test on the asphalt mixture, the load, displacement at the mid-span of the specimen and the number of times the load was applied when the specimen fractured were recorded in each test, and the number of times the load was applied when the specimen fractured was taken as the fatigue life of the asphalt mixture. The conversion formula for the recorded measured bending tensile stress is as follows: σ m = ； The recorded displacement parameters are converted into bending tensile strain using the following formula: ε m = ； in: σ m —Measured bending tensile stress; ε m —Measured bending tensile strain; d —Specimen span; F —Measured load; b — Width of the inter-interview document; h —Height of the inter-interruption interview document; l — Mid-span displacement of the specimen.

5. The method for predicting the fatigue life of asphalt mixtures according to claim 4, characterized in that: In step S3, the stress-strain hysteresis curve of the asphalt mixture is obtained by curve fitting based on the bending tensile stress and bending tensile strain using Matlab software, and the morphological parameters of the hysteresis curve are obtained: major axis, minor axis, center point coordinates, and the angle between the major axis and the x-axis of the coordinate system.

6. The method for predicting the fatigue life of asphalt mixtures according to claim 5, characterized in that: Step S4, verifying the accuracy of the obtained stress-strain hysteresis curve, includes the following steps: S41. Calculate the relationship between the abscissa of the center point of the hysteresis curve and the theoretical bending tensile strain. The calculation formula is as follows: ； ； ； ； in: A, B, C —Process parameters; a —The major axis of the hysteresis curve; b —The minor axis of the hysteresis curve; θ —Long axis a and x The included angle of the axis; x 0 — x-coordinate of the center point of the hysteresis curve; ε t —Theoretical bending strain; S42. The error between the theoretical bending tensile strain and the measured bending tensile strain is calculated using the following formula: V errors = 100% ； in: ε t —Theoretical bending strain; ε m —Measured bending tensile strain; V errors —— ε t and ε m The error value; S43. When the curve showing the relationship between theoretical bending tensile strain and measured bending tensile strain is distributed near the 45° contour line, it indicates the accuracy of the fitted hysteresis curve.

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