A method for constructing a random model of fiber-matrix bond slip

Abstract

The present invention provides a method for constructing a random model of fiber-matrix bonding slip, and belongs to the technical field of composite materials. The method includes designing fiber burial depth and pull-out angle parameters, preparing bidirectional single fiber pull-out specimens, performing pull-out tests to obtain load-displacement data and draw curves, analyzing the curve eigenvalue data, simplifying the bonding-slip relationship into a three-fold line model, introducing Weibull random distribution and performing parameter estimation and testing on it, and finally establishing a functional relationship between Weibull random distribution parameters and fiber burial depth and pull-out angle. The present invention adopts the above-mentioned method for constructing a random model of fiber-matrix bonding slip, and the constructed model can generate its unique single fiber pull-out curve according to the characteristics of each fiber in the composite material, solving the problem that previous theoretical models are difficult to describe the randomness of single fiber pull-out.

Description

Technical Field

[0001] The invention relates to the technical field of composite materials, and in particular to a method for constructing a fiber-matrix bonding slip random model. Background Art

[0002] Ultra-high Ductile Concrete (UHDC) is a multiphase composite material composed of fibers, matrix and fiber-matrix interface. Its macroscopic mechanical properties are deeply affected by the properties of each component material and the internal microstructure characteristics. Given the complexity of the defect distribution of fibers and matrix inside UHDC, the interfacial bond-slip behavior between fibers and matrix exhibits strong random characteristics. However, previous studies often overlooked this key factor when constructing relevant models, relying on a large number of assumptions and simplifications for theoretical derivation, which made it difficult for deterministic theoretical models to accurately capture the randomness of the fiber pullout process.

[0003] In the theory of strain hardening material design, the interfacial bonding relationship between fiber and cement matrix is ​​crucial to understanding the tensile strain hardening performance and multi-crack cracking mode of composite materials. Single fiber pull-out test is an effective means to study the interfacial interaction between fiber and matrix. Although it can provide valuable data, the pull-out process involves many complex factors due to the influence of the random characteristics of the fiber and matrix themselves. Therefore, although the single fiber bond-slip model based on theoretical derivation introduces multiple assumptions to simplify the problem, it inevitably leads to deviations between theoretical results and actual conditions. The classical theoretical formula cannot provide a unique pull-out curve for each fiber, while the actual fiber pull-out process shows significant discreteness.

[0004] Although existing literature (such as Yang EH, Wang S, Yang Y, et al. Fiber-BridgingConstitutive Law of Engineered Cementitious Composites[J].ACT, 2008, 6(1):181-193.DOI:10.3151 / jact.6.181.) has attempted to consider various factors in the fiber pull-out process, such as fracture, bidirectional debonding and pull-out, Cook-Gordon effect, blocking effect and matrix peeling, in order to establish a single fiber pull-out theoretical model based on microscopic parameters, the complexity of fiber pull-out from the matrix still poses a severe challenge to model construction. The limitations of deterministic models in describing the randomness of fiber pull-out are becoming increasingly prominent. Summary of the invention

[0005] The purpose of the present invention is to provide a method for constructing a random model of fiber-matrix bonding slip, which can characterize the random distribution characteristics of the pull-out curve eigenvalues ​​using a probability density function based on experiments. Furthermore, by deriving the functional relationship between the Weibull random distribution parameters and the fiber burial depth and the pull-out angle, a single fiber pull-out random mechanical model based on mathematical statistics characteristics can be established. This model aims to more accurately reflect the randomness of the fiber pull-out process and provide a more realistic description of the fiber-matrix bonding slip behavior under various pulling conditions. This innovative method will provide important support for optimizing the composition design and performance prediction of UHDC.

[0006] To achieve the above object, the present invention provides a method for constructing a random model of fiber-matrix bonding slip, comprising the following steps:

[0007] Step S1, designing fiber embedding depth and fiber extraction angle parameters;

[0008] Step S2, preparing a bidirectional single fiber pull-out specimen based on the parameters designed in step S1;

[0009] Step S3, using the bidirectional single fiber pull-out specimen prepared in step S2, performing a bidirectional single fiber pull-out test, obtaining pull-out load-slip displacement data during the single fiber pull-out process and drawing a pull-out curve;

[0010] Step S4, analyzing the characteristic value data of the pull-out curve, and dividing the characteristic values ​​into debonding displacement, debonding force, peak displacement and peak force;

[0011] Step S5, according to the analysis of the pull-out curve characteristic value data in step S4, simplifying the bond-slip relationship of the single fiber pull-out cement matrix into a three-fold line model;

[0012] Step S6: Based on the three-fold line model, introduce Weibull random distribution to perform parameter estimation and test of eigenvalue Weibull random distribution;

[0013] Step S7: Establish Weibull proportional parameters With shape parameters About fiber embedding depth and extraction angle The functional relationship of .

[0014] Preferably, in step S1, the fiber embedding depth is In 0~ between, is the fiber length; fiber extraction angle Between 0~90°, with 0° being the straight pull-out angle.

[0015] Preferably, in step S3, the testing machine used for the bidirectional single fiber pull-out test is a universal testing machine.

[0016] Preferably, in step S5, the bond-slip relationship of pulling a single fiber out of a cement matrix is ​​simplified to a three-fold line model, comprising the following steps:

[0017] In the debonding stage, as the pull-out load of the single fiber increases, the single fiber and the cement matrix are continuously peeled off. When the peeling of the single fiber and the cement matrix develops to the buried depth of the single fiber, the relative slip between the single fiber and the cement matrix is ​​at a critical point, and the corresponding pull-out load and displacement are the debonding force and debonding displacement, respectively.

[0018] In the slip strengthening stage, the single fiber begins to be gradually pulled out of the cement matrix. Due to the interaction between the single fiber and the cement matrix, the load does not decrease immediately but shows an upward trend. The critical point of this stage is the peak point, and the corresponding force and displacement are the peak force and peak displacement respectively.

[0019] In the sliding pull-out stage, after reaching the peak force, the single fiber is pulled out by sliding with a constant interface friction coefficient, that is, as the displacement increases, the pull-out load decreases linearly until it reaches 0, and the single fiber is completely pulled out;

[0020] The three-fold line model is obtained according to the debonding point determined by the two eigenvalues ​​of debonding force and debonding displacement, and the peak point determined by the two eigenvalues ​​of peak force and peak displacement.

[0021] Preferably, in step S6, on the basis of the three-fold line model, Weibull random distribution is introduced to perform parameter estimation and test of eigenvalue Weibull random distribution, including the following steps:

[0022] The maximum likelihood estimation method was used to estimate the parameters of Weibull random distribution for debonding displacement, debonding force, peak displacement and peak force, and Matlab software was used for analysis and calculation;

[0023] The KS test method was used to test the Weibull random distribution of single fiber pull-out debonding force, debonding displacement, peak force and peak displacement.

[0024] Preferably, in step S7, a Weibull proportional parameter is established. With shape parameters About fiber embedding depth and extraction angle The functional relationship includes:

[0025] Establishing the Weibull scale parameter for the peak displacement Fiber burial depth and extraction angle The expression is:

[0026] ;

[0027] in, , , All represent undetermined coefficients;

[0028] Establishing the Weibull scaling parameter for peak force Fiber burial depth and extraction angle The expression is:

[0029] ;

[0030] in, , , All represent undetermined coefficients;

[0031] Weibull proportional parameter of debonding displacement Fiber burial depth The expression is:

[0032] ;

[0033] in, , All represent undetermined coefficients;

[0034] Weibull proportional parameter of debonding force Fiber burial depth The expression is:

[0035] ;

[0036] in, , All represent undetermined coefficients;

[0037] Weibull shape parameter of peak displacement Take the constant value according to the test;

[0038] Weibull shape parameters of peak force Fiber burial depth and extraction angle The expression is:

[0039] ;

[0040] in, , All represent undetermined coefficients; It represents the influencing parameter caused by the extraction angle, and the calculation formula is as follows:

[0041] ;

[0042] in, , All represent undetermined coefficients;

[0043] Weibull shape parameters of debonding displacement Take the constant value according to the test;

[0044] Weibull shape parameters of debonding force Take a constant value based on the experiment.

[0045] Therefore, the present invention adopts the above-mentioned method for constructing a random model of fiber-matrix bonding slip, and the beneficial technical effects are as follows: the present invention adopts a method for parameter fitting and testing of simplified model parameters using a random probability density function, taking into account the random characteristics of single fiber pullout, and deriving the Weibull random distribution parameter with respect to fiber embedding depth and extraction angle The obtained pull-out curve is simplified by the functional relationship of , and the model fitting results are highly consistent with the experimental data, which can be used to study the microstructural characteristics of composite materials. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 is a schematic diagram of the process of this method;

[0047] Figure 2 Schematic diagram of single fiber pull-out specimen;

[0048] Figure 3 A simplified model of three-fold lines is drawn for single fiber pullout;

[0049] Figure 4 is the bidirectional single fiber pull-out curve; where, Figure 4 (a) in the equation is L f / 6 curve; Figure 4 (b) in the equation is L f / 3 curve; Figure 4 (c) in L f / 2 curve.

[0050] Reference numerals

[0051] 1. Single fiber; 2. Polytetrafluoroethylene film; 3. Cement matrix. DETAILED DESCRIPTION

[0052] The technical solution of the present invention is further described below through the accompanying drawings and embodiments.

[0053] Unless otherwise defined, technical or scientific terms used in the present invention shall have the common meanings understood by one having ordinary skills in the field to which the present invention belongs.

[0054] Embodiment 1

[0055] like Figure 1 As shown, a method for constructing a random model of fiber-matrix bonding slip is provided. The accuracy and applicability of the method can be estimated and verified by measuring the actual values ​​of a single fiber pull-out test. The method comprises the following steps:

[0056] (1) Design the fiber embedment depth and fiber pull-out angle parameters.

[0057] 1) Set three fiber embedding depths : , , ; Indicates fiber length. This embodiment uses polyethylene fiber with a length of 18 mm.

[0058] 2) Set five fiber extraction angles : 0°, 15°, 30°, 45° and 60°.

[0059] 3) For each working condition, 40 groups of parallel tests are set up.

[0060] (2) Preparation of bidirectional single fiber pull-out specimens.

[0061] 1) placing the polytetrafluoroethylene film 2 in the groove of the single fiber extraction cement matrix mold according to the fiber embedding depth designed in step (1), at a distance of 3 mm, 6 mm, and 9 mm from the edge of the groove respectively;

[0062] 2) Pass the single fiber 1 through the polytetrafluoroethylene film 2 in the groove of the mold and fix it on the two side pillars to ensure that the single fiber 1 is straight and passes through the center of the groove;

[0063] 3) Pull the single fiber 1 out of the cement matrix 3 and assemble the mold to ensure the sealing and integrity of the mold;

[0064] 4) Accurately weigh raw materials such as cement, water, fly ash, quartz sand, etc. according to the proportion, stir evenly, and prepare a cement matrix mixture;

[0065] 5) Pour the cement matrix mixture into the mold, fill it to both sides of the polytetrafluoroethylene film 2 in the groove, use a tool to fill the groove with the mixture, continue pouring to the top of the mold, and smooth the surface; cast a total of 600 sets of test pieces according to the working conditions designed in step (1);

[0066] 6) The cast single fiber 1 is pulled out of the cement matrix mold and cured under standard conditions for 1 day before demolding. The curing is continued for 28 days. After demolding, a bidirectional single fiber pull-out specimen is obtained. Figure 2 .

[0067] (3) Bidirectional single fiber pull-out test.

[0068] According to the working conditions designed in different steps (1), single fiber pulling specimens with different buried depths are bonded and fixed at angles of 0°, 15°, 30°, 45° and 60° on a microcomputer-controlled electronic universal testing machine, and an external 5 kg load sensor is connected to record the pull-out load. The loading process adopts displacement loading control, and the loading is performed at a rate of 0.5 mm / min until the fiber is pulled out, and the displacement recorded by the universal testing machine is used as the sliding displacement.

[0069] Table 1 Bidirectional single fiber pull-out test results

[0070] ;

[0071] (4) Analyze the characteristic value data of the pull-out curve.

[0072] Analysis of straight single fiber pull-out curves: The pull-out curves all show obvious three-stage characteristics, namely the debonding stage, the slip strengthening stage and the slip pull-out stage.

[0073] The debonding stage is characterized by continuous peeling between the single fiber and the cement matrix. Due to the hydrophobicity of the polyethylene fiber interface, there is no chemical bonding between the polyethylene fiber and the cement matrix. The pull-out of the single fiber is only controlled by friction bonding. Therefore, there is no sudden drop in the debonding force after the debonding stage. Figure 4 The strengthening stage is when the single fiber is completely debonded and begins to be pulled out of the cement matrix. The pull-out load increases to a certain extent with the increase of the slip displacement, such as Figure 4 This is because the hardness of a single fiber is less than that of the surrounding matrix. When a single fiber is pulled out from the cement matrix, the interaction between the cement matrix and the single fiber interface causes severe scratches on the surface of the single fiber. At the same time, some hydration products are attached, which increases the friction of the interface and makes the pull-out curve show a certain upward trend. After the single fiber pull-out load reaches the peak value, it enters the sliding pull-out stage. At this time, as the sliding displacement continues to increase, the pull-out load continues to decrease, such as Figure 4 , until the fiber is completely pulled out.

[0074] Analysis of the angled single fiber pull-out curve: The angled single fiber pull-out curve can also be divided into three stages: debonding stage, slip strengthening stage, and slip pull-out stage. At the same fiber embedding depth, compared with the straight single fiber pull-out curve, the slip strengthening stage of the single fiber pull-out curve at a certain angle is more obvious. The displacement corresponding to the maximum pull-out load of the angle pull-out curve is significantly increased, and with the increase of the pull-out angle, the peak displacement tends to increase, as shown in Table 1. Correspondingly, the pull-out load also shows an upward trend with the increase of the pull-out angle, and the increase in the debonding force is somewhat improved, such as Figure 4 .

[0075] (5) Simplified single fiber pull-out curve model.

[0076] The pull-out process of a single fiber is simplified into three stages: the debonding stage, the sliding strengthening stage, and the sliding pull-out stage. In the debonding stage, as the pull-out load of the single fiber increases, the single fiber and the cement matrix continue to peel off. When the peeling between the single fiber and the cement matrix develops to the buried depth of the single fiber, the relative slip between the single fiber and the cement matrix is ​​at the critical point (debonding point), and the corresponding pull-out load and displacement are the debonding force and debonding displacement, respectively. In the sliding strengthening stage, the single fiber begins to be gradually pulled out of the cement matrix. Due to the interaction between the single fiber and the cement matrix, the load does not drop immediately but shows a certain upward trend. The critical point of this stage is the peak point, and the corresponding force and displacement are the peak force and peak displacement, respectively. In the sliding pull-out stage, after reaching the peak force, the single fiber is pulled out by sliding with a constant interface friction coefficient, that is, as the displacement increases, the pull-out load decreases linearly to 0, and the single fiber is completely pulled out. According to the debonding point determined by the two eigenvalues ​​of debonding force and debonding displacement, and the peak point determined by the two eigenvalues ​​of peak force and peak displacement, a simplified three-fold line model of single fiber pullout can be obtained, as shown in Figure 3 .

[0077] (6) Estimation and testing of parameters of eigenvalue Weibull random distribution.

[0078] 1) The maximum likelihood estimation method is used to estimate the parameters of Weibull random distribution, and Matlab software is used to analyze and calculate. The Weibull probability density parameters of the four eigenvalues ​​of debonding displacement, debonding force, peak displacement and peak force are obtained by analysis;

[0079] ;

[0080] in, represents sample data, represents the shape parameter, Represents the scale parameter.

[0081] 2) The Kolmogorov-Smirnov (KS) test method was used to test the Weibull random distribution of the single fiber pull-out characteristic values ​​(debonding displacement, debonding force, peak displacement and peak force in Table 1); the Kolmogorov-Smirnov (KS) expression is:

[0082] ;

[0083] in, represents the theoretical sequence value of the sample, Represents the observed sequence value.

[0084] 3) The Weibull random distribution parameters of the four eigenvalues ​​are obtained based on parameter estimation, and the distribution test is performed using the following command of Matlab software:

[0085] pd=makedist['Weibull','k','λ'];

[0086] In the command: 'pd' means to store the probability distribution object created by makedist. The makedist function is used to create a probability distribution object; 'Weibull' means the created distribution type is Weibull distribution; 'k' and 'λ' represent the shape parameter and scale parameter of Weibull respectively.

[0087] [h,p,k,c]=kstest[x,'cdf',pd,'alpha',0.05];

[0088] In the command: [h,p,k,c], h represents the test conclusion (0 means pass, 1 means fail), p represents the probability of the observed sample data when the null hypothesis is true, k represents the Kolmogorov-Smirnov (KS) statistic, and c represents the critical value of the KS statistic at a given significance level. The kstest function is used to perform the Kolmogorov-Smirnov (KS) test to test whether the sample data follows the Weibull distribution; x Represents the sample data to be tested; 'cdf ' specifies that the distribution type to be tested is the cumulative distribution function (CDF), which is used here with 'pd' to indicate that the cumulative distribution function of the Weibull distribution represented by 'pd' is used as the theoretical distribution function of the test; 'alpha', 0.05 specifies that the significance level of the test is 0.05, that is, if the null hypothesis is true, there is a 5% probability of incorrectly rejecting the null hypothesis.

[0089] Test results: The debonding force and debonding displacement, peak force and peak displacement all passed the Weibull random distribution test.

[0090] (7) Establish Weibull proportional parameters and shape parameters About fiber embedding depth and extraction angle Functional relationship:

[0091] First, establish the Weibull scale parameter About fiber embedding depth and extraction angle The function expression of .

[0092] 1) Weibull scale parameter of peak displacement and and The sine value of shows a more obvious linear relationship.

[0093] The weight factor of the data volume under each working condition is introduced. The linear numerical regression parameters are solved using the fminsearch function, and the obtained values ​​are as follows:

[0094] =0.0612, =0.832, =0.3218;

[0095] Therefore, the Weibull scale parameter of the peak displacement is The expression is:

[0096] ;

[0097] 2) Weibull proportional parameter of peak force Fiber burial depth and extraction angle The sine value of is also in an obvious linear relationship. Using the fminsearch function to solve the linear numerical regression parameters, the values ​​obtained are as follows:

[0098] =0.0612, =3.3251, =0.2367;

[0099] Therefore, the Weibull proportionality parameter of the peak force is The expression is:

[0100] ;

[0101] 3) The single fiber pull-out debonding displacement data is highly discrete. In order to avoid the problem of overfitting, the Weibull proportional parameter of the debonding displacement only considers the fiber burial depth length. Simple linear regression of the Weibull proportional parameter of the debonding displacement Fiber embedment length It shows a simple linear relationship, and the fitted function expression is:

[0102] ;

[0103] 4) Weibull proportional parameter of debonding force Fiber embedment length It shows a simple linear relationship, and the fitted function expression is:

[0104] ;

[0105] Then the Weibull shape parameters of peak displacement, peak force, debonding displacement and debonding force are established About fiber embedding depth and extraction angle The function expression of .

[0106] 1) Weibull shape parameter of peak displacement Take the constant according to the test value:

[0107] ;

[0108] 2) Weibull shape parameters of peak force Consider fiber embedment depth and extraction angle The Weibull shape parameters are calculated independently. About the extraction angle The fitted regression of Then the fiber embedment length The fitting regression results are as follows:

[0109] =0.8963, =2.6622, =0.1415, =2.658;

[0110] Weibull shape parameters of peak force Fiber embedment length and extraction angle The expression is:

[0111] ;

[0112] 3) Weibull shape parameters of debonding displacement Due to the large dispersion of data, Take it as a constant:

[0113] ;

[0114] 4) Weibull distribution shape parameters of debonding force Take it as a constant:

[0115] ;

[0116] It is worth noting that the contents not elaborated in detail in the present invention are all prior art and are well known to those skilled in the art.

[0117] Therefore, the present invention adopts the above-mentioned method for constructing a random fiber-matrix bond slip model. The constructed model can generate a unique single fiber pull-out curve according to the characteristics of each fiber in the composite material, solving the problem that previous theoretical models are difficult to describe the randomness of single fiber pull-out.

[0118] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A method for constructing a random fiber-matrix bond slip model, characterized in that: The following steps are involved: Step S1, designing fiber embedding depth and fiber extraction angle parameters; Step S2, preparing a bidirectional single fiber pull-out specimen based on the parameters designed in step S1; Step S3, using the bidirectional single fiber pull-out specimen prepared in step S2, performing a bidirectional single fiber pull-out test, obtaining load-displacement data during the single fiber pull-out process and drawing a pull-out curve; Step S4, analyzing the characteristic value data of the pull-out curve, and dividing the characteristic values ​​into debonding displacement, debonding force, peak displacement and peak force; Step S5, according to the analysis of the pull-out curve characteristic value data in step S4, simplifying the bond-slip relationship of the single fiber pull-out cement matrix into a three-fold line model; Step S6: Based on the three-fold line model, introduce Weibull random distribution to perform parameter estimation and test of eigenvalue Weibull random distribution; Step S7: Establish Weibull proportional parameters With shape parameters About fiber embedding depth and extraction angle The functional relationship includes: Establishing the Weibull scale parameter for the peak displacement Fiber burial depth and extraction angle The expression is: ； in, , , All represent undetermined coefficients; Establishing the Weibull scaling parameter for peak force Fiber burial depth and extraction angle The expression is: ； in, , , All represent undetermined coefficients; Weibull proportional parameter of debonding displacement Fiber burial depth The expression is: ； in, , All represent undetermined coefficients; Weibull proportional parameter of debonding force Fiber burial depth The expression is: ； in, , All represent undetermined coefficients; Weibull shape parameter of peak displacement Take the constant value according to the test; Weibull shape parameters of peak force Fiber burial depth and extraction angle The expression is: ； in, , All represent undetermined coefficients; It represents the influencing parameter caused by the extraction angle, and the calculation formula is as follows: ； in, , All represent undetermined coefficients; Weibull shape parameters of debonding displacement Take the constant value according to the test; Weibull shape parameters of debonding force Take a constant value based on the experiment.

2. The method for constructing a random fiber-matrix bonding slip model according to claim 1, characterized in that: In step S1, the fiber embedding depth In 0~ between, is the fiber length; fiber extraction angle Between 0~90°, with 0° being the straight pull-out angle.

3. The method for constructing a random fiber-matrix bonding slip model according to claim 1, characterized in that: In step S3, the testing machine used for the bidirectional single fiber pull-out test is a universal testing machine.

4. The method for constructing a random fiber-matrix bond slip model according to claim 1, characterized in that: In step S5, the bond-slip relationship of a single fiber pulled out of a cement matrix is ​​simplified to a three-fold line model, including the following steps: In the debonding stage, as the pull-out load of the single fiber increases, the single fiber and the cement matrix are continuously peeled off. When the peeling of the single fiber and the cement matrix develops to the buried depth of the single fiber, the relative slip between the single fiber and the cement matrix is ​​at a critical point, and the corresponding pull-out load and displacement are the debonding force and debonding displacement, respectively. In the slip strengthening stage, the single fiber begins to be gradually pulled out of the cement matrix. Due to the interaction between the single fiber and the cement matrix, the load does not decrease immediately but shows an upward trend. The critical point of this stage is the peak point, and the corresponding force and displacement are the peak force and peak displacement respectively. In the sliding pull-out stage, after reaching the peak force, the single fiber is pulled out by sliding with a constant interface friction coefficient, that is, as the displacement increases, the pull-out load decreases linearly until it reaches 0, and the single fiber is completely pulled out; The three-fold line model is obtained according to the debonding point determined by the two eigenvalues ​​of debonding force and debonding displacement, and the peak point determined by the two eigenvalues ​​of peak force and peak displacement.

5. The method for constructing a random fiber-matrix bond slip model according to claim 1, characterized in that: In step S6, based on the three-fold line model, the Weibull random distribution is introduced to perform parameter estimation and testing of the eigenvalue Weibull random distribution, including the following steps: The maximum likelihood estimation method was used to estimate the parameters of Weibull random distribution for debonding displacement, debonding force, peak displacement and peak force, and Matlab software was used for analysis and calculation; The KS test method was used to test the Weibull random distribution of single fiber pull-out debonding force, debonding displacement, peak force and peak displacement.

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