Self-sensing CFRP plate reinforced steel structure fatigue crack analysis and crack monitoring and identification method

Abstract

The present invention relates to a self-sensing CFRP plate reinforced steel structure fatigue crack analysis and crack monitoring and identification method, constructs a CFRP plate reinforced steel structure fatigue crack analysis model, selects a micro-segment corresponding to a CFRP plate at any crack position to establish a force balance equation, obtains a first relationship between the axial deformation of the CFRP plate and the shear stress at the interface between the CFRP plate and the adhesive layer; obtains a second relationship between the shear stress at the interface between the steel structure matrix and the adhesive layer and the axial deformation of the CFRP plate; obtains a third relationship between the axial deformation of the steel structure matrix, the shear deformation of the adhesive layer, the crack opening displacement and the far-field nominal strain of the steel structure matrix, and uses the constitutive relationship of the adhesive layer as the fourth relationship to obtain a crack opening displacement-strain analysis model in the elastic stage and the softening stage of the adhesive layer. Based on the obtained crack opening displacement-strain analysis model, crack monitoring and length growth identification of the CFRP plate reinforced steel structure are realized, so that it is easier to grasp the crack development status of the steel structure after CFRP plate reinforcement.

Description

Technical Field

[0001] The present invention relates to the technical field of steel structure crack analysis and monitoring, and in particular to a self-sensing CFRP plate reinforced steel structure fatigue crack analysis and crack monitoring and identification method. Background Art

[0002] At present, steel structures have become an indispensable and important part of various fields. Various fatigue defects will inevitably appear in the steel structure during the processing process. These fatigue defects will evolve into cracks and continue to expand when the steel structure is subjected to cyclic loads during service, which will have a serious impact on the safety performance of the steel structure itself. In order to accurately evaluate the impact of cracks on steel structures, it is necessary to monitor the crack development in real time.

[0003] In order to limit the expansion of crack defects in steel structures, a common method in engineering is to use carbon fiber composite material (CFRP) plates to reinforce the surface cracks of steel structures. The specific operation is to directly paste the CFRP plates on the cracks of the steel structure, and use the lightweight and high-strength CFRP plates to assist the steel structure in bearing stress, eliminating or delaying the development of fatigue cracks. After treatment, the surface cracks of the steel structure are sealed by the CFRP plates to form a "black box", and the cracks are no longer directly visible. It is difficult to detect the development of cracks in real time using conventional detection methods, and it is not easy to verify whether the reinforcement is effective.

[0004] With current technology, after ordinary CFRP plates are used to reinforce steel structures, it is not easy to grasp the crack development status due to crack closure, making it difficult to effectively evaluate the reinforcement effect. Summary of the invention

[0005] The technical problem to be solved by the present application is to provide a self-sensing CFRP plate reinforced steel structure fatigue crack analysis and crack monitoring and identification method, which has the characteristic of being able to more easily grasp the crack development status of the steel structure after CFRP plate reinforcement.

[0006] In a first aspect, an embodiment provides a self-sensing CFRP plate reinforced steel structure fatigue crack analysis method, comprising:

[0007] A fatigue crack analysis model of a CFRP plate reinforced steel structure is constructed; a crack exists on the surface of the steel structure, a carbon fiber composite material plate is bonded to the crack through an adhesive layer, and a distributed optical fiber and a point strain gauge are arranged on the composite material plate;

[0008] The strain data at different crack positions are obtained by arranging distributed optical fibers and point strain gauges; the strain data include the far-field nominal strain of the steel structure matrix and the strain at the cracks at different positions;

[0009] For any crack position, select any micro-segment of the corresponding CFRP plate, and establish the force balance equation at the micro-segment position, and obtain the relationship between the axial deformation of the CFRP plate and the shear stress at the interface between the CFRP plate and the adhesive layer as the first relationship; the axial direction is the direction perpendicular to the crack length;

[0010] Based on the first relational expression, the relational expression between the shear stress at the interface between the steel structure matrix and the adhesive layer and the axial deformation of the CFRP plate is obtained as the second relational expression;

[0011] Obtaining the relationship between the axial deformation of the steel structure matrix, the shear deformation of the adhesive layer, the crack opening displacement and the far-field nominal strain of the steel structure matrix at any crack position as the third relationship; obtaining the constitutive relationship of the adhesive layer as the fourth relationship;

[0012] Based on the first relational expression, the second relational expression, the third relational expression and the fourth relational expression, crack opening displacement-strain analysis models in the elastic stage and the softening stage of the adhesive layer are obtained respectively.

[0013] In a second aspect, an embodiment provides a method for monitoring cracks in a steel structure, comprising:

[0014] The strain data at different positions of the CFRP plate are measured and determined by arranging a CFRP plate, a distributed optical fiber and a point strain gauge on a steel structure substrate; the strain data includes the far-field nominal strain of the steel structure substrate and the strain at cracks at different positions; the CFRP plate is bonded to the steel structure substrate with cracks by an adhesive layer;

[0015] For any crack, the strain at the crack position is obtained, and the shear stress at the interface between the steel structure matrix and the adhesive layer is calculated based on the strain, and the stage of the adhesive layer is determined based on the shear stress at the interface between the steel structure matrix and the adhesive layer; the stage includes an elastic stage and a softening stage;

[0016] If the stage of the adhesive layer is the elastic stage, the crack opening displacement of the steel structure matrix is ​​calculated based on the crack opening displacement-strain analysis model of the adhesive layer in the elastic stage obtained in the fatigue crack analysis method of the steel structure reinforced with the self-sensing CFRP plate;

[0017] If the adhesive layer is in the softening stage, the crack opening displacement of the steel structure matrix is ​​calculated based on the crack opening displacement-strain analysis model of the adhesive layer in the softening stage obtained in the fatigue crack analysis method of the steel structure reinforced with the self-sensing CFRP plate;

[0018] For any crack, the depth of the crack of the steel structure matrix is ​​calculated based on the crack opening displacement of the steel structure matrix.

[0019] In a third aspect, an embodiment provides a method for identifying cracks in a steel structure, which is implemented based on the above-mentioned method for monitoring cracks in a steel structure, and includes:

[0020] By extending the CFRP plate, distributed optical fiber and point strain gauge arranged at the crack position on the steel structure substrate, the strain data of the CFRP plate at different positions where the crack has not grown are measured and determined; for any strain data detection position, if the measured strain is greater than 1.05 times the far-field nominal strain of the steel structure substrate, it is considered that the crack has grown to any strain data detection position, and the length of the crack is further calculated based on this.

[0021] The beneficial effects of the present invention are:

[0022] By constructing a self-sensing CFRP plate reinforced steel structure fatigue crack analysis model, selecting any micro-segment of the CFRP plate corresponding to any crack position, and establishing the force balance equation at the micro-segment position, the relationship between the axial deformation of the CFRP plate and the shear stress at the interface between the CFRP plate and the adhesive layer is obtained as the first relationship; based on the first relationship, the relationship between the shear stress at the interface between the steel structure matrix and the adhesive layer and the axial deformation of the CFRP plate is obtained as the second relationship; the relationship between the axial deformation of the steel structure matrix, the shear deformation of the adhesive layer, the crack opening displacement and the far-field nominal strain of the steel structure matrix at any crack position is obtained as the third relationship, and the constitutive relationship of the adhesive layer is obtained as the fourth relationship; based on the first relationship, the second relationship, the third relationship and the fourth relationship, the crack opening displacement-strain analysis model of the elastic stage and the softening stage of the adhesive layer is obtained respectively. Based on the obtained crack opening displacement-strain analysis model of the elastic stage and the softening stage of the adhesive layer, the crack monitoring of the CFRP plate reinforced steel structure is realized, so that it is easier to grasp the crack development of the steel structure after CFRP plate reinforcement. In addition, based on the monitoring of crack development, the CFRP plates, distributed optical fibers and point strain gauges arranged at the crack position on the steel structure substrate can be extended to measure and determine the strain data of the CFRP plates at different positions where the crack has not grown, thereby obtaining the expansion growth of the crack in the length direction and realizing the detection and identification of the development changes of the crack length. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 This is a schematic diagram of a process flow of a self-sensing CFRP plate reinforced steel structure fatigue crack analysis method according to an embodiment of the present application;

[0024] Figure 2 is a schematic diagram of a three-dimensional structure of a crack detection component according to an embodiment of the present application;

[0025] Figure 3 This application Figure 2 A schematic diagram of the cross-sectional structure of a crack detection component of the illustrated embodiment;

[0026] Figure 4 This application Figure 2 A schematic diagram of the planar structure of the crack detection component of the illustrated embodiment;

[0027] Figure 5 This application Figure 2 A schematic diagram of the longitudinal section structure of the crack detection component of the illustrated embodiment;

[0028] Figure 6 This application Figure 2 A schematic diagram of a stress-strain transfer analysis model of the illustrated embodiment;

[0029] Figure 7 This is a schematic flow chart of a steel structure crack monitoring method according to an embodiment of the present application;

[0030] Figure 8 This application Figure 7 Schematic diagram of the method flow of step S200;

[0031] Fig. 9 It is a structural schematic diagram of extending and arranging optical fibers according to an embodiment of the present application.

[0032] In the figure: 01-CFRP plate, 02-steel structure matrix, 03-crack, 04-optical fiber, 05-adhesive layer. DETAILED DESCRIPTION

[0033] The present invention is further described in detail below by specific embodiments in conjunction with the accompanying drawings. Wherein similar elements in different embodiments adopt associated similar element numbers. In the following embodiments, many detailed descriptions are for making the present application better understood. However, those skilled in the art can easily recognize that some features can be omitted in different situations, or can be replaced by other elements, materials, methods. In some cases, some operations related to the present application are not shown or described in the specification, this is to avoid the core part of the present application being overwhelmed by too much description, and for those skilled in the art, it is not necessary to describe these related operations in detail, and they can fully understand the related operations according to the description in the specification and the general technical knowledge in the art.

[0034] In addition, the features, operations or characteristics described in the specification can be combined in any appropriate manner to form various implementations. At the same time, the steps or actions in the method description can also be interchanged or adjusted in a manner that is obvious to those skilled in the art. Therefore, the various sequences in the specification and the drawings are only for the purpose of clearly describing a certain embodiment and are not meant to be a required sequence, unless otherwise specified that a certain sequence must be followed.

[0035] The serial numbers assigned to the components herein, such as "first", "second", etc., are only used to distinguish the objects described and do not have any order or technical meaning. The "connection" and "coupling" mentioned in this application, unless otherwise specified, include direct and indirect connections (couplings).

[0036] To facilitate the description of the inventive concept of the present application, the technology of reinforcing steel structures with CFRP plates is briefly described below.

[0037] For crack defects on the surface of steel structures, a commonly used method in engineering is to use carbon fiber composite material (CFRP) plates to reinforce the cracks on the surface of steel structures. Specifically, the CFRP plates are bonded above the cracks on the surface of the steel structures through an adhesive layer.

[0038] However, since the cracks on the surface of the steel structure are not directly visible after the CFRP plates are bonded, it is difficult to detect the development of the cracks in real time using conventional detection methods, and it is also difficult to verify whether the reinforcement is effective.

[0039] In view of this, the present application provides a self-sensing CFRP plate reinforced steel structure fatigue crack analysis and crack monitoring method, by constructing a self-sensing CFRP plate reinforced steel structure fatigue crack analysis model and analyzing the model, respectively obtaining the crack opening displacement-strain analysis model in the elastic stage and the softening stage of the adhesive layer, and based on the obtained crack opening displacement-strain analysis model, crack monitoring of the CFRP plate reinforced steel structure is realized, thereby making it easier to grasp the crack development status of the steel structure after CFRP plate reinforcement.

[0040] In order to clearly explain the present application scheme, the fatigue crack analysis method of the self-sensing CFRP plate reinforced steel structure is first described below.

[0041] In one embodiment of the present application, a self-sensing CFRP plate reinforced steel structure fatigue crack analysis method is provided. Please refer to Figure 1 ,include:

[0042] Step S10, constructing a self-sensing CFRP plate reinforced steel structure fatigue crack analysis model. There are cracks on the surface of the steel structure, and a carbon fiber composite material plate is bonded to the crack through an adhesive layer, and a distributed optical fiber and a point strain gauge are arranged on the composite material plate.

[0043] To facilitate analysis, a crack is cut in advance in the middle of the crossbeam on a gate-shaped steel structure. The two legs of the gate-shaped steel structure are connected with a long screw. By tightening the nut, the two legs are subjected to opposite forces. The gate-shaped steel structure deforms under the opposite forces, which causes the width of the cut crack to change. In this way, the crack opening displacement can be controlled to simulate the expansion of cracks in actual steel structures.

[0044] On the crossbeam of the cracked gate-shaped steel structure, a CFRP plate is bonded through an adhesive layer to simulate the CFRP plate reinforcement steel structure in the actual structure. Distributed optical fiber and point strain gauges are arranged on the CFRP plate to self-sensingly measure the strain of the CFRP plate.

[0045] Step S20, obtaining strain data at different crack positions through the arranged distributed optical fibers and point strain gauges, wherein the strain data includes the far-field nominal strain of the steel structure matrix and the strain at the cracks at different positions.

[0046] The axial deformation of the steel structure matrix is ​​mainly composed of two parts: the strain caused by the crack opening displacement (COD) and the far-field nominal strain of the steel structure matrix. Among them, the nominal strain is also the strain far away from the crack, which is the result of the overall force. The influence of the strain caused by the crack is negligible and can be ignored, which is a constant.

[0047] In one embodiment, the signal of the distributed optical fiber can be demodulated and recorded by the NBX-7000 instrument, and the point strain gauge data can be recorded by the TML strain collector. The strain of the CFRP plate at different positions can be measured by arranging the optical fiber and strain gauge in the horizontal and vertical directions. Among them, the strain data measured by the strain gauge is more accurate, but the number of points is scattered, and the strain data measured by the optical fiber is rougher, but the strain distribution can be measured. Therefore, the strain gauge measurement results can be used to calibrate the optical fiber measurement results to obtain distributed strain data, and realize self-sensing measurement of strain data.

[0048] Step S30, for any crack position, select any micro-segment of the corresponding CFRP plate, and establish a force balance equation at the micro-segment position, and obtain the relationship between the axial deformation of the CFRP plate and the shear stress at the interface between the CFRP plate and the adhesive layer as the first relationship. The axial direction refers to the direction perpendicular to the crack length.

[0049] Based on the constructed self-sensing CFRP plate reinforced steel structure fatigue crack analysis model, we can establish a stress-strain transfer analysis model, please refer to Figures 2 to 5 , the CFRP plate 01 is bonded to the surface of the cracked steel structure member through the adhesive layer 05. The initial crack 03 is located in the middle of the steel structure matrix 02. The far-end distance L (that is, the position far away from the crack) can be used to measure the far-field nominal strain of the steel structure matrix 04 through the optical fiber 04 / or the strain gauge, that is, at the same crack position, the far-field nominal strain is measured at the position where both ends are at a distance of L (the sum of the distances at both ends is 2L). In one embodiment, L can be set to 560mm.

[0050] Please refer to Figure 6When the crack in the steel structure develops, the crack 03 will open and produce stress concentration. The strain of the steel structure matrix 02 will be transferred to the adhesive layer 05 through shear force, and finally to the CFRP plate 01. Due to the strain transfer effect, there will be bonding slip deformation between the CFRP plate 01 and the steel structure matrix 02.

[0051] In an ideal situation, it is assumed that the interface between the adhesive layer 05 and the steel structure substrate 02 and the interface between the adhesive layer 05 and the CFRP plate 01 are well connected, and the CFRP plate 01 and the steel structure substrate 02 are both in a linear elastic working state. The adhesive layer 05 uses a bilinear cohesive force model to represent its bonding-slip relationship. In one embodiment, the constitutive relationship of the adhesive layer can be expressed as follows:

[0052] (1)

[0053] in, represents the constitutive function of the adhesive layer, s represents the shear deformation of the adhesive layer, Indicates the maximum bonding slip of the adhesive layer, represents the limit slip of the adhesive layer, represents the elastic stiffness of the adhesive layer, Indicates the softening stiffness of the glue layer.

[0054] When the steel structure matrix is ​​at a lower stress level, the crack opening displacement (COD) is small, and the CFRP plate 01, steel structure matrix 02 and adhesive layer 05 are all in the elastic stage; as the applied load increases, the COD gradually increases, and the stress concentration effect at the crack 03 becomes more obvious. Due to the high stress level of the steel structure matrix 02, the adhesive layer at the crack area on the steel structure matrix first reaches the maximum shear strength and then begins to soften gradually. The shear strength and stiffness of the adhesive layer 05 will decrease, and the length of the softening section will gradually increase until complete debonding.

[0055] For the convenience of analyzing crack 03, please refer to Figure 5 In one embodiment, due to the symmetry of the "V"-shaped crack structure, half of the "V"-shaped crack structure can be analyzed. Considering that when the adhesive layer is in the elastic stage, half of the length of the softening section of the adhesive layer, that is, half of the length of the section where the stiffness of the adhesive layer degrades, is 0.

[0056] In one embodiment, a micro-segment is taken at the CFRP plate corresponding to the crack. , based on this micro segment The force balance equation of the CFRP plate can be expressed as:

[0057] (2)

[0058] in, represents any section x of the CFRP plate along the x-axis direction.1 The axial stress at , where the x-axis and the z-axis are both located on the surface of the CFRP plate away from the adhesive layer in the coordinate system where the x-axis is located, the z-axis is parallel to the length direction of the crack, and the y-axis passes through the lowest point of the crack and extends toward the depth direction of the crack; and Represent the width and thickness of the CFRP plate, respectively, where the width refers to the dimension perpendicular to the crack length, Represents the shear stress at the interface between the CFRP plate and the adhesive layer.

[0059] The first relationship can be obtained from the force balance equation of the CFRP plate mentioned above, including:

[0060] (3)

[0061] in, represents the elastic modulus of the CFRP plate, represents the axial deformation of the CFRP plate, express The second derivative of .

[0062] Step S40: Based on the first relationship, a relationship between the shear stress at the interface between the steel structure matrix and the adhesive layer and the axial deformation of the CFRP plate is obtained as a second relationship.

[0063] Assuming that the adhesive layer between the steel structure matrix and the carbon fiber composite material plate has only shear deformation and is only subjected to shear stress, the shear stress on the upper and lower surfaces of the adhesive layer should be equal. Based on the first relationship, the relationship between the shear stress at the interface between the steel structure matrix and the adhesive layer and the axial deformation of the CFRP plate can be obtained as the second relationship.

[0064] In one embodiment, the second relational expression can be expressed as:

[0065] (4)

[0066] in, Represents the shear stress at the interface between the steel structure matrix and the adhesive layer.

[0067] Step S50, obtaining the relationship between the axial deformation of the steel structure matrix, the shear deformation of the adhesive layer, the crack opening displacement and the far-field nominal strain of the steel structure matrix at any crack position as the third relationship; obtaining the constitutive relationship of the adhesive layer as the fourth relationship.

[0068] Please refer to Figure 6 ,based on Figure 6 The strain transfer relationship and the corresponding deformation coordination conditions, the axial deformation of the steel structure matrix along the x-axis It is equal to the axial deformation of the CFRP plate Plus the shear deformation of the adhesive layer At the same time, it is the far-field nominal strain of the steel structure matrix and the axial deformation of the steel structure matrix caused by COD. Therefore, in one embodiment, the third relationship can be expressed as:

[0069] (5)

[0070] in, represents the axial deformation of the steel structure matrix, represents the shear deformation of the adhesive layer, represents half of the crack opening displacement, represents the far-field nominal strain of the steel structure matrix.

[0071] In one embodiment, the fourth relationship can be expressed in the form of formula (1).

[0072] Step S60, based on the first relational expression, the second relational expression, the third relational expression and the fourth relational expression, respectively obtain crack opening displacement-strain analysis models in the elastic stage and the softening stage of the adhesive layer.

[0073] For the convenience of explanation, the process of obtaining the crack opening displacement-strain analysis model in the elastic stage of the adhesive layer is first described below.

[0074] In one embodiment, in the elastic stage of the adhesive layer, based on the fourth relation, the shear deformation of the adhesive layer in the elastic stage can be expressed as:

[0075] (6)

[0076] in, represents the shear deformation of the adhesive layer in the elastic stage, , Indicates the maximum shear stress of the adhesive layer.

[0077] Substituting the second relation into formula (6), we have:

[0078] (7)

[0079] Combined with the third relation, we have:

[0080] (8)

[0081] in, , It is a constant that represents the shear stress hysteresis effect between the CFRP plate, steel structure matrix and adhesive layer in the elastic stage, which is mainly affected by the material properties of the CFRP plate and the adhesive layer.

[0082] Formula (8) is a common second-order linear homogeneous differential equation with constant coefficients. By solving the general solution of formula (8), we can obtain:

[0083] (9)

[0084] Among them, C 1 and C 2 is a constant, Represents the axial deformation of the CFRP plate in the elastic stage of the glue layer.

[0085] In the elastic stage of the adhesive layer, based on the first relationship and the basic relationship of material mechanics, the axial normal strain of the CFRP plate can be obtained by first derivative of its axial deformation, and the interfacial shear stress between the CFRP plate and the adhesive layer can be obtained by second derivative of the axial deformation of the CFRP plate, so:

[0086] (10)

[0087] (11)

[0088] in, Indicates the elastic stage of the adhesive layer. 1 The strain at , It represents the strain of the CFRP plate at a position L away from the origin in the x-axis direction during the elastic stage of the adhesive layer, and L is the far-field nominal distance of the steel structure matrix, which is a preset distance; It represents the shear stress at the interface between CFRP plate and adhesive layer in the elastic stage of adhesive layer.

[0089] Since the strain of the CFRP plate far away from the crack is equal to the far-field nominal strain of the steel structure matrix, Since both ends of the CFRP plate are under tensile stress, the displacement at the crack position is 0, that is, Based on the boundary conditions and , we can solve it and get:

[0090] (12)

[0091] (13)

[0092] Wherein, e represents a natural number exponent;

[0093] Considering , therefore, based on formula (12) and formula (13), we can get and , substituting into formulas (9), (10) and (11), we can obtain:

[0094] (14)

[0095] (15)

[0096] (16)

[0097] Among them, formula (15) is the crack opening displacement-strain analysis model in the elastic stage of the adhesive layer.

[0098] When the crack width continues to expand, the crack opening displacement increases, and the stress concentration at the crack will increase the stress of the steel matrix, which will correspondingly increase the shear stress of the adhesive layer. When the shear stress of the adhesive layer continues to increase to more than τ max , which will cause the adhesive layer at the crack to enter the softening stage first, and as the crack expands, the shear stress continues to increase, and the softening section extends to the l direction in the x direction. s Position. At 0

[0099] In one embodiment, in the softening stage of the adhesive layer, based on the fourth relational equation, the shear deformation of the adhesive layer in the softening stage can be expressed as:

[0100] (17)

[0101] in, It represents the shear deformation of the adhesive layer in the softening stage. , Indicates the maximum shear stress of the adhesive layer.

[0102] Substituting the second relation into formula (17), we have:

[0103] (18)

[0104] Combined with the third relation, we have:

[0105] (19)

[0106] in, , It is a constant that represents the shear stress hysteresis effect between the CFRP plate, steel structure matrix and adhesive layer in the softening stage, which is mainly affected by the material properties of the CFRP plate and the adhesive layer.

[0107] Formula (19) is a common second-order linear homogeneous differential equation with constant coefficients. By solving the general solution of formula (19), we can obtain:

[0108] (20)

[0109] Among them, C 3and C 4 is a constant, It indicates the axial deformation of the CFRP plate when the adhesive layer is in the softening stage. It represents half the length of the softening section of the glue layer.

[0110] In the softening stage of the adhesive layer, similar to the process of obtaining formulas (10) and (11), based on the first relationship and the basic relationship of material mechanics, we can obtain:

[0111] (twenty one)

[0112] (twenty two)

[0113] in, Indicates the softening stage of the adhesive layer at the cross section x of the CFRP plate 1 The strain at It represents the shear stress at the interface between the CFRP plate and the adhesive layer during the softening stage of the adhesive layer.

[0114] For the elastic section of the glue layer, In the case of , due to the change in force, the axial deformation, strain and shear stress of the CFRP plate and the interface with the adhesive layer are the same as those in formulas (9), (10) and (11), but with different integral constants D 1 and D 2 ,include:

[0115] (twenty three)

[0116] (twenty four)

[0117] (25)

[0118] in, Indicates the elastic stage of the adhesive layer. 1 The strain at , It represents the strain of the CFRP plate at a position L away from the origin in the x-axis direction during the elastic stage of the adhesive layer, and L is the far-field nominal distance of the steel structure matrix, which is a preset distance; It represents the shear stress at the interface between CFRP plate and adhesive layer in the elastic stage of adhesive layer.

[0119] Combining formulas (25) to (29), based on the boundary conditions , , and It can be solved to get:

[0120] (26)

[0121] (27)

[0122] (28)

[0123] (29)

[0124] Where e represents a natural number exponent, Represents CFRP plate x= The axial deformation of the cross section when the adhesive layer is in the softening stage, Represents CFRP plate x= The axial deformation of the cross section when the adhesive layer is in the elastic stage, Represents CFRP plate x= The shear stress at the interface between the CFRP plate and the adhesive layer when the cross section is in the softening stage of the adhesive layer. Represents CFRP plate x= Shear stress at the interface between CFRP plate and adhesive layer when the cross section is in the elastic stage of the adhesive layer.

[0125] Based on the continuity condition , we can get:

[0126] (30)

[0127] in, Represents CFRP plate x= The strain of the cross section when the adhesive layer is in the softening stage, Represents CFRP plate x= The strain of the cross section when the glue layer is in the elastic stage.

[0128] Considering and , formula (30) can be simplified to:

[0129] (31)

[0130] Based on formulas (30) and (31), In this case, we have:

[0131] (32)

[0132] It can be further simplified as:

[0133] (33)

[0134] Substituting formulas (33), (28) and (29) into formula (21), we can obtain:

[0135] (34)

[0136] Among them, formula (34) is the crack opening displacement-strain analysis model in the softening stage of the adhesive layer.

[0137] In one embodiment of the present application, a steel structure crack monitoring method is provided, which can be implemented by obtaining a crack opening displacement-strain analysis model based on the self-sensing CFRP plate reinforced steel structure fatigue crack analysis method in any of the above embodiments.

[0138] Please refer to Figure 7 , steel structure crack monitoring methods may include:

[0139] Step S100, by arranging the CFRP plate, distributed optical fiber and point strain gauge on the steel structure substrate, the strain data at different positions of the CFRP plate are measured and determined. The strain data includes the far-field nominal strain of the steel structure substrate and the strain at different crack positions; the CFRP plate is bonded to the steel structure substrate with cracks by an adhesive layer.

[0140] Step S200, for any crack, obtain the strain at the crack position, and calculate the shear stress at the interface between the steel structure matrix and the adhesive layer based on the strain, and judge the stage of the adhesive layer based on the shear stress at the interface between the steel structure matrix and the adhesive layer, including the elastic stage and the softening stage.

[0141] In one embodiment, please refer to Figure 8 , step S200 may include:

[0142] Step S2001, for any crack, obtain the strain at the crack position.

[0143] That is to get the cross section x along the x-axis 1 = 0 stress , which can be obtained based on actual measurements.

[0144] Step S2002, based on material mechanics and the strain at the crack position obtained, calculate the cross section x of the CFRP plate along the x-axis direction. 1 =0 axial stress.

[0145] In one embodiment, step S2002 may include:

[0146] (35)

[0147] in, represents the strain at the crack location, represents the cross section x of the CFRP plate along the x-axis 1 = 0 axial stress, It represents the elastic modulus of the CFRP plate.

[0148] Step S2003: based on the first relationship and the calculated cross-section x of the CFRP plate along the x-axis direction 1 =0, and calculate the shear stress at the interface between the CFRP plate and the adhesive layer.

[0149] The strain at the crack location In the case of 1 The relationship between the axial stress at the point and the shear stress at the interface between the CFRP plate and the adhesive layer can be obtained.

[0150] Step S2004, obtaining the shear stress at the interface between the steel structure matrix and the adhesive layer based on the second relationship.

[0151] Based on the second relationship, since the shear stress at the interface between the CFRP plate and the adhesive layer is equal to the shear stress at the interface between the steel structure matrix and the adhesive layer, the shear stress at the interface between the steel structure matrix and the adhesive layer can be obtained.

[0152] Step S2005, if the shear stress at the interface between the steel structure matrix and the adhesive layer is less than or equal to the maximum shear force of the adhesive layer, the adhesive layer is in an elastic stage; if the shear stress at the interface between the steel structure matrix and the adhesive layer is greater than the maximum shear force of the adhesive layer, the adhesive layer is in a softening stage.

[0153] Step S300, if the stage of the adhesive layer is the elastic stage, the crack opening displacement of the steel structure matrix is ​​calculated based on the adhesive layer elastic stage crack opening displacement-strain analysis model obtained in the self-sensing CFRP plate reinforced steel structure fatigue crack analysis method in any of the above embodiments.

[0154] Step S400, if the adhesive layer is in the softening stage, the crack opening displacement of the steel structure matrix is ​​calculated based on the crack opening displacement-strain analysis model of the adhesive layer in the softening stage obtained in the self-sensing CFRP plate reinforced steel structure fatigue crack analysis method in any of the above embodiments.

[0155] Step S500: For any crack, the depth of the crack of the steel structure matrix is ​​calculated based on the crack opening displacement of the steel structure matrix.

[0156] According to existing theoretical research, it can be determined that there is a linear relationship between COD and crack depth. Therefore, in order to determine the proportion of the linear relationship, a finite element model is established for calculation and verified through actual experiments, and the linear proportional coefficient β = 0.13103 is obtained. That is, after the COD is obtained, the crack depth at the corresponding position can be obtained through the linear proportional coefficient.

[0157] Therefore, by measuring the strain of the CFRP plate at different positions, the corresponding crack opening displacement COD can be obtained, and then the crack depth can be obtained through the linear proportional coefficient. Therefore, after CFRP reinforcement, the crack development can be effectively monitored to determine the effectiveness of the reinforcement.

[0158] In one embodiment of the present application, a steel structure crack identification method is provided, which is implemented based on the above-mentioned steel structure crack monitoring method.

[0159] Please refer to Fig. 9 , the CFRP plate 01, distributed optical fiber 04 and point strain gauges are extended at the crack position on the steel structure substrate 02 to measure and determine the strain data of the CFRP plate at different positions where the crack 03 has not grown. For any strain data detection position, if the measured strain is greater than 1.05 times the far-field nominal strain of the steel structure substrate, it is considered that the crack has grown to any strain data detection position, and the length of the crack is further calculated based on this.

[0160] exist Fig. 9 In the figure, optical fiber 04 is arranged not only at the position where cracks exist, but also at the position where cracks have not grown in the direction of the crack development trend. In this way, the strain at the position where cracks have not grown can be detected. It has been found that under the influence of crack growth, the strain near the crack will change. When the strain changes to more than 1.05 times the far-field nominal strain of the steel structure matrix, a crack appears at the measured position. Therefore, for any strain data detection position, if the measured strain is greater than 1.05 times the far-field nominal strain of the steel structure matrix, it is considered that the crack has grown to any strain data detection position. In this way, based on any strain data detection position, on the one hand, the identification of the growing crack can be realized, and on the other hand, the length of the crack at this time can be calculated.

[0161] In one embodiment of the present application, a computer-readable storage medium is provided, on which a program is stored. The stored program includes a method that can be loaded by a processor and process any one of the above embodiments.

[0162] Those skilled in the art will appreciate that all or part of the functions of the various methods in the above-mentioned embodiments can be implemented by hardware or by computer programs. When all or part of the functions in the above-mentioned embodiments are implemented by computer programs, the program can be stored in a computer-readable storage medium, and the storage medium can include: read-only memory, random access memory, disk, optical disk, hard disk, etc., and the program is executed by a computer to implement the above-mentioned functions. For example, the program is stored in the memory of the device, and when the program in the memory is executed by the processor, all or part of the above-mentioned functions can be implemented. In addition, when all or part of the functions in the above-mentioned embodiments are implemented by computer programs, the program can also be stored in a storage medium such as a server, another computer, disk, optical disk, flash disk or mobile hard disk, and can be downloaded or copied and saved in the memory of the local device, or the system of the local device is updated, and when the program in the memory is executed by the processor, all or part of the functions in the above-mentioned embodiments can be implemented.

[0163] The above specific examples are used to illustrate the present invention, which is only used to help understand the present invention and is not intended to limit the present invention. For those skilled in the art, according to the concept of the present invention, some simple deductions, modifications or substitutions can be made.

Claims

1. A self-sensing CFRP plate reinforced steel structure fatigue crack analysis method, characterized in that: include: A fatigue crack analysis model of a CFRP plate reinforced steel structure is constructed; a crack exists on the surface of the steel structure, a carbon fiber composite material plate is bonded to the crack through an adhesive layer, and a distributed optical fiber and a point strain gauge are arranged on the composite material plate; The strain data at different crack positions are obtained by arranging distributed optical fibers and point strain gauges; the strain data include the far-field nominal strain of the steel structure matrix and the strain at the cracks at different positions; For any crack position, select any micro-segment of the corresponding CFRP plate, and establish the force balance equation at the micro-segment position to obtain the relationship between the axial deformation of the CFRP plate and the shear stress at the interface between the CFRP plate and the adhesive layer as the first relationship, including: Take a micro-segment at the CFRP plate corresponding to the crack , based on the micro segment, the force balance equation of the CFRP plate is established, including: （2）； in, It represents the axial stress at any section x1 of the CFRP plate along the x-axis direction, where in the coordinate system where the x-axis is located, the x-axis and the z-axis are both located on the surface of the CFRP plate away from the adhesive layer, the z-axis is parallel to the length direction of the crack, and the y-axis passes through the lowest point of the crack and extends toward the depth direction of the crack; and Represent the width and thickness of the CFRP plate, respectively, where the width refers to the dimension perpendicular to the crack length, Represents the shear stress at the interface between the CFRP plate and the adhesive layer; The first relationship can be obtained from the force balance equation of the CFRP plate, including: （3） in, represents the elastic modulus of the CFRP plate, represents the axial deformation of the CFRP plate, express The second-order derivative of Indicates the CFRP plate edge x Axial section x strain at 1; The axial direction is a direction perpendicular to the crack length; Based on the first relationship, the relationship between the shear stress at the interface between the steel structure matrix and the adhesive layer and the axial deformation of the CFRP plate is obtained as the second relationship, including: （4） in, Represents the shear stress at the interface between the steel structure matrix and the adhesive layer; The relationship between the axial deformation of the steel structure matrix, the shear deformation of the adhesive layer, the crack opening displacement and the far-field nominal strain of the steel structure matrix at any crack position is obtained as a third relationship, including: （5） in, represents the axial deformation of the steel structure matrix, represents the shear deformation of the adhesive layer, represents half of the crack opening displacement, represents the far-field nominal strain of the steel structure matrix; Obtain the constitutive relation of the adhesive layer as the fourth relation, including: （1） in, represents the constitutive function of the adhesive layer, s represents the shear deformation of the adhesive layer, Indicates the maximum bonding slip of the adhesive layer, represents the limit slip of the adhesive layer, represents the elastic stiffness of the adhesive layer, Indicates the softening stiffness of the adhesive layer; Based on the first relational expression, the second relational expression, the third relational expression and the fourth relational expression, crack opening displacement-strain analysis models in the elastic stage and the softening stage of the adhesive layer are obtained respectively.

2. The self-sensing CFRP plate reinforced steel structure fatigue crack analysis method according to claim 1, characterized in that: The relationship between the strain at the crack and the crack opening displacement in the elastic stage and the softening stage of the adhesive layer, respectively, is obtained based on the first relationship, the second relationship, the third relationship and the fourth relationship, including: Based on the first relational expression, the second relational expression, the third relational expression and the fourth relational expression, the relational expression between the strain at the crack in the elastic stage of the adhesive layer and the crack opening displacement is obtained, including: Based on the fourth relationship, the shear deformation of the adhesive layer in the elastic stage includes: （6） in, represents the shear deformation of the adhesive layer in the elastic stage, , Indicates the maximum shear stress of the adhesive layer; Substituting into the second relation, we have: （7） Combined with the third relation, we have: （8） in, , is a constant, which indicates the shear stress hysteresis effect between the CFRP plate, steel structure matrix and adhesive layer in the elastic stage; Solving formula (8) yields: （9） Among them, C1 and C2 are constants, represents the axial deformation of the CFRP plate in the elastic stage of the glue layer; In the elastic stage of the adhesive layer, based on the first relationship and the basic relationship of material mechanics, we can get: （10） （11） in, represents the strain of the CFRP plate at section x1 during the elastic stage of the adhesive layer, and satisfies , It represents the strain of the CFRP plate at a position L away from the origin in the x-axis direction during the elastic stage of the adhesive layer, and L is the far-field nominal distance of the steel structure matrix, which is a preset distance; It represents the shear stress at the interface between the CFRP plate and the adhesive layer in the elastic stage of the adhesive layer; Based on boundary conditions and , we can solve it and get: （12） （13） Wherein, e represents a natural number exponent; Considering , therefore, based on formula (12) and formula (13), we can get and , substituting into formulas (9), (10) and (11), we can obtain: （14） （15） （16） Among them, formula (15) is the crack opening displacement-strain analysis model in the elastic stage of the adhesive layer.

3. The self-sensing CFRP plate reinforced steel structure fatigue crack analysis method according to claim 2, characterized in that: The relationship between the strain at the crack and the crack opening displacement in the elastic stage and the softening stage of the adhesive layer, respectively, is obtained based on the first relationship, the second relationship, the third relationship and the fourth relationship, including: Based on the first relational expression, the second relational expression, the third relational expression and the fourth relational expression, the relational expression between the strain at the crack in the softening stage of the adhesive layer and the crack opening displacement is obtained, including: Based on the fourth relationship, the shear deformation of the adhesive layer in the softening stage includes: （17） in, It represents the shear deformation of the adhesive layer in the softening stage. , Indicates the maximum shear stress of the adhesive layer; Substituting into the second relation, we have: （18） Combined with the third relation, we have: （19） in, , is a constant, which indicates the shear stress hysteresis effect between the CFRP plate, steel structure matrix and adhesive layer in the softening stage; Solving formula (19) yields: （20） Among them, C3 and C4 are constants, It indicates the axial deformation of the CFRP plate when the adhesive layer is in the softening stage. It represents half of the length of the softening section of the adhesive layer; In the softening stage of the adhesive layer, based on the first relationship and the basic relationship of material mechanics, we can get: （21） （22） in, represents the strain of the CFRP plate at section x1 during the softening stage of the adhesive layer, It represents the shear stress at the interface between the CFRP plate and the adhesive layer during the adhesive layer softening stage; For the elastic section of the glue layer, In the case of , due to the change in force, the axial deformation, strain of the CFRP plate and the shear stress at the interface with the adhesive layer are the same as those in formulas (9), (10) and (11), but with different integral constants D1 and D2, including: （23） （24） （25） in, represents the strain of the CFRP plate at section x1 during the elastic stage of the adhesive layer, and satisfies , It represents the strain of the CFRP plate at a position L away from the origin in the x-axis direction during the elastic stage of the adhesive layer, and L is the far-field nominal distance of the steel structure matrix, which is a preset distance; It represents the shear stress at the interface between the CFRP plate and the adhesive layer in the elastic stage of the adhesive layer; Combining formulas (25) to (29), based on the boundary conditions , , and It can be solved to get: （26） （27） （28） （29） Where e represents a natural number exponent, Indicates CFRP plate The axial deformation of the cross section when the adhesive layer is in the softening stage, Indicates CFRP plate The axial deformation of the cross section when the adhesive layer is in the elastic stage, Indicates CFRP plate The shear stress at the interface between the CFRP plate and the adhesive layer when the cross section is in the softening stage of the adhesive layer. Indicates CFRP plate The shear stress at the interface between the CFRP plate and the adhesive layer when the cross section is in the elastic stage of the adhesive layer; Based on the continuity condition , we can get: （30） in, Indicates CFRP plate The strain of the cross section when the adhesive layer is in the softening stage, Indicates CFRP plate The strain of the cross section when the adhesive layer is in the elastic stage; Considering and , formula (30) can be simplified to: （31） Based on formulas (30) and (31), In this case, we have: (32) It can be further simplified as: (33) Substituting formulas (33), (28) and (29) into formula (21), we can obtain: （34) Among them, formula (34) is the crack opening displacement-strain analysis model in the softening stage of the adhesive layer.

4. A method for monitoring cracks in a steel structure, characterized in that: include: The strain data at different positions of the CFRP plate are measured and determined by arranging a CFRP plate, a distributed optical fiber and a point strain gauge on a steel structure substrate; the strain data includes the far-field nominal strain of the steel structure substrate and the strain at cracks at different positions; the CFRP plate is bonded to the steel structure substrate with cracks by an adhesive layer; For any crack, the strain at the crack position is obtained, and the shear stress at the interface between the steel structure matrix and the adhesive layer is calculated based on the strain, and the stage of the adhesive layer is determined based on the shear stress at the interface between the steel structure matrix and the adhesive layer; the stage includes an elastic stage and a softening stage; If the stage of the adhesive layer is the elastic stage, the crack opening displacement of the steel structure matrix is ​​calculated based on the crack opening displacement-strain analysis model of the elastic stage of the adhesive layer obtained in the self-sensing CFRP plate reinforced steel structure fatigue crack analysis method as described in any one of claims 1 to 3; If the stage of the adhesive layer is the softening stage, the crack opening displacement of the steel structure matrix is ​​calculated based on the crack opening displacement-strain analysis model of the adhesive layer in the softening stage obtained in the self-sensing CFRP plate reinforced steel structure fatigue crack analysis method as described in any one of claims 1 to 3; For any crack, the depth of the crack of the steel structure matrix is ​​calculated based on the crack opening displacement of the steel structure matrix.

5. The steel structure crack monitoring method according to claim 4, characterized in that: The method of obtaining the strain at the crack position for any crack, calculating the shear stress at the interface between the steel structure matrix and the adhesive layer based on the strain, and judging the stage of the adhesive layer based on the shear stress at the interface between the steel structure matrix and the adhesive layer includes: For any crack, obtain the strain at the crack location; The axial stress at the section x1=0 of the CFRP plate along the x-axis direction is calculated based on material mechanics and the strain obtained at the crack position; Based on the first relation and the calculated axial stress at the section x1=0 of the CFRP plate along the x-axis direction, the shear stress at the interface between the CFRP plate and the adhesive layer is calculated; The shear stress at the interface between the steel structure matrix and the adhesive layer is obtained based on the second relational expression; If the shear stress at the interface between the steel structure matrix and the adhesive layer is less than or equal to the maximum shear force of the adhesive layer, the adhesive layer is in the elastic stage; if the shear stress at the interface between the steel structure matrix and the adhesive layer is greater than the maximum shear force of the adhesive layer, the adhesive layer is in the softening stage.

6. A method for identifying cracks in a steel structure, characterized in that: The steel structure crack monitoring method according to claim 4 or 5 is implemented, comprising: By extending the CFRP plate, distributed optical fiber and point strain gauge arranged at the crack position on the steel structure substrate, the strain data of the CFRP plate at different positions where the crack has not grown are measured and determined; for any strain data detection position, if the measured strain is greater than 1.05 times the far-field nominal strain of the steel structure substrate, it is considered that the crack has grown to any strain data detection position, and the length of the crack is further calculated based on this.

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