Interface failure evaluation method considering shear stress reversal phenomenon and data discreteness

Abstract

The present invention discloses an interface damage evaluation method that takes into account the shear stress reversal phenomenon and data discreteness. A fluctuation distribution function is introduced into a typical interface slip function, and a bonding-slip analysis model that can simultaneously reflect the interface shear stress reversal phenomenon and the discreteness of the bonding-slip curve is theoretically derived. The model is verified using experimental data from different scholars, and a corresponding interface debonding damage evaluation method is established. The interface debonding damage evaluation method disclosed by the present invention does not require the introduction of additional empirical parameters in its bonding-slip model, has a clear physical meaning, and can explain that both the discreteness of the bonding-slip curve and the shear stress reversal phenomenon are derived from interface microcracks, further clarifying the interface debonding damage mechanism.

Description

Technical Field

[0001] The invention relates to mechanics and civil engineering technology, and in particular to an interface damage evaluation method taking into account shear stress inversion phenomenon and data discreteness. Background Art

[0002] As the basic constitutive relationship to characterize the debonding failure behavior of the FRP (fiber reinforced composite)-concrete interface, the bond-slip model has attracted the attention of many scholars. There are many types of these interface bond-slip models, including various linear and nonlinear models, which have been widely used in various finite element analyses. However, the existing bond-slip models still cannot explain the source of the discreteness of the FRP-concrete interface bond-slip experimental curve, and cannot characterize the reverse phenomenon of the interface shear stress.

[0003] The reasons for the discreteness of the interface bond-slip curve in the existing literature can be summarized into three categories: 1) Insufficient testing technology: Due to the brittle extension and high nonlinearity of local cracks, the FRP debonding process is difficult to capture; 2) Material inhomogeneity: The inhomogeneity of coarse and fine aggregates in concrete; 3) Insufficient specimen preparation technology: The bonding layer between FRP and concrete cannot guarantee its uniformity, and the surface treatment of concrete cannot guarantee its uniformity. However, these reasons are only external reasons for the discreteness of the bond-slip test curve. Previous experimental results show that even in the interface failure experiment of FRP-steel structure, the obtained bond-slip curve is discrete and there is a shear stress reversal phenomenon. In other words, the essential reasons for the discreteness of the bond-slip test curve and the shear stress reversal phenomenon have not yet been clarified. Therefore, it is particularly necessary to develop a bond-slip model that can characterize the discreteness and shear stress reversal phenomenon of the interface bond-slip test curve, and to establish an evaluation method for this type of interface debonding failure, so as to deeply explore the debonding failure mechanism of the FRP-concrete interface. Summary of the invention

[0004] The purpose of the present invention is to overcome the shortcomings of the above prior art and provide an interface damage evaluation method that takes into account the shear stress reversal phenomenon and data discreteness. This interface damage evaluation method that takes into account the shear stress reversal phenomenon and data discreteness does not require the introduction of additional empirical parameters, has a clear physical meaning, and can explain the source of the discreteness of the interface adhesion-slip test curve, rather than just characterizing its discreteness.

[0005] The purpose of the present invention is achieved through the following technical solutions:

[0006] The interface damage evaluation method considering the shear stress reversal phenomenon and data discreteness includes the following steps:

[0007] S1. Introduce the wave function into the typical slip function to determine the new slip function s(x):

[0008] This is formula (1),

[0009] Where s is the slip, x is the position coordinate of the FRP-concrete interface from the free end, α and β are constants, x0 is the position coordinate corresponding to the maximum shear stress in the slip curve, and the wave function Φ(x) is:

[0010] This is formula (2),

[0011] Where A is the amplitude of the wave function, and T is the period of the wave function;

[0012] S2. Determine the expression of the period T of the wave function: Assume the wave period T and the effective bonding length L of FRP e Equal, T = L e , which is formula (3),

[0013] And there are: This is formula (4),

[0014] In the formula, δ is a constant coefficient;

[0015] S3. The expression for determining the amplitude A of the wave function is:

[0016] This is formula (5),

[0017] S4. Using experimental data to fit the parameters in the expression, the bonding-slip analysis model is finally determined;

[0018] S5. Use the analytical model obtained in S4 to evaluate the interface debonding failure behavior.

[0019] Preferably, the process of determining the expression of the amplitude A in step S3 includes the following steps:

[0020] S3-1. Substitute equation (1) into the strain formula of FRP along the interface direction: In the equation, we get the strain function of FRP:

[0021] This is formula (6), where ρ is Where E f ,t f and b f are the elastic modulus, thickness and width of FRP, E c ,t c and b c are the elastic modulus, thickness and width of concrete respectively;

[0022] S3-2. Let x equal the length L of FRP f , and the FRP end strain is obtained:

[0023] This is formula (7);

[0024] S3-3. According to formula (6), combined with the strain ε(L f ) and the load to determine the anti-correlation relationship between x0 and the load P;

[0025] S3-4. Taking into account the principle of dimensional matching, the expression of amplitude A is constructed as follows:

[0026] k0 is a constant, which is formula (8);

[0027] S3-5. Determine the value of k0 by the physical meaning of the maximum shear stress:

[0028] This is formula (9);

[0029] S3-6. Substitute equation (9) into equation (8) to obtain the amplitude A:

[0030] This is formula (5).

[0031] Preferably, in step S4, determining the analysis model includes the following steps:

[0032] S4-1. Substitute equation (1) into the relationship between shear stress and slip To obtain the shear stress function:

[0033] This is formula (10),

[0034] S4-2. Combining equations (1), (2), (3), (5), (6) and (10), we can obtain the final slip function, strain function and bond-slip model:

[0035] This is formula (11),

[0036] This is formula (12),

[0037] This is formula (13);

[0038] S4-3. Substituting equation (11) into equation (12), combined with the relationship between the load and strain on the free end of the FRP, the expression of the load-slip curve is obtained:

[0039] This is formula (14);

[0040] S4-4. According to the load-slip experimental curve, the parameters α and β in equation (14) are fitted, and then the values ​​of the parameters α and β are substituted into equation (13) to obtain the analytical model of interface adhesion-slip.

[0041] The present invention has the following advantages over the prior art:

[0042] (1) The bond-slip model of the FRP-concrete interface of the present invention does not require the introduction of additional empirical parameters and has a clear physical meaning. Compared with the traditional analytical model, its advantage is that it can explain the source of the discreteness of the interface bond-slip experimental curve, rather than just characterizing its discreteness.

[0043] (2) The present invention explains that the discreteness of the bond-slip curve and the shear stress reversal phenomenon are both derived from the volatility of the slip function, and that the discreteness of the bond-slip curve and the shear stress reversal phenomenon are twin phenomena and will not appear in isolation.

[0044] (3) The physical significance of the present invention is that it explains that discontinuous interface microcracks are generated during the process of interface debonding damage, and the interface microcracks cause the volatility of the slip function, which in turn leads to the discreteness of the adhesion-slip test curve and the shear stress reversal phenomenon. However, the inhomogeneity of the material, the inadequate testing technology, the lack of specimen preparation technology, etc. are not the essential reasons for the discreteness of the adhesion-slip test curve and the shear stress reversal phenomenon. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 2 are the prediction results of the model of the present invention, wherein (a) is the τ-s curve of specimen C50-400-2, and (b) is the τ-s curve of another specimen shown in the literature of Wu et al.

[0046] Figure 2 The predicted results of the present invention for the specimen EB 300-1, wherein (a) is the load-slip curve, (b) is the slip distribution of the interface, (c) is the strain distribution of the FRP, and (d) is the bond-slip curve.

[0047] Figure 3 Bond-slip curve of EB 300-1 specimen given by Zhou et al. DETAILED DESCRIPTION

[0048] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0049] The interface damage evaluation method considering the shear stress reversal phenomenon and data discreteness includes the following steps:

[0050] S1. Introduce the wave function into the typical slip function and determine the new slip function.

[0051] A typical slip function s(x) is selected as:

[0052] This is formula (15), where α and β are constants that can be obtained by fitting the load-slip experimental curve; x0 is the interface position corresponding to the maximum shear stress in the slip curve.

[0053] The wave function Φ(x) is introduced into the above slip function to reflect the wave nature of the interface slip field obtained from the experiment, that is,

[0054] This is formula (1),

[0055] The introduced wave function is a trigonometric function, which conforms to the principle of simplicity.

[0056] This is formula (2), and the final new slip function is:

[0057] This is formula (16),

[0058] Wherein, A is the amplitude of the wave function, and T is the period of the wave function, which are determined as follows.

[0059] S2. Determine an expression for the period T of the wave function.

[0060] Set the fluctuation period T and the effective bonding length L of FRP e Its physical meaning is that the slip function fluctuates within the range of the effective bonding length as the minimum positive period. That is: T = L e , which is formula (3),

[0061] Effective bonding length L e The expression is:

[0062] This is formula (17),

[0063] but This is formula (4),

[0064] In the formula, δ is a constant coefficient, and the value of δ is close to 1, such as δ = 0.96, 0.98 or 0.99.

[0065] S3. Determine an expression for the amplitude A of the wave function.

[0066] Substitute the slip function expression (1) into the strain formula of FRP along the interface direction: In the equation, we get the strain function of FRP:

[0067] This is formula (6), where ρ is a constant and Where E f ,t f and b f are the elastic modulus, thickness and width of FRP, E c ,t c and b c are the elastic modulus, thickness and width of concrete respectively;

[0068] Let x be equal to the length L of the FRP f :

[0069] This is formula (7),

[0070] From formula (7), we can see that according to the strain ε(L f ) and the corresponding relationship between load P, we can solve it as follows:

[0071] This is formula (18),

[0072] It can be seen from the above formula that x0 and load P are inversely correlated.

[0073] From formula (16), we can see that as the load P increases, the interface between FRP and concrete gradually peels off, the volatility of the displacement function gradually weakens, and the amplitude A gradually tends to 0, that is, A and P have an inverse correlation, so A and x0 have a positive correlation. Moreover, since x0 is always less than L f ,Right now

[0074] Taking into account the principle of dimensional matching, the present invention constructs A into the following simple form:

[0075] k0 is a constant, which is formula (8),

[0076] Substituting equation (16) into the relationship between shear stress and slip In the equation, the shear stress function can be obtained as:

[0077]

[0078] This is formula (10),

[0079] Through function analysis, we can know that when When , substituting equation (8) into equation (10), we can get the maximum shear stress τ max for:

[0080] This is formula (19);

[0081] After the present invention introduces the wave function into the classical slip function, the τ represented by equation (10) is max Affected by the magnitude of trigonometric functions If we further give a reasonable k0, we can make σ max exist The amplitudes of these The key factor of size is k0. The present invention determines the size of k0 through the physical meaning of the maximum value of shear stress.

[0082] Substituting equation (15) into equation (10), the adhesion-slip relationship at different interface positions x can be obtained: This is formula (20);

[0083] When the slip s is large enough, From formula (20), we can determine the minimum value τ in the negative shear stress region at different positions x: min :

[0084] This is formula (21). From formula (21), it can be seen that the minimum value of shear stress is in the interval The fluctuations in the inner and outer surfaces are consistent with the distribution law of the shear stress reversal phenomenon observed in the experiment, namely: 1) the shear stress reversal phenomenon exists in some positions and not in some positions; 2) the part where the shear stress reversal phenomenon occurs in the adhesion-slip curve is also discrete; 3) as the load gradually increases, The shear stress in the reverse part of the bond-slip curve also gradually approaches 0.

[0085] Since the shear stress reversal phenomenon is only the reverse extension behavior of the interface crack, it does not change the shear strength τ bond , so the strength in the reverse phase of the bond-slip curve is Strength in the positive phase of the bond-slip curve Equal, that is:

[0086] This is formula (22),

[0087] τ max-stable Considered as interfacial shear strength According to the above physical meaning, the value of k0 can be determined. In the bonding-slip response in the shear stress reversal region, the shear stress does not reach the peak value at all locations. Therefore, the minimum value min[τ min(x)] as the shear strength in the reverse phase Right now:

[0088] This is formula (23),

[0089] Combining equation (22) and equation (23), we have:

[0090] This is formula (24),

[0091] From equation (24), we can solve k0:

[0092] This is formula (9),

[0093] Substituting equation (9) into equation (8), we can get the complete expression of amplitude A:

[0094] This is formula (5);

[0095] S4. Determine the bond-slip analysis model.

[0096] Combining equations (1), (2), (3), (5) and (10), we can obtain the expression of adhesion-slip:

[0097] This is formula (13),

[0098] Combining equations (1), (2), (3), (5) and (6), we can obtain the final slip function and strain function:

[0099] This is formula (11),

[0100] This is formula (12);

[0101] Substituting equation (11) into equation (12), combined with the relationship between the load and strain on the free end of the FRP The expression of the load-slip curve can be further sorted out:

[0102] This is formula (14),

[0103] According to the load-slip experimental curve, the parameters α and β in equation (14) can be determined by fitting, and then the values ​​of the parameters α and β are substituted into equation (13) to obtain the adhesion-slip analysis model.

[0104] S5. Evaluate the interface debonding failure behavior according to the analytical model obtained above.

[0105] The bond-slip analysis model proposed in this invention is used to evaluate the debonding failure behavior of the FRP-concrete interface. The comparison is mainly made with the experimental data and models of different scholars from the following aspects: 1) Whether the bond-slip model can reflect the shear stress reversal phenomenon; 2) Whether the bond-slip model can explain the source of discreteness; 3) Whether the bond-slip model can reflect the characteristic points and distribution law in the experimental curve.

[0106] 1) Comparison with the model and experimental data of Wu et al. (Wu Y, Jiang C. Quantification of Bond-Slip Relationship for Externally Bonded FRP-to-Concrete Joints [J]. Journal of Composites for Construction. 2013; 17(5): 673-86.)

[0107] Wu et al. proposed the following bond-slip analysis model:

[0108] This is formula (25),

[0109] The bond-slip curve predicted by the present invention is as follows: Figure 1 As shown in (a) and (b), they can match the adhesion-slip experimental curves well and clearly show the shear stress reversal phenomenon and discreteness. However, the prediction curve of Wu et al.'s analytical model (Eq. (25)) is a single curve. Although it is in the middle of the experimental curve, it cannot reflect the discreteness and shear stress reversal phenomenon of the experimental curve and cannot deeply explain the complex mechanism of interface failure.

[0110] for Figure 1 For the specimen in (a), the maximum shear stress τ predicted by the present invention max The mean of and the corresponding slip amount s0 are 10.4% and 9.9% smaller than the prediction results of Wu et al.’s analytical model (Eq. (25)). Figure 1 For the specimen in (b), the maximum shear stress τ predicted by the present invention max The error of the mean is 19% greater than the prediction result of Wu et al.'s analytical model (Formula (25)), while the error of the slip amount s0 predicted by the present invention is 6.9% smaller than the prediction result of Wu et al.'s model (Formula (25)).

[0111] 2) Comparison with the experimental data and model of Zhou et al. (Zhou YW, Wu YF, Yun Y. Analytical modeling of the bond–slip relationship at FRP-concrete interfaces for adhesively-bonded joints [J]. Composites Part B, 2010, 41(6): 423-433.)

[0112] According to formula (17), taking δ = 0.98, we can obtain Figure 2 The effective bonding length L of the specimen in e =134.7. Then according to formula (1), the period T of the wave function is determined to be 134.7. In addition, according to the slip test curve (Fig. 2), it can be observed that its wave period is 140. Comparing it with the effective bonding length, it can be seen that the difference between the two is only 3.8%, which shows that the assumption of formula (3) is reasonable. At the same time, the slip curve calculated according to formula (20) is also in good agreement with the experimental curve, reproducing the volatility of the experimental curve, as shown in Figure 2 (b) as shown.

[0113] The comparison between the strain curve calculated by formula (12) and the experimental curve is as follows: Figure 2 As shown in (c), although the experimental curve has strong oscillation, the calculated curve also reproduces similar volatility, and the location of the peak and valley values ​​is close to the experimental curve. For example, the strain at a distance of 30 mm from the loading end has a peak value. In addition, when the interface is gradually peeled off, the peak of the strain curve gradually decreases, which is also consistent with the actual experimental observation.

[0114] For the bond-slip prediction curve, Figure 2 As shown in (d), the calculated curve and the experimental curve both show similar discreteness and shear stress reversal. The similarities between the two are mainly reflected in: 1) the maximum shear stress and the corresponding slip amount at different positions are different; 2) the dispersion of the descending section is large; 3) the shear stress reversal phenomenon occurs at some positions, while it does not occur at some positions. The descending section at some positions in the experimental curve is reduced to a negative value, such as Figure 2 At the end of the descending section of the bond-slip curve shown in the elliptical box in (d), negative shear stress also appears at some locations in the calculated curve.

[0115] Next, the analysis model of the present invention is compared with the model proposed by Zhou et al. First, after Zhou et al. introduced the position parameter x into the classical analysis model, they obtained a model reflecting the discreteness of the adhesion-slip curve:

[0116] This is formula (26),

[0117] For the maximum shear stress τ in the bond-slip curve max As for the prediction results of the corresponding slip amount s0, by comparing the prediction results of the analytical model of the present invention with the prediction results of the model of Zhou et al., it can be seen that the maximum shear stress τ calculated by the analytical model of the present invention is max The mean error of is 12.7% smaller than the prediction result of the model proposed by Zhou et al., and the corresponding mean error of slip s0 is 5.3% smaller than the prediction result of the model proposed by Zhou et al.

[0118] like Figure 3 As shown in Figure 2, first, the discreteness of the bond-slip curve calculated by Zhou et al.'s model is not obvious between 10 mm and 130 mm from the loading end. The variances of the maximum shear stress and its corresponding slip amount are only 0.008 MPa and 0.003 mm, respectively. The discreteness only appears at a position close to the free end (more than 200 mm from the loading end), which is different from the Figure 2 (d) is inconsistent with the experimental results of the discreteness between 10mm and 130mm shown in Figure 2; secondly, the model cannot explain why the discreteness of the bond-slip curve only appears at a position close to the free end; furthermore, the model cannot characterize the interface shear stress reversal phenomenon. On the contrary, the present invention has a good effect on characterizing the discreteness of the bond-slip data and the shear stress reversal phenomenon after introducing the wave function into the slip function based on the wave nature of the interface slip field.

[0119] The above embodiments are preferred implementation modes of the present invention, but the implementation modes of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications made without departing from the spirit and principle of the present invention shall be equivalent replacement modes and shall be included in the protection scope of the present invention.

Claims

1. An interface damage evaluation method considering shear stress reversal phenomenon and data discreteness, characterized in that: The following steps are involved: S1. Introduce the wave function into the typical slip function to determine the new slip function s(x): Where s is the slip, x is the position coordinate of the FRP-concrete interface from the free end, α and β are constants, x0 is the position coordinate corresponding to the maximum shear stress in the slip curve, and the wave function Φ(x) is: Where A is the amplitude of the wave function, and T is the period of the wave function; S2. Determine the expression of the period T of the wave function: Assume the wave period T and the effective bonding length L of FRP e Equal, T = L e , which is formula (3), And there are: In the formula, δ is a constant coefficient; S3. The expression for determining the amplitude A of the wave function is: S4. Using experimental data to fit the parameters in the expression, the bonding-slip analysis model is finally determined; S5. Evaluate the interface debonding failure behavior using the analytical model obtained in S4; The process of determining the expression of the amplitude A in step S3 includes the following steps: S3-1. Substitute equation (1) into the strain formula of FRP along the interface direction: In the equation, the strain function of FRP is obtained: Where ρ is a constant, and Where E f ,t f and b f are the elastic modulus, thickness and width of FRP, E c ,t c and b c are the elastic modulus, thickness and width of concrete respectively; S3-2. Let x equal the length L of FRP f , and the FRP end strain is obtained: S3-3. According to formula (6), combined with the strain ε(L f ) and the load to determine the anti-correlation relationship between x0 and the load P; S3-4. Taking into account the principle of dimensional matching, the expression of amplitude A is constructed as follows: k0 is a constant, which is formula (8); S3-5. Determine the value of k0 by the physical meaning of the maximum shear stress: This is formula (9); S3-6. Substitute equation (9) into equation (8) to obtain the amplitude A: This is formula (5); In step S4, determining the analysis model includes the following steps: S4-1. Substitute equation (1) into the relationship between shear stress and slip To obtain the shear stress function: S4-2. Combining equations (1), (2), (3), (5), (6) and (10), we can obtain the final slip function, strain function and bond-slip model: S4-3. Substituting equation (11) into equation (12), combined with the relationship between the load and strain on the free end of the FRP, the expression of the load-slip curve is obtained: S4-4. According to the load-slip experimental curve, the parameters α and β in equation (14) are fitted, and then the values ​​of the parameters α and β are substituted into equation (13) to obtain the analytical model of interface adhesion-slip.

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