Construction method for constitutive model of ECC tensile stiffening effect of GFRP rib

Abstract

The invention provides a construction method of a GFRP rib ECC tensile stiffening effect constitutive model, which comprises the following steps: determining analysis variables as rib material diameter, ECC fiber mixing amount and ECC cross section area based on a GFRP rib ECC interface slippage relationship, establishing finite element analysis models, and performing finite element analysis on multiple groups of finite element analysis models to obtain a GFRP rib ECC tensile stiffening effect constitutive model. The relation of the effective deformation area of the component along with the deformation under the conditions of different ECC fiber mixing amounts, different GFRP rib material diameters and different reinforcement ratios is obtained; based on a GFRP rib ECC cross-crack stress two-way transmission mechanism, a GFRP rib ECC tensile stiffening effect energy model is established, and a direct tensile component tensile stiffening effect model is established; obtaining a load-displacement relation of the component through a refined finite element calculation result, obtaining a tensile stiffness effect model, and calculating a difference value between the load borne by the GFRP bare rib and the refined finite element result to obtain an ECC contribution value; and taking the tensile stiffening effect as the tensile stress-strain relationship of the ECC material in the tensile region of the component, and establishing an ECC material constitutive model considering the ECC tensile stiffening effect of the GFRP rib in direct stretching.

Description

Technical Field

[0001] The present invention relates to the technical field of structural mechanics, and particularly relates to a method for constructing a constitutive model of the tensile stiffening effect of GFRP bars in ECC. Background Art

[0002] Glass Fiber Reinforced Polymer (GFRP) bars reinforced Engineering Cementitious Composites (ECC) components have mechanical characteristics of large deformation and low stiffness, and are widely used in bridge deck connection plates, energy dissipation structures, pipeline connection components, dam repair, structural reinforcement, and composite structures, etc.

[0003] In the prior art, when applying the existing tensile stiffening constitutive model to predict the deformation and stiffness of GFRP bar ECC components, there are large errors. This is because the existing analysis models are all established based on steel bar / FRP concrete structures and cannot consider the influence of the ECC bridging stress. Therefore, it is necessary to propose a constitutive model of the tensile stiffening effect that conforms to the mechanical evolution law of GFRP bar ECC components to provide a theoretical basis for the analysis of GFRP bar ECC bridge deck connection plates. Summary of the Invention

[0004] To solve the problem of errors in deformation and stiffness prediction, the present invention provides a method for constructing a constitutive model of the tensile stiffening effect of GFRP bars in ECC.

[0005] To achieve the above object, the present invention provides the following technical solutions:

[0006] A method for constructing a constitutive model of the tensile stiffening effect of GFRP bars in ECC, comprising the following steps:

[0007] Based on the interfacial slip relationship of GFRP bars in ECC, determine the analysis variables as the bar diameter, ECC fiber content, and ECC cross-sectional area, establish multiple groups of finite element analysis models, and set different reinforcement ratios;

[0008] Through finite element analysis of multiple groups of finite element analysis models, obtain the relationship between the effective deformation area of the component and the deformation amount under different ECC fiber contents, GFRP bar diameters, and reinforcement ratios;

[0009] Based on the two-way stress transfer mechanism of GFRP bars in ECC across cracks, establish an energy model of the tensile stiffening effect of GFRP bars in ECC; based on the energy model of the tensile stiffening effect of GFRP bars in ECC, establish a tensile stiffening effect model for direct tensile components;

[0010] The load-displacement relationship of the component is obtained through refined finite element calculation results, and the tensile stiffening effect model of the direct tension component is established. The contribution value of ECC is calculated by taking the difference between the load borne by the GFRP bare bar and the refined finite element results, which is the tensile stiffening effect.

[0011] Taking the tensile stiffening effect as the tensile stress-strain relationship of the ECC material in the tension zone of the component, a constitutive model of the ECC material considering the tensile stiffening effect of GFRP bars under direct tension is established.

[0012] Preferably, based on the interfacial slip relationship between GFRP bars and ECC, the analysis variables are determined as the bar diameter, ECC fiber content, and ECC cross-sectional area, and multiple finite element analysis models are established, including the following steps:

[0013] A three-dimensional solid model of the tensile stiffening of GFRP bars in ECC is established. After the element size sensitivity analysis, the element size is determined. The element types of ECC and GFRP bars are C3D8R, and the interface element type is COH2D4.

[0014] Since the specimen is a symmetric model, a quarter model is selected for calculation, and the loading method is concentrated force loading; zero-thickness interface bond-slip elements are inserted at the interface between GFRP bars and ECC.

[0015] Preferably, the tensile stiffening effect model of the direct tension component is:

[0016]

[0017] PΔU = E E (Ae,ΔU) = E E-e (ρ,ΔU) + E E-sc (D,ρ,ΔU) + E R-E (D,ρ,ΔU)

[0018] In the formula, σ E,t represents the tensile stiffening effect of the component contributed by ECC, P GFRP represents the load borne by the elastic strain of the bar, ρ s is the reinforcement ratio of GFRP bars; E is the total input energy of the test; E R-e is the elastic strain energy of GFRP bars; E E-e is the elastic strain energy of ECC; E E-sc is the energy for the development of microcracks in ECC; E R-E is the interfacial slip energy between GFRP bars and ECC; Ae is the effective area; U is the deformation of GFRP bars in the component.

[0019] Preferably, it also includes the construction of a constitutive model of the tensile stiffening effect of GFRP bars in ECC considering the bending-tension coupling condition, including the following steps:

[0020] Based on the interfacial slip relationship between GFRP bars and ECC, a three-dimensional solid flexure-tension coupling analysis model is established;

[0021] Based on the three-dimensional solid flexure-tension coupling analysis model, multiple finite element models are constructed according to different bar diameters, ECC fiber dosages, and reinforcement ratios, and finite element parameter analysis is carried out to obtain the evolution laws of the cross-sectional stress field, load, and relative height of the neutral axis of the component under the flexure-tension coupling action of GFRP bars and ECC, and a constitutive model considering the tension stiffening effect of GFRP bars and ECC under the flexure-tension coupling condition is established.

[0022] Preferably, for the three-dimensional solid flexure-tension coupling analysis model, constructing multiple finite element models according to different bar diameters, ECC fiber dosages, and reinforcement ratios includes the following steps:

[0023] Establish a three-dimensional solid model of the tension stiffening of GFRP bars and ECC, and insert zero-thickness interfacial bonding slip elements at the interface between GFRP bars and ECC;

[0024] Through element size sensitivity analysis, determine the element size. The element types of ECC and GFRP bars are C3D8R, and the interfacial element type is COH2D4;

[0025] The loading method of the model is a bending load, loaded by four-point bending, and the axial tension is loaded in a displacement control manner, and the loading deflection is set; according to the deformation state of the GFRP bar and ECC connection plate, select the axial deformation amount.

[0026] Preferably, establishing the constitutive model of the tension stiffening effect of GFRP bars and ECC considering the flexure-tension coupling condition includes the following steps:

[0027] Use numerical analysis methods to determine the distribution of the maximum principal stress and principal strain of the ECC material in the tension zone of the GFRP bar and ECC flexure-tension coupling component. According to the plane section assumption, determine the average stress-strain relationship of the ECC material in the pure bending section, and then obtain the tension stiffening effect of the ECC material;

[0028] Construct multiple finite element models according to different bar diameters, ECC fiber dosages, and reinforcement ratios, and conduct finite element analysis to obtain the principal stress and principal strain fields of the flexure-tension coupling component in the final state of deformation, as well as the vertical and horizontal load-displacement relationships of the GFRP bar and ECC flexure-tension coupling component; obtain the vertical strain distribution at the mid-span of the component, and determine the variation law of the relative height of the neutral axis of the GFRP bar and ECC flexure-tension coupling component during the loading process during the deformation process;

[0029] According to the evolution laws of the cross-sectional stress field, load, and relative height of the neutral axis of the component, establish a constitutive model of the tension stiffening effect of GFRP bars and ECC considering the flexure-tension coupling condition.

[0030] Advantages of the present invention:

[0031] Based on the interfacial slip relationship between GFRP bars and ECC, a three-dimensional solid direct tension and flexure-tension coupling analysis model is established in the present invention to study the influence of GFRP reinforcement ratio, ECC material properties, etc. on the tensile stiffening effect of components, analyze the interfacial between GFRP bars and ECC, the development process of material damage, the evolution law of the relative height of the neutral axis, and the constitutive model of the tensile stiffening effect considering the flexure-tension coupling effect in components, and establish a constitutive model for the tensile stiffening effect of GFRP bar ECC, which can accurately simulate the development process of the tensile stiffening of GFRP bar ECC. Description of the drawings

[0032] Figure 1 is the flowchart of the method of the embodiment of the present invention;

[0033] Figure 2 is the schematic diagram of the cohesive unit and the opening-mode crack of the embodiment of the present invention;

[0034] Figure 3 is the GFRP bar ECC bond-slip model of the embodiment of the present invention;

[0035] Figure 4 is the support and loading form of the embodiment of the present invention;

[0036] Figure 5 is the schematic diagram of the GFRP bar ECC interface element of the embodiment of the present invention;

[0037] Figure 6 is the schematic diagram of the damage degree of the bonded interface of the embodiment of the present invention;

[0038] Figure 7 is the calculation result diagram of the bond-slip of the embodiment of the present invention;

[0039] Figure 8 is the GFRP bar ECC tensile stiffening model of the embodiment of the present invention;

[0040] Figure 9 is the main stress nephogram of typical tensile stiffening components of the embodiment of the present invention;

[0041] Figure 10 is the comparison diagram of the finite element and test results of the embodiment of the present invention;

[0042] Figure 11 is the stress distribution of the GFRP bar ECC interface element during the tensile deformation process of the embodiment of the present invention;

[0043] Figure 12 is the influence of the ECC fiber content on the deformation performance of the tensile stiffening component of the embodiment of the present invention;

[0044] Figure 13 Comparison of results with different reinforcement ratios of the finite element model in the embodiments of the present invention;

[0045] Figure 14 Influence of the diameter of GFRP bars with the same ECC cross-sectional area on the results in the embodiments of the present invention;

[0046] Figure 15 Cracking process of ECC in the tensile stiffening specimen in the embodiments of the present invention;

[0047] Figure 16 Schematic diagram of conical surface damage cracking of ECC during the tensile process in the embodiments of the present invention;

[0048] Figure 17 Results of the tensile stiffening effect test of GFRP bar ECC components in the embodiments of the present invention;

[0049] Figure 18 Results of the tensile stiffening effect of components in the embodiments of the present invention;

[0050] Figure 19 Comparison of the tensile stiffening effects with different bar diameters and fiber dosages in the embodiments of the present invention;

[0051] Figure 20 Schematic diagram of the tensile stiffening effect of GFRP bar ECC in the embodiments of the present invention;

[0052] Figure 21 Constitutive model of ECC material considering the tensile stiffening effect of GFRP bar ECC in the embodiments of the present invention;

[0053] Figure 22 Flexural-tensile coupled tensile stiffening effect of GFRP bar ECC in the embodiments of the present invention;

[0054] Figure 23 Flexural-tensile coupled component model and loading method in the embodiments of the present invention;

[0055] Figure 24 Load-displacement relationship of different component thicknesses in the embodiments of the present invention;

[0056] Figure 25 Influence of the load-displacement relationship of the combined component in the embodiments of the present invention;

[0057] Figure 26 Influence of different ECC fiber dosages on the load-displacement relationship of components in the embodiments of the present invention;

[0058] Figure 27 Variation relationship of the relative height of the neutral axis with different component thicknesses in the embodiments of the present invention;

[0059] Figure 28It is the influence of the relative height of the neutral axis of multi-GFRP bars in the embodiments of the present invention;

[0060] Figure 29 It is the relative height of the neutral axis of components with different ECC material properties in the embodiments of the present invention;

[0061] Figure 30 It is the verification of the tensile stiffening effect of the flexural-tensile coupling component in the embodiments of the present invention;

[0062] Figure 31 It is the influence of the thickness of different components on the tensile stiffening effect in the embodiments of the present invention;

[0063] Figure 32 It is the influence of ECC material properties on the tensile stiffening effect in the embodiments of the present invention

[0064] Figure 33 It is the influence of the number of GFRP bars on the tensile stiffening effect in the embodiments of the present invention. Detailed implementation manners

[0065] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention, and are not used to limit the present invention.

[0066] Embodiment 1

[0067] A method for constructing a constitutive model of the tensile stiffening effect of GFRP bar ECC of the present invention, the specific process is as Figure 1 shown, and includes the following steps:

[0068] 1. Based on the interface slip relationship between GFRP bars and ECC, establish a direct tensile analysis model of a three-dimensional entity

[0069] The interface bonding slip relationship between GFRP bars and ECC is simulated by using Cohesive elements. The Cohesive elements simulate the three-dimensional interface by presetting the crack surface, and the unit thickness is 0. The cohesive elements include: the top surface, the middle surface and the bottom surface, as Figure 2 shown, Figure 2 (a) is a schematic diagram of the structure of the cohesive element, Figure 2 (b) is a schematic diagram of the opening mode (Type II) crack. The damage degree is judged by the fracture criterion. When the damage criterion is met, the element starts to be damaged. According to the predefined damage evolution model, when the element completely fails, the element separates from the middle surface, generating geometric discontinuity and forming a crack. The opening mode (Type II) crack can be simulated by the cohesive element.

[0070] To verify whether the mechanical properties of the GFRP bar - ECC interface can accurately simulate the test results, a three - dimensional GFRP bar - ECC bond - slip model was established as shown in Figure 3 and 4 . Among them, both the GFRP bars and the ECC material were modeled using solid elements. The model fixed the compressed surface of the ECC through hinge supports, which was the same as the test supports. Displacement loading was applied through the loading points coupled at the ends of the bars. Existing research chose to simulate the bond - failure relationship at the GFRP bar - ECC interface using Cohesive elements. The schematic diagram of inserting Cohesive elements in the model is shown in Figure 5 . The element has zero thickness, and the element constitutive relationship was calculated using the GFRP bar - ECC follower bond - slip model.

[0071] The model variables were: bar diameter (13mm, 16mm, 19mm), ECC fiber content (1.6%, 1.8%, 2.0%, 2.2%, 2.4), a total of 15 models. The damage degree of the GFRP bar - ECC interface elements is shown in Figure 6 . The interface damage degree was represented by SDEG (damage stiffness degradation). When SDEG≥0.9, the element was considered to have failed. The comparison between the model calculation results and the test results is shown in Figure 7 , which proves that the zero - thickness Cohesive element can accurately simulate the slip process between the GFRP bars and the ECC.

[0072] 2. Verification of the GFRP bar - ECC finite - element model and calculation results

[0073] A three - dimensional solid model of GFRP bar - ECC tensile stiffening was established. After the element - size sensitivity analysis, the element size was selected as 3mm. The element types of ECC and GFRP bars were C3D8R, and the interface element type was COH2D4. Since the specimen was a symmetric model, to improve the calculation efficiency, a quarter - model was selected for calculation, as shown in Figure 8 . The loading method was concentrated - force loading. Zero - thickness interface bond - slip elements were inserted at the GFRP bar - ECC interface. The main - stress nephograms of each component of typical tensile stiffening calculated are shown in Figure 9 . The cracking area of the ECC in the later stage of loading was in agreement with the test results. The cracking area in the figure was the gray part of the ECC, with a judgment criterion of greater than the cracking stress. The stress of the bars basically remained stable after reaching the debonding zone, and this part of the bars and the ECC were stressed and deformed synergistically. The length of the debonding zone and the shear - stress distribution between the GFRP bars and the ECC could also be judged through the shear - stress distribution of the interface elements.

[0074] To further study the influence of different parameters on the tensile stiffening performance of GFRP-reinforced ECC, the analysis variables of the GFRP-reinforced ECC tensile stiffening model are selected as follows: the diameter of the reinforcement (13 mm, 16 mm, 19 mm), the fiber content of ECC (1.6%, 1.8%, 2.0%, 2.2%, 2.4), and the cross-sectional area of ECC (7333.3 mm 2 , 8800 mm 2 , 11000 mm 2 , 16000 mm 2 , 26400 mm 2 ), a total of 75 finite element analysis models. The model settings are shown in Table 1. The naming rule of the model name in the table is taken as an example of T13-F1.6-R0.5. T represents tensile stiffening, 13 represents the diameter of the reinforcement is 13 mm, F1.6 represents the fiber content is 1.6%, and R0.5 represents the reinforcement ratio is 0.5%. The remaining naming rules are similar.

[0075] Table 1 Reinforcement ratio of the model

[0076]

[0077]

[0078] In the tensile stiffening test, the nine groups of specimens correspond to the GFRP reinforcement ratios of 1.5%, 2.28%, and 3.22% (corresponding to the reinforcement diameters of 13 mm, 16 mm, and 19 mm), as compared with the test results Figure 10 shown. By comparing the tensile stiffening results of specimens with different reinforcement diameters, it can be seen that the test results are in good agreement with the model calculation results. The model based on the bond-slip relationship interface element of GFRP-reinforced ECC can accurately predict the tensile stiffening deformation process of GFRP-reinforced ECC.

[0079] During the tensile process of the model, obvious slip occurs between the GFRP reinforcement and ECC at the end of the specimen. By comparing and analyzing the shear stress distribution of the interface element, the debonding length of the component during the tensile deformation process can be obtained, as Figure 11 shown. By comparing and analyzing, the comparison between the debonding zone length of the finite element model and the test results is shown in Table 2. By comparing and analyzing, it can be seen that the finite element model can accurately simulate the debonding length of the component during the tensile deformation process, indicating that the constitutive model of the component interface element can accurately predict the debonding development process of the component.

[0080] Table 2 Comparison between the test values and calculation results of the debonding development length of GFRP reinforcement

[0081]

[0082] 3. Analysis of the finite element results of the tensile stiffening of GFRP-reinforced ECC

[0083] (1) Influence of ECC fiber content

[0084] The cracking process of ECC has a great influence on the tensile stiffening performance. Taking the direct tension test specimens of 13-mm bars as an example, by analyzing the relationship between load and deformation, it can be seen that the fiber content affects the deformation of the tensile stiffening specimens in the second stage, as Figure 12 shown. When the ECC fiber content is appropriately increased (less than 2.2%), it can improve the deformation range of the GFRP bar-ECC direct tension members in the first stage. This is because in the initial stage of deformation, the uncracked ECC in the members can provide a large effective area for the GFRP bars. As the load increases, microcracks develop in the ECC, and the tensile stiffening effect of the members mainly comes from the development of microcracks in the ECC and the stress transfer at the GFRP bar-ECC interface. In the second stage, the tensile stiffening effect of the members remains at a relatively high level. During the deformation process, the bridging stress of the ECC affects the stress transfer process between the GFRP bars and the ECC. For specimens with the same ECC fiber content, the influence law of different GFRP bar diameters on the tensile stiffening effect is similar to that of the 13-mm bar specimens. Analysis shows that during the process of increasing the fiber content from 1.6% to 2.2%, the deformation of the specimens in the first stage gradually increases to 1.25 mm. Reasonably increasing the ECC fiber content can improve the tensile stiffening effect of the members to a certain extent.

[0085] (2) Influence of GFRP bar diameter

[0086] When the ECC fiber content is 1.6%, by comparing the variation laws of the models under three bar diameter conditions with the reinforcement ratio, as Figure 13 (a), (b), (c) shown. The variation laws of the specimens with three bar diameters with the reinforcement ratio are similar. Under the condition of a relatively high reinforcement ratio (such as specimen T13-F1.6-R1.8), when the deformation of the member exceeds 1 mm, the ECC in the member reaches the saturated working state of large-scale microcrack cracking. For specimens with a low reinforcement ratio (T13-F1.6-R0.5), due to the large cross-sectional area of the ECC, the member reaches the cooperative working state when the deformation is greater than 3.5 mm. This phenomenon also has a similar law in the 16-mm and 19-mm specimens. Among them, for the 16-mm specimen (T16-F1.6-R0.76) and the 19-mm specimen (T19-F1.6-R1.07), the member reaches the cooperative deformation state when the deformation is about 1.7 mm. As the reinforcement ratio of the member decreases, the deformation in the first stage of the member increases significantly, indicating that when the reinforcement ratio of the member is low, the GFRP bars need a larger deformation to transfer the tensile stress to the ECC, and the cracking range of the ECC is also continuously decreasing, affecting the cooperative performance between the GFRP bars and the ECC. Comparative analysis shows that reasonably increasing the reinforcement ratio of the GFRP bars can improve the cooperative working performance between the GFRP bars and the ECC, but their deformation stiffness increases accordingly.

[0087] For the same ECC cross-sectional area, the diameter of the reinforcement directly affects the deformation stiffness of the component. The results of the simulation curves are as shown in Figure 14 (a). Under the condition of the same reinforcement ratio, the deformation stiffness of the component increases with the increase of the cross-sectional area of the GFRP reinforcement. When the ECC cross-sectional area is the same, the deformation of the component is mainly affected by the diameter of the reinforcement. This phenomenon is significantly weakened under the condition of low reinforcement ratio, as shown in Figure 14 (b). This is because as the ECC cross-sectional area of the component increases, the influence of the ECC on the deformation capacity of the component increases. After the diameter of the reinforcement decreases, a larger deformation amount of the GFRP reinforcement is required to cause the development of large-scale microcracks in the ECC. Therefore, for components with the same ECC cross-sectional area, the deformation stiffness of the component is related to the diameter of the GFRP reinforcement, and the deformation laws of the 13mm and 16mm diameter reinforcements are relatively similar.

[0088] (3) Analysis of the ECC damage process

[0089] Analysis shows that by judging the damage process of the ECC microcrack development through the maximum principal stress and deleting the elements in the ECC cracking area, the schematic diagram of the ECC cracking process during the specimen loading process is obtained, as shown in Figure 15 . Under the stressed state of the GFRP reinforcement, the reinforcement at the end of the specimen is debonded, and the tensile stress is transmitted to the ECC through the interface between the GFRP reinforcement and the ECC. The stress of the ECC in the middle of the specimen is relatively complex, and it is affected by the tensile stress of the ECC at the end of the specimen and the deformation of the GFRP reinforcement (in the middle of the specimen) at the same time. As can be seen from Figure 15 , the tensile stress of the ECC at the center of the specimen (close to the GFRP reinforcement) is relatively high and microcrack cracking damage appears first. After that, as the tensile stress increases, the ECC microcracks gradually develop horizontally until the specimen surface. This phenomenon indicates that in the co-deformation area of the ECC and the GFRP reinforcement, a non-linear microcrack development process occurs horizontally. It shows that in the co-deformation area of the GFRP-reinforced ECC component, the cracking and failure mechanism of the component is different from that of the concrete component. The ECC damage first starts at the position close to the surface of the GFRP reinforcement and then continuously develops horizontally to the specimen surface as the load increases. In the concrete component, due to the brittle cracking of the concrete, this process is not obvious. The different ECC damage cracking modes make the GFRP-reinforced ECC component affected by more factors during the deformation process, such as the properties of the ECC (ECC cracking stress, elastic modulus, etc.), the bond-slip relationship between the GFRP reinforcement and the ECC (bonding stress), the diameter of the GFRP reinforcement (contact area per unit length), etc.

[0090] As the loading progresses, the ECC development area continuously expands towards the specimen surface. At the same time, affected by the tensile stress transmitted by the GFRP reinforcement at the end of the ECC, a conical surface is formed in the uncracked area of the ECC, as shown in Figure 16As shown, the conical surface surrounds the GFRP reinforcement and continuously develops towards the end of the specimen as the loading progresses, and the conical surface continuously expands. In the final stage of loading, microcracks develop in most of the ECC, and its damage range is in good agreement with the test results. The cracking process of ECC shows that the distance between the matrix and the reinforcement affects the cracking process of ECC. Through comparative analysis, it can be seen that when the reinforcement ratio is high (the cross-sectional area of ECC is small), the initial internal cracking phenomenon of ECC is not obvious. Therefore, in the analysis of components with a small reinforcement ratio, this model method can be used to judge the internal process of ECC. Among them, the mechanism of the formation of the ECC cracking failure conical surface is as follows: the GFRP reinforcement transfers the tensile stress to the ECC within the failure conical surface in the debonding zone. The ECC close to the GFRP reinforcement has a tensile stress in the same direction as the reinforcement. The ECC far from the reinforcement is under the action of tensile stress, and the direction of the tensile stress is affected by the free boundary conditions of the ECC and gradually forms an angle with the direction of the reinforcement. The different internal and external boundary conditions of the ECC result in stress redistribution, and finally the cracking strength of the ECC is reached at the failure conical surface, causing the ECC outside the conical surface to crack and fail. This phenomenon of conical surface failure has a similar damage process in the process of pulling out reinforced concrete, and this phenomenon exists in the overall development process of tension-stiffening components.

[0091] To sum up, in the co-deformation region of GFRP reinforcement and ECC, the development of microcracks in ECC starts around the GFRP reinforcement and continuously expands laterally as the tensile stress increases until it reaches the specimen surface. And this phenomenon is more obvious when the reinforcement ratio of the component is small. It shows that the co-deformation of GFRP reinforcement and ECC is not a process of simply adding the deformation amounts of the two, but is jointly affected by factors such as the material properties of ECC, the bond-slip relationship between GFRP reinforcement and ECC, and the diameter of GFRP reinforcement, which is of great significance for analyzing the deformation process of components.

[0092] 4. Constitutive model of the tension-stiffening effect of GFRP-reinforced ECC

[0093] The test results of the tension-stiffening effect of GFRP-reinforced ECC components obtained by calculation are as Figure 17 (a), (b), and (c) show that the GFRP-reinforced ECC direct tension component has a tension-stiffening effect different from that of reinforced / FRP-reinforced concrete components. During the deformation process of the component, the tension-stiffening effect of GFRP-reinforced ECC does not decay. It should be noted that in the 13-mm reinforcement specimen, the tension-stiffening effect shows obvious strengthening. By comparing the tension-stiffening effects of nine groups of specimens, it can be divided into an uncracked stage and a stable cracking stage. In the stable cracking stage, the microcrack density and cracking range of ECC continue to increase, and the bridging stress between cracks can ensure that ECC continues to participate in the force, and the tension-stiffening effect forms a stable development stage. The tension-stiffening effect of the component reaches a stable stage at a relatively low stress level. Figure 17In (c), G19-1.6 and G19-2.0 cross at the position where the strain is 0.6%. The reason is that in the G19-2.0 specimen, obvious two-way cross-crack tensile stress transfer phenomenon occurs due to the high density of ECC microcracks. The tensile stress borne by ECC attenuates, resulting in the reduction of the tensile stiffening effect of the component at about 0.6% strain.

[0094] Based on the energy model, the tensile stiffening effect of the component is calculated. The energies of each part in the energy model are summed up, the stress of GFRP bars and the total stress corresponding to each loading step are calculated, and the stress value contributed by ECC at each loading step is obtained through difference conversion, which is the tensile stiffening effect of the component. The results are as Figure 18 shown. Comparing with the test results, it is proved that the energy model can be used to calculate the tensile stiffening effect of the model. Therefore, based on the GFRP bar-ECC energy model, the tensile stiffening effect model of the direct tension component is established as shown in Equation (2). This model introduces the interface relationship between GFRP bars and ECC, the diameter of GFRP bars, and the material properties of ECC, etc., and can consider the influence of the above parameters on the tensile stiffening effect, making up for the deficiencies of the existing models. In the formula, σ E,t represents the tensile stiffening effect of the component contributed by ECC, P GFRP represents the load borne by the elastic strain of the bars, and ρ s is the reinforcement ratio of GFRP bars.

[0095]

[0096] PΔU = E E (Ae, ΔU) = E E-e (ρ, ΔU) + E E-sc (D, ρ, ΔU) + E R-E (D, ρ, ΔU) (2)

[0097] Based on the finite element calculation results, the tensile stiffening effect of GFRP bar-ECC is obtained as Figure 19 . The specific calculation process is as follows: the load-displacement relationship of the component is obtained through the refined finite element calculation results, the load borne by the GFRP bare bars is calculated, and the contribution value of ECC is obtained by the difference from the refined finite element results, which is the tensile stiffening effect. Figure 19It shows the tensile stiffening effect of different ECC fiber contents and GFRP bar diameters under the condition of the same ECC cross-sectional area. The influence of the ECC fiber content on the tensile stiffening effect of the component is mainly concentrated in the stable cracking stage and is related to the cracking strength and ultimate strength of ECC. The three groups of specimens in the figure have similar variation laws. However, during the process of increasing the bar diameter from 13 mm to 19 mm, the difference in the tensile stiffening effect decreases, indicating that the tensile stiffening effect is not only affected by the material properties of ECC, but also by the interfacial slip relationship between GFRP bars and ECC and the bar diameter. In the specimens with 19-mm bars, the proportion of the load borne by GFRP bars increases, and the influence of the ECC material properties is reduced. The influence of the reinforcement ratio on the tensile stiffening effect is as Figure 19 shown. The co-deformation of ECC and GFRP bars is greatly affected by the reinforcement ratio, which is mainly reflected in that after ECC cracks in the component deformation, with the increase of the tensile deformation amount, the tensile stiffening effect increases accordingly.

[0098] Based on the above analysis, the constitutive model of the tensile stiffening effect of GFRP bar ECC components is as Figure 20 shown. Regarding the tensile stiffening effect as the tensile stress-strain relationship of the ECC material in the tensile zone of the component, a constitutive model of the ECC material considering the tensile stiffening effect of GFRP bar ECC is established, as Figure 21 shown. In the model, σ t ' represents the ECC stress at the turning point of the tensile stiffening effect, and ε t ' is the corresponding strain. The tensile stiffening effect model believes that during the unloading process, the tensile stiffening tends to zero. The tensile stiffening effect of GFRP bars is mainly divided into two stages: the elastic deformation stage and the non-linear deformation stage. First, in the elastic deformation stage, the ECC material undergoes linear deformation, and the deformation elastic modulus is the tensile elastic model of ECC. Then it enters the plastic deformation stage, in which the ECC constitutive model considers the development of ECC micro-cracks and the interfacial bond-slip relationship between GFRP bars and ECC. There is an obvious enhancement phenomenon in the later stage of the tensile stiffening effect, which is due to the continuous increase in the micro-crack density during the development of ECC micro-cracks, resulting in an increase in the tensile stiffening effect.

[0099] 6. Analysis of the tensile stiffening effect of GFRP bar ECC flexural-tensile coupling components

[0100] In order to further study the evolution process of the tensile stiffening effect during the deformation of GFRP bar ECC flexural-tensile components, a GFRP bar ECC flexural-tensile coupling component model is used to explore the co-performance of GFRP bars and ECC and the variation law of the neutral axis, and to study the evolution law of the mechanical properties of flexural-tensile coupling components under different material properties, reinforcement ratios and multi-bar conditions.

[0101] (1) Tensile stiffening effect of GFRP bar ECC flexural-tensile coupling

[0102] During the stress and deformation process of the GFRP bar ECC flexural-tensile member, the tensile stiffening effect is affected by the flexural-tensile coupling effect of the ECC material in the tensile zone and the GFRP bars. Based on the analysis method of the stress distribution in the tensile zone of flexural members, the tensile stiffening effect of the GFRP bar ECC flexural-tensile coupling member is calculated and determined under different ECC material properties, GFRP bar reinforcement ratios, and multi-bar conditions. The calculation method is to use the numerical analysis method to determine the maximum principal stress and principal strain distributions of the ECC material in the tensile zone of the GFRP bar ECC flexural-tensile coupling member, as Figure 22 shown. According to the plane section assumption, the average stress-strain relationship of the ECC material in the pure bending section is determined, and then the tensile stiffening effect of the ECC material is obtained.

[0103] (2) Setting of GFRP bar ECC flexural-tensile coupling member

[0104] The model studied the influence of 5 numbers of GFRP bars, 5 fiber contents of ECC, 3 diameters of GFRP bars, and 5 effective heights of members on the mechanical properties of flexural-tensile members. A total of 31 groups of models were designed, and the model settings are shown in Table 5.6. The model naming method is: BT-1.6-13-80, where BT represents flexural-tensile coupling, 1.6 represents the fiber content of 1.6%, 13 represents the diameter of the GFRP bar of 13 mm, and 80 represents the height of the member of 80 mm. In the setting of the flexural-tensile coupling member, the influence of single GFRP bar and multi-bars in the flexural-tensile coupling member was compared and analyzed. The number of longitudinal bars in the member numbered BT-1.6-13-80-2 is 2.

[0105] Table 3 Model parameters of flexural-tensile coupling members

[0106]

[0107]

[0108] According to the model size and boundary conditions of the GFRP bar ECC connection plate, the width of the flexural-tensile coupling member is selected as 200 mm, the effective length of the member is 1000 mm, and the cover thickness is 25 mm. The element types of ECC and GFRP bars are C3D8R, the interface element type is COH2D4, and zero-thickness interface bonding slip elements are inserted at the interface between GFRP bars and ECC. The model element composition is as Figure 23 (a) shown. After the element size sensitivity analysis, the element size of 5 mm is selected, as Figure 23 (b) shown. The loading method is: the bending load is applied by four-point bending, displacement control, and the loading deflection is 20 mm. The axial tensile load is applied in a displacement control manner. According to the deformation state of the GFRP bar ECC connection plate, the axial deformation amount of 3 mm is selected, and the loading method is as Figure 23(c). To consider the influence of multiple GFRP bars on the tensile stiffening effect of flexural-tensile coupling members, a total of 5 groups of models with 1 to 5 GFRP bars were set. The multi-bar models are as shown in Figure 23 (d).

[0109] (3) Analysis of the principal tensile stress and principal strain field of flexural-tensile members

[0110] The distributions of the principal stress and principal strain field of the flexural-tensile coupling members in the final state of deformation of the flexural-tensile members were statistically obtained. For members with a high reinforcement ratio, the interface of the pure bending section of the member is under tensile stress as a whole, and the entire cross-section of the member bears tensile strain. This is because under the flexural-tensile coupling condition, the transverse load of the GFRP bar ECC member provides a sectional reaction force. Under the condition of a low reinforcement ratio of the member, a compression zone appears in the member. Existing research believes that the calculation of the tensile stiffening effect of flexural members depends on the range of the tensile zone of the member. In the pure bending section of the GFRP bar ECC flexural-tensile member, the strain distribution is uniformly distributed along the length direction, indicating that in the pure bending section of the flexural-tensile coupling member, the strain distribution can be unified. During the deformation process of the flexural-tensile member, the axial deformation amounts are the same. Therefore, the diameter of the GFRP bar has little influence on the principal stress and principal strain field of the member. By comparing and analyzing the influence of different numbers of GFRP bars on the principal stress and principal strain field of the flexural-tensile coupling member, it can be seen that during the process of increasing the number of GFRP bars from 1 to 5, the member has similar principal stress and principal strain distributions. This is because flexural-tensile coupling members with different numbers of GFRP bars have the same reinforcement ratio and effective height of the member.

[0111] (4) Load-displacement relationship curve of flexural-tensile members

[0112] The vertical and horizontal load-displacement relationships of the GFRP bar ECC flexural-tensile coupling members were statistically obtained as shown in Figure 24 (a), (b), (c). As the thickness of the member increases, the load-displacement curve increases significantly. This is because the member bears flexural-tensile coupling deformation, and the ECC still bears tensile stress after cracking. At the same time, the increase in the member thickness causes the relative compression zone height to decay. It is found that by comparing the load-displacement relationships of the three types of GFRP bar specimens, during the process of increasing the bar diameter from 13 mm to 19 mm, the initial stiffness of the member changes little because the initial stiffness is greatly affected by the ECC material. However, as the bar diameter increases, both the vertical load and the axial load of the member increase significantly because in the later stage of the member deformation, the bars bear an increasing load. The influence of multiple GFRP bars on the load-displacement relationship of the flexural-tensile coupling member is as shown in Figure 25 . It can be analyzed that under the condition of unchanged reinforcement ratio and effective height, the load-displacement relationship of the GFRP bar ECC flexural-tensile coupling member increases with the increase in the number of GFRP bars, and the increase multiples of the vertical load and the horizontal load are related to the number of GFRP bars.

[0113] The influence of different ECC fiber dosages on the load-displacement relationship of components is as follows Figure 26 (a), (b), and (c) show. First, the influence of ECC fiber dosage on the initial stage of component deformation is small. This is because when the component is in the uncracked state, its compressive strength and elastic modulus are relatively close. Second, during the cracking deformation process of the component, a higher ECC cracking strength can significantly improve the load level of the component. For example, for the component with an ECC fiber dosage of 2.2%, the ECC cracking strength is 5.58 MPa, which is higher than the other four groups of ECC materials. Among them, during the deformation process of the component with an ECC fiber dosage of 2.4%, an obvious load attenuation process occurs. This is because the ultimate tensile strain of this group of ECC is 0.76%, and the ECC in the tension zone of the component reaches the ultimate cracking strain, resulting in the attenuation of the bridging stress.

[0114] (5) Variation law of the neutral axis of flexure-tension coupling components

[0115] Based on the vertical strain distribution at the mid-span of the component, the variation law of the relative height of the neutral axis of the GFRP-reinforced ECC flexure-tension coupling component during the deformation process is as follows Figure 27 (a), (b), and (c) show. First, when the thickness of the component is less than or equal to 55 mm, the relative height of the neutral axis of all specimens is close to 0.95 and can remain stable during the deformation process of the component. This is because when the thickness of the component is small, the axial tensile load causes most areas of the component section to be subjected to tensile stress, keeping the height of the neutral axis of the component stable at a relatively high level. Second, for components with a thickness greater than 55 mm, under the action of flexure-tension load, the height of the neutral axis shows an obvious increase at the initial stage of loading. This is because the axial load of the component continuously increases during the initial stage of deformation, reducing the relative compression zone range of the component section. It should be noted that the relative height of the neutral axis of the 80-mm-thick component decays after reaching the extreme point of 0.93. This is because the axial load cannot satisfy the interface stress balance of the 80-mm component in the large-deformation state, thus causing the relative height of the neutral axis of the component section to decay after the extreme point. This does not occur in the 132-mm-thick component because the relatively large effective height of the component can satisfy the interface stress balance in the deformation state of the component. The influence law of multiple GFRP bars on the relative height of the neutral axis of the flexure-tension coupling component is as follows Figure 28 shown. Analysis shows that the influence of multiple bars on the relative height of the neutral axis of the flexure-tension coupling component is small. During the process of increasing the number of GFRP bars from 1 to 5, the height of the neutral axis slightly increases. This is because with the increase in the number of bars, the uniformity of ECC cracking damage in the GFRP-reinforced ECC flexure-tension coupling component during the deformation process increases.

[0116] The variation process of the relative height of the neutral axis of the component with the deformation amount under different ECC fiber dosage conditions is as follows Figure 29(a), (b), and (c) as shown. Analysis shows that the influence of ECC material properties on the relative height of the neutral axis of the component is mainly concentrated in the initial stage of component deformation and cracking. For specimens with higher ECC cracking strength, the deflections corresponding to the extreme points of the neutral axis height are all greater than 2.5 mm. This is because higher ECC cracking strength has greater crack bridging stress, and the development of the cracking height of ECC in the tensile zone of the component is relatively slow. The ultimate tensile strain of the ECC material with a fiber content of 2.4% is 0.76%. Therefore, when the deflection of the component is greater than 12.5 mm, the relative height of the neutral axis increases. This is because as the ECC in the tensile zone reaches the ultimate tensile strain, the bridging stress in this area decreases. Therefore, in order to maintain the stress balance of the component cross-section, the relative compressive area decreases. However, when the deflection of the component increases to 17.5 mm, the tensile stress borne by the GFRP bars in the tensile zone increases, so the phenomenon of the relative height of the neutral axis decreasing occurs, and this phenomenon is more obvious in the 19 mm GFRP bar specimens.

[0117] (6) Verification of the tensile stiffening effect model of flexural-tensile coupling components

[0118] The comparison between the tensile stiffening effect of GFRP bar ECC flexural-tensile coupling specimens and the test results is sorted out as Figure 30 (a), (b), and (c) as shown, and the test results are the corresponding tensile stiffening test results. Through comparative analysis, it can be seen that the tensile stiffening effect of the flexural-tensile coupling component is in good agreement with the test results. Among them, the 13 mm GFRP bar flexural-tensile coupling specimen has an obvious process of enhancing the tensile stiffening effect after the ECC cracks. The 16 mm and 19 mm GFRP bar flexural-tensile coupling specimens maintain stability in the tensile stiffening effect after the ECC cracks. When the ECC fiber content is 2.4, the tensile stiffening effect of the GFRP bar ECC flexural-tensile coupling component decays when the tensile strain is greater than about 0.5%, which is in agreement with the results of the ECC uniaxial tensile test, indicating that the flexural-tensile coupling component can be used to describe the tensile stiffening effect of GFRP bars and ECC.

[0119] (7) Analysis of the tensile stiffening effect of flexural-tensile coupling components

[0120] Based on the stress-strain relationship in the tensile zone of GFRP bar ECC components, the tensile stiffening effect of flexural-tensile coupling components is determined as Figure 31(a), (b), and (c) are shown. The specific method is as follows: According to the method in the literature, the stress in the tensile zone along the direction of the reinforcement is averaged, and then the strain value is obtained by the change of the strain in the vertical tensile zone of the component, and the tensile stiffening effect of the flexural-tensile coupling component can be obtained. First, during the process of the thickness of the flexural-tensile component changing from 37 mm to 132 mm, there is a similar tensile stiffening effect because the component has the same ECC material properties. However, at the initial stage of the cracking of the tensile stiffening effect, the deformation stiffness decreases with the increase of the component thickness because as the component thickness increases, the change process of the relative height of the neutral axis is relatively slow. Through comparative analysis, it can be seen that the diameter of the GFRP reinforcement has little influence on the tensile stiffening effect of the flexural-tensile component because at the initial stage of the cracking deformation of the component, the cracking process in the tensile zone of the ECC is mainly affected by the component size, and the stress of the GFRP reinforcement is small, so the influence on the tensile stiffening effect is limited.

[0121] The influence of different ECC material properties on the tensile stiffening effect of the flexural-tensile component is as Figure 32 (a), (b), and (c) are shown. Through analysis, it can be seen that the tensile stiffening effect of the flexural-tensile component is mainly affected by the cracking strength and ultimate tensile strain of the ECC. The ECC with a fiber content of 1.8% has the smallest cracking strength of 0.89 MPa. Therefore, the specimens BT-1.8-13-80 / BT-1.8-16-80 / BT-1.8-19-80 all show relatively low cracking strengths. Similarly, the ECC with a fiber content of 2.4% has the smallest ultimate tensile strain. When the tensile strain of the specimens BT-2.4-13-80 / BT-2.4-16-80 / BT-2.4-19-80 is higher than 0.005, an obvious attenuation occurs. The comparison of the influence of different numbers of GFRP reinforcements on the tensile stiffening effect is as Figure 33 shown. Through analysis, it can be seen that the number of GFRP reinforcements has little influence on the tensile stiffening effect because the GFRP reinforcement and the ECC have good cooperative working performance under the flexural-tensile coupling stress state. When the number of GFRP reinforcements increases, the tensile stiffening effect shows slight fluctuations and reaches a stable state after the number of GFRP reinforcements increases to 3, indicating that the GFRP reinforcements have a small degree of mutual influence during the deformation process of the flexural-tensile coupling component.

[0122] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A construction method of a constitutive model for the tensile stiffening effect of GFRP bars in ECC, characterized in that, It includes the following steps: Based on the interfacial slip relationship between GFRP bars and ECC, the analysis variables are determined as bar diameter, ECC fiber content, and ECC cross-sectional area. Multiple finite element analysis models are established and different reinforcement ratios are set; Through finite element analysis of multiple finite element analysis models, the relationship between the effective area of member deformation and the deformation amount under different ECC fiber contents, GFRP bar diameters, and reinforcement ratios is obtained; Based on the two-way stress transfer mechanism of GFRP bars and ECC across cracks, an energy model for the tensile stiffening effect of GFRP bars and ECC is established; Based on the energy model for the tensile stiffening effect of GFRP bars and ECC, a tensile stiffening effect model for direct tension members is established; Through the refined finite element calculation results, the load-displacement relationship of the member and the tensile stiffening effect model of the direct tension member are obtained. The difference between the load borne by the GFRP bare bar and the refined finite element results is calculated to obtain the ECC contribution value, which is the tensile stiffening effect; Taking the tensile stiffening effect as the tensile stress-strain relationship of the ECC material in the tension zone of the member, an ECC material constitutive model considering the tensile stiffening effect of GFRP bars and ECC under direct tension is established.

2. The construction method of a constitutive model for the tensile stiffening effect of GFRP bars in ECC according to claim 1, characterized in that, The step of determining the analysis variables as bar diameter, ECC fiber content, and ECC cross-sectional area based on the interfacial slip relationship between GFRP bars and ECC and establishing multiple finite element analysis models includes the following steps: Establish a three-dimensional solid model for the tensile stiffening of GFRP bars and ECC. After unit size sensitivity analysis, the unit size is determined. The unit types of ECC and GFRP bars are C3D8R, and the interface unit type is COH2D4; Since the specimen is a symmetric model, a quarter model is selected for calculation, and the loading method is concentrated force loading; Zero-thickness interface bonding slip units are inserted at the interface between GFRP bars and ECC.

3. The construction method of a constitutive model for the tensile stiffening effect of GFRP bars in ECC according to claim 2, characterized in that, The tensile stiffening effect model of the direct tension member is as follows: PΔU = E E (Ae,ΔU) = E E-e (ρ,ΔU) + E E-sc (D,ρ,ΔU) + E R-E (D,ρ,ΔU) In the formula, σ E,t represents the tensile stiffening effect of the component contributed by ECC, P GFRP represents the load borne by the elastic strain of the reinforcement, ρ s is the reinforcement ratio of GFRP bars; E is the total input energy of the test; E R-e is the elastic strain energy of GFRP bars; E E-e is the elastic strain energy of ECC; E E-sc is the energy for the development of micro-cracks in ECC; E R-E is the interface slip energy between GFRP bars and ECC; Ae is the effective area; U is the deformation of GFRP bars in the component.

4. The construction method of a constitutive model for the tensile stiffening effect of GFRP bars in ECC according to claim 1, characterized in that It also includes the construction of a constitutive model for the tensile stiffening effect of GFRP bars and ECC considering the bending-tension coupling condition, including the following steps: Based on the interfacial slip relationship between GFRP bars and ECC, a three-dimensional solid bending-tension coupling analysis model is established; Based on the three-dimensional solid bending-tension coupling analysis model, multiple finite element models are constructed according to different bar diameters, ECC fiber contents, and reinforcement ratios, and finite element parameter analysis is carried out to obtain the evolution laws of the cross-sectional stress field, load, and relative height of the neutral axis of the member under the bending-tension coupling action of GFRP bars and ECC, and a constitutive model for the tensile stiffening effect of GFRP bars and ECC considering the bending-tension coupling condition is established.

5. The construction method of a constitutive model for the tensile stiffening effect of GFRP bars in ECC according to claim 4, characterized in that, The step of constructing multiple finite element models according to different bar diameters, ECC fiber contents, and reinforcement ratios based on the three-dimensional solid bending-tension coupling analysis model includes the following steps: Establish a three-dimensional solid model for the tensile stiffening of GFRP bars and ECC, and insert zero-thickness interface bonding slip units at the interface between GFRP bars and ECC; After unit size sensitivity analysis, the unit size is determined. The unit types of ECC and GFRP bars are C3D8R, and the interface unit type is COH2D4; The loading mode of the model is bending load. It is loaded by four-point bending, and axial tension is loaded in a displacement control mode, setting the loading deflection; according to the deformation state of the GFRP bar ECC connection plate, the axial deformation amount is selected.

6. The construction method of a constitutive model for the tension stiffening effect of GFRP bars in ECC according to claim 5, characterized in that, The establishment of the constitutive model of the tensile stiffening effect of GFRP bar ECC considering the bending-tension coupling condition includes the following steps: The numerical analysis method is used to determine the distribution of the maximum principal stress and principal strain of the ECC material in the tensile zone of the GFRP bar ECC bending-tension coupling member. According to the plane section assumption, the average stress-strain relationship of the ECC material in the pure bending section is determined, and then the tensile stiffening effect of the ECC material is obtained; Multiple finite element models are constructed according to different bar diameters, ECC fiber dosages and reinforcement ratios, and finite element analysis is carried out to obtain the principal stress and principal strain fields of the bending-tension coupling member at the final state of the deformation of the bending-tension member, as well as the vertical and horizontal load-displacement relationships of the GFRP bar ECC bending-tension coupling member; the vertical strain distribution at the mid-span of the member is obtained, and the variation law of the relative height of the neutral axis with the loading process during the deformation process of the GFRP bar ECC bending-tension coupling member is determined; According to the evolution laws of the stress field, load and relative height of the neutral axis of the member section, a constitutive model of the tensile stiffening effect of GFRP bar ECC considering the bending-tension coupling condition is established.

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