Long-term creep prediction method for prestressed hybrid fiber reinforced polymer (hfrp) tendon

Abstract

The application discloses a long-term creep prediction method for a prestressed hybrid fiber reinforced polymer (HFRP) tendon, and comprises the following steps: determining each fiber phase of the HFRP tendon to form a composite stress system; establishing a strain coordination relationship and an overall cross-section balance relationship among the fiber phases; respectively establishing a creep constitutive expression of each fiber phase; solving a theoretical creep model of the HFRP tendon under a sustained load by simultaneously solving the strain coordination relationship, the overall cross-section balance relationship and the creep constitutive expressions of the fiber phases; determining a pre-tension correction term of the HFRP tendon based on influences of straightening, initial defect closure and interface stress homogenization of the HFRP tendon caused by pre-tension treatment; and coupling the theoretical creep model and the pre-tension correction term to obtain an actual creep model for accurately predicting a long-term creep behavior of the HFRP tendon. The application solves the problem that an existing long-term creep behavior prediction model for the hybrid fiber HFRP tendon has a narrow application range and is difficult to accurately predict the creep.

Description

Technical Field

[0001] This invention relates to the field of building material performance evaluation technology, specifically to a method for predicting long-term creep of prestressed hybrid fiber HFRP bars. Background Technology

[0002] Fiber-reinforced polymer (FRP) bars possess advantages such as light weight, high strength, corrosion resistance, and good fatigue resistance, making them promising candidates for applications in marine engineering, bridge engineering, underground structures, and other concrete structures with high durability requirements. Compared to traditional steel bars, FRP bars effectively prevent structural durability degradation caused by steel corrosion, thus gradually becoming an important alternative reinforcement material in civil engineering. Common FRP bars include glass fiber reinforced polymer (GFRP) bars, carbon fiber reinforced polymer (CFRP) bars, and basalt fiber reinforced polymer (BFRP) bars.

[0003] However, FRP bars exhibit significant time-dependent deformation, or creep, under long-term continuous loading. For prestressed members or long-term load-bearing members, creep of FRP bars not only causes additional deformation but may also lead to prestress loss, reduced structural stiffness, and deterioration of long-term service performance. Therefore, accurately predicting the long-term creep behavior of FRP bars is a crucial foundation for conducting long-term structural performance analysis, durability assessment, and design optimization.

[0004] Existing research indicates significant differences in the creep behavior of different types of FRP (fiberglass reinforced polymer) bars. GFRP bars typically exhibit larger creep deformation and lower creep rupture stress levels under long-term continuous loading. In contrast, CFRP bars, due to their higher fiber modulus and stronger creep resistance, generally possess superior long-term deformation control capabilities. Therefore, to balance the requirements of high stiffness, high durability, and cost control, hybrid fiber reinforced composite (HFRP) bars, formed by blending two or more fiber components, are gradually gaining attention. Hybrid fiber HFRP bars can achieve a balance between mechanical properties, deformation performance, and economy through the complementary advantages of different fiber components.

[0005] Although hybrid fiber HFRP bars possess good overall performance, their long-term creep behavior is more complex than that of single-fiber FRP bars. On one hand, differences in elastic modulus, strength, creep characteristics, and interfacial behavior exist among different fiber components, leading to synergistic stress distribution and stress redistribution under sustained loads. On the other hand, variations in the hybridization ratio significantly alter the overall material stiffness and long-term deformation response. Furthermore, in engineering applications, pre-stretching treatment can reduce FRP bar creep. This treatment tends to straighten the fibers, promotes the closure of initial defects, and improves the uniformity of interfacial stress, thereby further influencing subsequent creep evolution. Therefore, the creep behavior of hybrid fiber HFRP bars is typically controlled by multiple factors, including material composition, hybridization ratio, stress level, and pre-stretching treatment.

[0006] Currently, prediction models for the long-term creep behavior of FRP materials or FRP ribs can be broadly classified into two categories based on different modeling approaches: physical constitutive models and empirical / phenomenological models.

[0007] Physical constitutive models are typically based on the viscoelastic theory of materials, using a combination of spring and damping elements to describe the time-dependent deformation behavior of materials under sustained loads. These models have a certain mechanical mechanism basis and are often used to simulate the creep response of materials from initial loading to long-term deformation. Common existing physical constitutive models mainly include the following categories: Maxwell model, Kelvin model, three-element model, Burgers model, and improved physical models.

[0008] Empirical or phenomenological models primarily rely on experimental data, directly using empirical functions to describe the change in creep strain over time. These models are typically simple in form, have few parameters, and are easy to apply in engineering, thus they are widely used in the long-term creep prediction of FRP (fiberglass reinforced plastic) reinforcement. Existing common models mainly include the following categories: power function models, exponential function models, Findley models, semi-logarithmic models, and other phenomenological models.

[0009] Existing long-term creep behavior prediction models have the following problems: 1. Existing FRP reinforcement creep prediction methods have a narrow scope of application and are difficult to accurately predict the creep of hybrid fiber HFRP reinforcement.

[0010] Most existing methods for predicting creep in FRP (fiber reinforced plastic) reinforcement are designed for single-fiber FRP composites, with model parameters and approaches typically determined based on a single material system. However, for hybrid fiber HFRP reinforcements composed of two or more fiber components, significant synergistic stress distribution and stress redistribution occur under sustained loading due to differences in elastic modulus, strength, creep characteristics, and interfacial interactions among the different fiber components. Existing models often treat these as homogeneous materials, making it difficult to accurately reflect the true long-term creep behavior of hybrid fiber HFRP reinforcements. Therefore, their applicability is limited, and the accuracy of prediction results is insufficient.

[0011] 2. Most existing technologies only consider a single factor, which makes it difficult to meet the unified prediction requirements under multi-factor coupled conditions.

[0012] Most existing creep models only consider a single factor such as stress level, material type, or a specific mix ratio, and are often established through empirical fitting under specific experimental conditions. When the mixture ratio, service stress level, or pre-stretching treatment conditions change, it is usually necessary to refit the model parameters, resulting in poor model versatility. For the multi-factor combined conditions commonly encountered in actual engineering, existing technologies lack a unified prediction method, leading to low model application efficiency and limiting its widespread use.

[0013] 3. Existing technologies do not adequately consider the effects of pre-stretching treatment, resulting in significant deviations from actual working conditions.

[0014] In practical applications of hybrid fiber HFRP reinforcement, pre-stretching treatment tends to straighten the fibers and causes changes such as initial defect closure and interface stress homogenization, thus significantly affecting the subsequent creep development process of the material. However, existing models usually do not explicitly introduce pre-stretching treatment as an independent influencing factor, and can only describe the creep behavior under untreated or idealized conditions, making it difficult to accurately reflect the long-term deformation response under actual service conditions. Therefore, the predicted results are prone to deviation from engineering reality.

[0015] 4. Existing technologies are not sufficiently applicable to engineering applications for long-term creep prediction.

[0016] While some existing models can fit experimental results under certain conditions, they suffer from problems such as a large number of parameters, complex solution processes, and unclear applicability boundaries. Some models rely too heavily on specific experimental data, while others are difficult to directly apply across different material systems. These issues lead to high model usage costs, low analytical efficiency, and hinder their direct application in engineering design, long-term performance evaluation, and durability analysis.

[0017] 5. Existing technologies often rely on a large number of long-term experiments to obtain high-precision prediction results, which is time-consuming and costly.

[0018] Due to the complex long-term creep behavior of hybrid fiber HFRP bars, existing technologies, lacking a unified model, often require lengthy continuous loading tests to obtain data and perform fitting analysis. These tests are time-consuming, costly, and inefficient, hindering rapid material selection, structural design, and long-term performance evaluation. Therefore, existing technologies suffer from low efficiency in practical engineering applications. Summary of the Invention

[0019] To overcome the shortcomings of existing technologies, a method for predicting the long-term creep of prestressed hybrid fiber HFRP bars is provided to address the problem that existing models for predicting the long-term creep behavior of hybrid fiber HFRP bars have a narrow scope of application and are difficult to accurately predict creep.

[0020] To achieve the above objectives, a method for predicting the long-term creep of prestressed hybrid fiber HFRP bars is provided, comprising the following steps: Determine the fiber phases of the HFRP reinforcement to form a composite stress-bearing system; Establish the strain compatibility relationship and overall cross-sectional equilibrium relationship among the various fiber phases; Establish the creep constitutive expressions for each fiber phase; By combining the strain compatibility relationship, the overall cross-sectional equilibrium relationship, and the creep constitutive expression of each fiber phase, the theoretical creep model of the HFRP reinforcement under continuous load is established. Based on the effects of pre-stretching treatment on the straightening, initial defect closure, and interface stress homogenization of the HFRP bar, a pre-stretching correction term for the HFRP bar is determined. The theoretical creep model is coupled with the pre-stretching correction term to obtain the actual creep model for accurately predicting the long-term creep behavior of HFRP bars. Furthermore, the strain compatibility relationship ensures that the axial strain of each fiber phase is always equal, and is expressed by Formula 1, which is: ; in, e C (t) Strain for the high-modulus FRP phase; e G (t) Strain for the low-modulus FRP phase; e H (t) This represents the total axial strain of the mixed reinforcement.

[0021] Furthermore, the overall cross-sectional equilibrium relationship is that the nominal stress of the HFRP reinforcement is proportionally shared by each fiber phase and expressed by Formula 2, which is: ; in, s The nominal stress of the HFRP reinforcement; r C The area ratio / hybridity of high modulus FRP fibers; s C (t) The actual stress of the high-modulus FRP phase; r G The area ratio / hybridity of low modulus FRP fibers; s G (t) This represents the actual stress of the low-modulus FRP phase.

[0022] Furthermore, the creep constitutive expression is: ; in, E i It is the elastic modulus; s i (t) For stress; e cr,i (t,s i (t)) For creep strain; i For the first i Fiber phase.

[0023] Furthermore, the strain of the HFRP reinforcement consists of two parts: elastic strain and creep strain increment. For the fiber phase with high elastic modulus and good creep resistance, the creep strain increment is expressed by Formula 3, which is: ; in, ; .

[0024] Furthermore, for fiber phases with low elastic modulus and poor creep resistance, the creep strain increment is expressed by Formula 4, which is: .

[0025] Furthermore, the theoretical creep model is as follows: .

[0026] Furthermore, the pre-stretch correction term is e p (r C ,η,t), where η It is the ratio of service stress to pre-tension stress.

[0027] Furthermore, when the pre-stretching correction term simultaneously represents the rapid corrective effect of pre-stretching in the early stages and its sustained influence on creep in the middle and later stages, the pre-stretching correction term is: ; in, A p (r C ,or) The coefficient of the logarithmic term represents the long-term, gradual correction effect of pretension on creep; B p (r C ,or) The coefficient of the rapid saturation term represents the early and rapid adjustment effect of pretension on creep; t p The characteristic timescale associated with the pre-stretching effect.

[0028] Furthermore, the actual creep model is as follows: .

[0029] The beneficial effect of this invention is that the long-term creep prediction method for prestressed hybrid fiber HFRP bars has a wider range of applications and can be accurately applied to HFRP bars. Most existing superior creep prediction models are mainly established for single-fiber FRP bars, making it difficult to accurately reflect the synergistic stress distribution and stress redistribution process among different fiber components in HFRP bars. This invention establishes a unified creep prediction method for HFRP bars, which can more accurately describe the long-term creep behavior under the combined action of different fiber components, thus having a wider range of applications and stronger specificity.

[0030] The long-term creep prediction method for prestressed hybrid fiber HFRP bars of the present invention can uniformly consider the coupled effects of hybridization ratio, stress level, and pre-stretching treatment. Existing technologies typically only consider single factors such as stress level, material type, or a specific mix ratio, making it difficult to meet the prediction requirements under conditions where multiple factors act together. The present invention can comprehensively consider the combined effects of hybridization ratio, stress level, and pre-stretching treatment on creep behavior within the same model framework, thus exhibiting better uniformity and engineering applicability.

[0031] The long-term creep prediction method for prestressed hybrid fiber HFRP bars of the present invention can explicitly characterize the impact of pre-stretching treatment on subsequent creep evolution, resulting in higher prediction accuracy. Existing models typically do not explicitly introduce pre-stretching treatment as an independent influencing factor, making it difficult to reflect the effects of pre-stretching treatment on fiber straightening, initial defect closure, and interface stress homogenization. Therefore, the prediction results are prone to deviation from actual operating conditions. The present invention introduces a pre-stretching correction term, incorporating the impact of pre-stretching treatment on subsequent creep development into the prediction model, thereby making the prediction results closer to the actual service conditions and improving the model's prediction accuracy.

[0032] The long-term creep prediction method for prestressed hybrid fiber HFRP reinforcement of this invention combines theoretical foundation with engineering practicality, reducing reliance on experiments and improving analytical efficiency. Existing physical models often have many parameters and complex solutions, while existing empirical models usually lack descriptions of the synergistic effects within the hybrid fibers, and often require extensive long-term experiments for refitting under different working conditions. This invention combines multiphase synergistic stress analysis with a unified prediction model, which has a sound mechanical mechanism foundation and is easy to apply in engineering. It can achieve long-term creep prediction under limited experimental data conditions, thereby reducing reliance on long-term experiments and improving analytical efficiency. Attached Figure Description

[0033] Other features, objects, and advantages of this application will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings: Figure 1 This is a schematic diagram of the cross-section of HFRP reinforcement in an embodiment of the present invention.

[0034] Figure 2 This is a schematic flowchart of a method for predicting long-term creep of prestressed hybrid fiber HFRP reinforcement according to an embodiment of the present invention.

[0035] Figure 3 to Figure 7 This is a schematic diagram showing the creep prediction results and experimental results of HFRP tendons.

[0036] Figure 8 This is a schematic diagram of the creep loading device according to an embodiment of the present invention. Detailed Implementation

[0037] The present application will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, only the parts relevant to the invention are shown in the accompanying drawings.

[0038] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0039] This invention provides a method for predicting the long-term creep of prestressed hybrid fiber HFRP bars, comprising the following steps: S1. Determine the fiber phases of the HFRP reinforcement to form a composite stress system.

[0040] See Figure 1 As shown, HFRP reinforcement is considered as a composite stress system composed of at least two different fiber components.

[0041] S2. Establish the strain coordination relationship between each fiber phase and the overall cross-sectional equilibrium relationship.

[0042] The deformation compatibility condition is satisfied, and the strain compatibility relationship is such that the axial strain of each fiber phase is always equal, expressed by Formula 1, which is: ; in, e C (t) Strain (με) for high-modulus FRP phase; e G (t) Strain (με) for the low-modulus FRP phase; e H (t) The total axial strain (με) of the mixed reinforcement.

[0043] The cross-sectional equilibrium condition is satisfied, and the overall cross-sectional equilibrium relationship is that the nominal stress of the HFRP reinforcement is shared proportionally by each fiber phase and expressed by Formula 2, which is: ; in, s The nominal stress (MPa) of the HFRP reinforcement. r C The area ratio / hybridity of high modulus FRP fibers; s C (t)The actual stress (MPa) of the high-modulus FRP phase; r G The area ratio / hybridity of low modulus FRP fibers; s G (t) The actual stress (MPa) of the low-modulus FRP phase.

[0044] in, r G =1- r C .

[0045] S3. Establish the creep constitutive expressions for each fiber phase.

[0046] During creep, the strain of HFRP reinforcement consists of two parts: elastic strain and creep strain increment.

[0047] Specifically, the creep constitutive expression is: ; in, E i Elastic modulus (GPa); s i (t) Stress (MPa); e cr,i (t,s i (t)) The creep strain is (με). i For the first i Fiber phase.

[0048] For fiber phases with high elastic modulus and good creep resistance, the creep strain increment is expressed by Formula 3, which is: ; in, ; It can be input and corrected according to the elastic modulus of the specific fiber phase.

[0049] For fibrous phases with low elastic modulus and poor creep resistance, the creep strain increment is expressed by Formula 4, which is: .

[0050] in, a(t)、b 1 (t)、b 2 (t)These are time-varying coefficients obtained from the GFRP creep regression model, which can be corrected according to the specific fiber phase performance parameters.

[0051] S4. By combining the strain compatibility relationship, the overall cross-sectional equilibrium relationship, and the creep constitutive expression of each fiber phase, the theoretical creep model of HFRP reinforcement under continuous load is established.

[0052] Specifically, by combining the strain compatibility relationship, the cross-sectional equilibrium relationship, and the creep constitutive relationship of each fiber phase, the theoretical creep model of HFRP reinforcement under continuous load is solved.

[0053] From the cross-sectional equilibrium relationship, we can obtain: .

[0054] From the deformation compatibility condition, we get: .

[0055] Combining the two formulas above, we can obtain the result only for the low-modulus FRP fiber phase. s G (t) cubic equation: ; in: ; ; .

[0056] Solving the cubic equation yields the theoretical creep model for the hybrid reinforcement: .

[0057] S5. Based on the effects of pre-stretching treatment on the straightening, initial defect closure, and interface stress homogenization of HFRP bars, determine the pre-stretching correction term for HFRP bars.

[0058] Pre-stretch correction term is e p (r C ,η,t), where η It is the ratio of service stress to pre-tension stress.

[0059] Specifically, the revised theoretical creep model is as follows: .

[0060] When the pre-stretching correction term simultaneously represents the rapid corrective effect of pre-stretching in the early stages and its sustained impact on creep in the middle and later stages, the pre-stretching correction term is: ; in, A p (r C ,or) The coefficient of the logarithmic term represents the long-term, gradual correction effect of pretension on creep; B p (r C ,or) The coefficient of the rapid saturation term represents the early and rapid adjustment effect of pretension on creep; t p The characteristic timescale associated with the pre-stretching effect.

[0061] Logarithmic terms describe the gradual decay of the pre-stretch memory effect over time, while introducing... t+t p This is to capture the rapid adjustment process during the initial loading phase and ensure that the correction term is zero at t=0.

[0062] parameter t p It is a characteristic timescale related to the pre-stretching effect, not a material constant. t p The value is determined based on the pre-stretching time.

[0063] S6. Couple the theoretical creep model with the pre-stretching correction term to obtain the actual creep model for accurate prediction of the long-term creep behavior of HFRP bars. By coupling the theoretical creep model with the pre-stretching correction term, we obtain the actual creep model that comprehensively considers the effects of the mixture ratio, stress level, and pre-stretching treatment: The actual creep model is as follows: .

[0064] The long-term creep prediction method for prestressed hybrid fiber HFRP bars of the present invention can be applied to two-phase HFRP bars, and can also be extended to multi-phase HFRP bars composed of three or more fiber components. In the two-phase case, they can be represented as the first fiber phase and the second fiber phase, respectively; in the multi-phase case, it can be extended to the third fiber phase. i A unified form of fibrous phase.

[0065] Combination Figure 1As shown, HFRP reinforcement is formed by combining at least two different fiber components (low-modulus fiber 1 and high-modulus fiber 2) with a resin matrix. The different fiber components can be any two or more combinations of carbon fiber, glass fiber, basalt fiber, aramid fiber, or other reinforcing fibers. Each fiber component is arranged along the axial direction of the reinforcement and, under the bonding effect of the resin matrix, together forms an integral load-bearing unit.

[0066] For HFRP bars, the overall load-bearing capacity is not simply equal to the linear sum of the load-bearing capacities of each fiber component. Instead, under continuous load, due to the differences in elastic modulus, strength, and creep characteristics of different fiber components, a synergistic stress distribution and stress redistribution occur within the overall structure. Therefore, this invention treats HFRP bars as a composite stress system composed of multiple parallel fiber phases in order to establish a creep prediction model that better reflects the actual stress state.

[0067] The proportion of each fiber phase in the cross-section can be represented by the area fraction, which reflects the mixing ratio of different fiber components. The higher the mixing ratio, the greater the contribution of the corresponding fiber component to the overall stress, thus significantly affecting the long-term creep response of the overall reinforcement.

[0068] Structural description of the HFRP reinforcement of the present invention: 1. The principle of strain coordination.

[0069] Under the premise that the different fiber phases of the HFRP reinforcement are continuous and deform together along the axial direction, the total axial strain of each fiber phase remains consistent at the same moment. That is, the overall strain of the HFRP reinforcement and the corresponding strain of each fiber phase satisfy the strain compatibility relationship.

[0070] For two-phase HFRP reinforcement, it can be represented as: Axial strain of the first fiber phase; Axial strain of the second fiber phase; Axial strain of integral HFRP reinforcement; All three are equal at the same time.

[0071] This relationship reflects that although different fiber components have different material properties, their macroscopic axial deformation remains consistent when they are composite molded and subjected to stress together, which is the basis for establishing a unified creep model.

[0072] 2. Principle of cross-sectional equilibrium.

[0073] Under sustained load, the nominal external stress borne by the HFRP reinforcement as a whole is shared by each fiber phase according to its respective stress. The overall stress satisfies the section equilibrium relationship, that is, the overall external load is equal to the sum of the loads borne by each fiber phase.

[0074] For two-phase HFRP reinforcement, the overall nominal stress is shared by the first and second fiber phases according to their cross-sectional area fractions. Due to the different creep deformation rates of the different fiber phases, the stress borne by each phase will change over time, resulting in a stress redistribution phenomenon.

[0075] 3. The principle of total strain composition of each fiber phase.

[0076] In this invention, the total strain of each fiber phase under sustained load consists of two parts: Elastic strain; Creep strain increment.

[0077] Elastic strain is determined by the instantaneous stress and elastic modulus of the fiber phase; creep strain increment is determined by the creep characteristics of the fiber phase and the duration of loading. Therefore, different fiber phases exhibit different creep strain evolution patterns due to their different material properties.

[0078] In this invention, corresponding creep constitutive expressions are established based on existing experimental laws or empirical formulas for different fiber materials. Then, the constitutive properties of each phase are combined with the strain compatibility relationship and the cross-sectional equilibrium relationship to form a theoretical creep model for HFRP reinforcement.

[0079] 4. Explanation of the principle of pre-stretching correction.

[0080] After pre-stretching, the internal structure of HFRP bars changes, mainly in the following ways: Fibers that were previously bent or slightly undulating tend to straighten; Initial pores, microcracks, or localized defects close or weaken; The interfacial forces between different fiber phases and between fibers and the resin matrix are more uniform; The initial stress distribution inside the material is more stable.

[0081] These changes will directly affect the creep development process under subsequent continuous loading, especially the rapid deformation stage in the early stage of loading and the long-term evolution trend in the middle and later stages. Therefore, this invention does not simply equate the pre-stretching treatment to a fixed constant, but instead constructs a time-varying pre-stretching correction term.

[0082] This pre-stretching correction term includes at least two types of effects: (1) The rapid adjustment effect in the initial stage.

[0083] It is used to describe the rapid effect of pre-stretching treatment on creep behavior in the early stages of sustained loading, such as the rapid straightening of fibers and the rapid adjustment of local interfacial stress.

[0084] (2) The continuous decay effect in the middle and late stages.

[0085] This is used to describe how pre-stretching treatment still affects creep evolution in the mid-to-late stages, but this effect gradually weakens over time, i.e., there is a decay process of the "pre-stretch memory effect".

[0086] Furthermore, the parameters of the pre-stretching correction term in this invention can also be associated with the following factors: Mixing ratio; The stress ratio between the service stress and the pre-tensioned reference stress; Pre-stretch duration.

[0087] Therefore, the pre-stretching correction term of the present invention is not simply an empirical coefficient, but a correction mechanism that can reflect the combined effect of pre-stretching treatment, mixing ratio and stress level.

[0088] Combination Figure 3 to Figure 7 As shown, the comparison between the predicted and experimental results of HFRP tendon creep is presented. The results show that within the range of hybridization ratios and stress levels studied in the experiment, the predicted model and experimental values ​​agree well. The coefficient of determination R0 for the five groups of HFRP specimens is also shown. 2 All values ​​are greater than 0.98, and the prediction error at the 1000h endpoint is controlled within 6.2%, indicating that the proposed pre-tensioning correction term can effectively improve the prediction accuracy of the theoretical model for actual creep behavior.

[0089] See also Figure 3 to Figure 7 To verify the long-term creep prediction method for prestressed hybrid fiber HFRP reinforcement proposed in this invention, five groups of hybrid fiber HFRP reinforcement specimens were prepared and subjected to long-term creep tests. The hybrid fiber HFRP reinforcements were prepared using a pultrusion molding process. The reinforcing fibers included high-modulus carbon fiber and high-modulus glass fiber, with epoxy resin as the matrix, and the total fiber integral was approximately 70%. All prepared specimens were circular reinforcements, preferably with a nominal diameter of 8 mm. To prevent premature failure at the loading end, steel sleeve anchoring sections were provided at both ends of the specimens, and expanding cement grout was injected into the steel sleeves for anchoring. The total length of each specimen was preferably 1080 mm to match the clamping and measurement requirements of the creep loading device.

[0090] according to Figure 3 to Figure 7 According to the labeling, the five groups of specimens can be prepared as follows: The first group of specimens corresponds to Figure 3 The specimen, numbered C / G-1:4-0.30, is a hybrid fiber HFRP reinforcement with a carbon fiber to glass fiber ratio of 1:4. The sustained load stress level is 0.30 times the design value of the tensile strength of this group of specimens. f f ; The second set of specimens corresponds to Figure 4The specimen was designated C / G-1:4-0.35, indicating a carbon fiber to glass fiber blend ratio of 1:4 and a sustained load stress level of 0.35. f f ; The third set of specimens corresponds to Figure 5 The specimen was designated C / G-1:4-0.55, indicating a carbon fiber to glass fiber blend ratio of 1:4 and a sustained load stress level of 0.55. f f ; The fourth group of specimens corresponds Figure 6 The specimen was designated C / G-1:2-0.35, indicating a carbon fiber to glass fiber blend ratio of 1:2 and a sustained load stress level of 0.35. f f ; The fifth group of specimens corresponds to Figure 7 The specimen was designated C / G-1:6-0.35, indicating a carbon fiber to glass fiber blend ratio of 1:6 and a sustained load stress level of 0.35. f f .

[0091] in, f f The tensile strength design value is determined with a 95% guarantee rate for the corresponding hybrid fiber HFRP reinforcement. Before the formal creep test, the elastic modulus, ultimate tensile strength, and ultimate strain of each group of specimens are measured by uniaxial tensile test, and the target load value required for subsequent creep loading is determined accordingly.

[0092] For each group of specimens, at least 3 parallel specimens should be prepared, preferably 5 parallel specimens, in order to reduce the influence of the dispersion of mixed fibers, local defects of resin and differences in interface state on the long-term creep results. Figure 3 to Figure 7 The experimental data can be plotted using the average creep strain increment at each measuring point for parallel specimens in the same group. This setting can more realistically reflect the long-term creep response of hybrid fiber HFRP bars under different hybridization ratios and stress levels.

[0093] To improve the internal fiber straightening of the hybrid fiber HFRP reinforcement and reduce the impact of initial defects on long-term creep, the five groups of specimens underwent a uniform pre-stretching treatment before the formal long-term creep test. The pre-stretching treatment preferably used a 0.3 mm diameter. f f The pre-tension stress level was maintained for 3 hours. Under this pretreatment condition, the hybrid fiber HFRP bar achieved good fiber straightening while maintaining low internal damage and superior subsequent creep stability. Therefore, it was used as the unified pretreatment condition for subsequent long-term creep tests.

[0094] During long-term creep tests, the anchored specimen is installed in a creep loading device, and the load is slowly increased to 0.3. f f The specimen was pre-stretched and held for 3 hours. After the pre-stretching was completed, the load was removed, allowing the specimen to return to a state without external load. Subsequently, a formal long-term creep test was performed on the specimen. Through the above pretreatment, the initially bent fibers in the fiber bundle tend to straighten, and the interfacial stress distribution becomes more uniform.

[0095] The creep test method for the specimen is as follows: (a) Creep testing device.

[0096] The creep test was conducted using a long-term creep loading device. The loading device employed a double-lever amplification loading mechanism to ensure the stable application of continuous load; the displacement or strain acquisition system used an automatic displacement measurement and data acquisition device to collect the axial deformation of the specimen under continuous load in real time.

[0097] Combination Figure 8 As shown, the creep loading device includes a base 3. The base has a first end and a second end opposite to each other. A pull-down head 4 is vertically mounted on the first end of the base. A support column 5 is provided in the middle of the base. A first rocker arm 7 is rotatably mounted on the support column via a first hinge shaft 6. An upper pull-up head 8 is rotatably mounted on one end of the first rocker arm. The upper pull-up head and the pull-down head are arranged in the same direction. The two ends of the specimen 9 are respectively mounted on the pull-down head and the upper pull-up head. A hanging rod 10 is rotatably mounted on the other end of the first rocker arm. A second rocker arm 11 is rotatably mounted on the lower end of the hanging rod. The rotation axis of the second rocker arm is located in the middle of the second rocker arm. A pull rod 12 is vertically mounted on the second end of the base. The upper end of the pull rod is hinged to one end of the second rocker arm via a second hinge shaft 13. A tray 14 is suspended from the other end of the second rocker arm. The tray is used to place weights 15.

[0098] (II) Specific testing steps Step 1: Specimen installation.

[0099] The anchored hybrid fiber HFRP bar specimens were installed on the long-term creep loading device, ensuring the specimen axis was aligned with the loading direction to prevent eccentric loading. After installation, the displacement gauge or strain acquisition device was zeroed, and the specimen number, hybridization ratio, diameter, pre-tension state, and target sustained load stress level were recorded.

[0100] Step 2: Determine the target load value.

[0101] Based on the 95% guaranteed tensile strength design value ff of each group of specimens, calculate the loading force value corresponding to the target sustained load stress level. For Figure 3 to Figure 7 The corresponding 5 groups of specimens were subjected to continuous loads of 0.30ff, 0.35ff, or 0.55ff, respectively.

[0102] Step 3: Pre-stretching treatment.

[0103] The test specimens are first loaded to 0.3 ff and held for 3 hours to complete the pre-stretching treatment before being unloaded. This step is used to standardize the initial state of the specimens and improve the comparability between different groups. This step can be omitted for control groups that do not require pre-stretching.

[0104] Step 4: Begin continuous loading.

[0105] The pretreated specimens were reloaded to their respective sustained load levels, and timing was started. The moment the target load was reached was recorded as the start time of the creep test. The loading process should be as smooth as possible to avoid impact loading from interfering with the initial deformation data.

[0106] Step 5: Record deformation in different time periods.

[0107] After the target load is reached, the axial deformation data of the specimen is recorded at predetermined time points. The preferred sampling time is: 1 min, 3 min, 6 min, 9 min, 15 min, 30 min, 45 min; 1 h, 1.5 h, 2 h, 4 h, 10 h, 24 h, 48 h, 72 h, 96 h, 120 h; Records were then taken every 120 hours until 1000 hours.

[0108] By using the aforementioned phased sampling method, the strain evolution patterns of the rapid creep stage in the initial loading phase and the stable creep stage in the middle and later stages can be captured simultaneously.

[0109] Step 6: Calculate the creep strain increment.

[0110] Using the instantaneous elastic deformation of the specimen after being loaded with the target sustained load as a benchmark, the creep strain increment at each subsequent time point is obtained by subtracting the instantaneous elastic deformation from the total deformation measured at each subsequent time point. By plotting time t on the x-axis and creep strain increment on the y-axis, the creep strain increment-time relationship curves for each group of specimens can be plotted.

[0111] Step 7: Obtain Figure 3 to Figure 7 Experimental results.

[0112] The creep strain increment data of the above 5 groups of specimens were processed over time to obtain: Figure 3 The creep strain increment-time relationship corresponding to group C / G-1:4-0.30; Figure 4 The creep strain increment-time relationship corresponding to group C / G-1:4-0.35; Figure 5 Creep strain increment-time relationship corresponding to group C / G-1:4-0.55; Figure 6 The creep strain increment-time relationship corresponding to group C / G-1:2-0.35; Figure 7 The creep strain increment-time relationship corresponding to group C / G-1:6-0.35.

[0113] Step 8: Model prediction and comparison plotting.

[0114] The mixing ratio, sustained load stress level, and pre-stretching parameters of each group of specimens were substituted into the long-term creep prediction model established in this invention to calculate the theoretically predicted creep strain increment at each time point. The calculated predicted values ​​and experimentally measured values ​​were then plotted on the same coordinate system to obtain the predicted values. Figure 3 to Figure 7 The "experimental value - predicted value" comparison curve is shown in the figure. This step is used to verify the applicability and accuracy of the prediction model of the present invention for the long-term creep behavior of hybrid fiber HFRP bars under different hybridization ratios and stress levels.

[0115] The long-term creep prediction method for prestressed hybrid fiber reinforced polymer (HFRP) bars of this invention treats HFRP bars as a composite stress system composed of different fiber phases, and establishes a synergistic stress analysis method among different fiber phases to describe the common working state among different fiber components under continuous load. Instead of simply treating HFRP bars as a single homogeneous material for empirical fitting, a unified synergistic stress creep analysis framework is established for different fiber components of HFRP bars.

[0116] The long-term creep prediction method for prestressed hybrid fiber reinforced polymer (HFRP) bars of the present invention is based on a stress redistribution solution mechanism using strain compatibility and cross-sectional equilibrium relationships. This invention solves the stress redistribution process among different fiber components of HFRP bars under long-term continuous loading by establishing strain compatibility relationships between different fiber phases and the overall cross-sectional equilibrium relationship, thereby obtaining the overall creep response.

[0117] The long-term creep prediction method for prestressed hybrid fiber HFRP bars of the present invention is a unified creep prediction method that comprehensively considers the hybridization ratio, stress level and pre-stretching treatment.

[0118] The long-term creep prediction method for prestressed hybrid fiber HFRP bars of the present invention simultaneously introduces three key influencing factors—hybridization ratio, stress level, and pre-stretching treatment—in the same prediction model, and establishes a unified creep prediction method applicable to different working conditions.

[0119] The long-term creep prediction method for prestressed hybrid fiber HFRP tendons of the present invention sets up a special pre-stretching correction term to reflect the effects of pre-stretching treatment on subsequent creep evolution, such as fiber straightening, initial defect closure and interface stress homogenization caused by pre-stretching treatment.

[0120] The long-term creep prediction method for prestressed hybrid fiber HFRP bars of the present invention has a wider range of applications and can be accurately applied to HFRP bars. Most existing superior creep prediction models are mainly established for single-fiber FRP bars, which are difficult to accurately reflect the synergistic stress and stress redistribution process among different fiber components in HFRP bars. The present invention establishes a unified creep prediction method for HFRP bars, which can more accurately describe the long-term creep behavior under the combined action of different fiber components, and therefore has a wider range of applications and is more targeted.

[0121] The long-term creep prediction method for prestressed hybrid fiber HFRP bars of the present invention can uniformly consider the coupled effects of hybridization ratio, stress level, and pre-stretching treatment. Existing technologies typically only consider single factors such as stress level, material type, or a specific mix ratio, making it difficult to meet the prediction requirements under conditions where multiple factors act together. The present invention can comprehensively consider the combined effects of hybridization ratio, stress level, and pre-stretching treatment on creep behavior within the same model framework, thus exhibiting better uniformity and engineering applicability.

[0122] The long-term creep prediction method for prestressed hybrid fiber HFRP bars of the present invention can explicitly characterize the impact of pre-stretching treatment on subsequent creep evolution, resulting in higher prediction accuracy. Existing models typically do not explicitly introduce pre-stretching treatment as an independent influencing factor, making it difficult to reflect the effects of pre-stretching treatment on fiber straightening, initial defect closure, and interface stress homogenization. Therefore, the prediction results are prone to deviation from actual operating conditions. The present invention introduces a pre-stretching correction term, incorporating the impact of pre-stretching treatment on subsequent creep development into the prediction model, thereby making the prediction results closer to the actual service conditions and improving the model's prediction accuracy.

[0123] The long-term creep prediction method for prestressed hybrid fiber HFRP reinforcement of this invention combines theoretical foundation with engineering practicality, reducing reliance on experiments and improving analytical efficiency. Existing physical models often have many parameters and complex solutions, while existing empirical models usually lack descriptions of the synergistic effects within the hybrid fibers, and often require extensive long-term experiments for refitting under different working conditions. This invention combines multiphase synergistic stress analysis with a unified prediction model, which has a sound mechanical mechanism foundation and is easy to apply in engineering. It can achieve long-term creep prediction under limited experimental data conditions, thereby reducing reliance on long-term experiments and improving analytical efficiency.

[0124] The above description is merely a preferred embodiment of this application and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of the invention involved in this application is not limited to technical solutions formed by specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the inventive concept. For example, technical solutions formed by substituting the above features with (but not limited to) technical features with similar functions disclosed in this application.

Claims

1. A method for predicting long-term creep of prestressed hybrid fiber HFRP bars, characterized in that, Includes the following steps: Determine the fiber phases of the HFRP reinforcement to form a composite stress-bearing system; Establish the strain compatibility relationship and overall cross-sectional equilibrium relationship among the various fiber phases; Establish the creep constitutive expressions for each fiber phase; By combining the strain compatibility relationship, the overall cross-sectional equilibrium relationship, and the creep constitutive expression of each fiber phase, the theoretical creep model of the HFRP reinforcement under continuous load is established. Based on the effects of pre-stretching treatment on the straightening, initial defect closure, and interface stress homogenization of the HFRP bar, a pre-stretching correction term for the HFRP bar is determined. The theoretical creep model is coupled with the pre-stretching correction term to obtain the actual creep model for accurately predicting the long-term creep behavior of HFRP bars.

2. The method for predicting long-term creep of prestressed hybrid fiber HFRP reinforcement according to claim 1, characterized in that, The strain compatibility relationship is that the axial strain of each fiber phase is always equal, and is expressed by Formula 1, which is: ； in, ε C (t) Strain for the high-modulus FRP phase; ε G (t) Strain for the low-modulus FRP phase; ε H (t) This represents the total axial strain of the mixed reinforcement.

3. The method for predicting long-term creep of prestressed hybrid fiber HFRP reinforcement according to claim 2, characterized in that, The overall cross-sectional equilibrium relationship is that the nominal stress of the HFRP reinforcement is proportionally shared by each fiber phase and expressed by Formula 2, which is: ； in, σ The nominal stress of the HFRP reinforcement; ρ C The area ratio / hybridity of high modulus FRP fibers; σ C (t) The actual stress of the high-modulus FRP phase; ρ G The area ratio / hybridity of low modulus FRP fibers; σ G (t) This represents the actual stress of the low-modulus FRP phase.

4. The method for predicting long-term creep of prestressed hybrid fiber HFRP reinforcement according to claim 3, characterized in that, The creep constitutive expression is: ； in, E i It is the elastic modulus; σ i (t) For stress; ε cr,i (t,σ i (t)) For creep strain; i For the first i Fiber phase.

5. The method for predicting long-term creep of prestressed hybrid fiber HFRP reinforcement according to claim 4, characterized in that, The strain of the HFRP reinforcement consists of two parts: elastic strain and creep strain increment. For the fiber phase with high elastic modulus and good creep resistance, the creep strain increment is expressed by Formula 3, which is: ； in, ; 。 6. The method for predicting long-term creep of prestressed hybrid fiber HFRP reinforcement according to claim 5, characterized in that, For fiber phases with low elastic modulus and poor creep resistance, the creep strain increment is expressed by Formula 4, which is: 。 7. The method for predicting long-term creep of prestressed hybrid fiber HFRP reinforcement according to claim 6, characterized in that, The theoretical creep model is as follows: 。 8. The method for predicting long-term creep of prestressed hybrid fiber HFRP reinforcement according to claim 7, characterized in that, The pre-stretching correction term is: ε p (ρ C ,η,t), where η It is the ratio of service stress to pre-tension stress.

9. The method for predicting long-term creep of prestressed hybrid fiber HFRP reinforcement according to claim 8, characterized in that, When the pre-stretching correction term simultaneously represents the rapid corrective effect of pre-stretching in the early stages and its sustained impact on creep in the middle and later stages, the pre-stretching correction term is: ； in, A p (ρ C ,η,t) The coefficient of the logarithmic term; B p (ρ C ,η,t) The coefficients of the fast saturation term; τ p The characteristic timescale associated with the pre-stretching effect.

10. The method for predicting long-term creep of prestressed hybrid fiber HFRP reinforcement according to claim 9, characterized in that, The actual creep model is as follows: 。

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