Non-parametric prediction method for fatigue life of steel-fiber reinforced polymer composite bars

Abstract

The application discloses a non-parametric prediction method for fatigue life of steel-FRP composite bars, belonging to the field of fatigue performance evaluation of civil engineering materials and structures, comprising: initializing component material properties, load conditions and initial state of the steel-FRP composite bars, wherein the component materials include inner core steel bars and FRP layers; calculating fatigue stresses of the component materials respectively according to equivalent stiffness distribution principle; obtaining theoretical fatigue lives of the component materials respectively according to the fatigue stresses of the component materials in combination with S-N curve relationship, and performing cycle skipping; calculating cumulative fatigue damages of the component materials respectively based on results after the cycle skipping; and cyclically updating dynamic stiffness and equivalent cycle number of the component materials until the cumulative fatigue damage of any component material reaches a critical threshold value, then determining failure of the component material and outputting the fatigue life. The application can efficiently and accurately predict the fatigue life of the steel-FRP composite bars, and significantly reduce test cost.

Description

Technical Field

[0001] The present invention belongs to the technical field of fatigue performance evaluation of civil engineering materials and structures, and in particular relates to a non-parametric prediction method for fatigue life of steel-FRP composite bars. Background Art

[0002] Steel-FRP composite bars (SFCBs) are an emerging reinforcement material that leverages the complementary properties of steel and fiber-reinforced plastic (FRP). They combine the ductility of steel with the corrosion resistance of FRP, using steel as the inner core and FRP as the outer layer. In modern engineering structures, SFCBs are widely used in various load-bearing structures due to their excellent mechanical properties and durability. SFCBs, composed of an inner steel core and an FRP layer, exhibit unique fatigue behavior under cyclic loading. However, the complexity of their fatigue properties presents challenges for engineering design and application.

[0003] Experimental studies have shown that the fatigue behavior of SFCBs is highly dependent on the dynamic damage evolution of its component materials (core steel and FRP layer). Under cyclic loading, there is a significant difference in the stiffness degradation rate of the core steel and FRP layer, which triggers stress redistribution. Generally, the component with greater stiffness loss (such as the core steel) will transfer the fatigue load to the component with better stiffness retention (such as the FRP layer). However, this stress transfer is not absolute. For example, under high stress levels, the FRP layer may be subjected to stress levels above its fatigue limit, which accelerates damage and causes the load to transfer back from the core steel to the FRP layer. This dynamic coupling effect makes it difficult to accurately predict the fatigue life of SFCBs using models based on single-component materials.

[0004] In engineering practice, to meet design requirements for load-bearing capacity and durability, SFCBs of varying specifications, such as varying inner core diameters and FRP layer thicknesses, are often required. Predicting fatigue life using the traditional method recommended by current standards requires separate fatigue testing for each SFCB specification. This approach is not only time-consuming and labor-intensive, but also costly, severely restricting the large-scale application of SFCBs in real-world projects. Therefore, developing an efficient and accurate fatigue life prediction method is crucial for promoting the widespread application of SFCBs in engineering. Summary of the Invention

[0005] To solve the above technical problems, the application provides a non-parametric prediction method for fatigue life of steel-FRP composite bars, which comprises the following steps:

[0006] The application provides a non-parametric prediction method for fatigue life of steel-FRP composite bars, which comprises the following steps:

[0007] Initializing the component material properties, load conditions and initial state of the steel-FRP composite bar, wherein the component materials include the inner core steel bar and the FRP layer;

[0008] According to the equivalent stiffness distribution principle, the fatigue stresses of the component materials are calculated respectively;

[0009] According to the fatigue stresses of the component materials, the theoretical fatigue life of the component materials is obtained respectively in combination with the S-N curve relationship, and the cycle jump is performed;

[0010] Based on the results after the cycle jump, the cumulative fatigue damage of the component materials is calculated respectively;

[0011] The dynamic stiffness and the equivalent cycle number of the component materials are updated cyclically until the cumulative fatigue damage of any component material reaches a critical threshold, and then it is determined that the component material fails and the fatigue life is output.

[0012] Optionally, the process of initializing the component material properties, load conditions and initial state of the steel-FRP composite bar comprises the following steps:

[0013] Based on the input elastic modulus and cross-sectional area of the inner core steel bar, the elastic modulus and cross-sectional area of the FRP layer and the overall cross-sectional area of the steel-FRP composite bar, the component material properties are initialized; based on the input stress level, the load conditions are initialized; the initial cycle number is set to zero, the cycle number is set to one, and the initial state is set.

[0014] Optionally, the process of calculating the fatigue stresses of the component materials respectively according to the equivalent stiffness distribution principle comprises the following steps:

[0015] Based on the component material properties of the inner core steel bar and the FRP layer, the strain of both under the peak fatigue load is calculated; based on the strain synergy assumption, the fatigue modulus of the inner core steel bar and the FRP layer is calculated; based on the fatigue modulus and the cross-sectional area, the fatigue stress borne by the inner core steel bar and the FRP layer is calculated respectively.

[0016] Optionally, the theoretical fatigue life of the component materials is obtained respectively according to the fatigue stress of the component materials in combination with the S-N curve relationship, and the process of cycle jumping is performed, specifically:

[0017] Based on the fatigue stress level of the inner core steel bar and the FRP layer, the improved S-N curve relationship is substituted, wherein the improved S-N curve relationship adopts the Batsoulas formula; based on the Batsoulas formula, the theoretical fatigue life of the inner core steel bar and the FRP layer is calculated; based on the theoretical fatigue life, the step length of cycle jumping is determined, and the cycle jumping is performed.

[0018] Optionally, the process of calculating the cumulative fatigue damage of the component materials based on the results after cycle jumping is specifically:

[0019] Based on the results after cycle jumping, the fatigue stiffness degradation degree of the inner core steel bar and the FRP layer is calculated; the fatigue stiffness degradation degree includes a damage index based on fatigue stiffness degradation and a damage index based on residual strength attenuation; the damage index based on fatigue stiffness degradation is used to represent the nonlinear cumulative damage of the component materials in the early stage of fatigue loading, and the damage index based on residual strength attenuation is used to describe the damage mutation in the late stage of fatigue loading.

[0020] Optionally, the process of cyclically updating the dynamic stiffness and the equivalent cycle number of the component materials until the cumulative fatigue damage of any component material reaches a critical threshold, and then determining the failure of the component materials and outputting the fatigue life is specifically:

[0021] Based on the current cycle state, the dynamic stiffness of the inner core steel bar and the FRP layer is updated; based on the updated dynamic stiffness, the equivalent cycle number is calculated; the program state is updated, including the cycle number and the cycle serial number; it is judged whether the cumulative fatigue damage of the inner core steel bar or the FRP layer reaches the critical threshold, if so, the cycle is terminated and the fatigue life is output.

[0022] The application also provides a non-parametric prediction system for the fatigue life of steel-FRP composite bars for implementing the method, comprising:

[0023] A parameter initialization module is used to initialize the component material properties, load conditions and initial state of the steel-FRP composite bars, wherein the component materials include the inner core steel bar and the FRP layer.

[0024] A fatigue stress calculation module is configured to calculate fatigue stresses of the component materials respectively according to an equivalent stiffness distribution principle;

[0025] A fatigue life calculation module is configured to obtain theoretical fatigue lives of the component materials respectively according to the fatigue stresses of the component materials in combination with S-N curve relations, and perform cycle jumps.

[0026] A fatigue damage calculation module is configured to calculate cumulative fatigue damages of the component materials respectively based on results after the cycle jumps.

[0027] A cycle updating module is configured to cyclically update dynamic stiffnesses and equivalent cycle numbers of the component materials until the cumulative fatigue damage of any component material reaches a critical threshold value, and then determine that the component material fails and output a fatigue life.

[0028] The application further provides a computer device comprising a memory, a processor and a computer program stored in the memory, wherein the processor executes the computer program to implement steps of the method.

[0029] The application further provides a computer readable storage medium having a computer program stored thereon, wherein the computer program is executed by a processor to implement steps of the method.

[0030] The application further provides a computer program product comprising a computer program, wherein the computer program is executed by a processor to implement steps of the method.

[0031] Compared with the prior art, the application has the following advantages and technical effects:

[0032] The application provides accurate initial parameters for a fatigue life prediction model based on component material properties, load conditions and initial states of the initial steel-FRP composite bar, ensures that a prediction result is accurate and reliable, and lays a foundation for subsequent prediction.

[0033] The application calculates fatigue stresses of the component materials respectively based on an equivalent stiffness distribution principle, accurately distributes stresses of the inner core steel bar and the FRP layer, provides accurate stress input for fatigue life prediction, and truly reflects an actual stress state of the material.

[0034] The application obtains theoretical fatigue lives respectively based on fatigue stresses of the component materials in combination with improved S-N curve relations, performs cycle jumps, efficiently predicts the theoretical fatigue lives, reduces a calculation amount and improves efficiency through the cycle jumps, and ensures calculation accuracy.

[0035] The application calculates cumulative fatigue damages of the component materials respectively based on results after the cycle jumps, dynamically tracks a fatigue damage accumulation process, provides a basis for fatigue failure determination, and comprehensively reflects a material damage development trend.

[0036] The application is based on the dynamic stiffness of the cyclic updating component materials and the equivalent cycle number until the cumulative fatigue damage reaches the critical threshold, real-time updating of material properties, accurate determination of fatigue failure time, output of accurate fatigue life, improvement of prediction accuracy, and enhancement of model adaptability and practicality. BRIEF DESCRIPTION OF DRAWINGS

[0037] The accompanying drawings, which form a part of this application, are intended to provide further understanding of the application and are incorporated herein in their entirety, and together with the general description of the application and brief description of the drawings, to explain the application. In the drawings:

[0038] Figure 1 The figure is a schematic diagram of the equal damage curve of the embodiment of the application;

[0039] Figure 2 The figure is a schematic diagram of the fatigue damage development curve of the embodiment of the application;

[0040] Figure 3 The figure is a schematic diagram of the cycle jump method of the embodiment of the application;

[0041] Figure 4 The figure is a schematic diagram of the SFCBs fatigue life prediction process of the embodiment of the application. DETAILED DESCRIPTION

[0042] It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other without conflict. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0043] It should be noted that the steps shown in the flowchart of the accompanying drawings can be executed in a computer system such as a group of computer executable instructions, and although the logical order is shown in the flowchart, in some cases, the steps shown or described herein can be executed in an order different from that shown herein.

[0044] Embodiment one

[0045] The present embodiment provides a non-parametric prediction method for the fatigue life of steel-FRP composite bars, comprising the following steps:

[0046] Initialize the component material properties, load conditions and initial state of the steel-FRP composite bar, wherein the component materials include the inner core steel bar and the FRP layer;

[0047] According to the equivalent stiffness distribution principle, the fatigue stress of the component materials is calculated respectively;

[0048] According to the fatigue stress of the component materials, the theoretical fatigue life of the component materials is obtained respectively in combination with the S-N curve relationship, and the cycle jump is performed;

[0049] Based on the results after cycle jump, the cumulative fatigue damage of the component materials is calculated respectively;

[0050] The dynamic stiffness and equivalent cycle number of the component materials are updated in cycles until the cumulative fatigue damage of any component material reaches the critical threshold, then the component material is determined to fail and the fatigue life is output.

[0051] As a specific implementation, it specifically includes the following steps:

[0052] The basic framework of the damage model:

[0053] Improvement of S-N curve:

[0054] In fatigue design, Basquin formula is generally used to represent the fatigue life curve (S-N curve). According to Basquin formula, S-N curve can be represented by formula (1):

[0055] (1)

[0056] In the formula, σ is the fatigue stress; σ f ' is the fatigue strength coefficient; b is the fatigue strength index; N f is the failure cycle number, i.e. theoretical fatigue life; A and B are constants. Basquin formula shows a linear relationship between logarithmic stress level (lgS) and logarithmic fatigue life (lgN f ) in double logarithmic coordinate system.

[0057] However, for materials with obvious fatigue limit (such as steel bars and FRP bars), Basquin formula has significant limitations: when the stress level approaches the material fatigue limit, the predicted curve intersects with the horizontal axis (lgN f ), resulting in a continuous decrease in the predicted value in the ultra-high cycle fatigue region, overestimating the damage degree of the material and deviating seriously from the actual material progressive damage behavior. In addition, the service stress level of FRP layer is usually lower than its own fatigue limit due to the significantly lower elastic modulus than the inner core steel bar, further highlighting the applicability defects of traditional models. The current specification assumes that the fatigue life greater than 2×10 6 cycles is "infinite life", which simplifies the design process by artificially defining the fatigue limit, but ignores the progressive damage accumulation of materials in the ultra-high cycle region, which may underestimate the actual service risk. It is worth mentioning that low cycle fatigue is usually defined as the region with fatigue life less than 10 3 cycles, while ultra-high cycle fatigue is defined as the region with fatigue life reaching the order of magnitude of million cycles, and the region between the two is the medium-high cycle fatigue. To solve the above problems, an improved S-N curve representation method is proposed, as shown in formula (2).

[0058] (2)

[0059] where C is a material constant, σ0is the fatigue limit, N e is the minimum number of cycles required to cause fatigue damage. Batsoulas formula adopts a hyperbolic function form, whose curve is consistent with the trend of Basquin formula in the medium-high cycle fatigue region (10 3 ≤N f ≤2×10 6 ) and gradually converges to σ0, i.e. the theoretical fatigue limit of the material, in the super-high cycle fatigue region (N f ≥2×10 6 ). This characteristic not only corrects the overestimation of Basquin formula for super-high cycle fatigue damage, but also reveals the boundary condition of material durability under high cycle loading from the physical essence.

[0060] Damage accumulation under multi-stage loading:

[0061] Different from the fatigue mechanism of pure steel bars or pure FRP bars, the fatigue damage of SFCBs under tensile fatigue is affected by the interaction between the inner steel bars and FRP layers, and the influence of variable amplitude stress needs to be considered when predicting the damage of SFCBs. According to the fatigue damage accumulation criterion, the damage of material before fatigue loading is D=0%, and when fatigue failure occurs, the fatigue damage D=100%. Therefore, in the Batsoulas curve, the S-N curve and the coordinate axis together form the envelope of the fatigue damage value, where the S-N curve represents the equal damage line when D=100%, and the two vertical coordinate axes represent the equal damage line when D=0%. The curve between them represents the equal damage line of damage degree in the range of 0~100%. According to the physical meaning of fatigue damage, the equal damage lines of different damage values do not intersect. Therefore, in the Batsoulas model, the equal damage lines of fatigue damage in the range of 0~100% are represented by non-intersecting hyperbolic curves, as shown in Figure 1 .

[0062] It can be seen from Figure 1 that any point on the equal damage line is just the vertex of its equivalent rectangle in the coordinate graph, such as point F on equal damage line D1 is the vertex of rectangle (OEFM), and point K on the S-N curve is the vertex of rectangle (OEKL). Therefore, the equivalent rectangular area ratio of equal damage line D1 to D=100% (S-N curve) can be used to represent the fatigue damage when the cycle loading is n times at a given stress level, as shown in formula (3).

[0063] (3)

[0064] According to the concept of equal damage line, points at different stress levels on the same equal damage line have the same damage. Therefore, when the F point in Figure 1 moves to G point, we have:

[0065] (4)

[0066] Substituting formula (2) into formula (4), we can obtain:

[0067] (5)

[0068] Where n1 * is the equivalent number of cycles when the damage generated under the loading history (σ1, n1) is converted to the stress level σ2. Similarly, when Figure 1 When point H moves to point I, the equivalent cycle number n2 * for:

[0069] (6)

[0070] Where n2 * The damage generated under the loading history (σ1, n1) and (σ2, n2) is converted into the equivalent number of cycles when the stress level is σ3. Similarly, the cumulative damage calculation formula under multi-level loading is:

[0071] (7a)

[0072] (7b)

[0073] Where, subscript i represents the i-th cycle block in the loading process, N fi represents the fatigue life of the material under the i-th loading spectrum.

[0074] Phenomenological definition of injury:

[0075] The macroscopic phenomena of materials in a fatigue-damaged state are primarily fatigue stiffness degradation and a decrease in residual strength. Fatigue stiffness degradation reflects the attenuation of the material's overall load-bearing capacity due to accumulated internal damage under cyclic loading, and can be monitored in real time through non-destructive dynamic testing. Residual strength, on the other hand, represents the ultimate stress that a material can still withstand in a damaged state. However, its acquisition requires destructive loading tests (such as stretching to fracture), resulting in high testing costs, low efficiency, and the inability to reuse specimens. To address these issues, this embodiment proposes macroscopic definition parameters for fatigue damage in SFCBs based on the concept of isodamage lines.

[0076] Damage definition based on fatigue stiffness degradation:

[0077] In this embodiment, the fatigue modulus shown in formula (8) is used to calculate the dynamic stiffness of SFCBs.

[0078] (8)

[0079] where n is the number of cycles; F is the fatigue modulus, F(n) is a representation of dynamic stiffness; σ max and ε max are the peak fatigue load and corresponding strain, respectively; ε p is the fatigue creep; E c is the elastic modulus under static loading. According to equation (8), when n = 0, fatigue creep ε p (0) = 0, F(0) = E c ; when n = N f , F(N f ) = F u . The fatigue damage defined by the degradation of fatigue stiffness is given by the following equation:

[0080] (9)

[0081] where D F is the fatigue damage defined by the degradation of stiffness. The degradation of fatigue stiffness under cyclic loading presents a typical three-stage trend. The first stage is the rapid development stage, which is originated from the activation of internal defects and the rapid accumulation of damage. For the steel component, dislocation slip induces micro-cracks to nucleate at grain boundaries / inclusions, while for the FRP layer, it is characterized by the nucleation and propagation of matrix micro-cracks and the debonding of fiber / matrix interface. The test shows that this stage accounts for about 10% of the fatigue life. Then it enters the second stage of constant rate development, after experiencing the reconstruction of initial damage, the stiffness degradation rate tends to be stable, which accounts for about 90% of the fatigue life. Finally, it is the failure stage, when the damage accumulation breaks through the critical threshold, the stiffness occurs cliff-like attenuation, and the failure process presents the burst characteristics. The duration of this stage is usually less than 5% of the total life, and often only a few hundred cycles.

[0082] Due to the unpredictability of the fatigue stiffness failure stage and its short duration, when establishing the fatigue stiffness prediction model, the embodiment focuses on the first stage and the second stage which account for the vast majority of the fatigue life. Therefore, the fatigue stiffness prediction model is established by combining equations (3) and (9).

[0083] (10)

[0084] Damage definition based on residual strength:

[0085] According to the damage mechanics theory, the decrease of the residual strength of the material can be attributed to the continuous decrease of the effective cross-section bearing area due to the increase of fatigue damage. The residual strength after a certain number of cycles n can be expressed as:

[0086] (11)

[0087] where σ R is the residual strength; σu is the static tensile strength; A(n) is the actual cross-sectional area after fatigue damage. From the perspective of damage mechanics, under the condition of constant fatigue load P, the effective stress σ * gradually increases with the continuous decrease of the effective bearing cross-section. The nominal stress σ * and the effective stress σ u are calculated by formula (12) and formula (13) respectively:

[0088] (12)

[0089] (13)

[0090] where A0 is the cross-sectional area without damage. Combining formula (11), (12) and (13), the mathematical relationship between the residual strength and the effective stress can be derived as:

[0091] (14)

[0092] From formula (14), it can be seen that the residual strength and the nominal stress σ u are inversely proportional to each other. Therefore, the fatigue damage based on the residual strength can be defined as:

[0093] (15)

[0094] where D S is the fatigue damage defined based on the residual strength; A u is the critical cross-sectional area at fatigue failure. Substituting formula (12) and (13) into formula (15), the fatigue damage defined based on the effective stress can also be obtained:

[0095] (16)

[0096] where σ u * is the failure threshold of the effective stress. The evolution law of the effective stress in the cycle process is obtained. Unlike the three-stage development trend of fatigue stiffness, the effective stress increases slowly in the early stage of fatigue loading and suddenly rises near the fatigue failure. When the fatigue damage D = 0, the effective stress σ * = σ; when the fatigue damage D = 1, the material fails in fatigue, and the effective stress σ * = σ u * .

[0097] In view of the difficulty in directly measuring the time-varying characteristics of the effective load section of the material in the fatigue damage process by experiment, the traditional effective stress theory faces a significant application bottleneck. Therefore, a fatigue effective stress definition method based on the residual life backstepping mechanism is proposed: assuming that the effective stress σ * corresponding to the residual life N f -n corresponds to the critical stress value on the S-N curve.

[0098] Therefore, combined with the S-N curve equation of formula (2), the relationship between the effective stress and the residual fatigue life can be expressed as:

[0099] (17)

[0100] By simple conversion, formula (17) can be changed to:

[0101]

[0102] The curve represented by formula (18) satisfies the initial condition of the effective stress when n=0, σ * =σ.

[0103] Binary failure criterion of fatigue damage:

[0104] As Figure 2 shown in the figure is a fatigue damage evolution process diagram constructed based on the phenomenological angle (fatigue stiffness degradation and residual strength attenuation) proposed in this embodiment, which reveals the cooperative evolution law of the two damage variables:

[0105] (1) Damage variable D F : based on the fatigue stiffness degradation damage index, which can effectively represent the nonlinear accumulation process of the material in the early stage of fatigue loading (stage I and stage II);

[0106] (2) Damage variable D S : based on the residual strength attenuation damage index, which is suitable for describing the damage mutation characteristics caused by failure in the late stage of fatigue loading (stage III), and its evolution rate is significantly related to the change of effective stress.

[0107] Therefore, according to formula (9) and formula (16), this embodiment provides a binary damage criterion for the fatigue failure of the material:

[0108] (19)

[0109] The physical meaning of this criterion is that when the fatigue cumulative damage D F or D SAny variable reaching the critical threshold (D≥1) can be determined as material failure. Among them, the damage based on stiffness degradation provides the basis for stress redistribution between SFCBs component materials, and the application of effective stress can capture the sudden failure caused by local stress concentration, both of which form the progressive representation of fatigue damage.

[0110] The failure criterion of the material can be determined by the fatigue fracture strain and the stress state. According to the strain equivalence hypothesis, the critical fracture strain and the nominal fatigue stress σ max , the critical fracture strength σ u * There is the following equation relationship:

[0111] (20)

[0112] In the formula, ε u * is the critical fracture strain. Thus, only the critical fracture strength σ u * can be obtained under a given stress level:

[0113] (21)

[0114] According to the test observation, the material damage reaches the critical threshold and shows transient failure, and the duration of the failure is less than 5% of the total life. Therefore, the failure condition of the embodiment is conservatively set as the remaining life N f -n=5%N f , and the critical fracture strength σ u * is determined by formula (18).

[0115] Stress redistribution mechanism in SFCBs:

[0116] Dynamic description of stress redistribution:

[0117] According to the strain coordination hypothesis, SFCBs and the inner core steel and FRP layer have the following equation relationship:

[0118] (22)

[0119] In the formula, n is the number of cycles; ε max is the strain of the material under the peak fatigue load; σ b,max , σ s,max and σ f,max are the stresses of SFCBs, inner core steel and FRP layer under the peak fatigue load; F b , F s and F fare the fatigue moduli of SFCBs, inner core steel bars, and FRP layers, respectively. Therefore, according to the principle of equivalent stiffness distribution, the fatigue stresses of the inner core steel bars and FRP layers can be calculated using Equations (23a) and (23b).

[0120] (23a)

[0121] (23b)

[0122] Where A b 、A s and A f are the cross-sectional areas of SFCBs, inner core steel bars and FRP layers, respectively.

[0123] According to formulas (7a), (7b), (8) and (9), the dynamic fatigue modulus F of the inner core steel bar and FRP layer can be calculated respectively. s (n) and F f (n), and then substitute it into formulas (23a) and (23b) to calculate the fatigue stress borne by the component materials (core steel bar and FRP layer).

[0124] According to Equations (23a) and (23b), as the fatigue stiffness of the core steel and FRP layers gradually degrades, their stresses exhibit a continuous dynamic redistribution in each fatigue cycle. Specifically, the fatigue load shared by the two undergoes a non-steady-state evolution with the number of cycles. This stress evolution mechanism is equivalent to the core steel and FRP layers being subjected to multi-stage variable-amplitude fatigue loads with a time-dependent nature. Therefore, if the traditional prediction model based on the constant-amplitude fatigue stress assumption (i.e., assuming that the stress levels of the core steel and FRP layers are constant) is used to evaluate the fatigue life of SFCBs, significant errors will result from ignoring the stress redistribution effect. To accurately simulate this process, theoretically, it is necessary to calculate the stress redistribution state of each fatigue cycle one by one. However, this method requires a lot of computational time and carries the risk of error accumulation, making it unacceptable.

[0125] To address the above issues, this embodiment proposes a loop skipping method:

[0126] like Figure 3 As shown in the figure, the Cycle Jump Method divides the fatigue process into several groups of fatigue cycles. , by calculating each set of cycles one by one The damage development of the entire fatigue process can be obtained by calculating the damage within the fatigue period. This method will greatly reduce the calculation cost. The calculation accuracy of the cyclic jump method is better than related to, increase It can improve the calculation speed, but it will introduce errors due to the linear extrapolation assumption; reduce The precision can be improved, but the calculation resource consumption is significantly increased. Therefore, a suitable needs to be selected to balance the relationship between the calculation efficiency and the calculation precision.

[0127] To achieve the dynamic balance between the calculation efficiency and the accuracy in the fatigue damage evolution process, the embodiment proposes a damage mechanism driven segmented adaptive step algorithm. The core idea is to use a small step in the damage active period to capture the nonlinear accumulation effect, and to increase the step in the damage steady state period to improve the calculation efficiency according to the stage characteristics of the fatigue damage rate. The specific implementation strategy is as follows: in the range of 0~100 fatigue cycles, a fine step size Δn=10 is used to accurately represent the stress redistribution effect caused by the initial micro-crack initiation; in the range of 100~1000 fatigue cycles, the step size is adjusted to Δn=100 to balance the nonlinear attenuation of damage accumulation and the calculation resource consumption; in the range of 1000~10000 fatigue cycles, the step size is expanded to Δn=1000 to match the steady evolution rate of material stiffness degradation; in the range of 10000~2000000 fatigue cycles, the step size Δn=10000 is used, and the step size Δn is increased to 100000 after 2000000 cycles to avoid over iteration. Before using the cycle jumping method, the following assumptions need to be met:

[0128] (1) In the cycle step size Δn, the component materials (inner core steel and FRP layer) of SFCBs maintain a constant stress level, and the fatigue creep of the inner core steel and the FRP layer increases with the increase of the cycle, thereby causing the fatigue stiffness degradation of each other.

[0129] (2) After each jump, the fatigue stiffness of the component materials is updated according to the current damage state, and the distribution of the stress state of the components is completed before the next cycle jump.

[0130] (3) The damage irreversibility principle needs to be met during the cycle jumping process, that is, the damage is monotonically increasing with the increase of the cycle (dD / dn>0).

[0131] Based on the above assumptions, the fatigue life prediction process of SFCBs is as follows, as shown in Figure 4 , the specific steps are as follows:

[0132] Step 1: Initialize parameters.

[0133] Input material properties (E s , E f , A s , A f , A b ), load conditions and initial state (σ, n=0, i=1);

[0134] wherein, E s and E fare the initial elastic moduli of the inner core steel bar and FRP layer, respectively, which are used to calculate their initial fatigue moduli.

[0135] Step 2: Stress distribution calculation.

[0136] According to the current material properties, the fatigue stresses borne by the inner core steel bar and the FRP layer are calculated using formulas (23a) and (23b) respectively.

[0137] Step 3: Fatigue life mapping and jumping.

[0138] Substituting the fatigue stress level of the component materials into the SN curve relationship shown in formula (2), the theoretical fatigue life N of the inner core steel bar and FRP layer is obtained. f,steel and N f,FRP , after which a loop jump Δn is performed.

[0139] Step 4: Damage criterion check.

[0140] The cumulative fatigue damage of the component materials is calculated based on formulas (9) and (16). At this time, the damage states of the inner core steel bar and FRP layer are obtained respectively: D steel ={D F,steel , D S,steel} and D FRP ={D F,FRP , D S,FRP The subscripts steel and FRP are used to distinguish the inner steel bar from the FRP. Failure is determined using the binary failure criterion formula (19).

[0141] (1) If D steel ≥1 and D FRP < 1, it is determined that the SFCBs have suffered fatigue failure due to the fracture of the inner core steel bars;

[0142] (2) If D FRP ≥1 and D steel < 1, it is determined that the SFCBs suffered fatigue failure due to the rupture of the FRP layer.

[0143] (3) If D FRP ≥1 and D steel ≥ 1, it is determined that the SFCBs have suffered fatigue failure due to the simultaneous rupture of the inner core steel bar and the FRP layer.

[0144] The above D steel and D FRP are the cumulative damage of the inner core steel bar and FRP layer respectively. When the SFCBs fail, the calculation is terminated and the calculated fatigue life M of the SFCBs is output. i =∑Δn, where ∑ is the summation symbol. Otherwise, proceed to step 5.

[0145] Step 5: Parameter update and iteration.

[0146] The properties and loading state of the component materials are changed after the cycle jump, so the dynamic stiffness of the materials can be calculated by equation (10) before entering the next cycle jump; the equivalent cycle number n * The calculated value needs to be rounded down by equation (7a). After updating the material properties, the program state becomes: n = n * + Δn, i = i + 1, and then return to step 2.

[0147] Model verification:

[0148] This embodiment takes the equal damage line theory constructed by Batsoulas formula as the core, considers the stress redistribution mechanism between component materials, and proposes a non-parametric damage model for predicting the fatigue life of SFCBs based on the S-N curve of component materials. Since the prediction accuracy of the model directly depends on the calibration of the S-N curve of the component materials, this embodiment first verifies the applicability of the Batsoulas formula to the steel bars and FRP based on the fatigue test data, and compares it with the Basquin formula ] Then, by predicting the fatigue life and dynamic stiffness degradation curve of three SFCBs specimens (SG12, SG16 and SG20), the prediction ability and physical reasonableness of the model are systematically verified. Specifically:

[0149] Calibration of S-N curve parameters of component materials:

[0150] To establish the input parameters of the SFCBs fatigue life prediction model, this embodiment calibrates the S-N curve of the component materials (inner core steel bars and FRP layers) based on the tensile fatigue test data, taking SFCBs composed of round steel inner core and glass fiber composite (GFRP) protective layer as an example. The calibration specimens are selected to be completely consistent with the component properties of SFCBs, among which the inner core steel specimen S8 and the GFRP layer specimen G12 are selected. The Basquin formula and the Batsoulas formula are used to fit the fatigue test data in Table 1, and the S-N curve formulas of the inner core steel and the GFRP layer are shown in equations (24) and (25), respectively.

[0151] Table 1

[0152]

[0153] Wherein, the first item of the specimen number is the type of the reinforcing bar, and the second item is the stress level of the fatigue loading, such as "SG12-F96" indicating that the tensile fatigue test is performed on the SFCBs of type SG12 with a stress level of 0.96; P max is the maximum fatigue load; σ max is the maximum fatigue stress; S is the stress level; σ aσa=0.5(σmax-σmin), σmin=0.5(σmax-σa) a =0.5(σ max -σ min ), σ min =0.5(σ f -σa) max , Nf=1 / (σa / S0)n y . In the failure mode, S represents steel bar fracture, F represents GFRP fracture, SF then FF represents steel bar fatigue fracture first and then GFRP is pulled off, and RO represents run out.

[0154] (24)

[0155] (25)

[0156] where S is the stress level, S=σ max / f y for the inner steel bar, and S=σ max / f u for the FRP layer. f y and f u represent the yield strength of the inner steel bar and the tensile strength of the FRP, respectively. According to the comparison of the fitting curves of the two models with the test data, it can be seen that both the Batsoulas formula and the Basquin formula can well fit the test data, and the fitting coefficients R 2 of the two are less than 5%, indicating that both can effectively characterize the life attenuation law of the material in the medium-high cycle fatigue region. However, in the super-high cycle fatigue region (N f ≥ 2 × 10 6 ), the linear property of the Basquin formula prediction curve leads to a continuous decline, while the Batsoulas formula converges to infinity at S0=0.17 (inner steel bar) or S0=0.09 (FRP layer) through the hyperbolic property, thus accurately characterizing the fatigue limit of the material.

[0157] Based on the above analysis, the Batsoulas formula directly reflects the fatigue limit stress level of the material, avoids the super-high cycle prediction distortion similar to the Basquin formula through the asymptotic convergence property, and has clear physical meaning. Therefore, the Batsoulas formula is selected as the model for component material S-N curve calibration in this embodiment.

[0158] Fatigue life prediction:

[0159] To verify the prediction ability of the proposed model for the fatigue life of SFCBs, the model calculation results were compared with those of three SFCBs specimens (SG12, SG16 and SG20) in this embodiment. The specimen parameters are as follows: the inner core steel bar diameter is constant (8 mm), and the FRP layer thickness is 2 mm, 4 mm and 6 mm, respectively. The model prediction results were compared with the test data, and the equal damage line with a core steel bar damage degree of 95% was introduced as the engineering safety threshold. To evaluate the prediction performance of the model, the mean absolute error (MAE) was used to reflect the average deviation of the predicted value and the test value, and the root mean square error (RMSE) was used to measure the dispersion degree of the prediction error, as shown in equations (26) and (27), respectively.

[0160] (26)

[0161] (27)

[0162] In the formula, m is the number of specimens; N pred,i and N exp,i are the predicted value and the test value of the fatigue life, respectively. However, both MAE and RMSE directly depend on the magnitude of the data, for example, if the predicted life range is in the order of millions, the values of MAE and RMSE will naturally be larger than those in the order of thousands, which cannot intuitively and uniformly describe the accuracy of the model. Therefore, normalization processing was performed on them, as shown in equations (28) and (29).

[0163] (28)

[0164] (29)

[0165] In the formula, R MAE and R RMSE are the normalized statistical indicators; N exp,ave is the average value of the same group of fatigue life test values.

[0166] The results show that the model prediction curve can well reflect the fatigue life development trend of different SFCBs in the double logarithmic coordinate system, and is in good agreement with the test fitting curve. The normalized statistical indicators R MAE = 0.53 (overall), R RMSE = 0.54 (overall). Among them, for the specimen SG12, R MAE = 0.67, R RMSE = 0.69; for the specimen SG16, R MAE = 0.50, R RMSE = 0.50; for the specimen SG20, R MAE = 0.41, R RMSE= 0.44. It can be seen that the thicker FRP layer specimens (SG16 and SG20) have higher prediction accuracy. The average deviation of the predicted values from the test values is about half an order of magnitude, which is probably due to the dispersion of the fatigue data and the limitation of the test data. The dispersion of the material performance in the high-cycle fatigue region leads to the failure of the model calibration parameters to completely cover the extreme working conditions, and the lack of test samples of the SFCBs in the ultra-high cycle fatigue region (N f ≥ 2 × 10 6 ) affects the accuracy of the type extrapolation.

[0167] Meanwhile, based on the damage evolution data output by the model, this embodiment defines an equal-damage line of the core steel damage degree of 95%, which is used to quickly evaluate the fatigue life threshold of the SFCBs. To quantitatively evaluate the conservatism of the equal-damage line, this embodiment quantifies the conservative deviation of the predicted values by using the statistical index value shown in formula (30).

[0168] (30)

[0169] In the formula, n 保守 is the number of samples in the same group of specimens whose predicted values are lower than the test values. The results show that the equal-damage line can provide a conservative life estimate for most specimens, and the conservative rate (the percentage of the number of conservatively predicted specimens to the total number of specimens) is as high as 78%. The overall conservative deviation CBP = 42%, indicating that the equal-damage line is on average 42% lower than the life of the conservative samples. The overestimated predictions of the specimens are mainly distributed in the low stress level region, mainly due to the high dispersion of the fatigue data in the low life region. Although there is dispersion, the model can still capture the main control trend of the fatigue life of the SFCBs, indicating that it can provide a reliable theoretical basis for engineering safety design.

[0170] Verification of fatigue stiffness degradation and stress redistribution mechanism:

[0171] To reveal the representation ability of the model for the dynamic evolution of the internal damage of the composite bar, this embodiment predicts the stiffness degradation curve of the SFCBs specimens based on the proposed non-parametric damage model, and compares and analyzes it with the test monitoring data. Comparison shows that the model prediction curve reproduces the typical two-stage characteristics of stiffness degradation: fast attenuation in the early loading stage (n ≤ 10%N f ) and stable development in the later stage (n > 10%N f ), which is consistent with the trend of the test data. However, the model overestimates the stiffness degradation degree of the SFCBs (average deviation 20%), which is mainly due to the fact that the critical fracture strength σ u * is highly dependent on the exponential rise of the effective stress before failure, leading to an overestimation of the fatigue stiffness failure threshold. It is suggested that the parameters of the failure criterion should be calibrated in the future to improve the critical accuracy. However, the model can still effectively capture the main control law of the stiffness degradation, providing a reference for preliminary engineering evaluation.

[0172] To quantitatively reveal the load transfer mechanism between the component materials (the inner steel and the FRP layer), the non-parametric damage model proposed in this embodiment outputs the dynamic stress level. Analysis shows that the stress level of the inner steel (S = σ s / f y ) decreases significantly at the initial loading stage (n≤10%N f ) and tends to be stable later. The stress level of the FRP (S = σ f / f u ) remains stable or slightly increases throughout the loading process. The starting point of the ultra-high cycle fatigue zone is set to 2×10 6 cycles. According to formula (24), the fatigue strength of the inner steel is S = 0.74 at 2×10 6 cycles, while the fatigue strength of the FRP layer is S = 0.21. Obviously, the stress transfer of the inner steel slows down the local damage rate, thereby prolonging its fatigue life. However, since the stress level of the inner steel is always higher than the fatigue strength, it fails before the FRP layer. Although the stress of the FRP layer increases, it does not exceed its fatigue strength, mainly playing a role in load sharing rather than being the dominant factor of failure, which is consistent with the previous assumption.

[0173] The decrease in the initial stress level will intensify the degree of stress redistribution. Taking SG16 as an example, when the initial stress level decreases from S = 1 to S = 0.9, the stress level of the inner steel decreases from about 0.02 to 0.05. This is due to the increased fatigue life of the material at low stress levels, which in turn leads to more stress redistribution. In addition, the increase in the thickness of the FRP layer also intensifies the stress redistribution. Under the condition of the initial stress level S = 0.9, the thickness of the FRP layer increases from 2mm to 6mm (i.e., from SG12 to SG20), and the stress level of the inner steel decreases from about 0.03 to 0.07. This finding proves that increasing the thickness of the FRP layer can effectively share the load and delay the damage accumulation process of the steel.

[0174] The above analysis shows that the non-parametric damage model proposed in this embodiment accurately reveals the stress redistribution mechanism of SFCBs under different stress levels and FRP layer thicknesses, and quantifies the sensitivity of the initial stress level and the FRP thickness to damage evolution and life prediction, providing a theoretical basis for the fatigue optimization design of SFCBs.

[0175] Comparison with the fitting model:

[0176] To comprehensively evaluate the performance of the non-parametric damage model proposed in this embodiment in fatigue life prediction, in this embodiment, it is compared and analyzed in detail with the traditional multi-parameter damage model. For SFCBs specimens (SG12, SG16 and SG20), the fatigue life of each specimen is predicted by using the two models respectively. At the same time, according to the statistical indexes defined by formula (28) and (29), the accuracy of the prediction results is quantitatively evaluated.

[0177] By comparing the prediction results of the two models, the prediction results of the multi-parameter model generally show a conservative trend, and the calculation shows that the conservative rate is 64%. In contrast, the non-parametric damage model proposed in this embodiment shows a conservative trend in the medium-high cycle fatigue region (N f ≤10 6 ) of the life prediction; while in the ultra-high cycle fatigue region (N f >10 6 ), the life prediction value appears to be overestimated, and the conservative rate of the model is 39%. In addition, the overall prediction accuracy of the non-parametric damage model is at the same level as that of the multi-parameter damage model. However, the non-parametric model shows a prediction deviation of more than 50% when predicting some specimens (such as SG12-F76). Further investigation shows that the main reason is the lack of data of the run-out specimen (i.e. the sample that has not failed) in the ultra-high cycle stage, which leads to the failure of the extrapolation process.

[0178] In engineering practice, in order to meet the design requirements of bearing capacity and durability, different specifications of SFCBs (such as different core diameters and FRP layer thicknesses) are often used. The prediction accuracy of the multi-parameter damage model is highly dependent on the fitting of test data, and if the fatigue life of each specification of SFCBs is predicted by this method, separate fatigue tests need to be carried out, which is a huge cost and effort. Under the premise of equivalent overall prediction accuracy, the non-parametric damage model of this embodiment has a significant advantage in reducing the number of tests. According to the current international standard ISO 10406, at least 3 different stress levels are required to determine the S-N curve of a tendon, and at each stress level, there should be at least 3 repeated specimens. Therefore, at least 9 specimens are required to construct a damage model for a tendon, assuming that the test period is 1 month. Then, according to the traditional method, 5 groups of a total of 45 specimens are required for the design of 5 kinds of SFCBs, and the test period is 5 months in total. While using the method of this embodiment, only 2 groups of a total of 18 specimens (only the core steel and FRP layer are tested and calibrated) are required for the design of 5 kinds of SFCBs, and the test period can be shortened to 2 months. According to the calculation, this method saves 60% of the number of tests and the test period compared with the traditional method, which is more economical.

[0179] In summary, the non-parametric model proposed in this embodiment has comparable overall prediction performance to traditional methods, and is less dependent on experiments (only 2 sets of component tests are required), demonstrating higher engineering economy in fatigue design, laying a solid theoretical foundation for the widespread application of SFCBs in practical engineering.

[0180] Advantages of the model:

[0181] This embodiment proposes a non-parametric damage model for SFCBs based on the S-N curves of component materials (inner core steel bars and FRP layers) through the concept of equal damage curves. The biggest feature of this model is that it only considers the S-N curves of component materials without introducing additional experimental fitting parameters, while ensuring comparable prediction accuracy to traditional models. Compared to traditional fitting-type multi-parameter models, this model can significantly reduce experimental costs and improve engineering application feasibility.

[0182] In addition, by adjusting the parameter of the cross-sectional ratio of component materials (As / Af), the model can be automatically converted into a damage model for pure steel bars or pure FRP bars, thereby realizing unified characterization of the fatigue behavior of composite bars and single bars and expanding its application scope.

[0183] The existing non-linear fatigue damage model based on equal damage curves can only calculate the remaining life and cannot obtain the actual damage values at different cycle stages. In contrast, this model establishes a quantitative mapping relationship between stiffness degradation and damage accumulation, while considering the interaction between component materials, thereby providing a direct quantitative basis for evaluating structural fatigue performance.

[0184] The existing non-linear fatigue damage model based on equal damage curves is mostly limited to remaining life calculation and cannot obtain the actual damage evolution process at different cycle stages. The model constructed in this embodiment breaks through this limitation, establishes a quantitative mapping relationship between stiffness degradation and damage accumulation, and fully considers the interaction between the inner core steel bars and the FRP layers, making the fatigue damage calculation more refined and physically reasonable. This model not only can effectively predict the fatigue life of multiple types of bars, but also can depict the entire process of material damage evolution under multi-level loading conditions, providing a direct quantitative basis for evaluating structural fatigue performance.

[0185] In summary, the fatigue life prediction of steel-FRP composite bars (SFCBs) is a key issue in promoting their large-scale application in engineering. However, traditional methods often rely on a large amount of experimental data and are difficult to accurately characterize the dynamic stress redistribution effect. To address this challenge, this embodiment proposes a non-parametric fatigue damage prediction method based on the S-N curves of component materials to predict the fatigue life of SFCBs. Through theoretical modeling and experimental verification, the damage evolution law and life control mechanism of SFCBs are systematically revealed. The main conclusions are as follows:

[0186] (1) Based on the reasonable prediction of ultra-high cycle fatigue life based on Batsoulas formula, combined with the concept of equal damage line, a material cumulative damage criterion suitable for multi-stage loading conditions is established, and through the phenomenological definition of damage, a quantitative mapping relationship between fatigue stiffness degradation and cumulative damage is constructed. In addition, the model uses an improved effective stress definition, proposes a binary criterion for SFCBs fatigue failure, and reasonably considers the stress redistribution mechanism between component materials through the stiffness equivalent distribution principle. On this basis, a non-parametric damage model is constructed, which can predict the fatigue life of SFCBs only by relying on the S-N curve of the component material.

[0187] (2) In the process of calibrating the S-N curve of the component material, Batsoulas formula can well characterize the fatigue life in the range of N f ≤2×10 6 The parameters of the inner core steel are S0=0.17 (relative yield strength), C=4.08, and the S0 of the FRP layer is 0.09 (relative ultimate strength), C=2.51. However, due to the lack of ultra-high cycle test data support, the prediction of stiffness degradation by the proposed non-parametric model has some errors.

[0188] (3) The verification of dynamic stiffness degradation and stress redistribution mechanism shows that there is a complex interaction between the inner core steel and the FRP layer, and the proposed model reveals the influence of load transfer on damage accumulation. The results also show that the increase of FRP layer thickness can significantly enhance the stress redistribution effect, thereby slowing down the damage accumulation rate of the inner core steel. This provides a theoretical basis for optimizing the cross-section design of SFCBs (such as adjusting the proportion of FRP layer), and realizes the comprehensive improvement of material performance.

[0189] (4) Compared with traditional multi-parameter models, the non-parametric damage model proposed in this embodiment only needs to calibrate the S-N curve of the component material, without the need for repeated fatigue tests for different specifications of SFCBs. Case analysis shows that in the prediction of 5 kinds of SFCBs design, this model can reduce the test amount by 60% (the number of test specimens is reduced from 45 to 18), and the test period is shortened by 60% (from 5 months to 2 months). The normalized statistical index shows that the model is equivalent in prediction accuracy to the traditional method, but has a significant advantage in test cost and engineering efficiency.

[0190] Embodiment Two

[0191] The application also provides a non-parametric prediction system for the fatigue life of steel-FRP composite bars, which is used to implement the method, comprising:

[0192] A parameter initialization module is used to initialize the component material properties, load conditions and initial state of the steel-FRP composite bar, wherein the component materials include the inner core steel and the FRP layer.

[0193] a fatigue stress calculation module configured to calculate fatigue stresses of the component materials according to an equivalent stiffness distribution principle;

[0194] a fatigue life calculation module configured to obtain theoretical fatigue lives of the component materials according to the fatigue stresses of the component materials in combination with S-N curve relations, and perform cycle jumps;

[0195] a fatigue damage calculation module configured to calculate cumulative fatigue damages of the component materials based on results after the cycle jumps;

[0196] a cycle updating module configured to cyclically update dynamic stiffnesses and equivalent cycle numbers of the component materials until the cumulative fatigue damages of any of the component materials reach a critical threshold, and then determine that the component material fails and output a fatigue life.

[0197] Embodiment Three

[0198] The embodiment also discloses a computer device, which comprises a memory, a processor and a computer program stored in the memory, and the processor executes the computer program to implement steps of the method in the embodiment one.

[0199] Embodiment Four

[0200] The embodiment also discloses a computer readable storage medium, which stores a computer program, and the computer program is executed by a processor to implement steps of the method in the embodiment one.

[0201] Embodiment Five

[0202] The embodiment also discloses a computer program product, which comprises a computer program, and the computer program is executed by a processor to implement steps of the method in the embodiment one.

[0203] The above is only a preferred specific implementation of the present application, but the protection scope of the present application is not limited to this, any person skilled in the art can easily think of changes or replacements within the technical range disclosed in the present application, which should be covered in the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A nonparametric prediction method for fatigue life of steel-FRP composite bars, characterized in that: The following steps are involved: Initialize the component material properties, loading conditions, and initial states of the steel-FRP composite reinforcement, where the component materials include the core steel bar and the FRP layer; According to the principle of equivalent stiffness distribution, the fatigue stress of component materials is calculated separately; According to the fatigue stress of the component materials, combined with the improved SN curve relationship, the theoretical fatigue life of the component materials is obtained respectively, and the cycle jump is performed; Based on the results after cyclic skipping, the cumulative fatigue damage of the component materials is calculated separately; The dynamic stiffness and equivalent cycle number of the component materials are updated cyclically until the cumulative fatigue damage of any component material reaches a critical threshold. Then the component material is judged to be failed and the fatigue life is output; The process of calculating the fatigue stress of component materials respectively according to the equivalent stiffness distribution principle is specifically as follows: Based on the component material properties of the inner core steel bar and FRP layer, the strain of both under peak fatigue load is calculated; the fatigue modulus of the inner core steel bar and FRP layer is calculated based on the strain; based on the principle of equivalent stiffness distribution, the fatigue stress borne by the inner core steel bar and FRP layer is calculated separately in combination with their fatigue modulus and cross-sectional area; The process of calculating the cumulative fatigue damage of the component materials based on the results after the cycle jump is specifically as follows: Based on the results after cyclic jumping, the degree of fatigue stiffness degradation of the inner core steel bar and FRP layer is calculated; the fatigue stiffness degradation degree includes a damage index based on fatigue stiffness degradation and a damage index based on residual strength decay; the damage index based on fatigue stiffness degradation is used to characterize the nonlinear cumulative damage of the component material in the early stage of fatigue loading, and the damage index based on residual strength decay is used to describe the damage mutation at the end of fatigue loading.

2. The method according to claim 1, characterized in that The process of initializing the component material properties, load conditions and initial state of the steel-FRP composite reinforcement is specifically as follows: Initialize the component material properties based on the input elastic modulus and cross-sectional area of ​​the inner core steel bar, the elastic modulus and cross-sectional area of ​​the FRP layer, and the overall cross-sectional area of ​​the steel-FRP composite bar; initialize the load conditions based on the input stress level; Set the initial loop count to zero and the loop sequence number to one to complete the initial state setting.

3. The method according to claim 1, characterized in that The process of cyclically updating the dynamic stiffness and equivalent cycle number of the component materials until the cumulative fatigue damage of any component material reaches a critical threshold, then determining that the component material has failed and outputting the fatigue life is specifically as follows: Based on the current cycle status, the dynamic stiffness and equivalent cycle number of the inner core steel bar and FRP layer are updated; the program status, including the cycle number and cycle sequence, is updated; and it is determined whether the accumulated fatigue damage of the inner core steel bar or FRP layer has reached the critical threshold. If so, the cycle is terminated and the fatigue life is output.

4. A non-parametric prediction system for fatigue life of steel-FRP composite bars, characterized in that: The method for implementing any one of claims 1 to 3 comprises: A parameter initialization module is used to initialize the component material properties, load conditions, and initial states of the steel-FRP composite reinforcement, where the component materials include the inner core steel bar and the FRP layer; Fatigue stress calculation module, used to calculate the fatigue stress of component materials separately according to the principle of equivalent stiffness distribution; Fatigue life calculation module, used to obtain the theoretical fatigue life of component materials based on the fatigue stress of component materials and combine with the improved SN curve relationship, and perform cycle skipping; Fatigue damage calculation module, used to calculate the cumulative fatigue damage of component materials based on the results after cyclic jumping; The cyclic update module is used to cyclically update the dynamic stiffness and equivalent cycle number of the component materials until the cumulative fatigue damage of any component material reaches a critical threshold. In this case, the component material is judged to be failed and the fatigue life is output.

5. A computer device comprising a memory, a processor, and a computer program stored in the memory, wherein: The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 3.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 3 are implemented.

7. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 3 are implemented.

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