Fatigue analysis method for adhesive corrugated key interface of composite steel bridge deck

Abstract

The present application relates to a kind of fatigue analysis methods of bonded corrugated key interface of composite steel bridge deck, comprising the following steps: input initial parameter simulation glue bonding corrugated key interface part and natural connection interface part, propose interface cohesive zone damage evolution equation with amplification factor, the fatigue behavior of glued corrugated key interface is simulated using exponential traction-separation law, propose the traction-separation constitutive relationship under damage state, establish damage irreversible fatigue load cycle path, update the constitutive relationship of cyclic cohesion model and interface damage value of collaborative analysis, update traction-separation constitutive relationship to realize interface fatigue damage update iterative calculation, realize the fatigue damage accumulation of glued corrugated key interface and interface failure propagation analysis;The purpose of the present application is to provide efficient technical approach for the fatigue accumulation damage evolution and interface fatigue failure analysis of glued corrugated key interface of composite steel bridge deck.

Description

Technical Field

[0001] This invention belongs to the field of bridge engineering technology, specifically relating to a fatigue analysis method for the adhesive corrugated key interface between the composite load-bearing layer and the steel bridge deck. It proposes a cohesive force model considering the accumulation of damage along the cyclic path and a damage evolution equation for the interface cohesive zone with an amplification factor. This enables the analysis of fatigue damage development and interface debonding propagation process at the adhesive corrugated key interface of the composite steel bridge deck, providing a method for fatigue analysis of the adhesive corrugated key interface of the composite steel bridge deck. Background Technology

[0002] Corrugated keys are a type of high-efficiency shear key suitable for composite steel bridge decks. By using adhesive-bonded corrugated keys to create a composite load-bearing layer on the top plate of the steel bridge deck, not only is the local stiffness of the top plate improved, the stress level of typical fatigue details in the steel bridge deck reduced, and the stress on the pavement layer improved, but it also avoids introducing welding manufacturing details to the steel bridge deck and does not increase the technical difficulty of later replacement of the composite layer. Therefore, the adhesive-bonded corrugated key composite design method, which offers stable force transmission and reliable durability, is of great significance for strengthening and extending the service life of steel bridge decks.

[0003] Physical fatigue testing can reveal the long-term damage accumulation and fatigue failure characteristics of adhesive corrugated key interfaces. However, physical fatigue testing is time-consuming and costly. Therefore, establishing a fatigue analysis method for adhesive corrugated key interfaces in composite steel bridge decks is of great significance. Currently, scholars both domestically and internationally mostly use cohesive force models to analyze the behavior of adhesive shear key interfaces, and the theory of monotonic cohesive force models is relatively mature. However, monotonic cohesive force models are suitable for analyzing the monotonic damage development behavior of adhesive corrugated key interfaces under static loads. Although cyclic cohesive force models for fatigue problems of adhesive corrugated key interfaces have been developed to some extent, the fatigue damage model is relatively simple and lacks a mature theory.

[0004] This invention addresses the lack of research on the cumulative damage analysis method of the adhesive corrugated key interface in composite steel bridge decks under fatigue loading, and the absence of efficient simulation analysis methods. It establishes a fatigue resistance analysis method for the adhesive corrugated key interface in composite steel bridge decks based on a cyclic path damage accumulation cohesive force model, realizing the analysis of the cumulative evolution of fatigue damage at the adhesive corrugated key interface, and providing support for the fatigue resistance analysis of the adhesive corrugated key interface in composite steel bridge decks. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to overcome the shortcomings of the prior art and provide a fatigue analysis method for the interface of adhesive corrugated key in composite steel bridge deck. The purpose is to provide an efficient technical approach for the analysis and research of fatigue cumulative damage evolution and interface fatigue failure of adhesive corrugated key interface in composite steel bridge deck.

[0006] This invention establishes an analysis that couples the fatigue damage evolution process of the adhesive corrugated key interface with the cohesive force model, and realizes the fatigue resistance analysis of the adhesive corrugated key interface of the composite steel bridge deck based on the cumulative cohesive force model of cyclic path damage.

[0007] The technical solution adopted to solve the above technical problems is: a fatigue analysis method for the interface of adhesive corrugated keys in composite steel bridge decks, including the following steps:

[0008] Step 1: Input initial parameters; Input the initial parameters of the interface, including the adhesive corrugated key interface and the natural connection interface.

[0009] Step 2: A method for analyzing the D-evolution of damage at the adhesive corrugated bond interface with a fatigue damage amplification factor a is proposed. The method is as follows:

[0010]

[0011] In the formula, D represents interface damage; The damage effect of cyclic loading on the interface; denoted as α, representing the damage effect of monotonic load on the interface; α is the fatigue damage amplification factor. The increment of the separation value; δ ∑ For cumulative cohesion length; For traction force; σ max C represents the current interface normal intensity. f The ratio of the cohesive model strength; H is the Heaviside function; δ is the separation value; δ0 is the adhesion length; T n T is the traction force in the normal cohesive region. t σ is the tangential cohesive force; q is the cohesive energy ratio; f σ represents the durability limit of the cohesive model element; max,0 The interface normal intensity in the initial state; Δu n Δu is the separation length of the normal cohesive region. t The separation length of the tangential cohesive region; Let be the separation value at time t; The separation value at time t-Δt; Let t be the current state i Time Δ n The maximum value; For the previous time increment state t i-1 Time Δ n The maximum value;

[0012] Step 3: Establish the traction-separation constitutive relation under the damage state;

[0013] The exponential traction-separation law is used to simulate the fatigue behavior of the adhesive corrugated key interface. The interface damage D under fatigue loading is introduced into the traction-separation law to obtain the cohesive traction force under damage state. and the effective cohesive strength (σ) under damaged conditions max τ max ), and proposes a traction-separation constitutive relation under damage conditions;

[0014]

[0015] In the formula, T is the cohesive traction force obtained in the initial state; σ max,0 τ represents the interface normal intensity in the initial state. max,0 This represents the tangential strength of the interface in the initial state;

[0016] Step 4: Repair the damaged interface of the adhesive corrugated key;

[0017] Establish an irreversible fatigue load cycle path and define the normal stiffness T of the adhesive corrugated key interface during the loading-unloading process. n and tangential stiffness T t It degrades with increasing fatigue loading cycles;

[0018] T n =T n,max +k n (Δu n -Δu n,max )

[0019] T t =T t,max +k t (Δu t -Δu t,max )

[0020] In the formula, T n,max For Δu n,max The corresponding normal traction force; Δu n,max The maximum normal separation value; k n For normal stiffness and T t,max For Δu t,max The corresponding normal traction force; Δu t,max k is the maximum tangential separation value. t For tangential stiffness and

[0021] Step 5: Update material strength: Update the material parameters of the adhesive corrugated key interface to collaboratively analyze the constitutive relationship of the cyclic cohesive force model;

[0022] Step 6: Control cell deletion: Update the calculated interface damage value based on the interface material strength in Step 4, and control cell deletion based on the interface damage value;

[0023] Step 7: Update the matrix: Based on the calculation results in Step 5, update the stress matrix and Jacobian matrix, update the traction-separation constitutive relation in Step 2, and repeat Steps 1 to 5 to calculate the next load step.

[0024] Step 8: Adhesive Layer Interface Analysis: Update the structural stress calculation based on the calculation results of Step 5, extract the cumulative damage degree of the adhesive corrugated key interface, the cumulative damage increment of interface fatigue, and the monotonic damage increment index of the interface, and realize the analysis of cumulative fatigue damage and interface failure extension of the adhesive layer interface.

[0025] In step one of this invention, the initial interface parameters of the adhesive corrugated key interface include: normal strength, tangential strength, strain corresponding to tangential strength, strain corresponding to normal strength, fatigue limit to static strength ratio, and viscosity coefficient.

[0026] In step one of this invention, the initial parameters of the natural connection interface include: normal intensity and strain corresponding to the normal intensity.

[0027] Step five of this invention involves updating the material parameters for the adhesive corrugated key interface, including: the cohesive unit normal strength σ. n and the corresponding strain δ n Tangential strength σ t and the corresponding strain δ t The ratio of the durability limit to the static strength of the cohesive model element.

[0028] For interfacial fatigue analysis of adhesive shear bonds, commonly used research methods include physical experimental studies and analysis based on cohesive force models. Compared with existing technologies, this invention has the following advantages:

[0029] (1) Physical fatigue testing is an important method for studying the fatigue performance of the bonded corrugated key interface of composite steel bridge decks. However, this method is costly and time-consuming. Compared with physical fatigue testing, the fatigue resistance analysis method of the bonded corrugated key interface of composite steel bridge decks proposed in this invention has been significantly improved in terms of research cost and efficiency, and can be regarded as an important extension of physical fatigue testing.

[0030] (2) For analysis methods based on cohesion models, the monotonic cohesion model theory is mature and widely used in the analysis of monotonic damage development behavior of adhesive corrugated key interfaces under static loads. While cyclic cohesion models have seen some development in addressing fatigue problems at adhesive corrugated key interfaces, their fatigue damage models are relatively simple and lack mature theories. To address these shortcomings, this invention proposes a fatigue analysis method for adhesive corrugated key interfaces in combined steel bridge decks with a fatigue damage amplification factor, based on a cyclic path damage accumulation cohesion model. This method achieves highly efficient calculation and analysis of the cumulative evolution of fatigue damage at adhesive corrugated key interfaces. Attached Figure Description

[0031] Figure 1 This is a diagram of the normal traction-separation law for the cohesive force model under cyclic cumulative damage.

[0032] Figure 2 This is a diagram of the tangential traction-separation law for the cohesive force model under cyclic cumulative damage.

[0033] Figure 3 This is a finite element model of a full-scale segment of the UHPFRC composite steel bridge deck.

[0034] Figure 4 This is a diagram showing the division of the paste zigzag key combination interface area.

[0035] Figure 5 It is a cloud map of cumulative fatigue damage to the composite interface when natural connection fails.

[0036] Figure 6 This is a cumulative fatigue damage cloud map of the initiation of fatigue damage between the corrugated key and the steel plate.

[0037] Figure 7 This is a curve showing the cumulative damage development of the interface between the corrugated key and the steel plate due to fatigue details.

[0038] Figure 8 This is a diagram showing the cumulative development trend of interface damage under different load conditions.

[0039] Figure 9 This is a fatigue life diagram of the interface under different load conditions.

[0040] Figure 10 This is a graph showing the growth of the debonding area at the interface. Detailed Implementation

[0041] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments, but the present invention is not limited to these embodiments.

[0042] Example 1

[0043] The present invention relates to a fatigue analysis method for the interface of adhesive corrugated keys in composite steel bridge decks, comprising the following steps:

[0044] Step 1: Input initial parameters; Input initial interface parameters, including the adhesive corrugated key interface and the natural connection interface; The initial interface parameters for the adhesive corrugated key interface include: normal strength, tangential strength, strain corresponding to tangential strength, strain corresponding to normal strength, ratio of fatigue limit to static strength, and viscosity coefficient; The initial interface parameters for the natural connection interface include: normal strength and strain corresponding to normal strength.

[0045] Step 2: A method for analyzing the D-evolution of damage at the adhesive corrugated bond interface with a fatigue damage amplification factor a is proposed. The method is as follows:

[0046]

[0047] In the formula, D represents interface damage; The damage effect of cyclic loading on the interface; denoted as α, representing the damage effect of monotonic load on the interface; α is the fatigue damage amplification factor. The increment of the separation value; δ ∑ For cumulative cohesion length; For traction force; σ max C represents the current interface normal intensity. f The ratio of the cohesive model strength; H is the Heaviside function; δ is the separation value; δ0 is the adhesion length; T n T is the traction force in the normal cohesive region. t σ is the tangential cohesive force; q is the cohesive energy ratio; f σ represents the durability limit of the cohesive model element; max,0 The interface normal intensity in the initial state; Δu n Δu is the separation length of the normal cohesive region. t The separation length of the tangential cohesive region; Let be the separation value at time t; The separation value at time t-Δt; Let t be the current state i Time Δ n The maximum value; For the previous time increment state t i-1 Time Δ n The maximum value;

[0048] Step 3: Establish the traction-separation constitutive relation under the damage state;

[0049] The exponential traction-separation law is used to simulate the fatigue behavior of the adhesive corrugated key interface. The interface damage D under fatigue loading is introduced into the traction-separation law to obtain the cohesive traction force under damage state. and the effective cohesive strength (σ) under damaged conditions max τ max ), and proposed the traction-separation constitutive relation under damage state (e.g. Figure 1 , Figure 2 (as shown);

[0050]

[0051] In the formula, T is the cohesive traction force obtained in the initial state; σ max,0 τ represents the interface normal intensity in the initial state. max,0 This represents the tangential strength of the interface in the initial state;

[0052] By analyzing the changes in strain increment of the cohesive elements before and after the loading step, the interface loading, unloading, contact, and compression can be determined.

[0053] Step 4: Repair the damaged interface of the adhesive corrugated key;

[0054] Establish an irreversible fatigue load cycle path and define the normal stiffness T of the adhesive corrugated key interface during the loading-unloading process. n and tangential stiffness T t It degrades with increasing fatigue loading cycles;

[0055] T n =T n,max +k n (Δu n -Δu n,max )

[0056] T t =T t,max +k t (Δu t -Δu t,max )

[0057] In the formula, T n,max For Δu n,max The corresponding normal traction force; Δu n,max The maximum normal separation value; k n For normal stiffness and T t,max For Δu t,max The corresponding normal traction force; Δu t,max k is the maximum tangential separation value. t For tangential stiffness and

[0058] Step 5: Update Material Strength: Update the material parameters for the adhesive corrugated bond interface to collaboratively analyze the constitutive relation of the cyclic cohesive force model; specifically, updating the material parameters for the adhesive corrugated bond interface includes: the normal strength σ of the cohesive element.n and the corresponding strain δ n Tangential strength σ t and the corresponding strain δ t The ratio of the durability limit to the static strength of the cohesive model element. When fatigue damage initiation begins at the corrugated key interface, the natural bonding interface almost completely debonds, the natural bonding interface fails, and the element ceases to function.

[0059] Step 6: Control cell deletion: Update the calculated interface damage value based on the interface material strength in Step 4, and control cell deletion based on the interface damage value;

[0060] Step 7: Update the matrix: Based on the calculation results in Step 5, update the stress matrix and Jacobian matrix, update the traction-separation constitutive relation in Step 2, and repeat Steps 1 to 5 to calculate the next load step.

[0061] Step 8: Adhesive Layer Interface Analysis: Update the structural stress calculation based on the calculation results of Step 5, extract the cumulative damage degree of the adhesive corrugated key interface, the cumulative damage increment of interface fatigue, and the monotonic damage increment index of the interface, and realize the analysis of cumulative fatigue damage and interface failure extension of the adhesive layer interface.

[0062] Experiment 1

[0063] Physical experiments were conducted on a full-scale segmental model of a UHPFRC composite steel bridge deck with adhesive corrugated keys to investigate the force transmission mechanism and failure mechanism of the adhesive corrugated key interface. Fatigue analysis of the corrugated key bonding interface was performed using finite element analysis software based on the fatigue analysis method proposed in this application, clarifying the interface failure mechanism.

[0064] A full-scale segmental finite element model of the UHPFRC composite steel bridge deck with corrugated key bonding was established using finite element software, such as... Figure 3 The steel bridge deck top slab, UHPFRC composite layer, and corrugated key in the finite element model are modeled using solid elements, while the composite layer reinforcement mesh is modeled using truss elements. The constitutive relationship curves of the cohesive elements are defined by calling the UMAT subroutine in the finite element analysis software, and the damage accumulation of the cohesive elements during cyclic loading and unloading is updated to achieve fatigue analysis of the adhesive bonding interface.

[0065] The physical test results show that the initial peel load of the specimen designed with bonded corrugated keys is 71 kN. Taking 50% of the initial peel load level, the peak fatigue load is determined to be 35.5 kN. Four indicators—damage degree of cohesive elements (SDV1), interface damage degree, damage area, and debonding area—were extracted to analyze the damage initiation and evolution of the corrugated key-steel plate interface. Wherein, SDV1 = D, the interface damage degree is the average of the damage degrees SDV1 of all elements on the interface; the damage area is the area of ​​the interface where SDV1 is greater than 0; and the debonding area is the area of ​​the interface where SDV1 is greater than 1.

[0066] In the assembly interface, the bonding corrugated key assembly interface is divided into four areas: adhesive layer 1, adhesive layer 2, adhesive layer 3, and adhesive layer 4, as follows: Figure 4 .

[0067] Calculation results show that the fatigue behavior of the corrugated key bond interface can be divided into four segments: fatigue failure in the natural bond region, initiation of fatigue damage between the corrugated key and the steel plate, cumulative development of fatigue damage between the corrugated key and the steel plate, and debonding propagation at the corrugated key-steel plate interface. The calculation and analysis results for each stage are as follows:

[0068] (1) Fatigue failure stage in the naturally bonded area: Under fatigue load, fatigue damage initiation and debonding propagation first occur in the naturally bonded area of ​​the composite steel bridge deck. After the natural bond interface has almost completely debonded, fatigue damage initiation begins at the bond interface of the corrugated key, such as... Figure 5 .

[0069] (2) Fatigue damage initiation stage at the corrugated key-steel plate bond interface: Under fatigue load, no monotonic damage behavior occurs at the bond interface, i.e., SDV1 = 0; the cumulative interface damage SDV1 comes from the interface fatigue damage increment (SDV6) under cyclic loading, i.e., SDV1 = ∫SDV6dt; as the number of fatigue load cycles increases, fatigue damage initiation occurs first at the right-angle position of adhesive layer 4 near the movable end support in the corrugated key-steel plate bond interface, and enters the interface debonding and propagation stage; as the number of fatigue load cycles continues to increase, damage initiation begins at the right-angle position of adhesive layer 3. The integration point at the lower right corner of adhesive layer 4 is taken as fatigue detail 1, and the integration point at the lower right corner of adhesive layer 3 is taken as fatigue detail 2. The cumulative fatigue damage cloud diagram is as follows. Figure 6 When the fatigue load is applied for 2.2 million cycles, the cumulative fatigue damage value of detail 1 reaches 0.338, while detail 2 shows no fatigue damage; when the fatigue load is applied for 2.4 million cycles, the cumulative fatigue damage value of detail 1 reaches 1, while detail 2 still shows no fatigue damage; when the fatigue load is applied for 2.8 million cycles, the debonding and propagation stage has begun at the location of detail 1, and the cumulative fatigue damage value of detail 2 reaches 0.312.

[0070] (3) Stages of fatigue damage accumulation and development between the corrugated key and the steel plate: Fatigue damage initiation first occurred at the lower right corner of adhesive layer 4 and the lower right corner of adhesive layer 3, and the cumulative fatigue damage (SDV1) developed most rapidly. Detail 1 and Detail 2 were selected as representative points to calculate fatigue damage growth, such as... Figure 7 .Depend on Figure 7 It can be seen that when the number of fatigue load cycles reaches 2 million, the cumulative fatigue damage values ​​of detail 1 and detail 2 are 0.274 and 0.086, respectively, and the epoxy resin adhesive layer interface between the corrugated key and the steel plate shows excellent fatigue resistance.

[0071] Under fatigue loading, the number of fatigue load cycles before interface failure exhibits different performance characteristics under different working conditions. The cumulative damage of the interface cohesive elements minus the number of load cycles, and the corresponding fatigue life (when the cumulative damage value of local cohesive elements reaches 1) under different cyclic loading conditions are shown below. Figure 8 and 9 .

[0072] (4) During the failure propagation stage of the bond interface between the corrugated key and the steel plate: the area of ​​local cohesive unit failure will expand outwards, and the debonding area of ​​the interface will continuously increase. As the number of load cycles increases, the interface debonding propagation rate is as follows: Figure 10 .Depend on Figure 10 It can be seen that with repeated fatigue loading, the debonding propagation rate of the interface continues to increase; the debonding area increases by 8.9% from 2.8 million cycles to 3.3 million cycles, and by 11.6% from 3.3 million cycles to 3.8 million cycles. The analysis results show an approximately exponential development with the fatigue cumulative damage rate of the interface cohesive unit.

Claims

1. A method for fatigue analysis of the interface of adhesive corrugated keys in composite steel bridge decks, characterized in that... Includes the following steps: Step 1: Input initial parameters; Input the initial parameters of the interface, including the adhesive corrugated key interface and the natural connection interface; Step 2: A method for analyzing the D-evolution of damage at the adhesive corrugated bond interface with a fatigue damage amplification factor a is proposed. The method is as follows: In the formula, D represents interface damage; The damage effect of cyclic loading on the interface; The damage effect of monotonic load on the interface; a is the fatigue damage amplification factor; δ∑ represents the increment of the separation value; δ∑ represents the cumulative cohesion length. For traction force; σ max C represents the current interface normal intensity. f The ratio of the cohesive model strength; H is the Heaviside function; δ is the separation value; δ0 is the adhesion length; T n T is the traction force in the normal cohesive region. t σ is the tangential cohesive force; q is the cohesive energy ratio; f σ represents the durability limit of the cohesive model element; max,0 The interface normal intensity in the initial state; Δu n Δu is the separation length of the normal cohesive region. t The separation length of the tangential cohesive region; Let be the separation value at time t; The separation value at time t-Δt; Let t be the current state i Time Δ n The maximum value; For the previous time increment state t i-1 Time Δ n The maximum value; Step 3: Establish the traction-separation constitutive relation under the damage state; The exponential traction-separation law is used to simulate the fatigue behavior of the adhesive corrugated key interface. The interface damage D under fatigue loading is introduced into the traction-separation law to obtain the cohesive traction force under damage state. and the effective cohesive strength (σ) under damaged conditions max τ max ), and proposes a traction-separation constitutive relation under damage conditions; In the formula, T is the cohesive traction force obtained in the initial state; σ max,0 τ represents the interface normal intensity in the initial state. max,0 This represents the tangential strength of the interface in the initial state; Step 4: Repair the damaged interface of the adhesive corrugated key; Establish an irreversible fatigue load cycle path and define the normal stiffness T of the adhesive corrugated key interface during the loading-unloading process. n and tangential stiffness T t It degrades with increasing fatigue loading cycles; T n =T n,max +k n (D) n -Yes n,max ) T t =T t,max +k t (D) t -Yes t,max ) In the formula, T n,max For Δu n,max The corresponding normal traction force; Δu n,max The maximum normal separation value; k n For normal stiffness and T t,max For Δu t,max The corresponding normal traction force; Δu t,max k is the maximum tangential separation value. t For tangential stiffness and Step 5: Update material strength: Update the material parameters of the adhesive corrugated key interface to collaboratively analyze the constitutive relationship of the cyclic cohesive force model; Step 6: Control cell deletion: Update the calculated interface damage value based on the interface material strength in Step 4, and control cell deletion based on the interface damage value; Step 7: Update the matrix: Based on the calculation results in Step 5, update the stress matrix and Jacobian matrix, update the traction-separation constitutive relation in Step 2, and repeat Steps 1 to 5 to calculate the next load step. Step 8: Adhesive Layer Interface Analysis: Update the structural stress calculation based on the calculation results of Step 5, extract the cumulative damage degree of the adhesive corrugated key interface, the cumulative damage increment of interface fatigue, and the monotonic damage increment index of the interface, and realize the analysis of cumulative fatigue damage and interface failure extension of the adhesive layer interface.

2. The fatigue analysis method for the interface of the adhesive corrugated key in the composite steel bridge deck according to claim 1, characterized in that... The initial parameters of the interface portion of the adhesive corrugated key in step one include: normal strength, tangential strength, strain corresponding to tangential strength, strain corresponding to normal strength, ratio of fatigue limit to static strength, and viscosity coefficient.

3. The fatigue analysis method for the interface of the adhesive corrugated key in the composite steel bridge deck according to claim 1, characterized in that... The initial parameters of the natural connection interface in step one include: normal intensity and strain corresponding to the normal intensity.

4. The fatigue analysis method for the interface of the adhesive corrugated key in the composite steel bridge deck according to claim 1, characterized in that... Step five, which involves updating the material parameters for the adhesive corrugated key interface, includes: the cohesive unit normal strength σ. n and the corresponding strain δ n Tangential strength σ t and the corresponding strain δ t The ratio of the durability limit to the static strength of the cohesive model element.

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