Evolution evaluation method for bolting steel-UHPC interface friction effect under influence of fretting wear

Abstract

The invention discloses a bolting steel-UHPC (Ultra High Performance Concrete) interface friction effect evolution evaluation method under the influence of fretting wear. Dividing the calculation process into a plurality of calculation steps, and calculating the average pressure stress of the bolting steel-UHPC interface before fretting wear as an initial calculation value; assuming a bolting steel-UHPC interface pressure stress value in each step, calculating an interface pressure stress true value in the step by considering the fretting wear influence, judging and adjusting an interface pressure stress assumption value until the interface pressure stress assumption value is equal to the interface pressure stress true value, and calculating an interface friction effect in the step according to the interface pressure stress assumption value; and entering the next step, taking the actual value of the interfacial pressure stress determined in the previous step as the initial value of the interfacial pressure stress for recalculation, and finally obtaining the evolution rule of the bolting steel-UHPC interfacial friction effect in the whole abrasion process. According to the method, the friction effect evolution of the bolting steel-UHPC interface under the influence of fretting wear can be effectively revealed, and a scientific basis is provided for accurate evaluation of the fatigue life of the bolting steel-UHPC interface.

Description

Technical Field

[0001] The present invention relates to the technical field of methods for evaluating the evolution of compressive stress and friction at the interface of a steel-UHPC composite structure, and in particular to a method for evaluating the evolution of friction effects at the interface of a bolt-connected steel-UHPC composite structure taking into account the effect of fretting wear on the interface. Technical Background

[0002] In recent years, steel-UHPC (ultra-high performance concrete) composite structures, particularly orthotropic steel-UHPC composite bridge decks, have been widely used in my country. Compared to conventional steel-concrete interfaces, the shear stiffness and strength of studded steel-UHPC interfaces are significantly enhanced. Formulas recommended by current design codes underestimate the shear capacity of studded steel-UHPC interfaces by 10%-50%. Although extensive research has investigated the effects of factors such as stud diameter, aspect ratio, and UHPC plate thickness on the shear behavior of studded steel-UHPC interfaces, the impact of interfacial wear on the interfacial friction of steel-UHPC composite structures has largely been overlooked.

[0003] The mechanism for enhancing the shear capacity of bolted steel-UHPC composite structures has garnered widespread attention. In recent years, many researchers have investigated this mechanism. Some have considered the contribution of the weld ring at the bottom of the bolt to the shear capacity, others have considered the contribution of the UHPC wedge formed in front of the bolt root, and still others believe that friction at the steel-UHPC interface is the fundamental reason for the increased shear capacity. On this basis, some researchers have proposed a calculation model for the shear capacity of steel-UHPC that considers friction, which has higher prediction accuracy than the formulas proposed in the specifications. However, during the actual use of steel-UHPC composite structures, the degree of interface wear is constantly changing, and this change in wear results in a constantly changing interfacial compressive stress, making it difficult to determine the interfacial compressive stress value based on the interface wear at a specific moment.

[0004] To this end, the present invention proposes a method for evaluating the evolution of friction effects at the bolted steel-UHPC interface under the influence of fretting wear. This method can effectively decouple the interfacial compressive stress and wear amount and determine the interfacial pressure loss value caused by wear. The calculation method is simple and the physical meaning is clear. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for evaluating the evolution of friction effect at the bolted steel-UHPC interface under the influence of fretting wear, which can obtain the interface contact pressure value, wear depth and interface friction effect value within any calculation step.

[0006] In order to effectively solve the above technical problems, the technical solutions adopted by the present invention are as follows:

[0007] A method for evaluating the evolution of friction effects at the bolted steel-UHPC interface under the influence of fretting wear includes the following steps:

[0008] (1) The calculation process of the evolution of the friction effect of the bolted steel-UHPC interface under the influence of fretting wear is divided into n calculation steps. The number of fretting wear times N of the bolted steel-UHPC interface in each step is the total number of fretting wear times N. z Divide by the number of computation steps n.

[0009] The extrusion force P0 generated by the bolt on UHPC can be expressed as formula (1):

[0010]

[0011] Where d is the bolt diameter; f cu is the tensile strength of the stud, which is taken as 50% in calculation.

[0012] Then, the formula derived from the force streamline model was used to calculate the initial value of the average compressive stress e and the initial value of the friction effect P at the bolted steel-UHPC interface before fretting wear. f，0 , which can be expressed as formulas (2) and (3):

[0013]

[0014]

[0015] Where a is the height of the bolt extrusion force, h is the range of the extrusion force, t is the equivalent width of the extrusion force, and μ is the friction coefficient between the steel and UHPC interface;

[0016] (2) Given the assumed value of the compressive stress σ at the bolted steel-UHPC interface in step i under the influence of fretting wear n,i , the interface wear depth Δ in step i i It can be expressed as formula (3):

[0017] Δ i =sNKσ n,i ;

[0018] Where s is the fretting amplitude set in the wear test, and K is the wear rate of the steel-UHPC interface.

[0019] The total wear amount Δ caused by interface fretting wear from step 1 to step i n,i Calculation is as follows:

[0020]

[0021] Then the interface compressive stress loss value Δσ caused by fretting wear in step i can be obtained n,i , which can be expressed as formula (5):

[0022]

[0023] Where L is the clearance between the bolt cap and the welded steel plate, E c is the elastic modulus of UHPC.

[0024] (3) The true value of the compressive stress at the bolted steel-UHPC interface in step i, σ t，i It can be expressed as formula (6):

[0025] σ t，i =σ t，i-1 -Δσ n，i ;

[0026] Where σ t,i-1 is the true value of the compressive stress at the bolted steel-UHPC interface in step i-1.

[0027] Then determine the assumed value of the interface compressive stress σ n,i and the true value of the interface compressive stress σ t，i Are they equal? ​​If not, adjust the assumed value of the interface compressive stress σ n，i And recalculate σ n，i =σ t，i ; If they are equal, the interface friction effect value in step i can be expressed as formula (7):

[0028]

[0029] (4) Enter step i+1, take the actual value of the interface compressive stress determined in step i as the initial value of the interface compressive stress, and give the assumed value σ of the bolted steel-UHPC interface compressive stress in step i+1 n,i+1 The next calculation step was restarted, and finally the evolution law of the friction effect of the bolted steel-UHPC interface during the entire wear process was obtained. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 This is a schematic diagram of the calculation step division process of the friction effect evolution process of the bolted steel-UHPC interface under the influence of fretting wear in the present invention.

[0031] Figure 2 This is the calculation flow chart of the present invention

[0032] Figure 3 This is the interface friction effect fretting wear degradation diagram of the present invention DETAILED DESCRIPTION

[0033] The present invention will be further described below with reference to the accompanying drawings and embodiments. When the following description refers to the drawings, the same symbols in different drawings represent the same or similar elements unless otherwise indicated.

[0034] Example 1

[0035] Divide the calculation steps and calculate the initial value of the interface compressive stress σ under no interface fretting wear t，0 and the initial value of friction effect P f，0 .

[0036] The evolution calculation process of the friction effect of the bolted steel-UHPC interface under the influence of fretting wear is divided into n calculation steps. Assuming that the interface compressive stress, interface friction coefficient, and wear depth are constant in calculation step i, the number of fretting wear times N in each step is the total number of fretting wear times N. z Divide by the number of calculation steps n. The schematic diagram of the calculation step division of the friction effect evolution process is as follows Figure 1 shown.

[0037] According to the transverse stress distribution model of the steel-UHPC interface in the literature "Xuhui Zhang, Long Cheng, Fu Xu, Caiqian Yang, Lei Wang. A novel model for shear strength prediction of steel-UHPC composite structure considering interface friction [J]. Journal of Structural Engineering, 2024, DOI: 10.1061 / JSENDH / STENG-13164", the extrusion force P0 generated by the bolt on the UHPC and the initial compressive stress value σ between the steel-UHPC interface when there is no interface fretting wear t，0 The calculation formula is as follows:

[0038]

[0039] Where f cu is the tensile strength of the bolt, which is taken as 50% in the calculation, a is the height of the bolt extrusion force, h is the range of the extrusion force, t is the equivalent width of the extrusion force, and μ is the friction coefficient between the steel and UHPC interface.

[0040] The interface friction effect is affected by the friction coefficient. Due to the lack of steel-UHPC material interface wear test data, it is impossible to accurately describe the change of the interface friction coefficient. According to the test results of the steel-UHPC interface friction coefficient in the literature "Semendary AA, Stefaniuk HL, Yamout D, Svecova D. Static performance of stud shear connectors and UHPC in deck-to-girder composite connection. Engineering Structures. 2022; 255: 113917.", the friction coefficient μ is taken as a constant value of 0.73, and the initial value of the friction effect P is f，0 The calculation formula is as follows:

[0041]

[0042] Example 2

[0043] Repeat Example 1, and assume the value of the compressive stress at the bolted steel-UHPC interface in step i under the influence of fretting wear σ n,i And calculate the interface compressive stress loss value Δσ of this step n,i .

[0044] Assumed value of the compressive stress at the bolted steel-UHPC interface in step i under the influence of given fretting wear σ n,i , then the interface wear depth of step i can be roughly determined according to formula (5), that is,

[0045] Δ i =sNK i σ n,i (5)

[0046] Where s is the fretting amplitude set for the wear test, K i is the wear rate of the bolted steel-UHPC interface at step i.

[0047] Then the total wear amount Δ from step 1 to step i can be obtained n，i , as shown in formula (6):

[0048]

[0049] Interface compressive stress loss Δσ caused by interface fretting wear n，i It can be calculated by formula (7):

[0050]

[0051] Where L is the clearance between the bolt cap and the welded steel plate; E c is the elastic modulus of UHPC;

[0052] Example 3

[0053] Repeat Example 2 to establish the interface compressive stress relationship between step i and step i-1, and adjust the assumed interface compressive stress value σ n,i Make the equation true.

[0054] The true value of the compressive stress at the bolted steel-UHPC interface in step i, σ t，i It can be expressed as formula (8):

[0055] σ t，i =σ t,i-1 -Δσ n，i (8)

[0056] Where σ t,i-1 is the true value of the compressive stress at the bolted steel-UHPC interface in step i-1.

[0057] True value of compressive stress at the bolted steel-UHPC interface σ t，i and the assumed value of interface compressive stress σ n,i There should also be an equality relationship:

[0058] σ t，i =σ n，i (9)

[0059] Adjust the assumed value of the compressive stress at the bolted steel-UHPC interface σ n,i Make equations (8) and (9) valid: If the equations are not uniformly valid, adjust the assumed value of the interface compressive stress σ n,i And recalculate to satisfy the equation; if the equations are all true, then the interface friction effect P in step i f，i It can be expressed as formula (10):

[0060]

[0061] Enter step i+1 and use the true value of the interface compressive stress σ determined in step i t，i As the initial value of the interface compressive stress, the assumed value of the bolted steel-UHPC interface compressive stress σ in step i+1 is given n，i+1 The next calculation step was restarted, and finally the evolution law of the friction effect of the bolted steel-UHPC interface during the entire wear process was obtained.

[0062] Example 4

[0063] Example 3 was repeated to verify the feasibility of the present invention using simulated data.

[0064] An interface wear test was conducted on a steel-UHPC composite structure with an interface size of 150 mm × 280 mm. 500,000 wear cycles occurred in calculation segment 1, and the fretting amplitude s was 0.1 mm. The diameter d of the welded stud was 22 mm, the stud height was 110 mm, the extrusion force range h was 58.96 mm, the extrusion force equivalent width t was 112 mm, and the bolt extrusion force height a was 36.841 mm. Assuming that the tensile strength of the stud is 480 MPa, the extrusion force P0 generated by the bolt on the UHPC is calculated according to formula (1) to be approximately 91.23185 kN. The elastic modulus of UHPC is 40 GPa.

[0065] Assume that K is set to 5×10 -15 , for calculation segment 1, according to formula (2) we can calculate:

[0066]

[0067] At this time, according to Figure 2 The process shown calculates the true value of the interface compressive stress σ in step 1 t，1 , assuming that the interface compressive stress σ n,1 The magnitude is 7.6 MPa. If the true value of the compressive stress at the bolted steel-UHPC interface σ t，i With the assumed interface compressive stress σ n,i If the relationship between equations (8) and (9) is not satisfied, the assumed interface compressive stress σ is gradually increased. n，i , the calculation results are as follows:

[0068] Table 1 Iterative calculation results of assumed interface compressive stress

[0069]

[0070]

[0071] According to the calculation results in Table 1, it can be determined that when the assumed interface compressive stress σ n,1 When it is 7.90 MPa, it is closest to the difference between the initial value and the loss value of the interface compressive stress. Therefore, the true value of the bolted steel-UHPC interface compressive stress σ in step 1 is determined. t，1 is 7.90. The true value of the interface compressive stress σ t，1 Substitute into formula (10) to determine the interface friction effect value P at this time f，1 :

[0072]

[0073] For step 1, the initial value of the interface compressive stress σ t，0is 8.6362, and the interface friction effect value calculated according to formula (10) is about 13.8771 kN. After the interface fretting wear in step 1, the interface compressive stress becomes 7.90 MPa, and the interface friction effect value at this time is about 12.7223 kN, and the interface friction force loss is 8.32%;

[0074] Example 5

[0075] Repeat Example 4 and calculate the fretting wear degradation process up to step 4, generating a total of 2 million fretting wear cycles. The calculated interface friction loss values ​​for each calculation step are shown in the following table:

[0076] Table 2 Calculation table of interface friction effect fretting wear degradation

[0077]

[0078] Figure 3 It reflects the change of friction effect loss with the number of wear times N. The horizontal axis is the number of fretting wear times, and the vertical axis is the ratio of the friction effect loss value to the interface friction effect value before fretting wear occurs.

Claims

1. A method for evaluating the evolution of friction effect at the bolted steel-UHPC interface under the influence of fretting wear, characterized in that: The method comprises the following steps: (1) The calculation process is divided into multiple calculation steps, and the number of fretting wears at the bolted steel-UHPC interface in each step is determined; (2) The formula derived from the force streamline model was used to calculate the average compressive stress and friction effect of the bolted steel-UHPC interface before fretting wear as the initial value of step 1; (3) Given the assumed value of the interfacial compressive stress of the bolted steel-UHPC in step i under the influence of fretting wear, calculate the fretting wear depth and interfacial compressive stress loss value in this step; (4) Calculate the true value of the interface compressive stress between bolted steel and UHPC in this step according to the initial value of the interface compressive stress and the loss value of the interface compressive stress in this step, iteratively adjust the assumed value of the compressive stress in step (3) to make it equal to the true value, and calculate the interface friction effect in this step; (5) Go to the next step, use the true value of the interface compressive stress determined in the previous step as the initial value of the interface compressive stress to recalculate, and finally obtain the evolution law of the friction effect of the bolted steel-UHPC interface during the entire wear process; In step (1), the calculation process is divided into n calculation steps, and the number of fretting wear times N of the bolted steel-UHPC interface in each step is the total number of fretting wear times N z Divide by the number of computation steps n; In step (2), the formula derived from the force streamline model is used to calculate the initial value of the average compressive stress σ at the bolted steel-UHPC interface before fretting wear: t，0 and the initial value of friction effect P f，0 It can be expressed as formula (1) and (2): Where a is the height of the bolt extrusion force, h is the range of the extrusion force, t is the equivalent width of the extrusion force, P0 is the extrusion force generated by the bolt on UHPC, and μ is the friction coefficient between the steel-UHPC interface; In step (3), the assumed value of the compressive stress at the bolted steel-UHPC interface in step i under the influence of fretting wear is given as n，i , the interface wear depth Δ in step i i It can be expressed as formula (3): D i =sNKσ n，i Where s is the fretting amplitude set in the wear test, and K is the wear rate of the steel-UHPC interface; In the i-th step, the total wear amount Δ caused by the interface fretting wear n，i The calculation is as follows: In the i-th step, the interface compressive stress loss value Δσ caused by fretting wear n,i It can be expressed as formula (5): Where L is the clearance between the bolt cap and the welded steel plate, E c is the elastic modulus of UHPC; In step (4), the true value of the compressive stress at the bolted steel-UHPC interface in step i is t，i It can be expressed as formula (6): s t，i =s t,i-1 -Board n,i Where σ t，i-1 is the true value of the compressive stress at the bolted steel-UHPC interface in step i-1; Determine the assumed value of interface compressive stress σ n，i and the true value of the interface compressive stress σ t，i Are they equal? ​​If not, adjust the assumed value of the interface compressive stress σ n，i Make it equal to the true value of the interface compressive stress σ t，i are equal; if they are equal, then the interface friction effect P in step i f，i It can be expressed as formula (7): Entering the i+1th step, the actual value of the interface compressive stress determined in the i-th step is used as the initial value of the interface compressive stress to recalculate, and finally the evolution law of the friction effect on the bolted steel-UHPC interface during the entire wear process is obtained.

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