A fatigue life assessment method for parallel steel wires considering the coupling effect of corrosion and fatigue

Abstract

The present invention discloses a method for evaluating the fatigue life of parallel steel wires considering the corrosion-fatigue coupling effect. This method includes three stages: the initiation of pitting corrosion pits, the propagation of fatigue short cracks, and the propagation of fatigue long cracks in parallel steel wires under the corrosion-fatigue coupling effect. In addition, considering the unique physical properties of parallel steel wires, namely the existence of internal tensile force, a fatigue life evaluation model for parallel steel wires is established. The present invention provides a method for evaluating the fatigue life considering the corrosion-fatigue interaction coupling relationship and the physical characteristics of parallel steel wires themselves, which can be used to predict the fatigue life of parallel steel wires.

Description

Technical Field

[0001] The present invention relates to the fatigue life assessment of parallel steel wires. Specifically, it relates to a method for assessing the fatigue life of parallel steel wires considering the corrosion-fatigue coupling effect. Background Art

[0002] Parallel steel wires are important load-bearing components of cable-supported bridges. However, when not properly protected, the steel wires are easily affected by environmental corrosion. Under this effect, corrosion pits will form on the surface of the steel wires and then develop into cracks, damaging the steel wire structure, thus significantly reducing the service life of the steel wires. Therefore, the corrosion environment has a great impact on the service life of parallel steel wires. In addition, as the service life of the steel wires extends, cracks will occur under the action of fatigue loads, and the corrosion rate at the crack will also increase. Therefore, it is necessary to carry out research on the fatigue life of parallel steel wires considering the corrosion-fatigue coupling effect. At present, the existing theoretical models are still difficult to fully characterize the corrosion-fatigue coupling process of the steel wires, so the obtained fatigue life curves cannot fully reflect the actual service conditions of the steel wires. In addition, due to the special physical properties of the steel wire material itself, that is, it needs to bear a certain tensile force during service, and the change in the magnitude of the tensile force will also affect its fatigue life. Therefore, it is necessary to establish a fatigue life assessment method considering the corrosion-fatigue interaction coupling relationship and the physical characteristics of the parallel steel wires themselves to improve the prediction accuracy of the fatigue life of parallel steel wires. Summary of the Invention

[0003] Aiming at the defects of the existing theoretical models, the purpose of the present invention is to establish a method for assessing the fatigue life of parallel steel wires considering the corrosion-fatigue coupling effect.

[0004] To achieve the above purpose, the present invention proposes a fatigue life assessment method considering the corrosion-fatigue interaction coupling relationship and the physical characteristics of the parallel steel wires themselves, including the following steps:

[0005] In the initiation stage of corrosion fatigue pitting, according to Faraday's law, the pitting growth rate can be expressed as:

[0006]

[0007]

[0008]

[0009] In the formula, V is the volume of the pitting; a, b, and c are the depth, width, and length of the pitting respectively; M is the molar mass of the steel; n is the number of electrons released; F is the Faraday constant, and its value is 96500 C / mol; ρ is the material density; I p is the current at the pitting; is the electro-erosion current coefficient; ΔH is the change in activation energy per unit volume, ΔH = 15.5×10 3 J / mol; R is the gas constant, R = 8.314 J / mol·K; T is the absolute temperature, T = 293 K.

[0010] With the continuous enhancement of the corrosion effect, the pitting pits will gradually expand into short cracks. Expansion threshold:

[0011]

[0012] Therefore, the critical size a for the conversion of corrosion pits into cracks psc can be expressed as:

[0013]

[0014] In the formula, K t is the stress concentration coefficient, which is related to the size of the corrosion pit morphology (b / a) and the applied load;

[0015] Combined with the above calculation process, the duration t of the pitting pit initiation stage d can be expressed as:

[0016]

[0017] To consider the acceleration effect of fatigue load on the corrosion process, the duration t of the pitting pit initiation stage d can be corrected to:

[0018]

[0019] In the formula, C p is the cyclic load action factor; S is the stress amplitude.

[0020] As the corrosion pits continue to grow, the corrosion pits will gradually convert into cracks. At this time, short cracks will appear on the surface of the steel wire. According to the fracture mechanics theory, we can get:

[0021]

[0022]

[0023]

[0024] In the formula, C corr is the crack growth corrosion acceleration factor; C s is the fatigue coefficient of short cracks; m s is the short crack fatigue exponent; S is the stress amplitude; N s is the number of stress cycles, which can be obtained by multiplying the time t by the frequency f. Y is the crack shape factor; D is the diameter of the steel wire

[0025] Therefore, during the propagation stage of short cracks, the duration t s is as follows:

[0026]

[0027] a tr is the critical size for the transition of short cracks to long cracks; when the crack further propagates and becomes a long crack, its expression is:

[0028]

[0029] In the formula, C l is the long crack fatigue coefficient; m l is the long crack fatigue exponent.

[0030] Therefore, during the propagation stage of long cracks, the duration t l is as follows:

[0031]

[0032] In the formula, a lr is the critical size for the propagation of long cracks to failure, and its value is 0.5D.

[0033] C corr The crack propagation corrosion acceleration factor can be expressed as:

[0034]

[0035] In the formula, A1 and m are parameters in the traditional fatigue life curve and the non-coupled corrosion fatigue life.

[0036] Traditional fatigue life curve:

[0037] log N + m log(S) = log A

[0038] In the formula, N is the number of cycles; S is the fatigue stress amplitude; m is a constant related to the wire material, and its value is 3.5; A is a constant related to the wire material.

[0039] Parameters in the traditional non-coupled corrosion fatigue life:

[0040] A1 = A / K f

[0041] K f = 1.2 + 5.77C(t)

[0042] C(t) = kt r

[0043] Wherein, C(t) represents the pitting depth function; t is the service life; k is the corrosion depth (mm) after one year of service; r is the corrosion rate; K f is the fatigue reduction coefficient.

[0044] When considering the stress state of the steel wire, A can be corrected as:

[0045]

[0046] Wherein, S b is the ultimate tensile strength of parallel steel wires; S m is the stress state of parallel steel wires;

[0047] According to the above corrosion fatigue pitting initiation duration, corrosion fatigue short crack propagation duration and corrosion fatigue long crack propagation duration, the fatigue life under corrosion action can be obtained:

[0048]

[0049] After integration and multiplying both sides by the loading frequency, the corresponding number of stress cycles can be calculated, that is, the three-stage fatigue-life (S-N) curve considering pitting initiation - short crack propagation - long crack propagation under corrosion action is obtained:

[0050]

[0051] The beneficial effects of the present invention are:

[0052] The present invention comprehensively considers the corrosion-fatigue coupling effect and the physical characteristics of parallel steel wires; based on the three stages of pitting initiation, fatigue short crack propagation and fatigue long crack propagation of parallel steel wires, a fatigue life assessment model of parallel steel wires is established, which can improve the fatigue prediction accuracy and can be used to predict the fatigue life of parallel steel wires. Description of the Drawings

[0053] Figure 1 is the pitting morphology.

[0054] Figure 2 is the comparison of three fatigue life curves. Detailed Embodiments

[0055] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the drawings and embodiments.

[0056] In the corrosion fatigue pitting initiation stage, according to Faraday's law, the pitting growth rate can be expressed as:

[0057]

[0058]

[0059]

[0060] Wherein, V is the volume of the pitting pit; a, b, and c are the depth, width, and length of the pitting pit respectively, as Figure 1 shown; M is the molar mass of the steel; n is the number of electrons released; F is the Faraday constant, the value of which is 96500 C / mol; ρ is the material density; I p is the current at the pitting pit; is the electro-erosion current coefficient; ΔH is the change in activation energy per unit volume, ΔH = 15.5×10 3 J / mol; R is the gas constant, R = 8.314 J / mol·K; T is the absolute temperature, T = 293 K.

[0061] With the continuous enhancement of the corrosion effect, the pitting pit will gradually expand into a short crack expansion threshold:

[0062]

[0063] Therefore, the critical size a of the conversion of the corrosion pit to a crack psc can be expressed as:

[0064]

[0065] Wherein, K t is the stress concentration coefficient, which is related to the morphology and size of the corrosion pit and the load applied;

[0066] Combining the above calculation process, the duration of the pitting pit initiation stage can be expressed as:

[0067]

[0068] To consider the acceleration effect of the fatigue load on the corrosion process, the duration of the pitting pit initiation stage can be corrected to:

[0069]

[0070] Wherein, C p is the cyclic load action factor; S is the stress amplitude.

[0071] As the corrosion pit continuously increases, the corrosion pit will gradually convert to a crack. At this time, short cracks will appear on the surface of the steel wire. According to the fracture mechanics theory, it can be obtained that:

[0072]

[0073]

[0074]

[0075] In the formula, C corr is the crack growth corrosion acceleration factor; C s is the fatigue coefficient of short cracks; m s is the short crack fatigue exponent; S is the stress amplitude; N s is the number of stress cycles, which can be obtained by multiplying the time t and the frequency f. Y is the crack shape factor; D is the wire diameter

[0076] Therefore, in the short crack propagation stage, its duration is:

[0077]

[0078] When the crack further propagates, that is, when it becomes a long crack, its expression is:

[0079]

[0080] In the formula, C l is the long crack fatigue coefficient; m l is the long crack fatigue exponent.

[0081] Therefore, in the long crack propagation stage, its duration is:

[0082]

[0083] In the formula, a lr is the critical size for the long crack to propagate to failure, and its value is 0.5D.

[0084] C corr The crack growth corrosion acceleration factor can be expressed as:

[0085]

[0086] In the formula, A1 and m are parameters in the traditional fatigue life curve and the non-coupled life of corrosion fatigue.

[0087] Traditional fatigue life curve:

[0088] log N + m log(S) = log A

[0089] In the formula, N is the number of cycles; S is the fatigue stress amplitude; m is a constant related to the wire material, and its value is 3.5; A is a constant related to the wire material.

[0090] Parameters in the traditional non-coupled life of corrosion fatigue:

[0091] A1 = A / K f

[0092] K f = 1.2 + 5.77C(t)

[0093] C(t)=kt r

[0094] In the formula, C(t) represents the pitting depth function; t is the service life; k is the corrosion depth (mm) after one year of service; r is the corrosion rate; K f is the fatigue reduction coefficient.

[0095] When considering the stress state of the steel wire, A can be corrected to:

[0096]

[0097] In the formula, S b is the ultimate tensile strength of parallel steel wires; S m is the stress state of parallel steel wires

[0098] According to the above pitting initiation duration of corrosion fatigue, short crack propagation duration of corrosion fatigue, and long crack propagation duration of corrosion fatigue, the fatigue life under corrosion action can be obtained:

[0099]

[0100] After integration and multiplying both sides by the loading frequency, the corresponding number of stress cycles can be calculated, that is, the three-stage fatigue-life (S-N) curve considering pitting initiation - short crack propagation - long crack propagation under corrosion action is obtained:

[0101]

[0102] Calculation example: Assume that the pitting morphology dimensions are a = b = c = 1mm, D = 14mm, K t = 2.34, C p = 1.01, I p = 1.31×10 -9 C / s, k = 0.047, r = 0.39, f = 1Hz, a tr is taken as 1mm, C s is taken as 9.38×10 -13 , m s is taken as 3, C l is taken as 2.7×10 -11 , m l is taken as 2.88, C p is taken as 1, M is 56×10 -3 kg / mol, n is 2; ρ is 7850kg / m 3 ; ΔK th is taken as 2MPa·m 0.5 ; The ultimate tensile strength is 1860MPa, and the stress state is 1050MPa.

[0103] According to the "Code for Design of Steel Structures" GB50017-2017, the total number of cycles N of the allowable stress range is specified as 2×10 6 times. Therefore, it is assumed that when the total number of cycles N = 2×10 6 times, the stress range calculated based on the fatigue life curve is 143 MPa; the stress range calculated based on the corrosion fatigue life curve (uncoupled) is 106 MPa; the stress range calculated based on the corrosion fatigue coupled life curve is 53 MPa, as Figure 2 shown.

[0104] It can be seen that after considering the corrosion effect, its fatigue performance will decrease rapidly; when considering the corrosion fatigue coupling effect, its anti-fatigue performance is reduced by half compared to the uncoupled effect.

[0105] Those skilled in the art can easily understand that the above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for evaluating the fatigue life of parallel steel wires considering the coupling effect of corrosion and fatigue, characterized in that It includes the following steps: Based on the pitting pit growth rate formula of Faraday's law, the duration of the pitting pit initiation stage of parallel steel wires is derived : ， where b and c are the width and length of the pitting corrosion pit respectively; C p is the cyclic load action factor; φ is the corrosion pit shape parameter; M is the molar mass of the steel; n is the number of electrons released; F is the Faraday constant, whose value is 96500 C / mol; ρ is the material density; I p is the current at the pitting corrosion pit; a psc is the critical size for the transformation of the corrosion pit to a crack; S is the stress amplitude; Based on the fracture mechanics theory, the propagation durations of parallel wire short cracks and long cracks are respectively derived; Parallel wire short crack propagation duration : ， ， where f is the loading frequency of cyclic load; a tr is the critical size for the transition from short cracks to long cracks; C corr is the crack growth corrosion acceleration factor; C s is the fatigue coefficient of short cracks; m s is the short crack fatigue exponent; Y is the crack shape factor, a is the pitting depth; the propagation duration of parallel wire long cracks : ， Where C l is the long crack fatigue coefficient; m l is the long crack fatigue exponent; a lr is the critical size of the long crack extending to failure, and its value is 0.5D; D is the wire diameter; Based on the traditional S-N curve and the pre-corrosion process, the crack growth corrosion acceleration factor expression; ， ， ， ， ， Where, S b is the ultimate tensile strength of parallel wires; S m is the stress state of parallel wires; m is a constant related to the material, and its value is 3.5; C(t) represents the pitting depth function; t is the service life; k is the corrosion depth after one year of service, with the unit of mm; r is the corrosion rate; K f is the fatigue reduction coefficient; The sum of the initiation duration of corrosion fatigue pitting pits, the propagation duration of corrosion fatigue short cracks, and the propagation duration of corrosion fatigue long cracks is the fatigue life under corrosion action, namely: ， Thus, a three-stage fatigue-life curve expression considering pitting pit initiation - short crack propagation - long crack propagation is established, which is: ， N is the number of cycles.

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