Method for simulating and predicting corrosion fatigue evolution process of steel structure

Abstract

The invention discloses a method for simulating and predicting a corrosion fatigue evolution process of a steel structure, which comprises the following steps of: establishing an integral finite element stress simulation model of the steel structure, and reserving a local finite element corrosion fatigue simulation model insertion gap of the steel structure on the integral finite element stress simulation model of the steel structure; establishing a local finite element corrosion fatigue simulation model of the steel structure, wherein the local finite element corrosion fatigue simulation model of the steel structure comprises a steel structure finite element corrosion simulation unit and a steel structure finite element fatigue simulation unit which are coupled and associated; inserting and binding the steel structure local finite element corrosion fatigue simulation model into the steel structure local finite element corrosion fatigue simulation model insertion gap to form a steel structure overall finite element corrosion fatigue simulation model; and obtaining simulation and prediction results of the corrosion fatigue evolution process of the steel structure through operation of the integral finite element corrosion fatigue simulation model of the steel structure. And multi-scale and coupling simulation of the whole process of corrosion pit formation and crack propagation is realized.

Description

Technical Field

[0001] The invention relates to a simulation and prediction method for the corrosion fatigue evolution process of a steel structure. Background Art

[0002] Corrosion fatigue of steel structures is essentially an irreversible damage evolution process under the coupling of electrochemical corrosion and mechanical factors. Analyzing its internal mechanism is the basis and key to effectively predict the fatigue life of materials and structures. The evolutionary damage process of corrosion fatigue of steel structures includes three stages: pitting, crack initiation and expansion. In this process, the electrochemical reaction at inclusions, pores and holes becomes the source of corrosion pit nucleation, and electrochemical corrosion dominates the formation of corrosion pits in the early stage of damage evolution; with the increase of pit size and the continuous action of fatigue load, the pit gradually turns into cracks, eventually leading to structural fatigue failure. It can be seen that the corrosion cracking process of steel structures is the result of the combined action of electrochemical corrosion and mechanical factors. The early stage of the corrosion fatigue damage process is the evolution of corrosion pits, and then transitions to crack development, that is, the early stage is volume corrosion damage, and the later stage is crack surface expansion.

[0003] The cohesive element method can realize continuous three-dimensional fatigue crack initiation and propagation simulation (i.e. crack surface initiation and propagation). However, the initial stage of corrosion fatigue damage evolution of steel structure is mainly manifested as the volume change of corrosion pits, rather than the initiation and propagation of crack surfaces. Therefore, the cohesive element method alone cannot fully simulate and predict the evolution process of corrosion fatigue damage of steel structure. For the evolution of corrosion fatigue damage in the process of corrosion pit formation, most methods are based on complex electrochemical and stress coupling theories, and there is no authoritative and widely used standard method. Summary of the invention

[0004] The present invention aims to provide a method for simulating and predicting the corrosion fatigue evolution process of a steel structure.

[0005] A simulation and prediction method for the corrosion fatigue evolution process of a steel structure is provided, comprising: establishing an overall finite element stress simulation model of the steel structure, wherein a notch for inserting a local finite element corrosion fatigue simulation model of the steel structure is reserved on the overall finite element stress simulation model of the steel structure; establishing a local finite element corrosion fatigue simulation model of the steel structure, wherein the local finite element corrosion fatigue simulation model of the steel structure comprises a coupled and associated steel structure finite element corrosion simulation unit and a steel structure finite element fatigue simulation unit; inserting the local finite element corrosion fatigue simulation model of the steel structure into the notch bound to the local finite element corrosion fatigue simulation model of the steel structure to form an overall finite element corrosion fatigue simulation model of the steel structure; and obtaining simulation and prediction results of the corrosion fatigue evolution process of the steel structure by calculating the overall finite element corrosion fatigue simulation model of the steel structure.

[0006] Furthermore, the steel structure finite element corrosion simulation unit is a solid unit, the solid unit is endowed with a corrosion damage evolution constitutive model, and the corrosion damage evolution constitutive model is used to calculate the corrosion damage of the solid unit; the steel structure finite element fatigue simulation unit is a cohesion unit, the cohesion unit is endowed with a cyclic cohesion constitutive model, and the cyclic cohesion constitutive model is used to calculate the fatigue damage of the cohesion unit; the solid unit is a polyhedron and each surface corresponds to a cohesion unit with a thickness of zero; each cohesion unit with a thickness of zero shares the vertices of the surface with the surface of the polyhedron where the cohesion unit with a thickness of zero is located. Furthermore, the solid unit is a tetrahedron; the cohesion unit is a triangle.

[0007] Furthermore, the coupling association is achieved through the following strategy adopted in the operation process: identifying the entity unit of the contact corrosion element and calculating the corrosion damage of the entity unit through the corrosion damage evolution constitutive method; then calculating the fatigue damage caused by the cohesive force unit adjacent to the entity unit of the contact corrosion element through the cyclic cohesive force constitutive method, and then taking the maximum value of the fatigue damage of the cohesive force unit and the corrosion damage of the entity unit adjacent to the cohesive force unit as the current damage value of the cohesive force unit; if the current damage value of any cohesive force unit adjacent to a entity unit belongs to corrosion damage, then the entity unit is determined to be in contact with the corrosion element.

[0008] Furthermore, the corrosion damage evolution constitutive model uses the corrosion damage rate of the solid unit to calculate the corrosion damage of the solid unit; wherein the corrosion damage rate of the solid unit is obtained in the following manner:

[0009] Firstly, k pitting initiation position coordinates are randomly generated on the surface of the local finite element corrosion fatigue simulation model of the steel structure through the MATLAB program, and the corrosion rate scaling factor z of each pitting position is calculated according to formula (37): k , these coordinates and the corresponding scaling factor z k Stored in the user-defined subroutine UMAT array; then, the minimum horizontal distance d between the solid unit integration point and each pitting initiation position is obtained k , assign the corresponding scaling factor z k ; According to the adjacent unit nodes and damage information stored in the common variables, determine the solid units that accumulate corrosion damage in the current analysis step and obtain their number Then, equations (39) and (40) are combined to make them equal, and the equivalent corrosion damage height of the current analysis step is obtained: See formula (41); the bottom of the corrosion pit is arc-shaped, with the center of the corrosion pit as the peak value, and based on the minimum horizontal distance dk, it decreases outward according to the cosine function relationship, which will lead to a reduction in the total amount of corrosion damage. Therefore, the shape compensation factor Gs is introduced and calculated by formula (42); considering the stress corrosion effect, the corrosion damage rate of the solid unit is finally obtained by formula (44);

[0010] in:

[0011]

[0012] Where Z is the corrosion rate scaling factor, R is the gas constant, γ is the scale parameter, m is the shape parameter, and u is a random number generated in the uniformly distributed [0,1] interval;

[0013]

[0014] Where: ΔDthe and ΔDfem are the corrosion damage increments of the current analysis step obtained by theoretical and numerical calculations, respectively; hmod is the height of the finite element model consistent with the corrosion depth direction, is the number of entity elements for corrosion damage accumulation in the current analysis step, nent is the number of entity elements in the corrosion sub-model, is the equivalent corrosion damage height of the current analysis step;

[0015]

[0016] Where: dkn is the horizontal distance between entity element n and the initiation position k, is the corrosion pit radius of the current analysis step;

[0017]

[0018] Where: Rmax is the maximum radius of the pit, and variables p and q are used to control the change of pit radius;

[0019]

[0020] Where: Rd is the corrosion damage rate of the solid unit, I is the deformed anode current, and In is the undeformed anode current.

[0021] Furthermore, the corrosion damage evolution constitutive model uses the statistical eigenvalues ​​of the corrosion model to calculate the corrosion damage of the solid unit; wherein the statistical eigenvalues ​​of the corrosion model are obtained in the following manner: the average corrosion depth (d) is obtained by equation (45); the corrosion surface is cut into n×m “pixel points” to simulate the three-dimensional scanning view in the actual measurement process, the corrosion depth in the grid is obtained by the unit geometric topology information, and the arithmetic mean height (S) is calculated by equations (46) and (47) respectively. q) and RMS height (S a );

[0022]

[0023] Where p is the number of solid elements in the corrosion submodel, D q corrsion is the corrosion damage of the solid element

[0024]

[0025] Where i, j are the pixel coordinates, and d(i, j) is the corrosion depth within the grid.

[0026] The simulation and prediction method of the corrosion fatigue evolution process of steel structures of the present invention realizes multi-scale and coupled simulation of the whole process of corrosion pit formation and crack propagation by integrating the overall finite element stress simulation model of the steel structure and the local finite element corrosion fatigue simulation model of the steel structure. This method overcomes the limitations of a single model and provides a comprehensive, flexible and practical analysis tool that can effectively simulate the interaction between electrochemical corrosion and mechanical fatigue. It not only improves the computational efficiency and prediction accuracy, but also provides important support for the safety assessment, life prediction and optimization design of steel structures, and has significant value in improving the long-term performance and reliability of steel structures in corrosive environments.

[0027] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments. Additional aspects and advantages of the present invention will be partially given in the following description, partially become apparent from the following description, or be learned through practice. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] The drawings constituting a part of this specification are used to assist the understanding of the present invention. The contents provided in the drawings and the related descriptions in this specification can be used to explain the present invention, but do not constitute improper limitations on the present invention.

[0029] Figure 1 Schematic diagram of the bilinear cohesive force constitutive model.

[0030] Figure 2 Schematic diagram of 8-node cohesive element and node displacement.

[0031] Figure 3 Schematic diagram of the mixed mode cohesive constitutive model.

[0032] Figure 4 Schematic diagram of adjacent cohesive force units and entity units in an embodiment of the present invention.

[0033] Figure 5 It is a schematic diagram of a local finite element corrosion simulation model of a steel structure and a local finite element fatigue simulation model of a steel structure in an embodiment of the present invention.

[0034] Figure 6 It is a schematic diagram of the overall finite element corrosion fatigue simulation model of the steel structure in an embodiment of the present invention.

[0035] Figure 7 It is a distribution diagram of the corrosion simulation morphology characteristic parameters in an embodiment of the present invention.

[0036] Figure 8 Graph showing the evolution of corrosion pits in an embodiment of the present invention.

[0037] Fig. 9 Graph showing the evolution of corrosion pit damage in an embodiment of the present invention.

[0038] Fig.10 It is a Mises stress variation diagram of the corrosion model in an embodiment of the present invention.

[0039] Fig.11 Graph showing the distribution of corrosion pits and corrosion fatigue cracks in different simulation groups in an embodiment of the present invention. DETAILED DESCRIPTION

[0040] The present invention is described clearly and completely below in conjunction with the accompanying drawings. A person skilled in the art will be able to implement the present invention based on these descriptions. Before describing the present invention in conjunction with the accompanying drawings, it should be particularly noted that:

[0041] The technical solutions and technical features provided in each section, including the following description, can be combined with each other without conflict. In addition, where possible, these technical solutions, technical features and related combinations can be assigned specific technical themes and protected by relevant patents.

[0042] The embodiments of the present invention involved in the following description are generally only a part of the embodiments rather than all the embodiments. Based on these embodiments, all other embodiments obtained by ordinary technicians in this field without making creative work should fall within the scope of patent protection.

[0043] Regarding the terms and units in this specification: The terms "include", "comprises", "have" and any variations thereof in this specification and the corresponding claims and related parts are intended to cover non-exclusive inclusions. In addition, other relevant terms and units can be reasonably interpreted based on the relevant content provided in this specification.

[0044] Theoretical Framework

[0045] 1.1 Cohesive damage constitutive model

[0046] 1.1.1 Traditional cohesive force

[0047] The cohesive force model assumes that there is a small cohesive force region in the plastic region near the crack tip. In this region, microvoids form, develop and combine with the crack tip, thereby pushing the crack forward. The cohesive force model regards the crack tip as a crack surface separated from the upper and lower parts, and defines the functional relationship between the crack surface opening displacement δ and the cohesive force σ as the traction displacement law (TSL for short), as shown in Equation (1). The energy released during the cracking process is defined as the fracture energy G C , expressed by formula (2).

[0048] σ=f(δ) (1)

[0049] G C =∫σdδ=∫f(δ)dδ (2)

[0050] According to different application environments, researchers have developed various types of TSL, among which the most widely used is the bilinear TSL, whose constitutive form is as follows: Figure 2 shown. Figure 2 Mode 1 represents the normal mode, and mode 2 represents the tangential mode. The constitutive model is divided into two stages. In the linear elastic stage, the stress σ on the crack surface increases linearly with the opening displacement δ, and the slope is the initial stiffness k. When the opening displacement δ reaches the damage initiation displacement, the stress σ reaches the critical stress. After exceeding the damage initiation displacement, the opening displacement is negatively correlated with the stress σ, and the damage amount Dt gradually accumulates from 0 to 1, and the stiffness degenerates to 0, as shown in formula (3). At this time, the cohesive force area is completely broken and develops forward. The area contained in the cohesion-opening displacement curve is the fracture energy. In the normal mode, damage will only occur when the opening displacement is positive; while in the tangential mode, the positive and negative opening displacements represent that damage will occur in both directions. Figure 1 The cohesion parameters are shown in Table 1.

[0051] k t =(1-D t )k (3)

[0052] Where: k t is the stiffness at the current moment, D t is the damage amount at the current moment, and k is the initial stiffness.

[0053] Table 1: Basic parameters of the bilinear cohesion model

[0054]

[0055]

[0056] The cohesive region is equivalent to the cohesive unit (i.e., cohesive unit, the same below) in the finite element model. The nodes of the cohesive unit usually have displacements in only three directions, such as Figure 2 As shown, there is no coupling relationship between the displacements in each direction, and the corresponding constitutive equation is shown in equation (4).

[0057]

[0058] Where: k s , k t , k n They are Figure 3 The tangential stiffness in the x, y, and z directions is calculated according to formula (5); σ s , σ t , σ n are the tangential traction forces in the x, y, and z directions respectively; δ s , δ t , δ n are the tangential opening displacements in the x, y, and z directions respectively.

[0059]

[0060] Where, T 0 It is the calculated thickness of the cohesive element, which has nothing to do with the geometric thickness of the element, so the geometric thickness can be set to 0mm during modeling. E is the elastic modulus, and v is the Poisson's ratio.

[0061] The traction displacement law in mixed mode can be used to describe the fracture under complex stress conditions, such as Figure 3 The figure shows the cohesion parameters in the mixed mode, where δ m is the displacement change in mixed mode, is the critical stress, is the initial stiffness, is the critical displacement, is the failure displacement. There is a transformation relationship between the traction displacement laws of the tangential, normal and mixed modes. The displacement change in the mixed mode is calculated by formula (6), and the initial critical displacement and initial failure displacement in the mixed mode are calculated by formulas (7) and (8), respectively.

[0062]

[0063]

[0064] Where: β is the mixed loading ratio, η is the BK criterion coefficient.

[0065] 1.1.2 Cyclic cohesive force constitutive model

[0066] Turo and Costa derived the quantitative relationship equation between the number of fatigue loading and the damage of the cohesive unit. This model couples the basic theory of fracture mechanics and the damage theory of the cohesive unit. Combining the cohesive parameters and crack propagation parameters of the material, it can predict the fatigue life and crack propagation path of the structure. The Turo-Costa damage evolution equation is as follows:

[0067]

[0068] Where: is the unit cumulative damage rate, A CZ is the area of ​​the cohesive region, calculated by formula (10), D t is the unit damage at the current moment, is the damage area growth rate of the Cohesive unit at the crack tip, which is calculated by formula (13):

[0069]

[0070] Where: T b is the crack front thickness, E is the elastic modulus of the adjacent solid element, G C is the fracture toughness of the material, calculated by formula (11), is the critical strength in the mixed mode, calculated by formula (12).

[0071]

[0072] In the formula, G IIC , G I-IIC are the fracture energies of the tangential modes in two directions, respectively.

[0073]

[0074] Where: C 1 , m 1 is the fatigue crack growth parameter in the form of energy release rate, G th is the threshold of energy release rate, ΔG is the range of energy release rate under cyclic loading, which is calculated by formula (14).

[0075]

[0076] Where: max is the maximum opening displacement in a single loading, and R is the stress ratio. The relationship between the strain energy release rate variation range ΔG and the stress intensity factor amplitude ΔK is shown in formula (15).

[0077]

[0078] According to the above formula and Paris formula (16), the fatigue crack growth parameter C in the form of energy release rate can be deduced: 1 and m 1 The corresponding relationship with C and m is shown in Eq.

[0079]

[0080] Corrosive environment can accelerate fatigue crack growth, thus shortening the service life of materials. The literature points out that the corrosive environment accelerates crack growth by dissolving the anodic tip at the crack tip and reducing the free energy of the metal at the crack tip. Based on the basic principles of thermodynamics and from the perspective of energy conservation, a formula for the growth rate of anodic dissolution corrosion fatigue cracks is proposed, see formula (18).

[0081]

[0082] Where E is the elastic modulus, v is the Poisson's ratio, σ a is the stress amplitude, σ s is the yield strength, N 0 is the average number of dislocation sources per unit volume, L is the average length of the slip plane, a is the crack length, n is the atomic valence, F is the Faraday constant, ρ is the material density, and M is the molar mass. 0 is the cyclic strength coefficient, β is the cyclic strain hardening exponent, and the above two values ​​are the parameters of the Ramberg–Osgood equation, which can be converted from the basic parameters in the Manson–Coffin equation. The conversion relationship is shown in equations (19) and (20). c is the electrochemical energy released by the anode dissolution at the crack tip during the cycle, calculated by formula (21).

[0083] β=b / c (19)

[0084]

[0085] In the formula, σ' f is the fatigue strength coefficient in the Manson–Coffin equation, ε' f is the fatigue plasticity coefficient, b is the fatigue strength index, and c is the fatigue plasticity index.

[0086]

[0087] Where ΔQ is the amount of electricity carried by the dissolved metal in one cycle, E + is the standard electrode potential, R is the gas constant, T is the absolute temperature, T Z is the fatigue load cycle, a M n+ Metal ion activity, i 0 is the anodic dissolution current density, S 0is the newly exposed metal area at the crack tip during a cyclic loading process, calculated by formula (22), T Z0 Calculated by formula (23).

[0088]

[0089] Ignoring the electrochemical energy u released by the crack tip anode dissolution during the cycle in equation (18), c As well as the decrease in surface free energy of microcracks under corrosive conditions, the crack growth rate formula based on the basic principles of thermodynamics is obtained:

[0090]

[0091] The rate amplification factor A caused by the anodic dissolution at the crack tip is cor , which can be calculated by formula (25).

[0092] The Turo-Costa damage evolution equation after considering the corrosion factor is shown in equation (26).

[0093]

[0094] 1.2 Statistical model of corrosion damage

[0095] Corrosion damage is manifested in the form of the damage evolution of corrosion pits. In actual measurements, the corrosion damage process is usually characterized by characteristic values ​​such as average corrosion depth, corrosion pit depth distribution, and surface roughness, and statistical analysis is performed. Measured statistics can provide a basis for parameter selection in the process of characteristic numerical reconstruction of corrosion damage evolution, and can also provide a reference for numerical simulation analysis results.

[0096] Statistical data show that the average corrosion depth of different metal materials in an atmospheric corrosion environment follows basically the same law. The average corrosion depth evolution data conforms to the kinetic relationship shown in formula (27), while the change law of corrosion rate with respect to exposure time conforms to formula (29).

[0097] d=βt n (27)

[0098] Where: d is the average corrosion depth, calculated by formula (28); β is the corrosion depth in the first year; t is the corrosion time exposed to the atmosphere; n is the corrosion index, which reflects the atmospheric corrosion characteristics.

[0099]

[0100] Where: m 1 is the initial mass of the sample, m 2 is the mass after corrosion and rust removal, ρ is the material density, and A is the area of ​​the corrosion region.

[0101]

[0102] Where: R c is the corrosion rate, is the change in the average corrosion depth per unit time step; A 1 is a constant that characterizes the initial corrosion rate; b is a constant that characterizes how fast the corrosion rate decreases; r 0 is a constant that characterizes the stable corrosion state.

[0103] The change in the average corrosion depth reflects the overall corrosion degree, while the corrosion surface morphology is related to the specific characteristics of the corrosion pit, such as depth distribution, shape, aspect ratio, and distribution density. It is generally believed that the depth of the corrosion pit usually conforms to the normal distribution, extreme value distribution, and Weibull distribution. In this paper, the Weibull distribution is used as the depth distribution function of the corrosion pit, and its cumulative distribution function is shown in formula (30).

[0104]

[0105] Where: x is the depth of the etch pit; σ u is the location parameter; γ is the scale parameter; m is the shape parameter. In practical applications, σ u Usually regarded as 0, the above formula can be simplified to a two-parameter Weibull cumulative distribution function, and its probability density function is as follows:

[0106]

[0107] In order to reflect the difference in corrosion rate at different locations on the metal surface, the corrosion rate scaling factor z is introduced. The probability density distribution of z can be inferred from the probability density distribution of the pit depth and the time-varying relationship of the corrosion rate. The scaled corrosion rate function G(t,z) is constructed, as shown in formula (32), and integrated with respect to time t to obtain t 1 The average corrosion depth after time is shown in formula (33).

[0108] G(z)=Rc×z=(A 1 e (-t / b) +r 0 )×z (32)

[0109]

[0110] Substituting equation (33) into equation (31) yields the probability density distribution function of the scaling factor z, as shown in equation (34). Integrating the probability density distribution function yields the probability distribution function, as shown in equation (35), where z is greater than 0.

[0111]

[0112] Transform equation (35) to obtain the inverse function of F(z), see equation (36). Generate a random number u in the uniformly distributed [0,1] interval, substitute u into the inverse function, and you can get a scaling factor z that conforms to the probability distribution.

[0113]

[0114] The shape of the corrosion pit is usually assumed to be a cylinder, cone, semi-ellipsoid, etc. Similar to the above shape characteristics, this paper will use the cosine function and the coordinate axis rotation to form a geometric body to simulate the corrosion pit for easy calculation, and take the extreme point of the cosine function as the deepest point of the corrosion pit. As the horizontal distance from this point increases, the corrosion rate gradually decreases.

[0115] Stress level affects the growth rate of corrosion pits. Since the deformation caused by stress can increase the anodic activity of metals, Gutman established a model to describe the mechanical electrochemical effect of metals, which is expressed by equation (38). According to the Faraday electrolysis principle, the corrosion rate is proportional to the current density. Therefore, the higher the stress level, the faster the corrosion pits develop.

[0116]

[0117] Where I is the deformed anode current, I n is the anode current without deformation, ΔP is the hydrostatic pressure, V m is the molar volume, Δε is the plastic strain, and ε 0 is the onset of strain hardening, σ m is the spherical part of the macroscopic stress tensor depending on the applied load, R is the gas constant, and T is the temperature.

[0118] Corrosion-Fatigue Coupling Simulation Strategy

[0119] In order to simulate the evolution of corrosion pits, the transformation of corrosion pits into cracks, and the propagation of cracks in the process of coupled corrosion-fatigue damage, this section will couple the corrosion damage evolution constitutive model and the cyclic cohesive force constitutive model. In the numerical simulation, the corrosion damage is reflected by the stiffness degradation of the solid unit, and the fatigue damage is reflected by the stiffness degradation of the cohesive unit. Through the information transmission of the two damage constitutive models, the coupled correlation of corrosion-fatigue damage is realized. This subroutine follows the basic physical laws of corrosion damage evolution, including the corrosion evolution sequence and pit development characteristics. The specific implementation strategy is as follows.

[0120] 2.1 Extracting unit geometry information

[0121] In the finite element software ABAQUS, a corrosion simulation sub-model of the global interpolation 0 thickness cohesive unit is established and coupled with the overall model. After completing the pre-processing, the "inp" file is exported. The unit and node number information is extracted from the "inp" file using the MATLAB program and saved as an array in UMAT. According to the characteristics that the adjacent cohesive units and the solid units share three nodes, the adjacent two solid units and four cohesive units (such as Figure 4 ). These unit information are stored separately in public arrays for global use.

[0122] 2.2 Damage sequence and coupling criteria

[0123] Based on the geometric topology information, the surface solid elements contacting the corroded elements are identified, and these elements are first damaged by corrosion. The cohesive elements adjacent to the solid elements produce fatigue damage (D cohesive ), and receives the corrosion damage information of two adjacent entity units through common variables (D corrosion ), since the adjacent cohesive unit should fail at the same time after the failure of the solid unit, the maximum value of the adjacent solid unit and fatigue damage is taken as the current damage value of the cohesive unit (D t ). The solid unit inside the corrosion sub-model obtains the corrosion damage information of the four adjacent cohesive units through the common variables, thereby determining whether the solid unit contacts the corrosion element. In addition, the pit merging criterion is introduced in the pit evolution process. When the average value of the radius of adjacent pits is greater than twice the distance between the pit centers, the two pits will be merged, and the midpoint of the line connecting the coordinates of the two pit centers will be used as the center of the merged pit.

[0124] 2.3 Corrosion and fatigue damage rates

[0125] Obtain the state variables related to the corrosion damage rate of the solid unit. First, k pitting initiation position coordinates are randomly generated on the surface of the corrosion model through the MATLAB program, and the corrosion rate scaling factor z of each pitting position is calculated according to formula (37): k , these coordinates and the corresponding scaling factor z k Stored in the user-defined subroutine UMAT array. Next, obtain the minimum horizontal distance d between the solid unit integration point and each pitting initiation position k , assign the corresponding scaling factor z k According to the adjacent unit nodes and damage information stored in the common variables, determine the entity units that accumulate corrosion damage in the current analysis step and obtain their number Then, equations (39) and (40) are combined to make them equal, and the equivalent corrosion damage height of the current analysis step is obtained: See formula (41). The bottom of the corrosion pit is arc-shaped, with the center of the corrosion pit as the peak and the minimum horizontal distance d k Based on the cosine function, it decreases outward, which will lead to a reduction in the total amount of corrosion damage. Therefore, the shape compensation factor G is introduced. s , calculated by formula (42). In summary, considering the stress corrosion effect, the corrosion damage rate of the solid unit is finally obtained by formula (44). According to the Turon-Costa cyclic cohesive damage criterion, the acceleration effect of corrosion on the crack growth rate is considered, see formula (9), and the fatigue damage accumulation rate of the cohesive unit adjacent to the corrosion damage unit is accelerated. At the same time, considering the influence of the corrosion effect on the fatigue crack threshold of the material, the cohesive unit threshold value of the contact corrosion unit is reduced to 1 / 3 of the original value.

[0126]

[0127] Where: ΔD the and ΔD fem The corrosion damage increment of the current analysis step is obtained by theoretical and numerical calculations, h mod is the height of the finite element model consistent with the corrosion depth direction, The number of solid elements for corrosion damage accumulation in the current analysis step, n ent is the number of solid elements in the corrosion sub-model, is the equivalent corrosion damage height of the current analysis step.

[0128]

[0129] Where: d kn is the horizontal distance of entity element n corresponding to the initiation position of k, Is the radius of the corrosion pit in the current analysis step.

[0130]

[0131] Where: R max is the maximum radius of the pit, and the variables p and q are used to control the change of the pit radius.

[0132]

[0133] Where: R d is the corrosion damage rate of the solid unit, I is the deformed anode current, and I n is the anode current without deformation.

[0134] 2.4 Obtaining statistical eigenvalues ​​of the corrosion model

[0135] The average corrosion depth (d) is obtained by equation (45). The corrosion surface is cut into n×m “pixel points” to simulate the three-dimensional scanning view in the actual measurement process. The corrosion depth in the grid is obtained through the unit geometric topology information. The arithmetic mean height (S) is calculated by equations (46) and (47) respectively. q ) and RMS height (S a ).

[0136]

[0137] Where p is the number of solid elements in the corrosion submodel, D q corrsion is the corrosion damage of the solid element

[0138]

[0139] Where i, j are the pixel coordinates, and d(i, j) is the corrosion depth within the grid.

[0140] Numerical simulation and experimental verification

[0141] 3.1 Simulation of corrosion pit evolution

[0142] The electrochemical corrosion test obtained the average corrosion depth and surface roughness characteristics when the corrosion time was 1h, 3h, and 5h, respectively. In the finite element pre-processing, the test time of 5h was equivalent to 45 analysis steps, and the maximum analysis step was set to 0.1. According to the time-varying data of the average corrosion depth, the time-varying relationship curve of the average corrosion depth was obtained by fitting equation (27) through the MATLAB program, and the parameter A in equation (27) was obtained. h , n, are 0.0077 and 0.94 respectively. Integrate equation (29) and fit the time-varying relationship curve of the average corrosion depth to obtain the parameters b and A in equation (29): 1 、r 0 , 24.79, 0.013, and 0.0056, respectively, to obtain the time-varying relationship curve of the corrosion rate. The coordinates of the pitting initiation position are randomly obtained on the metal surface in contact with the corrosive element, and the corrosion rate at each coordinate point is scaled by taking the value from the probability density distribution of the corrosion rate scaling factor derived in Section 2 (see formula (35)). According to the three-dimensional scanning view of the corrosion morphology provided by the literature experiment, the number of pitting initiation is set to 100. The scale parameter γ of the probability density distribution of the corrosion rate scaling factor is 0.276 mm, and the shape parameter m is set to 2.

[0143] Establish as Figure 5The local finite element corrosion fatigue simulation model of the steel structure shown in the figure is set to 0.2mm in the finite element model to take into account both computational efficiency and simulation effect. The length, width and height of the model are set to 6.5mm, 6.5mm and 2mm respectively. By identifying the node numbers of adjacent units in the "inp" file, a Python script is used to insert a 0mm thick Cohesive. Although the Cohesive unit does not produce fatigue damage in the simulation of this section, the node information of the Cohesive unit is used to judge the adjacent solid unit in the programming logic of the subroutine. The unit type of the solid unit is set to C3D4, and the unit type of the Cohesive unit is set to COH3D6. The user-defined UMAT constitutive is assigned to the solid unit and the Cohesive unit in the model, and the Turo-Costa damage evolution constitutive is assigned to the Cohesive unit by judging the material name in UMAT, and the corrosion damage evolution constitutive is assigned to the solid unit. The material parameters of the corrosion damage constitutive are shown in Table 2. The pit radius parameter in the table is fitted by the trial and error method to control the roughness of the corrosion surface morphology.

[0144] Table 2: Constitutive materials for corrosion damage of solid elements

[0145]

[0146] The random pitting initiation position is changed and the value is updated from the probability density distribution of the corrosion rate amplification factor. 100 sets of simulation operations are performed to obtain the distribution value of the corrosion simulation results, such as Figure 7 As shown in the figure, the corrosion characteristic test results at the corresponding time are marked in the figure. Figure 7 It can be seen that due to the differences in the initial positions of the corrosion pits and the corrosion rates, the corrosion morphology characteristic values ​​obtained by different simulation groups have a certain degree of discreteness, and are generally in line with the normal distribution, which is in line with the basic law of corrosion damage evolution. The test results of the surface morphology roughness characterization values ​​of corrosion of different durations obtained from the experiment are located close to the average value in the distribution, and the simulation method is basically reliable in quantitative analysis.

[0147] The corrosion morphology evolution process is obtained through simulation calculation. Figure 8 As shown in the figure, the subroutine state variable "SDV36" is the accumulated amount of corrosion damage of the entity unit; "SDV61" is the depth of the entity unit relative to the surface of the corrosion simulation model. Figure 8It can be seen that the corrosion simulation results have the following characteristics: pitting originates from the surface of the corrosion model in contact with the corrosive elements. In the initial development stage, the pits appear circular on the model surface, and as the corrosion time increases, the adjacent pits gradually merge into one; the corrosion damage in the model presents a typical diffusion form. After contacting the fully corroded entity unit, the adjacent entity units begin to accumulate corrosion damage, and finally the corrosion pits gradually expand in depth and width; the morphology and development rate of the corrosion pits are different, the surface morphology is uneven, and a uniform corrosion thinning layer and hemispherical corrosion pits are formed. In summary, the basic laws of corrosion simulation in the evolution of pit damage and morphological changes are similar to the experimental results, and the numerical reconstruction method of corrosion morphology has been further verified.

[0148] 3.2 Corrosion-fatigue damage evolution simulation

[0149] 3.2.1 Selection of cohesion parameters

[0150] The traditional cohesive force constitutive model mainly includes basic parameters such as critical strength, initial stiffness and fracture energy. In the embodiment of the present invention, the fracture stress is 914 MPa as the critical stress value. For the value of fracture energy, the fracture energy G in the cohesive force model is C Compared with the fracture toughness in traditional fracture mechanics IC The concepts are the same, both are the energy required for material fracture, and the fracture toughness value can be obtained by formula (48):

[0151]

[0152] In the formula, λ is the constraint factor, which is 1.2, σ y is the yield strength, σ u is the ultimate strength, δ is the opening displacement, and the references take the values ​​of 690MPa, 880MPa, and 0.311mm respectively. The fracture toughness calculated by the formula is 292.962N / mm. The initial stiffness of the cohesive unit can be obtained by formula (5). The thickness of the cohesive unit is 0.001mm, and the elastic modulus is 218913MPa. Therefore, the corresponding normal initial stiffness is 2.19×10 8 MPa / mm, the initial tangential stiffness is calculated by the formula, which is 8.4×10 7 MPa / mm.

[0153] 3.2.2 Corrosion-fatigue simulation model

[0154] Establish as Figure 6The overall finite element stress simulation model of the steel structure shown in the figure adopts the same mesh density setting as in Section 3.1, and the boundary conditions are set according to the experimental loading in the literature. According to the test case, the amplitude is set to 35MPa, the stress ratio is R=-1, and the sinusoidal load is used. A rectangular notch is cut in the middle of the simulation model and the corrosion simulation sub-model is inserted, and the two are connected by binding. The simulation sub-model consists of solid units and cohesive units globally inserted through Python scripts. The unit type used by the solid unit is C3D4, and the unit type of the cohesive unit is COH3D6. The solid unit in the corrosion simulation sub-model is given the corrosion damage evolution constitutive model, and the material parameter values ​​are the same as in Section 3.1. The cohesive unit in the corrosion sub-model is given the cyclic cohesive damage constitutive model. At the same time, in order to improve the convergence of the damage constitutive model, the viscosity coefficient is introduced. According to the Q690D fatigue crack growth rate parameter values ​​given in the literature, that is, m=2.95 and lgC=-10.802, the corresponding C can be obtained according to formula (23): 1 and m 1 All material parameters used in the Turon-Costa model are shown in Table 2. Linear elastic constitutive model is used outside the corrosion sub-model, elastic modulus E = 218913MPa, Poisson's ratio v = 0.3. Amplification effect factor A of anodic dissolution corrosion on fatigue crack growth rate cor , calculated by the formula, the material parameters used are shown in Table 3, and the calculated A cor It is 5.414, that is, the anodic dissolution fatigue crack growth rate is 5.414 times the non-corrosion fatigue crack growth rate.

[0155] Table 2: Turon-Costa model parameters

[0156]

[0157] Table 3: Material parameters for calculating the amplification effect factor Acor

[0158]

[0159]

[0160] 3.2.3 Corrosion-fatigue simulation results

[0161] The established corrosion fatigue simulation finite element model is operated and the following results are obtained: Fig. 9 The evolution of the corrosion pits shown in Fig.10 The stress distribution changes of the sub-model shown in the figure and Fig.11 The schematic diagram of the evolution of corrosion pits and cracks is shown in Figure 1. Fig. 9It can be seen that the damage evolution process of the corrosion pit is exactly the same as that in Section 3.2.2. In the early stage of the evolution of corrosion fatigue damage, corrosion pits gradually form on the model surface. The changes and development of pit corrosion change the original surface morphology of the specimen. In this process, the stress distribution of the model gradually changes with the development of the corrosion pit. The stiffness of the entity unit with complete corrosion damage is reduced to a minimum value close to 0, and the stress response generated under the load is very small, which causes the stress concentration effect at the bottom of the corrosion pit. As the fatigue loading proceeds, the corrosion rate at the bottom of the corrosion pit is lower than the crack growth rate, which leads to the transformation of the corrosion pit into a crack. As the crack develops, there is a more obvious stress concentration effect in a small range at the front, which causes the crack growth rate to gradually accelerate and eventually form a fracture. Fig.11 The red solid element is a fully corroded damaged element, while the blue element is a fully fatigue damaged cohesive element. Fig.11 It can be seen that in the process of corrosion fatigue damage, the evolution of corrosion pits dominates in the early stage. With the evolution of corrosion pits and the progress of fatigue loading, fatigue cracks initiate in multiple locations and develop downward perpendicular to the specimen surface. Multiple cracks gradually merge into a single crack, and then form a crack surface that runs through the entire cross-section.

[0162] Another 9 groups of corrosion fatigue simulation models were established and calculated respectively to obtain the distribution of corrosion pits and corrosion fatigue cracks. The fatigue cracks maintained basically the same characteristics, that is, multiple cracks perpendicular to the surface of the specimen developed at the bottom of different corrosion pits, and there were cases where multiple cracks merged into a single crack. The life during fatigue loading was taken as the fatigue life when the high-frequency fatigue machine frequency reduction reached the critical value. By comparing the fatigue life values ​​of the two samples in the experiment, namely 1333700 and 1329400, it can be seen that it is similar to the secondary fatigue loading required when the crack expands to 1 / 6 of the thickness in this article, which basically verifies the reliability of the corrosion fatigue life prediction method.

[0163] Conclusion

[0164] The present invention proposes a corrosion-fatigue coupled damage evolution simulation analysis method for analyzing the fatigue damage fracture process of metal components in a corrosive environment. In this method, a cyclic cohesive force model and a corrosion damage statistical model are used, and based on the stress-electrochemical model and the anodic dissolution crack growth model, the mutual coupling relationship between corrosion and fatigue is considered. The test results of corrosion depth change, roughness change, fatigue life, crack development characteristics in the electrochemical corrosion test and the corrosion-fatigue coupling test are respectively compared with the simulation results. The main conclusions are as follows:

[0165] (1) By using the corrosion damage evolution simulation model with interpolated Cohesive units and considering the mutual coupling relationship between corrosion and fatigue, the entire process of corrosion fatigue damage evolution, including the evolution of corrosion pits, the transformation of corrosion pits to cracks, and the development of cracks to fracture, can be realized, and the fatigue life under the coupling of corrosion and fatigue can be predicted. In the simulation, the corrosion damage statistical constitutive model is assigned to the solid unit in the corrosion simulation model to realize the damage evolution of corrosion pits, and the Turon-Costa cyclic cohesion zone model is assigned to the Cohesive unit to simulate the formation of crack surfaces.

[0166] (2) The established corrosion damage evolution method is also applicable to the pitting evolution process in a single corrosion environment without fatigue loading. The corrosion pit damage evolution process in the simulation is consistent with the observed experimental phenomenon. The 100 groups of corrosion damage evolution simulation results obtained the average corrosion depth and roughness time-varying values ​​that conform to the normal distribution and are close to the measured results.

[0167] (3) The results obtained by different corrosion-fatigue damage evolution simulation groups have common characteristics. After the corrosion pits are transformed into cracks, multiple parallel cracks will be formed in the corrosion sub-model, all of which are perpendicular to the specimen surface. Multiple cracks will gradually merge into a single crack during the development process, and eventually penetrate the entire cross section. The fusion and development of multiple cracks in corrosion fatigue will also accelerate the fatigue fracture process and reduce the fatigue life of the specimen.

[0168] (4) Under the test conditions and physical material parameters, the anodic dissolution corrosion fatigue crack growth model based on thermodynamic principles was used, and the calculated crack growth rate was 5.414 times that in the absence of corrosion. Therefore, in the corrosion fatigue calculation, if the acceleration effect of electrochemical corrosion crack growth is ignored, and only the stress concentration effect caused by the change of pits is considered to accelerate the crack tip growth rate, the fatigue life obtained is often unsafe.

[0169] The above is a description of the relevant contents of the present invention. A person skilled in the art will be able to implement the present invention based on these descriptions. Based on the above contents of this specification, all other embodiments obtained by a person skilled in the art without making any creative work shall fall within the scope of patent protection.

Claims

1. A simulation and prediction method for the corrosion fatigue evolution process of steel structures, characterized by: include: Establishing an overall finite element stress simulation model of the steel structure, wherein a notch for inserting a local finite element corrosion fatigue simulation model of the steel structure is reserved on the overall finite element stress simulation model of the steel structure; Establishing a local finite element corrosion fatigue simulation model of a steel structure, wherein the local finite element corrosion fatigue simulation model of a steel structure comprises a coupled and associated steel structure finite element corrosion simulation unit and a steel structure finite element fatigue simulation unit; Inserting the local finite element corrosion fatigue simulation model of the steel structure into the insertion gap bound to the local finite element corrosion fatigue simulation model of the steel structure to form an overall finite element corrosion fatigue simulation model of the steel structure; The simulation and prediction results of the corrosion fatigue evolution process of the steel structure are obtained by calculating the overall finite element corrosion fatigue simulation model of the steel structure.

2. The method for simulating and predicting the corrosion fatigue evolution process of a steel structure according to claim 1, characterized in that: The steel structure finite element corrosion simulation unit is a solid unit, and the solid unit is endowed with a corrosion damage evolution constitutive model, and the corrosion damage evolution constitutive model is used to calculate the corrosion damage of the solid unit; The steel structure finite element fatigue simulation unit is a cohesive force unit, and the cohesive force unit is endowed with a cyclic cohesive force constitutive model, and the cyclic cohesive force constitutive model is used to calculate the fatigue damage of the cohesive force unit; The solid unit is a polyhedron and each surface corresponds to a cohesion unit with a thickness of zero; each cohesion unit with a thickness of zero shares each vertex of the surface with the surface of the polyhedron where the cohesion unit with a thickness of zero is located.

3. The method for simulating and predicting the corrosion fatigue evolution process of a steel structure according to claim 2, characterized in that: The solid unit is a tetrahedron; the cohesive force unit is a triangle.

4. The method for simulating and predicting the corrosion fatigue evolution process of a steel structure according to claim 2, characterized in that: The coupling association is achieved through the following strategy adopted in the operation process: identifying the entity unit of the contact corrosion element and calculating the corrosion damage of the entity unit through the corrosion damage evolution constitutive method; then calculating the fatigue damage caused by the cohesive force unit adjacent to the entity unit of the contact corrosion element through the cyclic cohesive force constitutive method, and then taking the maximum value of the fatigue damage of the cohesive force unit and the corrosion damage of the entity unit adjacent to the cohesive force unit as the current damage value of the cohesive force unit; if the current damage value of any cohesive force unit adjacent to a entity unit belongs to corrosion damage, then the entity unit is determined to be in contact with the corrosion element.

5. The method for simulating and predicting the corrosion fatigue evolution process of a steel structure according to claim 2, 3 or 4, characterized in that: The corrosion damage evolution constitutive model uses the solid unit corrosion damage rate to calculate the corrosion damage of the solid unit; wherein the solid unit corrosion damage rate is obtained in the following manner: Firstly, k pitting initiation position coordinates are randomly generated on the surface of the local finite element corrosion fatigue simulation model of the steel structure through the MATLAB program, and the corrosion rate scaling factor z of each pitting position is calculated according to formula (37): k , these coordinates and the corresponding scaling factor z k Stored in the user-defined subroutine UMAT array; then, the minimum horizontal distance d between the solid unit integration point and each pitting initiation position is obtained k , assign the corresponding scaling factor z k ; According to the adjacent unit nodes and damage information stored in the common variables, determine the solid units that accumulate corrosion damage in the current analysis step and obtain their number Then, equations (39) and (40) are combined to make them equal, and the equivalent corrosion damage height of the current analysis step is obtained: See formula (41); the bottom of the corrosion pit is arc-shaped, with the center of the corrosion pit as the peak and the minimum horizontal distance d k Based on the cosine function, it decreases outward, which will lead to a reduction in the total amount of corrosion damage. Therefore, the shape compensation factor G is introduced. s , calculated by formula (42); considering the stress corrosion effect, the corrosion damage rate of the solid unit is finally obtained by formula (44); in: Where Z is the corrosion rate scaling factor, R is the gas constant, γ is the scale parameter, m is the shape parameter, and u is a random number generated in the uniformly distributed [0,1] interval; Where: ΔD the and ΔD fem The corrosion damage increment of the current analysis step is obtained by theoretical and numerical calculations, h mod is the height of the finite element model consistent with the corrosion depth direction, t n d The number of solid elements for corrosion damage accumulation in the current analysis step, n ent is the number of solid elements in the corrosion submodel, h t e is the equivalent corrosion damage height of the current analysis step; Where: d kn is the horizontal distance of entity element n corresponding to the initiation position of k, r t k is the corrosion pit radius of the current analysis step; Where: R max is the maximum radius of the pit, and the variables p and q are used to control the change of the pit radius; Where: R d is the corrosion damage rate of the solid unit, I is the deformed anode current, and I n is the anode current without deformation.

6. The method for simulating and predicting the corrosion fatigue evolution process of a steel structure according to claim 2, 3 or 4, characterized in that: The corrosion damage evolution constitutive method uses the statistical eigenvalues ​​of the corrosion model to calculate the corrosion damage of the solid unit; wherein the statistical eigenvalues ​​of the corrosion model are obtained in the following manner: The average corrosion depth (d) is obtained by formula (45); The corrosion surface is cut into n×m “pixel points” to simulate the three-dimensional scanning view in the actual measurement process. The corrosion depth in the grid is obtained through the unit geometric topology information. The arithmetic mean height (S) is calculated by equations (46) and (47) respectively. q ) and RMS height (S a ); Where p is the number of solid elements in the corrosion submodel, D q corrsion is the corrosion damage of the solid element Where i, j are the pixel coordinates, and d(i, j) is the corrosion depth within the grid.

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