Simulation and prediction method for corrosion fatigue evolution process of steel structure

Abstract

The application discloses a simulation and prediction method for corrosion fatigue evolution process of a steel structure, and comprises the following steps: establishing a whole finite element stress simulation model of the steel structure, wherein a local finite element corrosion fatigue simulation model insertion gap of the steel structure is reserved on the whole finite element stress simulation model; establishing a local finite element corrosion fatigue simulation model of the steel structure, wherein a coupling-related steel structure finite element corrosion simulation unit and a steel structure finite element fatigue simulation unit are contained in the local finite element corrosion fatigue simulation model of the steel structure; inserting and binding the local finite element corrosion fatigue simulation model of the steel structure in the local finite element corrosion fatigue simulation model insertion gap of the steel structure to form a whole 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 through operation of the whole finite element corrosion fatigue simulation model of the steel structure. 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 method for simulating and predicting 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 predicting the fatigue life of materials and structures. The evolutionary damage process of corrosion fatigue of steel structures includes three stages: pitting, crack initiation, and propagation. In this process, electrochemical reactions at inclusions, pores, and holes become the source of corrosion pit nucleation. Electrochemical corrosion dominates the formation of corrosion pits in the early stages of damage evolution. With the increase in pit size and the continuous action of fatigue load, the pits gradually transform 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, which then transitions to crack development. That is, the early stage is volume corrosion damage, and the later stage is crack surface propagation.

[0003] The cohesive element method enables continuous three-dimensional fatigue crack initiation and propagation simulation (i.e., crack surface initiation and propagation). However, the initial evolution of corrosion fatigue damage in steel structures is primarily manifested by changes in the volume 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 of corrosion fatigue damage in steel structures. Most methods for analyzing the evolution of corrosion fatigue damage during pit formation are based on complex electrochemical and stress coupling theories, and there is no authoritative and universally accepted 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] Provided is a method for simulating and predicting the corrosion fatigue evolution process of a steel structure, comprising: establishing an overall finite element stress simulation model of the steel structure, wherein a notch is reserved on the overall finite element stress simulation model for inserting a local finite element corrosion fatigue 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 operating 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, which 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, which 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 zero thickness; each cohesion unit with zero thickness shares the vertices of the surface with the surface of the polyhedron where the cohesion unit with zero thickness 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 calculation 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 is 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 solid element corrosion damage rate to calculate the corrosion damage of the solid element; wherein the solid element corrosion damage rate is obtained as follows:

[0009] First, k pitting initiation position coordinates are randomly generated on the surface of the local finite element corrosion fatigue simulation model of the steel structure using the MATLAB program, and the corrosion rate scaling factor z of each pitting position is calculated according to Equation (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, combine equations (39) and (40) to make them equal, and obtain the equivalent corrosion damage height of the current analysis step: See formula (41); the bottom of the corrosion pit is arc-shaped, with the center of the corrosion pit as the peak, 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 of entity element n corresponding to the initiation position of k, is the radius of the corrosion pit in 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 the pit radius;

[0019]

[0020] Where: Rd is the corrosion damage rate of the solid unit, I is the anode current with deformation, and In is the anode current without deformation.

[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 way: 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 by the unit geometric topology information, and the arithmetic mean height (S) is calculated by formula (46) and formula (47) respectively. q) and RMS height (S a );

[0022]

[0023] Where p is the number of solid elements in the corrosion sub-model, 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 present method for simulating and predicting the corrosion fatigue evolution of steel structures integrates a finite element stress simulation model for the entire steel structure with a local finite element corrosion fatigue simulation model, enabling multi-scale, coupled simulation of the entire process of corrosion pit formation and crack propagation. This method overcomes the limitations of a single model and provides a comprehensive, flexible, and practical analytical tool that can effectively simulate the interaction between electrochemical corrosion and mechanical fatigue. It not only improves computational efficiency and prediction accuracy but also provides important support for the safety assessment, life prediction, and optimized design of steel structures, significantly contributing to the long-term performance and reliability of steel structures in corrosive environments.

[0027] The present invention will be further described below with reference to 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 that constitute a part of this specification are used to assist in understanding 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 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 units and entity units in an embodiment of the present invention.

[0033] Figure 5 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 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 3 is a distribution diagram of characteristic parameters of corrosion simulation morphology 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] Figure 9 Graph showing the evolution of corrosion pit damage in an embodiment of the present invention.

[0038] Figure 10 This is a Mises stress change diagram of the corrosion model in an embodiment of the present invention.

[0039] Figure 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 with reference to 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 with reference to the accompanying drawings, it should be noted that:

[0041] The technical solutions and technical features provided in each section, including the following description, may be combined with each other unless they conflict. In addition, where possible, these technical solutions, technical features, and related combinations may 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 any creative work should fall within the scope of patent protection.

[0043] Regarding terms and units in this specification: The terms "include," "comprising," "having," and any variations thereof in this specification, the corresponding claims, and related sections are intended to cover non-exclusive inclusions. Other relevant terms and units are to 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 constitutive model

[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. This 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, with the slope being 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, the damage amount Dt gradually accumulates from 0 to 1, and the stiffness degenerates to 0, as shown in Equation (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; in the tangential mode, the positive or negative opening displacement means 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 T0 is the calculated thickness of the cohesive element and is independent of the geometric thickness of the element. Therefore, the geometric thickness can be set to 0 mm 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 situation under complex stress conditions, such as Figure 3 As shown. The figure marks 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 tangential, normal and mixed mode traction displacement laws. 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 constitutive force

[0066] Turo and Costa derived a quantitative relationship between the number of fatigue loadings and cohesive element damage. This model couples the basic theory of fracture mechanics and the cohesive element damage theory. 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 element 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, which is calculated by formula (11). is the critical strength in the mixed mode, which is calculated by formula (12).

[0071]

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

[0073]

[0074] Where: C1, m1 are fatigue crack growth parameters in the form of energy release rate, G th is the threshold value of energy release rate, ΔG is the variation range of energy release rate under cyclic loading, which is calculated by formula (14).

[0075]

[0076] Where: δ 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 Equation (15).

[0077]

[0078] According to the above formula, the fatigue crack propagation parameters C1 and m1 in the form of energy release rate can be derived from the Paris formula (16), as shown in the following formula.

[0079]

[0080] Corrosion environment can accelerate the fatigue crack propagation, thereby shortening the service life of the material. Literature indicates that corrosion environment accelerates crack propagation through crack tip anodic dissolution and reduces the free energy of the metal at the crack tip, and according to the basic principles of thermodynamics, a formula for the anodic dissolution type corrosion fatigue crack propagation rate is proposed from the perspective of energy conservation, as shown in formula (18).

[0081]

[0082] In the formula, E is the elastic modulus, v is the Poisson's ratio, σ a is the stress amplitude, σ s is the yield strength, N0 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, M is the molar mass. σ0 is the cyclic strength coefficient, β is the cyclic strain hardening exponent, 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, and the conversion relationship is shown in formulas (19) and (20).u c is the electrochemical energy released by crack tip anodic dissolution in a cycle, which is 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] In the formula, ΔQ is the amount of electricity carried by the dissolved metal in a 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+ is the metal ion activity, i0 is the anodic dissolution current density, S0 is the newly exposed metal area at the crack tip during the first cycle loading, which is calculated by formula (22), T Z0 which is calculated by formula (23).

[0088]

[0089] Ignore the electrochemical energy u released by the crack tip anode dissolution during the cycle in Eq. (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 morphologically manifested as the evolution of corrosion pits. Field measurements typically characterize the damage process using characteristic values ​​such as average corrosion depth, pit depth distribution, and surface roughness, followed by statistical analysis. These measured statistics provide a basis for selecting parameters for reconstructing the corrosion damage evolution process using characteristic values ​​and serve as a reference for numerical simulation analysis results.

[0096] Statistical data show that the average corrosion depth of different metal materials in atmospheric corrosion environments follows basically the same rules. The average corrosion depth evolution data conforms to the kinetic relationship shown in formula (27), while the change law of corrosion rate with 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: m1 is the initial mass of the specimen, m2 is the mass after corrosion and derusting, ρ is the material density, and A is the area of ​​the corrosion region.

[0101]

[0102] Where: R cis the corrosion rate, is the change in the average corrosion depth per unit time step; A1 is a constant that characterizes the initial corrosion rate; b is a constant that characterizes how fast the corrosion rate decreases; and r0 is a constant that characterizes the stable corrosion state.

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

[0104]

[0105] Where: x is the depth of the erosion pit; σ u is the location parameter; γ is the scale parameter; m is the shape parameter. In practical applications, σ u It is 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] To reflect the differences in corrosion rates at different locations on the metal surface, a 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 Equation (32). Integrating it with respect to time t yields the average corrosion depth after time t1, as shown in Equation (33).

[0108] G(z)=Rc×z=(A1e (-t / b) +r0)×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] Transforming Equation (35) yields the inverse function of F(z), as shown in Equation (36). Generate a random number u on the uniformly distributed interval [0,1] and substitute u into the inverse function to obtain 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 wrap the geometric body to simulate the corrosion pit for easy calculation. The extreme point of the cosine function is taken as the deepest point of the corrosion pit. As the horizontal distance from this point increases, the corrosion rate gradually decreases.

[0115] Stress levels affect the growth rate of corrosion pits. Since stress-induced deformation can increase the anodic activity of metals, Gutman established a model to describe the mechanical electrochemical effect of metals, expressed by Equation (38). According to Faraday's principle of electrolysis, the corrosion rate is proportional to the current density. Therefore, the higher the stress level, the faster the corrosion pit develops.

[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, ε0 is the onset of strain hardening, σ m is the spherical part of the macroscopic stress tensor that depends on the applied load, R is the gas constant, and T is the temperature.

[0118] Corrosion-Fatigue Coupling Simulation Strategy

[0119] To simulate the evolution of corrosion pits, their transformation into cracks, and crack propagation during the coupled corrosion-fatigue damage process, this section couples the corrosion damage evolution constitutive model with the cyclic cohesive force constitutive model. In the numerical simulation, corrosion damage is reflected by the stiffness degradation of solid elements, while fatigue damage is reflected by the stiffness degradation of cohesive elements. By transferring information between these two damage constitutive models, a coupled correlation between corrosion and fatigue damage is achieved. This subroutine adheres to the fundamental physical laws of corrosion damage evolution, including the corrosion evolution sequence and pitting 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 MATLAB program is used to extract the unit and node number information from the "inp" file and save it as an array to UMAT. According to the characteristics of the adjacent cohesive units and the solid units sharing 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 corrosion elements are identified, and these elements are the first to be damaged by corrosion. The cohesive elements adjacent to the solid elements will produce fatigue damage (D cohesive ), and receives the corrosion damage information of two adjacent entity units through public 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 elements within the corrosion sub-model obtain corrosion damage information from the four adjacent cohesive elements through common variables, thereby determining whether the solid element is in contact with the corroded element. Furthermore, a pit merging criterion is introduced during the pitting evolution process. When the average radius of adjacent pits is greater than twice the distance between pit centers, the two pits are merged, and the midpoint of the line connecting the coordinates of the two pit centers is 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 element 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 public variables, determine the entity units that accumulate corrosion damage in the current analysis step and obtain their number Then, combine equations (39) and (40) to make them equal, and obtain the equivalent corrosion damage height of the current analysis step: See formula (41). The bottom of the corrosion pit is an arc 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. sThe corrosion damage increment of the solid element at the current analysis step is calculated by equation (42). In summary, the corrosion damage rate of the solid element is finally obtained by equation (44) considering the stress corrosion effect. According to the Turon-Costa cyclic cohesive damage criterion, the fatigue damage accumulation rate of the Cohesive element adjacent to the corrosion damage element is accelerated considering the acceleration effect of corrosion on the crack propagation rate, see equation (9). At the same time, the threshold value of the Cohesive element in contact with the corrosion element is reduced to 1 / 3 of the original value considering the influence of corrosion effect on the fatigue crack threshold value of the material.

[0126]

[0127] where ΔD the and ΔD fem are the theoretical and numerical calculated corrosion damage increment of the solid element at the current analysis step, respectively, h mod is the height of the finite element model in the direction consistent with the corrosion depth, is the number of solid elements at the current analysis step for corrosion damage accumulation, n ent is the number of solid elements in the corrosion submodel, is the equivalent corrosion damage height at the current analysis step.

[0128]

[0129] where d kn is the horizontal distance of the solid element n corresponding to the k initiation position, is the corrosion pit radius at the current analysis step.

[0130]

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

[0132]

[0133] where R d is the corrosion damage rate of the solid element, I is the anode current with deformation, I n is the anode current without deformation.

[0134] 2.4 Obtain the statistical characteristic values of the corrosion model

[0135] The average corrosion depth (d) is obtained by equation (45). The corrosion surface is cut into n x m "pixels" to simulate the three-dimensional scanning view in the actual measurement process. The corrosion depth in the square is obtained through the geometric topological information of the element, and the arithmetic mean height (S q ) and the root mean square height (S a ) are calculated by equations (46) and (47), respectively.

[0136]

[0137] Where p is the number of solid elements in the corrosion sub-model, 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. Equation (29) is integrated and fitted to the time-varying curve of the average corrosion depth. The parameters b, A1, and r0 in Equation (29) are obtained as 24.79, 0.013, and 0.0056, respectively, to obtain the time-varying curve of the corrosion rate. The coordinates of the pitting initiation locations are randomly obtained on the metal surface exposed to the corrosive element. The corrosion rate at each coordinate point is scaled using the probability density distribution of the corrosion rate scaling factor derived in Section 2 (see Equation (35)). Based on the three-dimensional scanning view of the corrosion morphology provided by the literature experiment, the number of pitting initiation locations 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 finite element corrosion fatigue simulation model of a localized steel structure shown in the figure uses a 0.2 mm mesh density, with the model length, width, and height set to 6.5 mm, 6.5 mm, and 2 mm, respectively, to balance computational efficiency and simulation performance. A 0 mm thick cohesive element was inserted using a Python script by identifying the node numbers of adjacent elements in the "inp" file. Although fatigue damage did not occur in the cohesive elements during the simulations in this section, the subroutine logic used the cohesive element's node information to identify adjacent solid elements. The element type was set to C3D4 for the solid elements, and COH3D6 for the cohesive elements. User-defined UMAT constitutive models were assigned to both the solid and cohesive elements within the model. Within UMAT, the Turo-Costa damage evolution constitutive model was assigned to the cohesive elements, while the corrosion damage evolution constitutive model was assigned to the solid elements, respectively, based on the material name. The material parameters for the corrosion damage constitutive model for the solid elements are shown in Table 2. The pit radius parameter in this table was fitted using a trial-and-error method to control the surface roughness of the corroded surface.

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

[0145]

[0146] Change the random pitting initiation position and update the value from the probability density distribution of the corrosion rate amplification factor. Perform 100 sets of simulation operations 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 generally conform to 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 close to the average value within 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 cumulative 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 8The corrosion simulation results show 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, adjacent pits gradually merge into one. The corrosion damage within the model exhibits a typical diffusion pattern. After contacting a fully corroded solid unit, adjacent solid units begin to accumulate corrosion damage, ultimately manifesting as the gradual expansion of the corrosion pit in depth and width. The morphology and development rate of the corrosion pits vary, and the surface morphology is uneven, forming a uniform corrosion thinning layer and hemispherical corrosion pits. In summary, the basic laws of corrosion simulation on the evolution of pit damage and morphological changes are similar to those of experimental results, further verifying the numerical reconstruction method of corrosion morphology.

[0148] 3.2 Corrosion-fatigue damage evolution simulation

[0149] 3.2.1 Cohesion parameter selection

[0150] The traditional cohesive 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 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 690 MPa, 880 MPa, and 0.311 mm, respectively. The fracture toughness calculated by the formula is 292.962 N / mm. The initial stiffness of the cohesive element can be obtained by formula (5). The thickness of the cohesive element is 0.001 mm, and the elastic modulus is 218913 MPa. 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 finite element stress simulation model of the steel structure shown uses the same mesh density settings 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 35 MPa, the stress ratio is R = -1, and a sinusoidal load is used. A rectangular notch is cut in the middle of the simulation model and the corrosion simulation submodel is inserted, and the two are connected by binding. The simulation submodel consists of solid elements and cohesive elements inserted globally through a Python script. The element type used for the solid elements is C3D4, and the element type for the cohesive elements is COH3D6. The solid elements in the corrosion simulation submodel are assigned a corrosion damage evolution constitutive model, with the same material parameter values ​​as in Section 3.1. The cohesive elements in the corrosion submodel are assigned a cyclic cohesive damage constitutive model. At the same time, to improve the convergence of the damage constitutive model, a viscosity coefficient is introduced. Based on the fatigue crack growth rate parameter values ​​of Q690D given in the literature, namely m = 2.95 and lgC = -10.802, the corresponding C1 and m1 can be obtained according to Equation (23). All material parameters used in the Turon-Costa model are shown in Table 2. A linear elastic constitutive model is used outside the corrosion sub-model, with an elastic modulus E = 218913 MPa and a Poisson's ratio v = 0.3. Amplification 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 to obtain the following Figure 9 The evolution of the corrosion pits shown in Figure 10 The stress distribution changes of the sub-model shown in the figure and the Figure 11 The schematic diagram of the evolution of corrosion pits and cracks is shown in Figure 2. Figure 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 completely corroded damaged entity is reduced to a minimum value close to 0, and the stress response generated under the load is very small, which causes a stress concentration effect at the bottom of the corrosion pit. As the fatigue loading progresses, 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. Figure 11 The red solid element is a fully corroded damaged element, while the blue element is a fully fatigue damaged cohesive element. Figure 11 It can be seen that in the corrosion fatigue damage process, the evolution of corrosion pits dominates in the early stage. As the corrosion pits evolve and fatigue loading proceeds, fatigue cracks initiate in multiple locations and develop downward perpendicular to the specimen surface. Multiple cracks gradually merge into a single crack, forming a crack surface that runs through the entire cross-section.

[0162] Nine additional corrosion fatigue simulation models were established and run separately to determine the distribution of corrosion pits and corrosion fatigue cracks. The fatigue cracks maintained essentially the same characteristics: multiple cracks perpendicular to the specimen surface developed at the bottom of different corrosion pits, and multiple cracks sometimes merged into a single crack. The fatigue life during fatigue loading was defined as the fatigue life at the critical value of the high-frequency fatigue machine frequency reduction. Comparing the fatigue life values ​​of the two samples in the experiment (1,333,700 and 1,329,400), it was found that these values ​​were similar to the secondary fatigue load required for crack expansion to 1 / 6 of the thickness in this study, essentially validating the reliability of the corrosion fatigue life prediction method.

[0163] Conclusion

[0164] This paper proposes a corrosion-fatigue coupled damage evolution simulation analysis method for analyzing the fatigue damage and fracture processes of metal components in corrosive environments. This method utilizes a cyclic cohesive force model and a statistical corrosion damage model. Based on a stress-electrochemical model and an anodic dissolution crack growth model, the coupled relationship between corrosion and fatigue is considered. Experimental results from electrochemical corrosion tests and corrosion-fatigue coupled tests, including corrosion depth changes, roughness changes, fatigue life, and crack development characteristics, are compared with simulation results. The main conclusions are as follows:

[0165] (1) By using a corrosion damage evolution simulation model with interpolated cohesive elements 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 into cracks, and the development of cracks into fractures, 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 elements 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 elements to simulate the formation of crack surfaces.

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

[0167] (3) The results obtained from different corrosion-fatigue damage evolution simulation groups share common characteristics. After the corrosion pits transform into cracks, multiple parallel cracks will form in the corrosion sub-model, all perpendicular to the specimen surface. During the development process, multiple cracks will gradually merge into a single crack, eventually penetrating 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 these 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 the pit is considered to accelerate the crack tip growth rate, the fatigue life obtained is often unsafe.

[0169] The above describes the relevant contents of the present invention. Based on this description, a person of ordinary skill in the art will be able to implement the present invention. Based on the above contents of this specification, all other embodiments obtained by a person of ordinary skill in the art without making any creative effort should fall within the scope of patent protection.

Claims

1. A method for simulating and predicting the evolution of corrosion fatigue of steel structures, characterized by: include: Establishing an overall finite element stress simulation model of the steel structure, wherein a notch is reserved on the overall finite element stress simulation model of the steel structure for inserting a local finite element corrosion fatigue 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. 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; The corrosion damage evolution constitutive model uses the solid element corrosion damage rate to calculate the corrosion damage of the solid element; wherein the solid element corrosion damage rate is obtained as follows: First, k pitting initiation position coordinates are randomly generated on the surface of the local finite element corrosion fatigue simulation model of the steel structure using the MATLAB program, and the corrosion rate scaling factor z of each pitting position is calculated according to Equation (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, combine equations (39) and (40) to make them equal, and obtain the equivalent corrosion damage height of the current analysis step: 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, n t 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 sub-model, 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 radius of the corrosion pit in 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 anodic current without deformation; The corrosion damage evolution constitutive model uses the statistical eigenvalues ​​of the corrosion model to calculate the corrosion damage of the solid element; wherein the statistical eigenvalues ​​of the corrosion model are obtained as follows: 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, and the arithmetic mean height S is calculated by Equation (46) and Equation (47) respectively. q and RMS height S a ; Where v is the number of solid elements in the corrosion sub-model, D v 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.

2. The method for simulating and predicting the corrosion fatigue evolution process of steel structures according to claim 1, wherein: The solid unit is a tetrahedron; the cohesive force unit is a triangle.

3. The method for simulating and predicting the evolution of corrosion fatigue of steel structures according to claim 1, wherein: The coupling association is achieved through the following strategy adopted in the calculation 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 generated by the cohesion unit adjacent to the entity unit of the contact corrosion element through the cyclic cohesion constitutive method, and then taking the maximum value of the fatigue damage of the cohesion unit and the corrosion damage of the entity unit adjacent to the cohesion unit as the current damage value of the cohesion unit; if the current damage value of any cohesion unit adjacent to a entity unit is corrosion damage, then the entity unit is determined to be in contact with the corrosion element.

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