CN113435099A - Fatigue life prediction method based on multi-scale fatigue damage evolution model - Google Patents

Fatigue life prediction method based on multi-scale fatigue damage evolution model Download PDF

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CN113435099A
CN113435099A CN202110782659.7A CN202110782659A CN113435099A CN 113435099 A CN113435099 A CN 113435099A CN 202110782659 A CN202110782659 A CN 202110782659A CN 113435099 A CN113435099 A CN 113435099A
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fatigue
grain
grains
crack
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崔闯
周银龙
张清华
胡继丹
徐威
劳武略
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Southwest Jiaotong University
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Abstract

The invention discloses a fatigue life prediction method based on a multi-scale fatigue damage evolution model, which is characterized in that a multi-scale fatigue damage evolution model is constructed, the short crack nucleation period and the short crack propagation period of a welding joint are calculated, the nucleation and propagation processes of a micro crack are evolved, and the long crack propagation period is combined to obtain the evolution process of a macro crack, so that the propagation rate and the fatigue life of the crack of the welding joint are predicted, the result is more consistent with the experimental data, and the accuracy of fatigue life prediction is improved.

Description

Fatigue life prediction method based on multi-scale fatigue damage evolution model
Technical Field
The invention relates to the technical field of fatigue crack testing, in particular to a fatigue life prediction method based on a multi-scale fatigue damage evolution model.
Background
Orthotropic steel bridge panels (OSD) are widely applied to large-span bridges due to the advantages of high volume-weight ratio, easiness in field assembly and the like, however, the fatigue failure problem of a bridge panel-U rib (DTR) welding joint is more prominent under the action of moving load, and the stress threatens the performance and safety of the bridges. Cracks in DTR welded joints are mainly present in the Heat Affected Zone (HAZ), including the Coarse Grain Heat Affected Zone (CGHAZ), the Fine Grain Heat Affected Zone (FGHAZ), and the critical heat affected zone (ICHAZ). Crack initiation and propagation at the root of the DTR weld FGHAZ weld is the most sensitive and dangerous because of its concealment and difficulty in inspection and maintenance. Therefore, the weld root microcosmic in the DTR weld joint FGHAZ is accurately evaluated: (
Figure 169157DEST_PATH_IMAGE001
m to
Figure 668184DEST_PATH_IMAGE002
m) crack initiation and propagation and macroscopical (C), (D) and (D)
Figure 389015DEST_PATH_IMAGE004
m to
Figure 101887DEST_PATH_IMAGE006
m) crack propagation is an important, but challenging task.
Currently, the S-N curve method based on Palmgren-Miner linear accumulated damage is widely used to evaluate fatigue damage of steel bridges and related fatigue tests, as represented by nominal stress, hot spot stress, structural stress or notch stress. The S-N curve method can semi-empirically assess the fatigue life of a steel bridge, but cannot be used to reveal the fatigue damage evolution from microcrack nucleation to macrocracks propagation in the DTR joint of OSD. Some non-linear fatigue damage models based on macroscopically continuous damage mechanics and macroscopically fracture mechanics are used for fatigue failure analysis of steel bridges, but do not take into account the microscopic short crack nucleation and propagation periods that predominate in the fatigue life of steel bridges.
Recently, a multi-scale fatigue damage evolution model is proposed, which is used for researching the nucleation and the expansion of micro-scale short cracks and the fatigue damage expansion of macro-scale. However, the multi-scale models they have built on the assumption of isotropic homogeneity and fatigue damage homogeneity of the metallic material and are therefore more suitable for the base material of steel bridges than for DTR welded joints. In fact, fatigue damage to DTR weld joints is non-uniform due to geometric discontinuities and weld non-uniformities. At present, some simple mesoscale models are applied to a numerical simulation method for the initiation and the expansion of microcracks, but the real microstructure is difficult to present. Other mesoscale methods that take into account crystal plasticity, random grain morphology, grain size, and crystal orientation may be more efficient methods of describing micro-short crack nucleation and propagation of microstructures, as well as associating microstructures with structural members under complex loading conditions. Several Fatigue Index Parameters (FIPs), such as cumulative plastic strain and dislocation density, energy dissipation, mean effective strain and mean effective tensile stress, etc. develop accordingly as non-local variables, which are different for different failure mechanisms. These FIPs do provide a parameter that can be calculated to quantify the micro-scale fatigue damage of high cycle fatigue of steel bridges, but they have not been used for microcrack nucleation and growth in the heterogeneous heat affected zone of the DTR weld joint of steel bridge OSD and the DTR weld joint of steel structures. Furthermore, these mesoscale models do not account for macroscopically long crack propagation. Obviously, the existing method cannot well describe the evolution of fatigue damage at the orthotropic steel bridge deck-U rib welded joint.
Disclosure of Invention
The invention aims to solve the technical problem that the existing method cannot well describe the evolution of the fatigue damage at the welding joint of the orthotropic steel bridge deck plate and the U rib, so that the invention provides a fatigue life prediction method based on a multi-scale fatigue damage evolution model. The method has important significance for fatigue crack propagation speed prediction and residual life prediction widely existing in key important projects such as aerospace, high-speed railways, highway bridges and the like.
The invention is realized by the following technical scheme:
a fatigue life prediction method based on a multi-scale fatigue damage evolution model comprises the following steps:
s1: establishing two substructures according to a DTR welding joint to be detected, inputting crystal plasticity constitutive of all crystal grains in the first substructure as input parameters into a multi-scale fatigue damage evolution model, and obtaining initial local stress and initial plastic strain of each crystal grain slippage system through Abaqus;
s2: calculating initial fatigue index parameters of each crystal grain slippage system through a fatigue index parameter calculation formula based on the initial local stress and the initial plastic strain of each crystal grain slippage system;
s3: selecting the maximum initial fatigue index parameter, taking the crystal grain corresponding to the maximum initial fatigue index parameter as a first fracture crystal grain, and calculating by combining a short crack nucleation period calculation formula to obtain a corresponding short crack nucleation period;
s4: based on the fracture crystal grains, obtaining the local stress and the plastic strain of each crystal grain slippage system through Abaqus again to serve as the current local stress and the current plastic strain, and repeatedly executing the step S2 based on the current local stress and the current plastic strain to obtain the current fatigue index parameters of the crystal grain slippage system;
s5: selecting the maximum current fatigue index parameter, taking the crystal grain corresponding to the maximum current fatigue index parameter as a fracture crystal grain for next short crack propagation simulation, and calculating by combining a short crack propagation period calculation formula to obtain a short crack propagation period corresponding to the fracture crystal grain;
s6: repeating steps S4-S5 until propagation of the short crack of the first substructure to a multi-grain volume-unit-representative failure ceases;
s7: when the short crack of the first substructure is expanded to a multi-grain representative volume unit and fails, calculating the long crack expansion period of a second substructure by linear elastic fracture mechanics;
s8: and adding the short crack nucleation period of the first broken crystal grain, the short crack propagation periods and the long crack propagation periods of all the broken crystal grains by a fatigue life calculation formula to obtain the fatigue life of the DTR welding joint to be tested.
Further, the fatigue index parameter calculation formula is specifically as follows:
Figure 464736DEST_PATH_IMAGE008
in the formula,
Figure 828721DEST_PATH_IMAGE010
is as follows
Figure 235300DEST_PATH_IMAGE011
A fatigue index parameter of each grain slip system,
Figure 153578DEST_PATH_IMAGE012
is as follows
Figure 602008DEST_PATH_IMAGE013
Initial FIP value before crack propagation in the individual grain slip system,
Figure 289341DEST_PATH_IMAGE014
and
Figure 883133DEST_PATH_IMAGE015
is a constant, equal to 0.5 and 2 respectively,
Figure 803554DEST_PATH_IMAGE016
is the length of the critical slip band in the grain,
Figure 773784DEST_PATH_IMAGE017
is the crack length.
Further, the short crack nucleation period calculation formula is specifically as follows:
Figure 331935DEST_PATH_IMAGE018
in the formula,
Figure 96629DEST_PATH_IMAGE020
is a short crack nucleation period of the crystal grains,
Figure 989498DEST_PATH_IMAGE022
for the irreversibility coefficients obtained from the regression analysis,
Figure 12687DEST_PATH_IMAGE024
the length of the volume unit is represented by multiple grains.
Further, the calculation formula for calculating the length of the multiple-grain representative volume unit is specifically as follows:
Figure 674612DEST_PATH_IMAGE026
in the formula,
Figure 626519DEST_PATH_IMAGE027
the length of a volume unit is represented by a plurality of grains,
Figure 6685DEST_PATH_IMAGE028
is the length of the critical slip band in the grain,
Figure 562126DEST_PATH_IMAGE029
for each grain an orientation error factor related to the orientation error of its neighboring grains,
Figure 344137DEST_PATH_IMAGE030
is as follows
Figure 466945DEST_PATH_IMAGE031
The length of intersecting slip bands in adjacent grains.
Further, the formula for calculating the short crack propagation period is specifically as follows:
Figure 599986DEST_PATH_IMAGE032
in the formula,
Figure 450130DEST_PATH_IMAGE033
is as follows
Figure 335916DEST_PATH_IMAGE035
A short crack propagation period of the individual broken grains,
Figure 613313DEST_PATH_IMAGE036
is as follows
Figure 453224DEST_PATH_IMAGE037
The individual grain sliding is the length of the crack,
Figure 841480DEST_PATH_IMAGE038
is a scale constant, is 2 μm,
Figure 332504DEST_PATH_IMAGE039
the length of a volume unit is represented by a plurality of grains,
Figure 515224DEST_PATH_IMAGE041
the average grain length of a volume unit is represented by a plurality of grains,
Figure 606546DEST_PATH_IMAGE042
is as follows
Figure 532913DEST_PATH_IMAGE043
A fatigue index parameter of each grain slip system,
Figure 878444DEST_PATH_IMAGE044
the minimum threshold required for dislocations to occur.
Further, the fatigue life calculation formula is specifically as follows:
Figure 248377DEST_PATH_IMAGE046
in the formula,
Figure 312148DEST_PATH_IMAGE047
for the fatigue life of the DTR welded joint to be tested,
Figure 42206DEST_PATH_IMAGE048
is the short crack nucleation period of the first fractured grains,
Figure 491511DEST_PATH_IMAGE049
for a short crack propagation period of all the broken grains,
Figure 547192DEST_PATH_IMAGE050
the long crack propagation period of all the grains in the DTR welded joint to be measured.
Further, the multi-scale fatigue damage evolution model comprises a full-bridge model, a segment model and a local solid model;
the fatigue life prediction method based on the multi-scale fatigue damage evolution model further comprises the following steps:
the method comprises the following steps of (1) adopting segment model analysis on a fatigue damage critical section of a main beam, and simulating a critical beam section comprising an orthotropic steel bridge deck and a partition plate; identifying key DTR welding nodes between the partition plates from the fatigue damage key section of the main beam to form a local entity model; the full-bridge model and the segment model are coupled using a multi-point constraint, and the local solid model and the segment model are coupled using a multi-point constraint.
In order to numerically model the multi-grain microstructure, the size of solid elements in the local solid model needs to be further refined to the micron level. The invention adopts a substructure technology, and selects part of DTR welding joints from a local solid model as a substructure.
For the numerical simulation of micro short crack initiation and macro long crack propagation, the grid division of the substructure is different. In order to simulate the nucleation and propagation of micro-short cracks, a microstructure is embedded in the DTR welded joint for regridding, and a substructure 1 is obtained. Once the initial macroscopically long crack is formed, the macroscopically long crack propagation is simulated by a fracture mechanics method, the substructure 1 is changed into the substructure 2, and the macroscopically long crack propagation in the substructure 2 is numerically simulated by a linear fracture mechanics method based on finite elements.
The invention provides a fatigue life prediction method based on a multi-scale fatigue damage evolution model, which is characterized in that a multi-scale fatigue damage evolution model is constructed, the short crack nucleation period and the short crack propagation period of a welding joint are calculated, the nucleation and propagation processes of a micro crack are evolved, and the long crack propagation period is combined to obtain the evolution process of a macro crack, so that the propagation rate and the fatigue life of the crack of the welding joint are predicted, the result is more consistent with the experimental data, and the accuracy of fatigue life prediction is improved.
Drawings
The accompanying drawings, which are included to provide a further understanding of the embodiments of the invention and are incorporated in and constitute a part of this application, illustrate embodiment(s) of the invention and together with the description serve to explain the principles of the invention. In the drawings:
FIG. 1 is a flowchart of a fatigue life prediction method based on a multi-scale fatigue damage evolution model according to the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to examples and accompanying drawings, and the exemplary embodiments and descriptions thereof are only used for explaining the present invention and are not meant to limit the present invention.
Examples
A fatigue life prediction method based on a multi-scale fatigue damage evolution model comprises the following steps:
s1: establishing two substructures according to the DTR welding joint to be measured, inputting crystal plasticity constitutive of all crystal grains in the first substructure as input parameters into a multi-scale fatigue damage evolution model, and obtaining initial local stress and initial plastic strain of each crystal grain slippage system through Abaqus.
Specifically, the multi-scale fatigue damage evolution of DTR welded joints can be divided into two stages: nucleation and propagation of short cracks; and secondly, the propagation of long cracks. The present example shows the nucleation and propagation stages of a short crack by a short crack nucleation period and a short crack propagation period, and shows the propagation stages of a long crack by a long crack propagation period.
The multi-scale fatigue damage evolution model in the embodiment comprises a full-bridge unit model, a middle-stage shell unit model and a local entity model. In order to facilitate calculation of a polycrystalline microstructure requiring numerical simulation of a DTR weld joint, the size of a solid unit in the local solid model of this embodiment needs to be further refined to micron level, and therefore, a substructure technology is adopted, a smaller part of the DTR joint is selected from the local solid model as a substructure, boundary conditions of the substructure are obtained by the local solid model having a unit size of millimeter level, and a polycrystalline microstructure of a 2 μm grid is simulated by using a polycrystalline random representative volume unit (SRVE).
S2: and calculating the initial fatigue index parameters of each crystal grain slippage system through a fatigue index parameter calculation formula based on the initial local stress and the initial plastic strain of each crystal grain slippage system.
In particular, since the nucleation process of a short crack in a welded joint is a crystallographic process, manifested as a crystal plane slip, the constitutive model for simulating the nucleation and growth of a short crack needs to take into account the elastic and plastic anisotropy of the crystal. Under the assumption of small deformation, the rotation of the lattice can be neglected, and the total strain tensor is increased
Figure 832680DEST_PATH_IMAGE051
Simple decomposition into elastic strain tensor and
Figure 117162DEST_PATH_IMAGE052
tensor of plastic strain
Figure 171705DEST_PATH_IMAGE053
And (4) summing.
Wherein,
Figure 132708DEST_PATH_IMAGE054
，
Figure 160619DEST_PATH_IMAGE056
wherein C is the fourth-order elastic modulus tensor of the crystal material,
Figure 232480DEST_PATH_IMAGE057
is the stress tensor; the symbol ": denotes the inner product of the two tensors. Tensor of strain
Figure 672689DEST_PATH_IMAGE058
Caused by dislocations in the grain slip system, the rate of plastic strain can be expressed as:
Figure 539014DEST_PATH_IMAGE059
in the formula,
Figure 815405DEST_PATH_IMAGE060
、
Figure 425378DEST_PATH_IMAGE061
are respectively the first
Figure 720093DEST_PATH_IMAGE062
The slip direction and slip plane unit vector of the individual crystal grain slip system,
Figure 6587DEST_PATH_IMAGE063
is the number of the crystal grain sliding system "
Figure 19542DEST_PATH_IMAGE064
"means
Figure 698785DEST_PATH_IMAGE065
And
Figure 598739DEST_PATH_IMAGE066
the product of the two unit vectors.
According to the flow law of the rate-dependent deformation of the crystalline material, the grain slip system can be determined
Figure 338025DEST_PATH_IMAGE067
Slip rate of
Figure 307118DEST_PATH_IMAGE068
。
Figure 773741DEST_PATH_IMAGE069
In the formula,
Figure 777469DEST_PATH_IMAGE070
is as follows
Figure 422077DEST_PATH_IMAGE071
The slip rate of the individual grain slip system,
Figure 629198DEST_PATH_IMAGE072
are respectively the first
Figure 650244DEST_PATH_IMAGE073
Shear stress, resistance strength and back stress in the individual grain sliding system,
Figure 774058DEST_PATH_IMAGE074
for reference to the shear strain rate,
Figure 838834DEST_PATH_IMAGE075
is the strain rate sensitive coefficient.
First, the
Figure 48099DEST_PATH_IMAGE076
The resistance strength coefficient of each crystal grain sliding system is as follows:
Figure 341677DEST_PATH_IMAGE078
in the formula,
Figure 70730DEST_PATH_IMAGE079
is as follows
Figure 57140DEST_PATH_IMAGE080
A latent hardening modulus of a crystal grain sliding system, wherein,
Figure 753701DEST_PATH_IMAGE081
in order to be a self-hardening modulus,
Figure 383395DEST_PATH_IMAGE082
。
Figure 950642DEST_PATH_IMAGE084
in the formula,
Figure 107954DEST_PATH_IMAGE085
is a constant number of times, and is,
Figure 42543DEST_PATH_IMAGE086
in order to be the initial hardening modulus,
Figure 677924DEST_PATH_IMAGE087
for the saturated hardening modulus during short crack nucleation and propagation,
Figure 630836DEST_PATH_IMAGE088
in order to obtain the initial shear yield stress,
Figure 959050DEST_PATH_IMAGE089
in order to achieve the saturation stress,
Figure 613891DEST_PATH_IMAGE090
and
Figure 318542DEST_PATH_IMAGE091
are respectively the first
Figure 125961DEST_PATH_IMAGE092
Crystal grain sliding system and
Figure 641387DEST_PATH_IMAGE093
the total shear strain of the individual grain slip systems,
Figure 268677DEST_PATH_IMAGE094
is as follows
Figure 245860DEST_PATH_IMAGE095
Crystal grain sliding system and
Figure 422633DEST_PATH_IMAGE096
the crystal grain sliding system.
The nonlinear evolution law of motion hardening is as follows:
Figure 358228DEST_PATH_IMAGE097
in the formula,
Figure 472814DEST_PATH_IMAGE098
、
Figure 270000DEST_PATH_IMAGE099
is a material parameter of a crystal grain sliding system;
Figure 786432DEST_PATH_IMAGE100
is a parameter describing the simger effect of a material package.
And obtaining the local stress and plastic strain of the grain sliding system by adopting a multi-scale fatigue damage evolution model. The Fatigue Index Parameter (FIP) provided based on the critical plane method represents the driving force of fatigue crack propagation as the displacement range of the cyclic crack tip under the mixed condition (
Figure 892928DEST_PATH_IMAGE101
) Effective surrogate markers of (1). The calculation formula of the fatigue index parameter is specifically as follows:
Figure 744078DEST_PATH_IMAGE103
in the formula,
Figure 328644DEST_PATH_IMAGE104
is as follows
Figure 965161DEST_PATH_IMAGE105
The cyclic plastic shear strain range of the individual grain sliding system,
Figure 976980DEST_PATH_IMAGE106
is the maximum stress perpendicular to the slip plane,
Figure 816891DEST_PATH_IMAGE107
for the reference strength (355MPa),
Figure 205147DEST_PATH_IMAGE108
is constant, typically between 0.5 and 1.
Grain sliding subdivides a grain into a number of layers parallel to a major sliding plane directly related to the crystallographic orientation of the grain. In order to simulate the inter-grain short crack propagation, considering the evolution of the short crack between grains, the fatigue index parameter calculation formula in this embodiment is equivalent to:
Figure 696171DEST_PATH_IMAGE110
in the formula,
Figure 134018DEST_PATH_IMAGE111
is as follows
Figure 976072DEST_PATH_IMAGE112
A fatigue index parameter of each grain slip system,
Figure 902439DEST_PATH_IMAGE113
is as follows
Figure 733123DEST_PATH_IMAGE114
Initial FIP value before crack propagation in the individual grain slip system,
Figure 617903DEST_PATH_IMAGE115
and
Figure 681674DEST_PATH_IMAGE116
is a constant, equal to 0.5 and 2 respectively,
Figure 395421DEST_PATH_IMAGE117
is the length of the critical slip band in the grain,
Figure 595458DEST_PATH_IMAGE017
is the crack length.
S3: and selecting the maximum initial fatigue index parameter, taking the crystal grain corresponding to the maximum initial fatigue index parameter as a first fracture crystal grain, and calculating by combining a short crack nucleation period calculation formula to obtain a corresponding short crack nucleation period.
Further, the short crack nucleation period calculation formula is specifically as follows:
Figure 651138DEST_PATH_IMAGE119
in the formula,
Figure 671047DEST_PATH_IMAGE120
is a short crack nucleation period of the crystal grains,
Figure 221108DEST_PATH_IMAGE121
irreversibility coefficient obtained for regression analysis was 41.6
Figure 275652DEST_PATH_IMAGE122
，
Figure 236655DEST_PATH_IMAGE123
The length of the volume unit is represented by multiple grains.
Further, the calculation formula of the length of the multiple grains representing the volume unit is specifically as follows:
Figure 258706DEST_PATH_IMAGE124
in the formula,
Figure 330567DEST_PATH_IMAGE125
the length of a volume unit is represented by a plurality of grains,
Figure 505197DEST_PATH_IMAGE126
is the length of the critical slip band in the grain,
Figure 387833DEST_PATH_IMAGE127
for each grain an orientation error factor related to the orientation error of its neighboring grains,
Figure 647913DEST_PATH_IMAGE128
is as follows
Figure 523465DEST_PATH_IMAGE129
The length of intersecting slip bands in adjacent grains.
S4: and based on the fractured crystal grains, obtaining the local stress and the plastic strain of each crystal grain sliding system through the Abaqus again to serve as the current local stress and the current plastic strain, and repeatedly executing the step S2 based on the current local stress and the current plastic strain to obtain the current fatigue index parameters of the crystal grain sliding systems.
S5: and selecting the maximum current fatigue index parameter, taking the crystal grain corresponding to the maximum current fatigue index parameter as the fracture crystal grain of the next short crack propagation simulation, and calculating by combining a short crack propagation period calculation formula to obtain the short crack propagation period corresponding to the fracture crystal grain.
Further, the formula for calculating the short crack propagation period is specifically as follows:
Figure 67448DEST_PATH_IMAGE131
in the formula,
Figure 104674DEST_PATH_IMAGE132
is as follows
Figure 117630DEST_PATH_IMAGE133
Short crack propagation cycle of individual broken grainsDuring the period of time of the operation,
Figure 547605DEST_PATH_IMAGE134
is as follows
Figure 431247DEST_PATH_IMAGE135
The individual grain sliding is the length of the crack,
Figure 639375DEST_PATH_IMAGE136
is a scale constant, is 2 μm,
Figure 874047DEST_PATH_IMAGE137
the length of a volume unit is represented by a plurality of grains,
Figure 334810DEST_PATH_IMAGE138
the average grain length of a volume unit is represented by a plurality of grains,
Figure 338538DEST_PATH_IMAGE139
is as follows
Figure 983146DEST_PATH_IMAGE140
A fatigue index parameter of each grain slip system,
Figure 190268DEST_PATH_IMAGE141
to minimize the threshold required for dislocations to occur, the definition of mecelli brackets is: if it is nota >0, then 〈a〉 = aOtherwise 〈a〉 = 0。
In the present embodiment
Figure 211313DEST_PATH_IMAGE142
，
Figure 69548DEST_PATH_IMAGE143
，
Figure 399904DEST_PATH_IMAGE144
，
Figure 78010DEST_PATH_IMAGE145
。
Further, in order to simulate the crack propagation of the next fractured grain, the stress-strain state of the multi-grain representative volume unit needs to be re-analyzed after the ith fractured grain is fractured, i.e., step S6 needs to be performed.
S6: steps S4-S5 are repeated until the propagation of the short crack of the first substructure to the polycrystalline grain-representative volume cell failure ceases.
Under cyclic loading, the short cracks continue to propagate until multiple grains represent a volume unit failure. Finally, the
Figure 637167DEST_PATH_IMAGE146
The short crack propagation life of (a) can be calculated by accumulating short crack propagation cycles in all the broken grains.
S7: when the short crack of the first substructure propagates to a point where multiple grains represent a volume unit failure, the long crack propagation period of the second substructure is calculated by the Line Elastic Fracture Mechanics (LEFM).
In particular, the propagation of long cracks is not limited by the microstructure, and the propagation rate of long cracks is related to the threshold value of the stress intensity factor.
Figure 615488DEST_PATH_IMAGE147
Wherein C, m,
Figure 352630DEST_PATH_IMAGE148
Is a constant of the material, and is,
Figure 49191DEST_PATH_IMAGE149
，
Figure 146460DEST_PATH_IMAGE150
、
Figure 228554DEST_PATH_IMAGE151
the lengths of the ith crack and the i-1 crack at the jth node of the crack tip line are respectively,
Figure 385866DEST_PATH_IMAGE152
is the range of the effective stress intensity factor of the jth node of the crack tip line under the action of the ith cyclic load,
Figure 304144DEST_PATH_IMAGE153
the number of cycles under the action of the ith cyclic load.
This example considers the effect of heat affected zone material, residual stress, crack tip closure and stress ratio on the propagation of a DTR weld joint crack. The stress intensity factor can be obtained by using an interaction integration method. The stress ratio of the crack propagation constant of the DTR weld joint is small and is ignored in this example. This example considers the effect of typical type I-II mixed crack multi-modal long crack propagation in DTR joints.
Figure 955836DEST_PATH_IMAGE154
In the formula,
Figure 908749DEST_PATH_IMAGE155
and
Figure 236962DEST_PATH_IMAGE156
the stress intensity factor ranges for the three crack propagation modes.
Figure 891803DEST_PATH_IMAGE157
，
Figure 330874DEST_PATH_IMAGE158
，
Figure 872714DEST_PATH_IMAGE159
，
Figure 637408DEST_PATH_IMAGE160
The maximum value and the minimum value of the stress intensity factor under cyclic loading are respectively. And (3) directly solving by adopting an interaction integration method through numerical simulation of the finite element model under the action of the cyclic load. Accordingly, the torsion angle of the crack
Figure 15431DEST_PATH_IMAGE161
May be determined according to a maximum circumferential stress criterion for crack growth perpendicular to the direction of maximum circumferential stress.
Figure 523772DEST_PATH_IMAGE163
The fatigue life corresponding to long crack propagation can be predicted by:
Figure 185698DEST_PATH_IMAGE164
s8: and adding the short crack nucleation period of the first fractured crystal grain, the short crack propagation periods and the long crack propagation periods of all the fractured crystal grains by a fatigue life calculation formula to obtain the fatigue life of the DTR welding joint to be measured.
Further, the fatigue life calculation formula is specifically as follows:
Figure 376420DEST_PATH_IMAGE165
in the formula,
Figure 225427DEST_PATH_IMAGE166
for the fatigue life of the DTR welded joint to be tested,
Figure 537460DEST_PATH_IMAGE167
is the short crack nucleation period of the first fractured grains,
Figure 804624DEST_PATH_IMAGE168
for a short crack propagation period of all the broken grains,
Figure 645541DEST_PATH_IMAGE169
the long crack propagation period of all the grains in the DTR welded joint to be measured.
Further, the multi-scale fatigue damage evolution model in this embodiment includes a full-bridge model, a segment model and a local solid model, and the fatigue life prediction method based on the multi-scale fatigue damage evolution model further includes:
the full-bridge model mainly uses beam cells, each cell having two nodes and each node having six degrees of freedom, for modeling structures such as piers, beams, towers, and the like. For the related bridge, the critical section of fatigue damage caused by vehicle load to the main beam is analyzed by adopting a section shell unit, the shell unit is provided with four nodes on each unit, and each node is provided with six degrees of freedom. The segment model is used to simulate critical beam segments including OSDs and bulkheads, and the full-bridge model and the segment model are coupled using multi-point constraints (MPCs).
And identifying a key DTR welding node between two partition plates from a fatigue damage key section of the main beam, and subdividing the grid by using eight-node entity units with six degrees of freedom of each node to form a local entity model. Wherein the local solid model comprises asphalt pavement and welding geometrical details. The physical element size around the DTR weld joint is refined to the millimeter level, ranging from 20mm of pavement element to 2mm of weld area. Using MPC to couple the node degrees of freedom of the solid elements in the local solid model boundary and the node degrees of freedom of the shell elements of the key segment model boundary at the same position.
In order to numerically model the multi-grain microstructure, the size of solid elements in the local solid model needs to be further refined to the micron level. However, in a large bridge multi-scale model having a ten-meter-scale beam element and a micron-scale solid element, it is difficult to calculate the stress-strain response of the microstructure. Therefore, the invention adopts a substructure technology, a DTR joint with the length of 0.5m and the width of 0.6m is selected from a local solid model to be used as a substructure, and the boundary condition of the substructure is obtained from the local solid model (0.9m multiplied by 0.9m) with the unit size of millimeter. And for the numerical simulation of micro short crack initiation and macro long crack propagation, the grid division of the substructure is different. In order to simulate the nucleation and propagation of micro-short cracks, a microstructure of 0.2mm × 0.3mm × 0.5mm embedded in the DTR weld joint FCHAZ was regridded to the micrometer level, resulting in a substructure 1. The longitudinal position of the weld root structure is located in the centre of the substructure 1. Thus, the size of the solid units in substructure 1 varied from 4mm to 2 μm, and a 2 μm grid of multi-grain microstructures was simulated using multi-grain representative volume units (SRVE).
The invention makes the critical micro short crack length equal to the initial macro long crack length. A SRVE was used to simulate a 0.2mm x 0.3mm x 0.5mm multi-grain microstructure to simulate the nucleation and propagation of micro-short cracks. When the micro-short crack penetrates the entire multi-grain microstructure, its corresponding micro-short crack length is the critical micro-crack length and the initial macro-long crack length.
Once the initial macro-scale crack is formed, fracture mechanics is used to simulate the macro-scale crack propagation. At this time, the substructure 1 was changed to a substructure 2, and similar to the substructure 1, the initial macrocracks at the root of the weld were located longitudinally in the middle of the substructure 2. The linear fracture mechanics method based on finite elements is adopted to carry out numerical simulation on the macroscopic long crack propagation in the substructure 2.
According to the fatigue life prediction method based on the multi-scale fatigue damage evolution model, the crystal plastic constitutive model can be used for simulating nucleation and growth of short cracks in a three-dimensional polycrystalline microstructure embedded in a substructure, under the condition that a mixed crack mode is considered, a linear fracture mechanics method can be used for simulating macroscopic long crack expansion in the substructure after critical micro short cracks appear, the expansion rate of cracks of a welding joint and the fatigue life are predicted, the result is more consistent with experimental data, and the accuracy of fatigue life prediction is improved.
The above embodiments are provided to further explain the objects, technical solutions and advantages of the present invention in detail, it should be understood that the above embodiments are merely exemplary embodiments of the present invention and are not intended to limit the scope of the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (7)

1. A fatigue life prediction method based on a multi-scale fatigue damage evolution model is characterized by comprising the following steps:
s1: establishing two substructures according to a DTR welding joint to be detected, inputting crystal plasticity constitutive of all crystal grains in the first substructure as input parameters into a multi-scale fatigue damage evolution model, and obtaining initial local stress and initial plastic strain of each crystal grain slippage system through Abaqus;
s2: calculating initial fatigue index parameters of each crystal grain slippage system through a fatigue index parameter calculation formula based on the initial local stress and the initial plastic strain of each crystal grain slippage system;
s3: selecting the maximum initial fatigue index parameter, taking the crystal grain corresponding to the maximum initial fatigue index parameter as a first fracture crystal grain, and calculating by combining a short crack nucleation period calculation formula to obtain a corresponding short crack nucleation period;
s4: based on the fracture crystal grains, obtaining the local stress and the plastic strain of each crystal grain slippage system through Abaqus again to serve as the current local stress and the current plastic strain, and repeatedly executing the step S2 based on the current local stress and the current plastic strain to obtain the current fatigue index parameters of the crystal grain slippage system;
s5: selecting the maximum current fatigue index parameter, taking the crystal grain corresponding to the maximum current fatigue index parameter as a fracture crystal grain for next short crack propagation simulation, and calculating by combining a short crack propagation period calculation formula to obtain a short crack propagation period corresponding to the fracture crystal grain;
s6: repeating steps S4-S5 until propagation of the short crack of the first substructure to a multi-grain volume-unit-representative failure ceases;
s7: when the short crack of the first substructure is expanded to a multi-grain representative volume unit and fails, calculating the long crack expansion period of a second substructure by linear elastic fracture mechanics;
s8: and adding the short crack nucleation period of the first broken crystal grain, the short crack propagation periods and the long crack propagation periods of all the broken crystal grains by a fatigue life calculation formula to obtain the fatigue life of the DTR welding joint to be tested.
2. The method for predicting the fatigue life based on the multi-scale fatigue damage evolution model according to claim 1, wherein the fatigue index parameter calculation formula is specifically as follows:
Figure 258526DEST_PATH_IMAGE002
in the formula,
Figure 362617DEST_PATH_IMAGE004
is as follows
Figure 80037DEST_PATH_IMAGE006
A fatigue index parameter of each grain slip system,
Figure 662197DEST_PATH_IMAGE008
is as follows
Figure 210990DEST_PATH_IMAGE010
Initial FIP value before crack propagation in the individual grain slip system,
Figure 502294DEST_PATH_IMAGE012
and
Figure 690699DEST_PATH_IMAGE014
is a constant, equal to 0.5 and 2 respectively,
Figure 358441DEST_PATH_IMAGE016
is the length of the critical slip band in the grain,
Figure 496161DEST_PATH_IMAGE018
crack length.
3. The method for predicting the fatigue life based on the multi-scale fatigue damage evolution model according to claim 1, wherein the short crack nucleation period calculation formula is specifically as follows:
Figure 473213DEST_PATH_IMAGE020
in the formula,
Figure 696384DEST_PATH_IMAGE022
is a short crack nucleation period of the crystal grains,
Figure 902238DEST_PATH_IMAGE024
for the irreversibility coefficients obtained from the regression analysis,
Figure 346994DEST_PATH_IMAGE026
the length of the volume unit is represented by multiple grains.
4. The method for predicting fatigue life based on the multi-scale fatigue damage evolution model as claimed in claim 3, wherein the formula for calculating the length of the multi-grain representative volume unit is specifically as follows:
Figure 245680DEST_PATH_IMAGE028
in the formula,
Figure 956147DEST_PATH_IMAGE030
the length of a volume unit is represented by a plurality of grains,
Figure 965692DEST_PATH_IMAGE032
is the length of the critical slip band in the grain,
Figure 333131DEST_PATH_IMAGE034
for each grain an orientation error factor related to the orientation error of its neighboring grains,
Figure 137139DEST_PATH_IMAGE036
is as follows
Figure 334902DEST_PATH_IMAGE038
The length of intersecting slip bands in adjacent grains.
5. The method for predicting the fatigue life based on the multi-scale fatigue damage evolution model according to claim 1, wherein the formula for calculating the short crack propagation period is specifically as follows:
Figure 335088DEST_PATH_IMAGE040
in the formula,
Figure 301907DEST_PATH_IMAGE042
is as follows
Figure 542395DEST_PATH_IMAGE044
A short crack propagation period of the individual broken grains,
Figure 945564DEST_PATH_IMAGE046
is as follows
Figure 765752DEST_PATH_IMAGE048
The individual grain sliding is the length of the crack,
Figure 39608DEST_PATH_IMAGE050
is a scale constant, is 2 μm,
Figure 450997DEST_PATH_IMAGE052
the length of a volume unit is represented by a plurality of grains,
Figure 357774DEST_PATH_IMAGE054
the average grain length of a volume unit is represented by a plurality of grains,
Figure 512811DEST_PATH_IMAGE056
is as follows
Figure 703490DEST_PATH_IMAGE058
A fatigue index parameter of each grain slip system,
Figure 489044DEST_PATH_IMAGE060
the minimum threshold required for dislocations to occur.
6. The method for predicting fatigue life based on the multi-scale fatigue damage evolution model according to claim 1, wherein the fatigue life calculation formula is specifically as follows:
Figure 883116DEST_PATH_IMAGE062
in the formula,
Figure 825533DEST_PATH_IMAGE064
for the fatigue life of the DTR welded joint to be tested,
Figure 355871DEST_PATH_IMAGE066
is the short crack nucleation period of the first fractured grains,
Figure 374643DEST_PATH_IMAGE068
for a short crack propagation period of all the broken grains,
Figure 256011DEST_PATH_IMAGE070
the long crack propagation period of all the grains in the DTR welded joint to be measured.
7. The method for predicting the fatigue life based on the multi-scale fatigue damage evolution model according to claim 1, wherein the multi-scale fatigue damage evolution model comprises a full-bridge model, a segment model and a local solid model;
the fatigue life prediction method based on the multi-scale fatigue damage evolution model further comprises the following steps:
the method comprises the following steps of (1) adopting segment model analysis on a fatigue damage critical section of a main beam, and simulating a critical beam section comprising an orthotropic steel bridge deck and a partition plate; identifying key DTR welding nodes between the partition plates from the fatigue damage key section of the main beam to form a local entity model; the full-bridge model and the segment model are coupled using a multi-point constraint, and the local solid model and the segment model are coupled using a multi-point constraint.
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