CN114239117A - Circular steel tube intersecting node high-cycle fatigue numerical simulation method based on expanded finite element - Google Patents
Circular steel tube intersecting node high-cycle fatigue numerical simulation method based on expanded finite element Download PDFInfo
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Abstract
The invention belongs to the field of structural engineering, and particularly relates to a circular steel tube intersecting node high-cycle fatigue numerical simulation method based on an expanded finite element, which comprises the following steps of: establishing a numerical model of the tubular steel pipe intersecting joint containing the initial crack in a software platform according to the mechanical property and specification size of the material used by the intersecting joint test piece; defining a crack region by using an expansion finite element method and a level set function to obtain a stress intensity factor of a crack front edge; applying a load and boundary conditions; establishing a high-cycle fatigue crack propagation program of the corresponding nodes; implanting a high-cycle fatigue crack propagation program into a software platform for operation; and processing the simulation data to obtain a propagation rate curve of the fatigue crack of the intersecting node, comparing the result with the test, and verifying the validity of the simulation result. The method avoids the need of grid reconstruction when the finite element method is used for simulating the problem by expanding one increment step.
Description
Technical Field
The invention belongs to the field of structural engineering, and particularly relates to a circular steel tube intersecting node high-cycle fatigue numerical simulation method based on an expanded finite element.
Background
The intersecting nodes are convenient to process and easy to construct, and are widely applied to large-span public buildings such as large stadiums, station buildings and the like, so that a plurality of scholars can research the mechanical properties of the intersecting nodes to ensure the reliability of the intersecting nodes in service.
Compared with low-cycle fatigue damage caused by earthquake, the high-cycle fatigue damage process is longer, no obvious sign is generated when the high-cycle fatigue damage occurs, and serious economic and property accidents are easily caused, such as the collapse accident of a 2E waiting hall of a French Gaoye airport in 2004, because the crack at the joint of the ceiling of the waiting hall and the strut is continuously expanded under the action of long-term wind load and is suddenly broken. However, in 1980, 123 casualties were directly caused by accidents occurring in the ocean platform of Alexander l. Therefore, it is necessary to study the propagation of the high cycle fatigue crack at the intersection.
The intersecting joint comprises a circular steel pipe intersecting joint, a square steel pipe intersecting joint and the like. The conventional common numerical simulation method for the propagation of the high-cycle fatigue crack of the intersecting node of the circular steel tube comprises a finite element method and a boundary element method, wherein the finite element method is most widely applied and the technology is the most mature. The operational flow of the method is shown in fig. 1. In the process, once grid reconstruction is needed to be carried out on the integral model every time the crack is expanded by one step, so that the operation time is greatly increased, and meanwhile, the grid reconstruction difficulty is high and the operation is difficult.
The finite element expansion method is developed on the basis of a unit decomposition method, and the method does not need to divide a grid again when simulating fatigue crack expansion, thereby solving the defects of processing the fatigue crack by the finite element method. However, the existing software cannot simulate the high-cycle fatigue crack propagation by using the finite element expansion method. Therefore, a method is needed to solve the defect of the grid repartitioning of the finite element method, and meanwhile, the existing software is used as a platform to realize the application of the expansion finite element method in the propagation of the high-cycle fatigue cracks of the intersecting nodes of the circular steel pipe.
Disclosure of Invention
The invention aims to provide a circular steel tube intersecting node high cycle fatigue numerical simulation method based on an expanded finite element, so as to avoid the defect that the calculation efficiency is low because a grid needs to be reconstructed every time an incremental step is expanded when a finite element method is used for simulating the problem, and simultaneously solve the problem that the existing software does not have the basic function of simulating the circular steel tube intersecting node high cycle fatigue crack expansion.
The invention is realized by the following technical scheme: a circular steel tube intersecting node high cycle fatigue numerical simulation method based on an expanded finite element comprises the following steps:
step 2, defining a crack area by using an expansion finite element method and a level set function to obtain a stress intensity factor of the crack front edge, wherein the stress intensity factor calculation method comprises the following steps:
in the formula, KI，KII，KIIIStress intensity factors corresponding to the type I cracks, the type II cracks and the type III cracks respectively; j. the design is a squareI int，JII int，JIII intRespectively corresponding interaction J integrals of the type I crack, the type II crack and the type III crack; b is a logarithmic energy system matrix;
step 4, establishing a high cycle fatigue crack propagation program of the corresponding node, which specifically comprises the following steps: establishing a fatigue crack propagation criterion, determining a fatigue crack propagation direction, extracting a stress intensity factor and a crack front edge coordinate, calculating a next increment step crack propagation increment, calculating a next increment step crack front edge coordinate, and updating a next increment step crack model;
In the step 1, a numerical model of the tubular steel pipe intersecting node containing the initial crack is established in a software platform based on a coordinate mapping method.
In the step 2, the grid cells containing cracks are divided into three types through a level set function, namely crack non-penetrating cells, crack complete penetrating cells and crack incomplete penetrating cells; for the first unit, the same displacement field calculation method as the finite element method is adopted, and for the latter two units, the displacement field needs to be corrected, and the specific expression is as follows:
in the formula (I), the compound is shown in the specification,
a displacement field in which the crack does not pass through the cell;
displacement field for the complete penetration of the crack through the cell, wherein aiH (x) is a level set function, and the calculation formula is
x is an integral point, x is the integral of distance on the crack surfaceThe point closest to the point, n is the normal vector of x on the crack surface;
displacement field for incomplete penetration of the crack through the cell, biF (x) is an expansion function of the crack incomplete penetration unit under a polar coordinate system;
according to the grid unit displacement field, the stress at the integral point of each grid unit and the stress at each node of the overall grid can be obtained, the interaction J integral of the crack is obtained through the stress field, and further the stress intensity factor of the crack can be obtained.
In the step 2, since the fatigue crack of the tubular steel joint is a mixed crack composed of a type i crack, a type ii crack and a type iii crack, an equivalent stress intensity factor needs to be calculated according to a stress intensity factor corresponding to the type i crack, a stress intensity factor corresponding to the type ii crack and a stress intensity factor corresponding to the type iii crack, and the calculation formula is as follows:
in the formula, B is an empirical parameter and is 1.0; Δ KI，ΔKII，ΔKIII，ΔKeqRespectively corresponding stress intensity factor increment and equivalent stress intensity factor increment of the I type crack, the II type crack and the III type crack; the calculation method of the stress intensity factor increment comprises the following steps:
ΔK＝Kmax-Kmin
in the formula KmaxThe stress intensity factor, K, obtained for the maximum value of the load under the action of a constant amplitude loadminThe stress intensity factor is obtained for the minimum load under the action of constant amplitude load.
In step 4, the fatigue crack propagation criterion adopts Paris criterion, and the expression of the criterion is as follows:
in the formula, a is the length of a crack, N is the fatigue load cycle number, and C and m are material parameters; wherein C is 2.66704 × 10-11m/circle, m is 2.75.
In step 4, the fatigue crack propagation direction adopts a three-dimensional maximum circumferential stress criterion, and the criterion expression is as follows:
in the formula,. DELTA.KIeqTo account for the equivalent stress intensity factor increment for the type III stress intensity factor effect, the expression is:
ΔKIeq＝ΔKI+B|ΔKII|
in the formula, B is an empirical parameter and is 1.0.
In the step 4, the extraction method of the stress intensity factor and the crack front edge coordinate comprises the following steps: and setting output process variables, submitting job generation, generating an odb file, determining a path and a name of a result file, extracting a stress intensity factor and a crack front edge coordinate, and inputting a final result into a txt file.
In step 4, the calculation method of the crack propagation increment of the next increment step depends on the control method of fatigue crack propagation; the control method of fatigue crack propagation adopts load cycle frequency control or single increment step crack maximum propagation increment control;
the load cycle number is controlled to be that fatigue crack propagation analysis is carried out once every delta N cycles of actual load, the stress intensity factor distribution condition of the crack front edge and the coordinates of the crack front edge discrete point of the next increment step are obtained, and the method for calculating the crack propagation increment comprises the following steps:
Δai＝C(ΔKeq,i)m·ΔN
the maximum crack propagation increment is controlled by specifying the point with the maximum stress intensity factor as the maximum propagation increment delta a according to the stress intensity factor distribution of the crack front edgemaxThe extended increments for the remaining points are calculated according to the following formula:
in the step 4, the lower surface of the crack is assumed to be a horizontal plane, x-y-z is a global coordinate system, wherein an xy plane is coplanar with the lower surface of the crack, and a z axis is perpendicular to the xy plane; establishing a local coordinate system X-Y-Z at any point of the front edge of the crack, wherein the X axis coincides with the normal direction of the point, the Y axis coincides with the tangential direction of the point, and the Z axis is vertical to the XY plane; while setting two straight lines x at that point*And y*Wherein x is*Parallel to the x-axis, y*Parallel to the y-axis; the calculation method of the crack front coordinate of the next increment step is as follows:
Δx＝Δacosθ*cosα
Δy＝Δacosθ*sinα
Δz＝Δasinθ。
in step 4, the method for updating the crack model in the next incremental step comprises the following steps: and sequentially establishing an nth-step crack front two-dimensional projection model, adjusting the coordinates of the discrete points of the crack front to form a three-dimensional model, dividing grids, introducing an nth-1-step crack model, and finally combining grid nodes to form the nth-step crack model.
The invention has the beneficial effects that: compared with the prior art, the method for simulating the propagation of the high-cycle fatigue cracks of the intersecting nodes of the circular steel tube based on the finite element expansion method calculates the stress intensity factor of the fatigue cracks of the intersecting nodes by adopting a fracture mechanics theory, overcomes the defect of a grid reconstruction strategy required by a finite element expansion method by utilizing an expansion finite element, and can realize the numerical simulation of the propagation of the high-cycle fatigue cracks of the intersecting nodes of the circular steel tube by utilizing the expansion finite element expansion method in the existing software platform to obtain the fatigue crack propagation rate curve under the action of a normal fatigue load. The method provided by the invention has the advantages of lower realization difficulty, higher calculation efficiency and capability of ensuring the precision.
Drawings
FIG. 1 is a flow chart of the prior art;
FIG. 2 is a flow chart of the present invention;
FIG. 3 is a schematic diagram of a tubular intersection of T-shaped circular steel tubes according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of components of a tubular joint of a T-shaped circular steel tube according to an embodiment of the present invention;
FIG. 5 is a schematic illustration of a "slab-to-round tube" coordinate map provided in accordance with an embodiment of the present invention;
FIG. 6 is a schematic illustration of fatigue crack propagation directions provided in accordance with an embodiment of the present invention;
FIG. 7 is a flow chart of a method for extracting crack front stress intensity factors and crack tip coordinates according to an embodiment of the invention;
FIG. 8 is a schematic diagram of a next incremental step fatigue crack front discrete point coordinate calculation method according to an embodiment of the present invention;
FIG. 9 is a flow chart of a crack model update method provided in accordance with an embodiment of the invention;
FIG. 10 is a comparison of fatigue crack growth rates and tests provided in accordance with an embodiment of the present invention;
FIG. 11 is a comparative graph of fatigue crack propagation paths and tests provided in accordance with an embodiment of the present invention;
FIG. 12 is a comparison of fatigue crack aspect ratio changes and tests provided in accordance with an embodiment of the present invention;
FIG. 13 is a schematic diagram of the fatigue crack final propagation results provided in accordance with an embodiment of the present invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings. The following examples are only for illustrating the technical solutions of the present invention more clearly, and the protection scope of the present invention is not limited thereby.
Example 1
Fig. 2 shows a flow chart of the present invention, which includes the following steps:
step 2, defining a crack area by using an expansion finite element method and a level set function, and enriching a unit through which a crack passes to obtain a stress intensity factor of the front edge of the crack;
step 4, establishing a high cycle fatigue crack propagation program of the corresponding node, which specifically comprises the following steps: establishing a fatigue crack propagation criterion, determining a fatigue crack propagation direction, extracting a stress intensity factor and a crack front edge coordinate, calculating a next increment step crack propagation increment, calculating a next increment step crack front edge coordinate, and updating a next increment step crack model;
and 5, implanting a high-cycle fatigue crack propagation program into a software platform for operation. And processing the simulation data to obtain a propagation rate curve of the fatigue crack of the intersecting node, comparing the result with the test, and verifying the validity of the simulation result.
Example 2
This example discloses a specific implementation on the basis of the above examples.
Specifically, the intersecting nodes of the T-shaped circular steel tubes adopt C3D8R units, the crack regions adopt C3D8 units, and the total model is 297974 grid units and 429762 grid nodes.
TABLE 1T-SHAPED ROUND STEEL TUBE INTERRUPTED JOINT COMPONENT SIZE
TABLE 2 Material Property parameters of materials used for intersecting nodes
Specifically, referring to fig. 4, the intersecting joint of the T-shaped circular steel tube is divided into five parts, which are: the joint comprises a branch pipe, a transition area 1 of a welding line and a main branch pipe, a main pipe 2, an intersection area 3 of the main pipe and the branch pipe, an initial crack 4 and a joint fixing end 5. Correspondingly, the establishment of the intersecting node model of the T-shaped circular steel tube comprises five steps: 1) obtaining transition areas of the branch pipes, the welding lines and the main branch pipes through coordinate mapping; 2) obtaining a master model through coordinate mapping; 3) obtaining a model of an intersection area of the main pipe and the branch pipe through coordinate mapping; 4) obtaining an initial crack model through coordinate mapping; 5) and establishing a fixed end model.
Specifically, referring to FIG. 5, a flat local coordinate system X-Y-Z and a circular tube local coordinate system X-Y-Z are established, R being the radius of the circular tube. The basic principle of the coordinate mapping method is as follows: firstly, establishing a flat plate model, and then converting the flat plate model into a circular tube model through coordinate mapping, wherein the formula of the coordinate mapping is as follows:
x＝Dcos(Y/D)
y＝Dsin(Y/D)
in the formula, x and y are coordinates in a local coordinate system of the circular tube; and Y is the coordinate in the local coordinate system of the flat plate. Taking D-R as the upper surface of the flat plate, namely the outer surface of the round pipe; for the lower surface of the flat plate, i.e., the inner surface of the circular tube, D-R-t is taken. And t is the plate thickness.
Furthermore, five parts of the intersecting joint of the T-shaped circular steel tube can be mapped into a tube model from a plate model by the method. Specifically, when the width of the flat plate is smaller than the circumference of the circular tube, the non-closed circular tube model obtained by the above formula can be called a curved plate model.
Furthermore, after the five parts of model building are completed, a T-shaped circular steel tube intersecting joint containing an initial crack is formed through model assembling.
And 2, defining a crack region by using an expansion finite element method and a level set function so as to obtain a stress intensity factor of the crack front.
Specifically, the application method of the extended finite element and the level set function comprises the following steps: the grid cells containing cracks are divided into three types through a level set function, namely, the cells are not penetrated by the cracks, the cells are completely penetrated by the cracks, and the cells are not completely penetrated by the cracks (namely, the cells are cracked tips). Then, for the first unit, the same displacement field calculation method as the finite element method is adopted, and for the latter two units, the displacement field needs to be corrected, and the specific expression is as follows:
in the formula (I), the compound is shown in the specification,
a displacement field in which the crack does not pass through the cell;
displacement field for the complete penetration of the crack through the cell, wherein aiH (x) is a level set function, and the calculation formula is
x is an integration point, x is a point on the crack surface nearest to the integration point, and n is a normal vector of x on the crack surface;
displacement field for incomplete penetration of the crack through the cell, biF (x) is the expansion function of the crack incomplete penetration unit under a polar coordinate system.
According to the grid unit displacement field, the stress at the integral point of each grid unit and the stress at each node of the overall grid can be obtained, the interaction J integral of the crack is obtained through the stress field, and further the stress intensity factor of the crack can be obtained.
Further, the calculation of the stress intensity factor of the crack front edge is calculated by adopting an interaction integration method, and the calculation formula is as follows:
in the formula, KI，KII，KIIIStress intensity factors corresponding to the type I cracks, the type II cracks and the type III cracks respectively; j. the design is a squareI int，JII int，JIII intRespectively, interaction J integral; and B is a logarithmic energy system matrix.
Furthermore, because the fatigue crack of the tubular steel joint is a mixed crack formed by the type I crack, the type II crack and the type III crack, an equivalent stress intensity factor needs to be calculated according to the stress intensity factor corresponding to the type I crack, the stress intensity factor corresponding to the type II crack and the stress intensity factor corresponding to the type III crack for the fatigue crack propagation criterion, and the calculation formula is as follows:
in the formula, B is an empirical parameter and is 1.0; Δ KI，ΔKII，ΔKIII，ΔKeqRespectively the stress intensity factor increment and the equivalent stress intensity factor increment corresponding to the type I crack, the type II crack and the type III crack. The calculation method of the stress intensity factor increment comprises the following steps:
ΔK＝Kmax-Kmin
in the formula KmaxThe stress intensity factor, K, obtained for the maximum value of the load under the action of a constant amplitude loadminThe stress intensity factor is obtained for the minimum load under the action of constant amplitude load.
It should be noted that the above calculation methods for the stress intensity factor and the equivalent stress intensity factor of a single discrete point at the front of the crack are the same as those for the other points.
Specifically, when the crack front stress intensity factor is calculated by the finite element propagation method, the crack front is dispersed into finite points, the stress intensity factor of each point is calculated, and the distribution condition of the stress intensity factor of the whole crack front is represented by the stress intensity factor. And the finite number of discrete points is determined by the number of grid cells passing through the crack. Thus, the number of discrete points of the crack front remains constant or increases throughout the propagation process.
And 3, applying load and boundary conditions.
Specifically, the fatigue load is a constant amplitude load, the load is applied to the end part of the branch pipe, the maximum value is 140kN, the stress ratio is 0.05, and fixed constraint is applied to the fixed ends at the two ends of the main pipe.
Step 4, establishing a high cycle fatigue crack propagation program of the corresponding node, which specifically comprises the following steps: establishing a fatigue crack propagation criterion, determining a fatigue crack propagation direction, extracting a stress intensity factor and a crack front edge coordinate, calculating a next increment step crack propagation increment, calculating a next increment step crack front edge coordinate, and updating a next increment step crack model.
Further, the fatigue crack propagation criterion adopts the Paris criterion, and the expression of the criterion is as follows:
wherein a is the crack length, N is the fatigue load cycle number, C and m are material parameters, and delta KeqIs the equivalent stress intensity factor increment. Wherein C is 2.66704 × 10-11m/circle, m is 2.75.
Further, referring to fig. 6, the fatigue crack propagation direction adopts a three-dimensional maximum circumferential stress criterion, and the criterion expression is as follows:
in the formula,. DELTA.KIeqTo account for the equivalent stress intensity factor increment for the type III stress intensity factor effect, the expression is:
ΔKIeq＝ΔKI+B|ΔKII|
in the formula, B is an empirical parameter and is 1.0.
Further, a method for extracting the stress intensity factor and the crack front coordinate is shown in the flow chart of fig. 7.
Further, the calculation method of the crack growth increment of the next increment step depends on the control method of fatigue crack growth. There are two methods of controlling fatigue crack propagation: the first is the control of the number of load cycles, and the second is the incremental control of the maximum crack propagation by using a single incremental step.
Specifically, the former is an increment step of the simulation method provided by the invention, namely, fatigue crack propagation analysis is performed once every delta N cycles of the actual load, and the stress intensity factor distribution condition of the crack front edge and the coordinates of the crack front edge discrete point of the next increment step are obtained, wherein the delta N cycles of the actual load are equivalent to the increment step of the simulation method, and the method for calculating the crack propagation increment comprises the following steps:
Δa＝C(ΔKeq)m·ΔN
the latter is that according to the stress intensity factor distribution condition of the crack front, the point spread length with the maximum stress intensity factor is defined as the maximum spread increment delta amaxThen the crack propagation increment at that point is:
Δamax＝C(ΔKeq,max)mΔN
the crack propagation increment of any point i of the crack front is as follows:
Δai＝C(ΔKeq,i)mΔN
the two calculation formulas are divided and the terms are shifted, so that the calculation formula for controlling the fatigue crack propagation through the maximum crack propagation increment of a single increment step can be obtained:
the present embodiment employs a second method for controlling crack propagation.
Furthermore, a calculation method for determining the coordinates of the crack front edge of the next increment step is needed. Assuming that a discrete point of the crack front always propagates along the normal to this point, see fig. 8. And assuming that the lower surface of the crack is a horizontal plane, and x-y-z is a global coordinate system, wherein an xy plane is coplanar with the lower surface of the crack, and a z axis is vertical to the xy plane. In crackAnd establishing a local coordinate system X-Y-Z at any point of the fringe front, wherein the X axis coincides with the normal direction of the point, the Y axis coincides with the tangential direction of the point, and the Z axis is vertical to the XY plane. While setting two straight lines x at that point*And y*Wherein x is*Parallel to the x-axis, y*Parallel to the y-axis. The calculation method of the crack front coordinate of the next increment step is as follows:
Δx＝Δa cosθ*cosα
Δy＝Δa cosθ*sinα
Δz＝Δa sinθ
further, the next incremental step crack model updating method refers to the flowchart of fig. 9.
It is noted that the above only describes the calculation method of the high cycle fatigue crack propagation of one discrete point of the crack front, and the calculation method of the remaining discrete points is the same as that.
And 5, embedding the high-cycle fatigue crack propagation program into a software platform for operation. And processing the simulation data to obtain a propagation rate curve of the fatigue crack of the intersecting node, comparing the result with the test, and verifying the validity of the simulation result.
Fig. 10 to 13 show simulation results of this example.
Specifically, the final crack model propagation result is shown in fig. 10. When the crack penetrates the wall thickness of the main pipe, the crack length 2c is 100.614mm, and the depth a is 12.212 mm. The corresponding test results are 2c 105mm and a 12 mm.
Specifically, the crack growth rate curve is shown in FIG. 11. The crack propagation rate curve obtained by the method provided by the invention is similar to the test result. It is noted that since the crack is propagated from the initial size, the number of load cycles obtained by the simulation is smaller than the actual case, and therefore the number of load cycles is corrected.
Specifically, the change in the aspect ratio of the crack during the expansion process is shown in fig. 12. In the figure, c is the half of the crack length, a is the crack depth, and T is the main pipe wall thickness. The change process of the crack aspect ratio obtained by the method provided by the invention is similar to the test result.
Specifically, the results of the propagation path of the crack at the intersecting node surface are shown in fig. 13.
Claims (10)
1. A circular steel tube intersecting node high cycle fatigue numerical simulation method based on an expanded finite element is characterized by comprising the following steps:
step 1, establishing a numerical model of the tubular steel tubular intersection node containing an initial crack in a software platform according to the mechanical property and specification size of a material used for the intersection node test piece;
step 2, defining a crack area by using an expansion finite element method and a level set function to obtain a stress intensity factor of the crack front edge, wherein the stress intensity factor calculation method comprises the following steps:
in the formula, KI，KII，KIIIStress intensity factors corresponding to the type I cracks, the type II cracks and the type III cracks respectively; j. the design is a squareI int，JII int，JIII intRespectively corresponding interaction J integrals of the type I crack, the type II crack and the type III crack; b is a logarithmic energy system matrix;
step 3, applying load and boundary conditions;
step 4, establishing a high cycle fatigue crack propagation program of the corresponding node, which specifically comprises the following steps: establishing a fatigue crack propagation criterion, determining a fatigue crack propagation direction, extracting a stress intensity factor and a crack front edge coordinate, calculating a next increment step crack propagation increment, calculating a next increment step crack front edge coordinate, and updating a next increment step crack model;
step 5, implanting a high-cycle fatigue crack propagation program into a software platform for operation; and processing the simulation data to obtain a propagation rate curve of the fatigue crack of the intersecting node, comparing the result with the test, and verifying the validity of the simulation result.
2. The method for simulating the high and low cycle fatigue of the intersecting nodes of the circular steel tube based on the extended finite element as claimed in claim 1, wherein in the step 1, a numerical model of the intersecting nodes of the circular steel tube containing the initial cracks is established in a software platform based on a coordinate mapping method.
3. The method for simulating the high-cycle fatigue numerical value of the intersecting node of the circular steel tube based on the extended finite element as claimed in claim 1, wherein in the step 2, the grid cells containing the cracks are divided into three types, namely, a crack non-passing cell, a crack complete-penetrating cell and a crack non-complete-penetrating cell through a level set function; for the first unit, the same displacement field calculation method as the finite element method is adopted, and for the latter two units, the displacement field needs to be corrected, and the specific expression is as follows:
in the formula (I), the compound is shown in the specification,
a displacement field in which the crack does not pass through the cell;
displacement field for the complete penetration of the crack through the cell, wherein aiH (x) is a level set function, and the calculation formula is
x is an integration point, x is a point on the crack surface nearest to the integration point, and n is a normal vector of x on the crack surface;
displacement field for incomplete penetration of the crack through the cell, biF (x) is an expansion function of the crack incomplete penetration unit under a polar coordinate system;
according to the grid unit displacement field, the stress at the integral point of each grid unit and the stress at each node of the overall grid can be obtained, the interaction J integral of the crack is obtained through the stress field, and further the stress intensity factor of the crack can be obtained.
4. The method for simulating the high and low cycle fatigue values of the intersecting nodes of the circular steel tube based on the extended finite element as claimed in claim 1, wherein in the step 2, since the fatigue cracks of the intersecting nodes of the circular steel tube are mixed cracks formed by type i cracks, type ii cracks and type iii cracks, the equivalent stress intensity factor is calculated according to the stress intensity factor corresponding to the type i cracks, the stress intensity factor corresponding to the type ii cracks and the stress intensity factor corresponding to the type iii cracks, and the calculation formula is as follows:
in the formula, B is an empirical parameter and is 1.0; Δ KI，ΔKII，ΔKIII，ΔKeqRespectively corresponding stress intensity factor increment and equivalent stress intensity factor increment of the I type crack, the II type crack and the III type crack; the calculation method of the stress intensity factor increment comprises the following steps:
△K＝Kmax-Kmin
in the formula KmaxThe stress intensity factor, K, obtained for the maximum value of the load under the action of a constant amplitude loadminThe stress intensity factor is obtained for the minimum load under the action of constant amplitude load.
5. The method for simulating the high and peripheral fatigue of the intersecting nodes of the circular steel tube based on the extended finite element as claimed in claim 4, wherein in the step 4, the fatigue crack extension criterion adopts Paris criterion, and the formula of the criterion is as follows:
in the formula, a is the length of a crack, N is the fatigue load cycle number, and C and m are material parameters; wherein C is 2.66704 × 10- 11m/circle, m is 2.75.
6. The method for simulating the high and peripheral fatigue numerical values of the intersecting nodes of the circular steel tube based on the extended finite element as claimed in claim 4, wherein in the step 4, the fatigue crack extension direction adopts a three-dimensional maximum peripheral stress criterion, and the criterion expression is as follows:
in the formula,. DELTA.KIeqTo account for the equivalent stress intensity factor increment for the type III stress intensity factor effect, the expression is:
△KIeq＝△KI+B|△KII|
in the formula, B is an empirical parameter and is 1.0.
7. The method for simulating the high-cycle fatigue numerical value of the intersecting node of the circular steel tube based on the extended finite element as claimed in claim 4, wherein in the step 4, the extraction method of the stress intensity factor and the crack front edge coordinate comprises the following steps: and setting output process variables, submitting job generation, generating an odb file, determining a path and a name of a result file, extracting a stress intensity factor and a crack front edge coordinate, and inputting a final result into a txt file.
8. The numerical simulation method for the high-cycle fatigue of the intersecting nodes of the circular steel tube based on the extended finite element as claimed in claim 4, wherein in the step 4, the calculation method of the crack growth increment of the next increment step depends on the control method of the fatigue crack growth; the control method of fatigue crack propagation adopts load cycle frequency control or single increment step crack maximum propagation increment control;
the load cycle number is controlled to be that fatigue crack propagation analysis is carried out once every delta N cycles of actual load, the stress intensity factor distribution condition of the crack front edge and the coordinates of the crack front edge discrete point of the next increment step are obtained, and the method for calculating the crack propagation increment comprises the following steps:
△ai＝C(△Keq,i)m△N
the maximum crack propagation increment is controlled by specifying the point with the maximum stress intensity factor as the maximum propagation increment delta a according to the stress intensity factor distribution of the crack front edgemaxThe extended increments for the remaining points are calculated according to the following formula:
9. the method for simulating the high-cycle fatigue numerical value of the intersecting node of the circular steel tube based on the extended finite element as claimed in claim 4, wherein in the step 4, the lower surface of the crack is assumed to be a horizontal plane, and x-y-z is a global coordinate system, wherein an xy plane is coplanar with the lower surface of the crack, and a z axis is perpendicular to the xy plane; establishing a local coordinate system X-Y-Z at any point of the front edge of the crack, wherein the X axis coincides with the normal direction of the point, the Y axis coincides with the tangential direction of the point, and the Z axis is vertical to the XY plane; while setting two straight lines x at that point*And y*Wherein x is*Parallel to the x-axis, y*Parallel to the y-axis; the calculation method of the crack front coordinate of the next increment step is as follows:
△x＝△acosθ*cosα
△y＝△acosθ*sinα
△z＝△asinθ。
10. the method for simulating the high-cycle fatigue numerical value of the intersecting node of the circular steel tube based on the extended finite element as claimed in claim 4, wherein in the step 4, the method for updating the next incremental step crack model comprises the following steps: and sequentially establishing an nth-step crack front two-dimensional projection model, adjusting the coordinates of the discrete points of the crack front to form a three-dimensional model, dividing grids, introducing an nth-1-step crack model, and finally combining grid nodes to form the nth-step crack model.
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| CN117649901A (en) * | 2023-11-29 | 2024-03-05 | 哈尔滨工业大学 | Interaction integration method for solving stress intensity factors of cracks of revolving body |
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| CN117649901A (en) * | 2023-11-29 | 2024-03-05 | 哈尔滨工业大学 | Interaction integration method for solving stress intensity factors of cracks of revolving body |
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