Finite element calculation method for predicting ultra-low cycle fatigue cracking of steel structure

Abstract

The invention discloses a finite element calculation method for predicting ultra-low cycle fatigue cracking of a steel structure. According to the method, an ICVGM model for predicting fatigue cracking based on a micromechanism is utilized, a USDFLD subprogram for calculating ultra-low cycle fatigue damage indexes of all units of the model in real time in the finite element analysis process is established, the cracking state of the units is judged and marked, and finally the cracked units are deleted by utilizing the unit deletion function of the USDFLD. And simulation of ultralow-cycle fatigue cracking opportunity, position and post-cracking performance is realized. According to the method, parameters such as stress three-axis degree and equivalent plastic strain are calculated, a cyclic hole expansion index and a critical hole index are updated, and finally cracking judgment is achieved. The method is suitable for steel structure fatigue analysis under extreme load conditions of earthquake engineering and the like, has relatively high calculation precision and efficiency, and is widely applied to engineering structure safety assessment and material performance research.

Description

Technical Field

[0001] The present invention relates to a computer simulation method, and in particular to a finite element calculation method for calculating the timing, location and post-crack performance of ultra-low cycle fatigue cracking of a steel structure. Background Art

[0002] Ultra-Low Cycle Fatigue (ULCF) of steel refers to the fatigue failure phenomenon that occurs in steel within a very small number of cycles (usually less than 100 times), mainly occurring under conditions of large plastic strain. Unlike traditional low-cycle fatigue and high-cycle fatigue, the failure mechanism of ultra-low cycle fatigue involves plastic strain accumulation and damage evolution, and the cracks show ductile fracture characteristics. It is common when steel structures are subjected to short-term, large-amplitude cyclic loads such as earthquakes. Currently, the ultra-low cycle fatigue performance of steel can be evaluated and predicted through experimental methods, theoretical models and numerical simulations. In earthquake engineering and extreme environmental loads, the study of ultra-low cycle fatigue is of great significance to ensuring structural safety.

[0003] Among existing ultra-low-cycle fatigue life prediction models, the improved cyclic void growth model (ICVGM), based on microscopic mechanisms, has been shown to have high prediction accuracy and is widely used in scientific research. This model, developed from the void growth and aggregation fracture mechanism of ductile fracture, calculates the accumulated plastic strain of the material to determine the microscopic void growth index within the material. When this index reaches a critical value, cracking is determined. However, the current application of this model is limited to small steel specimens with simple geometric configurations. No computational method is currently available for predicting ultra-low-cycle fatigue cracking in larger steel structures.

[0004] Therefore, a simple, convenient and sufficiently accurate calculation method is needed to intuitively show the location and timing of ultra-low cycle fatigue cracking that may occur in steel structures under high-strain cyclic loads. Summary of the Invention

[0005] Purpose of the invention: To solve the problem in the prior art of the lack of suitable calculation methods in the calculation of ultra-low cycle fatigue problems of large-sized steel structures, and the inability to determine the cracking location, timing and post-crack performance, the present invention provides a finite element calculation method for predicting ultra-low cycle fatigue cracking of steel structures, and proposes a subroutine that can calculate the ultra-low cycle fatigue damage index of the ABAQUS finite element solid unit model based on the ICVGM model, and perform unit cracking judgment and status marking. The method calculates the damage index of each unit through the USDFLD user subroutine, and determines that the unit is in a cracked state when the damage index reaches a critical value. The damage index is calculated based on material response parameters such as stress invariant and equivalent plastic strain through a specific formula. This method simplifies the cracking judgment process and improves calculation efficiency while ensuring improved calculation accuracy.

[0006] Technical solution: The finite element calculation method for predicting ultra-low cycle fatigue cracking of steel structures described in the present invention utilizes the ICVGM model for predicting fatigue cracking based on microscopic mechanisms, establishes a USDFLD subroutine for real-time calculation of the ultra-low cycle fatigue damage index of each unit of the model during the finite element analysis process, judges and marks the cracking status of the unit, and finally utilizes the unit deletion function of USDFLD to delete the cracked unit, thereby realizing the simulation of the timing, location and post-crack performance of ultra-low cycle fatigue cracking.

[0007] Furthermore, the USDFLD subroutine implements the following process:

[0008] (1) Obtain the stress invariant and equivalent plastic strain of the element and calculate the stress triaxiality;

[0009] (2) Update the cyclic void expansion index and critical void index based on stress triaxiality and equivalent plastic strain;

[0010] (3) Calculate the damage index and determine whether it reaches the critical value;

[0011] (4) When the damage index reaches a critical value, the unit is marked as failed;

[0012] (5) Determination of whether the crack is through-going or not;

[0013] (6) Delete the failed unit through the unit deletion function.

[0014] Furthermore, the calculation formula of the cyclic hole expansion index is:

[0015]

[0016] Where T is stress triaxiality:

[0017]

[0018] Where σ m and σ e are the hydrostatic stress and Von Mises stress, respectively, which are expressed as follows, where σ1, σ2 and σ are the first, second and third principal stresses, respectively.

[0019]

[0020] is the equivalent plastic strain.

[0021] Furthermore, the calculation formula of the critical hole index is:

[0022]

[0023] Where λ is a material-related parameter and η is the critical void growth index, which is related to the material properties and can be measured experimentally. p accumulate is the accumulated equivalent plastic strain before the most recent tensile deformation, and only the equivalent plastic strain accumulation in the compression cycle is considered.

[0024] The damage indicators are:

[0025]

[0026] Furthermore, the method uses the built-in unit deletion function of the USDFLD subroutine to achieve unit deletion, and the specific settings are as follows:

[0027] A. In the user subroutine, the damage index and cracking flag are stored through the state variable (STATEV).

[0028] Specifically include:

[0029] STATEV(6) stores the current damage value;

[0030] STATEV(7) stores the cracking flag (1 for uncracked, 0 for cracked);

[0031] STATEV(8) is used to determine whether the crack of the shell element is through (1 means no crack or the crack is not through, 0 means cracked and the crack is through)

[0032] B. Add material behavior "non-independent variable" in the material properties, and the subroutine will automatically determine whether cracking occurs based on the value of STATEV(8).

[0033] Compared with the prior art, the present invention has the following beneficial effects:

[0034] 1. This method aims to solve the problem of predicting the cracking location, timing and post-crack performance of large-scale steel structures under ultra-low cycle fatigue (ULCF) conditions. Based on the improved cyclic void expansion model (ICVGM) and combined with ABAQUS finite element analysis software, a unit cracking judgment and deletion method is proposed. This method uses the USDFLD user subroutine to calculate the damage index of the unit, and marks the unit as a failure state when the damage index reaches a critical value, and then simulates the structural performance after cracking through the unit deletion function. This method updates the cyclic void expansion index and critical void index by calculating parameters such as stress triaxiality and equivalent plastic strain, and finally realizes cracking judgment. The present invention is suitable for fatigue analysis of steel structures under extreme load conditions such as earthquake engineering. It has high calculation accuracy and efficiency and is widely used in engineering structure safety assessment and material performance research.

[0035] 2. In the present invention's method for determining and deleting element cracking based on fatigue damage indicators in the ICVGM model, a user subroutine enables precise simulation of element damage evolution, enabling accurate prediction of the location and timing of ultra-low-cycle fatigue cracking in solid element finite element model analysis. By determining damage indicators and marking element status, the ABAQUS element deletion function automatically deletes failed elements, achieving a simple and feasible simulation of the model's post-crack performance. This invention has broad application prospects in fields such as engineering structure analysis and material performance research. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 Flowchart of the subroutine of the present invention;

[0037] Figure 2 is a schematic diagram of the example model;

[0038] Figure 3 This is a schematic diagram of the loading position of the example model;

[0039] Figure 4 The loading scheme for the instance model;

[0040] Figure 5 is the damage index cloud map of the example model;

[0041] Figure 6 This is the effect of element deletion after the instance model is cracked;

[0042] Figure 7 The fatigue damage index of the horizontal reaction force at the pier top and the failure position unit at the pier bottom of the model changes with the loading history. DETAILED DESCRIPTION

[0043] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be further described below.

[0044] The subroutine of the present invention is implemented based on the user subroutine interface USDFLD of the finite element analysis software ABAQUS, and is used to calculate the unit damage index and determine whether the unit is cracked. The overall structure of the subroutine includes the following parts:

[0045] (1) Obtain the stress invariant and equivalent plastic strain of the element and calculate the stress triaxiality;

[0046] (2) Update the cyclic void expansion index and critical void index based on stress triaxiality and equivalent plastic strain;

[0047] (3) Calculate the damage index and determine whether it reaches the critical value;

[0048] (4) When the damage index reaches a critical value, the unit is marked as failed;

[0049] (5) Delete failed elements through the element deletion function of the finite element software.

[0050] Attachment Figure 1 This is a flowchart of the subroutine of this embodiment, which shows the damage index calculation and cracking judgment logic performed by the subroutine for a specific unit of the ABAQUS finite element solid unit model.

[0051] The implementation steps of the subroutine are as follows:

[0052] S 1. Calculate stress triaxiality and equivalent plastic strain. Use the GETVRM function in the finite element software to obtain the stress invariant (SINV) and equivalent plastic strain (PE) of the current element. Stress triaxiality is calculated as the ratio of the first stress invariant (ARRAY(1)) to the third stress invariant (ARRAY(3)). The result is stored in the intermediate variable XNEWVAL(1). The equivalent plastic strain is stored in the intermediate variable XNEWVAL(2).

[0053] S2. Update the cyclic hole expansion index. Define the state variable STATEV(4) and the intermediate variable XNEWVAL(4) as the cyclic hole expansion index at the end of the previous increment and the end of the current increment, respectively. XNEWVAL(4) will refer to the calculation formula of the cyclic hole expansion index and superimpose the exponential change of the current increment on STATEV(4). Among them, the conditional statement will distinguish the superposition method of the change according to the positive or negative value of the current stress triaxiality XNEWVAL(1). If XNEWVAL(1) is positive, the change is added, and if it is negative, the change is subtracted. Finally, XNEWVAL(4) is updated to STATEV(4).

[0054] S3. Update the critical void index. Determine the sign of stress triaxiality XNEWVAL(1). If it is positive, it means the unit is in tension; if it is negative, it means it is in compression. When the unit is in tension, update the state variable STATEV(3) to XNEWVAKL(3), indicating that the cumulative equivalent plastic strain is not increased, where the state variable STATEV(3) is the cumulative equivalent plastic strain of the compression cycle during the previous incremental step; when the unit is in compression, let XNEWVAL(3) = STATEV(3) + XNEWVAL(2) - STATEV(2), indicating that the cumulative equivalent plastic strain is increased. Where STATEV(3) is the cumulative equivalent plastic strain after the end of the previous incremental step, and XNEWVAL(2) and STATEV(2) are the equivalent plastic strains after the end of this incremental step and the previous incremental step, respectively. Subsequently, according to the calculation formula of the critical void index, update the critical void index and store it in the state variable STATEV(5). At the same time, the stress triaxiality, equivalent plastic strain and cumulative equivalent plastic strain calculated in the current incremental step are updated and stored in STATEV(1), STATEV(2) and STATEV(3) respectively.

[0055] S4. Calculate the damage index. Divide STATEV(4) by STATEV(5) to obtain the damage index and assign it to STATEV(6).

[0056] S5. Crack determination and unit status mark. Determine the size of the damage indicator STATEV(6) and 1. If it is greater than 1, set STATEV(7) = 0; otherwise, set STATEV(7) = 1. STATEV(7) is the unit status mark, 1 indicates no crack, and 0 indicates crack.

[0057] S6. Determination of whether the crack is through (applicable to shell element models). If STATEV(7) of a certain integration point of the shell element is marked as 0, determine whether the integration point is the last layer in the direction of the expected crack through. If so, set the state variable STATEV(8) = 0, indicating that the element has cracked and the crack is through. Otherwise, set STATEV(8) = 1, indicating that the element has not cracked or the crack is not through.

[0058] S7. Cell deletion: When STATEV(8) = 0, the cell is deleted directly by the built-in cell deletion function of USDFLD.

[0059] in,

[0060] STATEV(1) is the stress triaxiality.

[0061] STATEV(2) is the accumulated equivalent plastic strain.

[0062] STATEV(3) is the accumulated equivalent plastic strain of the compression cycle.

[0063] STATEV(4) is the cyclic hole expansion index.

[0064] STATEV(5) is the critical exponent of the cyclic hole expansion index.

[0065] STATEV(6) is the ultra-low cycle fatigue damage index, which is the ratio of STATEV(4) to STATEV(5).

[0066] STATEV(7) is the unit status flag, 1 means uncracked, 0 means cracked.

[0067] STATEV(8) is a mark for judging whether the shell element crack is through-through, 1 means no through-through, and 0 means through-through.

[0068] Hereinafter, this method will be described in detail with reference to a specific embodiment.

[0069] This example uses the simulation of a scaled model of a steel tube concrete pier member as an example. Figure 2 shown.

[0070] First, the target model is meshed and multiple finite element meshes are formed for the target model. A mechanical finite element model is established based on the meshed geometric model. Mechanical material parameters and load boundaries are set for the mechanical finite element model to perform mechanical analysis. The mechanical material parameters include elastic modulus, Poisson's ratio, and yield strength. The load boundaries include force loads and displacement loads, which are usually cyclic reciprocating loads. Generally, the maximum strain of the model during the loading process must reach 1% or more. The load loading position of this example is shown in Figure 3 , vertical constant force load and horizontal displacement load are applied to the top of the steel pipe pier to simulate earthquake action. Figure 4 , which is a constant amplitude reciprocating cyclic loading method.

[0071] Before the mechanical analysis begins, select the for file of the subroutine described in the present invention on the job editing page, and check the "State / Field / User / Time" option on the "Field Variable Output" editing page so that the final result file can output the state variable STATEV (1~8) and display it in the cloud chart.

[0072] After the mechanical analysis is completed, in the "ODB" result file, display the result cloud map in the "Visualization" module, and check "SDV6" in the output variable selection box above to display the fatigue damage index of the model unit in the cloud map, such as Figure 5 When the element fatigue damage index reaches or exceeds 1, the element will be deleted, as shown in Figure 6 shown.

[0073] Figure 7 The following diagram shows the changes in the horizontal reaction force at the top of the pier and the fatigue damage index of the model element at the pier base during loading. At step time 1.75, the element damage index reaches 1 for the first time, indicating cracking. At this point, the horizontal reaction force at the top of the pier drops significantly, indicating that the subroutine successfully deleted the element and simulated the decrease in the model's horizontal bearing capacity after cracking.

[0074] Finally, it should be noted that the above examples are intended only to illustrate the technical solution of the present invention and are not intended to limit it. Those skilled in the art will understand that the method described herein can be used to replace the example model with any steel structure model and, by applying sufficient reciprocating loads, achieve the functions described herein.

[0075] The above description is merely a preferred embodiment of the present invention and does not limit the present invention in any way. Any person skilled in the art who, without departing from the scope of the present invention, makes any equivalent substitution, modification, or other changes to the technical solution and technical content disclosed in the present invention shall be deemed to be within the scope of the present invention and still fall within the scope of protection of the present invention.

Claims

1. A finite element calculation method for predicting ultra-low cycle fatigue cracking of steel structures, characterized by: Using the ICVGM model for predicting fatigue cracking based on microscopic mechanisms, a USDFLD subroutine was established to calculate the ultra-low cycle fatigue damage index of each unit in the model in real time during the finite element analysis process. The cracking status of the unit was determined and marked. Finally, the unit deletion function of USDFLD was used to delete the cracked unit, realizing the simulation of the ultra-low cycle fatigue cracking timing, location and post-crack performance.

2. The finite element calculation method for predicting ultra-low cycle fatigue cracking of steel structures according to claim 1 is characterized in that: The implementation process of the USDFLD subroutine: (1) Obtain the stress invariant and equivalent plastic strain of the element and calculate the stress triaxiality; (2) Update the cyclic void expansion index and critical void index based on stress triaxiality and equivalent plastic strain; (3) Calculate the damage index and determine whether it reaches the critical value; (4) When the damage index reaches a critical value, the unit is marked as failed; (5) Determination of whether the crack is through-going or not; (6) Delete the failed unit through the unit deletion function.

3. The finite element calculation method for predicting ultra-low cycle fatigue cracking of steel structures according to claim 2, characterized in that: The cyclic hole expansion index is: Where T is stress triaxiality: Where, σ m and σ e are the hydrostatic stress and Von Mises stress, respectively, which are expressed as follows, where σ1, σ2 and σ are the first, second and third principal stresses, respectively. is the equivalent plastic strain.

4. The finite element calculation method for predicting ultra-low cycle fatigue cracking of steel structures according to claim 2 is characterized in that: The critical hole expansion index is: Where λ is a material-related parameter, η is the critical void growth index, which is related to the material properties and can be measured by experiment, and D = ε p accumulate is the accumulated equivalent plastic strain before the most recent tensile deformation, and only the equivalent plastic strain accumulation in the compression cycle is considered.

5. The finite element calculation method for predicting ultra-low cycle fatigue cracking of steel structures according to claim 2, characterized in that: The damage indicators are:

6. The finite element calculation method for predicting ultra-low cycle fatigue cracking of steel structures according to claim 2, characterized in that: The specific settings for deleting invalid units using the unit deletion function are as follows: A. In the user subroutine, the damage index and cracking flag are stored through the state variable (STATEV), including: STATEV(6) stores the current damage value; STATEV(7) stores the cracking flag, 1 indicates no cracking, 0 indicates cracking; STATEV(8) is used to determine whether the crack of the shell element is through-going. 1 means no crack or the crack is not through-going, and 0 means cracked and the crack is through-going. B. Add material behavior as a non-independent variable in the material properties. The subroutine will automatically determine whether cracking occurs based on the value of STATEV(8).

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