Ingot mold crack stress field calculation method based on finite element calculation

Abstract

The invention relates to an ingot mold crack stress field calculation method based on finite element calculation, belongs to the technical field of numerical simulation in a metal casting process, and solves the problems that when an existing method is used for simulating ingot mold cracks, a simulation result has deviation from an actual situation, and the accuracy is not high. Comprising the following steps: establishing a casting system three-dimensional geometric model with crack features for finite element calculation; exporting an x-t format file from the model, importing the x-t format file into casting simulation software, carrying out non-uniform finite element grid division to obtain a finite element grid file, carrying out parameter setting on the finite element grid file, and executing stress field calculation; the parameter setting comprises material parameters, initial conditions, interface heat exchange conditions, boundary conditions and calculation parameters; the boundary conditions comprise displacement boundary condition setting, and the displacement boundary condition setting is that displacement constraint in the gravity direction is applied to all areas of the bottom face of the steel ingot mold chassis and the bottom face of the steel ingot in the model, and the translation freedom degree in the gravity direction is limited to be 0.

Description

Technical Field

[0001] This invention relates to the field of numerical simulation technology for metal casting processes, and in particular to a method for calculating the stress field of cracks in steel ingot molds based on finite element analysis. Background Technology

[0002] The ingot mold is a key tool in the steel ingot casting process. Under the long-term exposure to severe cyclic thermal shock, mechanical friction, and phase transformation stress, its inner surface is prone to developing a network of microcracks, also known as "crazing". These cracks can reduce the service life of the ingot mold, affect the surface quality of the steel ingot, and even lead to serious accidents such as steel leakage.

[0003] Currently, the industry commonly uses general-purpose casting simulation software such as ProCAST and Magma to calculate the temperature and stress fields during the casting process, predict deformation or cracking, and optimize the process. However, existing technologies have the following limitations:

[0004] Coarse Modeling: Existing simulations typically perform macroscopic stress analysis on the complete ingot-mold system, failing to incorporate actual crack features into the geometric model and ignoring the geometric discontinuities of the cracks. This results in an inability to accurately capture the stress concentration effect in the crack region. Inappropriate Mesh Generation: Using a uniform fine mesh across the entire model leads to extremely high computational costs and low efficiency; conversely, using a uniform coarse mesh fails to achieve sufficient accuracy in the crack region. Empirical Constraint Setting: The setting of boundary conditions (especially displacement constraints) significantly impacts the stress field results. Existing methods lack specific constraint strategies for crack stress analysis, often employing local point or surface constraints. This leads to distortions in macroscopic displacement and local contact between models, such as unreasonable ingot floating or excessively large gaps, severely affecting the accuracy of the stress state at the crack.

[0005] Therefore, there is an urgent need in this field for a stress field calculation method that can perform refined modeling, efficient mesh generation, and accurate displacement constraints on the cracks in steel ingot molds, so as to improve the reliability of simulation results and their guiding value for actual production. Summary of the Invention

[0006] In view of the above analysis, the present invention aims to provide a stress field calculation method for ingot mold cracks based on finite element method, in order to solve the problem that existing methods are mostly focused on macroscopic modeling and simulation of steel ingots and ingot molds, lacking refined modeling and constraint optimization strategies for the characteristics of ingot mold cracks. As a result, when existing methods are used to simulate ingot mold cracks, the simulation results deviate from the actual situation, the accuracy is not high, and it is difficult to guide actual production.

[0007] The objective of this invention is mainly achieved through the following technical solutions:

[0008] This invention provides a method for calculating the stress field of cracks in steel ingot molds based on finite element analysis, comprising the following steps:

[0009] S1: Establish a three-dimensional geometric model of the casting system with crack features for finite element calculation;

[0010] S2: Export the three-dimensional geometric model of the casting system as an .xt format file, import it into the casting simulation software, perform non-uniform finite element mesh generation, and obtain the finite element mesh file;

[0011] S3: Set parameters for the finite element mesh file and perform stress field calculation;

[0012] The parameter settings include material parameters, initial conditions, interfacial heat transfer conditions, boundary conditions, and calculation parameters;

[0013] The boundary conditions include displacement boundary conditions, which are set to apply displacement constraints in the direction of gravity to the entire area of ​​the bottom surface of the ingot mold base and the entire area of ​​the bottom surface of the ingot in the three-dimensional geometric model of the casting system, restricting its translational degree of freedom in the direction of gravity to 0.

[0014] Further, step S1 includes:

[0015] S11: Based on the axisymmetric structure and volume of the actual casting system, take one symmetric period of the actual casting system to establish the first basic model. The basic model includes a steel ingot without crack features, a steel ingot mold, a heat insulation layer, and a heat-generating covering agent, which serve as the geometric carrier for the subsequent introduction of cracks.

[0016] S12: By observing and measuring the morphology of the inner surface of the steel ingot mold after actual use, the distribution and size data of the cracks are obtained, and the data are statistically analyzed to determine the characteristic parameters of the key cracks used for modeling.

[0017] S13: Select one maximum longitudinal crack and three maximum transverse cracks as the modeling objects, and simplify them into standard triangular sections. The three transverse cracks should be located in the upper, middle and lower feature areas of the inner surface of the steel ingot mold, respectively.

[0018] S14: Based on the determined width and depth of one maximum longitudinal crack and three maximum transverse cracks, determine whether to enlarge to 10mm during modeling;

[0019] S15: On the inner surface of the ingot mold of the first basic model, based on the determined position and size of one maximum longitudinal crack and three maximum transverse cracks, grooves with triangular cross sections are respectively established, called "crack grooves", to obtain the second basic model;

[0020] S16: On the outer surface of the steel ingot in the second basic model, a protrusion with a triangular cross section that corresponds completely to all the crack grooves in terms of position, shape and size is established. This protrusion is called a "crack protrusion". The model obtained after establishing the "crack grooves" and "crack protrusions" is the three-dimensional geometric model of the casting system with crack features for finite element calculation.

[0021] Further, in step S12, the key cracks used for modeling include the largest longitudinal crack and the largest transverse crack. The characteristic parameters of the largest longitudinal crack include the width W1, depth D1, length L1 of the largest longitudinal crack and its position on the inner surface of the ingot mold; the characteristic parameters of the largest transverse crack include the width W2, depth D2, length L2 of the largest transverse crack and its position on the inner surface of the ingot mold.

[0022] Furthermore, in step S14, if the width and depth of the maximum longitudinal crack and the three maximum transverse cracks are ≥10mm, then the dimensions of the maximum longitudinal crack and the three maximum transverse cracks remain unchanged during modeling.

[0023] If the width and depth of the largest longitudinal crack and the three largest transverse cracks are less than 10 mm, then the size of the largest longitudinal crack and the three largest transverse cracks will be enlarged to 10 mm during modeling.

[0024] Further, in step S2, the non-uniform finite element mesh generation includes:

[0025] The mesh size of the "crack groove" and "crack protrusion" areas is 2-5mm;

[0026] In the three-dimensional geometric model of the casting system, the local areas with smaller dimensions have a mesh size of 10-20mm. These local areas with smaller dimensions include chamfers, steps, and edge regions.

[0027] The three-dimensional geometric model of the casting system includes areas for the ingot mold, ingot, and other components, with a grid size of 10-60mm. Other components include insulation layers and heat-generating coverings.

[0028] The casting simulation software automatically generates transition meshes between meshes of different sizes.

[0029] Furthermore, in step S3, the setting of the initial conditions includes:

[0030] The initial temperature of the steel ingot is the casting temperature, the filling state is either empty or full, and the stress model is an "elastoplastic model".

[0031] The initial temperature of the steel ingot mold is the baking temperature, the filling state is the full state, and the stress model is the "elastoplastic model";

[0032] The initial temperature of all components except the steel ingot and the steel ingot mold is the baking temperature, the filling state is the full state, and the stress model is the "rigid model".

[0033] Further, in step S3, the setting of the interface heat exchange conditions includes:

[0034] The heat transfer coefficient at the ingot-mold interface is set as a function of temperature or time, or as an equivalent constant.

[0035] The heat transfer coefficients at the interfaces of steel ingot-insulation layer and steel ingot-heating covering agent are set to constants.

[0036] Furthermore, the calculation parameters include calculation step size, stopping condition, and saving frequency;

[0037] The setting of the calculation step size includes:

[0038] In the initial stage of solidification, the calculation step is 5-10 seconds, where the initial stage of solidification refers to the simulated solidification amount of the steel ingot in the three-dimensional geometric model of the casting system being 0-50%.

[0039] During the middle stage of solidification, the calculation step is 10-60s, where the middle stage of solidification refers to the simulated solidification amount of the steel ingot in the three-dimensional geometric model of the casting system being 50-80%.

[0040] In the later stage of solidification, the calculation step is 60-100s, where the later stage of solidification refers to the simulated solidification amount of the steel ingot in the three-dimensional geometric model of the casting system being 80-100%.

[0041] Furthermore, the stopping condition is: the temperature of all molten steel units in the three-dimensional geometric model of the casting system drops to 10°C below the solidus temperature of the steel ingot material.

[0042] Furthermore, the storage frequency is 60-120 seconds.

[0043] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects:

[0044] 1. This invention provides a modeling method for surface cracks in steel ingot molds, helping designers improve modeling efficiency.

[0045] 2. This invention provides a mesh generation method and a constraint setting method for stress field calculation of cracks on the surface of steel ingot molds. This can improve the accuracy of stress field calculation results for cracks on the surface of steel ingot molds, and the simulation results are closer to reality, which helps in the optimization of steel ingot mold structure and life prediction.

[0046] In this invention, the above-described technical solutions can be combined with each other to achieve more preferred combinations. Other features and advantages of this invention will be set forth in the following description, and some advantages may become apparent from the description or be learned by practicing the invention. The objects and other advantages of this invention can be realized and obtained from what is particularly pointed out in the description and drawings. Attached Figure Description

[0047] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts.

[0048] Figure 1 The example shows the inner surface of a steel ingot mold after actual use of a certain type of steel ingot;

[0049] Figure 2 A schematic diagram of the overall appearance of the cracked grooves on the inner surface of the ingot mold in the three-dimensional geometric model of the casting system with cracked features established for the example;

[0050] Figure 3 A schematic diagram of the overall appearance of the crack protrusions on the outer surface of the steel ingot in a three-dimensional geometric model of a casting system with crack features established for an example.

[0051] Figure 4 The heat transfer coefficient at the steel ingot-steel ingot mold interface in this embodiment is a curve showing how it changes with temperature.

[0052] Figure 5 This is a schematic diagram of displacement constraints in the embodiment;

[0053] Figure 6 This is a schematic diagram of displacement constraints in Comparative Example 1;

[0054] Figure 7a This is a schematic diagram illustrating the displacement of the steel ingot and steel ingot mold in the direction of gravity, as shown in the embodiment.

[0055] Figure 7b This is a schematic diagram showing the displacement of the steel ingot and steel ingot mold in the direction of gravity for Comparative Example 1.

[0056] Figure 8a This is a schematic diagram showing the air gap between the steel ingot and the steel ingot mold in an embodiment.

[0057] Figure 8b This is a schematic diagram showing the air gap between the steel ingot and the steel ingot mold in Comparative Example 1.

[0058] Figure 9a This is a stress variation diagram of the transverse crack in the middle of the example model;

[0059] Figure 9b The stress variation diagram is shown for the transverse crack in the middle of the model in Comparative Example 1.

[0060] Figure 10 This is a schematic diagram showing the stress conditions on the outer surface of the steel ingot in the examples and Comparative Example 1.

[0061] Figure 11 This is a schematic diagram showing the stress conditions on the inner surface of the steel ingot mold in the embodiments and Comparative Example 1.

[0062] Figure 12a This is a schematic diagram of the temperature field on the inner surface of the steel ingot mold in an embodiment.

[0063] Figure 12b This is a schematic diagram of the temperature field on the inner surface of the steel ingot mold in Comparative Example 1.

[0064] Figure 13 This is a schematic diagram showing the temperature at sampling points on the inner surface of the steel ingot mold in both the embodiment and Comparative Example 1.

[0065] Figure 14a This is an actual steel ingot mold base after multiple uses in the embodiment;

[0066] Figure 14b This is the lower half of the steel ingot during demolding in the example embodiment;

[0067] Figure 15 Comparative images of the mesh morphology of the "crack groove" and "crack protrusion" regions in Examples 1, 2, and 3 are shown.

[0068] Figure 16 This is a comparison chart showing the calculated stress field results of the steel ingot and steel ingot mold surfaces for Examples 1, 2, and 3. Detailed Implementation

[0069] Preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which form part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not intended to limit the scope of the present invention.

[0070] This invention provides a method for calculating the stress field of cracks in steel ingot molds based on finite element analysis, comprising the following steps:

[0071] S1: Establish a three-dimensional geometric model of the casting system with crack features for finite element calculation;

[0072] Specifically, step S1 includes:

[0073] S11: Based on the axisymmetric structure and volume of the actual casting system, a first basic model is established by taking one symmetric period of the actual casting system. The basic model includes components such as steel ingots without crack features, steel ingot molds, insulation layers, and heat-generating covering agents, which serve as the geometric carrier for the subsequent introduction of cracks.

[0074] It should be noted that the actual casting system is an axisymmetric structure. In practice, to improve computational efficiency, it is not necessary to establish a complete three-dimensional geometric model of the casting system. Instead, based on its axisymmetric structural characteristics and volume, a partial model with a symmetrical period is directly established, which is referred to as the first basic model. For example, for a casting system with 24 edges, a 1 / 24 model is directly established; for a casting system with 8 or 16 edges, a 1 / 8 model and a 1 / 16 model are established accordingly. The first basic model includes components such as the steel ingot and ingot mold without crack features, the insulation layer, and the heat-generating covering agent, which serve as the geometric carrier for subsequently introducing crack features.

[0075] S12: By observing and measuring the morphology of the inner surface of the steel ingot mold after actual use, the distribution and size data of the cracks are obtained, and the data are statistically analyzed to determine the characteristic parameters of the key cracks used for modeling.

[0076] The key cracks used for modeling include the largest longitudinal crack and the largest transverse crack. The characteristic parameters of the largest longitudinal crack include the width W1, depth D1, length L1 and its position on the inner surface of the ingot mold. The characteristic parameters of the largest transverse crack include the width W2, depth D2, length L2 and its position on the inner surface of the ingot mold.

[0077] S13: Select one maximum longitudinal crack and three maximum transverse cracks as the modeling objects, and simplify them into standard triangular sections. The three transverse cracks should be located in the upper, middle and lower feature areas of the inner surface of the steel ingot mold, respectively.

[0078] It should be noted that, in order to facilitate finite element mesh generation and ensure computational stability, the complex cross-sectional shapes of all the selected cracks are simplified to standard triangular cross-sections. This simplification is based on observations of a large number of actual crack morphologies, and the triangular profile can effectively characterize the stress field of the crack.

[0079] S14: Based on the determined width and depth of one maximum longitudinal crack and three maximum transverse cracks, determine whether to enlarge to 10mm during modeling;

[0080] It should be noted that, in order to solve the mesh generation problem caused by the huge difference between the actual crack size (millimeter level) and the steel ingot mold size (meter level), this invention can adaptively enlarge the crack size. If the original width and depth of the crack are ≥10mm, the size remains unchanged during modeling; if the original width and depth of the crack are <10mm, the width and depth are enlarged to 10mm during modeling while keeping the length unchanged. This operation can ensure that a sufficient number of high-quality meshes can be generated in the crack area, thereby controlling the total number of meshes in the model within a computable range while ensuring computational accuracy.

[0081] S15: On the inner surface of the ingot mold of the first basic model, based on the determined position and size of one maximum longitudinal crack and three maximum transverse cracks, grooves with triangular cross sections are respectively established, called "crack grooves", to obtain the second basic model;

[0082] S16: On the outer surface of the steel ingot in the second basic model, a protrusion with a triangular cross section that corresponds completely to all the crack grooves in terms of position, shape and size is established. This protrusion is called a "crack protrusion". The model obtained after establishing the "crack grooves" and "crack protrusions" is the three-dimensional geometric model of the casting system with crack features for finite element calculation.

[0083] It should be noted that the assembly structure of "crack groove" and "crack protrusion" is the key to accurately simulating the complex mechanical interactions such as contact and interference between the steel ingot and the steel ingot mold in the crack area during the casting process.

[0084] S2: Export the three-dimensional geometric model of the casting system as an .xt format file, import it into the casting simulation software, perform non-uniform finite element mesh generation, and obtain the finite element mesh file;

[0085] The casting simulation software can be ProCAST. This invention employs a non-uniform mesh generation method for the three-dimensional geometric model of the casting system: a smaller mesh size (approximately 2-5 mm) is set for all "crack grooves" and "crack protrusions" to ensure that the crack feature areas are distributed across at least three mesh layers; a smaller mesh size (approximately 10-20 mm) is set for smaller local feature areas, such as chamfers, steps, and edges; and a relatively larger mesh size (approximately 10-60 mm) is set for other areas besides the crack feature areas and smaller local feature areas, such as ingot molds, ingots, and other components. Simultaneously, after setting the size, one-click automatic mesh generation is performed. During the generation process, the software automatically generates transition meshes between fine and coarse mesh areas, thereby ensuring the calculation accuracy of critical areas while keeping the total number of meshes in the entire model within a calculable range, achieving a balance between accuracy and efficiency.

[0086] S3: Set parameters for the finite element mesh file and perform stress field calculation;

[0087] Specifically, parameter settings include material parameters, initial conditions, interfacial heat transfer conditions, boundary conditions, and calculation parameters;

[0088] Material parameters: Based on the actual casting process, set the corresponding material parameters for each component of the three-dimensional geometric model of the casting system; the material parameters of the steel ingot and steel ingot mold (such as thermal conductivity, specific heat, density, solidity, elastic modulus, Poisson's ratio, coefficient of thermal expansion, etc.) can be obtained through the built-in thermal property calculation module of the software, or input through experimental measurement.

[0089] Initial conditions: Initial conditions are used to define the physical state of the three-dimensional geometric model of the casting system at the start of the calculation (i.e., t=0);

[0090] The initial temperature of the steel ingot is the pouring temperature, and the filling state is set to either empty or full. The stress model is selected as "elastoplastic model". The pouring temperature is determined according to the actual casting process specifications, generally specified as 50-80℃ above the liquidus temperature of the steel ingot material. If the filling process is calculated, the filling state is set to empty; otherwise, the filling state is selected as full. According to the actual physical process, after the molten steel is poured into the ingot mold, it will undergo different stages as the temperature decreases. The stress model of the steel ingot should also be set in stages: Newtonian fluid behavior in the liquid stage, viscoplastic behavior in the early solidification stage, elastoplastic behavior in the late solidification stage, and elastoplastic behavior in the solid cooling stage. However, in ProCAST software, only one stress model can be selected for calculation from beginning to end, and it is not possible to set it in stages. Using the elastoplastic model is closer to the actual situation and provides reliable results for predicting residual stress, deformation, and hot cracking. Therefore, the stress model of the steel ingot is selected as "elastoplastic model".

[0091] The initial temperature of the ingot mold is the baking temperature, and it is set to a full state. The stress model selected is the "elastoplastic model". Baking refers to the preheating of the ingot mold in a baking machine before use to remove moisture. The baking temperature is determined according to the actual production process, and for example, it can be a specific value within the range of 50℃-300℃ (such as 60℃, 70℃, 80℃, 90℃, 100℃, 110℃, 120℃, 130℃, 140℃, 150℃, 160℃, 170℃, 180℃, 190℃, 200℃, 210℃, 220℃, 230℃, 240℃, 250℃, 260℃, 270℃, 280℃, 290℃). According to the actual physical process, when molten steel is poured into the ingot mold, the ingot mold will be heated and undergo plastic deformation. Selecting the elastoplastic model can truly reflect its mechanical behavior and predict the residual stress of the ingot mold itself and its thermal fatigue life under long-term use. Therefore, the stress model for the steel ingot mold is chosen to be the "elastoplastic model".

[0092] The initial temperature of other components (such as insulation layers, heating coatings, etc.) is the baking temperature, and they are set to a full state. The stress model is set to "rigid model". The "rigid model" is chosen because the thermal deformation of these components during the process is much smaller than that of the steel ingot and the steel ingot mold, aiming to significantly improve calculation efficiency while ensuring calculation accuracy.

[0093] Interfacial heat transfer conditions: The intensity of heat exchange between contacting components is characterized by interfacial heat transfer coefficients, such as the ingot-mold interface heat transfer coefficient, the ingot-insulation layer interface heat transfer coefficient, and the ingot-heating agent interface heat transfer coefficient. Among these, determining the ingot-mold interface heat transfer coefficient is crucial to the accuracy of solidification process and stress field simulation. This invention can adopt two setting principles: One principle is to set the ingot-mold interface heat transfer coefficient as a function of temperature or time, which can be obtained through inverse algorithms derived from experimental data or calculations based on multiphysics coupling models. The other principle, in the absence of a precise functional relationship, is to use an equivalent constant heat transfer coefficient for simulation. This equivalent constant can be determined in two ways: referring to recommended values ​​for similar processes in the parameter database of the simulation software used; or using typical values ​​similar to the current process conditions obtained through empirical formulas or literature reviews. For other contact surfaces, such as the ingot-insulation layer interface and the ingot-heating agent interface, their heat transfer coefficients can be set as corresponding constants according to material properties.

[0094] Boundary conditions: Boundary conditions are key settings that define the interaction between the computational domain and the external environment, and are used to ensure the mathematical completeness and physical authenticity of the finite element calculation model. The boundary conditions involved in this invention mainly include heat transfer boundary conditions, flow boundary conditions, symmetry boundary conditions, and displacement boundary conditions.

[0095] Specifically, the heat exchange boundary condition is used to define the heat exchange between the outer surface of the system and the surrounding environment. In this invention, the outer surface of the system (such as the outer wall of the steel ingot mold or the outer surface of the insulation layer) is usually set as an air-cooled heat exchange boundary, that is, heat is dissipated to the environment through convection and radiation. This condition can be characterized by setting a comprehensive heat transfer coefficient and the ambient temperature.

[0096] Flow boundary conditions are used to define the flow behavior of molten steel during the filling stage. In the stress field calculation of this invention, it is usually assumed that the filling process has been completed, so flow boundary conditions do not need to be set. If the filling process needs to be simulated, the pouring port position and initial pouring speed of the molten steel need to be specified. As mentioned above, the three-dimensional geometric model of the casting system of this invention is a partial model (e.g., taking 1 / 8, 1 / 16, or 1 / 24 of the symmetrical structure of the actual casting system). Therefore, when performing stress field calculations, symmetry boundary conditions must be applied to all symmetry planes. This condition forces the model to have zero displacement in the normal direction of the symmetry plane, and there is no penetration of heat flow and flow on the symmetry plane, thereby ensuring that the partial model can equivalently represent the behavior of the entire system.

[0097] Regarding the setting of displacement boundary conditions, conventional settings constrain a local area on the bottom surface of the ingot mold base. This invention, however, applies displacement constraints in the direction of gravity to the entire bottom surface of both the ingot mold base and the ingot itself, limiting the translational degree of freedom in this direction to zero. Compared to traditional local constraints, the global constraints of this invention more accurately reflect the actual contact state, effectively avoiding stress concentration distortion and macroscopic displacement anomalies caused by improper constraints, thereby significantly improving the reliability of the crack stress field calculation. It should be noted that the constraint settings of this invention are not only applicable to the calculation of the crack stress field in the ingot mold, but also to the stress field calculation of the entire ingot-mold system.

[0098] The calculation parameters refer to the calculation step size, stopping conditions, and save frequency. The calculation step size refers to the minimum time interval at which the solver advances. An excessively large step size can lead to non-convergence or inaccurate results, while an excessively small step size will result in excessively long calculation times. In this invention, the calculation step size is set in segments according to time. A small step size is set during the initial solidification stage, for example, 5-10 seconds. This is because during the initial solidification stage (the simulated solidification amount of the steel ingot in the three-dimensional geometric model of the casting system is 0-50%), the temperature field of the molten metal undergoes drastic changes, resulting in solidification shrinkage. The material changes fundamentally from a liquid state (no strength) to a pasty region (very low strength) and then to a solid state (gradually increasing strength). Using a small time step during this stage allows for accurate capture of these rapid and drastic physical changes. An excessively large step size will miss key results or even lead to inaccurate or non-convergent results. During the later stages of solidification (when the simulated solidification amount of the steel ingot in the three-dimensional geometric model of the casting system is 80-100%), a larger step size is used, for example, a step size of 60-100 s. This is because the temperature gradient and stress changes of the steel ingot tend to be gradual at this time, and a larger step size can meet the accuracy requirements. At the same time, because the cooling at the riser is extremely slow, a larger step size can effectively avoid computational time consumption and resource waste. During the middle stages of solidification (when the simulated solidification amount of the steel ingot in the three-dimensional geometric model of the casting system is 50-80%), an intermediate step size between a smaller and a larger step size can be used, for example, a step size of 10-60 s. This allows for a smooth transition in the calculation, ensuring both calculation accuracy and improving calculation efficiency.

[0099] Stopping Criteria: This refers to the criteria for terminating the calculation. In this invention, the stopping criterion is set as follows: the calculation automatically stops when the temperature of all molten steel units in the model drops to 10°C below their solidus temperature. This ensures that the simulation fully covers the entire solidification process from casting to complete solidification. Saving Frequency: This refers to the time interval at which the calculation results file is saved. Saving too frequently will consume a large amount of storage space, while saving too infrequently will result in the loss of some key calculation results, which is detrimental to result analysis. In this invention, the saving frequency can be set to save once every fixed physical time interval (e.g., 60-120 seconds). This setting achieves a good balance between ensuring data integrity and saving storage resources.

[0100] Stress field calculations were performed on the finite element mesh file with the above-mentioned parameter settings. After the calculations were completed, the distribution and evolution of stress fields (such as Mises equivalent stress and principal stress) in the steel ingot, steel ingot mold, and cracked areas were analyzed to provide a basis for optimizing the steel ingot mold structure, optimizing the casting process, and evaluating the fatigue life of the steel ingot mold.

[0101] Example

[0102] In this embodiment, a certain type of steel ingot actually produced is selected. The steel ingot has 24 edges, and the materials of the steel ingot and the steel ingot mold are 45Cr5NiMoV and HT150, respectively.

[0103] This embodiment provides a method for calculating the stress field of cracks in a steel ingot mold based on finite element analysis, including the following steps:

[0104] S1: Establish a three-dimensional geometric model of the casting system with crack features for finite element calculation;

[0105] S11: The actual casting system in this embodiment is an axisymmetric structure. The steel ingot has 24 edges. Taking one symmetry period of the actual casting system, i.e. 1 / 24, a first basic model is established. The basic model includes components such as a steel ingot without crack features, a steel ingot mold, a heat insulation layer, and a heat-generating covering agent, which serve as the geometric carrier for the subsequent introduction of cracks.

[0106] S12: By observing and measuring the morphology of the inner surface of the steel ingot mold after actual use, the distribution and size data of the cracks are obtained, and the data are statistically analyzed to determine the characteristic parameters of the key cracks used for modeling.

[0107] Among them, the inner surface of the steel ingot mold after actual use is as follows: Figure 1 As shown, morphological observation and measurement were performed to obtain data on the distribution and size of the cracks. Statistical analysis of the data determined the characteristic parameters of the key cracks used for modeling:

[0108] Maximum longitudinal crack: The longitudinal crack is nearly vertical and is distributed on the inner surface of the recessed part of the ingot mold; the maximum longitudinal crack width W1 is about 4 mm, the depth D1 is about 4 mm, and the length L1 is about 1300 mm.

[0109] The largest transverse crack: The transverse crack has a complex and tortuous shape, varying in length, and is diffusely distributed on the raised surface of the steel ingot mold; the width W2 of the largest transverse crack is about 4 mm, the depth D2 is about 4 mm, and the length L2 is about 80 mm.

[0110] S13: Select one maximum longitudinal crack and three maximum transverse cracks as the modeling objects, and simplify them into standard triangular sections. The three transverse cracks should be located in the upper, middle and lower feature areas of the inner surface of the steel ingot mold, respectively.

[0111] S14: Based on the determined width and depth of the largest longitudinal crack and the three largest transverse cracks, it can be known that the depth of the largest longitudinal crack and the largest transverse crack is 4mm, which is less than 10mm. Therefore, when modeling, its width and depth are enlarged to 10mm, while keeping its length unchanged.

[0112] S15: On the inner surface of the ingot mold of the first basic model, based on the determined position and size of one maximum longitudinal crack and three maximum transverse cracks, grooves with triangular cross sections are respectively established, called "crack grooves", to obtain the second basic model;

[0113] S16: On the outer surface of the steel ingot in the second basic model, a protrusion with a triangular cross section that corresponds completely to all the crack grooves in terms of position, shape and size is created. This protrusion is called a "crack protrusion". After creating the "crack grooves" and "crack protrusions", the model is obtained, which is the three-dimensional geometric model of the casting system with crack features for finite element calculation.

[0114] in, Figure 2 A schematic diagram of the overall appearance of the cracked grooves on the inner surface of the ingot mold in the three-dimensional geometric model of the casting system with cracked features established for finite element calculation in this embodiment. Figure 3 This is a schematic diagram showing the overall appearance of the crack protrusions on the outer surface of the steel ingot in the three-dimensional geometric model of the casting system with crack features established for finite element calculation in this embodiment.

[0115] S2: Export the three-dimensional geometric model of the casting system as an .xt format file, import it into the casting simulation software ProCAST, perform non-uniform finite element mesh generation, and obtain the finite element mesh file.

[0116] Set a smaller grid size of 4mm for all "crack groove" and "crack protrusion" areas;

[0117] The grid size is set to 40mm at the ingot mold, 30mm at the ingot itself, and 20mm at the insulation layer. For smaller, localized areas such as chamfers, steps, and edges, the grid size is set to 10mm. After setting the dimensions, a one-click automatic mesh generation is performed. During the generation process, the software automatically generates transition meshes between the finer and coarser mesh areas.

[0118] S3: Set the parameters for the finite element mesh file generated above and perform stress field calculation;

[0119] Parameter settings include material parameters, initial conditions, interfacial heat transfer conditions, boundary conditions, and calculation parameters;

[0120] Material parameters: Based on the actual casting process, corresponding material parameters are set for each component of the three-dimensional geometric model of the casting system; the materials of the steel ingot and the steel ingot mold are 45Cr5NiMoV and HT150, respectively, and the material parameters are calculated by the thermophysical property calculation function of the ProCAST software; the material parameters of other components are obtained by actual testing.

[0121] Initial conditions: Initial conditions are used to define the physical state of the three-dimensional geometric model of the casting system at the start of the calculation (i.e., t=0);

[0122] The initial temperature of the steel ingot is the casting temperature of 1580℃, and it is set to be in a fully filled state. The stress model is selected as "elastoplastic model".

[0123] The initial temperature of the steel ingot mold is the baking temperature of 50℃, and it is set to be in a full state. The stress model is selected as "elastoplastic model".

[0124] The initial temperature of other components (such as insulation layer, heating cover, etc.) is 50°C (baking temperature), and they are set to be in a full state. The stress model is set to "rigid model".

[0125] Interfacial heat transfer conditions: the intensity of heat exchange between components in contact with each other, characterized by the interfacial heat transfer coefficient;

[0126] In this embodiment, the heat transfer coefficient at the ingot-mold interface is a curve that varies with temperature, specifically, at 20℃ and 500W / m. 2 / K, 1399℃, 1200W / m 2 / K, 1471℃, 1700W / m 2 / K, 2000℃, 2000W / m 2 / K, such as Figure 4 As shown; the heat transfer coefficients at the steel ingot-insulation layer interface and the steel ingot-heating covering agent interface are constants of 200 W / m. 2 / K.

[0127] Boundary conditions include heat transfer boundary conditions, flow boundary conditions, symmetry boundary conditions, and displacement boundary conditions.

[0128] Heat transfer boundary conditions: The outer surface of the system (such as the outer wall of the steel ingot mold, the outer surface of the insulation layer) is set as an air-cooled heat transfer boundary;

[0129] Flow boundary conditions: In this embodiment, the ingot mold is filled instantaneously, and the filling process is not calculated, so there is no need to set flow boundary conditions;

[0130] Symmetric boundary conditions: Apply symmetric boundary conditions to all symmetric surfaces of the above 1 / 24 model. These conditions force the model to have zero displacement in the normal direction of the symmetric surface.

[0131] Displacement boundary conditions: Apply displacement constraints in the direction of gravity to the entire area of ​​the bottom surface of the ingot mold base and the entire area of ​​the ingot bottom surface, respectively, so that they do not displace in the direction of gravity. The constrained areas are as follows: Figure 5 As shown;

[0132] Calculation parameters: The calculation step size is a function of time, namely, in the early stage of solidification (the simulated solidification amount of the steel ingot in the three-dimensional geometric model of the casting system is 0-50%), the calculation step size is 5s; in the middle stage of solidification (the simulated solidification amount of the steel ingot in the three-dimensional geometric model of the casting system is 50-80%), the calculation step size is 20s; and in the late stage of solidification (the simulated solidification amount of the steel ingot in the three-dimensional geometric model of the casting system is 80-100%), the calculation step size is 60s.

[0133] The stopping condition is 1389℃ (i.e., 10℃ below the solidus temperature of the material 1399℃), and the storage frequency is 60s.

[0134] Comparative Example 1

[0135] This comparative example uses the steel ingot in the embodiment as the calculation object. The calculation method is similar to that of the embodiment, except that the displacement boundary conditions used in Comparative Example 1 are set in a conventional manner, that is, only a local area of ​​the bottom surface of the steel ingot mold is constrained to prevent displacement in the direction of gravity. The constrained area is as follows: Figure 6 As shown.

[0136] The calculation results of Comparison Example 1 and the Example will be compared and analyzed:

[0137] Figure 7a This is a schematic diagram illustrating the displacement of the steel ingot and steel ingot mold in the direction of gravity, as shown in the embodiment. Figure 7b This is a schematic diagram showing the displacement of the steel ingot and ingot mold in the direction of gravity for Comparative Example 1; by Figure 7a and 7bAs can be seen, in the embodiment, the bottom surface of the ingot mold base and the bottom surface of the ingot basically do not move up and down. In contrast, in Comparative Example 1, only the constrained area of ​​the bottom surface of the ingot mold base does not move up and down; the other unconstrained areas move downwards. Simultaneously, the bottom surface of the ingot moves upwards.

[0138] Figure 8a This is a schematic diagram showing the air gap between the steel ingot and the steel ingot mold in an embodiment. Figure 8b This is a schematic diagram showing the air gap between the steel ingot and the ingot mold in Comparative Example 1; from Figure 8a and 8b As can be seen, no air gap is generated between the bottom surface of the steel ingot and the contact surface of the steel ingot mold base in the embodiment, while an air gap is generated between the bottom surface of the steel ingot and the contact surface of the steel ingot mold base in Comparative Example 1, and the air gap at both ends of the contact surface is larger.

[0139] Figure 9a This is a stress variation diagram of the transverse crack in the middle of the example model; Figure 9b The stress variation diagram is shown for the transverse crack in the middle of the model in Comparative Example 1. Figure 9a and 9b In the middle, the left side of the triangular crack is a steel ingot, and the right side is a steel ingot mold.

[0140] Figure 9a In the example model, because the bottom surface of the steel ingot is completely constrained, the steel ingot can only move inward and downward in the vertical direction by contraction. At the same time, because the bottom surface of the steel ingot mold is completely constrained, the steel ingot mold moves outward and slightly upward due to expansion. In addition, due to the relative motion, the lower end face of the steel ingot crack protrusion interferes with the lower end face of the steel ingot mold crack groove. The tensile stress at the interference point is large, and the tensile stress at the root of the lower end face of the crack groove is even greater. Figure 9b In Comparative Example 1, the steel ingot contracts and moves inward and upward, while the ingot mold moves outward and downward. Furthermore, due to the relative motion, the upper surface of the crack protrusion in the steel ingot interferes with the upper surface of the crack groove in the ingot mold. The tensile stress at the interference point is relatively large, and the tensile stress at the root of the upper surface of the crack protrusion is also high. Compared to the embodiment, the displacement changes of the crack protrusion and the crack groove in the direction of gravity are opposite in the comparative example.

[0141] Figure 7a-7b , Figure 8a-8b , Figure 9a-9b It can be shown that the macroscopic displacement of the steel ingot, steel ingot mold, crack groove, and crack protrusion in the direction of gravity is significantly different from, and even opposite to, that of the embodiment and Comparative Example 1. The displacement of the embodiment is more scientific and reasonable, because in reality, the steel ingot cannot move upward under the action of gravity, and the bottom surface of the steel ingot mold base cannot move downward when it is in contact with the ground.

[0142] Figure 10 This is a schematic diagram showing the stress conditions on the outer surface of the steel ingot in the examples and Comparative Example 1. Figure 10The upper part is the embodiment, and the lower part is Comparative Example 1. As can be seen from the figure, the stress conditions of the steel ingot in the early stage of solidification, the location near the transverse crack, the bottom corner of the steel ingot, and the bottom surface of the steel ingot are quite different between the embodiment and Comparative Example 1. The tensile stress development trend on the edge of the steel ingot is consistent in the later stage of solidification, but the size of the stress area is different; the stress conditions of the longitudinal crack are basically similar.

[0143] Figure 11 This is a schematic diagram showing the stress conditions on the inner surface of the steel ingot mold in the embodiments and Comparative Example 1. Figure 11 The upper part is the example, and the lower part is Comparative Example 1. As can be seen from the figure, the tensile stress range of the ingot mold base, corresponding riser and the part below the riser in the early stage of solidification is different between the example and Comparative Example 1. The tensile stress of the concave surface of the part below the riser in the later stage of solidification is significantly different; the stress conditions at the longitudinal crack are basically similar.

[0144] Figure 10 , Figure 11 It can be shown that there are significant differences in the stress distribution on the outer surface of the steel ingot, the inner surface of the steel ingot mold, the crack groove and its vicinity, and the crack protrusion and its vicinity between the embodiment and Comparative Example 1. The embodiment is more consistent with the actual stress distribution.

[0145] Figure 12a This is a schematic diagram of the temperature field on the inner surface of the steel ingot mold in an embodiment. Figure 12b This is a schematic diagram of the temperature field on the inner surface of the steel ingot mold in Comparative Example 1. Figure 13 This is a schematic diagram showing the temperature at specific points in the embodiment and Comparative Example 1. As can be seen from the figure, the temperature of the bottom surface and the periphery of the base of the ingot mold in the embodiment is higher, approximately 50°C higher than the temperature at the same location in Comparative Example 1. Therefore, when the ingot mold undergoes repeated use, under the complex effects of thermal erosion, fatigue, and stress, the ingot mold in the embodiment is more prone to cracking and peeling.

[0146] Figure 14 shows the actual steel ingot mold and the actual steel ingot used in production. Figure 14a For reusable steel ingot mold base, Figure 14b This is the lower half of the steel ingot after demolding. As shown in the image, the bottom surface of the ingot mold exhibits severe cracking and peeling, corresponding to a rough and mottled surface on the ingot itself. These phenomena are related to… Figure 12a The results of the temperature field analysis showed good agreement, thus further verifying the rationality of the embodiment.

[0147] Comparative Example 2

[0148] This comparative example uses the steel ingot in the embodiment as the calculation object. The calculation method is similar to that in the embodiment, except that the grid size is set to 5mm for all "crack grooves" and "crack protrusions" areas.

[0149] Comparative Example 3

[0150] This comparative example uses the steel ingot in the embodiment as the calculation object. The calculation method is similar to that in the embodiment, except that the grid size is set to 10mm for all "crack grooves" and "crack protrusions" areas.

[0151] Figure 15 Comparative images show the mesh morphology of the "crack groove" and "crack protrusion" regions in Examples 1, 2, and 3; the left image is Example 1, the middle image is Comparative Example 2, and the right image is Comparative Example 3.

[0152] Figure 16 The figures show a comparison of the calculated stress field results for the steel ingot and ingot mold surfaces of Examples 1, 2, and 3. Example 1 is on the left, Example 2 is in the middle, and Example 3 is on the right. As can be seen from the figures, with the increase of the mesh size, the stress-affected zone at the crack gradually expands and becomes coarser, indicating that Example 1 has higher calculation accuracy.

[0153] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for calculating the stress field of cracks in a steel ingot mold based on finite element analysis, characterized in that, Includes the following steps: S1: Establish a three-dimensional geometric model of the casting system with crack features for finite element calculation; S2: Export the three-dimensional geometric model of the casting system as an .xt format file, import it into the casting simulation software, perform non-uniform finite element mesh generation, and obtain the finite element mesh file; S3: Set parameters for the finite element mesh file and perform stress field calculation; The parameter settings include material parameters, initial conditions, interfacial heat transfer conditions, boundary conditions, and calculation parameters; The boundary conditions include displacement boundary conditions, which are set to apply displacement constraints in the direction of gravity to the entire area of ​​the bottom surface of the ingot mold base and the entire area of ​​the bottom surface of the ingot in the three-dimensional geometric model of the casting system, restricting its translational degree of freedom in the direction of gravity to 0.

2. The stress field calculation method according to claim 1, characterized in that, Step S1 includes: S11: Based on the axisymmetric structure and volume of the actual casting system, take one symmetric period of the actual casting system to establish the first basic model. The basic model includes a steel ingot without crack features, a steel ingot mold, a heat insulation layer, and a heat-generating covering agent, which serve as the geometric carrier for the subsequent introduction of cracks. S12: By observing and measuring the morphology of the inner surface of the steel ingot mold after actual use, the distribution and size data of the cracks are obtained, and the data are statistically analyzed to determine the characteristic parameters of the key cracks used for modeling. S13: Select one maximum longitudinal crack and three maximum transverse cracks as the modeling objects, and simplify them into standard triangular sections. The three transverse cracks should be located in the upper, middle and lower feature areas of the inner surface of the steel ingot mold, respectively. S14: Based on the determined width and depth of one maximum longitudinal crack and three maximum transverse cracks, determine whether to enlarge to 10mm during modeling; S15: On the inner surface of the steel ingot mold of the first basic model, based on the determined position and size of one maximum longitudinal crack and three maximum transverse cracks, grooves with triangular cross sections are respectively established, called "crack grooves", to obtain the second basic model; S16: On the outer surface of the steel ingot in the second basic model, a protrusion with a triangular cross section that corresponds perfectly to all the crack grooves in terms of position, shape and size is created. This protrusion is called a "crack protrusion". The model obtained after creating the "crack grooves" and "crack protrusions" is the three-dimensional geometric model of the casting system with crack features for finite element calculation.

3. The stress field calculation method according to claim 2, characterized in that, In step S12, the key cracks used for modeling include the largest longitudinal crack and the largest transverse crack. The characteristic parameters of the largest longitudinal crack include the width W1, depth D1, length L1 and its position on the inner surface of the ingot mold. The characteristic parameters of the largest transverse crack include the width W2, depth D2, length L2 and its position on the inner surface of the ingot mold.

4. The stress field calculation method according to claim 3, characterized in that, In step S14, if the width and depth of the maximum longitudinal crack and the three maximum transverse cracks are ≥10mm, then the dimensions of the maximum longitudinal crack and the three maximum transverse cracks shall remain unchanged during modeling. If the width and depth of the largest longitudinal crack and the three largest transverse cracks are less than 10 mm, then the size of the largest longitudinal crack and the three largest transverse cracks will be enlarged to 10 mm during modeling.

5. The stress field calculation method according to claim 2, characterized in that, In step S2, the non-uniform finite element mesh generation includes: The grid size of the "crack groove" and "crack protrusion" areas is 2-5mm; In the three-dimensional geometric model of the casting system, the local areas with smaller dimensions have a mesh size of 10-20mm. These local areas with smaller dimensions include chamfers, steps, and edge regions. The three-dimensional geometric model of the casting system includes areas for the ingot mold, ingot, and other components, with a grid size of 10-60mm. Other components include insulation layers and heat-generating coverings. The casting simulation software automatically generates transition meshes between meshes of different sizes.

6. The stress field calculation method according to claim 2, characterized in that, In step S3, the setting of the initial conditions includes: The initial temperature of the steel ingot is the casting temperature, the filling state is either empty or full, and the stress model is an "elastoplastic model". The initial temperature of the steel ingot mold is the baking temperature, the filling state is the full state, and the stress model is the "elastoplastic model"; The initial temperature of all components except the steel ingot and the steel ingot mold is the baking temperature, the filling state is the full state, and the stress model is the "rigid model".

7. The stress field calculation method according to claim 2, characterized in that, In step S3, the setting of the interface heat exchange conditions includes: The heat transfer coefficient at the ingot-mold interface is set as a function of temperature or time, or as an equivalent constant. The heat transfer coefficients at the interfaces of steel ingot-insulation layer and steel ingot-heating covering agent are set to constants.

8. The stress field calculation method according to claim 2, characterized in that, The calculation parameters include calculation step size, stopping condition, and saving frequency; The setting of the calculation step size includes: In the initial stage of solidification, the calculation step is 5-10 seconds, where the initial stage of solidification refers to the simulated solidification amount of the steel ingot in the three-dimensional geometric model of the casting system being 0-50%. During the middle stage of solidification, the calculation step is 10-60s, where the middle stage of solidification refers to the simulated solidification amount of the steel ingot in the three-dimensional geometric model of the casting system being 50-80%. In the later stage of solidification, the calculation step is 60-100s, where the later stage of solidification refers to the simulated solidification amount of the steel ingot in the three-dimensional geometric model of the casting system being 80-100%.

9. The stress field calculation method according to claim 8, characterized in that, The stopping condition is that the temperature of all molten steel units in the three-dimensional geometric model of the casting system drops to 10°C below the solidus temperature of the steel ingot material.

10. The stress field calculation method according to claim 8, characterized in that, The storage frequency is 60-120 seconds.

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