A method for determining internal reduction cracks of a casting blank based on a thermal coupling model

Abstract

The present application relates to the technical field of hot crack determination, and particularly relates to a kind of hot crack determination method of internal press-down of casting blank based on thermal coupling model, comprising using two-dimensional Fourier heat equation to calculate the solidification process of casting blank;Using equivalent specific heat capacity method to handle solidification latent heat;Calculate the center solid phase rate of the solidification process of casting blank;Calculate the average heat flux density of crystallizer stage, and the instantaneous heat flux density distributed along the casting direction of crystallizer;Thermal coupling model is constructed.The present application is based on thermal coupling model simulation, and determines whether the press-down process of continuous casting produces press-down hot crack.

Description

Technical Field

[0001] This invention relates to the field of hot crack detection technology, and in particular to a method for detecting internal pressure hot cracks in cast billets based on a thermo-mechanical coupling model. Background Technology

[0002] During the final stage of solidification of continuously cast billets, due to the effect of solidification shrinkage, concentrated molten steel gradually accumulates towards the core of the billet, easily leading to defects such as center segregation and center porosity of varying degrees after solidification. The reduction process is an effective technique for improving these center defects, and the appropriate reduction range and amount are key factors affecting the reduction effect. Too small a reduction amount cannot effectively eliminate center segregation and porosity, while too large a reduction amount may cause reduction cracks in the billet. Internal hot cracks generated during the casting process using the reduction process, also known as reduction cracks, are one of the common internal defects in continuously cast billets, causing significant damage to the uniformity and continuity of the steel material. Unlike low-temperature cold cracks formed after complete solidification, high-temperature hot cracks occur during the solidification process, and internal reduction hot cracks (hereinafter referred to as reduction cracks) also fall under the category of high-temperature hot cracks.

[0003] Avoiding and preventing pressure cracks is a key point to focus on during the pressure process; however, due to the complex changes inside the billet, there are still many unknowns and uncertainties in the actual production process for judging pressure cracks in the continuous casting process of steel billets.

[0004] Existing methods include numerous criteria for determining hot crack formation based on stress, strain, and strain rate, or other principles. These criteria were largely developed not specifically for continuous casting of steel, but primarily for aluminum alloys, or originated in the welding field. However, hot cracking in steel and other materials, or in continuous casting and welding, exhibits the same phenomenon. Some criteria define critical values ​​for hot crack formation, such as based on critical strain or stress; others define hot crack formation susceptibility, primarily considering the influence of chemical composition. Hot crack formation criteria in continuous casting of steel are mainly based on strain. The model compares the strain generated during the process with the critical strain for hot cracking; however, different researchers do not agree on this point. For example, some researchers believe that the crack susceptibility of steel first decreases and then increases with carbon content, while others believe that the higher the carbon content, the stronger the hot crack susceptibility. There are also different opinions on whether the critical strain value for hot crack formation is related to the strain rate and deformation mode. This makes it impossible to obtain a unified criterion for determining the occurrence of internal hot cracks in the billet, and thus it is impossible to effectively determine whether internal pressing hot cracks occur during the pressing process in continuous casting. Summary of the Invention

[0005] To address the shortcomings of existing methods, this invention uses a thermo-coupling model to simulate and determine whether hot cracks occur during the continuous casting reduction process.

[0006] The technical solution adopted in this invention is: a method for determining internal pressure-induced hot cracks in cast billets based on a thermo-coupling model, comprising the following steps:

[0007] Step 1: Construct a solidification heat transfer model: Calculate the solidification process of the billet using the two-dimensional Fourier heat transfer equation; process the latent heat of solidification using the equivalent specific heat capacity method; calculate the solid fraction of the core phase during the solidification process of the billet; calculate the average heat flux density during the crystallizer stage and the instantaneous heat flux density distributed along the casting direction of the crystallizer.

[0008] Furthermore, the formula for the average heat flux density is:

[0009]

[0010] The formula for instantaneous heat flux density is:

[0011]

[0012]

[0013] In the formula, q represents the average heat flux density within the crystallizer. mold ρ is the instantaneous heat flux density within the crystallizer. w Q represents the density of the cooling water. w C is the flow rate of the cooling water in the crystallizer. w ΔT is the specific heat capacity of cooling water. w The temperature difference between the inlet and outlet water of the crystallizer; S eff L is the effective contact area between the molten steel and the crystallizer; L is the distance from the meniscus to the location of the instantaneous heat flux density being calculated; L m ν represents the effective length of the crystallizer; ν is the casting speed.

[0014] Furthermore, heat flux density is calculated from the heat transfer coefficient to determine the heat flow in each zone. The formula for the heat transfer coefficient is:

[0015] h=α·W β +n (9)

[0016] Where W is the water flow density; α, β, and n are constants related to the secondary cooling zone equipment.

[0017] Furthermore, the formula for calculating heat flow is:

[0018] q=εσ[(T b +273) 4 -(T a +273) 4 (12)

[0019] Among them, ε is the radiation coefficient; σ is the Stefan-Boltzmann constant; T b is the surface temperature of the continuous casting billet; T a is the ambient temperature.

[0020] Furthermore, the heat transfer coefficient is divided into full water cooling and aerosol cooling.

[0021] Step 2: Construct a thermal-mechanical coupling model;

[0022] Furthermore, Step 2 specifically includes:

[0023] Step 21: Construct the elastic modulus under different temperature conditions;

[0024] Furthermore, when the temperature T < 500 °C, the elastic modulus E = 175 GPa;

[0025] When T = 500 - 900 °C, E = 347.6525 - 0.350305T(13);

[0026] When T = 900 °C to Ts, E = 968 - 2.33T + 1.9×10 -3 T 2 - 5.18×10 -7 T 3 (14); when T > Ts,

[0027] where, f ZST is the solid fraction corresponding to the zero strength temperature; E S is the elastic modulus value corresponding to the solidus temperature Ts; E ZST is a very small value approaching zero, f S is the solid fraction.

[0028] Step 22: Construct the Poisson's ratio under different temperature conditions;

[0029] Furthermore, when T < Ts, the Poisson's ratio ν = 0.278 + 8.23×10 -5 T(16);

[0030] When T ≥ Ts,

[0031] In the formula, v S is the Poisson's ratio corresponding to the solidus temperature; v ZST is a value approaching 0.5, f ZST is the solid fraction corresponding to the zero strength temperature.

[0032] Step 23: Calculate the bulk modulus according to the elastic modulus and Poisson's ratio.

[0033] Furthermore, the formula for bulk modulus is:

[0034]

[0035] Where E is the elastic modulus and ν is Poisson's ratio.

[0036] Furthermore, the values ​​of elastic modulus E and Poisson's ratio ν should be approximately equal to the bulk modulus in the liquid state and at room temperature.

[0037] The beneficial effects of this invention are:

[0038] 1. A comprehensive and effective consideration of both internal and external factors contributing to hot cracking within the billet: At the internal level, the crack resistance sensitivity of the steel itself is measured through actual differential thermal analysis and high-temperature mechanical tests, rather than calculated or derived values. This significantly improves the correspondence and reliability with the actual tested steel, enabling a more accurate determination of hot cracking within the billet. As for external factors, the equivalent combined effect of different types of strain acting on the crack-sensitive region is considered to achieve a comprehensive and effective determination.

[0039] 2. The method of the present invention is applicable to the determination of internal pressure hot cracks in billets of different steel grades, different cross sections, different billet shapes, and at different pressure positions during the solidification process of continuous casting, and has wide applicability. Attached Figure Description

[0040] Figure 1 This is a flowchart of the method for determining internal pressure-induced hot cracks in cast billets based on a thermo-coupling model, as described in this invention.

[0041] Figure 2 This is a schematic diagram of a slice of a solidification heat transfer model for cast billets;

[0042] Figure 3 This is a schematic diagram of the thermo-mechanical coupling model of the compression process;

[0043] Figure 4 This is a schematic diagram of a high-temperature tensile specimen;

[0044] Figure 5 This is a graph showing the overall trend of critical strain as a function of steel composition;

[0045] Figure 6 This is a graph showing the temperature changes during the casting process of the billet;

[0046] Figure 7 It is a distribution diagram of the actual solidification process during the casting process of the billet;

[0047] Figure 8 This is a distribution diagram of the comprehensive effective strain of the billet cross section corresponding to the pressing position when the pressing amount is 4mm;

[0048] Figure 9 This is a distribution diagram of the comprehensive effective strain of the billet cross section corresponding to the pressing position when the pressing amount is 5mm;

[0049] Figure 10 This is a DSC temperature curve of 86 steel.

[0050] Figure 11 (a) Figure 11 (b) Figure 11 (c) are metallographic images of the specimen cross sections when the strain values ​​are 0.003, 0.004, and 0.005, respectively;

[0051] Figure 12 This is a strain distribution diagram along the centerline of the billet cross-section when the reduction is 5mm;

[0052] Figure 13 This is a strain distribution diagram along the centerline of the billet cross-section when the reduction is 4mm;

[0053] Figure 14 This is a low-magnification view of the cross-section of the billet when the reduction is 5mm;

[0054] Figure 15 This is a low-magnification enlarged view of the central area of ​​the billet when the reduction is 5mm;

[0055] Figure 16 This is a low-magnification view of the cross-section of the billet when the reduction is 4mm. Detailed Implementation

[0056] The present invention will be further described below with reference to the accompanying drawings and embodiments. The drawings are simplified schematic diagrams, which only illustrate the basic structure of the present invention in a schematic manner, and therefore only show the components related to the present invention.

[0057] like Figure 1 As shown, a method for determining internal pressure-induced hot cracks in cast billets based on a thermo-coupling model includes the following steps:

[0058] Step 1: Construct a solidification heat transfer model;

[0059] Taking the continuously cast billet produced by a specific continuous casting machine as the research object, a geometric mathematical model was established using MSC.Marc software, with the width direction as the x-axis, the thickness direction as the y-axis, and the casting direction as the z-axis.

[0060] To simplify the equations and boundary conditions without sacrificing rationality, the following assumptions are made for the billet solidification heat transfer model based on the actual production conditions of the continuous casting process:

[0061] (11) The liquid steel surface in the crystallizer is insulated and the liquid level remains stable;

[0062] (12) The physical properties of steel are piecewise constants in the liquid, solid-liquid two-phase and solid states, and are isotropic.

[0063] (13) The billet is cooled uniformly in all directions in the same cooling section;

[0064] (14) To simplify the calculation process, it is assumed that the thermal conductivity of the solid phase region of the billet is a function of temperature. Meanwhile, since there is convective motion of molten steel in the liquid phase region, the equivalent thermal conductivity is used to characterize the enhanced heat transfer process in the liquid phase region.

[0065] (15) The heat transfer of each roller surface and the surface of the billet in the pouring path is added to the convection heat transfer coefficient of the secondary cooling water using the correction coefficient method.

[0066] Based on assumptions (11)-(15), the solidification process of the cast billet is calculated using the two-dimensional Fourier heat transfer equation. The governing equations are as follows:

[0067]

[0068] In this model, the latent heat of solidification is treated using the equivalent specific heat capacity method, which slows down the rate of temperature change in the region by amplifying the specific heat capacity, thereby achieving an equivalent release of latent heat. The formula for calculating the equivalent specific heat capacity of the two-phase region after treatment is as follows:

[0069]

[0070] Central solidity f s These are important parameters that determine the installation position of the end electromagnetic stirrer and the pressure range under light pressure. The calculation formula in this model is as follows:

[0071]

[0072] In the formula, ρ is the density of molten steel, kg·m -3 λ is the thermal conductivity of molten steel, W·m -1 ·℃ -1 C p Specific heat capacity of steel, J·kg -1 ·℃ -1 T represents the temperature at a certain moment, in °C; t represents the time, in seconds; x represents the width direction of the cast billet, in meters; y represents the thickness direction of the cast billet, in meters; T L T is the liquidus temperature of steel, in °C. S The solidus temperature of steel is ℃; C S and C L The solid and liquid phase heat capacities of steel, respectively, in J·kg⁻¹. -1 ·℃ -1 L f The latent heat of solidification of steel, kJ·kg -1 ;f sThe solid fraction during the solidification process of the billet is calculated using Jmatpro software.

[0073] When t = 0, that is, at the start of casting, the temperature of the molten steel in the crystallizer is equal to the casting temperature, which is the temperature value measured in the tundish:

[0074] T t＝0 =T 中包 (4)

[0075] During the solidification model calculation, the direction of billet pulling is considered adiabatic, and the boundary conditions are mainly the heat transfer process of the wide and narrow faces of the billet, which mainly includes three parts: heat transfer in the crystallizer, heat transfer in the secondary cooling zone, and heat transfer in the air-cooled radiation zone.

[0076] During the crystallization stage of the billet casting, the average heat flux density during the crystallization stage is calculated based on the on-site measurements of the crystallizer cooling water volume and the temperature difference between the inlet and outlet. The calculation formula is as follows:

[0077]

[0078] The formula for calculating the instantaneous heat flux density distributed along the casting direction of the crystallizer is as follows:

[0079]

[0080]

[0081] In the formula, The average heat flux density inside the crystallizer is W·m. -2 ;q mold The instantaneous heat flux density within the crystallizer is expressed in W·m. -2 ;ρ w The density of cooling water is kg·m³. -3 Q w The flow rate of the cooling water for the crystallizer is expressed in L·min. -1 C w The specific heat capacity of cooling water, J·kg -1 ·℃ -1 ;ΔT w The temperature difference between the inlet and outlet water of the crystallizer, in °C; S eff The effective contact area between the molten steel and the crystallizer is m. 2 L is the distance from the location of the instantaneous heat flux density to the meniscus, in meters. m ν is the effective length of the crystallizer, in meters; ν is the casting speed, in millimeters per minute. -1 .

[0082] It is difficult to directly calculate the heat flux density value of the second cooling zone, but the heat flow of each zone can be calculated through the heat transfer coefficient. The formulas for calculating heat flux density and heat transfer coefficient are as follows:

[0083] q sec =h(T) b -T w (8)

[0084] h=α·W β +n (9)

[0085] In the formula, q sec The heat flux density of the billet surface in the secondary cooling zone is W·m. -2 h is the convective heat transfer coefficient of the secondary cooling zone, W·m -2 ·℃ -1 ;T b T represents the surface temperature of the cast billet, in °C. w Where is the cooling water temperature, °C; W is the water flow density, L·m³. -2 ·s -1 α, β, and n are constants related to the secondary cooling zone equipment and are determined based on the actual production process.

[0086] The secondary cooling zone is divided into two types: full water cooling (foot roller section) and air mist cooling. The heat transfer coefficient calculation formulas for the different cooling types are as follows:

[0087] Water cooling zone:

[0088] h = 420W 0.351 ×η (10)

[0089] Aerosol cooling zone:

[0090] h = 1570W 0.55 (1-0.0075T w (11)

[0091] In the formula, η is a coefficient related to the cooling roller, which is adjusted according to the actual situation.

[0092] In the air-cooled zone, heat transfer mainly occurs through radiative heat exchange with the surrounding environment, as shown in the following calculation formula:

[0093] q=εσ[(T b +273) 4 -(T a +273) 4 (12)

[0094] Where ε is the radiation coefficient, with a value of 0.9; σ is the Stefan-Boltzmann constant, with a value of 5.67 × 10⁻⁶. -8 W·m -2 ·℃ -4 ;T b T represents the surface temperature of the cast billet, in °C. a The ambient temperature is in °C.

[0095] A two-dimensional solidification heat transfer model of the cast billet was established using the "slicing method." It was assumed that the slices moved sequentially downwards from the crystallizer to the foot roll zone, secondary cooling zone, and air cooling zone. The model and mesh generation diagram are shown below. Figure 2 As shown.

[0096] Step 2: Establishing the thermo-mechanical coupling model;

[0097] When establishing a thermo-mechanical coupling model for the cast billet based on the solidification heat transfer model, in order to simplify the equations and boundary conditions without losing rationality, the following basic assumptions are made to the model based on the actual production conditions of the continuous casting reduction process:

[0098] (21) The deformation size of the billet is much smaller than the actual size of the continuous casting billet. During the light pressing process, the direction of the force exerted by the pressing roller on the continuous casting billet will not change with the deformation. Therefore, the material is considered to satisfy the small deformation theory.

[0099] (22) In the deformation analysis of continuously cast billets, the billet size is much larger than the size of the discontinuous gap in the actual material, so the material is regarded as a continuous material;

[0100] (23) Ignoring the differences in physical properties of different billets, the material is regarded as uniformly distributed everywhere. Assuming that the material is isotropic, the physical property parameters of the continuously cast billet are independent of the location and only change with the temperature.

[0101] (24) Both the pressing roller and the support roller are rigid bodies;

[0102] (25) The coefficient of friction between the pressure roll and the support roll and the continuous casting billet is 0.3.

[0103] (26) The effect of static pressure of molten steel on the billet is not considered.

[0104] The high-temperature thermophysical properties and mechanical parameters of the material at high temperatures are set as follows in the thermo-mechanical coupling light-pressure model of the cast billet:

[0105] (1) Elastic modulus

[0106] Generally, the elastic modulus gradually decreases as temperature increases. Studies indicate that temperature has the greatest impact on the elastic modulus. When T < 500℃, the elastic modulus changes little with temperature and can be taken as a fixed value of 175 GPa. When the temperature T = 500-900℃, the following formula is used for calculation:

[0107] E = 347.6525 - 0.350305T (13)

[0108] When the temperature T = 900℃ to Ts solidus temperature, the following formula is used for calculation:

[0109] E = 968 - 2.33T + 1.9 × 10 -3 T2 -5.18×10 -7 T 3 (14)

[0110] When the temperature is below the zero intensity temperature T ZST At this point, the steel has a certain strength and can withstand the deformation of the cast billet. When the temperature is higher than T... ZST At this temperature, the elastic modulus can be ignored as zero; however, in numerical calculations, the elastic modulus cannot be zero, otherwise the stiffness matrix will be a non-positive definite matrix, making it impossible to solve. Therefore, when the temperature is higher than T... ZST When the elastic modulus takes a minimum value, the stiffness matrix becomes a positive definite matrix with a unique solution.

[0111] When temperature T > Ts, the following formula is used for calculation:

[0112]

[0113] In the formula, f ZST E represents the solid fraction at the zero intensity temperature. S Here, E represents the elastic modulus at the solidus temperature Ts, in GPa. ZST Gpa; f is an extremely small value approaching zero. S denoted as solid fraction.

[0114] (2) Poisson's ratio

[0115] Similar to the modulus of elasticity, temperature changes have a significant impact on Poisson's ratio of steel at high temperatures. Generally, Poisson's ratio gradually increases with increasing temperature and can be approximated as a linear function of temperature. When the temperature T is below the solidus temperature, the billet is entirely solid, and the Poisson's ratio is almost unaffected by temperature. The following formula is used for calculation:

[0116] ν = 0.278 + 8.23 ​​× 10 -5 T (16)

[0117] When the temperature is above the solidus temperature, the Poisson's ratio of the billet increases as the solid fraction decreases. When it is above the zero strength temperature, the material properties are similar to those of molten steel, and it can be regarded as an incompressible fluid with a Poisson's ratio of approximately 0.5.

[0118]

[0119] In the formula, ν S ν is the Poisson's ratio corresponding to the solidus temperature; ZST The value is close to 0.5.

[0120] Since the elastic modulus is related to Poisson's ratio, the bulk modulus K represents the material's ability to resist volume changes, i.e., its compressibility, and is expressed by the following formula:

[0121]

[0122] From the above equation, we can see that when E→0, K→0; when ν→0.5, K→∞. Therefore, to make the values ​​of E and ν approximately equal in terms of the bulk modulus in the liquid state and the bulk modulus at room temperature, we need to:

[0123]

[0124] The initial and boundary conditions are set as follows:

[0125] (31) Initial conditions

[0126] The temperature field results of the solidification heat transfer model of the billet corresponding to the moment of billet biting in are extracted and used as initial conditions in the thermo-mechanical coupling model of the large billet under light pressure. The internal stress of the billet during solidification at this moment is ignored. When the billet is bitten in, the billet is in contact with the upper and lower rollers but is not subjected to force.

[0127] (32) Boundary conditions

[0128] Thermal analysis boundary conditions: The pressed part is located in the air-cooled zone, and only the radiation heat transfer boundary conditions of the billet surface are considered, which are similar to those of the solidification heat transfer model; the cross sections at both ends of the billet are in an adiabatic state, and possible heat transfer at both ends is ignored.

[0129] Structural analysis boundary conditions: The billet remains stationary, and the upper and lower rolls move in opposite directions according to the drawing speed to bite into the billet; the surface of the billet is a free surface; of the two cross sections of the billet, the bitten cross section is a free surface, and the non-bitten cross section has zero displacement in the drawing direction.

[0130] The billet pressing model consists of a billet, pressing rolls, and support rolls. The model dimensions are the same as the actual dimensions of the billet and pressing rolls cast on a continuous casting machine. The billet length is set to 1m. A schematic diagram of the model is shown below. Figure 3 As shown.

[0131] (33) Determination of critical strain value

[0132] Regarding the formation of compression cracks in specific steel grades, it is known from the high-temperature mechanical properties of steel that high-temperature hot cracks usually begin to initiate at the solidus line. Therefore, for the determination of critical strain values, the test temperature for high-temperature tensile testing, i.e., its actual solidus line temperature, is first determined by differential thermal analysis. Then, different strain values ​​are applied at this test temperature to determine the critical strain values.

[0133] (331) Determination of high temperature tensile test temperature

[0134] The solidus temperature of the tested steel was analyzed using a Labsys thermogravimetric analyzer. To prevent the influence of central porosity and shrinkage cavities on the experimental results, a 0.5 mm thick sample was cut from the equiaxed grain region of the billet. A circular sample of approximately 20 mg in diameter (diameter) was placed in a 3 mm diameter corundum crucible, and the steel's t-value was measured. s The solidus temperature and heating regime of the steel sample were as follows: the temperature was increased from room temperature to 1500℃ at a rate of 10℃ / min, held for 5 min, and then decreased to 100℃ at a rate of 10℃ / min. Argon gas was used for protection during the experiment, with a gas flow rate of 30 ml / min.

[0135] Differential scanning calorimetry (DSC) can be used to measure the relationship between the heat flow rate difference of steel and temperature. During heating or cooling, as the sample undergoes a phase transformation, latent energy is released, and the curve fluctuates. The peak value represents the temperature point where the phase transformation rate reaches its maximum. Generally, upward peaks are considered exothermic peaks, and downward peaks are considered endothermic peaks. Currently, it is widely believed that measuring the solid-liquid phase line during heating is more accurate than measuring it during cooling because the heating process is not affected by the supercooling during solidification nucleation.

[0136] (332) High-temperature tensile test at a specific temperature

[0137] This test was conducted using the Gleeble thermal simulation system. Samples were taken from continuously cast billets of the actual tested steel grade. The sample direction was parallel to the casting direction, and sampling was avoided from porous areas. The samples were machined to Φ10mm × 120mm with 10mm threads at each end. The sample morphology is as follows: Figure 4 As shown.

[0138] In the high-temperature tensile test, the specimen was heated to 1300℃ at a heating rate of 10℃ / s and held isothermally for 5 minutes to achieve uniform temperature distribution. Subsequently, the specimen was heated to the test temperature at a heating rate of 0.5℃ / s, which was the actual solidus temperature of the tested steel grade measured by thermogravimetric analysis. After reaching the target temperature, it was held for 2 minutes before the high-temperature tensile test began. The strain rate during the continuous casting billet reduction process was approximately 10... -3 Up to 1 0-1 s -1 The tensile strain rate used in the test was also controlled at a specific value within this range based on the actual strain rate.

[0139] Before the high-temperature tensile test, the critical strain value was analyzed according to the trend diagram of the change of steel chemical composition, such as... Figure 5 The diagram roughly defines the critical strain range for crack initiation under pressure. Then, different tensile strains are applied to the specimen within this strain range, and the crack formation inside the specimen before and after the tensile test is compared using a metallographic microscope to determine the critical strain value ε for crack initiation. c .

[0140] (4) Crack prediction;

[0141] Here, the zero plasticity temperature ZDT (corresponding to central solid fraction fs = 1.0) and the zero strength temperature ZST range (corresponding to central solid fraction fs = 0.75) of the cast billet are set as the crack-sensitive zone, that is, the central solid fraction distribution range corresponding to the crack-sensitive zone is fs: 0.75-1.0.

[0142] Based on the calculation results of the thermo-coupling model, the distribution of equivalent tensile strain at the corresponding pressing position of the billet cross-section at a specific time node (during pressing) is obtained. Then, the calculated strain value within the crack-sensitive zone of the billet is compared with the measured critical strain value. If the calculated strain value within the crack-sensitive zone of the billet is less than the critical strain value, ε c If the compressive crack is greater than or equal to the critical strain value ε, then it is determined that no compression crack will occur. c If so, it is determined that a pressure crack will occur.

[0143] Example:

[0144] By establishing a solidification heat transfer model, a specific 160×160mm continuous casting machine was obtained. 2 The temperature change curves of different parts of the 86 steel billet at different positions from the meniscus under the conditions of cooling intensity of 0.5 L / min and casting speed of 2.3 m / min were obtained. The chemical composition of the 86 steel was tested to be: 0.86 wt% C, 0.25 wt% Si, 0.52 wt% Mn, 0.01 wt% P, 0.01 wt% S, and the remainder Fe.

[0145] The surface temperature of the cast billet calculated by the model is as follows: Figure 6 As shown, the measured surface temperature of the center of the cast billet is also... Figure 6 It was marked in the middle. By Figure 6 It can be seen that the surface temperature of the billet calculated by the model is in good agreement with the measured temperature, with an error of less than 3% (the accuracy requirement is usually <5%). This indicates that the calculation results of the mathematical model are relatively accurate and can be used to simulate the solidification process of the billet. According to equation (3), the solidification process of the billet under the above casting conditions, that is, the distribution of solid fraction fs at different centers, is further obtained, such as Figure 7 As shown; from Figure 7 The specific location distribution of crack-sensitive regions (fs = 0.75-1.0) at different pouring positions can be obtained (the colored areas in the figure).

[0146] Based on the solidification heat transfer model, a thermo-mechanical coupling model was further established to obtain the distribution of the comprehensive effective strain of the billet cross section at a specific reduction position, at a distance of 15m from the meniscus, with a roll reduction of 4mm. Figure 8 As shown, when the reduction is 4mm, the distribution of the comprehensive effective strain of the billet cross section at the reduction position is shown, and the circular position is the crack-sensitive area.

[0147] For this specific pressing position, when the pressing amount of the pressure roller increases to 5mm, the distribution of the comprehensive effective strain of the billet cross section is also obtained through a thermo-mechanical coupling model, such as... Figure 9 As shown, when the reduction is 5mm, the distribution of the comprehensive effective strain of the billet cross section at the reduction position is shown, and the circular position is the crack-sensitive area.

[0148] Determination of critical strain:

[0149] (1) Determination of the high-temperature tensile test temperature;

[0150] The actual solidus temperature of the tested steel was measured using a Labsys thermogravimetric analyzer. Figure 10 To test the DSC curve of the steel grade, the solidus temperature of the tested steel grade can be obtained as 1351℃.

[0151] (2) High-temperature tensile test;

[0152] High-temperature tensile testing was conducted using the Gleeble thermal simulation system. The sample collection method and temperature control for the high-temperature tensile test followed the procedures described above. The test process employed a strain rate consistent with the actual pressing process of the continuous casting machine, namely 8*10. -3 s -1 The strain range for testing is 0.003-0.005.

[0153] Comparison of the metallographic structures inside the specimens under different strains reveals that no crack defects were found in the internal cross-section of the specimens when a strain of 0.003 was applied. Figure 11 (a); when the applied strain reaches 0.004, cracks begin to initiate at the grain boundaries, such as Figure 11 As shown in (b); when the strain is further increased to 0.005, as Figure 11 As shown in (c), the crack length increased significantly, which can be considered as the crack expanding further after initiation; therefore, by comparing the internal metallographic structure of the sample cross section under different strains, the critical strain value for the steel to produce hot cracks can be determined to be 0.004.

[0154] Determination of hot cracks in cast billets:

[0155] Based on the distance between the billet and the billet surface during the pressing process, it can be seen that when the pressing amount is 5mm, if... Figure 12 As shown, when the strain value in the crack-sensitive zone (48mm-56mm from the upper surface of the billet) exceeds the critical strain value of 0.004, a pressure crack will occur. This is related to... Figure 14 , Figure 15 The actual crack distribution at low magnification of the corresponding billet cross-section is consistent; however, when the reduction is 4mm, such as Figure 13As shown, the strain values ​​within the crack-sensitive zone did not reach the critical strain value, therefore no compression cracks occurred. This prediction result is consistent with... Figure 16 The actual cross-section of the cast billet remains consistent even under low magnification.

[0156] Based on the above-described preferred embodiments of the present invention, and through the foregoing description, those skilled in the art can make various changes and modifications without departing from the inventive concept. The technical scope of this invention is not limited to the contents of the specification, but must be determined according to the scope of the claims.

Claims

1. A method for determining internal pressure-induced hot cracks in cast billets based on a thermo-coupling model, characterized in that, Includes the following steps: Step 1: Calculate the solidification process of the cast billet using the two-dimensional Fourier heat transfer equation; The latent heat of solidification is treated using the equivalent specific heat capacity method; the solid fraction of the core phase during the solidification process of the billet is calculated; the average heat flux density during the crystallizer stage is calculated, as well as the instantaneous heat flux density distributed along the casting direction of the crystallizer; The formula for average heat flux density is: The formula for instantaneous heat flux density is: In the formula, The average heat flux density inside the crystallizer; The instantaneous heat flux density inside the crystallizer; The density of the cooling water; This refers to the flow rate of the cooling water in the crystallizer. This refers to the specific heat capacity of the cooling water. The temperature difference between the inlet and outlet water of the crystallizer; The effective contact area between the molten steel and the crystallizer; L The distance from the meniscus to the location of the instantaneous heat flux density is the distance between the location and the meniscus. L m The effective length of the crystallizer; For billet casting speed; Heat flux density is calculated from the heat transfer coefficient to determine the heat flow in each zone. The formula for the heat transfer coefficient is: in, W The density of the water flow; , , n These are constants related to the secondary cooling zone equipment; The formula for calculating heat flow is: Where ε is the radiation coefficient; It is the Stefan-Boltzmann constant; T b The surface temperature of the cast billet; T a ambient temperature Step 2: Construct a thermo-mechanical coupling model.

2. The method for determining internal pressing hot cracks in cast billets based on a thermo-coupling model according to claim 1, characterized in that, Heat transfer coefficients are classified into all-water cooling and air mist cooling.

3. The method for determining internal pressing hot cracks in cast billets based on a thermo-coupling model according to claim 1, characterized in that, Step two specifically includes: Step 21: Construct the elastic modulus under different temperature conditions; Step 22: Construct Poisson's ratio under different temperature conditions; Step 23: The bulk modulus can be calculated based on the elastic modulus and Poisson's ratio.

4. The method for determining internal pressing hot cracks in cast billets based on a thermo-coupling model according to claim 3, characterized in that, In step 21, when the temperature T At <500℃, elastic modulus =175Gpa; when T At 500-900℃, ; when T =900℃~Ts, ; when T When >Ts, ; in, The solid fraction corresponding to the zero intensity temperature; This represents the elastic modulus value corresponding to the solidus temperature Ts. It is a very small value that approaches zero; .

5. The method for determining internal pressing hot cracks in cast billets based on a thermo-coupling model according to claim 3, characterized in that, In step 22, when the temperature T <Ts, the Poisson's ratio (16); when T When ≥Ts, ; In the formula, This represents Poisson's ratio corresponding to the solidus temperature. To approach a value of 0.5, The solid fraction is the solid fraction at the zero intensity temperature.

6. The method for determining internal pressing hot cracks in cast billets based on a thermo-coupling model according to claim 3, characterized in that, In step 23, the formula for bulk modulus is: in, For elastic modulus, .

7. The method for determining internal pressing hot cracks in cast billets based on a thermo-coupling model according to claim 6, characterized in that, To make the elastic modulus E and The value of is approximately equal to the bulk modulus in the liquid state and the bulk modulus at room temperature.

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