Method for determining reheating process window of nb-ti microalloyed steel and storage medium

Abstract

The application discloses a kind of Nb-Ti microalloy steel reheating process window determination method and storage medium, belong to steel material heat treatment and material calculation simulation technical field.It includes the following steps: constructing multi-sequence parameter phase field model, simulate the growth process of austenite grain under different holding temperature and different holding time, obtain the organization morphology and grain size distribution of austenite grain;According to the grain size distribution calculation mixed crystal index, and according to the mixed crystal index with the change relation of holding temperature and / or holding time, determine the reheating process window of the Nb-Ti microalloy steel;The reheating process window includes reheating temperature interval and / or holding time.For the determination of Nb-Ti microalloy steel reheating process window provides basis, to inhibit austenite mixed crystal, improve organization uniformity.

Description

Technical Field

[0001] This invention belongs to the field of heat treatment and material calculation simulation technology of steel materials, specifically involving a method for determining the reheating process window of Nb-Ti microalloyed steel and a storage medium. Background Technology

[0002] Nb-Ti microalloyed steel effectively suppresses grain boundary migration and refines the microstructure by forming second-phase particles such as Nb(C,N) and TiN that pin austenite grain boundaries. Therefore, it is widely used in high-strength, high-fatigue-performance structural components. This type of steel typically requires high temperatures and long holding times during reheating, carburizing, or austenitizing after continuous casting. As temperature increases, grain boundary migration capacity increases, while the second-phase particles gradually coarsen or dissolve, and the pinning effect weakens. Austenite grains tend to grow rapidly, easily forming a mixed-grain structure where coarse and fine grain regions coexist. This mixed-grain structure leads to uneven local phase transformation behavior, hardenability, and mechanical properties, affecting subsequent processing and service performance.

[0003] For continuously cast billets, during solidification, elements such as Nb, Ti, and C are redistributed as the solid / liquid interface advances, and are enriched to varying degrees in the residual liquid phase between dendrites after solidification. This results in different local compositions and precipitation states between the dendritic trunk region and the interdendritic region. Moreover, the compositional differences at the dendritic scale are difficult to completely eliminate during conventional cooling. Existing research on the aforementioned mixed-crystal problem mainly falls into two categories: The first is reheating experimental characterization. For example, Chakrabarti et al. (Materials Characterization, 2007; Metall. Mater. Trans. A, 2008) conducted reheating experiments on continuously cast billets of different microalloying systems at 1050℃–1225℃ and combined this with Thermo-Calc calculations, indicating that the difference in precipitate stabilization temperature between the solute-rich and depleted regions is the main reason for the formation of bimodal austenite grains. Roy et al. (Metall. Mater. Trans. A, 2013) also found that in Nb / Ti composite microalloyed steel, the precipitate-rich region can maintain strong grain boundary pinning for a long time, while the grains in the adjacent depleted region are significantly coarsened. The second category involves thermodynamic calculations and the Gladman pinning model, which predicts the limiting austenite grain size by calculating the volume fraction of the second-phase particles and substituting them into the Gladman formula.

[0004] However, the aforementioned existing technologies have the following shortcomings: They all share the commonality of relying on the average composition of the steel, the average amount of precipitation, or uniform parameters for a specific region, failing to consider the non-uniform spatial distribution of second-phase particles caused by dendrite segregation during continuous casting solidification, and the resulting differences in the migration capacity of local grain boundaries between the dendrite trunk and interdendritic regions. Specifically, the results of reheating experimental characterization methods depend on the grain boundary erosion effect and the statistical grain number, lacking stability and universality, and are difficult to describe the continuous evolution of the differences in grain boundary migration between the dendrite trunk and interdendritic regions with holding time; Gladman-type models can only provide the limiting grain size, failing to reflect regional differences, and the calculation deviation increases at higher temperatures; furthermore, existing methods are mostly limited to a single dimension of grain size or precipitate state, lacking a universal quantitative evaluation of the degree of mixed crystals.

[0005] Furthermore, the compositional inhomogeneity caused by dendritic segregation in continuously cast billets is coupled with the spatial differences in its precipitation behavior: while thermodynamic calculations can provide equilibrium precipitation in each region, it remains difficult to quantitatively correlate this spatial inhomogeneity with the grain growth process within a unified framework, and to provide quantitative criteria that can guide the reheating process. Existing methods are either limited by statistical and characterization errors or by the spatial homogeneity assumptions of the model, making it difficult to simultaneously consider regional precipitation differences, regional grain boundary migration differences, and the continuous evolution of grain structure. This makes the quantitative evaluation of mixed crystals and the determination of the reheating process window a technical challenge that urgently needs to be solved in this field. Especially for Nb-Ti microalloyed steels with a total Nb and Ti content of 0.01wt%–0.05wt%, the low content of microalloying elements and small volume fraction of second-phase particles (Nb(C,N), TiN) result in relatively weak pinning effects that are in a critical state. Austenite grain growth is particularly sensitive to local compositional fluctuations and holding temperatures. Within this content range, solidification dendrite segregation can significantly amplify the differences in precipitation amount and pinning strength between the dendrite trunk region and the interdendritic region, making mixed crystal tendency and its evolution with temperature more difficult to predict, and narrowing the usable reheating process window. Existing methods based on average composition are unable to accurately characterize these local differences within this low content range, further increasing the technical difficulty of mixed crystal prediction and process window determination. Summary of the Invention

[0006] To address the shortcomings of the existing technology, this invention provides a method and storage medium for determining the reheating process window of Nb-Ti microalloyed steel. The method quantitatively transforms the local compositional and precipitation differences caused by dendrite segregation during continuous casting solidification into differences in grain boundary migration capabilities between the dendrite trunk region and the interdendritic region. Based on this, the austenite grain growth process is continuously simulated, and the degree of austenite mixing is quantitatively evaluated. This provides a basis for determining the reheating process window of Nb-Ti microalloyed steel, thereby suppressing austenite mixing and improving microstructure uniformity.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: The present invention provides a method for determining the reheating process window of Nb-Ti microalloyed steel, wherein the total Nb and Ti content in the Nb-Ti microalloyed steel is 0.01wt% to 0.05wt%, comprising the following steps: constructing a multi-order parametric phase-field model; according to the spatial distribution of the dendritic trunk region and the interdendritic region formed by solidification dendrite segregation in the computational domain, assigning the equivalent grain boundary mobility of the dendritic trunk region and the equivalent grain boundary mobility of the interdendritic region to the corresponding regions in the computational domain respectively; simulating the growth process of austenite grains at different holding temperatures and different holding times to obtain the microstructure and grain size distribution of austenite grains; calculating the mixed crystal index based on the grain size distribution; and determining the reheating process window of the Nb-Ti microalloyed steel based on the relationship between the mixed crystal index and the holding temperature and / or holding time; the reheating process window includes a reheating temperature range and / or holding time.

[0008] Furthermore, in the multi-order parametric phase-field model, the dendrite stem composition corresponds to the solid fraction f. s When the liquid phase composition is 0.05, the interdendritic composition corresponds to the solid phase fraction f. s The liquid phase composition when it is 0.95.

[0009] Furthermore, in the multi-order parameter phase-field model, the interface migration coefficient L of region R at time t... R (t) is calculated using the following formula:

[0010] ;

[0011] in, Considering the effective grain boundary mobility of various second-phase pinning at time t in region R, This represents the grain boundary width.

[0012] Furthermore, the gradient energy coefficient κ in the multi-order parameter phase-field model is calculated by the following formula:

[0013] ;

[0014] Where, γ GB For grain boundary interface energy, l GB This represents the grain boundary width.

[0015] Furthermore, the aforementioned The calculation formula is:

[0016] ;

[0017] in, For grain boundary mobility, The number of second-phase species involved in pinning calculations. Let be the standard deviation of the particle radius distribution of the p-th precipitate in region R. Let be the average radius of the p-th precipitated particle in region R. The spatial distribution index of the p-th precipitate phase. The weighting coefficients for the p-th precipitation type are: The effective volume fraction of the p-th precipitate in region R. Let be the average austenite grain size in region R.

[0018] Furthermore, the aforementioned The calculation method is as follows:

[0019] ;

[0020] in, The equilibrium precipitation volume fraction is obtained from Thermo-Calc based on the local composition of the dendritic trunk or interdendritic space. Let t be the thermodynamic temperature at time t. This represents the initial volume fraction of the p-th precipitate in region R at the start of heating. Let be the cumulative thermal history variable of the p-th precipitated phase at time t. R is the shape index of precipitation or solid solution kinetics, where R=D is the dendritic trunk and R=I is the interdendritic space.

[0021] Furthermore, the aforementioned The calculation formula is:

[0022] ;

[0023] in, The precipitated phase is numbered, and t is the heating or holding time. For integration time variable, Let p be the pre-exponential coefficient of the kinetics of the p-th precipitate phase. Let R be the apparent activation energy for the coarsening or solid solution process of the p-th precipitated phase, and R be the gas constant. for The corresponding thermodynamic temperature.

[0024] Furthermore, the mixed crystal index The calculation formula is:

[0025] ;

[0026] in, This represents the total area of ​​the coarse-grained region. This represents the total area of ​​the fine-grained region. Characteristic grain size of the coarse-grained region. This represents the characteristic grain size of the fine-grained region.

[0027] This invention also provides a system for determining the reheating process window of Nb-Ti microalloyed steel, comprising: a multi-order parametric phase-field model calculation module, which, according to the spatial distribution of the dendritic trunk region and the interdendritic region formed by solidification dendrite segregation within the calculation domain, assigns the equivalent grain boundary mobility of the dendritic trunk region and the equivalent grain boundary mobility of the interdendritic region to corresponding regions within the calculation domain, respectively, to simulate the growth process of austenite grains at different holding temperatures and holding times, thereby obtaining the microstructure and grain size distribution of austenite grains; and a result output module, which calculates the mixed crystal index based on the grain size distribution, and determines the reheating process window of the Nb-Ti microalloyed steel based on the relationship between the mixed crystal index and the holding temperature and / or holding time; the reheating process window includes a reheating temperature range and / or holding time.

[0028] The present invention also provides a storage medium storing a computer program, which, when executed, implements the above-described method for determining the reheating process window.

[0029] Compared with the prior art, the present invention has the following beneficial effects:

[0030] (1) The compositional differences caused by solidification dendrite segregation are quantitatively converted into the equivalent grain boundary mobility of the dendrite trunk and the interdendritic region through thermodynamic precipitation calculation, and then assigned to the phase field model according to their spatial distribution. This allows for the description of the differences in regional grain boundary mobility and their continuous evolution with holding time within a unified framework, overcoming the shortcomings of existing models that are based on average composition / average precipitation and are difficult to reflect spatial non-uniform pinning.

[0031] (2) Define the mixed crystal index f mg This study provides a universal and quantitative evaluation of the degree of mixed crystals, overcoming the shortcomings of existing experimental characterization methods that rely on grain boundary erosion effects and statistical grain numbers, and Gladman-type models that only provide limiting grain sizes and exhibit increased deviations at high temperatures. Calculations show that as the holding temperature increases, f mg It first increases and then decreases, reaching 0.41 at 1050℃, increasing to about 0.6 at 1150℃ (when mixed crystals are most severe), and decreasing to about 0.25 at 1300℃.

[0032] (3) Based on the relationship between the mixed crystal index and temperature / time, the reheating process window (temperature range and / or holding time) can be determined, suggesting that long-term stay in the mixed crystal sensitive range should be avoided; the phase field simulation reproduced the overall coarsening and non-monotonic change of mixed crystals that occurred with the increase of temperature in the experiment (the average grain size increased from 59.28 μm at 1050℃ to 159.46 μm at 1300℃), which is in good agreement with the actual measurement.

[0033] (4) The process window output is a reheating temperature range and holding time that can be directly executed. It has industrial applicability and is suitable for microalloyed steel continuous casting billets containing Nb and Ti and their reheated steel.

[0034] (5) For Nb-Ti microalloyed steel with a total Nb and Ti content of only 0.01wt% to 0.05wt%, the volume fraction of the second phase particles (Nb(C,N) and TiN) is small, the pinning effect is relatively weak and it is in a critical state, which puts forward high requirements for the spatial resolution and quantitative accuracy of the simulation method. This invention finely incorporates the equivalent grain boundary mobility of the dendrite trunk and the interdendritic region into the phase field model according to their spatial distribution, and quantitatively incorporates the pinning effect of various second phase particles and their precipitation / solution kinetics. It can distinguish the weak regional pinning differences in this low content range, thereby accurately reproducing the non-uniform growth and mixed crystal evolution of austenite grains. Compared with the existing methods based on average composition, which are difficult to characterize local differences, this scheme has significant technical difficulty and advancement in determining the reheating process window in this low content system. Attached Figure Description

[0035] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0036] Figure 1 This is a dendritic segregation erosion morphology image near the surface of the billet provided in Embodiment 1 of the present invention;

[0037] Figure 2 This is a simulation diagram of the austenite grain structure of Embodiment 1 of the present invention when held at 1050℃ for 1 hour;

[0038] Figure 3 The frequency distribution of the simulated grain structure results of Example 1 of the present invention after heat treatment at 1050℃ for 1 hour;

[0039] Figure 4 This is a simulation diagram of the austenite grain structure of Embodiment 1 of the present invention when held at 1150℃ for 1 hour;

[0040] Figure 5 The frequency distribution of the simulated grain structure results of Example 1 of the present invention after heat treatment at 1150℃ for 1 hour;

[0041] Figure 6 This is a simulation diagram of the austenite grain structure of Embodiment 1 of the present invention when held at 1300℃ for 1 hour;

[0042] Figure 7The frequency distribution of the simulated grain structure results of Example 1 of the present invention after heat treatment at 1300℃ for 1 hour;

[0043] Figure 8 This is a diagram of the austenite grain structure of Experiment 1 of the present invention after being kept at 1050℃ for 1 hour;

[0044] Figure 9 This is a diagram of the austenite grain structure of Experiment 1 of the present invention after being kept at 1150℃ for 1 hour;

[0045] Figure 10 This is a diagram of the austenite grain structure of Experiment 1 of the present invention after being kept at 1300℃ for 1 hour. Detailed Implementation

[0046] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the scope of protection of the invention.

[0047] Unless otherwise specified, those skilled in the art will recognize that the parameter values ​​in the formulas provided in this invention are existing technologies, can be obtained from references, or can be derived from experience.

[0048] This invention provides a method for determining the reheating process window of Nb-Ti microalloyed steel, wherein the total Nb and Ti content in the Nb-Ti microalloyed steel is 0.01wt% to 0.05wt%, comprising the following steps:

[0049] (1) Construct a multi-order parameter phase field model. According to the spatial distribution of the dendritic trunk region and the interdendritic region formed by solidification dendrite segregation in the computational domain, assign the equivalent grain boundary mobility of the dendritic trunk region and the equivalent grain boundary mobility of the interdendritic region to the corresponding regions in the computational domain respectively. Simulate the growth process of austenite grains under different holding temperatures and different holding times to obtain the microstructure and grain size distribution of austenite grains.

[0050] (2) Calculate the mixed crystal index based on the grain size distribution, and determine the reheating process window of the Nb-Ti microalloyed steel based on the relationship between the mixed crystal index and the holding temperature and / or holding time; the reheating process window includes the reheating temperature range and / or holding time.

[0051] Phase-field simulation methods:

[0052] The phase-field method can simply and clearly characterize the geometric morphology of any complex grain structure through field variables, and it can simulate various phenomena such as nucleation, growth, coarsening, and externally induced grain structure changes. This study uses a multi-order parametric phenomenological phase-field model to construct an austenite grain growth model of the reheating process of experimental steel grades in MATLAB, and analyzes its grain growth behavior. In this model, a series of phase-field variables (η1(r, t), η2(r, t), ..., η...) are used to characterize the geometric morphology of any complex grain structure. o (r, t) are used to distinguish different crystal orientations of the grain. These order parameters are functions of time and spatial coordinates. In the grain η i Internally, η i =1 or -1, while other order parameters are 0. At grain boundaries, parameter η is... i The phase field parameters gradually change from 1 (or -1) to 0, while the parameters corresponding to adjacent grains gradually change from 0 to 1 or -1. In the calculation, the evolution of the phase field parameters is driven by the decrease in the total free energy of the system. The system free energy function can be expressed as:

[0053] ;

[0054] In the formula, κ i These are the gradient term coefficients, where Q is the total number of phase field parameters, with coefficients α=1, β=1, and γ=1.5. The evolution of the order parameters is described by the Ginzburg–Landau (time-dependent Ginzburg–Landau, TDGL) equation, namely:

[0055] ;

[0056] In the formula, L i This refers to the interface migration coefficient. Assuming that the mobility and gradient coefficients in the system are isotropic, the governing equations for the evolution of order parameters during grain growth can be obtained:

[0057] ;

[0058] The parameters required in the model are the interface migration coefficient L and the gradient energy coefficient κ, which are calculated by the following formulas:

[0059] ;

[0060] Where, γ GB Grain boundary interface energy; l GB The grain boundary width is taken as 5 × 10. -4 cm.

[0061] ;

[0062] in, Consider the effective grain boundary mobility at time t for various second phase pinnings in region R.

[0063] To account for the hindering effect of second-phase particles on austenite grain boundary migration, the pinning effect of second-phase particles is transformed into a correction for grain boundary mobility, i.e. The The calculation formula is:

[0064] ;

[0065] in, The unit is cm 4 J -1 s -1 ; The grain boundary mobility is expressed in cm. 4 J -1 s -1 ; The number of second-phase species involved in the pinning calculation is dimensionless. Let be the standard deviation of the radius distribution of the p-th precipitate particles in region R, in μm; Let be the average radius of the p-th precipitated particle in region R, in μm; Let be the spatial distribution index of the p-th precipitate phase, which is dimensionless; The weighting coefficient for the p-th precipitate is dimensionless. Let be the effective volume fraction of the p-th precipitate in region R at time t, which is dimensionless; Let be the average austenite grain size in region R, in μm.

[0066] The austenite grain boundary mobility is a function of temperature and composition, as shown in the following equation:

[0067] ;

[0068] In the formula, M0 is the pre-exponential constant, Q is the grain boundary migration activation energy, R is the universal gas constant, and T is the temperature. The activation energy can be obtained by regression analysis of experimental data, and its relationship with the carbon equivalent is shown in the following formula.

[0069] ;

[0070] ;

[0071] For Nb-containing microalloyed steel, the grain boundary mobility and interfacial energy at 1050℃ can be taken as 0.71 × 10⁻⁶. - 4 cm 4 / (J·s), 0.7×10 -4 J / cm 2The calculated grain boundary mobility at different temperatures is shown in Table 1, while the interface energy is set as a constant.

[0072] Table 1 Calculation results of grain boundary mobility

[0073] <![CDATA[M GB ]]> <![CDATA[7.1×10 -5 ]]> <![CDATA[1.26×10 -4 ]]> <![CDATA[2.14×10 -4 ]]> <![CDATA[3.52×10 -4 ]]> <![CDATA[5.59×10 -4 ]]> <![CDATA[8.63×10 -4 ]]>

[0074] The The calculation method is as follows:

[0075] ;

[0076] in, The equilibrium precipitation volume fraction obtained from Thermo-Calc based on the local composition of the dendritic trunk or interdendritic space is dimensionless. Let be the thermodynamic temperature at time t, in K. The initial volume fraction of the p-th precipitate in region R at the start of heating is dimensionless. Let be the cumulative thermal history variable of the p-th precipitated phase at time t, which is dimensionless; The shape index is the kinetic index of precipitation or solid solution, which is dimensionless; R=D represents the dendritic trunk, and R=I represents the interdendritic space.

[0077] The The calculation formula is:

[0078] ;

[0079] in, The precipitated phase is numbered, and t is the heating or holding time, in seconds; Let be the integration time variable, s; Let s be the pre-exponential coefficient of the kinetics of the p-th precipitate phase. -1 ; The apparent activation energy (J / mol) for the coarsening or solid solution process of the p-th precipitated phase. -1 R is the gas constant, 8.314 J / mol. -1 K -1 ; for The corresponding thermodynamic temperature, K.

[0080] The mixed crystal index The calculation formula is:

[0081] ;

[0082] in, The total area of ​​the coarse-grained region, in μm 2 ; The total area of ​​the fine-grained region is μm. 2 ; The characteristic grain size of the coarse-grained region is in μm; The characteristic grain size of the fine-grained region is in μm.

[0083] It should be noted that the threshold for the mixed crystal index can be determined based on the quenching conditions, and the mixed crystal index calculated by the model can be selected. The process window with a mixed crystal index threshold less than the threshold is used to determine the final re-annealing process window. For example, in Example 1 below, if the mixed crystal index threshold is 0.45, the process parameters of re-annealing temperature of 1050℃ and holding for 1h or re-annealing temperature of 1300℃ and holding for 1h can be selected. If the mixed crystal index threshold is 0.3, the process parameter of re-annealing temperature of 1300℃ and holding for 1h can only be selected.

[0084] The computational domain for the phase-field simulation was selected as 1000μm × 1000μm, with a grid spacing of 1μm and a time step of 0.04s. The model was solved using the finite difference method with periodic boundary conditions, implemented in MATLAB. To consider computational efficiency and minimize grain merging, the total number of order parameters was set to 48. During initialization, the order parameters at each node were randomly assigned values ​​between -0.001 and 0.001. A five-point Laplace operator was used for matrix operations. The time term was discretized using the backward difference method.

[0085]

[0086] This invention also provides a system for determining the reheating process window of Nb-Ti microalloyed steel, comprising: a multi-order parametric phase-field model calculation module, which, according to the spatial distribution of the dendritic trunk region and the interdendritic region formed by solidification dendrite segregation within the calculation domain, assigns the equivalent grain boundary mobility of the dendritic trunk region and the equivalent grain boundary mobility of the interdendritic region to corresponding regions within the calculation domain, respectively, to simulate the austenite grain growth process under different holding temperatures and holding times, thereby obtaining the microstructure and grain size distribution of the austenite grains; and a result output module, which calculates the mixed crystal index based on the grain size distribution, and determines the reheating process window of the Nb-Ti microalloyed steel based on the relationship between the mixed crystal index and the holding temperature and / or holding time; the reheating process window includes a reheating temperature range and / or holding time.

[0087] This invention also provides a storage medium storing a computer program that, when executed, implements the above-described method for determining the reheating process window.

[0088] The mixing index is calculated based on the grain size distribution, and the reheating process window for the Nb-Ti microalloyed steel is determined based on the relationship between the mixing index and the holding temperature and / or holding time. The reheating process window includes a reheating temperature range and / or holding time. For example, at 1050°C, the lower basic migration rate and stable particles jointly inhibit grain growth; at approximately 1150°C, the dendrite trunk region migrates faster while the interdendritic region remains pinned, resulting in the greatest difference in regional growth rates and the highest degree of mixing; at 1300°C, a large amount of precipitates dissolves, leading to the most significant overall coarsening, but the size contrast between coarse and fine regions decreases. From a process control perspective, prolonged stays in the mixing-sensitive range should be avoided; simply increasing the holding temperature may reduce the degree of mixing, but it will cause severe overall grain coarsening. The final process window is determined by the actual engineering requirements.

[0089] The experimental samples were taken from Nb-Ti microalloyed steel continuous casting billets from a domestic steel plant, and their chemical composition is shown in Table 2.

[0090] Table 2 Chemical composition (wt.%) of the experimental steel grades

[0091] 0.14 0.17 1.15 0.012 0.003 0.03 0.015 0.03 0.005

[0092] Characterization methods:

[0093] For measuring grain size in real sample tests: the heat-treated sample was polished, and the surface of the polished sample was etched with a saturated picric acid aqueous solution and an activator. The austenite grain boundaries were observed and photographed using a Leica DM4 M optical microscope. The grain structure diagram of austenite in the photographed image was outlined using AutoCAD software. The data was processed using a program edited using MATLAB software to obtain the austenite grain size.

[0094] Grain size analysis method: To characterize the austenite grain size distribution, approximately 1000 grains were statistically analyzed, and the equivalent circle diameter was calculated based on the grain area. A linear scale was used to divide all grains into 15 equal-width ECD intervals, and the grain size frequency distribution was plotted. The peak characteristics of the distribution curves were used to determine whether the grain size distribution exhibited a single-peak or double-peak characteristic. For microstructures with obvious double-peak characteristics, the method proposed by Chakrabarti et al. (Chakrabarti D, Davis C, Strangwood M. Characterisation of bimodal grain structures in HSLA steels[J]. Materials Characterization, 2007, 58(5): 423-438.) was used to determine the fine-grain peak and coarse-grain peak respectively.

[0095] The areas of the fine-grained and coarse-grained regions are mainly based on grain size histograms obtained from different experimental schemes, see [link to relevant documentation]. Figure 3 , Figure 5 , Figure 7 As shown, statistics were performed based on 15 equal-width ECD (equivalent diameter) intervals. The first peak is the peak value of the fine-grained region. All regions smaller than this value are fine-grained regions. The area of ​​the fine-grained region is obtained by converting the diameter to the equivalent circle area and then adding them together. The second peak is the peak value of the coarse-grained region. All regions larger than this value are coarse-grained regions. The area of ​​the coarse-grained region is obtained by converting the diameter to the equivalent circle area and then adding them together.

[0096] Example 1

[0097] Studies have shown that microsegregation in the billet leads to uneven distribution of precipitates, directly affecting the uneven distribution of austenite grains after reheating. Specifically, solute-depleted regions have fewer precipitates, which tend to form coarse grains, while solute-rich regions have more precipitates, which tend to form fine grains. To more significantly highlight the bimodal distribution of austenite after reheating, a region with severe segregation was selected for phase field calculations to better reflect the relationship between the degree of coarsening or mixed crystals in the reheated austenite and the degree of segregation in the billet. A 12.5mm × 12.5mm sample located 10mm from the billet surface was selected for characterizing the dendritic segregation morphology of the billet. The surface of the polished sample was dendriticized using a saturated picric acid aqueous solution with an surfactant, and the dendritic morphology of the sample cross-section was obtained and photographed. A 1000 μm × 1000 μm region with severe segregation was selected on the sample surface as the computational domain for phase-field simulation and thermodynamic analysis. The morphology of the dendritic segregation region within the computational domain was obtained by outlining with Photoshop software. The microsegregation model adopted the widely accepted Clyne-Kurz method (Roy S, Patra S, Neogy S, et al. Prediction of inhomogeneous distribution of microalloy precipitates in continuous-cast high-strength, low-alloy steelslab[J]. Metallurgical and Materials Transactions A, 2012, 43: 1845-1860;), where the composition of the solute-depleted region (dendritic trunk) corresponds to the solid fraction f. s When the liquid phase composition is 0.05, the composition of the solute-rich region (interdendritic zone) corresponds to the solid phase fraction f. sThe liquid phase composition is 0.95. The solid-liquid phase temperature of the target steel was calculated using Thermo-Calc thermodynamic software. The solidification front temperature was calculated according to the methods proposed by Ma et al. (Ma Z, Janke D. Characteristics of oxide precipitation and growth during solidification of deoxidized steel[J]. ISIJ International, 1998, 38(1): 46-52.) and Liu et al. (Liu Z, Wei J, Cai K. A coupled mathematical model of microsegregation and inclusion precipitation during solidification of silicon steel[J]. ISIJ International, 2002, 42(9): 958-963.). The average cooling rate was estimated based on the secondary dendrite arm spacing (SDAS) of the sample, thereby obtaining the local content of each element in the dendrite trunk and interdendritic region. The local composition of each element in the dendrite trunk and interdendritic region was calculated according to the above microsegregation model, and the results are shown in Table 3.

[0098] Table 3. Local chemical composition (wt.%) of dendritic trunk and interdendritic region

[0099] dendritic trunk 0.07 0.14 1.02 0.007 0.001 0.025 0.007 0.012 0.003 Dendrites 0.32 0.22 1.42 0.023 0.009 0.032 0.031 0.067 0.009

[0100] Dendritic segregation erosion results near the surface of the cast billet are as follows Figure 1 As shown, a 1000μm × 1000μm region with severe segregation was selected as the computational domain for phase-field simulation. The elemental contents of the interdendritic and dendritic trunk regions are taken from Table 3, and the model values ​​are shown in Table 4.

[0101] Table 4 Suggested values ​​for key input parameters of the phase-field model

[0102] grain boundary parameters Grain boundary width <![CDATA[l GB ]]> <![CDATA[5×10⁻ 4 ]]> cm grain boundary parameters Grain boundary interfacial energy <![CDATA[γ GB ]]> <![CDATA[0.7×10⁻ 4 ]]> J / cm² Grain boundary migration Pre-grain boundary migration factor M0 <![CDATA[3.0×10 4 ]]> <![CDATA[cm 4 / (J·s)]]> Grain boundary migration Grain boundary migration activation energy Q <![CDATA[2.0×10 5 ]]> J / mol Second phase Participating in the calculation of the number of second phase types Np 2 TiN, Nb(C,N) Second phase Initial volume fraction of TiN - 1.2×10⁻³ Dimensionless Second phase Nb(C,N) initial volume fraction - <![CDATA[6.0×10⁻ 4 ]]> Dimensionless Second phase Dendritic TiN volume fraction - <![CDATA[8.0×10⁻ 4 ]]> Dimensionless Second phase interdendritic TiN volume fraction - 1.8×10⁻³ Dimensionless Second phase Dendritic stem Nb(C,N) volume fraction - <![CDATA[3.0×10⁻ 4 ]]> Dimensionless Second phase interdendritic Nb(C,N) volume fraction - 1.5×10⁻³ Dimensionless Particle size Average radius and standard deviation of TiN - Radius: 0.10 μm Particle size Mean radius and standard deviation of Nb(C,N) - Standard deviation: 0.03 μm dynamics Precipitation / solution kinetics shape index - Radius: 0.05 Dimensionless Spatial distribution Second phase spatial distribution index - Standard deviation: 0.015 Dimensionless Weighting coefficient Second phase pinning weighting factor - 2 Dimensionless

[0103] Parameter value description

[0104] 1. The grain boundary migration parameters were adopted using typical Arrhenius form parameters from studies of austenite grain growth in Nb microalloyed steel. (The text abruptly ends here, likely due to an incomplete sentence or missing information.) GB Calculated using M0exp(-Q / RT), the grain boundary mobility near 1050℃ is approximately 7.1×10⁻⁻⁻⁶. 5 cm 4 / (J·s), consistent with the migration rate given in the patent embodiments.

[0105] 2. The second-phase parameters take into account the microsegregation effect of continuous casting. Nb, Ti, C, and N elements are enriched in the interdendritic region, so the volume fractions of TiN and Nb(C,N) are higher than those in the dendritic trunk region.

[0106] 3. The second phase type involved in the pinning calculation is set as TiN and Nb(C,N), i.e., N p =2.

[0107] 4. The precipitation / solution kinetic index adopts the commonly used value n=2 for diffusion-controlled processes.

[0108] The microstructure was simulated after holding at 1050℃, 1150℃, and 1300℃ for 1 hour, respectively. The peak values ​​of the fine-grained and coarse-grained regions were statistically analyzed, and the mixed crystal index was calculated. The three process regimes mentioned above used the same samples as the experimental examples, named Sample 1, Sample 2, and Sample 3, respectively. The simulation modeled the state of the samples before heat treatment and after erosion.

[0109] Sample 1: Figure 2 The austenite grain structure after holding at 1050℃ for 1 hour. Figure 3 The frequency distribution of the simulated grain structure after holding at 1050℃ for 1 hour is shown. Calculations indicate that the peak value in the fine-grained region is approximately 50 μm, and the peak value in the coarse-grained region is approximately 90 μm. It is 0.41.

[0110] Sample 2: Figure 4 The austenite grain structure after holding at 1150℃ for 1 hour. Figure 5 The frequency distribution of the grain structure simulation results after holding at 1150℃ for 1 hour is shown. Calculations indicate that the peak value in the fine-grained region is approximately 60 μm, and the peak value in the coarse-grained region is approximately 160 μm. It is 0.60.

[0111] Sample 3: Figure 6 The austenite grain structure after holding at 1300℃ for 1 hour. Figure 7 The frequency distribution of the grain structure simulation results after holding at 1300℃ for 1 hour is shown. Calculations show that the peak value in the fine-grained region is approximately 120 μm, and the peak value in the coarse-grained region is approximately 200 μm. It is 0.25.

[0112] Experimental Example 1

[0113] Samples 1, 2, and 3 were heated at 1050℃, 1150℃, and 1300℃ for 1 hour respectively. The peak values ​​of the fine-grained and coarse-grained regions were measured, and the mixed crystal index was calculated. .

[0114] Sample 1: Figure 8The austenite grain structure after holding at 1050℃ for 1 hour was calculated to have a peak value of approximately 51 μm in the fine-grained region and approximately 92 μm in the coarse-grained region. It is 0.40.

[0115] Sample 2: Figure 9 The austenite grain structure after holding at 1150℃ for 1 hour was calculated to have a peak value of approximately 62 μm in the fine-grained region and approximately 159 μm in the coarse-grained region. It is 0.62.

[0116] Sample 3: Figure 10 The austenite grain structure after holding at 1300℃ for 1 hour is shown. Calculations indicate that the peak value in the fine-grained region is approximately 118 μm, and the peak value in the coarse-grained region is approximately 203 μm. It is 0.24.

[0117] By comparing the examples and experimental cases, it can be seen that the calculation results of the improved model have a very small error compared with those of the experimental cases, and can be used to determine the reheating process window.

[0118] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for determining the reheating process window of Nb-Ti microalloyed steel, wherein the total Nb and Ti content in the Nb-Ti microalloyed steel is 0.01wt% to 0.05wt%, characterized in that, Includes the following steps: A multi-order parametric phase-field model is constructed. According to the spatial distribution of the dendritic trunk region and the interdendritic region formed by solidification dendrite segregation in the computational domain, the equivalent grain boundary mobility of the dendritic trunk region and the equivalent grain boundary mobility of the interdendritic region are respectively assigned to the corresponding regions in the computational domain. The growth process of austenite grains under different holding temperatures and different holding times is simulated to obtain the microstructure and grain size distribution of austenite grains. The mixed crystal index is calculated based on the grain size distribution, and the reheating process window of the Nb-Ti microalloyed steel is determined based on the relationship between the mixed crystal index and the holding temperature and / or holding time; the reheating process window includes the reheating temperature range and / or holding time.

2. The method for determining the reheating process window according to claim 1, characterized in that, In the multi-order parametric phase-field model, the dendritic stem component corresponds to the solid fraction f. s When the liquid phase composition is 0.05, the interdendritic composition corresponds to the solid phase fraction f. s The liquid phase composition when it is 0.

95.

3. The method for determining the reheating process window according to claim 1, characterized in that, The interface migration coefficient L in region R at time t in the multi-order parameter phase-field model R (t) is calculated using the following formula: ； in, Considering the effective grain boundary mobility of various second-phase pinning at time t in region R, This represents the grain boundary width.

4. The method for determining the reheating process window according to claim 3, characterized in that, The gradient energy coefficient κ in the multi-order parameter phase-field model is calculated by the following formula: ； Where, γ GB For grain boundary interface energy, l GB This represents the grain boundary width.

5. The method for determining the reheating process window according to claim 4, characterized in that, The The calculation formula is: ； in, For grain boundary mobility, The number of second-phase species involved in pinning calculations. Let be the standard deviation of the particle radius distribution of the p-th precipitate in region R. Let be the average radius of the p-th precipitated particle in region R. The spatial distribution index of the p-th precipitate phase. The weighting coefficients for the p-th precipitation type are: Let p be the effective volume fraction of the p-th precipitate in region R at time t. Let be the average austenite grain size in region R.

6. The method for determining the reheating process window according to claim 5, characterized in that, The The calculation method is as follows: ； in, The equilibrium precipitation volume fraction is obtained from Thermo-Calc based on the local composition of the dendritic trunk or interdendritic space. Let t be the thermodynamic temperature at time t. This represents the initial volume fraction of the p-th precipitate in region R at the start of heating. Let be the cumulative thermal history variable of the p-th precipitated phase at time t. R is the shape index of precipitation or solid solution kinetics, where R=D is the dendritic trunk and R=I is the interdendritic space.

7. The method for determining the reheating process window according to claim 6, characterized in that, The The calculation formula is: ； in, The precipitated phase is numbered, and t is the heating or holding time. For integration time variable, Let p be the pre-exponential coefficient of the kinetics of the p-th precipitate phase. Let R be the apparent activation energy for the coarsening or solid solution process of the p-th precipitated phase, and R be the gas constant. for The corresponding thermodynamic temperature.

8. The method for determining the reheating process window according to claim 1, characterized in that, The mixed crystal index The calculation formula is: ； in, This represents the total area of ​​the coarse-grained region. This represents the total area of ​​the fine-grained region. Characteristic grain size of the coarse-grained region. This represents the characteristic grain size of the fine-grained region.

9. A system for determining the reheating process window for Nb–Ti microalloyed steel, characterized in that, include: The multi-parameter phase field model calculation module, according to the spatial distribution of the dendritic trunk region and the interdendritic region formed by solidification dendrite segregation in the calculation domain, assigns the equivalent grain boundary mobility of the dendritic trunk region and the equivalent grain boundary mobility of the interdendritic region to the corresponding regions in the calculation domain, respectively, to simulate the growth process of austenite grains under different holding temperatures and different holding times, and obtains the microstructure and grain size distribution of austenite grains; The results output module calculates the mixed crystal index based on the grain size distribution, and determines the reheating process window of the Nb-Ti microalloyed steel based on the relationship between the mixed crystal index and the holding temperature and / or holding time; the reheating process window includes the reheating temperature range and / or holding time.

10. A storage medium, characterized in that, The storage medium stores a computer program that, when executed, implements the reheating process window determination method according to any one of claims 1-8.

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