Post-weld heat treatment process optimization method for g115 steel welded pipe

Abstract

The application discloses a post-weld heat treatment process optimization method for G115 steel welded pipes and relates to the technical field of heat treatment numerical simulation. Through three core technologies of multi-physical field coupling modeling, data-physical dual driving algorithm and closed-loop real-time regulation and control, the application realizes the full-process intelligentization from parameter design to process control, solves problems of traditional processes, such as experience dependence, lack of system coupling consideration, long optimization period, unstable performance and the like, and significantly improves the organizational stability of the post-weld heat treatment of the G115 steel welded pipes, reduces residual stress, and reduces energy consumption and cost.

Description

Technical Field

[0001] This application relates to the field of heat treatment numerical simulation technology, and in particular to an optimization method for post-weld heat treatment of G115 steel welded pipes. Background Technology

[0002] In the field of welding manufacturing, post-weld heat treatment is a crucial process for ensuring welding quality. Its core function is to eliminate residual welding stress, stabilize the microstructure, and improve the overall mechanical properties of the joint. For welded pipes made of advanced heat-resistant steels such as G115 steel, flexible ceramic resistance heating technology has become the preferred heat treatment process in engineering applications due to its flexibility and adaptability. However, traditional process parameter design mainly relies on empirical formulas and trial-and-error methods, lacking a systematic consideration of the coupling effect of the temperature field and stress field. This leads to insufficient control over the performance stability of welded joints, resulting in problems such as excessive hardness fluctuations or insufficient impact toughness in some workpieces. Furthermore, the process optimization cycle is long and costly, requiring multiple rework heat treatments to meet acceptance standards, increasing energy consumption. Summary of the Invention

[0003] This application provides a method for optimizing the post-weld heat treatment process of G115 steel welded pipes. This method addresses the problems of traditional process parameter design relying mainly on empirical formulas and trial-and-error methods, lacking a systematic consideration of the coupling effect of temperature field and stress field, resulting in insufficient control of the performance stability of welded joints, problems such as excessive hardness fluctuations or substandard impact toughness in some workpieces, long process optimization cycles, high costs, and the need for multiple rework heat treatments to meet acceptance standards, which increases energy consumption.

[0004] Firstly, an optimized method for post-weld heat treatment of G115 steel welded pipes is provided, including:

[0005] Obtain the geometric parameters and material property parameters of the G115 steel welded pipe, and determine the bevel type, bevel geometric parameters, and the number of weld layers and passes of the G115 steel welded pipe based on the geometric parameters.

[0006] Based on the bevel geometry parameters, the welding process parameters of the G115 steel welded pipe are estimated so that the welding heat input of G115 steel is within the preset heat input range.

[0007] Based on the analytical model of heat input and temperature field of G115 steel welding, the temperature field distribution of the G115 steel welded pipe after welding is calculated, and the post-weld microstructure distribution of the temperature field distribution is determined based on the temperature threshold judgment rule.

[0008] Based on the chemical composition and preset mixing rules of G115 steel, the thermophysical performance parameters of the welded pipe of G115 steel at different temperatures are calculated. Based on the empirical formula of material strength and temperature degradation relationship, the temperature-related elastoplastic constitutive model of G115 steel is constructed, and the creep constitutive model of G115 steel is constructed based on the time-hardening creep power law model.

[0009] Based on the welding heat input of the G115 steel, the geometric parameters, and the preset constraint state, the residual stress distribution of the G115 steel welded pipe after welding is calculated by a preset empirical formula for residual stress.

[0010] Based on the geometric parameters, the bevel form, the bevel geometry, the number of weld layers and passes, the thermophysical performance parameters, the elasto-plastic constitutive model, the creep constitutive model, and the residual stress distribution, a multiphysics coupled numerical model for the post-weld heat treatment of the G115 steel welded pipe is constructed. The multiphysics coupled numerical model includes heat conduction, elasto-plastic deformation, creep deformation, and coupling of convective heat transfer and radiative heat transfer.

[0011] In the multiphysics coupled numerical model, the surface heat source power is controlled by the Adam adaptive learning rate optimization algorithm to simulate the flexible ceramic resistance heating process, so as to obtain temperature distribution data and stress distribution data under different heat treatment process parameters. The heat treatment process parameters include heating width, holding width and heating rate.

[0012] Based on the temperature distribution data, the tempered martensite content and hardness distribution of the G115 steel welded pipe are calculated. Based on the coupling relationship model between the tempered martensite content and the hardness, the hardness distribution of the G115 steel welded pipe after welding is obtained. At the same time, based on the coupling model between the residual stress distribution and the hardness, the equivalent distribution of the residual stress distribution after welding is obtained.

[0013] The equivalent distributions of the geometric parameters, material property parameters, heat treatment process parameters, temperature field distribution, inner and outer wall temperature difference, post-weld microstructure distribution and hardness distribution of the inner and outer walls, and residual stress distribution of the inner and outer walls of the G115 steel welded pipe are correlated to construct a multi-source heterogeneous database. A composite model of Gaussian process regression algorithm and generative adversarial network is used to expand and improve the quality of the multi-source heterogeneous database.

[0014] Based on the principle of temperature difference control between inner and outer walls, a constraint function is constructed, and the constraint function is iteratively trained by a multi-physics coupling coefficient correction algorithm and a gradient boosting regression algorithm to minimize the deviation between the predicted inner and outer wall temperature difference and the actual temperature difference in the processed multi-source heterogeneous database, thus forming a physical-data dual-driven process optimization algorithm.

[0015] Based on the physical-data dual-driven process optimization algorithm, the target heating width and the target heat preservation width are calculated under the constraint of meeting the hardness requirements.

[0016] In the actual post-weld heat treatment process, the G115 steel welded pipe is subjected to post-weld heat treatment based on the target heating width, the target heat preservation width and the preset heating rate. The measured value of the temperature difference between the inner and outer walls of the pipe is obtained in real time during the heat treatment process. The heating power is dynamically adjusted based on the physical-data dual-driven process optimization algorithm to achieve real-time closed-loop control of the temperature difference between the inner and outer walls.

[0017] Secondly, a device for optimizing the post-weld heat treatment process of G115 steel welded pipes is provided, comprising:

[0018] The first acquisition module is used to acquire the geometric parameters and material property parameters of the G115 steel welded pipe, and determine the bevel form, bevel geometric parameters, and the number of weld layers and passes of the G115 steel welded pipe based on the geometric parameters.

[0019] The estimation module is used to estimate the welding process parameters of the G115 steel welded pipe based on the bevel geometry parameters, so that the welding heat input of G115 steel is within the preset heat input range.

[0020] The determination module is used to calculate the temperature field distribution of the G115 steel welded pipe after welding based on the analytical model of the welding heat input and temperature field of the G115 steel, and to determine the post-weld microstructure distribution of the temperature field distribution based on the temperature threshold judgment rule.

[0021] The first construction module is used to calculate the thermophysical performance parameters of the G115 steel welded pipe at different temperatures based on the chemical composition of G115 steel and the preset mixing rules, and to construct the temperature-related elastoplastic constitutive model of G115 steel based on the empirical formula of material strength and the temperature degradation relationship, and to construct the creep constitutive model of G115 steel based on the time-hardening creep power law model.

[0022] The first calculation module is used to calculate the residual stress distribution of the G115 steel welded pipe after welding based on the welding heat input of the G115 steel, the geometric parameters and the preset constraint state, and by using a preset empirical formula for residual stress.

[0023] The second construction module is used to construct a multi-physics field coupled numerical model for the post-weld heat treatment of the G115 steel welded pipe based on the geometric parameters, the bevel form, the bevel geometric parameters, the number of layers and passes of the weld, the thermophysical performance parameters, the elastoplastic constitutive model, the creep constitutive model, and the residual stress distribution. The multi-physics field coupled numerical model includes heat conduction, elastoplastic deformation, creep deformation, and coupling of convective heat transfer and radiative heat transfer.

[0024] The second acquisition module is used to control the surface heat source power to simulate the flexible ceramic resistance heating process in the multiphysics coupled numerical model by using the Adam adaptive learning rate optimization algorithm, so as to obtain temperature distribution data and stress distribution data under different heat treatment process parameters, wherein the heat treatment process parameters include heating width, heat holding width and heating rate.

[0025] The second calculation module is used to calculate the tempered martensite content and hardness distribution of the G115 steel welded pipe based on the temperature distribution data, and to obtain the hardness distribution of the G115 steel welded pipe after welding based on the coupling relationship model of the tempered martensite content and the hardness. At the same time, it obtains the equivalent distribution of the residual stress distribution after welding based on the coupling model of the residual stress distribution and hardness.

[0026] The third construction module is used to associate the equivalent distributions of the geometric parameters, material property parameters, heat treatment process parameters, temperature field distribution, inner and outer wall temperature difference, post-weld microstructure distribution and hardness distribution of the inner and outer walls, and residual stress distribution of the inner and outer walls of the G115 steel welded pipe, to construct a multi-source heterogeneous database, and to expand and improve the quality of the multi-source heterogeneous database using a composite model of Gaussian process regression algorithm and generative adversarial network.

[0027] The optimization module is used to construct a constraint function based on the principle of temperature difference control between inner and outer walls, and to iteratively train the constraint function by using a multi-physics coupling coefficient correction algorithm and a gradient boosting regression algorithm to minimize the deviation between the predicted temperature difference between inner and outer walls and the actual temperature difference in the processed multi-source heterogeneous database, thus forming a physical-data dual-driven process optimization algorithm.

[0028] The third calculation module is used to calculate the target heating width and the target heat preservation width based on the physical-data dual-driven process optimization algorithm, under the constraint of meeting the hardness requirements.

[0029] The adjustment module is used to perform post-weld heat treatment on the G115 steel welded pipe based on the target heating width, the target heat preservation width and the preset heating rate during the actual post-weld heat treatment process. It also acquires the measured value of the temperature difference between the inner and outer walls of the pipe in real time during the heat treatment process, and dynamically adjusts the heating power based on the physical-data dual-driven process optimization algorithm to achieve real-time closed-loop control of the temperature difference between the inner and outer walls.

[0030] Thirdly, an electronic device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the above-mentioned post-weld heat treatment process optimization method for G115 steel welded pipes.

[0031] Fourthly, a computer-readable storage medium is provided, which stores a computer program that, when executed by a processor, implements the steps of the above-described method for optimizing the post-weld heat treatment process of G115 steel welded pipes.

[0032] In the above-mentioned optimization method for post-weld heat treatment of G115 steel welded pipes, firstly, this application constructs a coupled numerical model that includes heat conduction, elastic-plastic deformation, creep deformation, and convective / radiative heat transfer. It integrates geometric parameters, bevel form, thermophysical performance parameters (such as thermal conductivity and specific heat capacity), constitutive model (elastic-plastic + creep), and residual stress distribution to achieve dynamic correlation prediction of temperature field, stress field, and microstructure field throughout the welding-heat treatment process.

[0033] By controlling the surface heat source power through the Adam optimization algorithm (simulating flexible ceramic resistance heating), the temperature / stress distribution under different heat treatment process parameters (heating width, holding width, heating rate) is simulated in the numerical model, realizing rapid iterative optimization of parameters.

[0034] This application constructs a multi-source heterogeneous database, linking data such as geometric parameters, material properties, process parameters, temperature field, microstructure distribution (e.g., tempered martensite content), hardness distribution, and residual stress. The reliability of the data is enhanced through expansion (e.g., introducing more measured workpiece data) and quality improvement (e.g., data cleaning and feature engineering).

[0035] Based on the principle of temperature difference control between inner and outer walls, a constraint function is constructed. The multi-physics coupling coefficient correction algorithm and gradient boosting regression algorithm are integrated. The model is iteratively trained to minimize the deviation between the predicted and actual temperature difference values, forming an algorithm for collaborative optimization of physical models (such as temperature field analytical models) and data models (such as machine learning).

[0036] In actual heat treatment processes, the heating power is dynamically adjusted by real-time monitoring of the measured temperature difference between the inner and outer walls, combined with a physics-data dual-drive algorithm (such as optimizing the heat source power using the Adam algorithm), to achieve closed-loop temperature difference control. For example, when the measured temperature difference exceeds a threshold, the algorithm automatically adjusts the heating width or heating rate to ensure temperature field uniformity.

[0037] Traditional process parameter design relies on empirical formulas and trial-and-error methods, lacking a systematic consideration of the coupling effects of temperature field, stress field, and microstructure field. This application quantifies the interaction among these three elements through a multiphysics coupling model (e.g., heat input affects the temperature field, the temperature field drives microstructure evolution, and microstructure evolution and stress field jointly affect performance), achieving a shift from "empirical-driven" to "model-driven" approaches.

[0038] Traditional processes often result in excessive hardness fluctuations or substandard impact toughness due to uneven temperature fields. This application integrates multi-dimensional data from a multi-source heterogeneous database, combines a dual-drive algorithm to accurately predict microstructure distribution (such as tempered martensite content) and hardness distribution, and adjusts process parameters in real time through closed-loop control to ensure that key performance indicators such as hardness and residual stress meet requirements (such as hardness fluctuations controlled within ±10 HV).

[0039] Traditional process optimization requires multiple rework heat treatments, resulting in long cycles, high costs, and high energy consumption. This application achieves virtual simulation optimization through numerical models and optimization algorithms, reducing the number of physical experiments. For example, by using a multiphysics coupling model to predict performance under different process parameters, and combining it with a gradient boosting regression algorithm to quickly select the optimal parameter combination, the optimization cycle is shortened from months to weeks, while also reducing energy consumption (e.g., by precisely controlling heating power to reduce ineffective heating).

[0040] Traditional processes rely heavily on post-treatment (such as mechanical stretching) to control residual stress, which has limited effectiveness. This application quantifies the distribution of residual stress using elastoplastic and creep constitutive models, and optimizes process parameters (such as heating width and holding time) by combining a residual stress-hardness coupling model. This simultaneously reduces residual stress (e.g., by more than 30%) and stabilizes the microstructure (e.g., uniform distribution of tempered martensite) during heat treatment, thereby improving the stability of joint performance.

[0041] In summary, this application achieves intelligent control of the entire process from parameter design to process control through three core technologies: multi-physics coupling modeling, data-physics dual-drive algorithm, and closed-loop real-time control. It solves the problems of traditional processes relying on experience, lacking system coupling consideration, long optimization cycle, and unstable performance. It significantly improves the microstructure stability of post-weld heat treatment of G115 steel welded pipes, reduces residual stress, and reduces energy consumption and cost. Attached Figure Description

[0042] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the scope of this application. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings:

[0043] Figure 1 This is a flowchart illustrating the optimized post-weld heat treatment process for a G115 steel welded pipe according to one embodiment of this application.

[0044] Figure 2 This is a schematic diagram of the mesh generation structure of a thermo-coupled finite element analysis model in a specific embodiment of this application;

[0045] Figure 3This is one of the schematic diagrams of numerical simulation results in a specific embodiment of this application, where the width of the heating area is a constant and the width of the heat preservation area is a variable;

[0046] Figure 4 This is the second schematic diagram of the numerical simulation results in a specific embodiment of this application, where the width of the heating area is a constant and the width of the heat preservation area is a variable.

[0047] Figure 5 This is the heat treatment process curve of a G115 steel welded pipe in a specific embodiment of this application. Detailed Implementation

[0048] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. It should be understood that the accompanying drawings in this application are only for illustrative and descriptive purposes and are not intended to limit the scope of protection of this application.

[0049] Please see Figure 1 This description and embodiment provide an optimized method for the post-weld heat treatment process of G115 steel welded pipes, the method specifically including the following steps:

[0050] Step 101: Obtain the geometric parameters and material property parameters of the G115 steel welded pipe, and determine the bevel type, bevel geometric parameters, and the number of weld layers and passes of the G115 steel welded pipe based on the geometric parameters.

[0051] It is understood that the executing entity of this application can be a post-weld heat treatment process optimization device for G115 steel welded pipes, or it can be a terminal or a server; the specific implementation is not limited here. This application's embodiment uses a server as an example for illustration.

[0052] In this step, geometric parameters characterize the structural features of the G115 steel welded pipe, mainly including key dimensional parameters such as the outer diameter, inner diameter, wall thickness, length, and shape and size of the welded area. These data form the basis for subsequent numerical simulations. Material property parameters cover thermophysical and mechanical properties, specifically including parameters such as thermal conductivity, specific heat capacity, elastic modulus, Poisson's ratio, and yield strength. These parameters determine the material's response characteristics under thermo-mechanical coupling.

[0053] Optionally, the wall thickness of the G115 steel welded pipe in this application ranges from 60mm to 120mm, which is a typical thick-walled pipe specification for ultra-supercritical units.

[0054] For embodiments of this disclosure, determining the bevel type, bevel geometry parameters, and the number of weld layers and passes for G115 steel welded pipes based on geometric parameters may specifically include:

[0055] Step 1: Obtain the geometric parameters of the G115 steel welded pipe, including the outer and inner diameters. Calculate the pipe wall thickness based on the difference between the inner and outer diameters using the pipe wall thickness calculation formula, as follows:

[0056]

[0057] In the formula, t is the pipe wall thickness, D0 is the outer diameter, and D i This is the inner diameter.

[0058] Step 2: The bevel type can be selected based on the ratio of pipe wall thickness to outer diameter using a preset bevel determination formula;

[0059] In this embodiment, the geometric parameters of the G115 steel welded pipe are obtained through experimental measurement. The ratio of outer diameter to wall thickness is calculated, and pipes with different ratio ranges exhibit significantly different temperature field distribution characteristics and stress evolution patterns during heat treatment. For example, thin-walled pipes with a larger ratio usually exhibit a faster thermal response speed and a more uniform temperature distribution, while thick-walled pipes with a smaller ratio often show obvious temperature gradients and thermal stress concentration.

[0060] Based on the calculated wall thickness and outer diameter, the weld bevel type can be automatically planned according to a preset bevel determination formula. The bevel type can include I-bevel, single V-bevel, double V-bevel, single U-bevel, or double U-bevel. The preset bevel determination formula is as follows:

[0061]

[0062] In the formula, The bevel is the form of the pipe joint, and t is the pipe wall thickness.

[0063] Step 3: Based on the preset bevel geometry formula, the bevel geometry parameters can be automatically calculated further. The bevel geometry parameters include at least the outer bevel angle, inner bevel angle, outer radius, inner radius, outer bevel depth, and inner bevel depth. The preset bevel geometry formula is shown below:

[0064]

[0065] In the formula, θ1 is the outer bevel angle, θ2 is the inner bevel angle, h1 is the outer bevel depth, h2 is the inner bevel depth, which are used to accurately describe the geometric shape of the bevel, b1 is the outer bevel width (i.e., the outer radius), and b2 is the inner bevel width (i.e., the inner radius). t represents the total bevel width, and t represents the pipe wall thickness.

[0066] Step 4: Based on the relationship between the effective weld thickness and the total bevel thickness, calculate the number of weld layers, and calculate the number of weld passes for each layer based on the bevel opening angle and center radius corresponding to each layer. Here, the number of weld layers is the number of weld filling layers, and the number of weld passes is the total number of weld passes.

[0067] In this embodiment, after obtaining the bevel geometry data, the number of filler layers of the weld can be automatically calculated according to the weld formation formula. The weld formation formula is as follows:

[0068]

[0069] In the formula, Number of filler layers for the weld. The effective weld thickness for each weld layer (typically 2–3 mm). The symbol is for rounding up, and t is the pipe wall thickness.

[0070] Furthermore, for each weld layer, the corresponding groove opening angle θ and the center radius of that weld layer can be used as a reference. The total number of weld passes can be calculated using the following formula:

[0071]

[0072] In the formula, Here, θ represents the number of weld passes per layer, and θ represents the groove opening angle corresponding to that layer of weld. Let be the center radius of the i-th weld layer. This refers to the width of the weld bead.

[0073]

[0074] In the formula, This represents the total number of weld passes. The number of weld passes per layer. The number of filler layers for the weld.

[0075] This step automates the determination of groove shape, calculation of groove geometry, and planning of weld layer and pass number, providing basic data for subsequent welding heat input allocation, weld morphology modeling, and welding thermal cycle simulation.

[0076] Step 102: Estimate the welding process parameters of G115 steel welded pipe based on the bevel geometry parameters, so that the welding heat input of G115 steel is within the preset heat input range.

[0077] For embodiments of this disclosure, welding process parameters during the welding process can be estimated based on the following formula, which may include welding current, welding voltage, welding speed, and heat-affected zone width.

[0078] Specifically, the welding current and welding voltage can be calculated using preset empirical formulas based on the welding position, electrode diameter, welding coefficient, and selected welding process. The welding current is directly proportional to the electrode diameter, and the welding coefficient is selected within a preset range depending on the welding posture. The preset empirical formulas are shown below:

[0079]

[0080] In the formula, I is the welding current, V is the welding voltage, and d is the electrode diameter (mm). This is the welding coefficient, and its value range varies depending on the welding posture and process. Flat-position and gravity-fed filling (easier to weld): .

[0081] Using the allowable welding heat input range of G115 steel as a constraint, the welding speed is derived based on the functional relationship between welding current, welding voltage, and welding heat input, so that the welding heat input per unit length is controlled within a preset range. The formula is as follows:

[0082]

[0083] In the formula, S is the welding speed, which is controlled by the heat input of G115 steel within the range of approximately 0.5 – 1.0 kJ / mm, I is the welding current, V is the welding voltage, and Q is the welding heat input per unit length.

[0084] Step 103: Based on the analytical model of heat input and temperature field of G115 steel welding, calculate the temperature field distribution of G115 steel welded pipe after welding, and determine the post-weld microstructure distribution of the temperature field distribution based on the temperature threshold judgment rule.

[0085] In this embodiment of the disclosure, based on the analytical model of heat input and temperature field of G115 steel welding, the temperature field distribution of the G115 steel welded pipe after welding is calculated, and the post-weld microstructure distribution of the temperature field distribution is determined based on the temperature threshold judgment rule. Specifically, this may include:

[0086] Based on analytical formulas for the heat input, material density, specific heat, temperature decay width of the heat-affected zone, and empirical coefficient of heat loss of G115 steel welding, the temperature field distribution of G115 steel welded pipes after welding is calculated. The temperature field distribution includes the peak temperatures at the weld center and at different locations along the pipe thickness and axial direction. The specific analytical formulas are shown below:

[0087]

[0088]

[0089]

[0090] In the formula, Let T be the peak temperature (°C) at location x, and T0 be the initial temperature. The peak temperature at the weld center is C, and L is a "width parameter" characterizing the temperature decay of the heat-affected zone with distance, typically ranging from 3 to 10. p An empirical coefficient (including heat loss effect) characterizing the temperature rise after heat absorption per unit volume is generally taken as 1~2, where Q is the welding heat input per unit length. Where ρ is the thickness of the weldment, c is the material density, and ρ is the material density. p For specific heat capacity, C L To represent the empirical ratio of the attenuation width to the heat input, a value of 0.05 to 0.15 is typically used.

[0091] The peak temperature is compared with the critical phase transformation temperature of G115 steel to determine the post-weld phase transformation behavior at each location. The post-weld microstructure distribution is then obtained by dividing the region into weld, fusion zone, coarse grain zone, fine grain zone, subcritical heat-affected zone, and base metal region. The formula is shown below:

[0092]

[0093] In the formula, Peak temperature Liquidus temperature This is the temperature at which the austenite transformation begins. This is the temperature at which the austenite transformation ends. It is the subcritical temperature. T can be taken as Ac1 -50℃, T Ac1 ≈ 720°C, T Ac3 ≈ 840°C At approximately 1400-1450°C, the weld seam is completely converted to lath martensite, the fusion zone is completely converted to lath martensite, the coarse grain zone is completely converted to lath martensite, the fine grain zone is 30% lath martensite + 70% martensite, the subcritical heat-affected zone is entirely tempered martensite, and the base metal is entirely tempered martensite.

[0094] Step 104: Calculate the thermophysical performance parameters of G115 steel welded pipes at different temperatures, construct a temperature-dependent elastoplastic constitutive model of G115 steel, and construct a creep constitutive model of G115 steel based on a time-hardening creep power-law model.

[0095] Thermophysical properties may include density, specific heat, thermal conductivity, coefficient of linear expansion, latent heat of phase change, and yield strength.

[0096] For the embodiments of this disclosure, the thermophysical performance parameters of G115 steel welded pipes at different temperatures can be calculated based on the chemical composition of G115 steel and preset mixing rules. A temperature-dependent elastoplastic constitutive model of G115 steel can be constructed based on empirical formulas for material strength and temperature degradation relationships. Furthermore, a creep constitutive model of G115 steel can be constructed based on a time-hardening creep power-law model. Specifically, this includes:

[0097] Step 1: Before obtaining the thermophysical properties of the material, it is necessary to obtain the chemical composition mass fraction of the G115 pipe, as shown in Table 1:

[0098] Table 1. Chemical composition (mass fraction) of G115 steel

[0099]

[0100] Step 2: Calculate the thermophysical properties of G115 pipes at different temperatures. Select temperature nodes: Temperature = 20℃, 100℃, 200℃, 300℃, 400℃, 500℃, 600℃, 700℃. Based on the chemical composition mass fraction of each element in G115 steel and the reference density, calculate the density of G115 steel at the reference temperature using the mixed density formula, as shown below:

[0101]

[0102] In the formula, This represents the density (kg / m³) of the alloy or composite material at the reference temperature. The mass fraction of element or phase i. Let be the density of element i or phase i.

[0103] Step 3: Based on the chemical composition and mass fraction of each element in G115 steel and the specific heat of each element at different temperatures, the specific heat of G115 steel at each temperature node can be calculated using the first weighted mixing formula, as shown below:

[0104]

[0105] In the formula, c p,mix (T) represents the specific heat of the mixture (J / kg·K), c p,i (T) represents the specific heat (J / kg·K) of element or phase i at temperature T. The mass fraction of element i or phase i.

[0106] Step 4: Based on the volume fraction of each element in G115 steel and the thermal conductivity of each element at different temperatures, the thermal conductivity of G115 steel at various temperature nodes can be calculated using the Reuss model formula, as shown below:

[0107]

[0108] In the formula, The thermal conductivity of the composite material is expressed in J / kg·K. Thermal conductivity (W / m·K) of an element or phase. is the volume fraction, and T is the temperature.

[0109] Step 5: Based on the volume fraction of each element in G115 steel and the linear expansion coefficient of each element or phase, the linear expansion coefficient of G115 steel can be calculated using the linear expansion coefficient formula, as shown below:

[0110]

[0111] In the formula, The coefficient of linear expansion of the composite material. 1 / K is the coefficient of linear expansion of an element or phase. This represents the volume fraction.

[0112] Step 6: Based on the chemical composition mass fraction of each element in G115 steel and the latent heat of phase transformation per unit mass of each element, the latent heat of phase transformation of G115 steel can be calculated using the second weighted mixing formula, as shown below:

[0113]

[0114] In the formula, L represents the latent heat of phase change in the hybrid material. i The latent heat of phase change per unit mass of an element or phase (J / kg). The mass fraction of element i or phase i.

[0115] Step 7: Based on the chemical composition mass fraction of each element in G115 steel and the yield strength at the reference temperature, the reference yield strength of G115 steel can be calculated using the third weighted mixing formula. The reference yield strength is then corrected for temperature using a temperature degradation coefficient to obtain the final yield strength. The third weighted mixing formula is shown below:

[0116]

[0117] In the formula, The reference yield strength of the composite material. The mass fraction of element or phase i. Let be the yield strength of element i at the reference temperature.

[0118] The temperature correction formula is shown below:

[0119]

[0120] In the formula, This refers to the temperature-corrected yield strength of the composite material. The temperature degradation coefficient (1 / K) is approximately 0.0005~0.0015 / K for G115 steel. The reference yield strength of the composite material. This is a reference temperature (typically 20°C).

[0121] Step 8: Construct a constitutive model of the G115 steel pipe as input for the finite element method:

[0122] Specifically, the multiphysics coupled numerical model consists of three core sub-models: The heat conduction model, based on Fourier's law, characterizes the spatiotemporal evolution of the temperature field and comprehensively describes the heat transfer behavior during welding. This model comprehensively considers material thermal properties such as thermal conductivity and specific heat capacity, as well as the spatiotemporal evolution of the temperature field. The elastoplastic constitutive model describes the nonlinear mechanical response of the material, accurately characterizing its mechanical response characteristics under complex thermo-mechanical coupling conditions. This model simultaneously considers elastic deformation, viscous flow, and plastic deformation mechanisms, making it particularly suitable for simulating material behavior under high-temperature multiaxial stress states. The creep-strain constitutive model simulates the progressive deformation during the high-temperature holding stage, quantitatively describing the mechanical phenomenon of the material's yield strength increasing with the accumulation of plastic strain. The introduction of this model significantly improves the simulation accuracy of the material's nonlinear mechanical behavior, providing a theoretical basis for predicting welding residual stress.

[0123] Specifically, the heat conduction model is as follows:

[0124]

[0125] In the formula, ρ is density, and c p Let T be the specific heat capacity, t be the temperature field, t be the loading time, and k be the thermal conductivity. This is the gradient operator, where Q is the heat source intensity per unit volume, mainly provided by resistance heating. This represents the rate of change of temperature over time.

[0126] Based on the elastic modulus, hardening modulus, and corresponding temperature degradation coefficient of G115 steel at room temperature, a temperature-dependent elastoplastic constitutive model is constructed, and the specific formulas are shown below:

[0127]

[0128]

[0129]

[0130] In the formula, E(T) is the elastic modulus at temperature T, E0 is the elastic modulus at room temperature (20°C), approximately 210 GPa for G115 steel, and T is the current temperature. =20°C, The temperature degradation coefficient is 1.5 × 10⁻⁶ for G115 steel. 4 K -1 H(T) is the hardening modulus at temperature T, and H0 is the hardening modulus at a reference temperature, which can be obtained from experiments or literature. The hardening degradation coefficient (1 / K) is typically about 1 × 10⁻⁶. - ³ / K, Let σ be the plastic strain, and σ be the stress experienced by the G115 steel pipe. This represents the temperature-corrected yield strength of the composite material.

[0131] A creep constitutive model for G115 steel can be constructed based on empirical creep parameters related to temperature, stress, and chemical composition, according to the following formula:

[0132]

[0133] In the formula, Let σ be the creep rate, and σ be the stress on the G115 steel pipe. Let be a material constant, t be the creep time, m be a material constant, and R be a gas constant, with a value of . T is the temperature, and A(C) is the material constant. The creep activation energy can be obtained using an empirical formula based on chemical composition:

[0134]

[0135] In the formula, A(C) is a material constant. For non-alloy steel, the creep pre-creep factor is... Let be the empirical coefficient of the i-th chemical element for the creep parameter. Let be the mass fraction of the i-th chemical element in the material;

[0136] n(C) is the stress index adjusted with chemical composition:

[0137]

[0138] In the formula, n(C) is the stress exponent. For non-alloy steel, the creep pre-creep factor is... Let be the empirical coefficient of the i-th chemical element for the creep parameter. Let be the mass fraction of the i-th chemical element in the material;

[0139] Activation energy varies depending on chemical composition.

[0140]

[0141] In the formula, For creep activation energy, Let i be the mass fraction of the i-th chemical element in the material. For non-alloy steel, the creep pre-creep factor is... is the empirical coefficient of the creep parameter for the i-th chemical element.

[0142] Step 105: Based on the welding heat input, geometric parameters and preset constraint state of G115 steel, calculate the residual stress distribution of the welded G115 steel pipe after welding using the preset empirical formula for residual stress.

[0143] The residual stress distribution may include axial residual stress distribution and circumferential residual stress distribution;

[0144] For embodiments of this disclosure, based on the welding heat input, geometric parameters, and preset constraint state of G115 steel, the residual stress distribution of the welded G115 steel pipe is calculated using a preset empirical formula for residual stress. Specifically, this may include:

[0145] Step 1: Based on the normalized welding heat input parameters of G115 steel, the yield strength of G115 steel, and the geometric and constraint coefficients, calculate the maximum residual stress near the weld using a preset empirical formula for residual stress. The preset empirical formula for residual stress is shown below:

[0146]

[0147]

[0148] In the formula, H is the heat input, V is the welding voltage (V), I is the welding current (A), and S is the welding speed (mm / min). The maximum residual stress is given by k, which is the geometric and constraint coefficient (typically 0.8~1.0). For yield strength, Reference heat input (used for normalization).

[0149] Step 2: Based on the analytical relationship of circumferential and axial stress distribution in a thick-walled circular tube, the maximum residual stress is expanded into a radial distribution function along the tube wall thickness direction, yielding the circumferential and axial residual stress distributions respectively. The specific formulas are shown below:

[0150]

[0151]

[0152] In the formula, For circumferential residual stress, The reference circumferential residual stress is given by r, which is the coordinate of the pipe wall radius (inner radius Ri≤r≤R0). The neutral radius of the pipe wall. For wall thickness, This is the axial residual stress. The constraint factor is approximately 0.5 to 0.8 for thick-walled pipes, and is typically 0.6 for constrained pipes.

[0153] Step 3: Import the circumferential residual stress distribution and axial residual stress distribution calculated by the formula into the finite element analysis software as predefined fields to model the initial stress state of the G115 steel welded pipe after welding. In the multiphysics coupled numerical model, the elastic-plastic relaxation, creep relaxation and heat treatment temperature field evolution process of residual stress are considered simultaneously to obtain the stress and temperature field distribution after heat treatment.

[0154] Step 106: Construct a multi-physics coupled numerical model for post-weld heat treatment of G115 steel welded pipes.

[0155] In this embodiment, a multi-physics coupled numerical model for the post-weld heat treatment of G115 steel welded pipes can be constructed based on geometric parameters, bevel form, bevel geometric parameters, number of weld layers and passes, thermophysical performance parameters, elastoplastic constitutive model, finite element analysis model, creep constitutive model, and residual stress distribution. The multi-physics coupled numerical model includes heat conduction, elastoplastic deformation, creep deformation, and coupling of convective heat transfer and radiative heat transfer.

[0156] Step 107: In the multiphysics coupled numerical model, the surface heat source power is controlled by the Adam adaptive learning rate optimization algorithm to simulate the flexible ceramic resistance heating process, so as to obtain temperature distribution data and stress distribution data under different heat treatment process parameters.

[0157] The heat treatment process parameters include heating width, holding width, and heating rate.

[0158] In a multiphysics coupled numerical model, flexible ceramic resistance heating can be simulated by applying a surface heat source to the outer surface of a G115 steel welded pipe. The surface heat source power is calculated based on the real-time temperature change of the pipe surface and is back-calculated using the Adam adaptive learning rate optimization algorithm. The flow state of the air around the pipe and the radiation and convection heat transfer of the pipe are automatically calculated by considering the temperature difference between the pipe surface and the air, the energy conservation inside the fluid, the heat conduction inside the solid, and the convection and radiation heat transfer at the interface. The power is dynamically adjusted during the simulation to maintain a constant heating rate, thereby achieving an accurate simulation of the real flexible heating process.

[0159] Based on a multiphysics coupled numerical model and the Adam adaptive learning rate optimization algorithm, the temperature and stress distributions of G115 welded pipes under different heat treatment heating widths, holding widths, and heating rates are calculated.

[0160] In this step, a series of corresponding thermo-mechanical coupled finite element analysis models are constructed based on the geometric parameters of the G115 steel welded pipe and the width of each heating-insulation zone in the heat treatment zone dataset. Material property parameters are imported into each model, and corresponding initial and boundary conditions are set.

[0161] In one embodiment of this application, a specific model building scheme is provided:

[0162] Step 1: Based on geometric parameters, material property parameters, and heat treatment zone dataset, construct a thermo-mechanical coupled finite element model of G115 steel welded pipe, and set the initial and boundary conditions of the thermo-mechanical coupled finite element model.

[0163] Step 2: A three-dimensional solid numerical model of the G115 steel welded pipe can be constructed based on geometric parameters using finite element classification technology.

[0164] In this step, a high-precision three-dimensional digital simulation model can be constructed based on the actual geometric parameters of the G115 steel welded pipeline and combined with finite element hierarchical discretization technology. This model, through a systematic mesh generation method, discretizes the pipeline structure into a series of interconnected finite element elements, achieving an accurate mathematical representation of the geometric morphology and structural characteristics of the real G115 steel welded pipeline. The establishment of this digital twin model provides a reliable geometric foundation for subsequent numerical calculations such as structural mechanical performance analysis and thermodynamic simulation.

[0165] Step 3: Based on the heat treatment area dataset, the three-dimensional solid numerical model can be divided into heating area and insulation area to generate a series of thermo-mechanical coupled finite element analysis models, where each thermo-mechanical coupled finite element analysis model corresponds to a set of heating area and insulation area.

[0166] In this step, based on multiple sets of heating-insulation zone widths in the heat treatment zone dataset, the three-dimensional solid numerical model is discretized into corresponding heating and insulation zones, constructing a series of finite element analysis models with different heat treatment zones. Each model accurately represents a specific heating-insulation condition, forming a complete set of parametric thermo-mechanical coupled finite element analysis models. Based on the ratio and the initial width setting rules for the heating-insulation zone, the initial width of the heating zone and its corresponding initial width of the insulation zone for the G115 steel welded pipe are determined.

[0167] In this step, the initial width setting rules for the heating and insulation zones are a set of parametric design criteria based on the pipe's structural characteristics. The core of these criteria is determining the initial dimensions of the heating and insulation zones through the ratio of outer diameter to wall thickness. Pipes with different geometries exhibit significantly different heat conduction characteristics and stress distribution patterns during heat treatment. For pipes with a large ratio (outer diameter / wall thickness), a wider heating zone is needed to ensure sufficient heat input, while matching a corresponding insulation zone width to maintain temperature field stability. For pipes with a small ratio, the heating zone distribution needs to be optimized to avoid localized overheating, and a reasonable insulation zone needs to be designed to control the cooling rate. Based on these setting rules and the calculated specific outer diameter / wall thickness ratio, the optimal initial widths of the heating and insulation zones for G115 steel welded pipes can be accurately derived. These two initial widths will serve as the basic input data for subsequent numerical simulations and process optimization.

[0168] In one embodiment of this application, the initial width setting rule for the heating area-insulation area includes the initial width setting rule for the heating area and the initial width setting rule for the insulation area.

[0169] Specifically, the initial width setting rules for the heating zone are as follows: the heating zone extends symmetrically to both sides along the pipe axis, based on the weld centerline of the G115 steel welded pipe; when the ratio of the outer diameter to the wall thickness is less than or equal to the first preset threshold, the initial width of the heating zone is greater than or equal to 6 times the wall thickness; when the ratio is greater than the first preset threshold and less than or equal to the second preset threshold, the initial width of the heating zone is greater than or equal to 7 times the wall thickness; when the ratio is greater than the second preset threshold and less than or equal to the third preset threshold, the initial width of the heating zone is greater than or equal to 9 times the wall thickness; when the ratio is greater than ... second preset threshold, the initial width of the heating zone is greater than or equal to 9 times the wall thickness; when the ratio is greater than the third preset threshold, the initial width of the heating zone is greater than or equal to 9 times the wall thickness. When the ratio is less than or equal to the fourth preset threshold, the initial width of the heating zone is greater than or equal to 12 times the wall thickness; when the ratio is greater than the fourth preset threshold, the initial width of the heating zone is greater than or equal to 15 times the wall thickness. The initial width setting rule for the insulation zone is as follows: the insulation zone extends symmetrically to both sides from the boundary of the heating zone away from the weld center, the initial width value of the insulation zone is greater than or equal to the preset width threshold, and the width value of the G115 steel welded pipe extending from the weld center to both sides to the boundary of the insulation zone is greater than or equal to the sum of the initial width of the heating zone and 2 times the wall thickness.

[0170] In this embodiment, the heating zone extends symmetrically to both sides along the pipe axis, using the weld centerline of the G115 steel welded pipe as a reference. When the outer diameter / wall thickness ratio is ≤ a first preset threshold: the initial width of the heating zone is required to be 6 times or more the wall thickness. When the first preset threshold < ratio ≤ second preset threshold: the initial width of the heating zone should be no less than 7 times the wall thickness. As the ratio increases, it indicates that the structural characteristics of the pipe have changed, and the heat transfer may be relatively more complex, requiring a wider heating zone to ensure the welding effect. When the second preset threshold < ratio ≤ third preset threshold: the initial width of the heating zone should be greater than or equal to 9 times the wall thickness. A further increase in the ratio means that the pipe has new characteristics in terms of heat transfer and mechanical properties, and a wider heating zone helps to achieve uniform heating and improve welding quality.

[0171] When the third preset threshold < ratio ≤ fourth preset threshold: the initial width of the heating zone needs to be 12 times or more the wall thickness. In this case, the outer diameter of the pipe is relatively larger than the wall thickness, increasing the difficulty of heat transfer and welding, thus requiring a wider heating range. When the ratio > fourth preset threshold: the initial width of the heating zone should be greater than or equal to 15 times the wall thickness. When the ratio is very large, the pipe structure significantly affects heat transfer; to ensure welding quality, a wider heating zone is needed to achieve uniform heating and good welding results.

[0172] Furthermore, the initial width setting rule for the insulation zone is as follows: the insulation zone extends symmetrically to both sides from the boundary of the heating zone away from the weld center, and its initial width setting must meet the following two conditions: (1) not less than the preset minimum process width threshold; (2) the total width from the weld center to the boundary of the insulation zone on either side is not less than the sum of the initial width of the heating zone and twice the pipe wall thickness. This setting ensures that there is sufficient insulation range around the heating zone, slows down the cooling rate of the heating zone, and avoids excessive residual stress caused by excessive cooling, which would affect the welding quality and the performance of the pipe.

[0173] In practical applications, for pipes with an outer diameter / wall thickness (D / t) ≤ 10, the width of the heating zone extends 6t from the weld center to both sides; when 10 < D / t ≤ 20, the width extends 7t; when 20 < D / t ≤ 40, the width extends 9t; when 40 < D / t ≤ 70, the width extends 12t; and when D / t > 70, the width extends 15t. Simultaneously, the initial width of the insulation zone is determined to ensure that the minimum width of the insulation zone extending from the weld center of the G115 steel welded pipe to both sides is twice the wall thickness of the heating zone and not less than 150mm. Taking a typical weld as an example, the initial width of the heating zone on one side is set to 420mm, and the initial width of the insulation zone is set to 150mm.

[0174] By using the above method, the range of heating and heat preservation areas can be adaptively adjusted through geometric parameters, ensuring both heat treatment effectiveness and avoiding energy waste.

[0175] Based on the initial width of the heating zone and the initial width of the insulation zone, multiple sets of dynamic change data of the heating zone and the insulation zone are generated through a progressive expansion method.

[0176] In this step, based on the initial width of the heating and insulation zones, a progressive expansion method is used to gradually expand the width of the heating and insulation zones to obtain a series of dynamic change data. This allows for the study of the effects of different heating and insulation conditions on the temperature distribution, stress relief effect, and material property improvement of G115 steel welded pipes, thereby finding the optimal heating and insulation process parameters.

[0177] With the initial width of the heating area remaining unchanged, the width of the insulation area is increased by 1.2 times the wall thickness as the incremental step, using a progressive expansion method, until the preset upper limit threshold is reached, thus forming a dynamic change sequence data of the insulation area width.

[0178] In this step, with a fixed initial width of the heating zone, the insulation zone is systematically expanded in increments of 1.2 times the wall thickness. For example, if the wall thickness of the G115 steel welded pipe is 10mm, then the width of the insulation zone increases by 1.2 × 10 = 12mm each time. Starting from the initial width of the insulation zone, the width is gradually increased in increments of 1.2 times the wall thickness. An 11-times wall thickness is set as the preset upper limit threshold for expansion; taking a 10mm wall thickness as an example, the expansion terminates when the width of the insulation zone reaches 11 × 10 = 110mm. During this gradual expansion process, the width value of the insulation zone after each expansion is recorded. These values ​​are arranged in the order of expansion, forming a dynamic sequence of changes in the width of the insulation zone. This sequence can be used to analyze the impact of different insulation zone widths on the heat treatment effect of the G115 steel welded pipe.

[0179] With the initial width of the insulation area remaining unchanged, the width of the heating area is increased by 1.2 times the wall thickness as the incremental step, using a progressive expansion method, until the preset upper limit threshold is reached, thus forming a dynamic change sequence data of the heating area width.

[0180] In this step, with a fixed initial width of the insulation zone, the heating zone is systematically expanded in increments of 1.2 times the wall thickness. For example, if the wall thickness of the G115 steel welded pipe is 10mm, then the width of the heating zone increases by 1.2 × 10 = 12mm each time. Starting from the initial width of the heating zone, the width is gradually increased in increments of 1.2 times the wall thickness. An 11-times wall thickness is set as the preset upper limit threshold for expansion; taking a 10mm wall thickness as an example, the expansion terminates when the expanded width reaches 11 × 10 = 110mm. During this gradual expansion process, the width value of the heating zone after each expansion is recorded. These values ​​are arranged in the order of expansion, forming a dynamic sequence of heating zone width changes. This sequence can be used to analyze the impact of different heating zone widths on the heat treatment effect of the G115 steel welded pipe.

[0181] Based on the dynamic change sequence data of the insulation zone width and the heating zone width, multiple sets of dynamic change data are generated. In this step, the dynamic change sequence data of the insulation zone width and the heating zone width are summarized to form complete dynamic change data. Based on the initial width of the heating zone, the initial width of the insulation zone, and the multiple sets of dynamic change data, a heat treatment zone dataset is constructed. In this step, the initial width of the heating zone, the initial width of the insulation zone, and the multiple sets of dynamic change data are synchronously aligned and integrated to construct a complete heat treatment zone dataset for the process, providing comprehensive heat treatment zone input for subsequent thermo-mechanical coupling numerical simulations.

[0182] In practical applications, taking a typical thick-walled G115 steel welded pipe weld as an example, the initial width of the single-sided heating zone is set to 420mm, and the initial width of the insulation zone is set to 150mm. Subsequently, two sets of process parameter combinations were designed using a bivariate parametric analysis method: When the initial width of the heating zone remains constant, the width of the insulation zone is increased incrementally in increments of 1.2t until the expansion width reaches the upper limit of 11t; when the initial width of the insulation zone remains constant, the width of the heating zone is increased incrementally in increments of 1.2t until the expansion width reaches the upper limit of 11t. For example, in the first set, the heating zone width is fixed at 420mm, and the insulation zone width gradually increases to: 150mm, 230mm, 310mm, 390mm, and 470mm; in the second set, the insulation zone width is fixed at 150mm, and the heating zone width gradually increases to: 420mm, 500mm, 580mm, 660mm, and 740mm.

[0183] Step 4: Refine the mesh for the heating and insulation regions corresponding to each thermo-coupled finite element analysis model.

[0184] In this step, the finite element model is a mesh composed of many small elements. In order to improve the calculation accuracy, the heating and insulation areas are subjected to mesh refinement, that is, the number of mesh elements is increased to make the mesh finer, thereby simulating the physical phenomena in these areas more accurately.

[0185] In practical applications, a refined 3D solid model was established for welded pipelines made of thick-walled G115 steel, and a structured mesh was created using hexahedral C3D8R elements. Mesh refinement was specifically implemented for key areas of the heat treatment process (heating and insulation zones). Figure 2 The diagram shows the mesh generation structure of the thermo-coupled finite element analysis model. Taking a typical 590mm (length) × 70mm (diameter) pipe as an example, the heating and insulation regions use a maximum mesh feature size of 10mm, while other non-critical regions use a mesh size of 30mm, generating approximately 196,800 mesh elements. This approach optimizes computational efficiency while ensuring computational accuracy and effectively capturing local temperature gradients and stress concentrations during the heat treatment process.

[0186] Step 5: Assign material property parameters to each thermo-coupled finite element analysis model.

[0187] In this step, the material properties of G115 steel welded pipes directly affect their thermodynamic response behavior. Considering the differences in characteristics between pipes of different materials, key parameters including density, specific heat capacity, elastic modulus, plastic hardening curve, coefficient of thermal expansion, and thermal conductivity must be accurately assigned to each thermo-mechanical coupled finite element analysis model. This process of defining material parameters ensures that the numerical simulation can realistically reflect the mechanical properties and thermal behavior characteristics of the pipe under actual operating conditions.

[0188] Step 6: Set the current indoor ambient temperature as the initial condition for each thermo-coupled finite element analysis model. In this step, the temperature relationship between the model and the external environment needs to be determined in the thermo-coupled analysis. The welding environment temperature is defined as room temperature and used as the temperature field distribution of the entire model at the beginning, meaning that the outer surface temperature of the model is the same as the indoor ambient temperature, used to simulate the heat exchange between the model and the outside world.

[0189] In practical applications, the ambient temperature is set to a constant 25°C as the basic temperature boundary condition.

[0190] Step 7: Set the convective heat transfer boundary conditions for the outer surface of the G115 steel welded pipe in each thermo-coupled finite element analysis model.

[0191] In this step, the thermo-mechanical coupling analysis of the G115 steel welded pipe requires accurate characterization of the heat exchange behavior between its outer surface and the surrounding air. Establishing convective heat transfer boundary conditions on the outer surface of the pipe can effectively simulate the heat transfer process between the pipe's outer wall and the air medium. The establishment of these boundary conditions needs to comprehensively consider the convective heat transfer coefficient (characterizing the influence of airflow state on heat transfer efficiency), ambient air temperature (serving as a reference for heat exchange), and surface thermal radiation characteristics (reflecting heat loss due to infrared radiation). The coordinated definition of these parameters fully constructs the heat exchange interface on the outer surface of the pipe.

[0192] In practical applications, the outer surface of the pipe, excluding the insulation area, is defined as a convection-radiation composite heat transfer boundary, where the convection heat transfer coefficient is set to... The surface thermal emissivity was set to 0.1. This boundary condition configuration accurately simulates the heat exchange process between the pipeline and the surrounding environment under natural cooling conditions, providing realistic thermal environment parameters for heat treatment analysis.

[0193] Step 8: Constrain the overall rigid body motion of the pipe in each thermo-coupled finite element analysis model by using three-point constraints.

[0194] In this step, to eliminate rigid body displacements (including three translational degrees of freedom and three rotational degrees of freedom) in the finite element numerical simulation, appropriate boundary constraints must be applied. Specifically, the three-point constraint method is used, selecting three non-collinear nodes on the thermo-coupled finite element analysis model and constraining their translational degrees of freedom in the X, Y, and Z directions respectively (UX=UY=UZ=0). This boundary condition treatment method effectively eliminates rigid body displacements while ensuring that the thermal deformation behavior of the pipeline during heat treatment is not affected by artificial constraints, thus truly reflecting the mechanical response characteristics under actual working conditions.

[0195] Step 9: Based on the thermo-coupled finite element analysis model, establish a multiphysics coupled numerical model of heat transfer and elastoviscoplastic behavior. This multiphysics coupled numerical model includes a heat conduction model, an elastoviscoplastic constitutive model, and a time-hardening power-law constitutive model. In this step, based on the thermo-coupled finite element analysis model, a multiphysics coupled numerical model is established by introducing the heat conduction equation and the elastoviscoplastic constitutive relationship. This model considers the dual coupling effect of the temperature field and the stress field. This bidirectional coupling mechanism can more accurately simulate the thermo-mechanical interaction during the welding process, providing a reliable theoretical basis for subsequent process optimization.

[0196] Compared to traditional pure heat conduction simulation methods, the thermo-mechanical coupling analysis method, by solving the heat conduction equation and the elastoviscoplastic constitutive relation in a coupled manner, fully characterizes the multi-physics coupling mechanism of Joule heat generation, heat conduction, and thermal radiation during resistance heating. This approach more realistically simulates the nonlinear behavior of thermo-mechanical co-evolution in actual processes and accurately reproduces the key influence of radiative heat dissipation on the temperature field distribution under high-temperature conditions. This significantly improves the simulation accuracy of resistance heating processes and provides a more reliable numerical experimental platform for process optimization.

[0197] Step 10: Based on the multiphysics coupling numerical model, numerical simulation is performed on the post-weld heat treatment of G115 steel welded pipes through flexible ceramic resistance heating process to obtain the temperature field, stress field, hardness, and microstructure of G115 steel welded pipes during the numerical simulation process.

[0198] In this step, flexible ceramic resistance heating has become the mainstream heat treatment process for G115 steel welded pipes due to its advantages of simple operation and strong adaptability. However, practical applications show that existing heat treatment processes still have shortcomings in controlling the performance stability of thick-walled G115 steel welded joints, mainly manifested in large fluctuations in joint performance or some indicators failing to meet design specifications. These problems often require multiple rework heat treatments to solve, resulting in a significant waste of electrical energy and labor costs, and a substantial increase in overall production costs. It is worth noting that flexible ceramic resistance heating has inherent limitations in heating efficiency and temperature field uniformity, which is particularly prominent for pipe components with large wall thicknesses, making it difficult to meet the stringent requirements of heat treatment processes for thick-walled components. Based on the above problems, this application proposes to use an established multi-physics coupled numerical model to simulate the post-weld heat treatment of G115 steel welded pipes using flexible ceramic resistance heating. During the simulation, the spatiotemporal evolution of the temperature field and stress field of the G115 steel welded pipes is calculated in real time throughout the heat treatment process, obtaining temperature distribution data and stress distribution data.

[0199] Step 11: Divide the post-weld heat treatment into three stages: heat treatment heating stage, heat treatment holding stage, and heat treatment cooling stage.

[0200] In this step, the welding thermal cycle causes significant residual stress and microstructure changes in the G115 steel welded pipe, directly affecting the mechanical properties and service life of the joint. Post-weld heat treatment, as a key post-processing step, can eliminate welding residual stress and optimize the microstructure by precisely controlling the evolution of the temperature field, thereby improving the overall performance of the joint. Specifically, post-weld heat treatment includes three characteristic stages: Heating stage: The G115 steel welded pipe is heated from the initial ambient temperature to the target heat treatment temperature at a controllable rate, ensuring that the temperature gradient does not exceed the material's allowable range and avoiding additional thermal stress. Holding stage: The target temperature is maintained for a specified time to promote the full progress of the stress relaxation process, while simultaneously achieving a homogenization and stabilization transformation of the microstructure. Cooling stage: The G115 steel welded pipe is uniformly cooled to room temperature using air cooling to ensure that the material obtains the ideal final microstructure and avoids the generation of secondary residual stress.

[0201] In practical applications, the process system is divided into three stages for accurate simulation: First, a surface heat flux density is applied to the heating region, and the surface heat source power is dynamically adjusted based on the deviation between the pipe surface temperature and the target heating curve using an adaptive learning rate optimization algorithm (Adam algorithm). This ensures a constant heating rate and a uniform temperature rise to the preset target temperature of 770℃, which is then maintained at a constant temperature. Next, in the holding stage, an elastoviscoplastic constitutive model considering temperature softening effects is employed, coupled with a time-hardening power-law creep model to characterize the material's high-temperature progressive deformation behavior. Finally, in the cooling stage, natural convection boundary conditions are used to simulate the air cooling process until the workpiece temperature uniformly drops to room temperature. The entire process is solved through a strong coupling of the heat conduction equation and the mechanical constitutive equation, achieving a synergistic evolution analysis of the temperature field, stress field, and deformation field.

[0202] Accordingly, the Adam adaptive learning rate optimization algorithm is used to control the surface heat source power to simulate the flexible ceramic resistance heating process, which may specifically include:

[0203] During the heat treatment heating stage, a spatially adjustable surface heat flux density is applied to the outer surface of the heating zone. The surface temperature of the pipe is monitored in real time and compared with the target heating curve to obtain the temperature deviation.

[0204] Using temperature deviation as input, the power correction amount at the current moment is calculated through the Adam adaptive learning rate optimization algorithm, and the surface heat source power applied to the outer surface of the pipe is updated based on the power correction amount.

[0205] Within each time step, the flow and heat transfer state of the air around the pipe are solved based on the fluid energy conservation, solid heat conduction, and interfacial convection and radiation heat transfer equations. The heat transfer coefficient of the pipe surface is dynamically calculated and updated, and the temperature field is corrected based on the updated heat transfer coefficient.

[0206] Through the above closed-loop control, the heating rate is maintained near the preset value to achieve high-fidelity simulation of the actual flexible ceramic resistance heating process.

[0207] Among them, the adaptive learning rate optimization algorithm (Adam algorithm) can be used to optimize the learning rate based on the deviation between the target heating rate and the current surface temperature. Dynamically update surface heat source power The calculation process includes:

[0208]

[0209] In the formula, For first-order moment estimation, For second-order moment estimation, The deviation between the target heating rate and the current surface temperature. The current surface heat source power, For the updated surface heat source power, To adjust the step size coefficient for power, , These are the first and second order moment attenuation factors. To prevent constants with a denominator of zero, the system can automatically adjust the heat source power based on temperature change trends through the above calculations, achieving constant heating rate control and thermal field stability optimization.

[0210] Step 12: During the heat treatment heating stage, a heat flux density is applied to the heating area to raise the temperature to the preset temperature and maintain it at a constant temperature.

[0211] In this step, heat flux density characterizes the amount of heat transferred per unit area per unit time and is a key parameter for controlling the post-weld heat treatment process. During the heating stage of heat treatment, controllable heating of the G115 steel welded pipe is achieved by applying precisely calculated heat flux density boundary conditions to the heating area. When the temperature reaches the preset temperature, a stable thermal equilibrium state is established by dynamically adjusting the heat flux density input intensity, providing the necessary temperature field conditions for the subsequent heat preservation stage. This heating method based on heat flux density control ensures a precise match between heat input and temperature response during the heat treatment process.

[0212] Step 13: During the heat treatment holding stage, the creep behavior is described by a time-creep constitutive model.

[0213] In this step, during the heat treatment and insulation stage of G115 steel welded pipes, the softening and creep effects under high-temperature conditions have a significant impact on structural integrity. Based on a creep constitutive model, a creep behavior characterization method considering temperature-stress coupling was established. This model accurately describes the nonlinear creep characteristics of the pipe material during the insulation stage by introducing a stress exponent and a time hardening term. This allows for precise prediction of dimensional evolution and residual stress redistribution behavior during heat treatment, providing a theoretical basis for optimizing the combination of insulation temperature and time parameters and improving welded joint performance. The creep deformation field and stress field distribution obtained through numerical simulation can effectively guide the design and optimization of heat treatment processes in practical engineering.

[0214] Step 14: In the heat treatment cooling stage, the temperature is cooled to room temperature by air cooling, and finally the temperature distribution data and stress distribution data of the numerical simulation process are obtained.

[0215] In this step, during the heat treatment cooling stage, the G115 steel welded pipe exchanges heat with the surrounding environment through natural convection, achieving a gradual cooling process from high temperature to room temperature.

[0216] Step 108: Calculate the tempered martensite content and hardness distribution of the G115 steel welded pipe, and obtain the hardness distribution of the G115 steel welded pipe after welding based on the coupling relationship model of tempered martensite content and hardness. At the same time, obtain the equivalent distribution of residual stress distribution after welding based on the coupling model of residual stress distribution and hardness.

[0217] For the embodiments of this disclosure, calculating the tempered martensite content and hardness distribution of G115 steel welded pipes based on temperature distribution data may specifically include: Step 1: Obtaining the temperature distribution and stress distribution of the G115 welded pipes, and calculating the tempered martensite content at each location based on the temperature-time history of each location during the post-weld heat treatment process using a preset tempering kinetic model formula. The preset tempering kinetic model formula is as follows:

[0218]

[0219]

[0220] In the formula, The tempering rate constant is temperature-dependent. For the empirical constant (h) - ¹), The tempering activation energy is given by R = 8.314 J / (mol·K), where 8.314 is the gas constant. The tempering temperature (K) is the temperature at which the metal is tempered. Formula for the content of tempered martensite. t represents the volume fraction of the original martensite after quenching (≈1, i.e., 100%), and t represents the tempering time (h).

[0221] Step 2: Based on the empirical relationship between tempering parameters and hardness, and the stress-hardness coupling coefficient after heat treatment, calculate the hardness distribution at various locations on the welded pipe after welding, as shown in the following formula:

[0222]

[0223]

[0224] In the formula, r represents the position (along the wall thickness or laterally), in mm. This is the local tempering temperature. The local tempering time is in hours (h). P(r) is the tempering temperature in K, P(r) is the HJ tempering parameter (K·(logh+C)), and C is the HJ constant (typically 20–22). H(r) is the tempering decomposition factor, 0–1, and H(r) is the local hardness (HV). The hardness (HV) of untempered martensite is given. The hardness (HV) is the hardness at full tempering, i.e., the reference hardness of tempered martensite. For circumferential and axial stresses (MPa). Equivalent stress (MPa). It is the stress-hardness coupling coefficient (HV / MPa). is the empirical fitting constant.

[0225] All parameters in the above formulas need to be calibrated. Multiple sets of simulation results with different parameters can be selected, and their residual stress, hardness distribution, temperature difference, and microstructure distribution can be compared with the actual heat treatment results under the same parameter conditions. The accuracy of the simulation results can be verified through metallographic observation, X-ray residual stress measurement, and temperature difference testing. After the accuracy verification is passed, subsequent steps can be performed.

[0226] Specifically, the numerical simulation results can be compared with the measured results. The parameters of the tempering kinetic model, the hardness coupling model, and the residual stress empirical formula parameters can be adjusted for iterative calibration until the numerical simulation results and the measured results are within the preset error range, thereby completing the calibration of the multiphysics coupling numerical model and related formula parameters.

[0227] Step 109: Construct a multi-source heterogeneous database, and use a composite model of Gaussian process regression algorithm and generative adversarial network to expand and improve the quality of the multi-source heterogeneous database.

[0228] For the embodiments of this disclosure, the geometric parameters, material property parameters, heat treatment process parameters, temperature field distribution, temperature difference between inner and outer walls, post-weld microstructure distribution and hardness distribution of inner and outer walls, and equivalent distribution of residual stress distribution of inner and outer walls of G115 steel welded pipes can be correlated to construct a multi-source heterogeneous database. A composite model of Gaussian process regression algorithm and generative adversarial network is then used to expand and improve the quality of the multi-source heterogeneous database. Specifically, the multi-source heterogeneous database is a process-temperature-microstructure-stress multi-source heterogeneous database for post-weld heat treatment of G115 steel, which may include:

[0229] The temperature field distribution, stress distribution, tempered martensite content distribution, and hardness distribution obtained through numerical simulation are correlated and stored with the measured temperature difference, metallographic observation results, X-ray residual stress measurement results, and hardness test results obtained under corresponding process parameters to obtain a multi-source heterogeneous database. The multi-source heterogeneous database includes at least scalar data, sequential data, spatial field distribution data, and microscopic image data.

[0230] For image-based data in multi-source heterogeneous databases, generative adversarial networks are used for data generation and enhancement to improve the coverage and quality of image data under different combinations of process parameters. Image-based data may include metallographic images, hardness distribution images, and other image-based data. For numerical data in multi-source heterogeneous databases, Gaussian process regression models are used for uncertainty modeling and interpolation expansion. Numerical data may include temperature fields, stress fields, and hardness fields, and other numerical data.

[0231] In this embodiment, based on the above numerical simulation steps, the temperature field, hardness, and microstructure evolution law of G115 steel welded pipe and the corresponding stress field distribution characteristics are obtained. The geometric parameters, material property parameters, heat treatment heating width, heat treatment heat preservation width, heat treatment heating rate, temperature field distribution, inner and outer wall temperature difference, inner and outer wall microstructure and hardness distribution, inner and outer wall stress distribution and microstructure distribution of G115 pipe are obtained. A multi-source heterogeneous database of heat treatment process-temperature-microstructure-stress of G115 pipe is constructed.

[0232] Based on a multi-source heterogeneous database of heat treatment process, temperature, microstructure, and stress for G115 pipes, a composite model of Gaussian Process Regression (GPR) and Generative Adversarial Network (GAN) is used to collaboratively learn the features of numerical and image data, thereby expanding the database and improving its quality, thus obtaining a high-quality multi-source heterogeneous database of heat treatment process, temperature, microstructure, and stress for G115 steel after welding.

[0233] Specifically, to address the sensitivity of GPR and GAN models to data distribution, a three-step preprocessing step is performed:

[0234] 1. Outlier Removal: The 3σ criterion is used to identify data points such as stress mutations and hardness anomalies (e.g., stress values ​​exceeding the reasonable range of 200-800MPa). The cause of the anomaly is determined by combining simulation logs and experimental records. If it is confirmed to be an error, it is removed. A total of 5%-8% of the outlier samples are processed.

[0235] 2. Dimensional normalization: The Min-Max normalization formula (x'=(x-x_min) / (x_max-x_min)) is used to convert parameters of different magnitudes, such as heating rate (℃ / min), hardness (HV), and stress (MPa), to the [0,1] interval, thereby eliminating dimensional interference;

[0236] 3. Feature dimensionality reduction: Through Pearson correlation analysis (threshold set to 0.95) and principal component analysis (PCA), strongly correlated parameters such as "insulation width and heating width" are removed, reducing the input features from 12 dimensions to 8 dimensions, and retaining principal components with a cumulative variance contribution of >90%.

[0237] To improve the feature learning efficiency of the GAN model, the metallographic images are standardized:

[0238] 1. Standardized Format: All experimental and simulated images were adjusted to 256×256 pixels and converted to single-channel grayscale images (pixel values ​​0-255); 2. Quality Enhancement: Gaussian filtering (convolution kernel 5×5, σ=0.5) was used to remove image noise, and histogram equalization was used to stretch the grayscale range to enhance the contrast between ferrite and bainite; 3. Label Association: Each image was labeled with a dual label of "process parameter ID + microstructure fraction" to establish a unique mapping between images and numerical data, ensuring data consistency for subsequent collaborative training.

[0239] The training set (175 sets), validation set (50 sets), and test set (25 sets) are divided in a 7:2:1 ratio to meet the needs of model training and evaluation: Training set: Covers the entire parameter range, containing 80% experimental data and 70% simulated data to ensure the model learns sufficient features; Validation set: Selects 20% experimental data and 20% simulated data, focusing on parameter boundary samples (such as heating rate of 5℃ / min, high temperature of 750℃, etc.), for hyperparameter tuning; Test set: Independent of the training process, selects 100% new experimental samples (not involved in model training), for objectively evaluating the model's generalization ability.

[0240] It adopts a multiple-input multiple-output (MIMO) architecture, and the core configuration is as follows:

[0241] Kernel function selection: Combining the radial basis function (RBF) and the linear kernel function (k(x,x')=σ²exp(-||x-x'||² / (2l²)) + σ_l²x·x'), where the RBF kernel captures the nonlinear relationship between parameters, and the linear kernel ensures global fitting ability; Input layer: 5-dimensional preprocessed feature vector, G115 pipe geometric parameters, material property parameters, heat treatment heating width, heat treatment insulation width, and heat treatment heating rate; Output layer: 6-dimensional target vector (internal and external wall temperature difference, ferrite fraction, martensite fraction, average hardness, circumferential stress distribution, and axial stress distribution); Noise setting: The initial noise variance is set to 1e-3 to balance the model fitting degree and generalization ability.

[0242] Iterative training is performed based on the training and validation sets, with the following steps:

[0243] 1. Initial Training: Input the training set into the model and initialize the kernel function hyperparameters (RBF kernel length scale l=1.2, variance σ²=0.8; linear kernel variance σ_l²=0.2) through maximum likelihood estimation (MLE).

[0244] 2. Error monitoring: Root mean square error (RMSE) and coefficient of determination (R²) are used as evaluation indicators.

[0245] Numerical data are normalized by using Min-Max standardization to convert parameters of different magnitudes (such as heating rate 5-20℃ / min, hardness 200-400HV) to the [0,1] interval to eliminate the influence of dimensions. Pearson correlation coefficient is used to analyze the correlation between parameters and remove redundant parameters (such as retaining one parameter with correlation > 0.95) to reduce the computational complexity of the model.

[0246] The metallographic images were standardized: the size was uniformly set to 256×256 pixels, converted to grayscale, and histogram equalization was used to enhance image contrast. Gaussian filtering was used to remove noise, and the contour features of the tissue phase were extracted by image segmentation algorithms (such as thresholding) to provide clear feature input for model learning.

[0247] The integrated database was divided into training, validation, and test sets in a 7:2:1 ratio: the training set was used for model parameter learning, the validation set was used for tuning model hyperparameters (such as the kernel function of GPR and the learning rate of GAN), and the test set was used to evaluate the final scaling and quality improvement of the model. This ensured consistency in parameter distribution across the datasets and avoided data skew.

[0248] Construct a model structure based on DCGAN (Deep Convolutional Generative Adversarial Network):

[0249] The generator takes the tissue parameters (phase volume fraction) output by the GPR model and random noise as input, and gradually improves the feature map resolution through 4 transposed convolutional layers, finally outputting a 256×256 tissue image, ensuring that the tissue phase ratio of the generated image matches the input numerical parameters.

[0250] Discriminator: It employs 4 convolutional layers to extract features from the input real tissue image and the generated image, and outputs a "true / false" judgment result. At the same time, it adds an auxiliary classification branch to output the predicted value of the tissue phase fraction in the image, realizing the dual constraint of "true / false discrimination + numerical matching".

[0251] First round of training: Fix the GPR model parameters, input the tissue parameters predicted by GPR into the GAN generator to generate tissue images; the discriminator receives both real and generated images at the same time, and optimizes the discriminator parameters through gradient descent so that the discriminator can accurately distinguish between real and fake images and predict tissue phase fractions;

[0252] Collaborative iteration: The discriminator's prediction error of the tissue fraction of the generated image is fed back to the GPR model, and the kernel function parameters of GPR are fine-tuned to improve the accuracy of the GPR output value. Then, the optimized GPR output is used as the input of GAN to continue training GAN. This process is repeated until the error between the tissue fraction of the generated image and the GPR prediction value is less than 5%, and the discriminator cannot distinguish between real and fake images (accuracy close to 50%).

[0253] Hyperparameter optimization: The learning rate of GAN (initially set to 0.0002), batch size (32), and number of iterations (200 rounds) were adjusted using the validation set to ensure model convergence and stability.

[0254] A fusion mechanism for the outputs of GPR and GAN is established: the numerical data (process-temperature-microstructure-stress parameters) output by GPR and the image data (microstructure images) generated by GAN are associated with a unique identifier to form a complete data sample of "numerical value + image"; the generated numerical data is calibrated using an experimental validation set to correct prediction bias (e.g., controlling the average error between the hardness prediction value and the experimental value to within ±3HV); the generated microstructure images are scored by metallographic experts (scoring from dimensions such as clarity and phase ratio accuracy) and the image similarity is calculated (using structural similarity).

[0255] Step 110: Implement real-time closed-loop control of the temperature difference between the inner and outer walls based on a physical-data dual-driven process optimization algorithm.

[0256] In this embodiment of the disclosure, a constraint function can be constructed based on the principle of temperature difference control between inner and outer walls. The constraint function is then iteratively trained using a multi-physics coupling coefficient correction algorithm and a gradient boosting regression algorithm to minimize the deviation between the predicted inner and outer wall temperature difference and the actual temperature difference in the processed multi-source heterogeneous database. This forms a physics-data dual-driven process optimization algorithm, which may specifically include:

[0257] A constraint function is constructed with the temperature difference between the inner and outer walls as the dependent variable and the heating width and insulation width as the independent variables. The initial values ​​of the coefficients of the constraint function are obtained by fitting the multiphysics simulation results.

[0258] The gradient boosting regression algorithm is used to learn from samples in a multi-source heterogeneous database to obtain an initial temperature difference prediction model. The physical model and the data-driven model are then fused through a multi-physics coupling coefficient correction algorithm. The constraint function is iteratively trained to minimize the error between the predicted inner and outer wall temperature difference and the actual value in the database.

[0259] After training is completed, the constraint function is used as a temperature difference control constraint, providing the objective function basis for the physical-data dual-driven process optimization algorithm that calculates the target heating width and the target insulation width.

[0260] In practical applications, a multivariate nonlinear regression method can be used to establish a physical coupling correction constraint function between post-weld heat treatment process parameters and temperature response. This model uses the temperature difference (ΔT) between the inner and outer walls of the pipe as the dependent variable, and the width of the heating zone (W) as the dependent variable. 加热 ) and the width of the insulation area (W) 保温 As the key independent variable, its basic equation form is:

[0261]

[0262] In the formula, For the temperature difference between the inner and outer walls of the pipe, W 加热 W represents the width of the heating area. 保温 denoted as the width of the insulation zone, and a and c as binomial regression coefficients, reflecting the intensity of the nonlinear influence of the corresponding process parameters on the temperature difference; e is the model residual, which includes unmodeled factors and measurement errors.

[0263] Based on a physical-data dual-driven process optimization algorithm, the target heating width and target insulation width can be calculated under the constraint of meeting hardness requirements. In the actual post-weld heat treatment process, the G115 steel welded pipe is subjected to post-weld heat treatment based on the target heating width, target insulation width and preset heating rate. The measured value of the temperature difference between the inner and outer walls of the pipe is obtained in real time during the heat treatment process. The heating power is dynamically adjusted based on the physical-data dual-driven process optimization algorithm to achieve real-time closed-loop control of the temperature difference between the inner and outer walls.

[0264] Specifically, the optimal heat treatment process can be calculated and the actual heat treatment control stage can be entered.

[0265] Based on the data obtained from the input GPR+GAN+physical coupling correction composite algorithm, the microstructure, stress and temperature distribution of the target are determined by the composite algorithm obtained through GPR+GAN+physical coupling correction. The target heat treatment process parameters of the G115 steel welded pipe are determined, and post-weld heat treatment is performed based on the target heat treatment process parameters. The target heat treatment process parameters include the heating zone width, the holding zone width, the heating rate, the holding rate and the holding time.

[0266] Closed-loop control of temperature difference is achieved by dynamically adjusting the heating power of flexible ceramics by identifying heat dissipation patterns through real-time temperature difference measurement.

[0267] Based on the measured outer wall temperature during the heat treatment of G115 pipes and the measured temperature difference between the inner and outer walls, the air heat dissipation pattern during the heat treatment of G115 pipes is identified, and the heating power of the flexible ceramic resistance heating of G115 pipes is actively adjusted.

[0268] Through the above methods, the thermo-mechanical coupling behavior of the entire process from high-temperature heat preservation to room-temperature cooling was completely simulated using multi-scale modeling, providing a reliable theoretical basis for process optimization.

[0269] In practical applications, multi-physics coupled numerical simulations were used to systematically analyze the temperature-stress co-evolution of thick-walled G115 steel welded pipelines under different working conditions during heat treatment. Table 2 shows the temperature difference between the inner and outer walls of the pipeline corresponding to different combinations of heating and insulation zone widths.

[0270] Table 2. Temperature difference between inner and outer walls of the pipe corresponding to different combinations of heating zone and insulation zone widths.

[0271]

[0272] In the process of numerical simulation, such as Figure 3 and Figure 4 The image shows a schematic diagram of the numerical simulation results, with the width of the heating zone as a constant and the width of the insulation zone as a variable. Specifically, Figure 3 This study demonstrates the impact of different insulation zone widths (150mm to 470mm) on the heat treatment temperature distribution of G115 steel welded pipes when the heating zone width is fixed at 420mm. The horizontal axis represents the measurement location along the axial direction of the G115 steel welded pipe, and the vertical axis represents the real-time temperature values ​​at different locations along the cross-section of the G115 steel welded pipe. Five sets of comparative experiments show that when the heating zone width is fixed at 420mm: a 150mm insulation zone results in a temperature difference of 13.26℃; a 470mm insulation zone results in a significantly reduced temperature difference, proving that increasing the insulation zone width effectively improves temperature uniformity. Figure 4This study demonstrates the influence of different insulation zone widths (150mm to 470mm) on the axial temperature distribution of G115 steel welded pipes with a fixed heating zone width (420mm). The temperature reaches 750°C at the weld center (0m), gradually decreasing with increasing axial distance to 300°C at the pipe end (2m), creating a significant axial temperature difference of 450°C. Data from five sets of insulation zone width variables (150-470mm) show that increasing the insulation zone width primarily expands the high-temperature range (>700°C) near the weld (0-0.28m), but has limited improvement on the low-temperature region of 300°C at the far end (2m). Figure 3 The radial temperature difference data of 13.26°C indicates that the axial coverage and radial width of the insulation layer need to be optimized simultaneously in order to comprehensively improve the uniformity of the temperature field.

[0273] The relationship between temperature difference and the width of the heating zone and the width of the insulation zone, analyzed using a multivariate nonlinear regression algorithm, is as follows:

[0274]

[0275] In the formula, For the temperature difference between the inner and outer walls of the pipe, W 加热 W represents the width of the heating area. 保温 This refers to the width of the insulation area.

[0276] Obtained through algorithm The optimal heating zone width and insulation zone width at ≤10℃ are 675mm and 497mm, respectively. To ensure the accuracy of the optimization results, the optimized heating zone-insulation zone width combination (675mm heating zone width, 497mm insulation zone width) was applied to the newly built finite element verification model. Verification showed that the actual temperature difference between the inner and outer walls of the pipe was 10℃, and the relative error with the predicted value from the multivariate nonlinear regression model was less than 5%, fully verifying the algorithm's prediction accuracy and engineering applicability. This result not only confirms the reliability of the thermo-coupling model, but more importantly, provides numerically verified optimal process parameters for engineering practice: the combination of a heating zone width of 675mm ± 5% and an insulation zone width of 497mm ± 3% can ensure that the temperature difference of the pipe cross-section is controlled within 10℃ during heat treatment, significantly improving the quality stability of the welded joint.

[0277] As can be seen, in the above scheme, firstly, a three-dimensional thermo-mechanical coupled finite element model is constructed based on the pipeline's geometric characteristics, clearly defining the initial temperature field distribution, residual stress state, and thermo-mechanical boundary conditions; secondly, a physical model of flexible ceramic resistance heating is integrated, and the thermo-electric coupling behavior of the material is characterized by temperature-related parameters such as resistivity, thermal conductivity, and specific heat capacity; then, finite element simulation is conducted to obtain the evolution law of the transient temperature field and stress field throughout the heating-holding-cooling process; finally, the simulation data is input into a multivariate nonlinear regression algorithm to establish a quantitative relationship model between process parameters (heating / holding width) and response variables (temperature difference / stress). By establishing a high-precision computer numerical model, multi-physics coupled simulation analysis of the post-weld heat treatment process is performed, providing a scientific theoretical basis and technical support for the parameter optimization of the flexible ceramic resistance heating process. This achieves precise control of heat treatment process parameters, significantly improves the energy utilization efficiency of the heat treatment process, and effectively reduces production costs and resource consumption. Simultaneously, the optimized process parameters ensure the mechanical properties and service reliability of the welded joint under high temperature and high pressure conditions, providing reliable quality assurance for engineering practice. The heat treatment process curves are shown below. Figure 5 As shown.

[0278] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. An optimized method for post-weld heat treatment of G115 steel welded pipes, characterized in that, include: Obtain the geometric parameters and material property parameters of the G115 steel welded pipe, and determine the bevel type, bevel geometric parameters, and the number of weld layers and passes of the G115 steel welded pipe based on the geometric parameters. Based on the bevel geometry parameters, the welding process parameters of the G115 steel welded pipe are estimated so that the welding heat input of G115 steel is within the preset heat input range. Based on the analytical model of heat input and temperature field of G115 steel welding, the temperature field distribution of the G115 steel welded pipe after welding is calculated, and the post-weld microstructure distribution of the temperature field distribution is determined based on the temperature threshold judgment rule. Based on the chemical composition and preset mixing rules of G115 steel, the thermophysical performance parameters of the welded pipe of G115 steel at different temperatures are calculated. Based on the empirical formula of material strength and temperature degradation relationship, the temperature-related elastoplastic constitutive model of G115 steel is constructed, and the creep constitutive model of G115 steel is constructed based on the time-hardening creep power law model. Based on the welding heat input of the G115 steel, the geometric parameters, and the preset constraint state, the residual stress distribution of the G115 steel welded pipe after welding is calculated by a preset empirical formula for residual stress. Based on the geometric parameters, the bevel form, the bevel geometry, the number of weld layers and passes, the thermophysical performance parameters, the elasto-plastic constitutive model, the creep constitutive model, and the residual stress distribution, a multiphysics coupled numerical model for the post-weld heat treatment of the G115 steel welded pipe is constructed. The multiphysics coupled numerical model includes heat conduction, elasto-plastic deformation, creep deformation, and coupling of convective heat transfer and radiative heat transfer. In the multiphysics coupled numerical model, the surface heat source power is controlled by the Adam adaptive learning rate optimization algorithm to simulate the flexible ceramic resistance heating process, so as to obtain temperature distribution data and stress distribution data under different heat treatment process parameters. The heat treatment process parameters include heating width, holding width and heating rate. Based on the temperature distribution data, the tempered martensite content and hardness distribution of the G115 steel welded pipe are calculated. Based on the coupling relationship model between the tempered martensite content and the hardness, the hardness distribution of the G115 steel welded pipe after welding is obtained. At the same time, based on the coupling model between the residual stress distribution and the hardness, the equivalent distribution of the residual stress distribution after welding is obtained. The equivalent distributions of the geometric parameters, material property parameters, heat treatment process parameters, temperature field distribution, inner and outer wall temperature difference, post-weld microstructure distribution and hardness distribution of the inner and outer walls, and residual stress distribution of the inner and outer walls of the G115 steel welded pipe are correlated to construct a multi-source heterogeneous database. A composite model of Gaussian process regression algorithm and generative adversarial network is used to expand and improve the quality of the multi-source heterogeneous database. Based on the principle of temperature difference control between inner and outer walls, a constraint function is constructed, and the constraint function is iteratively trained by a multi-physics coupling coefficient correction algorithm and a gradient boosting regression algorithm to minimize the deviation between the predicted inner and outer wall temperature difference and the actual temperature difference in the processed multi-source heterogeneous database, thus forming a physical-data dual-driven process optimization algorithm. Based on the physical-data dual-driven process optimization algorithm, the target heating width and the target heat preservation width are calculated under the constraint of meeting the hardness requirements. In the actual post-weld heat treatment process, the G115 steel welded pipe is subjected to post-weld heat treatment based on the target heating width, the target heat preservation width and the preset heating rate. The measured value of the temperature difference between the inner and outer walls of the pipe is obtained in real time during the heat treatment process. The heating power is dynamically adjusted based on the physical-data dual-driven process optimization algorithm to achieve real-time closed-loop control of the temperature difference between the inner and outer walls.

2. The method according to claim 1, characterized in that, The determination of the bevel type, bevel geometry parameters, and the number of weld layers and passes for the G115 steel welded pipe based on the geometric parameters specifically includes: Obtain the inner and outer diameters of the G115 steel welded pipe, and calculate the pipe wall thickness based on the difference between the inner and outer diameters; Based on the pipe wall thickness and the outer diameter, the bevel type is selected by a preset bevel determination formula. The bevel type includes I-type bevel, single V-type bevel, double V-type bevel, single U-type bevel, or double U-type bevel. The bevel geometric parameters are calculated based on a preset bevel geometric relationship. The bevel geometric parameters include at least the outer bevel angle, the inner bevel angle, the outer radius, the inner radius, the outer bevel depth, and the inner bevel depth. Based on the relationship between the effective weld deposition thickness and the overall groove thickness, the number of weld layers is calculated, and the number of weld passes for each layer is calculated based on the groove opening angle and center radius corresponding to each layer. The number of weld layers is the number of weld filling layers, and the number of weld passes is the total number of weld passes.

3. The method according to claim 1, characterized in that, The welding process parameters include at least welding current, welding voltage, and welding speed; The step of estimating the welding process parameters of the G115 steel welded pipe based on the bevel geometry parameters, so that the welding heat input of the G115 steel is within a preset heat input range, specifically includes: Based on the welding position, electrode diameter, welding coefficient, and selected welding process, the welding current and welding voltage are calculated using a preset empirical formula, wherein the welding current is proportional to the electrode diameter, and the welding coefficient is selected within a preset value range depending on the welding posture. Using the allowable welding heat input range of the G115 steel as a constraint, the welding speed is derived based on the functional relationship between the welding current, the welding voltage and the welding heat input of the G115 steel, so that the welding heat input per unit length of the G115 steel is controlled within the preset heat input range.

4. The method according to claim 1, characterized in that, The process involves calculating the temperature field distribution of the G115 steel welded pipe after welding based on the analytical model of heat input and temperature field of the G115 steel welded pipe, and determining the post-weld microstructure distribution of the temperature field distribution based on temperature threshold judgment rules. Specifically, this includes: Based on the analytical formulas for the welding heat input, material density, specific heat, temperature decay width of the heat-affected zone, and empirical coefficient of heat loss of the G115 steel, the temperature field distribution after welding of the G115 steel welded pipe is calculated, wherein the temperature field distribution is the peak temperature at the weld center and at different positions along the pipe thickness and axial direction. The peak temperature is compared with the critical phase transformation temperature of the G115 steel to determine the post-weld phase transformation behavior at each location, and the post-weld microstructure distribution is obtained by dividing the region. The post-weld microstructure distribution includes the weld, fusion zone, coarse grain zone, fine grain zone, subcritical heat-affected zone and base metal region.

5. The method according to claim 1, characterized in that, The thermophysical performance parameters include density, specific heat, thermal conductivity, coefficient of linear expansion, latent heat of phase change, and yield strength. Based on the chemical composition and preset mixing rules of G115 steel, the thermophysical performance parameters of the welded pipe made of G115 steel at different temperatures are calculated. A temperature-dependent elastoplastic constitutive model of the G115 steel is constructed based on empirical formulas for material strength and temperature degradation relationships. Specifically, this includes: Based on the chemical composition mass fraction and reference density of each element in the G115 steel, the density of the G115 steel at the reference temperature is calculated using the mixed density formula. Based on the chemical composition mass fraction of each element in the G115 steel and the specific heat of each element at different temperatures, the specific heat of the G115 steel at each temperature node is calculated using the first weighted mixing formula. Based on the volume fraction of each element in the G115 steel and the thermal conductivity of each element at different temperatures, the thermal conductivity of the G115 steel at each temperature node is calculated using the Reuss model formula. Based on the volume fraction of each element in the G115 steel and the linear expansion coefficient of each element or phase, the linear expansion coefficient of the G115 steel is calculated using the linear expansion coefficient formula. Based on the chemical composition mass fraction of each element in the G115 steel and the latent heat of phase transformation per unit mass of each element, the latent heat of phase transformation of the G115 steel is calculated using the second weighted mixing formula. Based on the chemical composition mass fraction of each element in the G115 steel and the yield strength at the reference temperature, the reference yield strength of the G115 steel is calculated using the third weighted mixing formula, and the temperature degradation coefficient is used to correct the reference yield strength to obtain the yield strength. Based on the elastic modulus, hardening modulus and corresponding temperature degradation coefficient of the G115 steel at room temperature, a temperature-dependent elastoplastic constitutive model is constructed.

6. The method according to claim 1, characterized in that, The residual stress distribution includes axial residual stress distribution and circumferential residual stress distribution; The calculation of the residual stress distribution of the G115 steel welded pipe after welding, based on the welding heat input of the G115 steel, the geometric parameters, and the preset constraint state, using a preset empirical formula for residual stress, specifically includes: Based on the normalized welding heat input parameters of the G115 steel, the yield strength of the G115 steel, and the geometric and constraint coefficients, the maximum residual stress near the weld is calculated using the preset empirical formula for residual stress. Based on the analytical relationship of circumferential and axial stress distribution of thick-walled circular pipes, the maximum residual stress is expanded into a radial distribution function along the pipe wall thickness direction, and the circumferential residual stress distribution and the axial residual stress distribution are obtained respectively. The circumferential residual stress distribution and the axial residual stress distribution are then imported into finite element analysis software as predefined fields to model the initial stress state of the G115 steel welded pipe after welding.

7. The method according to claim 1, characterized in that, The process of simulating flexible ceramic resistance heating by controlling the surface heat source power using the Adam adaptive learning rate optimization algorithm specifically includes: During the heat treatment heating stage, a spatially adjustable surface heat flux density is applied to the outer surface of the heating zone. The surface temperature of the pipe is monitored in real time and compared with the target heating curve to obtain the temperature deviation. Using the temperature deviation as input, the power correction amount at the current moment is calculated through the Adam adaptive learning rate optimization algorithm, and the surface heat source power applied to the outer surface of the pipe is updated based on the power correction amount; Within each time step, the flow and heat transfer state of the air around the pipe are solved based on the fluid energy conservation, solid heat conduction, and interfacial convection and radiation heat transfer equations. The heat transfer coefficient of the pipe surface is dynamically calculated and updated, and the temperature field is corrected based on the updated heat transfer coefficient. Through the above closed-loop control, the heating rate is maintained near the preset value to achieve high-fidelity simulation of the actual flexible ceramic resistance heating process.

8. The method according to claim 1, characterized in that, The calculation of the tempering martensite content and hardness distribution of the G115 steel welded pipe based on the temperature distribution data specifically includes: Based on the temperature-time history at each location during the post-weld heat treatment process, the tempered martensite content at each location is calculated using a pre-set tempering kinetic model formula. Based on the empirical relationship between tempering parameters and hardness, and the stress-hardness coupling coefficient after heat treatment, the hardness distribution at each location after welding is calculated.

9. The method according to claim 1, characterized in that, The multi-source heterogeneous database is the process-temperature-microstructure-stress multi-source heterogeneous database of the post-weld heat treatment of G115 steel. The construction of a multi-source heterogeneous database, and the expansion and quality improvement of the multi-source heterogeneous database using a composite model of Gaussian process regression algorithm and generative adversarial network, specifically includes: The temperature field distribution, stress distribution, tempered martensite content distribution, and hardness distribution obtained through numerical simulation are correlated and stored with the measured temperature difference, metallographic observation results, X-ray residual stress measurement results, and hardness test results obtained under corresponding process parameter conditions to obtain the multi-source heterogeneous database. The multi-source heterogeneous database includes at least scalar data, sequential data, spatial field distribution data, and microscopic image data. For image data in the multi-source heterogeneous database, generative adversarial networks are used for data generation and enhancement to improve the coverage and quality of image data under different combinations of process parameters. For numerical data in the multi-source heterogeneous database, a Gaussian process regression model is used for uncertainty modeling and interpolation extension.

10. The method according to claim 1, characterized in that, The constraint function is constructed based on the principle of inner and outer wall temperature difference control, and iteratively trained using a multi-physics coupling coefficient correction algorithm and a gradient boosting regression algorithm to minimize the deviation between the predicted inner and outer wall temperature difference and the actual temperature difference in the processed multi-source heterogeneous database, forming a physical-data dual-driven process optimization algorithm, specifically including: A constraint function is constructed with the temperature difference between the inner and outer walls as the dependent variable and the heat treatment heating width and the heat preservation width as independent variables. The initial values ​​of the coefficients of the constraint function are obtained by fitting the multiphysics simulation results. The gradient boosting regression algorithm is used to learn from the samples in the multi-source heterogeneous database to obtain an initial temperature difference prediction model. The physical model and the data-driven model are then fused through a multi-physics coupling coefficient correction algorithm. The constraint function is iteratively trained to minimize the error between the predicted inner and outer wall temperature difference and the actual value in the database. After training is completed, the constraint function is used as a temperature difference control constraint, providing the objective function basis for the physical-data dual-driven process optimization algorithm for calculating the target heating width and the target insulation width.

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