Quenching Internal Stress Evolution and Shape Control in Gigapascal Ultra-High-Strength Martensitic Steel

Abstract

Gigapascal ultra-high-strength steel holds significant applications in the energy and military sectors. Such steel is typically produced through quenching and tempering processes. However, during quenching, issues such as excessive internal stress often lead to significant deviations in flatness, thereby reducing product precision. This study adopts an approach integrating theoretical and practical methods to develop a control technology for achieving high flatness in gigapascal ultra-high-strength martensitic steel. Firstly, finite element simulation was employed to establish a temperature-phase transformation-stress coupling model for the quenching process of gigapascal martensitic steel. The study investigated the deformation behavior of steel plates under unilateral cooling, the influence of dynamic martensitic transformation on internal stress, and the effects of plate thickness and water ratio. This revealed how quenching process parameters affect the internal stress and deformation of steel plates. Based on theoretical calculations and considering on-site equipment conditions, industrial production line commissioning was conducted, which significantly reduced the quenching internal stress of gigapascal ultra-high-strength martensitic steel and greatly improved the flatness of the steel plates. The results surpassed those of international companies such as Sweden’s SSAB and other domestic enterprises, achieving an internationally leading level.

1. Introduce

The steel industry is a foundational sector of the national economy and plays a crucial supporting role in economic development. However, steel production is characterized by high resource and energy consumption. Under the “Carbon Peak and Carbon Neutrality” strategy, enhancing steel strength to reduce usage has become highly significant [1]. Consequently, the research and development of ultra-high-strength martensitic steel has increasingly become a priority [2,3,4].

Ultra-high-strength martensitic steel typically undergoes a quenching process during production to obtain a high-strength, high-hardness martensitic microstructure. This is followed by tempering to adjust its strength and ductility [5,6,7]. Due to the high cooling rate required to form martensite during quenching, uneven cooling readily occurs, leading to plate shape defects that result in excessive flatness deviations or outright scrapping of the product [8,9].

The reason for shape defects during the quenching process is that the internal stress of the steel exceeds its yield strength, combined with uneven cooling, resulting in uneven plastic deformation. To enhance efficiency and reduce costs, finite element simulation is generally employed to study the shape variation of metal materials. Ye et al. [10] used finite element simulation to investigate heat transfer behavior during air-jet quenching of steel plates, providing a theoretical foundation for shape control. Perzyński et al. [11] developed a finite element model to predict the shape change during the leveling process of S700MC high-strength steel, verified the model’s accuracy, and achieved high-strength steel with high flatness. Zhang et al. [12] established a temperature-microstructure-stress coupled finite element model to analyze the shape variation behavior of cold-rolled high-strength strip steel during quenching. Based on the simulation results, they proposed a shape optimization control strategy, though no actual industrial experiments were conducted. Temperature variation is the primary factor affecting steel plate deformation. It can be concluded that finite element simulation is an efficient and reliable method for predicting shape deformation behavior and proposing solutions.

Currently, research on the flatness and internal stresses of steel materials primarily focuses on grades below 960 MPa [13,14], involving only production processes such as rolling, laminar cooling, and online ultra-fast cooling. There is limited study on the correlation between flatness and internal stresses during the quenching and cooling process of ultra-high-strength steels with strengths of 1000 MPa and above. Some steel enterprises rely solely on empirical process adjustments to control quenched plate shape, often resulting in insufficient flatness [15,16]. Therefore, it is imperative to conduct an in-depth theoretical analysis of the evolution of internal stresses and their relationship with plate shape during complex quenching processes of the gigapascal-grade ultra-high-strength martensitic steel.

2. Research Methodology

2.1. Development of a Coupled Model

During the quenching process of gigapascal-grade ultra-high-strength martensitic steel, temperature variations across different sections generate thermal stresses. Simultaneously, the martensitic transformation induces microstructural stresses due to changes in lattice type and lattice constants. When the quenching stress exceeds the yield strength of the steel, plate deformation occurs, manifesting as warping and reduced flatness. This study aims to develop a temperature-transformation-stress coupled model for the quenching process of ultra-high-strength martensitic steel. Additionally, the latent heat released during phase transformation must be considered, as it influences both temperature distribution and stress evolution. To address various defects observed along the length direction of steel plates in practical investigations, it is essential to study the deformation behavior under asymmetric cooling conditions between the upper and lower surfaces. This work employs ABAQUS 2016 software to establish a coupled stress–strain and temperature field model, with the multiphysics finite element model illustrated in Figure 1.

Utilizing the DFLUX subroutine interface, a subroutine was developed to define the moving speed of the cooling water, the contact width of the cooling water on the steel plate surface, the heat transfer power of the cooling water, and the water flow ratio between the upper and lower surfaces of the plate. By establishing multiple sets of moving cooling sources on the upper and lower surfaces, the working conditions under asymmetric cooling were simulated. This approach enabled the investigation of the deformation process of a steel plate—uniformly heated and held at 890 °C—under varying cooling conditions.

2.2. Phase Transformation Kinetic Model for Dynamic Cooling Process

2.2.1. Phase Transformation Model Parameters

The isothermal transformation equation describes the relationship between the transformed fraction and time, with time being the sole independent variable. Given two different transformed fractions X₁ and X₂ at a specific temperature T, along with their corresponding times t₁ and t₂, the values of k and n at that temperature can be solved using the following formula [17].

$$n={\displaystyle \frac{\ln (1-X_1)}{\ln (1-X_2)}}/\ln ({\displaystyle \frac{t_1}{t_2}})$$

(1)

$$k=-\ln (1-X_1)/t^n$$

(2)

Based on Formulas (1) and (2) combined with experimental data, the values of k and n at different temperatures can be determined. By fitting the values of k and n using a cubic polynomial, the phase transformation kinetics equation for isothermal transformation at various temperatures can be obtained. This formula is suitable for diffusional phase transformations.

Below the temperature M_s, martensitic transformation is a time-independent process. Its nature is shear-type rather than diffusional [18]. Therefore, its kinetics are not influenced by cooling rate and cannot be described by the Avrami kinetics equation. The amount of martensite formed is often calculated using a temperature-dependent equation, which applies the law established by Koistinen and Marburger [19].

$${\xi }_m=1-exp\left[-\Omega \left(M_s-T\right)\right]$$

(3)

Ω is a constant in many steels, independent of chemical composition, with a value of 0.011 K⁻¹.

M_s can be determined using the following empirical formula [20]:

M_s = 539 − (423 × %C) − (30.4 × %Mn) − (17.7 × %Ni) − 12.1 × %Cr) − (7.5 × %Mo)

(4)

2.2.2. Continuous Cooling Transformation Kinetic Equation

Formula (5) describes an isothermal transformation process, but the phase transformation occurring during the cooling of steel plates is a non-isothermal process. Based on the additivity rule, the continuous cooling process is discretized into a finite number of isothermal transformation processes for superposition calculations. Assume that at the end of the i-th time step, the volume fraction of phase transformation is X_i. The step length of the (i + 1)-th time step is t, and the temperature at the beginning of this step is T_i+1. The virtual time t_v required to complete the transformation X_i at temperature T_i+1 is then calculated.

$$t_v=\sqrt[n]{{\displaystyle \frac{\ln (1-X_i)}{k}}}$$

(5)

Then, the virtual time for phase transformation at the (i + 1)-th time step is:

$$t_{i+1}^v=t_v+\Delta t$$

(6)

Substituting $t_{i+1}^v$ into Formula (6), the volume fraction of phase transformation at the (i + 1)-th time step can be determined.

2.2.3. Phase Transformation Plasticity and Latent Heat of Phase Transformation

Phase transformation plasticity is a special phenomenon that accompanies phase transformations during the quenching process [21,22]. It refers to the irreversible deformation caused by deviatoric stress under non-zero stress conditions during solid-state phase transformations. The description of phase transformation plasticity in the quenching process utilizes the Greenwood–Johnson model [23].

$${\dot{\epsilon }}_{ij}^{\mathrm{tr}}={\displaystyle \frac{3}{2}}K{\dot{\xi }}_k\left(1-{\xi }_k\right)S_{ij}$$

(7)

K is the phase transformation plasticity coefficient, typically taken as 4.2 × 10⁵, and S_ij is the deviatoric stress tensor.

During heating or cooling processes, when microstructural transformations occur, latent heat (q_V) is absorbed or released. Although the latent heat associated with solid-state phase transformations is not as significant as that during melting or solidification, it remains a non-negligible factor. In simulation calculations, this work treats the latent heat generated within each finite element as an internal heat source for that element. During the quenching process, the internal heat source term q_V is generated by the latent heat of phase transformations (A → F, A → P, A → B, and A → M). The enthalpy values during austenite decomposition are shown in

Table 1. The enthalpy value during the decomposition of austenite.

Generated Microstructure	Ferrite (F)	Pearlite (P)	Bainite (B)	Martensite (M)
ΔH/(J/m3)	5.9 × 108	6.0 × 108	6.2 × 108	6.5 × 108

.

Since the transformation of austenite is temperature-dependent, the latent heat of phase transformation is also a linear function related to temperature. Its calculation formula is as follows [24]:

$$q_V=\rho ∆H{\displaystyle \frac{f_{n+1}-f_n}{∆t}}=\rho ∆H∆f$$

(8)

f_n+1 represents the phase transformation fraction at time t_n+1, f_n represents the phase transformation fraction at time t_n, ΔH denotes the corresponding enthalpy for the formation of F, P, B, and M, and Δf is the phase transformation fraction per unit time.

2.2.4. Heat Transfer Mathematical Model for Heat Treatment Process

The three-dimensional transient nonlinear partial differential equation describing the temperature field within a solid is as follows [25]:

$${\displaystyle \frac{\mathsf{\partial }}{\mathsf{\partial }x}}\left(\lambda {\displaystyle \frac{\mathsf{\partial }T}{\mathsf{\partial }x}}\right)+{\displaystyle \frac{\mathsf{\partial }}{\mathsf{\partial }\mathrm{y}}}\left(\lambda {\displaystyle \frac{\mathsf{\partial }T}{\mathsf{\partial }y}}\right)+{\displaystyle \frac{\mathsf{\partial }}{\mathsf{\partial }\mathrm{z}}}\left(\lambda {\displaystyle \frac{\mathsf{\partial }T}{\mathsf{\partial }z}}\right)+Q=\rho c_p{\displaystyle \frac{\mathsf{\partial }T}{\mathsf{\partial }t}}$$

(9)

T is temperature, t is time, x, y, z are the three coordinates in the spatial coordinate system, λ is thermal conductivity, ρ is density, c_p is specific heat capacity, and Q is the internal heat source.

2.3. Model Development for the Evolution Behavior of Quenching Internal Stress

The geometric model drawn in ABAQUS has dimensions of 250 mm in length and 150 mm in width, with steel plates of varying thicknesses. A typical geometric model for a 6 mm thickness is shown in Figure 2. A corresponding martensitic ultra-high-strength steel material with a strength range of 1000–2000 MPa was created, incorporating properties that play a major role during the heat treatment process. These include thermal conductivity, density, elastic modulus, thermal expansion coefficient, thermoplastic parameters, and specific heat capacity. To account for changes in material properties with temperature during heat treatment, the thermal conductivity, elastic modulus, thermoplasticity, and specific heat in the material property editor were defined using temperature-dependent data. To more accurately calculate thermal stress and phase transformation analysis, we employed the C3D8T element. For a 6 mm thick steel plate, the total number of elements was 6000, and the number of nodes was 7905. The analysis step type was selected as coupled temperature-displacement.

To facilitate model calculations, a fully fixed constraint was applied at the tail end of the plate, allowing for the study of deformation characteristics at the head and middle sections. The cooling water ejected from nozzles primarily cools the steel plate by acting on its upper and lower surfaces. By setting the heat flux on these surfaces to simulate actual cooling conditions, the deformation behavior of a uniformly heated and insulated steel plate (at 890 °C) under varying cooling scenarios was investigated. The element type was selected for coupled temperature-displacement analysis.

After establishing the base model, parameters such as cooling power, the width of cooling water action on the plate surface, the water ratio between two cooling sets, and the spacing between them were adjusted to simulate various real-world cooling conditions. This approach was used to study the quenching deformation behavior of ultra-high-strength martensitic steel. Based on the numerical simulation results, industrial trials were conducted to develop a giga-grade ultra-high-strength martensitic steel high-flatness control technology.

3. Results and Discussion

3.1. Single-Side Cooling Condition

First, consider a simple single-side cooling condition. The initial temperature of the steel plate is 890 °C, and its entire upper surface is in contact with the external environment for convective heat transfer. Under this cooling mode, it can be observed that the overall deformation of the steel plate results in concavity on the cooled surface. A stable temperature gradient exists in the thickness direction from the cooled surface to the opposite surface. The single-side overall cooling model is shown in Figure 3.

Subsequently, a moving cooling water system was applied to the upper surface of the heated and insulated steel plate to analyze its flatness behavior. It is observed that during the initial movement of the single cooling water group across the head of the steel plate, the deformation characteristic exhibits concavity on the cooled surface where the water is applied. The initial model of single-side overall cooling is shown in Figure 4a. As the cooling water moves toward the tail end of the plate, the central region along the width direction gradually bulges toward the edges, eventually resulting in a crown-type flatness deformation on the cooled surface. From Figure 4b, it can be concluded that the heated steel plate undergoes an evolution process—from concavity on the cooled surface to crown deformation—under the moving cooling action of a single water group.

In the single-side overall cooling process compared to the moving cooling process using a single water group, the edge regions of the single-side overall cooling process do not exhibit uneven stress distribution. Meanwhile, as the cooling source acts continuously and stably on the upper surface, the steel plate maintains a stable temperature gradient along the thickness direction during single-side overall cooling. In contrast, during the moving cooling process, the area under the cooling source exhibits a stable temperature gradient. However, as the cooling source moves from the cooled section toward the uncooled tail end, the previously cooled region loses its original temperature gradient and cooling rate. Simultaneously, the primary heat conduction mechanism shifts to internal heat transfer between the high-temperature and low-temperature zones within the steel plate, which leads to crown deformation in the plate.

According to the simulation results, the entire deformation process when the plate head enters the high-pressure cooling section can be described as follows: Initially, the side with higher cooling intensity undergoes concavity, characterized by crowning in the central region and uplifted edges. Subsequently, as the cooling source moves relative to the plate surface toward the tail end, the concavity gradually evolves into convex deformation.

3.2. Influence of Martensitic Dynamic Phase Transformation on Internal Stress

3.2.1. Phase Transformation Behavior at Different Thickness Positions in the Longitudinal Section

In the phase transformation subroutine, 550 °C is set as the starting point of martensitic transformation. When the cooling rates of the upper and lower surfaces of the steel plate differ, their temperature changes occur at varying paces, with the temperature drop on the faster-cooling side being significantly greater than that on the slower-cooling side. This results in phase transformations occurring at different times across the thickness of the steel plate. Such temporal differences ultimately lead to flatness issues in the steel plate.

Figure 5 shows a contour plot of the phase transformation expansion over time on the longitudinal section of a 12 mm thick, 1500 MPa strength steel plate. The data in the figure are calculated based on the changes in the proportional fraction of phase transformation expansion and output by setting state variables. As illustrated in Figure 5a, the phase transformation begins first on the faster-cooling side, where only the faster-cooling surface undergoes transformation. This means the metal on the faster-cooling surface experiences phase transformation expansion, i.e., volume expansion, while simultaneously acquiring higher yield strength. As a result, the volume of the metal on the faster-cooling side expands, leading to plastic deformation where the metal on this side flows laterally toward the edges. In contrast, the slower-cooling side exhibits the opposite behavior, causing the steel plate to arch toward the faster-cooling side laterally and bend toward the slower-cooling side longitudinally.

After the metal on the faster-cooling side undergoes phase transformation for a period, the temperature of the metal on the slower-cooling side also reaches the phase transformation temperature, resulting in martensitic transformation and the same phase transformation expansion. At this stage, the phase transformation expansion generated per time increment is identical on both the upper and lower surfaces, so the flatness remains unchanged. However, due to the asynchrony of phase transformation along the length direction, localized flatness fluctuations occur in the longitudinal direction. Additionally, the temperature drop of the inner-layer metal in the ultra-high-strength steel plate is smaller compared to the surface layers, causing the phase transformation in the inner layers to occur later. Figure 5b shows that phase transformation occurs first on the faster-cooling side, followed by the slower-cooling side. The impact on the plate shape is the same as that observed in the outer-layer metal. Due to the higher cooling rate at the surface layer metal, both the temperature change and phase transformation are more intense compared to the inner-layer metal, resulting in greater transformation expansion in the surface layer.

As shown in Figure 6, the relationship between phase transformation expansion and time at different thicknesses is illustrated for a 12 mm thick, 1500 MPa strength steel plate under a water ratio of 1:1.1. Figure 6 indicates that phase transformation occurs earlier on the faster-cooling surface than on the slower-cooling surface, and the closer to the core, the slower the phase transformation due to a reduced temperature drop rate. The slower phase transformation rate results in a decrease in the magnitude of phase transformation expansion, meaning the incremental expansion due to phase transformation is smaller. The phase transformation increment on the faster-cooling surface is significantly large, leading to plastic deformation where the metal on this surface flows laterally toward both sides. This plastic deformation is the direct factor ultimately affecting the transverse shape of the plate.

The total amount of phase transformation expansion in the inner-layer metal is the same as that in the surface metal. However, due to the slower phase transformation rate, the expansion increment is smaller, resulting in a reduced impact on plastic deformation. As shown in Figure 7, when the water ratio increases to 1:1.2, the temperature drop rate of the metal on the faster-cooling surface accelerates, causing its phase transformation expansion to occur earlier. This further widens the time difference between the occurrence of phase transformation expansion on the faster-cooling side and the slower-cooling side.

3.2.2. Phase Transformation Behavior Across the Width

Figure 8 shows the variation curves of martensite content over time at different points across the width direction of the steel plate. In Figure 8a, the top-left point (A₀) on the operational side is subjected to both jet impingement cooling and flow water cooling, resulting in a rapid temperature drop. Once the martensite transformation point is reached, martensite transformation occurs. When transitioning from the high-pressure cooling zone to the low-pressure cooling zone, a temperature rebound phenomenon is observed. During this temperature rise, the martensite content ceases to increase because the temperature does not reach the threshold for reverse transformation from martensite to austenite. The martensite content only resumes its increase when the temperature drops back to the level at which low-pressure cooling begins. Points located 2 mm (A₁), 4 mm (A₂) below the upper surface of the steel plate, and at the center layer (A₃) undergo martensite transformation later. After about 30 s, the martensite content at all points converges to a similar value, which is attributed to the final cooling temperatures becoming nearly identical. The overall trend at the center position is consistent with that observed at the edge (Figure 8b). Figure 8c illustrates the variation in martensite content at points along the transverse direction on the drive side.

By comparison, it can be observed that the variation trends of surface points and center-layer points in the transverse direction are consistent. The difference lies in the timing of martensite transformation: points on the side edges undergo transformation earlier than those in the central region due to their lower temperatures.

3.3. The Influence Pattern of Quenching Process on the Temperature Drop of Steel Plate

3.3.1. Influence of Plate Thickness on the Quenching Cooling Temperature Variation Curves

Temperature is one of the most critical parameters in the quenching process. Figure 9 presents the temperature drop curves at different thicknesses for 12 mm and 20 mm thick products with a plate advancement speed of 0.25 m/s. They have a tensile strength grade of 1400 MPa. It can be observed that the temperature drop curves of the quenched ultra-high-strength steel vary significantly across different thicknesses. From the surface to the interior, the cooling rate gradually decreases. This is primarily because the material’s thermal conductivity (17–27 W/(M·K)) is relatively low compared to the heat transfer coefficient (about 5000 W/(M·K)) at the steel plate surface, resulting in lower heat flux in the interior and a slower temperature drop.

When the plate thickness increases from 12 mm to 20 mm, the overall cooling rate of the steel plate decreases slightly, as illustrated by the cooling rate at the temperature range of 900 °C to 200 °C at the upper quarter-thickness position dropping from 156 °C/s to 121 °C/s. By analyzing the surface temperature curve, a noticeable temperature rebound phenomenon is observed at 0.5 s. This occurs due to the gap between slit nozzles and high-density nozzles. When the quenched steel plate moves into this gap, the cooling intensity drops sharply. At this point, the heat dissipated from the surface metal becomes less than the heat received from the interior, leading to the temperature rebound.

Under the action of slit cooling water, cooling rates at the metal surface can be as high as 200–250 °C/s, entering the martensite transformation zone. Subsequently, it gradually cools down to room temperature under the cooling effect of high-pressure section cooling water. For the internal metal, although the cooling rate is relatively lower than that in the surface layer metal, martensite transformation generally begins within 5–6 s after cooling.

3.3.2. Influence of Water Ratio on the Quenching Cooling Temperature Variation

Figure 10 shows the temperature curves along the thickness direction of a 12 mm ultra-high-strength steel under different water ratios, with a plate advancement speed of 0.25 m/s. It can be observed that the greater the cooling intensity, the faster the temperature drops at the surface. When the water ratio is at a relatively low value of 1:1.1, the temperature difference between the upper and lower surfaces is small, with a maximum of 33 °C. However, when the water ratio increases to 1:1.2, the maximum temperature difference rises to 59 °C. Under a water ratio of 1:1.3, the maximum temperature difference can reach approximately 112 °C.

3.3.3. Influence of Roll Speed on the Quenching Cooling Temperature Variation

Figure 11 shows the surface temperature drop curves of 6 mm thick, 1400 MPa strength steel under different roll speeds with a single set of slit cooling water. It can be observed that during the rapid cooling phase, the temperature drop curves largely overlap. However, the steel plate with a slower roll speed reaches a lower minimum temperature. In the subsequent temperature rebound stage, the condition with a slower roll speed also results in a lower final temperature.

Figure 12 shows the surface temperature drop curves of 12 mm thick, 1400 MPa strength steel under different roll speeds. It can be observed that when the advancement speed of the medium-thick plate increases, the temperature rebound stage occurs earlier. Additionally, under higher advancement speeds, the temperature rise during the rebound stage is smaller. Due to this reduced temperature rise at higher speeds, the temperature curves after entering the high-pressure section remain relatively consistent across different speeds.

As clearly shown in Figure 13 and Figure 14, when the roller speed of the quenched steel plate increases, the temperature difference between the fast-cooling and slow-cooling surfaces gradually decreases. For the 12 mm thick steel plate, when the speed is 0.25 m/s, the maximum temperature difference between the upper and lower surfaces is 61 °C. When the speed increases to 0.5 m/s, the maximum temperature difference decreases to 44 °C. With a further increase in speed to 0.75 m/s, the temperature difference between the upper and lower surfaces becomes almost negligible. Similarly, for the 20 mm thick steel plate, when the roller speed reaches 0.75 m/s, the temperature difference between the surfaces is also virtually zero.

The time difference for phase transformation between the upper and lower surfaces also reduces, leading to a shorter delay in the occurrence of phase transformation expansion on these surfaces. When the delayed phase transformation expansion occurs on the slow-cooling side, the surrounding metal experiences a smaller temperature drop compared to when phase transformation expansion occurs on the fast-cooling side. As a result, the change in yield strength is also smaller. Therefore, higher roller speeds cause the temperature changes on the fast-cooling and slow-cooling sides to become more similar, leading to more uniform deformation patterns. This ultimately results in a reduction in the warping amount.

3.4. Control Technology for Quenching Stress in Martensitic Ultra-High-Strength Steel

Through the aforementioned research, mathematical models related to the phase transformation process—such as phase transformation thermodynamics, kinetics, latent heat, and expansion—during the quenching of 1000–2000 MPa martensitic ultra-high-strength steel have been established. By incorporating stress/strain calculations into the temperature field model, a thermo-mechanical coupling model is developed to elucidate the interactions among the flow field, temperature field, and microstructural stress field during the processes of temperature drop, deformation, and microstructural transformation in steel plate quenching, as well as the distribution patterns of quenching-induced internal stress. Based on these findings, the quenching cooling process is optimized through key control technologies, including “precise cooling water control at different phase transformation stages, ordered heat exchange processes, flexible temperature field control, and regulation of upper and lower cooling water ratios and flow rates”. These advancements allow for high flatness and precise control of low internal stress during the quenching of gigapascal-grade ultra-high-strength steel.

3.4.1. Application of Ordered Heat Exchange Technology and Flexible Temperature Field Control Technology During the Cooling Process

Based on the above research, this study adjusts the travel speed of the steel plate within the quenching machine according to the process parameters to achieve an optimal quenching path. In response to changes in the heat exchange conditions on the steel plate surface, the water flow density is dynamically adjusted to enable efficient and orderly heat transfer. During the quenching process, thick-gauge steel plates exhibit significant through-thickness temperature gradients. By optimizing the quenching cooling process, challenging bottlenecks such as deformation, delayed cracking, and poor formability caused by potential quenching internal stresses in large-thickness gigapascal-grade ultra-high-strength steels are resolved. The cooling rate indicators primarily focus on thick-gauge steel plates, with the quenching temperature drop curves for 50 mm and 80 mm steel grades shown in Figure 15. For the 50 mm thick steel plate, the temperature at various through-thickness positions gradually decreases as cooling progresses, with the surface layer exhibiting the highest cooling rate (Figure 15a). When the plate thickness increases to 80 mm, the overall cooling efficiency becomes lower than that of the 50 mm plate. Furthermore, due to the higher internal temperature of the thicker plate and the intermittent operation of cooling nozzles, the surface temperature may experience a slight rebound during cooling intervals (Figure 15b).

For gigapascal-grade ultra-high-strength steels of different thicknesses, under the ultra-fast cooling condition where the instantaneous cooling rate exceeds 50 °C/s during jet impingement heat exchange, the temperature drop curves at symmetric positions—such as the upper and lower surfaces and the upper and lower quarter-thickness points—tend to converge. This indicates that the heat exchange, phase transformation, and internal stress evolution at the upper and lower surfaces exhibit symmetrical changes centered on the mid-thickness point.

3.4.2. Full-Plate High Flatness Control Technology During Quenching

When local transverse bending deformation occurs in the steel plate during the quenching process, flexibly adjusting the cooling water ratio can effectively reduce the magnitude of such deformation. Using the controlled variable method, the water flow density on the upper surface is maintained at a constant value of 1.0 m³/(min·m²), while the water flow density on the lower surface is varied. The specific water cooling parameters and results are presented in

Table 2. Measurement results of the straightness of steel plates with different water flow densities.

Grade	Specification	Water Flow Density/(m3·min−1·m−2)		Roller Table Speed/(m·min−1)	Flatness /(mm·m−1)
		Upper	Lower
TS-1500 MPa	8 × 2000	1.0	1.5	30	1.9
		1.0	1.3	30	1.8
		1.0	1.0	30	1.6
TS-1800 MPa	8 × 2000	1.0	1.5	20	1.5
		1.0	1.3	20	1.2
		1.0	1.1	20	1.3
		1.0	1.0	20	1.6

.

Figure 16 illustrates the effect of water ratio on transverse bending deformation during the cooling of TS-1500 MPa and TS-1800 MPa steel plates. For the TS-1500 MPa steel plate, the transverse bending deformation gradually decreases as the water ratio increases. When the water ratio increases from 1:1.0 to 1:1.1, the maximum camber is reduced from −0.296 mm to −0.267 mm, representing an improvement of 9.8%. With a further increase in the water ratio to 1:1.3, the camber decreases to −0.186 mm, corresponding to a 37.2% improvement. When the water ratio reaches the maximum value of 1:1.5, the camber approaches zero. For the TS-1800 MPa steel plate, an increase in the water ratio from 1:1.0 to 1:1.1 leads to an improvement in shape flatness. However, when the ratio is increased to 1:1.3, the shape flatness deteriorates. A further increase to 1:1.5 results in additional deterioration of the flatness.

Therefore, the optimal flatness is achieved under process parameters where the water ratio ranges from 1:1.1 to 1:1.3. At a water ratio of 1:1.0, although the water flow density of the upper and lower nozzles is identical, the jet flow from the upper nozzles is affected by gravity and tends to accumulate on the upper surface of the steel plate. The equipment’s air knife systems cannot completely remove this water layer, resulting in a higher cooling capacity on the upper surface compared to the lower surface, which ultimately leads to greater plate deformation. When the water ratio increases to 1.3 and 1.5, the cooling capacity of the lower nozzles significantly exceeds that of the upper surface. The best plate flatness is achieved at a water ratio of 1:1.1 to 1.3 and a roller speed of 20 m/min.

4. Application Effectiveness

Through the regulation of quenching internal stress in martensitic ultra-high-strength steels of TS-1500 MPa and TS-1800 MPa grades, their flatness ranges were controlled within 0.1–2.9 mm/m and 0.1–3 mm/2m, respectively. Compared to the flatness requirements for H-class single-rolled steel plates specified in GB/T 709-2019 [26]—which allow 10–14 mm/2m and 6–7 mm/m—the macroscopic flatness improved by 37–155%. The transverse bending deformation of TS-1500 MPa was controlled within −0.3–0.3 mm, while that of TS-1800 MPa was within −0.75–0.75 mm. Compared to the delivery standards of Swedish company SSAB (−2 mm to 2 mm) and the other domestic steel enterprises (−4 mm to 4 mm), these results achieve internationally leading performance.

5. Conclusions

To address the issue of quenching deformation in gigapascal-grade ultra-high-strength steels, which often leads to significant flatness deviations, and considering that current production predominantly relies on empirical approaches with insufficient theoretical research, this study approaches the problem from a theoretical perspective. A finite element model coupling temperature, phase transformation, and stress was established to investigate in detail the effects of complex cooling conditions on the internal stress and deformation of ultra-high-strength martensitic steel. Based on simulation results, successful on-site debugging was conducted. The main conclusions are as follows:

(1)

The established temperature-phase transformation-stress coupled model comprehensively accounts for the effects of heat exchange, phase transformation, and phase transformation latent heat, achieving high accuracy. The construction of this high-precision coupled model provides a theoretical foundation for understanding the stress distribution and deformation behavior of gigapascal-grade ultra-high-strength steel plates during cooling under complex conditions.

(2)

During single-side cooling, the cooled surface contracts and concaves due to lower temperature and phase transformation. When a single-side cooling device moves along the plate, the cooled surface undergoes an evolution from concavity to transverse bending deformation. During double-side cooling, if the upper and lower surfaces cool asynchronously, inconsistencies in temperature and martensitic phase transformation-induced expansion between the surfaces lead to flatness issues.

(3)

The study systematically reveals the influence of plate thickness, water ratio, and roller speed on the internal stress and deformation of gigapascal-grade steel plates during quenching. Key technologies were developed for gigapascal-grade steel plates, including precise cooling water control at different phase transformation stages, ordered heat exchange during cooling, flexible temperature field control, and full-plate high flatness control during quenching.

(4)

The related technologies have been successfully applied on-site. The transverse bending deformation of TS-1500 MPa was controlled within −0.3–0.3 mm, and that of TS-1800 MPa within −0.75–0.75 mm, far exceeding the levels achieved by domestic and international peers and positioning the technology at an internationally leading level.