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Research on stress analysis of ingot and ingot mold during ingot solidification

Abstract: in this paper, the transient stress field of ingot and ingot mold during ingot solidification is studied by using the independently developed temperature field and stress field analysis finite element system, and the formation mechanism of the stress field is studied based on the numerical analysis conclusion of this paper

key words: finite element formation mechanism of transient stress field

1 introduction

in the process of ingot solidification, the ingot and ingot mold undergo complex thermal process, accompanied by complex phase transformation, coupled with the role of mechanical resistance and other factors, resulting in a time-varying stress field between the ingot and ingot mold. The formation mechanism of the stress field is complex, and has a significant impact on the quality of ingots and the life of ingot molds. At present, there is little systematic research on the stress field of ingot and ingot mold during ingot solidification in China. In this paper, the numerical simulation method will be used to analyze the reason why the temperature of 6T ingot and ingot mold in the solidification process of ingot has not been used in large quantities at present, which is mainly the problem field and stress field of cost and production efficiency. The formation mechanism of the transient stress field is studied, and the analysis is carried out from the aspects of mathematical model establishment and Simulation of stress field results and formation mechanism

2 Establishment of mathematical model

establishment of mathematical model for stress field analysis of ingot and ingot mold includes two aspects of constitutive theory and boundary conditions

2.1 use of constitutive model [1, 3]

when analyzing the stress field of ingot and ingot mold, this paper adopts different constitutive models for different materials, among which the internal state variable constitutive theory widely used in casting stress analysis in recent years is adopted for ingot, and it is considered that a, B, Φ—— Material constant

ε T、 ε nl、 ε E -- temperature strain, nonlinear strain and elastic strain respectively

ε—— Rate

dt -- temperature change

elastic deformation is obtained by generalized Hooke's law. For gray iron, the nonlinear deformation is decomposed into creep and plastic deformation. The plastic deformation is obtained from the plastic theory, and the different tensile and compressive properties are considered in the plastic theory of gray iron [3, 4]. The creep deformation is still described by hyperbolic sine function, so in

ε p、 ε C - respectively represent plastic and creep strain

constitutive models of various materials are shown in Table 1. Table 1 Selection of constitutive model

ingot mold, chassis refractory brick insulation agent solid state: elastoplastic creep constitutive theory described by unified internal state variables liquid state: do not participate in the overall equilibrium elastoplastic creep theory (considering the different tensile and compressive properties of gray iron) elastic theory does not participate in the overall equilibrium

2.2 analysis of boundary conditions

when establishing the boundary condition model, consider the contact between chassis and ground, so it is considered that the normal displacement of chassis is 0. For the 8-edge ingot mold shown in Figure 1, using symmetry, cut 1/16 along AB and AC as the research object. It is really necessary to pay patience to adjust and control various processing conditions, so that the normal displacement of AB and AC is 0. In addition, it is assumed that the contact boundary between the ingot and the ingot mold, while ignoring friction

3 research on the stress field of ingot and ingot mold during ingot solidification

analysis the 6T ingot and ingot mold shown in Figure 1, set the ingot casting temperature as 1500 ℃, the initial ingot mold casting temperature as 80 ℃, the ingot material as medium carbon steel, and the ingot mold material as gray iron, and assume that the casting is completed instantaneously. The temperature field and stress field of the process are analyzed by finite element method [2, 3]

figures 2 to 12 show the y-direction stress in the middle cross section of ingot and ingot mold at 120s, 180s, 250s, 300s, 360s, 600s, 900s, 1200s, 3600s, 7200s after casting and at the end of solidification σ Isoline of Y

from Figure 2 to figure 5, it can be seen that at the initial stage of ingot solidification, the ingot mold is internally pressurized and externally tensioned. In fact, at the initial stage of solidification, the inner surface of the ingot mold is subjected to a huge thermal shock, and the temperature of the inner surface rises rapidly. Due to the thermal resistance of the ingot mold, the temperature of the middle and outer surface of the ingot mold does not change at this time, so σ Y shows the thermal stress type stress distribution of internal compression and external tension as shown in figures 2 to 5; Due to stress concentration and other factors, the maximum compressive stress appears at the corner of the ingot mold; At the initial stage of casting, the intense heat exchange between the ingot and the ingot mold will last for 4 ~ 6 minutes. During this period, the surface temperature of the ingot rises rapidly, but the heat cannot be transferred to the middle of the ingot mold, so the temperature gradient of the ingot mold continues to rise, and then the ingot mold σ Y increases continuously, and the maximum value appears in 4 ~ 6 minutes. This time corresponds to the early cracking time of the ingot mold

due to the uneven thickness of the ingot mold (as shown in Fig. 2 ~ Fig. 6), the maximum tensile stress on the surface of the ingot mold appears on the outer surface of the middle of the reverse arc of the ingot mold

after that, with the sharp rise of the internal surface temperature of the ingot mold, the heat exchange capacity between the ingot and the internal surface of the ingot mold decreases, and the early endothermic heat of the ingot mold is continuously transferred outward, so that the middle and external temperatures of the ingot mold increase, so that the surface temperature gradient of the ingot mold continues to decrease; Especially when the air gap is formed, the heat exchange between the inner surface of the ingot mold and the ingot is further slowed down, which makes the temperature of the inner surface of the ingot mold fall back in the process of rising, on the contrary, the internal temperature of the ingot mold is further increased; The combined action of the above factors makes the temperature gradient of the ingot mold continuously reduce, so that the thermal stress of the ingot mold gradually decreases. Therefore, after the peak value appears in 4 ~ 6 minutes, the compressive stress on the inner surface and the tensile stress on the outer surface σ Y decreases continuously, and the maximum tensile stress on the outer surface of the ingot mold is only 66mpa at 10 minutes. After the ingot solidifies for 600 ~ 900s, the temperature drop caused by the air gap disappears, and the temperature of the inner surface continues to rise. As shown in Figure 16, a small area on the inner surface of the ingot mold reaches 700 ℃. Because the temperature of the inner surface rises at this time, the yield strength of the inner surface of the ingot mold decreases, so the stress value of the inner surface of the ingot mold decreases, so that the maximum compressive stress area of the ingot mold moves to the center (as shown in Figure 8 ~ Figure 9), The maximum compressive stress area on the central line of the reverse arc of the ingot mold moves towards the middle of the ingot mold, and the whole ingot mold σ Y further decreases and changes to the compressive stress. At 900s, there is only 11mpa tensile stress area on the intersection line of the reverse arc center line and the outer surface of the ingot mold, and most of the other areas of the ingot mold show compressive stress; After 20 minutes, the tensile stress in the ingot mold completely disappears. From 20 minutes to 1 hour, the internal surface of the ingot mold shows phase transformation, and the ingot mold shrinks with the increase of temperature. At this time, due to the joint action of phase transformation, the further uniformity of the temperature field in the cross section of the ingot mold and the reduction of yield strength, the internal surface of the ingot mold σ Y further decreases. By 7200s, because the phase transformation inside the ingot mold plays a major role, the stress distribution of the ingot mold will change greatly again. In the ingot mold close to the inner surface of the ingot mold, the stress in the phase transformation area will be reversed (as shown in FIG. 11 ~ Fig. 12), and the stress distribution of internal tension and external pressure will be formed in the phase transformation area, which is basically maintained until the end of ingot solidification

at the initial stage when the ingot forms a solidified shell, due to the joint action of fluid pressure and solidification shrinkage, the ingot is subjected to circumferential tensile stress, such as 900s σ Y is a typical tensile stress, especially in the corner of the small arc of the ingot, the temperature is low, the corresponding elastic modulus is large, and its cooling speed is fast, σ Y has a maximum value of 20MPa, and this trend continues to 3600s. After that, due to the reduction of the cooling rate of the ingot and the effect of creep, the stress value of the ingot becomes smaller. After 3600s, because the surface of the ingot is completely solidified, and the surface temperature is significantly lower than the central temperature of the ingot, plus the cooling rate inside the ingot is greater than the cooling rate on the surface of the ingot, at this time, the surface of the ingot has an obstruction effect on the shrinkage inside the ingot; And for quite a long time after the air gap is formed, the temperature on the surface of the ingot rises, while the internal temperature of the ingot continues to decrease. The above factors work together, and the surface stress of the ingot is reversed. By 7200s, the surface of the ingot is in a state of compressive stress, but the internal tensile stress of the ingot appears. This stress state is maintained until the end of ingot solidification, so when the ingot ends, it presents a stress state (5 ~ 10MPa) in which the surface is under pressure and the center is slightly stretched. From the above analysis, it can be seen that the dangerous time for the ingot to crack is the time when the maximum tensile stress appears on the surface (about 900 ~ 3600s for 6T ingot). Before and after solidification, the ingot generally presents a micro stress distribution of internal tension and external pressure (5 ~ 10MPa). Due to the influence of ingot mold shape, the stress distribution at the end of solidification is relatively complex

figures 13 ~ 15 are the isolines of the principal stress and Mises equivalent stress in the X and Z directions of the central cross section of the ingot and the ingot mold after the ingot solidifies for 360s. From the isolines, it can be seen that the principal stress of the ingot mold in the X direction of the whole cross section is compressive stress, and the maximum value of compressive stress appears in the corner of the ingot mold; The distribution of the principal stress in the Z direction is basically the same as that in the Y direction, showing the thermal stress type stress distribution of internal compression and external tension. At this time, the slight tension on the ingot surface is also particularly obvious. The maximum value of Mises equivalent stress also appears in the corner of the ingot mold

Table 2 shows the lowest cross section in the middle of the ingot mold σ Y and σ The relationship between the initial tension and compression value of Z and time. In addition to the above analysis conclusions, it can also be concluded from table 2 that the normal stress in the Y and Z directions of the ingot mold is greater than that in the X direction. Table 2. Maximum cross section of the upper part σ x、 σ y、 σ Change of Z with time at the initial stage of ingot solidification (unit MPa)

120s180s250s300s360s600s σ x/td>14.7625.4918.7615.2114.0710....... 00 σ y50.8482.0786.9686.6285.1766....... fifty-seven σ z47.0686.66487.7888.1288.7167....... 09

figures 13 to 15 show the isolines of the principal stress in X direction and Z direction and the Mises equivalent stress of the cross section of the ingot mold and the middle height at 360s respectively. The changes of the principal stress in Z direction and Y direction are corresponding, while the X direction is the compressive stress. It can be seen from Figure 15 that the Mises stress at the corner of the internal surface of the ingot mold reaches 150MPa, which locally exceeds 1/3 of the breaking strength of gray iron, and plastic deformation begins to occur. The area with tensile stress of 80MPa appears on the outer surface of the ingot mold (Fig. 3 ~ Fig. 1 Introduction 6), which exceeds 1/2 of the breaking strength and also produces plastic deformation. It can also be seen from the analysis that the tensile stress on the outer surface of the ingot mold is more dangerous than the compressive stress on the inner surface. The early fracture of all ingot molds is often caused by the tensile stress on the outer surface of the ingot mold exceeding the fracture strength

considering σ The change of Y is representative for the stress field analysis of ingot and ingot mold σ The stress change outside y is not analyzed in detail in this paper

3 conclusion

in this paper, the stress field of ingot and ingot mold is analyzed by finite element method. From the analysis, it can be seen that:

1) it is appropriate to analyze the formation mechanism of stress field with Y-direction stress

2) at the initial stage of ingot solidification, the ingot mold is subjected to internal pressure and the thermal stress type stress distribution of external tension, and in 6 ~ 1, China has independently developed a medium and high-level vibration experimental machine. For 0 minutes, the maximum tensile stress appears on the outer surface of the ingot mold

3) the formation and development of the stress field of the ingot mold are closely related to the heat exchange between the ingot and the ingot mold. After the formation of the air gap, the peak stress decreases significantly

4) due to the influence of geometric structure, the stress distribution in the ingot mold is extremely uneven

5) at the initial stage of solidification, the ingot stress field is pulled externally, but with the advance of solidification, the stress reverse appears. (end)

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