저탄소 강의 페라이트 변태중 오스테나이트 내 탄소 농축 전산 모사

Abstract

자동차용 강재로 널리 쓰이는 DP (Dual Phase) 와 TRIP (TRansformation Induced Plasticity-assisted) 강은 모두 페라이트 변태시 페라이트의 매우 낮은 탄소 고용도로 인한 오스테나이트 탄소 농축 (carbon enrichment) 현상을 이용하여 원하는 2차 상을 (DP: 마르텐사이트, TRIP: 잔류 오스테나이트) 얻는 방법을 통해 제조된다. 특히 열연 DP 강과 같은 3단 패턴 냉각에 의해 제조되는 강의 경우 CT (Coiling Temperature) 의 임계 온도 결정을 위해 오스테나이트 탄소 농축 예측의 높은 정밀도가 요구된다. 통상적으로 알려진 페라이트 변태는 빠른 핵생성 이후 site saturation 되어 전체 변태 kinetics 가 성장에 의존하는 것으로 알려져 있으며 성장은 parabolic law 를 따르는 확산 제어 성장으로 취급되어 왔다. 그러나 최근 in-situ hot stage TEM 및 EPMA (Electron Probe Micro-Analyzer) 결과에 따르면 성장이 확산 및 계면 제어의 혼합된 형태이며 온도 및 성분 등 상변태에 미치는 주요 인자들에 의해 성장 모드가 변화함이 밝혀졌다. 본 연구에서는 페라이트 변태에 영향을 미치는 인자인 온도, AGS (Austenite Grain Size), 성분에 대해 페라이트 성장 거동의 변화를 전산 모사하여 DP 강과 같은 저탄소 강의 오스테나이트 탄소 농축 거동의 변화를 파악하고자 하였다. 모사된 결과는 dilatation 1차 미분으로부터 측정된 탄소 농축 결과와 비교하여 모델의 정합성을 검증하였고 이를 이용하여 페라이트 성장 거동 및 오스테나이트 탄소 농축에 미치는 인자들의 영향을 고찰하였다. 본 연구에서 다루는 DP 강과 같은 저탄소 C-Mn-Si 강의 경우 (C < 0.1, Mn < 1.5, Si < 1 wt%) 합금 원소가 변태에 미치는 영향이 미미하므로 PE (Para Equilibrium) 하에서의 성장 모드 변화만을 다루었다. 성장 거동을 표현하는 모델은 2계 편미분 방정식인 확산 방정식이 포함되어 있으며 이에 대한 해석해는 존재하지 않는다. 이러한 문제는 시간 및 공간을 격자화하여 주어진 방정식을 유한 차분화시킨 수치 해법을 이용하여 풀 수 있다. 그러나 방정식을 유한 차분식으로 변환시 필연적으로 mass balance error 가 발생하게 되며 이는 특히 탄소 농축 계산에 심각한 영향을 주게 된다. 이를 해결하기 위해 추가적인 수치 계산이 필요하지 않고 음함수법을 적용하여 보다 정확한 해를 빠르게 얻을 수 있는 방법인 total mass balance 식을 적용하였다. Mass balance error 가 수정된 모델은 기존의 모델보다 격자수를 1/10 가량 줄이고도 해의 정확도를 유지할 수 있었으며 음함수법을 이용하였기에 시간 스텝의 크기에도 영향을 받지 않았다. 오스테나이트의 탄소 농축 측정은 페라이트 변태 이후 측정된 저온상의 변태 개시 온도를 주어진 Bs, Ms 를 이용하여 역계산하는 방법을 이용하였다. 저온상의 구분은 dilatation 1차 미분의 peak 온도 및 미세 조직 분석을 통해 결정하였다. 형성되는 저온상은 양이 많지 않을 경우 dilatation 1차 미분을 상에서도 구분하기 어려운 문제가 있으므로 WT (Wavelet Transform) 을 이용하여 노이즈를 제거하고 유사 dilatation 결과를 중첩하여 이를 해결하였다. 실험적으로 측정된 탄소 농축과 peak 온도는 등온 유지 온도에 따른 경향성이 보이지 않았다. 이는 페라이트의 성장 기구가 온도에 따라 다르다는 것을 의미한다. 페라이트의 성장 기구가 확산 제어 성장 또는 계면 제어 성장과 같이 극단적이라면 오스테나이트 계면 농도가 온도 및 페라이트 변태량에 따라 정해지므로 탄소 농축은 등온 유지 온도에 따른 경향성이 나타나야 하기 때문이다. 또한 미세 조직 분석상 페라이트가 평형 분율에 도달하였음에도 불구하고 탄소 농축 측정 결과는 오스테나이트 평형 성분에 도달하지 않는 것으로 나타났다. 이는 변태 후반부가 확산에 의해 지배되기 때문이며 이 시점에서의 확산은 농도 구배가 크지 않으므로 매우 느리게 진행되기 때문이다. 페라이트의 성장은 670 °C 에서는 계면 제어에 가까운 혼합 제어 거동이었고, 730 °C 는 확산 제어 거동을 보였다. 이는 온도가 낮을수록 mobility 가 작아지는 효과가 크기 때문이며 이로 인해 상대적으로 용이해진 확산이 계면 탄소 pile-up 을 해소하기 때문이다. 따라서 등온 유지 온도가 낮을수록 탄소 농축 속도는 증가하였다. AGS 가 증가하면 페라이트는 확산 제어 성장 거동을 보이며 탄소 농축이 느려졌다. 이는 AGS 가 클수록 확산해야 할 거리가 증가하므로 탄소 pile-up 할 시간이 충분해지기 때문이다. 따라서 AGS 가 클수록 계면으로부터의 탄소 농도 구배가 커지므로 저온상은 결정립 중심부는 soft 베이나이트, 계면 근처는 hard 마르텐사이트인 복합 조직이 나타나게 되며 이는 AGS 150 m, IT 730 °C 의 미세 조직에서도 잘 관찰되었다. Si 은 페라이트의 성장을 계면 제어 모드로 변화시켰다. 이는 Si 이 탄소의 확산 속도를 증가시켜 계면 탄소 pile-up 을 억제하고 탄소 농축 속도를 증가 시키기 때문이다. 이러한 경향은 AGS 가 작고 온도가 낮을수록 잘 나타났다. 이와 반대로 온도가 높거나 AGS 가 커지면 Si 에 의한 탄소 pile-up 억제 효과가 사라지게 되며 성장은 확산 제어 모드로 변화하였다. 이는 등온 유지 온도가 높을수록 mobility 가 증가하므로 계면 제어 성장 경향이 사라지게 되고, AGS 가 클수록 확산 거리 증가로 인해 Si 의 의한 탄소 pile-up 억제 효과가 사라지기 때문이다. |DP (Dual Phase) and TRIP (TRansformation Induced Plasticity-assisted) steels widely used in the automotive industry have been produced through the method obtaining the desired 2nd phase (DP: martensite, TRIP: retained austenite). The carbon enrichment in austenite during the ferrite transformation is the most important factor to control low temperature microstructure. The precise prediction of the carbon enrichment was required to determine the critical temperature of CT (Coiling Temperature) in the case of the steel produced by 3 steps cooling in the hot rolled DP steels. It was well known that the ferrite transformation kinetics was mainly controlled by the growth after site saturation and the growth was treated as the diffusion controlled growth following the parabolic time law. However, recently, according to the in-situ hot stage TEM and EPMA (Electron Probe Micro-Analyzer) results, the growth was mixed forms of the diffusion and interface controlled and it was clarified that enhancement mode changed by cooling patterns and compositional change during transformation. In this study, the effects of temperature, AGS (Austenite Grain Size) and composition on carbon enrichment in austenite were studied by using numerical simulation based on the mixed growth model and were compared with experimental measurements in low carbon steels. The mixed growth model was confirmed with experiments measured by 1st derivative of dilatation and effects of controlling factors on carbon enrichment were investigated. It was assumed that the ferrite grew under PE (Para Equilibrium) condition such that the diffusion of substitutional elements during transformation in steel compositions used was ignored. The equations used for the growth was the second order partial derivatives diffusional equations and the analytic solutions did not exist. These equations had to be solved by numerical method in finite difference form. However, when converting equations to the finite difference scheme, the mass balance error was inevitably accured, which resulted in the recognizable errors in the carbon enrichment calculation. To overcome the mass balance error, the total mass balance equation was applied, which was very effective to reduce the additional iteration and to reduce computational time. By 1/10 reduced the grid points compared to those in the existing model, the accuracy of solutions was not changed and because of using the implicit method, the model with the modified mass balance error was insensitive to the size of the time step. The method of measurement of carbon enrichment in austenite was a back-calculation through Bs and Ms measured by 1st derivative of dilatation and micrograph. The appearing 2nd phases was classified both the peak temperature of the dilatation 1st derivative and microstructure analysis. During analysis, LVDT (Linear Variable Differential Transformer) during continuous cooling in dilatation measurement, once filtered by WT (Wavelet Transform), was overlapped with each other to confirm the low temperature transformation. The isothermal holding temperature was not mainly proportional to the carbon enrichments and peak temperatures of 2nd phases. This observation meant that the growth mechanism of ferrite for each isothermal holding temperature was different, because the dependency of temperature had to be observed if only one mechanism such as diffusion controlled or interface controlled affected the growth of ferrite. In addition, the measured carbon enrichment was the austenite equilibrium composition although the measured ferrite by microstructure analysis reached the equilibrium fraction. In later stage of ferrite transformation, the growth was very slow as well as the carbon enrichment. At 670 °C, the ferrite growth was the mixed controlled mode which was close to the interface controlled. The result of 730 °C showed the diffusion controlled behavior. This results were explained that the major factor to determine the growth mechanism with decrease of temperature was a dramatically decrease of interface mobility, so the carbon pile-up at interface disappeared due to the diffusion to austenite grain interior. Therefore, it was claimed that the rate of carbon enrichment in austenite was increased with the decrease of isothermal holding temperature. If AGS increased, the ferrite showed the diffusion controlled growth behavior and the rate of carbon enrichment became slow. Since the distance to diffuse increases as AGS was large, the time for the carbon pile-up was sufficient. Therefore, since the carbon concentration gradient from the interface was enlarged as AGS was large, the mixed structure of 2nd phase constructed soft bainite at grain interior and hard martensite at interface was represented, and this mixed structure was experimentally observed in AGS 150 m condition. Si changed growth mechanism from diffusion controlled mode to interface controlled mode. Si restricted the carbon pile-up at interface and increased the rate of carbon enrichment in austenite due to the increase of carbon diffusivity. As AGS was small and temperature was low, the effect of Si was more dominant. On the contrary, if the temperature was high or AGS was enlarged, the carbon pile-up suppression effect by Si disappeared and the growth was changed to the diffusion controlled mode. Since the interface mobility increased as the isothermal temperature was high, the interface controlled growth tendency disappeared. As AGS was large, the carbon pile-up was disappeared because of the diffusion length increase.; DP (Dual Phase) and TRIP (TRansformation Induced Plasticity-assisted) steels widely used in the automotive industry have been produced through the method obtaining the desired 2nd phase (DP: martensite, TRIP: retained austenite). The carbon enrichment in austenite during the ferrite transformation is the most important factor to control low temperature microstructure. The precise prediction of the carbon enrichment was required to determine the critical temperature of CT (Coiling Temperature) in the case of the steel produced by 3 steps cooling in the hot rolled DP steels. It was well known that the ferrite transformation kinetics was mainly controlled by the growth after site saturation and the growth was treated as the diffusion controlled growth following the parabolic time law. However, recently, according to the in-situ hot stage TEM and EPMA (Electron Probe Micro-Analyzer) results, the growth was mixed forms of the diffusion and interface controlled and it was clarified that enhancement mode changed by cooling patterns and compositional change during transformation. In this study, the effects of temperature, AGS (Austenite Grain Size) and composition on carbon enrichment in austenite were studied by using numerical simulation based on the mixed growth model and were compared with experimental measurements in low carbon steels. The mixed growth model was confirmed with experiments measured by 1st derivative of dilatation and effects of controlling factors on carbon enrichment were investigated. It was assumed that the ferrite grew under PE (Para Equilibrium) condition such that the diffusion of substitutional elements during transformation in steel compositions used was ignored. The equations used for the growth was the second order partial derivatives diffusional equations and the analytic solutions did not exist. These equations had to be solved by numerical method in finite difference form. However, when converting equations to the finite difference scheme, the mass balance error was inevitably accured, which resulted in the recognizable errors in the carbon enrichment calculation. To overcome the mass balance error, the total mass balance equation was applied, which was very effective to reduce the additional iteration and to reduce computational time. By 1/10 reduced the grid points compared to those in the existing model, the accuracy of solutions was not changed and because of using the implicit method, the model with the modified mass balance error was insensitive to the size of the time step. The method of measurement of carbon enrichment in austenite was a back-calculation through Bs and Ms measured by 1st derivative of dilatation and micrograph. The appearing 2nd phases was classified both the peak temperature of the dilatation 1st derivative and microstructure analysis. During analysis, LVDT (Linear Variable Differential Transformer) during continuous cooling in dilatation measurement, once filtered by WT (Wavelet Transform), was overlapped with each other to confirm the low temperature transformation. The isothermal holding temperature was not mainly proportional to the carbon enrichments and peak temperatures of 2nd phases. This observation meant that the growth mechanism of ferrite for each isothermal holding temperature was different, because the dependency of temperature had to be observed if only one mechanism such as diffusion controlled or interface controlled affected the growth of ferrite. In addition, the measured carbon enrichment was the austenite equilibrium composition although the measured ferrite by microstructure analysis reached the equilibrium fraction. In later stage of ferrite transformation, the growth was very slow as well as the carbon enrichment. At 670 °C, the ferrite growth was the mixed controlled mode which was close to the interface controlled. The result of 730 °C showed the diffusion controlled behavior. This results were explained that the major factor to determine the growth mechanism with decrease of temperature was a dramatically decrease of interface mobility, so the carbon pile-up at interface disappeared due to the diffusion to austenite grain interior. Therefore, it was claimed that the rate of carbon enrichment in austenite was increased with the decrease of isothermal holding temperature. If AGS increased, the ferrite showed the diffusion controlled growth behavior and the rate of carbon enrichment became slow. Since the distance to diffuse increases as AGS was large, the time for the carbon pile-up was sufficient. Therefore, since the carbon concentration gradient from the interface was enlarged as AGS was large, the mixed structure of 2nd phase constructed soft bainite at grain interior and hard martensite at interface was represented, and this mixed structure was experimentally observed in AGS 150 m condition. Si changed growth mechanism from diffusion controlled mode to interface controlled mode. Si restricted the carbon pile-up at interface and increased the rate of carbon enrichment in austenite due to the increase of carbon diffusivity. As AGS was small and temperature was low, the effect of Si was more dominant. On the contrary, if the temperature was high or AGS was enlarged, the carbon pile-up suppression effect by Si disappeared and the growth was changed to the diffusion controlled mode. Since the interface mobility increased as the isothermal temperature was high, the interface controlled growth tendency disappeared. As AGS was large, the carbon pile-up was disappeared because of the diffusion length increase.