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Metallurgical Issues in Level 2

 Please refer to Mill Level 2 Model Basics for the symbols and basic terms used in the section.

Retained Strain

In a project to improve the Level 2 model force accuracy, flow stress coefficient C3, as indicated in the equation (1), was studied. The C3 for FIT4 (Table 2) indicated a medium value of about 0.22. The experimentally verified medium value for the hot forming is about 0.18 [2] from German colleagues, or 0.21 suggested for hot rolling Level 2 by Japanese researchers [4].

Table 2: C3 values for the FIT4

Avg. C3

































The question now is how to explain the difference between the values, and which one the right value is.

In fact, both the German and Japanese colleagues are right and their data are consistent. If the value from the Japanese colleagues is used, the pass strain should be used; while if the German colleagues' data is accepted, the true strain (the pass strain plus the retained strain), should be used.

Modern rolling practice has significantly reduced the rolling temperature, in order to achieve better mechanical properties (tensile, yield, etc.). The rolling practice with high draft plus low temperature is the basis for the modern controlled rolling. Due to the low rolling temperature, the recrystallization often cannot be completed and some strain from the previous pass would be retained. Table 3 shows the retained strain published by I. Tamura, et al [3] with Nb steel at an inter-pass time of 20 seconds (IT), and the value of the retained strain estimated by the author (BL) for a plate mill assuming an inter-pass time 30-40 seconds. At an inter-pass time of 1 second and rolling temperature of 750C (1380F), almost the entire pass strain was retained [3].

Table 3: Retained Strain













IT (%)






BL (%)






* Nb steel, with inter-pass time: I. Tamura (IT) 20s; B. Li (BL) 30-40s

Rolling in the two-phase region

Some thin grades often experiences high force errors in the last two passes. It seems that the distribution of measured flow stress is off the trend: the measured value in the last pass is a bit too low. In the Fig. 1, the measured flow stress is calculated into a reference condition with strain 0.3 and strain rate 10/s; the only effect left is the temperature for the given grade. From the second last pass to the last pass, the flow stress reduces with the decreasing temperature.

It is very likely that there was an α-γ phase transformation in the last pass, so the much softer ferrite was generated.

Research report from Suzuki, et al [5] shows that for low and medium carbon steel there can be phase transformation in the temperature 800-1000C (1470-1830F), sometimes it could be in the range 900-1000C (1650-1830F). Frequently some low carbon steels and some HSLA grades conduct phase transformation in the temperature range 850-900C (1560-1650F). This is the temperature range for the second last passes or the last pass of quite a number of grades rolled in many mills. The phase transformation temperatures for the newer grades rolled in recent years are much more difficult to determine, especially for those with addition of micro-alloys.

Fig. 1: Flow stress at strain 0.3 and strain rate 10/s

In general, one set of flow stress coefficients only applies to one material in a given temperature region, but the phase transformation here actually involves two materials, the austenite (γ-phase) and the ferrite (α-phase). If we have to model this process, two different sets of coefficients have to be known, one for austenite and the other for ferrite. The difficulty is that the integrated coefficients also depend on the percentages of the two phases.

Metallurgical Aspect of the Flow Stress

In view of the modern rolling technology, the flow stress has more metallurgical sense than mechanical one, though most Level 2 models only treat it as a mechanical property. Metallurgically, the hot deformation of the metal is a very dynamical process: the grain size and grain shape are under constant change; some strain can be quickly removed (by recrystallization, etc.) while the other from the past deformation (the retained strain) may need to be added to the current deformation stage.

Table 4: Flow stress and metallurgical parameters

Flow Stress
- Material
- Strain
- Strain rate
- Temperature

Metallurgical parameter
- Phase
- Grain size
- Retained strain
- Temperature

As showed in the Table 4, the Material in the flow stress section (left) is associated with both the Phase and the Grain size (right), and the Strain is affected by the Retained strain. In the high-speed rolling, the portion of the Strain rate contribution to the flow stress is affected by the Temperature due to the significant heat generation. In addition, the Phase transformation involves heat release or heat absorb as well as the change of the Material, and thus has a great impact to the flow stress. The metallurgical process would get much more complicated when the precipitation, etc., exists during the processes such as hold.


During the rolling, the grain is pressed flat, and as long as the deformation energy reaches certain level, the newer, smaller grains are generated. This is called recrystallization. During rolling there is dynamic recrystallization, and in the inter-pass period, there are static and metadynamic recrystallization. As long as about 95% of the metal is recrystallized, the grains start to grow. The finer the grain, the higher the flow stress (and other strength properties).

The effect of metallurgical factor on the roll separating force is through the flow stress. The flow stress is the property of the metal to resist deformation. For the same phase of the microstructure, flow stress is affected by the grain size; when multiple phases exist, such as austenite (γ) phase and ferrite (α) phase, the flow stress is based on strengths of all phases and their volume percentage. Most Level 2 models only take the flow stress as a mechanical parameter but ignore its metallurgical phenomenon. Metallurgical effects on flow stress are the primary source of roll force error in most Level 2 systems.

Traditionally, steel rolling was carried out in a high temperature, so after each pass, the steel could fully recrystallized and the strain from the previous pass was eliminated. However, in todays rolling practice, especially with the controlled rolling, a great number of passes are rolled below the recrystallization temperature (technically it is cold rolling). Due to the incomplete recrystallization, a significant portion, sometimes 80% [3], of the pass strain can be retained and transferred to the next pass. This causes the considerable error in the strain and thus the flow stress for the later passes. Currently almost every Level 2 model simply ignores the retained strain. The error caused in this way cannot be removed by the adaptive learning.

Many rolling processes are under controlled rolling. Through controlled temperature and controlled draft distribution to refine the grain in order to increase metal strength, the controlled rolling also greatly changes the flow stress. For micro-alloyed steels, which are quite popular today, precipitation also plays a considerable role on the steel strength and thus the flow stress.

For some X-grade and HSLA grades, the steel is held in the air for a certain length of time after certain number of passes of rolling, and before it is rolled in the next pass, the so-called resume pass. In the hold period, there is precipitation and microstructure evolution. As a result, the flow stress changes. Many Level 2 models have no reflection on this change in the flow stress model.

Rolling in the two-phase region is a good practice to increase mechanical properties of the rolled steel. However, general flow stress model would fail because there are two materials involved. Due to the complicity, most mills do not intentionally roll the steel in this temperature region. The problem is, sometimes due to the error in temperature prediction, the rolling process is actually performed in the two-phase region, beyond the plan. This would cause tremendous error for the conventional model.

For all those metallurgical phenomena, it is necessary to consider metallurgical evolution in the Level 2 model. However, due to lack of understanding of the nature of roll separating force, especially in the areas such as the flow stress and the retained strain, many (or maybe all) Level 2 vendors overly simplified the process and ignored the metallurgical effects on roll separating force.

Major progresses in industry development in recent years such as the intensive studies on physical metallurgy, have led to more models and data available in predicting metallurgical processes. More and more phenomena have been identified, and good results on the microstructure evolution have been published. This, in combination of the intelligent learning, has made it possible for Level 2 model to fully consider the metallurgical evolutions.

Metal Pass Consulting

Level 2 Development Issues

Level 2 Model as a Metallurgical System


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