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1 Computer Methods in Materials Science

1 2007

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Mathematical description of deformation resistance of IF steel including influence of phase transformations

Schindler I., Plura J., Jurko V., Rusz S., Suchanek P., Janosec M.

Computer Methods in Materials Science

2007

Vol. 7, No. 1

24-28

The aim of work was to describe by a single equation deformation resistance of IF steel with titanium in the temperature range of 700 to 1200 °C, in relation to the forming temperature T [°C], equivalent strain ? and equivalent strain rate ? [s-1]. Chemical composition of the investigated material (in wt %) was as follows: 0.004 C – 0.127 Mn – 0.008 Si – 0.008 P – 0.009 S – 0.041 Al – 0.003 N – 0.072 Ti – 0.040 Cu – 0.013 Ni – 0.003 Mo – 0.003 As – 0.003 Sn (other elements max. 0.002 % each). The mean equivalent stress ?m [MPa] was determined by an original procedure, based on laboratory rolling of flat samples with scaled-in thickness in the computer controlled mill Tandem. Values of ?m were computed from values of the registered roll forces by means of a specially developed methodology that uses (among others) knowledge of a particular equation for description of the forming factor for the stand A of the mill Tandem, in dependence on geometric conditions of rolling. Variables ? (in the range of ca 0.1 – 0.5) and ??(in the range of ca 10 – 120 s-1) were expressed by an automatic procedure from the registered actual revolutions of rolls and dimensions of samples measured before and after rolling. Due to an intended application of results in rolling at very low temperatures (above all in the ferrite region) and in accumulative roll bonding, the samples were heated directly to the forming temperature, which – of course – influenced the temperature boundaries between the ferrite region, a two-phase region ferrite + austenite and the austenite region. These temperature boundaries were determined experimentally as 917 °C, or 959 °C. Coefficients A, B, C and D were calculated in a simple equation of type ?m = A • ?B?• ?C • exp(-D • T) for each of the given temperature ranges. A proved method of multiple non-linear regression and statistic software Unistat 5.5 were utilized for this calculation. Due to effect of chemical composition of the investigated IF steel its deformation behaviour in all three temperature regions is very different. With decrease in temperature the deformation resistance of austenite and ferrite increases and, on the other side, fiercely falls in the two-phase region due to a rising share of softer ferrite. A top phase of the describing work was represented by an attempt to describe this deformation behaviour by a single equation. After a large analysis a certain way was proposed in the end, which uses a cumulative function in which particular members are multiplied by coefficient 1 or 0, in dependence on a specific temperature. Calculations of specific coefficients had to be proposed in such a way so that they could react to surpassing of temperature boundaries between individual phase regions. Relative deviations of values??m, calculated on the basis of the gained universal equation back for conditions of the laboratory rolling, from values of the mean equivalent stress expressed directly from roll forces do not surpass š 10 %. It may be considered to be very good accuracy, for instance from viewpoint of adaptive control systems in hot rolling mills. However, only practical applications suggest whether it will be possible to use a single (universal), but quite complicated, model for conditions of fast control of real rolling mills, or whether simple, but of course temperature limited, relationships creating partial fragments of this complex model will be preferred.

Opracowanie pojedynczego równania opisującego opór sta IF z dodatkami tytanu w różnych temperaturach (od 700°C i 1200°C) z uwzględnieniem wpływu temperatury procesu odkształcenia logarytmicznego e h i średniej wartości intensywności odkształcenia e jest tematem niniejszej pracy. Średnie wartości intensywności naprężenia om zostały wyznaczeni z testów walcowania próbek płaskich o zróżnicowanej wy|gch sokości na walcarce Tandem, bazując na zmierzonych siłach. Do obliczenia wartości sigma m z sił zastosowano opracowaną metodę wykorzystującą odpowiednie równania opisujące poszczególne parametry walcowania na walcarce Tandem.