Simulation of temperature gradients and equivalent stress of low

Simulation of temperature gradients and equivalent stress of low

Simulation of temperature gradients and equivalent stress of lowalloyed Cr-Mo based steel
Simulace teplotních gradientů a ekvivalentního napětí v
nízkolegované oceli na bázi Cr-Mo
Miroslav KVÍČALA 1, Karel FRYDRÝŠEK 2
Abstract: In the case of the Cr-Mo based low-alloyed steel hot rolling of square billets from round continuously cast
blooms is complicated by the fact that the internal defects are detected during ultrasonic inspection at the end of
production process on cooling bed. Final quality of hot rolled billets is influenced mostly by casting speed and
overheating temperature in a tundish, heating conditions in soaking pit and hot rolling factors. In our paper it is
demonstrated that for optimization of heating process in soaking pit before hot rolling it is necessary to respect the
thermophysical properties and stress-deformation behaviour of low-alloyed Cr-Mo based steels. Using FEM
software MSC.MARC was optimalised the heating strategy that led to statistically significantly lower occurence of
central defects in hot rolled billets with only minimum financial cost increase.
Abstrakt: V případě nízkolegovaných Cr-Mo ocelí, které jsou válcovány do bloků z kruhových plynule odlévaných
předlitků, je detekce vnitřních defektů komplikována skutečností, že jsou zjištěny až na chladícím loži. Výsledná
kvalita vývalků je ovlivněná především licí rychlostí, teplotou přehřátí oceli v mezipánvi, podmínkami ohřevu v
hlubinné peci a způsobem válcování. V našem příspěvku poukazujeme na skutečnost, že volba ohřevového režimu
před válcováním musí respektovat termofyzikální vlastnosti napěťově - deformační chování nízkolegovaných ocelí
na bázi Cr-Mo. Za použití MKP software MSC.MARC byl optimalizován ohřevový režim, přičemž tato úprava
vedla ke statisticky výrazně nižšímu výskytu vnitřních necelistvostí u vývalků při ultrazvukové zkoušce, a to vše s
pouze minimálním nárůstem finančních nákladů.
Keywords: FEM, Cr-Mo, internal voids, heating strategy, temperature gradient, equivalent stress
Klíčová slova: FEM, Cr-Mo, vnitřní necelistvosti, strategie ohřevu, teplotní gradient, ekvivalentní napětí
1. Introduction
The low-alloyed Cr-Mo based steel types are used for production of important technical
equipment parts in the petrochemical industry, for transportation of the gaseous hydrocarbons,
concentrated acids, and lyes. They are also used for rolling of seamless tubes, in the production
of pressure bottles, steel bolts, etc.
In the past, many researchers studied conditions which could possibly cause internal
defects creation and propagation. Among the potential reasons for creation of inhomogenities
(pores, cavities, cracks etc.) in the volume, the inappropriate casting conditions of the heat are
particularly important, especially the extraordinarily high overheating temperature in a tundish
and low casting speed [1, 2] which could cause central segregations of molybdenum [3],
1
M.Sc. & M.Sc. Miroslav KVÍČALA, MATERIAL AND METALLURGICAL RESEARCH Ltd., OstravaVítkovice, Pohraniční 693/61, +420 739 070 152, E-mail: [email protected].
2
Assoc. Prof. M.Sc. Karel FRYDRÝŠEK, Ph.D., ING-PAED IGIP, Department of Mechanics of Materials, Faculty
of Mechanical Engineering, VŠB - Technical University of Ostrava, 17. listopadu 15, Ostrava, Czech Republic,
Phone +420 597323495, E-mail [email protected].
microalloying elements precipitation on austenite grain boundaries [4, 5] during continuously
cast bloom straightening in temperature range 800 – 1050 °C (minimum ductility zone) [6]. The
other mentioned reasons for cracks initiation and propagation are improper tensile strain caused
by small contact between rolling mills and round continuously cast bloom [7] and low rolling
temperatures [8].
Heating and preheating process before hot rolling is necessary to obtain proper plastic
properties of steel. Continuously cast blooms are commonly heated up to 1300 °C if there are no
extensive differences in heat conductivity of steels and/or steels are not sensitive to internal
defects occurence there can be used wide varieties of heating strategy. In our paper we studied
two different heating strategies in temperature range 20 – 800 °C which is crucial for internal
defects occurence due to very different thermophysical properties among different steels. Above
those temperatures when austenite structure occures difference among thermophysical properties
of steels with different chemical composition are rather very small. We found out new heating
strategy which led to significant decrease of internal defects in continuously cast blooms. Main
aim of this paper is to make clear how the heating strategy can change the influence of
temperature gradients and equivalent stress in studied steel.
2. FEM simulation boundary conditions and material properties
In this paper, the FEM simulations of two heating strategies are made in
MSC.MARC/MENTAT software (see [9] and [10]).
First heating strategy consists of constant heating up to 800°C of continuously cast
bloom with 525 mm diameter (we assumed ambient temperature of bloom – 20 °C) in two
hours.
The second heating strategy consists of constant heating up to 800 °C in four hours.
In these simulations were applied heat fluxes (q = 2,5×104 W/m 2 for slow heating and
q = 5×104 W/m 2 for fast heating). For simulations was used transverse quadrant of continuously
cast bloom with 1536 finite elements (Fig. 1) as plane strain formulations.
Fig 1. Transverse quadrant of continuously cast bloom with diameter 525 mm loaded by heat
flux q. Every group of elements (m1, m2, ..., m8) is represented by specific chemical
composition, mechanical and thermophysical properties.
Because of known chemical inhomogenity of continuously cast blooms based on
experimental procedures and calculations in IDS Solidification Software we modified yield
stress, tensile stress, Young modulus, thermal conductivity, heat capacity and thermal
expansivity across the bloom diameter (Tab.1) and chemical composition (Tab.2) both for
different elements and temperature range 0 – 800 °C. Therefore, material dependences across
the bloom diameters were approximated by eight cells of materials m1, m2, ... , m8, see Fig.1.
Coefficient of
thermal
expansion
 (°C-1)
10
Min.:
139
180
8×10
19,41
0,44
10-5
Max.:
847
1100
2,5×1011
40,1
0,59
2,1×10-5
Tab 1. Overview of simulated mechanical and thermophysical properties for continuously cast
bloom with diameter 525 mm.
Yield
stress
Re (MPa)
Ultimate Modulus of
Thermal
Specific heat
stress
elasticity
conductivity
c
(kJ kg-1°C-1)
Rm (MPa)
E (MPa)
K (W m-1°C-1)
Chemical elements:
C
Cr
Mn
Mo
V
Si
Ni
S
P
Min.:
0,22
1,12
0,7
0,2
0,04
0,2
0,3
0,008
0,008
Max.:
0,35
2,25
1,4
0,7
0,3
0,3
0,1
0,015
0,015
Tab 2. Overview of chemical composition for continuously cast bloom with diameter 525 mm.
3. Thermophysical analysis
In the following text we assume constant heat flux at gas – bloom interface. Heat transfer
between soaking pit’s gas and continuously cast bloom is realized via radiation and convection
(we neglect conduction among blooms because their starting temperature is the same) heat
transfer via convection can be expressed as:
Q  hS  Tgas  Tsurf  t
(1)
where h heat transfer coefficient, S is area of heat transfer, t is time period of heat transfer, Tgas
and Tsurf are temperatures of gas and bloom’s surface.
Heat transfer via radiation is described by Stefan-Boltzmann law:

4
4
q   SB  gasTgas
  surf Tsurf

(2)
where  gas ,  surf are emissivities of gas and surface,  SB is Stefan-Boltzmann constant, Tgas is
gas temperature and Tsurf is bloom surface temperature.
Density of heat flux in continuously cast bloom can be expressed as:
q   K x, T .gradT
(3)
where q is heat flux and K is thermal conductivity. There can be assumed that thermal
conductivity is not only function of temperature but also cross section of the bloom due to its
chemical inhomogenity.
Connection between gas temperature and bloom surface temperature is given by
following formula:
Tgas  4

1  K .gradT
4 
  surf Tsurf

 SB   gas

(4)
dQ
(through bloom cross section between two
dt
layers with thickness dx or better after transformation from Cartesian to polar coordinates as
dr. cos  where dr is infinitesimally small increment of radial coordinate and  is angular
coordinate) can be defined in a case of one dimension solution (coordinates y and z can be
neglected because it is symmetrical problem) as:
Infinitesimally small heat increment
dQ
T 2
 K 2
dt
 r. cos  
(5)
The heat which must be supplied for infinitesimally small temperature increase dT of
bloom surface can be expressed as:
dQ

dS
dTn 1

dTn
H  .dT
  .r.dr.d
(6)
where H  is spectral density of emission intensity,   is spectral absorption capacity, dTn and
dTn1 are bloom surface temperatures before and after infinitesimally small temperature increase.
To fix constant temperature increase of heated bloom during heating, the following
equation must hold:
dT
 a  dq  b  dQ f
dt
1
K T 
(7)
where a and b are weight factors that represents contributions of infinitesimally small heat
radiation flux dq and infinitesimally small heat convection dQ to overall heat input from gas to
bloom in infinitesimally small time dt and f 1K T  is inverse function characterizing thermal
conductivity of material.
4. Results
In the first approach, the fast heating was simulated from ambient temperature up 800°C
– this fast heating strategy is commonly used in industrial companies. When the heating process
begins, the temperature gradient (between surface and internal elements) increases. The gradient
is affected by heat flux from furnace´s gas. Fig. 2 represents evolution of temperature gradients
across the bloom during heating for two different heat fluxes and heating times (A - fast heating,
B - slow heating).
Fig 2. Simulation of temperature gradients across continuously cast bloom during heating in
soaking pit; A – fast heating, q = 5×104 W/m2, t = 7200 s; B - slow heating, q = 2,5×104 W/m2,
t = 14400 s.
In the case of fast heating simulation, the maximum temperature difference T = 233 °C
between centre and surface occurs at the end of heating process, see Fig. 2A.
On the contrary, slow heating results in lower surface temperature and higher centre
temperature at the end of heating cycle. The maximum temperature difference between centre
and surface is T =100 °C (see Fig. 2B).
Dependence of temperature development during both slow and fast heating on bloom
radius for 50 % and 100 % of heating time is shown at Fig. 3.
Fig. 3. Simulation of temperature development during different heating strategies. A – fast
heating q = 5×104 W/m2, t = 7200 s; B – slow heating, q = 2,5×104 W/m2, t = 14400 s.
From Fig. 3 it is evident that chosen heating strategies doesn´t have relevant influence on
temperature difference after 50 % and 100 % of heating time.
If we focus on the equivalent von Mises stress values for both simulated heating
strategies, it can be clearly seen (Fig. 4) that the difference in von Mieses stress values is higher
in case of fast heating (Δσ = 2×108 Pa) than for slow heating (Δσ = 1,3×108 Pa). The difference
between two heating strategies in equivalent von Mieses stress development is magnified by the
fact that in case of fast heating strategy maximum of equivalent von Mieses stress is achieved
twice faster than for slow heating strategy.
Fig. 4. Simulation of equivalent von Mises stresses across the continuously cast bloom during
heating in soaking pit; A – fast heating, q = 5×104 W/m2, t = 7200 s; B – slow heating,
q = 2,5×104 W/m2, t = 14400 s.
Analysis of dependence of equivalent von Mieses stress development on bloom radius
after 50 % and 100 % of heating time for two different heating strategies is shown in Fig.5.
Fig. 5. Simulation of equivalent von Mises stresses development during heating in soaking pit;
A – fast heating, q = 5×104 W/m2, t = 7200 s; B – slow heating, q = 2,5×104 W/m2, t = 14400 s.
Conclusions
The presented FE simulations of two different heating strategies has shown that fast
heating at temperature range 20 – 800 °C (see Fig. 2A, 3A, 4A, 5A) or more precisely higher
heat flux at bloom surface is responsible for initiation and propagation of internal defects
presented in bloom centre. This is caused due to improper temperature gradient between bloom
surface and centre. This negative effect is amplified by the fact that maximum of equivalent
stress is achieved in shorter time in the case of fast heating strategy.
Prolongation
of
heating period (decrease of heat flux, the same temperature range 20 – 800 °C, see Fig. 2B, 3B,
4B, 5B) led to important decreasing of differences between bloom surface and centre
(temperature and equivalent stress). This optimisation is necessary especially if internal defects
are present in bloom already after continuous casting.
Nonuniform dependencies presented in figures 4 and 5 are caused by phase
transformations wihich is connected with volume changes too.
According to the results (Tab. 3) can be recommended only slow heating process.
Heating time t:
Heat flux q:
Init. temperature:
Max. temperature:
T (end of solutions):
σ (end of solutions):
See figures:
Conclusions:
Fast heating process:
Slow heating process:
7200 s
14400 s
5×104 W/m2
2,5×104 W/m2
20 °C
20 °C
800 °C
800 °C
233 °C
100 °C
8
2×10 Pa
1,3×108 Pa
2A, 3A, 4A, 5A
2B, 3B, 4B, 5B
Higher loading. More
Lower loading. Less
structural defects. Not
structural defects. Acceptable
acceptable
Tab 3. Review of some results.
Acknowledgements
This work was created as part of project CZ.1.05/2.1.00/01.0040 „Regionální materiálově
technologické výzkumné centrum“ it is included in Operational programme Research and
Development for Innovations, it is financially supported from structural EU funds and Czech
republic state budget.
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Reviewer: doc. Ing. Leo VÁCLAVEK, CSc., VŠB - Technical University of Ostrava,
Czech Republic