PHYSICAL AND MATHEMATICAL MODELLING OF THE INITIAL SHELL STRENGTH IN CONTINUOUS CASTING

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1 PHYSICAL AND MATHEMATICAL MODELLING OF THE INITIAL SHELL STRENGTH IN CONTINUOUS CASTING Schuetzenhoefer, W., C. Bernhard and H. Hiebler Department of Ferrous Metallurgy, University of Leoben, Austria ABSTRACT High caster productivity is a key target in modern continuous casting. To attain a defect-free product at high casting speed, consideration of the initial shell properties becomes important. This work attempts a contribution to improved knowledge as regards high temperature strength and ductility under continuous casting conditions. The first part describes the physical simulation of shell straining during solidification with the so called SSCT-test. The second part focuses on numerical modelling of the SSCT-test and of solidification microstructure and crack criterions derived from SSCT-tests. INTRODUCTION The physical simulation of shell straining under continuous casting conditions demands the adjustment of the testing method to the process conditions. The following characteristics can be defined: - stress and strain in the solidifying shell perpendicular to main dendrite growth axis - the initial cooling rate (10 2 to 10 3 K/s) - depending on casting process and mould lubrication - controls microstructure, and thus, number and distribution of weak points, like grain boundaries or precipitations, which have a dominating effect on crack initiation - the typical strain rate in continuous casting ranges from 10-4 to 10-2 /s FORCE, kn ,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 0 Elongation, mm TIME, s TEMPERATURE, C Test Body Submerges into the Liquid Steel T 1 T 2 T 3 Stress Solidifying Shell Melt Induction furnace Fig. 1: Experimental setup of SSCT-test, schematic, 1 = lower part of the test body, movable via hydraulic force; 2 = upper part, rigid. Top left: measured force versus elongation; top right: temperatures versus time within test body (red curve) and melt (blue curve) - 1 -

2 EXPERIMENTAL Most of the experimental techniques to measure high temperature mechanical properties neglect at least one of the above mentioned demands. Therefore a new technique, the so-called Submerged Split-Chill Tensile (SSCT) test has been developed [1,2]. Fig. 1 gives a schematic view of the SSCT-test method: A steel test body, split in two parts, submerges into the liquid steel. During a holding time, ranging from 2 to 14 seconds, a steel shell solidifies around the test body. The cooling conditions are controlled by means of a spray-coated zirconium-oxide layer on the test body surface with varying thickness. The use of an un-coated steel chill enables initial cooling rates of more than 10 3 K/s, equivalent to strip casting processes. Increasing coating thickness lowers heat transfer, even to the conditions of slab casting with powder lubrication. Thus, the microstructure of the solidifying shell corresponds to that one in the simulated process, for example easily to verify through primary or secondary dendrite arm spacing (PDS, SDAS) measurement. After holding time, the lower half of the test body moves velocity controlled downwards via hydraulic force. Force and elongation are recorded. The methode allows to vary the maximum applied strain between 0.1 and 10 %. During testing, temperature measurement on four positions inside the test body, the solidifying shell and the melt enables the estimation of heat transfer at the chill/shell interface via inverse calculation. As tensile testing is still carried out in the melt, the accuracy of numerical calculation of solidification is most important to assure reliable results. A one dimensional implicit finite difference calculation scheme, considering the influence of microsegregation, yields the temperature distribution and solidification progress during testing. The measured forces are related to the effective shell cross section for solid fraction (fs) of 1.0 (considering shell growth during testing), in order to calculate integral tensile stress. The SSCT-test is not an isothermal test method. The chill/shell - interface is, depending on holding time and coating thickness, at a temperature above 1000 C during testing. It is trivial to say, that the temperature dependence of strength leads to considerably higher stresses in the interface layer, whereas the mushy zone contributes only to a small part to the integral strength of the shell. But in terms of clarity of the results, the integral stress will further be used as the characterising mechanical property, and related with the mean temperature of the shell during testing. On basis of the simplified assumption that strain is regularly distributed over the height of the shell, integral strain during testing can be calculated from the ratio between elongation and length of the coated part of the chill. In reality, strain concentrates within macro- and microscopic weak spots (e.g. hot spots, depressions, grain boundaries, interdendritic spaces), leading to local stresses, which are in an extreme case an order of magnitude higher than the integral strain. This will later be an important argument for the interpretation of the results, but again, for the clear arrangement of the results, integral strain will characterise the extent of tensile loading. After testing, the solidified shell is subjected to metallographic examination and microprobe analysis. This allows the detection of cracks and the definition of critical limits of shell deformation. The definition of a crack index, summarizing number and character of defects, and the correlation with the testing parameters, like content of alloying elements or maximum applied strain, gives a new insight into the mechanisms of high temperature crack formation. Fig. 1 top left gives an example for the stress-strain curves of peritectic steels. After - 2 -

3 an initial, nearly linear increase, the slow transition to a constant, high stress begins. For this type of curves, the Peak-Stress σ p, a characteristic value of the SSCT-test (equivalent to integral tensile strength), corresponds to the maximum stress. It has to be noted, that this is only partially a consequence of the relatively lower shell thickness (macroscopic strain concentration), but also an effect of shell weakening in microscopic scale (microsegregation, precipitations). The results make clear, that critical strain limits may vary in wide ranges within a small variation of testing parameters. This proves the sensitivity of the testing method and explains the wide variation of critical strain limits in literature. The comparison of shell strength for different carbon steels shows, that low carbon (<0.04% C) steels, yield distinctly lower strength near solidus temperature - to say around 1 MPa - which corresponds to strength values given in literature. This and the reduced cracking tendency points to the influence of the large difference in microsegregation sensitivity between the ferritic and austenitic matrix, rather the extent of interdendritic and intergranular precipitates seems to be the overruling factor in crack susceptibility. Such factor also renders aspects of morphology, for example cellular dendritic growth of low C-steels versus side arm branching of high C-steels, negligible with respect to interdendritic decohesion. Thus, the estimated strength of high carbon steels (>0.56% C) at solidus temperature (2.5 MPa) remains clearly below comparable results from conventional hot tensile tests - which range from about 4 to 8 MPa. The characteristics of the SSCT-test method can be summarised as follows: - testing is performed in-situ during solidification and perpendicular to the main dendrite growth axis in order to reveal the effect of interdendritic and intergranular precipitates on cohesive strength under conditions closely simulating the CC process; - low strain rate testing is applied, about /s, again to closely simulate CC conditions; - cooling rates can be adjusted within a wide range, with heat flux intensities between 1.5 and more than 10.0 MW/m 2 to simulate various CC technologies for example mould lubrication by oil or powder and even strip casting processes. - the metallographic examination of the tested shells allows the detection and characterisation of cracks. The crack occurrence can thus be correlated with the process parameters and the steel composition. The measured data obtained from the SSCT test can provide a much more accurate basis to estimate high temperature mechanical properties and to develop a stress criterion for inner cracking. This has already been attempted previously, but based on inadequate strength data derived from hot tensile tests which do not simulate CC conditions as closely as the SSCT test. The following part will focus on the numerical simulation of the SSCT-test and on a new micromechanical model for hot tearing. Modelling of Microstructure In the process of shell deformation and tearing, the influence of microstructure appears to be predominant. Hence, modelling of microstructure and its effect on mechanical properties for the conditions of the SSCT- test is attempted by means of a probabilistic cellular automaton (CA), included in the commercial 2D-FE-code calcomos 1 [3}. For further calculations of mechanical behaviour, this code was - 3 -

4 coupled with another FE-code. Solidification progress and microstructure development are calculated with calcomos, then the results are transformed into a ABAQUS input file, and the tensile test is simulated in ABAQUS, under the assumption of a contact friction problem at the interface. The input data of the CA consists of calculated growth velocity of the solidification front and experimental nucleation data. The growth velocity of the dendrite tips is calculated with the KGT-(Kurz-Giovanola-Trivedi)-model. The required input data are the Gibbs-Thomson-coefficient of the alloy, concentrations, distribution- and diffusion-coefficients of alloying elements. Due to FE-clculations the growth velocity is calculated as a polynomial function of undercooling. The nucleation data are derived from casting experiments [4,5]. For the model the nucleation density, average value and standard deviation of undercooling of this distribution are needed. The microstructure is calculated with an coupling of FE and cellular automaton (CAFE). The FE-mesh is used for thermal calculation, the quadratic cells for the calculation of the microstructure. The cells are containing all information of the microstructure which consists of coordinates of the centre of the cell, the affiliation to a grain and their cristallographic orientation. Fig. 2: Comparison of calculated and real primary microstructure of low alloyed carbon steel - 4 -

5 Figure 3: Transformation of the calculated primary microstructure into 2 phase microstructure of ABAQUS mesh Results of the FE-calculations The right side of Figure 3 shows a primary etched part of the shell. The interface chill/shell is on the left hand side. The result of the calculation (left side) matches well with the primary microstructure. As a consequence of the high undercooling near the surface, lots of small equiaxed grains form during initial solidification. The change in temperature gradient with the on-going solidification leads to grain selection by cristallographic orientation. The different colours of the grains represent different cristallographic orientation against the horizontal axis. The transformation of the microstructure calculation results into a two phase ABAQUS mesh (grain and grain boundary) is necessary for the further calculations. Mechanical Model For the mechanical model the following assumptions are valid: - Yield strength ratios between grain boundaries and grains (ratios of 2, 5 and10 are suggested) [6] - Elastoplastic behaviour of the grains and primary creep behaviour of grain boundaries (dislocations concentrated within grain boundaries) [7] - 5 -

6 The amounts of local strain concentrations within grain boundaries perpendicular to stress direction are very high (figure 4). A slight change of direction causes a drop of one magnitude. The standardised strain (maximum strain divided by global strain) versus strain rate show different dependencies. Whereas at yield strength ratios behaviour a very slight influence is observed the influence of strain rate on creep behaviour of grain boundaries is strong. The decreasing of standardised strain with increasing strain rate can be explained by moving of dislocations. This movement, which determines creep is too slow for higher strain rates. Figure 4: Result of micromechanical calculations (columnar microstructure), strain in direction 2 at strain rate /s The introduction of the microstructure is not sufficient enough therefore the SSCTmodel has to be extended with a pore nucleation (=crack initiation) behaviour at locations with strain peaks as it was firstly introduced by Gurson [8] and was used for metals by Tvergaard and Needleman [9]. This model bases on a Gaussian distribution of the crack initiation strain. After initiation the crack grows under continuing stress. Figure 5 shows crack generation and growing within primary grain boundaries. Figure 6 shows reaction force versus displacement of the lower test body part. The calculation and experiment results match well and underline that this complex model is suitable for modelling of continuous casting process of steels. For further work, the following key targets can be defined: - Application of the model on different steels - Application of the model on other ductility minima - Determination of more accurate strain criterions by generating a structure parameter - 6 -

7 E22 VALUE -2.68E E E E E E E E E E E E E E Figure 5: Crack generation and growing within primary grain boundaries (yellow, orange and red color identify cracks) [ x10 3 ] REACTION FORCE - RF TOTAL TIME Figure 6: Calculated reaction force versus time Conclusion The results show that any crack criterion based on global strains is not sufficient, because local strain could be several times higher depending on microstructure. A crack initiation model must be implemented for modelling the SSCT-test to predict the behaviour of the solidifiing shell.this work is understood as a first step towards implementation of microstructure into the definition of critical limits of shell deformation in order to prevent hot tearing and a better understanding of hot temperature behaviour of continuously casted strand shells

8 References: [1] Hiebler, H. and C. Bernhard: Mechanical Properties and Crack Susceptibility of Steel during Solidification, steel research 70 (1999), No , [2] Bernhard, C.: Mechanische Eigenschaften und Rißanfälligkeit erstarrender Stähle unter stranggießähnlichen Bedingungen, Doctoral Thesis, University of Leoben 1998 [3] Rappaz, M. and Ch. Gandin: Probabilistic Modelling of Microstructure Formation in Solidification Processes, Acta metall. Mater. Vol. 41 (1993), No. 2, [4] Schuetzenhoefer, W., C. Bernhard, H. Hiebler and M. Wolf: Infl uence of Microstructure on Hot Tearing of Steel, Proceedings of the 9 th Conference on Modelling of Casting, Welding and Advanced Solidification Processes, Aachen, August 20-25, 2000 [5] Schuetzenhoefer, W., C. Bernhard and H. Hiebler: Modelling of Hot Tearing of Steels under conditions similar to Continuous Casting Process, Metal 2000, Ostrava, May 2000 [6] Chimani, C. and K. Mörwald (1999): Micromechanical Investigation of the Hot Ductility Behaviour of Steel, ISIJ International, Vol. 39, No. 11, [7] Suzuki, T., K.-H. Tacke, K. Wünnenberg and K. Schwerdtfeger: Creep Properties of Steel at Continuous Casting Temperatures, Ironmaking and Steelmaking Vol. 15, No. 2, [8] Gurson, A. L.: J. of Eng. Mat. And Techn. 99 (1977), 2 [9] Tvergaard, V. and A. Needlman: Analysis of the Cup-Cone Fracture in a round Tensile Bar, Acta Metallurgica, vol. 32 (1984), The thermal history and the microstructure were calculated with the finite element code calcomos of calcom S.A. in Lausanne, Switzerland