Prediction of cracks of the continuously cast carbon-steel slab

Transcription

1 Computer Methods and Experimental Measurements for Surface Effects and Contact Mechanics VII 111 Prediction of cracks of the continuously cast carbon-steel slab J. Dobrovska 1, V. Dobrovska 1, K. Stransky 2, F. Kavicka 2, J. Stetina 2, L. Camek 3, M.Masarik 3 & J. Heger 4 1 Faculty of Metallurgy and Material Engineering, VSB - Technical University of Ostrava, Czech Republic 2 Faculty of Mechanical Engineering, Brno University of Technology, Czech Republic 3 VITKOVICE STEEL a.s., Ostrava, Czech Republic 4 ALSTOM Power technology Centre, UK Abstract This paper deals with surface morphology, the mechanism of origination and causes of cross cracking of a concast low alloy manganese steel slab. The cross cracking was identified in a steel slab with a sectional size of 145x1300 mm and the length of the asymmetrical cracking was approximately 600 mm. The light microscopy and the scanning electron microscopy have been applied for determination of the metallographic structure of steel and for the study of micro-morphology and the trajectory of cracking. The chemical microheterogeneity of the steel matrix and the surface of cracking have been estimated by means of an X-ray micro-analyser JEOL JXA 8600/KEVEX. The analyses of Al, Si, P, Ti, Cr, Mn and Fe on the metallograpic samples of the matrix of steel, of the neighbourhood of cracking and of the surface of cracking have been realized. It has been found that the cross cracking is characterized by high macro-heterogeneity of manganese, carbon and sulphur. The causes of cross cracking have been explained by means of a thermokinetic calculation of a slab transient temperature field and by mean of an application of the theory of physical similarity and dimensionless criteria. It has been confirmed that two solidification cones are formed asymmetrically in the course of slab solidification and it is probable that the asymmetrically passing crack initiated on one of these two apexes.

2 112 Computer Methods and Experimental Measurements for Surface Effects and Contact Mechanics VII 1 Investigation into morphology and heterogeneity of a transversal crack in a concast slab 1.1 Introduction The crack was found inside a low-carbon steel slab with l300 l45 mm crosssection, after cutting. This, almost 600 mm tortuous crack, passed through the middle part of the slab thickness, and was displaced asymmetrically towards one edge of the slab. The chemical composition of the slab steel low-alloyed manganese-steel is (in wt.%): 0.16 C, 1.39 Mn, 0.37 Si, P, S, 0.06 Cr, Cu, Al(sum), Nb, Mo and 0.10 V. Two original models have been used for the investigation into the mechanism and causes of cross cracking in mentioned steel slab the 3D numerical model of the nonstationary temperature field of a concasting and the model of chemical heterogeneity of a concast slab. The first one is capable of simulating the temperature field of a caster. Experimental research and data acquisition have to be conducted simultaneously with the numerical computation not only to confront it with the actual numerical model, but also to make it more accurate throughout the process. The utilization of the numerical model of solidification and cooling of a concasting plays an indispensable role in practice. The potential change of technology on the basis of computation is constantly guided by the effort to optimize, i.e. to maximize the quality of the process. After computation, it is possible to obtain the temperatures at each node of the network, and at each time of the process. The user can therefore choose any appropriate longitudinal or cross-section of a slab and display the temperature field in a 3D or 2D graph. The second model the original model of chemical heterogeneity assesses critical points of slabs from the viewpoint of their increased susceptibility to crack and fissure. In order to apply this model, it is necessary to analyze the heterogeneity of the constituent elements (Mn, Si and others) and impurities (P, S and others) in characteristic places of the solidifying slab. The model, based on measurement results obtained by an electron micro-probe, generates distribution curves showing the dendritic segregation of the analyzed element, together with the partition coefficients of the elements between the liquid and solid phases. The combination of both models enables the prediction of cracks and fissures in critical points of the continuously cast carbon-steel slab. The first results of the investigation into mechanism and causes of the initiation of a transversal crack of the low alloy manganese steel slab were given in [1]. 1.2 Experiment and methods applied Measurement of the chemical heterogeneity first required a certain part of the crack with its surrounding to be extracted mechanically from the slab. The total sectional area with the course of the crack is shown in Figure 1, which also illustrates the method of extraction of the samples. The course of the crack is shown by a dot-and-dash line and shows discontinuity. The samples were

3 Computer Methods and Experimental Measurements for Surface Effects and Contact Mechanics VII 113 prepared from the section of the slab, whereby the samples 8.1.1, 8.1.2, 8.2, 8.3 and 8.8 were selected for the measurement of the heterogeneity of elements. The thickness of the samples varied around 13 mm. No sample with an evident crack fell apart, despite the fact that the crack was quite obvious both on the thinsection side as well as on the reverse side. Figure 1: The cracking corpus extraction schema, and the estimation of metallographic samples to the heterogeneity measuring. Concentration of elements was measured using energy-dispersing (ED) X- ray spectral microanalysis and with the help of the micro-analytic complex JEOL JXA-8600/KEVEX Delta V-Sesame. The preparation of metallographic thin

4 114 Computer Methods and Experimental Measurements for Surface Effects and Contact Mechanics VII sections is described in [1] in details. The concentrations of eight elements were determined, namely Al, Si, P, S, Ti, Cr, Mn and Fe. The measurement was carried out with each sample in 101 points along a section of 1000 µm, the distance between two consecutive points being 10 µm. Table 1 contains the measured concentrations and calculated parameters of each element in individual samples. Table 1: The calculated values of the average concentration of elements c av and its standard deviation σ n-1, the dimensionless numbers α and I s (see Appendix) for the matrix at a certain distance from crack. Sample Para Element meter Al Si P S Ti Cr Mn Fe c av σ n α I s c av σ n-1 α 10 2 Is c av σ n-1 α 10 2 I s c av σ n-1 α 10 2 I s c av σ n-1 α 10 2 I s Since none of the metallographic samples broke up in two parts, it was necessary to open the crack in the way described in Ref [1]. The sample was cooled to the temperature of liquid nitrogen (appr. 196 C) and broken into two parts by a hammer. After breaking, the fracture surfaces were briefly dipped into ethanol and immediately reheated to room temperature. The original surface of the crack was oxidized, compared to the freshly prepared fracture surface. The tortuous inter-dendritic course of the crack in sample 8.1.3, and the almost pure pearlitic matrix surrounding the crack, is shown in Figure 2. Microanalysis of the same elements, as in the matrix, was also carried out at the fracture surface. The distribution of elements was scanned on the surface of the fracture on an area of approx. 1 mm 2 for 300 s. The remaining measured parameters and the method of processing were the same as with the measurement of concentration of elements in the matrix. The measurements of concentration

5 Computer Methods and Experimental Measurements for Surface Effects and Contact Mechanics VII 115 of elements were performed both at the surface of the fresh crack and on the oxidized surface of the original crack [1]. The results are given in Table 2. Figure 2: Table 2: The perlitic structure of matrix surrounding the cracking in the samples No The cracking has the interdenritic course. Etched by nital. Magnification: 100x. Data used for calculation of the I s -values at the surface of crack. (Concentration at the surface of the original crack c orig and at the fresh fracture in liquid nitrogen c fresh ). Param. C Al Si P S Ti Cr Mn Fe c orig c fresh I s Results and their discussion The original cracks were found by metallographic examination only in places where the pearlitic structure had uniquely prevailed. Nevertheless, in the places of occurrence of almost pure pearlitic structure, the cracks were mutually separated by strips of compact and solid slab material. Furthermore, it was obvious from the samples that any material discontinuity in the slab disappears in the zone where the proportion of ferrite increases at the expense of pearlite. The measurements of concentration of elements in the matrix (Table 1) have shown that the areas with prevailing pearlitic structures (in which this type of crack propagates) have a higher concentration of Mn and also slightly Si, S and P than in the zones where ferrite and pearlite occur in the same ratio. The almost pure pearlitic structure indicates that the occurrence of cracks is also associated with a higher concentration of C.

6 116 Computer Methods and Experimental Measurements for Surface Effects and Contact Mechanics VII The measurements of concentration of elements on the crack surface (Table 2) indicate that the concentrations of Mn and S at the surface of the original crack are significantly higher than those in the matrix. The results of these measurements therefore confirm that the crack passes through places with a high segregation of Mn and furthermore a high segregation of S. As given in Table II a markedly elevated concentration of Mn and S and also somewhat higher concentration of Ti and Cr are obvious at the surface of the original transversal crack if compared with the surface of fresh fracture originated by breaking a crack after cooling down in liquid nitrogen. On the other hand the concentrations of Al, Si, P and Fe are somewhat reduced. Thus, the measurements of the concentration of elements have shown that the crack reveals interdendritic course. The occurrence of the transversal crack is associated mostly with significant zonal (macroscopic) and also dendritic (microscopic) segregation of Mn, C and S and is simultaneously associated with presence of shrinkage microporosity. There is much probability that the segregation takes place at slow solidification of the melt (there is much to believe in the immediate vicinity of cracks initiating afterwards) and that already during the solidification process carbon is adapted for decomposition of manganese, whereby carbon has almost eutectoid concentration (i.e. about 0.75 wt-%) in the neighbourhood of cracks. On the basis of the previous thermokinetic calculation of a non-stationary temperature field of a slab, two "cones" of solidification are formed in a solidifying slab, whereby the tops of cones are symmetrically divided over the sectional area of slab (see fig.1 in Ref. [1]). There is probable that the asymmetrically passing crack was initiated just in one of these two peaks. Table 3: I s -values in the matrix and at the surface of crack. Parameter C Al Si P S Ti Cr Mn Fe I s (Matrix) I s (Crack) Note: C-content determined on the basis of metallographic analysis. These conclusions are supported even by the results achieved with application of the theory of similarity to the processes of segregation of elements at crystallization of metals. Derivation of the applied dimensionless criteria is schematically shown in Appendix. Table 1 presents the calculated figures I s for the individual elements as measured in all samples taken-off at a certain distance from the crack (matrix). The average values of such magnitudes are listed in Table 3 in common with the I s parameter calculated from data measured immediately at the crack surface (see Table 2). The results of Table 3 confirm the crack to follow sites with a higher segregation of S, Mn and also C. Moreover, the dimensionless number α has been calculated from the asmeasured concentration data by using the original mathematical model [4]; here, Table 1 presents the values for elements measured in the matrix. The criterion α involves inside the effect of processes of mass transfer in the anisothropic field of a body (dendrite), hardly defined in a mathematical or

7 Computer Methods and Experimental Measurements for Surface Effects and Contact Mechanics VII 117 physical way, with mutual co-existency of liquid and solid phase. Accordingly, there is expressed the effect of the phenomenon being function of time and taking place in space, in a body e.g. in a dendrite three-dimensional in shape. In fact it can be characterized in a parametric way with the help of the magnitude L proportional to the dendrite arms spacing. According to numerous measurements [2] the mutual relation between the local solidification time θ and the dendrite arms spacing L with smooth crystallization can be expressed as n L = A θ, (1) where A is the material-technological constant and in which the exponent for non-alloyed and low-alloyed steels is equal to n = 0.45±0.14 [3]. For the purpose of further consideration the total differential of function α = Dθ/L 2 can be written as dα = ( θ/ L )dd + (D / L )dθ 2(Dθ/ L )dl, (2) and by modification it is transferred to ( L 2 / Dθ )dα = dd / D + dθ/ θ 2dL / L. (3) Let us assume in the first approach both the dimensionless number α and the diffusion coefficient D of the segregating element to be constant. In such case eqn (3) is reduced to form d θ / θ 2dL / L = 0, (4) which indicates the relative change in the figure of local solidification time of the relevant body to be equalized by the relative change in dendrite arms spacing. By integration the eqn (4) and by re-arrangement the integrated relation one gets here the causal relation among the dendrite arms spacing and the local solidification time in form L = ( θ / C), (5) where C is the integration constant. It is obvious from eqn (5) that the dendrite arms spacing should sensitively refer to variations in local solidification time, whereby extension in dendrite arms spacing i.e. coarsening of dendrites should encounter approximately with the square root of the local solidification time. It is noticeable that eqn (5) can be easily re-written to read 0.5 L = A θ, (6) which is in principle identical with eqn (1) determined earlier experimentally on the basis of numerous measurements [2]. The mean value of exponent 0.5 in eqn (6) is lying approximately in the middle of the interval (0.45±0.14) as determined for eqn (1) by processing the experimental data [3]. In addition from the definition of the number α there can be written L / θ = (D / α) = A, (7) which enables to perform a qualified estimation of the constant A in case of the ratio of number α and of the diffusion coefficient D of the segregating element known for the relevant chemical heterogeneity of element in the body. The values of constant A calculated from the average figures of the parameter α in Table 1 (i.e. in the matrix) and from the diffusion coefficients of

8 118 Computer Methods and Experimental Measurements for Surface Effects and Contact Mechanics VII the relevant elements taken from literature [5] are listed in Table 4. The geometrical mean of the parameter A determined from data arranged in Table 4 makes A (D/α) 0.5 =(1.073, , ) [cm 2 /s] 0.5 and/or A=10.73 µm/s 0.5. This value is numerically identical within the limits of medium errors with the constant A determined for the steel slab as-measured earlier [4]. With know local solidification time θ - which can be obtained from the original model of non-stationary temperature fields the characteristic dendrite arms spacing can be well-estimated with the help of eqn (6). Table 4: Data used for calculation of the A-constant and its values. Parameter Al Si P S Ti Cr Mn Fe α 10 2 σ α D 10 8 [cm 2 /s] A 10 3 [(cm 2 /s) -0.5 ] Conclusion and further work Investigation into transversal cracks in a slab showed as follows: 1) In sites in which a discontinuous transversal crack is initiated the character of solidification i.e. the segregation of elements is changing. This is evidenced by different indices of segregation I s determined for the material matrix and for the surface of crack (Table 3). 2) Thus, by the analogy of previous measurements [4] markedly coarse dendrites are expected to occur in sites with a discontinuous transversal crack. This fact is also confirmed by estimation of the size of dendrites according to the course of a discontinuous crack, see Fig. 2. 3) The discontinuous crack has arisen still before the solidification was finished (i.e. above the solidus temperature due to local stress) with occurrence of a certain ratio of the solid to liquid phase in the framework of growing relatively coarse dendrite and with relatively long local solidification time. This is the feature of the already mentioned cone of solidification from the model of non-stationary temperature fields. In this way the normal process of redistribution of elements between the solid and liquid phase has been interrupted in the slab with transversal crack; this process of redistribution is characterizing the dendritic segregation of elements with observance of continuity of solidification at the interval between the liquidus and solidus temperature. We assume the process of continuous solidification of slab and growth of dendrites to be governed apart from the relevant magnitudes such as the D, θ, L, c max and c0 also by the growing rate of dendrites w [m/s] and, in connection with the magnitudes and criteria examined till now, also by the dimensionless

9 Computer Methods and Experimental Measurements for Surface Effects and Contact Mechanics VII 119 number Th = wθ/l, see Appendix. For this reason we intend to continue in application of the models of non-stationary temperature field and of chemical heterogeneity upon description of slab with discontinuous transversal crack with the aim to contribute to semi-quantitative explanation of the reason for initiation of such crack in the CC-slabs. 3 Appendix (Application of the theory of physical similarity and dimensional analysis) The factors influencing significantly the liability of steels and steel casting to cracking include the dendritic structure of solidified casting whose parameters are governed by the following magnitudes: the diffusion coefficient (D) of relevant element in solid solution, the dendrite arms spacing (L), the local time of solidification (θ) and the rate of crystallization (w). The continuity among the cited magnitudes and the concentration of the relevant element in the structure c max (maximum) and c 0 (medium) can be in principle expressed by the following function f (D, θ, L, w,cmax,c0) = 0 (A1) On the basis of the theory of physical similarity this function can be substituted by means of dimensional analysis into function among the dimensionless groups (criteria). The required criteria and their number can be found by using the π-theorem [6], namely, with the help of the matrix of dimensions of the relevant magnitudes and its transformation to the matrix of criteria in which the relevant magnitudes encounter. The matrix of dimensions (A-matrix in table 1A) includes in this case some 6 magnitudes whose general dimensions can be expressed by means of 3 fundamental dimensions. Table 1A: Matrix of dimensions (A) and matrix of dimensionless groups (B). A-matrix B-matrix Dimension D θ L w c max c 0 Criterion D θ L w c max c 0 m π 1 = α s π 2 = Th wt-% π 3 = I s According to the mentioned theorem the relation among six fundamental magnitudes can be replaced in this case by means of 3 dimensionless criteria of similarity. By transformation of the A-matrix of dimensions to the matrix involving the dimensionless criteria we get the B-matrix in table 1A. The original eqn (1) involving six fundamental magnitudes can be substituted in above-cited way by a function among three criteria of similarity 2 F max 0 = ( π, π, π ) = F(Dθ / L, wθ / L,c / c ) 0 (A2)

10 120 Computer Methods and Experimental Measurements for Surface Effects and Contact Mechanics VII Here, the first criterion Dθ/L2 = α, known as the Fourier's diffusion number, is frequently used in models dealing with segregation of elements at crystallization of metal alloys and is one of widely applied criteria expressing mass transfer in the theories of physical similarity. In principle this number provides information on the intensity of diffusion processes in solid phase of a body at crystallization in the range between the liquidus and solidus and so it provides significant information on the intensity of such processes in the course of cooling down the body below the solidus temperature. The second group, called Thomson number Th = wθ/l, presents universal criterion of moving similarity of phenomena. This number can be used for description of non-stationary flowing of melt in the course of solidification in the framework of dendrites having characteristic size L. The third dimensionless group represents a simplex expressed by the ratio of max. concentration of the segregating element in the framework of dendrite to its average concentration in the crystallizing melt of a dendrite in question. The simplex can be denoted as index of segregation of the relevant element I s. Acknowledgments Realized thanks to the projects of the Grant Agency of the Czech Republic, (No.106/04/1334, 106/04/1006, 106/03/0271,106/03/0264 and 106/04/0949), of the COST-APOMAT-OC526.10, of the EUREKA No COOP and of the KONTAKT No.1/ References [1] Dobrovská, J., Dobrovská, V., Kavicka, F., Stransky, K., Stetina, J., Heger, J., Camek, L., Velička, B. Industrial application of two numerical models in concasting technology. Proc. of the 7 th Int. Conf. on Damage and Fracture Mechanics, eds. C.A. Brebbia & S.I. Nishida, WITpress Southampton: Boston, pp , [2] Kobayashi, S.: A Mathematical Model for Solute Redistribution during Dendritic Solidification. Trans. ISIJ, vol.28, 1988, pp [3] Levíček, P. & Stránský, K. Metallurgical defects of steel castings (causes and removing), in Czech. SNTL, Praha 1984, p [4] Dobrovská, J. et al. The temperature field and chemical heterogeneity of CC steel slab (in Czech). Metallurgical Journal, LVI (8), pp , [5] Smithells Metals Reference Book, Butterworth-Heinemann, Seventh Edition, [6] Coulston, J.M. & Richardson, J.F. Chemical Engineering, Volume 1. Pergamon Press: Oxford, New York, Seoul and Tokyo, pp.1-15, 1990.