Prediction of cracks of the continuously cast carbon-steel slab · 1 Investigation into morphology and heterogeneity of a transversal crack in a concast slab 1.1 Introduction The

Prediction of cracks of the continuously cast carbon-steel slab

J Dobrovska1 V Dobrovska1 K Stransky2 F Kavicka2 J Stetina2 L Camek3 MMasarik3 amp J Heger4 1Faculty of Metallurgy and Material Engineering VSB - Technical University of Ostrava Czech Republic 2Faculty of Mechanical Engineering Brno University of Technology Czech Republic 3VITKOVICE STEEL as Ostrava Czech Republic 4ALSTOM 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 8600KEVEX 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

Computer Methods and Experimental Measurements for Surface Effects and Contact Mechanics VII 111

copy 2005 WIT Press WIT Transactions on Engineering Sciences Vol 49 wwwwitpresscom ISSN 1743-3533 (on-line)

1 Investigation into morphology and heterogeneity of a transversal crack in a concast slab

11 Introduction

The crack was found inside a low-carbon steel slab with l300timesl45 mm cross-section 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 ndash low-alloyed manganese-steel ndash is (in wt) 016 C 139 Mn 037 Si 0015 P 0007 S 006 Cr 0030 Cu 0048 Al(sum) 0010 Nb 0010 Mo and 010 V

Two original models have been used for the investigation into the mechanism and causes of cross cracking in mentioned steel slab ndash 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 ndash 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 ndash on the basis of computation ndash is constantly guided by the effort to optimize ie 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 ndash the original model of chemical heterogeneity ndash 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]

12 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

112 Computer Methods and Experimental Measurements for Surface Effects and Contact Mechanics VII


prepared from the section of the slab whereby the samples 811 812 82 83 and 88 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 thin-section 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-8600KEVEX Delta V-Sesame The preparation of metallographic thin



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 microm the distance between two consecutive points being 10 microm 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 cav and its standard deviation σn-1 the dimensionless numbers α and Is (see Appendix) for the matrix at a certain distance from crack

Sample Para Element meter Al Si P S Ti Cr Mn Fe

811

cav σn-1 αsdot102

Is

0022 0025 2672 4953

0340 0105 2857 1649

0027 0026 2181 4365

0024 0025 3624 3766

0009 0016 1930 9646

0031 0034 2008 5443

1744 0346 2210 1450

9780 0459 1590 1008

812

cav σn-1 αsdot102

Is

0025 0030 1646 6860

0313 0081 1665 1695

0024 0024 2663 4119

0031 0027 2943 3582

0008 0016 2343

10204

0037 0036 1643 5139

1669 0225 1175 1384

9790 0295 1451 1006

82

cav σn-1 αsdot102

Is

0031 0028 3012 3538

0326 0088 1852 1688

0032 0034 1810 5549

0023 0024 2899 4290

0009 0017 2029

10067

0035 0035 4136 3164

1663 0247 0590 1563

9788 0346 0285 1006

83

cav σn-1 αsdot102

Is

0035 0030 1871 4282

0336 0082 2877 1487

0034 0034 1308 5907

0024 0026 2845 4530

0011 0020 2310 8897

0037 0036 2632 4023

1674 0228 1559 1356

9785 0311 1069 1005

88

cav σn-1 αsdot102

Is

0034 0027 2810 3261

0277 0061 1604 1916

0020 0021 2062 5035

0030 0026 2196 3934

0010 0019 2460 8991

0027 0026 2943 3670

1477 0158 1137 1307

9813 0186 0942 1005

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 ndash196 degC) 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 813 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 mm2 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



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 The perlitic structure of matrix surrounding the cracking in the samples No 813 The cracking has the interdenritic course Etched by nital Magnification 100x

Table 2 Data used for calculation of the Is-values at the surface of crack (Concentration at the surface of the original crack corig and at the fresh fracture in liquid nitrogen cfresh)

Param C Al Si P S Ti Cr Mn Fe corig 075 0090 0327 0020 0477 0157 0247 3313 95347 cfresh 016 0094 0435 0040 0105 0025 0105 1570 97625

Is 4688 0957 0752 0500 4543 6280 2352 2110 0977

13 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 ndash slightly ndash 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



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 (ie about 075 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 fig1 in Ref [1]) There is probable that the asymmetrically passing crack was initiated just in one of these two peaks

Table 3 Is-values in the matrix and at the surface of crack

Parameter C Al Si P S Ti Cr Mn Fe Is (Matrix) - 4597 1687 4995 4021 9561 4228 1412 1006 Is (Crack) 4688 0957 0752 0500 4543 6280 2352 2110 0977

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 Is 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 Is ndash 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 as-measured 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



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 eg 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 nAL θsdot= (1) where A is the material-technological constant and in which the exponent for non-alloyed and low-alloyed steels is equal to n = 045plusmn014 [3]

For the purpose of further consideration the total differential of function α = DθL2 can be written as dL)LD(2d)LD(dD)L(d 322 θminusθ+θ=α (2) and by modification it is transferred to LdL2dDdDd)DL( 2 minusθθ+=αθ (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 0LdL2d =minusθθ (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 )C(L θ= (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 ie 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 50AL θsdot= (6) which is in principle identical with eqn (1) determined earlier experimentally on the basis of numerous measurements [2] The mean value of exponent 05 in eqn (6) is lying approximately in the middle of the interval (045plusmn014) as determined for eqn (1) by processing the experimental data [3]

In addition from the definition of the number α there can be written A)D(L 5050 =α=θ (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 (ie in the matrix) and from the diffusion coefficients of



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 equiv (Dα)05 =(1073 +1885 -0684) [cm2s]05 andor A=1073 microms05 This value is numerically identical ndash within the limits of medium errors ndash 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 ndash 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 102

σα sdot102 2404 0607

2171 0642

2005 0498

2901 0506

2214 0224

2672 0964

1334 0599

1067 0512

D 108 [cm2s] 61942 0624 5340 59800 0585 1649 0237 0204

A 103 [(cm2s)-05] 5076 0536 1632 4540 0514 0786 0495 0437

2 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 ie the segregation of elements is changing This is evidenced by different indices of segregation Is 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 (ie above the solidus temperature ndash 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 ndash apart from the relevant magnitudes such as the D θ L cmax and c0 ndash also by the growing rate of dendrites w [ms] and in connection with the magnitudes and criteria examined till now also by the dimensionless



number Th = wθL 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 cmax (maximum) and c0 (medium) can be in principle expressed by the following function

0)ccwLD(f 0max =θ (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 cmax c0 Criterion D θ L w cmax c0 m 2 0 1 1 0 0 π1 = α 1 1 -

2 0 0 0

s -1

1 0 -1 0 0 π2 = Th 0 1 -1

1 0 0

wt- 0 0 0 0 1 1 π3 = Is 0 0 0 0 1 -1

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

0)ccLwLD(F)(F 0max2

321 =θθ=πππ (A2)



Here the first criterion DθL2 = α known as the Fouriers 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 = wθL 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 Is

Acknowledgments

Realized thanks to the projects of the Grant Agency of the Czech Republic (No106041334 106041006 106030271106030264 and 106040949) of the COST-APOMAT-OC52610 of the EUREKA No 2716 COOP and of the KONTAKT No12005-06

References

[1] Dobrovskaacute J Dobrovskaacute 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 7th Int Conf on Damage and Fracture Mechanics eds CA Brebbia amp SI Nishida WITpress Southampton Boston pp183-192 2002

[2] Kobayashi S A Mathematical Model for Solute Redistribution during Dendritic Solidification Trans ISIJ vol28 1988 pp535-344

[3] Leviacuteček P amp Straacutenskyacute K Metallurgical defects of steel castings (causes and removing) in Czech SNTL Praha 1984 p 180

[4] Dobrovskaacute J et al The temperature field and chemical heterogeneity of CC steel slab (in Czech) Metallurgical Journal LVI (8) pp 31-43 2001

[5] Smithells Metals Reference Book Butterworth-Heinemann Seventh Edition 1998

[6] Coulston JM amp Richardson JF Chemical Engineering Volume 1 Pergamon Press Oxford New York Seoul and Tokyo pp1-15 1990



1 Investigation into morphology and heterogeneity of a transversal crack in a concast slab

11 Introduction

The crack was found inside a low-carbon steel slab with l300timesl45 mm cross-section 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 ndash low-alloyed manganese-steel ndash is (in wt) 016 C 139 Mn 037 Si 0015 P 0007 S 006 Cr 0030 Cu 0048 Al(sum) 0010 Nb 0010 Mo and 010 V

Two original models have been used for the investigation into the mechanism and causes of cross cracking in mentioned steel slab ndash 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 ndash 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 ndash on the basis of computation ndash is constantly guided by the effort to optimize ie 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 ndash the original model of chemical heterogeneity ndash 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]

12 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











811

cav σn-1 αsdot102

Is

0022 0025 2672 4953

0340 0105 2857 1649

0027 0026 2181 4365

0024 0025 3624 3766

0009 0016 1930 9646

0031 0034 2008 5443

1744 0346 2210 1450

9780 0459 1590 1008

812

cav σn-1 αsdot102

Is

0025 0030 1646 6860

0313 0081 1665 1695

0024 0024 2663 4119

0031 0027 2943 3582

0008 0016 2343

10204

0037 0036 1643 5139

1669 0225 1175 1384

9790 0295 1451 1006

82

cav σn-1 αsdot102

Is

0031 0028 3012 3538

0326 0088 1852 1688

0032 0034 1810 5549

0023 0024 2899 4290

0009 0017 2029

10067

0035 0035 4136 3164

1663 0247 0590 1563

9788 0346 0285 1006

83

cav σn-1 αsdot102

Is

0035 0030 1871 4282

0336 0082 2877 1487

0034 0034 1308 5907

0024 0026 2845 4530

0011 0020 2310 8897

0037 0036 2632 4023

1674 0228 1559 1356

9785 0311 1069 1005

88

cav σn-1 αsdot102

Is

0034 0027 2810 3261

0277 0061 1604 1916

0020 0021 2062 5035

0030 0026 2196 3934

0010 0019 2460 8991

0027 0026 2943 3670

1477 0158 1137 1307

9813 0186 0942 1005










Is 4688 0957 0752 0500 4543 6280 2352 2110 0977





























σα sdot102 2404 0607

2171 0642

2005 0498

2901 0506

2214 0224

2672 0964

1334 0599

1067 0512

D 108 [cm2s] 61942 0624 5340 59800 0585 1649 0237 0204

A 103 [(cm2s)-05] 5076 0536 1632 4540 0514 0786 0495 0437

















2 0 0 0

s -1

1 0 -1 0 0 π2 = Th 0 1 -1

1 0 0

wt- 0 0 0 0 1 1 π3 = Is 0 0 0 0 1 -1




0)ccLwLD(F)(F 0max2

321 =θθ=πππ (A2)






Acknowledgments


References

















811

cav σn-1 αsdot102

Is

0022 0025 2672 4953

0340 0105 2857 1649

0027 0026 2181 4365

0024 0025 3624 3766

0009 0016 1930 9646

0031 0034 2008 5443

1744 0346 2210 1450

9780 0459 1590 1008

812

cav σn-1 αsdot102

Is

0025 0030 1646 6860

0313 0081 1665 1695

0024 0024 2663 4119

0031 0027 2943 3582

0008 0016 2343

10204

0037 0036 1643 5139

1669 0225 1175 1384

9790 0295 1451 1006

82

cav σn-1 αsdot102

Is

0031 0028 3012 3538

0326 0088 1852 1688

0032 0034 1810 5549

0023 0024 2899 4290

0009 0017 2029

10067

0035 0035 4136 3164

1663 0247 0590 1563

9788 0346 0285 1006

83

cav σn-1 αsdot102

Is

0035 0030 1871 4282

0336 0082 2877 1487

0034 0034 1308 5907

0024 0026 2845 4530

0011 0020 2310 8897

0037 0036 2632 4023

1674 0228 1559 1356

9785 0311 1069 1005

88

cav σn-1 αsdot102

Is

0034 0027 2810 3261

0277 0061 1604 1916

0020 0021 2062 5035

0030 0026 2196 3934

0010 0019 2460 8991

0027 0026 2943 3670

1477 0158 1137 1307

9813 0186 0942 1005










Is 4688 0957 0752 0500 4543 6280 2352 2110 0977





























σα sdot102 2404 0607

2171 0642

2005 0498

2901 0506

2214 0224

2672 0964

1334 0599

1067 0512

D 108 [cm2s] 61942 0624 5340 59800 0585 1649 0237 0204

A 103 [(cm2s)-05] 5076 0536 1632 4540 0514 0786 0495 0437

















2 0 0 0

s -1

1 0 -1 0 0 π2 = Th 0 1 -1

1 0 0

wt- 0 0 0 0 1 1 π3 = Is 0 0 0 0 1 -1




0)ccLwLD(F)(F 0max2

321 =θθ=πππ (A2)






Acknowledgments


References












811

cav σn-1 αsdot102

Is

0022 0025 2672 4953

0340 0105 2857 1649

0027 0026 2181 4365

0024 0025 3624 3766

0009 0016 1930 9646

0031 0034 2008 5443

1744 0346 2210 1450

9780 0459 1590 1008

812

cav σn-1 αsdot102

Is

0025 0030 1646 6860

0313 0081 1665 1695

0024 0024 2663 4119

0031 0027 2943 3582

0008 0016 2343

10204

0037 0036 1643 5139

1669 0225 1175 1384

9790 0295 1451 1006

82

cav σn-1 αsdot102

Is

0031 0028 3012 3538

0326 0088 1852 1688

0032 0034 1810 5549

0023 0024 2899 4290

0009 0017 2029

10067

0035 0035 4136 3164

1663 0247 0590 1563

9788 0346 0285 1006

83

cav σn-1 αsdot102

Is

0035 0030 1871 4282

0336 0082 2877 1487

0034 0034 1308 5907

0024 0026 2845 4530

0011 0020 2310 8897

0037 0036 2632 4023

1674 0228 1559 1356

9785 0311 1069 1005

88

cav σn-1 αsdot102

Is

0034 0027 2810 3261

0277 0061 1604 1916

0020 0021 2062 5035

0030 0026 2196 3934

0010 0019 2460 8991

0027 0026 2943 3670

1477 0158 1137 1307

9813 0186 0942 1005










Is 4688 0957 0752 0500 4543 6280 2352 2110 0977





























σα sdot102 2404 0607

2171 0642

2005 0498

2901 0506

2214 0224

2672 0964

1334 0599

1067 0512

D 108 [cm2s] 61942 0624 5340 59800 0585 1649 0237 0204

A 103 [(cm2s)-05] 5076 0536 1632 4540 0514 0786 0495 0437

















2 0 0 0

s -1

1 0 -1 0 0 π2 = Th 0 1 -1

1 0 0

wt- 0 0 0 0 1 1 π3 = Is 0 0 0 0 1 -1




0)ccLwLD(F)(F 0max2

321 =θθ=πππ (A2)






Acknowledgments


References













Is 4688 0957 0752 0500 4543 6280 2352 2110 0977





























σα sdot102 2404 0607

2171 0642

2005 0498

2901 0506

2214 0224

2672 0964

1334 0599

1067 0512

D 108 [cm2s] 61942 0624 5340 59800 0585 1649 0237 0204

A 103 [(cm2s)-05] 5076 0536 1632 4540 0514 0786 0495 0437

















2 0 0 0

s -1

1 0 -1 0 0 π2 = Th 0 1 -1

1 0 0

wt- 0 0 0 0 1 1 π3 = Is 0 0 0 0 1 -1




0)ccLwLD(F)(F 0max2

321 =θθ=πππ (A2)






Acknowledgments


References
































σα sdot102 2404 0607

2171 0642

2005 0498

2901 0506

2214 0224

2672 0964

1334 0599

1067 0512

D 108 [cm2s] 61942 0624 5340 59800 0585 1649 0237 0204

A 103 [(cm2s)-05] 5076 0536 1632 4540 0514 0786 0495 0437

















2 0 0 0

s -1

1 0 -1 0 0 π2 = Th 0 1 -1

1 0 0

wt- 0 0 0 0 1 1 π3 = Is 0 0 0 0 1 -1




0)ccLwLD(F)(F 0max2

321 =θθ=πππ (A2)






Acknowledgments


References




















σα sdot102 2404 0607

2171 0642

2005 0498

2901 0506

2214 0224

2672 0964

1334 0599

1067 0512

D 108 [cm2s] 61942 0624 5340 59800 0585 1649 0237 0204

A 103 [(cm2s)-05] 5076 0536 1632 4540 0514 0786 0495 0437

















2 0 0 0

s -1

1 0 -1 0 0 π2 = Th 0 1 -1

1 0 0

wt- 0 0 0 0 1 1 π3 = Is 0 0 0 0 1 -1




0)ccLwLD(F)(F 0max2

321 =θθ=πππ (A2)






Acknowledgments


References












σα sdot102 2404 0607

2171 0642

2005 0498

2901 0506

2214 0224

2672 0964

1334 0599

1067 0512

D 108 [cm2s] 61942 0624 5340 59800 0585 1649 0237 0204

A 103 [(cm2s)-05] 5076 0536 1632 4540 0514 0786 0495 0437

















2 0 0 0

s -1

1 0 -1 0 0 π2 = Th 0 1 -1

1 0 0

wt- 0 0 0 0 1 1 π3 = Is 0 0 0 0 1 -1




0)ccLwLD(F)(F 0max2

321 =θθ=πππ (A2)






Acknowledgments


References

















2 0 0 0

s -1

1 0 -1 0 0 π2 = Th 0 1 -1

1 0 0

wt- 0 0 0 0 1 1 π3 = Is 0 0 0 0 1 -1




0)ccLwLD(F)(F 0max2

321 =θθ=πππ (A2)






Acknowledgments


References












Acknowledgments


References









Documents

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