Interdendritic Strain Research Articles

Transient Simulation of Mold Heat Transfer and Solidification Phenomena of Continuous Casting of Steel

A comprehensive model of heat transfer and solidification phenomena has been developed including microstructure evolution and fluctuation macrosegregation in continuously cast steel slabs with an objective of evaluation of various mold cooling conditions. The study contains plant trials, metallographic examinations, and formulation of mathematical modeling. The plant trials involved sample collection from three slab casters in use at two different steel plants. The metallographic study combined measurements of dendrite arm spacings and macrosegregation analysis of collected samples. A one-dimensional mathematical model has been developed to characterize the thermal, solidification phases, microstructure evolution, interdendritic strain, and therefore, the macrosegregation distributions. Two cooling approaches were proposed in this study to evaluate the Newtonian heat transfer coefficient in various mold regions. The first approach is a direct estimation approach (DEA), whereas the second one is a coupled approach of the interfacial resistor model and direct estimation approach (CIR/DEA). The model predictions and standard analytical models as well as the previous measurements were compared to verify and to calibrate the model where good agreements were obtained. The comparison between the model predictions and the measurements of dendrite arm spacings and fluctuated carbon concentration profiles were performed to determine the model accuracy level with different cooling approaches. Good agreements were obtained by different accuracy levels with different cooling approaches. The model predictions of thermal parameters and isotherms were analyzed and discussed.

Modelling of heat flow and interdendritic crack formation in twin-roll strip casting of aluminium alloys

Preliminary mathematical analyses of different interdendritic cracks associated with variation of heat transfer and generation of interdendritic strain in horizontal twin-roll strip casting have been investigated. A 1-D transient finite difference model of heat flow, dendritic solidification and interdendritic thermo-metallurgical strain has been developed. The model contains two cracking criteria to predict qualitatively and quantitatively the tendency of interdendritic crack formation during dendritic solidification of pure aluminium and 6022 aluminium alloy. The model predictions are compared to available analytical methods and previous measurements. This is to verify and calibrate the model where good and reasonable agreements are obtained, respectively. The variations of heat transfer modes during different contact cooling zones and their effects on the generation of interdendritic thermo-metallurgical strain at the surface and central strip locations have been analysed. The model predictions point out that the different contact cooling zones of strip surface and surroundings control the stages of interdendritic crack formation in different mushy regions. The mechanism of interdendritic crack formation in twin-roll strip casting process with previous and present cracking criteria have been explained and discussed. These discussions show the importance of selection of mathematical treatment to predict the stages of interdendritic crack formation.

Modeling of Heat Transfer and Interdendritic Strain for Exuded Surface Segregation Layer in the Direct Chill Casting of Aluminum Alloys

This investigation on the formation of exuded surface segregation layer “ESSL” is intended to provide experimental and simulated comparison to verify the model developed previously by El-Bealy. Preliminary verification and calibration of the previous 2D mathematical model are demonstrated by quantitative errors between the previous measurements and predictions of temperature and macrosegregation. Also, the results from these comparisons reveal that the errors are in the reasonable and within allowable limits. These comparisons lead to the fact that the exuded surface segregation layer mostly forms on the middle slice of broad sheet ingot face and in the early stages of mold zone. The model predictions point out also that the different interdendritic strain hypotheses associated with fluctuations of mold cooling conditions. This affects the interdendritic liquid flow between the equiaxed crystals which influences the severity of ESSL formation and its macrosegregation level. The mechanism of ESSL with heat flow and interdendritic strain generation has been analyzed and discussed. The quantitative comparisons between the pervious experimental results and numerical simulation in this investigation reveal also several solutions to prevent this defect for future work.

On the Formation of Macrosegregation and Interdendritic Cracks During Dendritic Solidification of Continuous Casting of Steel

The aim of the current article is to elucidate the significant effects of macrosegregation distribution and its level on the different stages of interdendritic crack formation during dendritic solidification in continuously cast steel slabs. Couple formations of macrosegregation and interdendritic crack phenomena during dendritic solidification of peritectic carbon steels have been investigated by metallographic study of collected slab samples and by performing a set of mathematical analyses. The metallographic study involved plant trails to measure slab surface temperature of different secondary spray cooling conditions. Also, macro–microexaminations, measurements of dendrite arm spacing, macrosegregation analysis, and interdendritic distance between the dendrites of collected samples from plant trials have been performed. The experimental results show a fluctuation of carbon segregation with respect to distance from slab surface. These results also reveal that the interdendritic cracks vary with this fluctuation in various nano, macro, and microscales based on the cooling conditions. A mathematical model of heat transfer, solidification, structure evolution, interdendritic strain, macrosegregation, and elementary interdendritic area “EIA” has been developed. This model takes also into account the calculating of interdendritic distance between the dendrites “IDD” to evaluate the interdendritic crack width. The model predictions of different thermal and solidification phenomena show a good agreement with measurements. The results pointed out also that the coupled effect of interdendritic strain and macrosegregation phenomena and their distributions can be considered as the most important tools to evaluate the surface and internal interdendritic cracks in continuously cast steel slabs. The formation mechanisms of different types of interdendritic crack with interdendritic strain patterns and fluctuation of macrosegregation levels during various cooling zones have been explained, and the possible solutions to these problems have been discussed.

Advanced Solute Conservation Equations for Dendritic Solidification Processes Part I: Experiments and Theory

AbstractThe macrosegregation formed in dendritic equiaxed structure during early stages of solidification of Al‐4.5%Cu alloy has been studied by experimental work and by metallurgical study of cast samples taken from the experimental work. An experimental work was conducted to study the coupled effect of natural convection streams, interdendritic strain and mushy permeability of Al‐4.5%Cu aluminum alloy solidified in horizontal rectangular parallelepiped cavity at different superheats. The metallurgical study includes macro‐microstructure evaluation, measurements of grain size of equiaxed crystals and macrosegregation analysis. This study shows that the level of surface segregation exhibiting as positive segregation varies with superheat whereas the rest of inner ingot areas show the light fluctuation in segregation values. In addition to experimental work, there is a mathematical study which contains a complete derivation of local solute redistribution equations based on Fleming's approach under different solute diffusion mechanisms in the dendritic solid. This derivation includes also the effects of interdendritic strain and mushy permeability on the local solute redistribution distribution. Owing to the length of the study, it is presented in two parts. The first part describes the experimental work and its results as well as a detail derivation of solute conservation equations. This part also involves comparison and discussion between existing and proposed solute conservation equations. The second part contains the mathematical analyses of a two dimensional mathematical model of fluid flow, heat flow, solidification, interdendritic strain and macrosegregation. Also, this part also contains the numerical simulations by using finite difference technique “FDT” to create convection patterns, heat transfer, interdendritic strain, and macrosegregation distributions. This part also includes comparisons between the available measurements and model predications as well as full discussion of different model simulations. The mechanism of interdendritic strain generation and macrosegregation formation during solidification of dendritic equiaxed structure under different diffusion mechanisms in dendritic solid has also been explained and discussed.

Advanced Solute Conservation Equations for Dendritic Solidification Processes Part II: Numerical Simulations and Comparisons

AbstractThe mathematical model of derived solute equations in part I for equiaxed dendritic solidification with melt convection streams and interdendritic thermo‐metallurgical strain is applied numerically to predict macrosegregation distributions with different diffusing mechanisms in dendritic solid. Numerical and experimental results are present for solidification of a Al–4.5% Cu alloy inside horizontal rectangular cavity at different superheats. The numerical simulations were performed by using simpler method developed by Patanker. The experiments were conducted to measure the cooling curves via thermocouples and the metallurgical examinations to measure the grain size and macrosegregation distributions in Part I. Preliminary validity of the model is demonstrated by the qualitative and quantitative agreements between the measurements and predications of cooling curves and predicted macrosegregation distributions including mushy permeability and interdendritic strain. In addition, several important features of macrosegregation in equiaxed dendritic solidification are identified through this combined experimental and numerical study. Also, quantitative agreements between the numerical simulations and experiments reveal several areas for future research work. The differences and errors between predicted macrosegregation results under different diffusing mechanisms have been discussed.

On the Formation of Interdendritic Internal Cracks During Dendritic Solidification of Continuously Cast Steel Slabs

In this study of solidification during the continuous casting of steel slabs, the effect of the different spray cooling conditions on the interdendritic internal cracks formed between the columnar dendrites has been examined by a metallographic study of the slab samples and by performing a set of mathematical analyses. The metallographic study involved plant trials to measure the slab surface temperature within different secondary spray cooling conditions. Also, macro/microexaminations of the collected samples from plant trials, measurements of dendrite arm spacing, and interdendritic distance between the columnar dendrites, as well as a segment length of interdendritic crack, have been performed. The experimental results show that the morphology of the interdendritic cracks described by the segment width and length fluctuate with the distance from the slab surface based on the secondary spray cooling conditions. A one-dimensional mathematical model of the heat transfer, solidification, structure evolution, interdendritic strain, and elementary interdendritic area (EIA) has been developed. This model takes into account also calculating the width of interdendritic crack. The model predictions are in a good agreement with the measurements. The results pointed out also that this criterion can be considered as the most important tool to measure the inner quality of the continuously cast steel slabs. Therefore, it helps also to define the required mechanism and reduction level of hot working deformation to close these interdendritic internal cracks. The formation mechanism of these cracks during the dendritic solidification of continuously cast steel slabs has been discussed and the available solutions have been proposed.

Interdendritic Strain and Macrosegregation-Coupled Phenomena for Interdendritic Crack Formation in Direct-Chill Cast Sheet Ingots

In a study of the early stages of dendritic solidification in the direct-chill cast sheet ingots, the coupled effect of interdendritic strain and macrosegregation on the interdendritic cracks formation in dendritic equiaxed structure has been investigated by the metallographic study of ingot samples and by performing a set of mathematical analyses for AA-6061 and AA-1050 aluminum alloys. The metallographic investigation contains microstructure examinations and macrosegregation measurements of collected samples from plant trials. The mathematical analysis consists of a two-dimensional (2-D) fluid flow, heat flow, interdendritic strain, and macrosegregation-coupled model. Also, a simple approach to measure interdendritic crack has been developed based on the accumulative interdendritic strain criterion, local dendritic phases, and the crystal distortion correlation factor resulting from steep positive local segregation. The model predications have clarified the effect of high positive macrosegregation on the surface and subsurface interdendritic crack formation. It has been revealed that interdendritic strain starts to generate just below the liquidus temperature, resulting from shrinkage of liquid→solid phase transformation and contraction of dendritic solid in the incoherent mushy region. In this region, the coupled effect of the shrinkage/contraction mechanism increases the interdendritic distances between equiaxed crystals and the interdendritic crack begins to nucleate. Subsequently, in the coherent mushy region, the different interdendritic strain sources start to affect significantly the distances between equiaxed crystals in a diverse way, and therefore, the final morphology of interdendritic crack begins to form. The mechanism of interdendritic crack formation during dendritic equiaxed structure solidification and the possible solutions to this problem are discussed.

On The Formation of Extruded Surface Segregation Layer in Aluminum Direct Chill Casting Process

The aim of this research work was to develop a mathematical model to study the formation of extruded surface segregation phenomenon during the early stages of solidification in an aluminum direct chill casting process. The mathematical analyses contain a one dimensional mathematical model of heat flow, solidification, interdendritic strain and macrosegregation. Some typical cases in conventional direct chill casting processes related to increase surface segregation and fluctuation in macrosegregation with distance from the ingot surface were simulated. Good agreement was found by previous measurements and simulated results. Model results were discussed to explain the effects of different thermal solidification factors and interdendritic strain on the extruded surface segregation layer phenomenon. The results show that this phenomenon is sensitive to alloy composition and forms in the gap between the ingot surface and mould wall. Also, the model results point out that this phenomenon appears as a direct effect of the extrusion mechanism of interdendritic solute liquid associated with the interdendritic strain distribution in the coherent region in the mushy zone.

Modeling of interdendritic strain and macrosegregation for dendritic solidification processes: Part II. Computation of interdendritic strain and segregation fields in steel ingots

In Part II of this article, the models are applied to analyze the effects of various cooling conditions on the interdendritic-strain history and macrosegregation patterns. The temperature measurements are used to evaluate the heat-transfer coefficient between the ingot surface and the cooling fluid. The model predictions are compared to temperature measurements and carbon-concentration profiles in ingots, where good agreements are obtained. In examining the fluctuated cooling conditions on the interdendritic strain, the results show that the sudden increase in the heat flux is found to increase the compressive strain in the interdendritic-strain region. The drop in the heat flux shows completely opposite behavior, where the tensile strain generates through the same region. The model demonstrates also that interdendritic strain associated with the fluctuated cooling conditions is a major factor in determining macrosegregation quantitatively and qualitatively. The results show that the tensile interdendritic strain results in a positive segregation, whereas the compressive strain yields a negative one. The segregation level depends mainly on the interdendritic-strain history and its rate value. The mechanism of fluctuated-segregation phenomenon as a function of the interdendritic strain is extensively discussed.

Modeling of interdendritic strain and macrosegregation for dendritic solidification processes: Part I. Theory and experiments

In the first part of this two-part article, mathematical models have been developed to characterize temperature, interdendritic stain, and segregation distributions during dendritic solidification. This aims to predict the effect of interdendric strain associated with sudden changes in the cooling conditions on the macrosegregation distributions, i.e., the combined effect of interdendric strain and macrosegregation on the dendritic structure. These theoretical models were verified on a laboratory scale. Four laboratory ingots of 0.53 and 0.9 wt pct C steels were cast horizontally and unidirectionally in a static mold under cooling conditions designed to approximate those in the continuous-casting process. Thermocouples recorded temperatures in the ingot at different locations from copper chill. The ingots were examined for macro-microstructure, and the extent of carbon macrosegregation was determined by wet chemical analysis. The experimental results indicate that static mold with sudden changes in the cooling conditions on the copper chill provides an approximately similar structure and macrosegregation profiles to those in a continuous-casting process. It is concluded that these cooling conditions have a significant effect on the fluctuated macrosegregation phenomenon. The sudden drop in the heat flux on the chill causes a positive segregation, whereas a sudden increase in heat flux results in a negative segregation. Also, the metallographic examination shows that there is high inelastic deformation of the dendrites due to the sudden drop in heat flux on the chill.