TearSim: A two-phase model addressing hot tearing formation during aluminum direct chill casting

A two-phase mathematical model for the study of hot tearing formation is presented. The model accounts for the main phenomena associated with the formation of hot tears, i.e., the lack of feeding at the late stages of solidification and the localization of viscoplastic deformation. The model incorporates an advanced viscoplastic constitutive model for the coherent part of the mushy zone, allowing for the possibility of dilatation/densification of the semisolid skeleton under applied deformation. Based on quantities computed by the model, a hot tearing criterion is proposed where liquid feeding difficulties and viscoplastic deformation at the late stages of solidification are taken into account. The model is applied to study hot tearing formation during the start-up phase for direct-chill (DC) casting of extrusion ingots, and to discuss the effect of different phenomena and process parameters. The modeling results are also compared to experimentally measured hot tearing susceptibilities, and the model is able to reproduce known experimental trends such as the effect of the casting speed and the importance of the design of the starting block.     

Thermal strain in the mushy zone related to hot tearing

A volume-averaged two-phase model addressing the main transport phenomena associated with hot tearing in an isotropic mushy zone during solidification of metallic alloys has recently been presented elsewhere along with a new hot tearing criterion addressing both inadequate melt feeding and excessive deformation at relatively high solid fractions. The viscoplastic deformation in the mushy zone is addressed by a model in which the coherent mush is considered as a porous medium saturated with liquid. The thermal straining of the mush is accounted for by a recently developed model taking into account that there is no thermal strain in the mushy zone at low solid fractions because the dendrites then are free to move in the liquid, and that the thermal strain in the mushy zone tends toward the thermal strain in the fully solidified material when the solid fraction tends toward one. In the present work, the authors determined how variations in the parameters of the constitutive equation for thermal strain influence the hot tearing susceptibility calculated by the criterion. It turns out that varying the parameters in this equation has a signiicant effect on both liquid pressure drop and viscoplastic strain, which are key parameters in the hot tearing criterion. However, changing the parameters in this constitutive equation will result in changes in the viscoplastic strain and the liquid pressure drop that have opposite effects on the hot tearing susceptibility. The net effect on the hot tearing susceptibility is thus small.     

Two-phase modeling of mushy zone parameters associated with hot tearing

A two-phase continuum model for an isotropic mushy zone is presented. The model is based upon the general volume-averaged conservation equations, and quantities associated with hot tearing are included, i.e., after-feeding of the liquid melt due to solidification shrinkage is taken into account as well as thermally induced deformation of the solid phase. The model is implemented numerically for a one-dimensional model problem with some similarities to the aluminium direct chill (DC) casting process. The variation of some key parameters that are known to influence the hot-tearing tendency is then studied. The results indicate that both liquid pressure drop due to feeding difficulties and tensile stress caused by thermal contraction of the solid phase are necessary for the formation of hot tears. Based upon results from the one-dimensional model, it is furthermore concluded that none of the hot-tearing criteria suggested in the literature are able to predict the variation in hot-tearing susceptibility resulting from a variation in all of the following parameters: solidification interval, cooling contraction of the solid phase, casting speed, and liquid fraction at coherency.     

Modeling of macrosegregation caused by volumetric deformation in a coherent mushy zone

A two-phase volume-averaged continuum model is presented that quantifies macrosegregation formation during solidification of metallic alloys caused by deformation of the dendritic network and associated melt flow in the coherent part of the mushy zone. Also, the macrosegregation formation associated with the solidification shrinkage (inverse segregation) is taken into account. Based on experimental evidence established elsewhere, volumetric viscoplastic deformation (densification/dilatation) of the coherent dendritic network is included in the model. While the thermomechanical model previously outlined (M. M’Hamdi, A. Mo, and C.L. Martin: Metall. Mater. Trans. A, 2002, vol. 33A, pp. 2081–93) has been used to calculate the temperature and velocity fields associated with the thermally induced deformations and shrinkage driven melt flow, the solute conservation equation including both the liquid and a solid volume-averaged velocity is solved in the present study. In modeling examples, the macrosegregation formation caused by mechanically imposed as well as by thermally induced deformations has been calculated. The modeling results for an Al-4 wt pct Cu alloy indicate that even quite small volumetric strains (≈2 pct), which can be associated with thermally induced deformations, can lead to a macroscopic composition variation in the final casting comparable to that resulting from the solidification shrinkage induced melt flow. These results can be explained by the relatively large volumetric viscoplastic deformation in the coherent mush resulting from the applied constitutive model, as well as the relatively large difference in composition for the studied Al-Cu alloy in the solid and liquid phases at high solid fractions at which the deformation takes place.     

Thermomechanical analysis of direct chill casting using finite element method

The transient nature of the start-up phase is the most critical phase in the direct chill (DC) casting during which the quality of the ingot is questioned. The hot crack and cold crack are the two major problems in the DC casting which originate during and after the solidification. In this work, the thermal, metallurgical, and the mechanical fields of DC casting are modeled. The attention is focused on the mushy state of alloy where the chances are high for the hot tearing. The heat conduction and metallurgical phase-change phenomenon are modeled together in a strongly coupled manner. An isothermal staggered approach is followed to couple the thermal and mechanical parts within a time step. Finite element method is used to discretize the thermal and mechanical field equations. A temperature-based fixed grid method is followed to incorporate the latent heat. The mushy state of alloy is characterized through the Norton-Hoff viscoplastic law and the solid phase is modeled through the Garafalo law. An axisymmetric round billet is simulated. The casting material is considered as AA1201 aluminum alloy. It is found that all the components of stress and viscoplastic strain are maximum at the billet center. Further, the start-up phase stresses and strains are always higher than the steady state phase. Therefore, the chances of hot crack formation are higher during the start-up phase and specifically at the billet center. It is proved that through the ramping procedure, the vulnerability of start-up phase can be lowered.     

Modeling of De-cohesion and the Initiation of Hot Tearing in Coherent Mushy Zones of Metallic Alloys

The initiation of a hot tear in the coherent mushy zone of metallic alloys is associated commonly with the opening up of the solid skeleton caused by thermally induced deformation. A previously established constitutive model for the continuum modeling of coherent mushy zones has been further developed in the current study to address the opening up, or decohesion, of the solid skeleton associated with volumetric tensile deformation. Whereas the original model accounts for the cohesion of the solid skeleton caused by the deformation by means of an internal variable, an additional internal variable accommodating the decohesion has been introduced in the new model. The modeled decohesion is interpreted as the initiation of a hot tear.     

Tensile properties of the semi-solid state in solidifying aluminum alloys

Hot tearing is one of the most serious defects encountered in aluminum alloy castings. During solidification of aluminum alloys, the localized region of solidified alloys is submitted to thermally induced strains that can be lead to severe solidification defects, such as shrinkage porosity and hot tearing. The formation of hot tearing is related to the development of local stress or thermal strains. It is such a complicated phenomenon that a full understanding has not been achieved yet, though it has been extensively investigated for decades. Therefore, in order to further understand this complicated phenomenon and establish the mathematical models of hot tearing, it is necessary to obtain the accurate mechanical property data in the mushy zone of alloys. In response to the demand for this purpose, a newly experimental apparatus has been used to perform tensile measurements of aluminum alloys during solidification. Therefore, the tensile properties measurements of the mushy zone in A356 alloy have been carried out. The fracture surfaces and microstructures of the hot tearing samples have been examined by optical microscopy and scanning electron microscopy. The results show that the yield stresses are increasing with the increase of the solid fraction. When the solid fraction is close to one, they will keep stable to a certain value. According to the analysis, the yield stresses will change with the evolution of solid fraction, which is in accordance with the Boltzmann Function.     

Physical modeling of the deformation mechanisms of semisolid bodies and a mechanical criterion for hot tearing

The mechanical response of a semisolid body to an applied, uniaxial strain rate has been expressed as a function of strain by modifying an existing analysis based on an idealized representation of the microstructure. An existing mechanical criterion for hot tearing of the semisolid body has been adapted to the deformation mechanisms. The resulting hot tearing model shows that the strength of the body depends on the strain, the viscosity of the intergranular fluid, the solid fraction, the isothermal compressibility of the fluid, the surface tension of the liquid, the limiting liquid-film thickness for viscous flow and a parameter m, which describes microstructure. The effect of each parameter on the mechanical response and the onset of hot tearing has been examined for ranges of values relevant to aluminum alloys and the direct-chill (DC) casting process. The parameter testing has shown that the mechanical response predicted by the model agrees well with some experimental data for both the mechanisms of fracture and the parameters that govern the process. An adjustment of unknown model parameters to experimental data would permit use of the model as a constitutive law and a fracture criterion for numerical modeling of hot tearing during the solidification of Al alloys by DC casting.     

Numerical Investigation of Shell Formation in Thin Slab Casting of Funnel-Type Mold

The key issue for modeling thin slab casting (TSC) process is to consider the evolution of the solid shell including fully solidified strand and partially solidified dendritic mushy zone, which strongly interacts with the turbulent flow and in the meantime is subject to continuous deformation due to the funnel-type mold. Here an enthalpy-based mixture solidification model that considers turbulent flow [Prescott and Incropera, ASME HTD, 1994, vol. 280, pp. 59–69] is employed and further enhanced by including the motion of the solidifying and deforming solid shell. The motion of the solid phase is calculated with an incompressible rigid viscoplastic model on the basis of an assumed moving boundary velocity condition. In the first part, a 2D benchmark is simulated to mimic the solidification and motion of the solid shell. The importance of numerical treatment of the advection of latent heat in the deforming solid shell (mushy zone) is specially addressed, and some interesting phenomena of interaction between the turbulent flow and the growing mushy zone are presented. In the second part, an example of 3D TSC is presented to demonstrate the model suitability. Finally, techniques for the improvement of calculation accuracy and computation efficiency as well as experimental evaluations are also discussed.     

A mathematical model for surface segregation in aluminum direct chill casting

A two-dimensional mathematical model for the development of macrosegregation at and close to the ingot surface during direct chill (DC) casting of aluminum rolling sheet ingots is presented. The model accounts for macrosegregation caused by exudation of interdendritic melt and macrosegregation associated with solidification shrinkage. Equations for the conservation of energy, solute, momentum, and mass during the stationary phase of the process are solved numerically by a finite-element method. The solution domain corresponds to a vertical cross section at the middle of the longest side of the slab. The main simplifications in the modeling concept are to assume that the solid in the mushy zone moves with the casting speed, and that the alloy is binary and solidifies according to the lever rule. The thickness and solute concentration of the surface layer and the macrosegregation close to the surface are calculated, and modeling results are compared to measurements on full-scale castings.     

Effects of alloy composition and casting speed on structure formation and hot tearing during direct-chill casting of Al-Cu alloys

Effects of casting speed and alloy composition on structure formation and hot tearing during direct-chill (DC) casting of 200-mm round billets from binary Al-Cu alloys are studied. It is experimentally shown that the grain structure, including the occurrence of coarse grains in the central part of the billet, is strongly affected by the casting speed and alloy composition, while the dendritic arm spacing is mostly dependent on the casting speed. The hot cracking pattern reveals the maximum hot-tearing susceptibility in the range of low-copper alloys (1 to 1.5 pct) and at high casting speeds (180 to 200 mm/min). The clear correlation between the amount of nonequilibrium eutectics (representing the reserve of liquid phase in the last stage of solidification) and hot tearing is demonstrated. A casting speed-copper concentration-hot-tearing susceptibility chart is constructed experimentally for real-scale DC casting. Computed dimensions of the solidification region in the billet are used to explain the experimentally observed structure patterns and hot cracking. Thermomechanical finite-element simulation of the solidifying billet was used as a tool for testing the applicability to DC casting of several hot-tearing criteria based on different principles. The results are compared to the experimentally observed hot tearing. It is noted that hot-tearing criteria that account for the dynamics of the process, e.g., strain rate, actual stress-strain situation, feeding rate, and melt flow, can be successfully used for the qualitative prediction of hot tearing.     

A 3-D numerical prediction of turbulent flow,heat transfer and solidification in a continuous slab caster for steel

This study describes the numerical modeling of three-dimensional coupled turbulent flow, heat transfer, and solidification in a continuous slab caster for stainless steel. The model uses generalized transport equations which are applicable to the liquid, mushy and solid regions within the caster. The turbulent characteristics in the melt pool and mushy region are accounted for using the low-Reynolds number k–ε turbulence model by Launder and Sharma. This version of the low-Reynolds number turbulence model is found to be more easily adaptable to the coupled flow and mushy region solidification caster problem compared to the standard high-Reynolds number and other low-Reynolds number turbulence models. The macroscopic solidification process itself is based on the enthalpy-porosity scheme. The governing transport equations are solved employing the primitive variables and using the control volume based finite-difference scheme on a staggered grid. The process variables considered are the casting speed and the inlet superheat of the melt. The effects of these process variables on the velocity and temperature distributions and on the extent of the solidification and mushy regions are reported and discussed. The numerical predictions of solidification profile are compared with the limited experimental data available in the literature, and very good agreement was found.     

Elimination of Hot Tears in Steel Castings by Means of Solidification Pattern Optimization

A methodology of how to exploit the Niyama criterion for the elimination of various defects such as centerline porosity, macrosegregation, and hot tearing in steel castings is presented. The tendency of forming centerline porosity is governed by the temperature distribution close to the end of the solidification interval, specifically by thermal gradients and cooling rates. The physics behind macrosegregation and hot tears indicate that these two defects also are dependent heavily on thermal gradients and pressure drop in the mushy zone. The objective of this work is to show that by optimizing the solidification pattern, i.e., establishing directional and progressive solidification with the help of the Niyama criterion, macrosegregation and hot tearing issues can be both minimized or eliminated entirely. An original casting layout was simulated using a transient three-dimensional (3-D) thermal fluid model incorporated in a commercial simulation software package to determine potential flaws and inadequacies. Based on the initial casting process assessment, multiobjective optimization of the solidification pattern of the considered steel part followed. That is, the multiobjective optimization problem of choosing the proper riser and chill designs has been investigated using genetic algorithms while simultaneously considering their impact on centerline porosity, the macrosegregation pattern, and primarily on hot tear formation.     

Finite element method simulation of mushy zone behavior during direct-chill casting of an Al-4.5 pct Cu alloy

In this article, the stresses, strains, sump depth, mushy zone length, and temperature fields are calculated through the simulation of the direct-chill (DC) casting process for a round billet by using a finite-element method (FEM). Focus is put on the mushy zone and solid region close to it. In the center of the billet, circumferential stresses and strains (which play a main role in hot cracking) are tensile close to the solidus temperature, whereas they are compressive near the surface of the billet. The stresses, strains, depth of sump, and length of mushy zone increase with increasing casting speed. They are maximum in the start-up phase and are reduced by applying a ramping procedure in the start-up phase. Stresses, strains, depth of sump, and length of mushy zone are highest in the center of the billet for all casting conditions considered.     

Modeling of solute redistribution in the mushy zone during solidification of aluminum-copper alloys

A mathematical model has been established to predict the formation of macrosegregation for a unidirectional solidification of aluminum-copper alloys cooled from the bottom. The model, based on the continuum formulation, allows the calculation of transient distributions of temperature, velocity, and species in the solidifying alloy caused by thermosolutal convection and shrinkage-induced fluid flow. Positive segregation in the casting near the bottom (inverse segregation) is found, which is accompanied by a moving negative-segregated mushy zone. The effects of shrinkage-induced fluid flow and solute diffusion on the formation of macrosegregation are examined. It is found that the redistribution of solute in the solidifying alloy is caused by the flow of solute-rich liquid in the mushy zone due to solidification shrinkage. A higher heat-extraction rate at the bottom increases the solidification rate, decreasing the size of the mushy zone, reducing the flow of solute-rich liquid in the mushy zone and, as a result, lessening the severity of inverse segregation. Comparisons between the theoretical predictions from the present study and previous modeling results and available experimental data are made, and good agreements are obtained.     

The reheating-cooling method: A technique for measuring mechanical properties in the nonequilibrium mushy zones of alloys

The mushy zone of an alloy is in nonequilibrium during solidification. The mechanical properties of alloys in this nonequilibrium mushy zone, especially at small liquid fractions, are closely related to the formation of hot tears during the solidification of castings. It is difficult to measure the mechanical properties in the nonequilibrium mushy zones of alloys at a small liquid fraction, as the liquid fraction decreases rapidly during heating and during the isothermal hold needed to measure mechanical properties, due to backdiffusion in the solid. This article describes a new experimental method for determining mechanical properties in the nonequilibrium mushy zones of alloys. Initial results indicate that the method is better than traditional methods in capturing the brittle nature of alloys at temperatures close to the nonequilibrium solidus temperature.     

双辊铸轧过程轧制力计算的研究

 在对熔池内金属凝固和变形的机理分析的基础上,将铸轧区域分为2个求解区域。采用流体力学中Navier Stokes方程并引入流函数,对液相区、糊状区的流变特性进行分析并建立相应的速度场,同时引入固相百分率计算模型和粘度计算模型,根据速度边界条件推导出该区域单位压力分布解析式。对于凝固区的铸轧力建模仍沿用传统热轧模型。利用上述模型进行铸轧力计算,计算结果与实测结果吻合较好,为建立双辊铸轧过程铸轧力控制策略的提供了有力的支撑。     

Rheological behavior of Al-Mg-Si-Cu alloys in the mushy state obtained by partial remelting and partial solidification at high cooling rate

This work investigates the mechanical behavior of two aluminum alloys in the mushy state, the alloy AA6056 and an alloy based on mixing AA6056 and AA4047. These alloys have been studied to give insight into the susceptibility to hot tearing, which occurs during laser welding of AA6056 with 4047 filler wire. Two types of isothermal tensile tests have been conducted: (1) tests during partial remelting and (2) tests after partial solidification at a high cooling rate. Results show that the maximum tensile stress increases with increasing solid volume fraction. Both materials exhibit visco-plastic behavior for solid fractions in the range 0.9 to 0.99, except for a critical solid fraction of 0.97, where the semisolid material also shows minimum ductility. The stress levels observed for the remelting experiments are larger than those found for partial solidification experiments at the same solid fraction due to the influence of the microstructure. The influence of temperature and strain rate on the maximum stress is described by using a constitutive law that takes into account the fraction of grain boundaries wetted by the liquid.