Two-phase modeling directed toward hot tearing formation in aluminum direct chill casting

The two-phase mass and momentum conservation equations governing shrinkage-driven melt flow and thermally induced deformation are formulated for the aluminum direct chill (DC) casting process. Two main mechanisms associated with hot tearing formation during solidification and subsequent cooling are thus addressed simultaneously in the same mathematical model. The approach unifies the two-phase mushy zone model outlined by Farup and Mo, the constitutive relations that treat the mushy zone as a viscoplastic porous medium saturated with liquid outlined by Martin et al., and the “classical” mechanics approach to thermally induced deformations in solid (one-phase) materials using the linear kinematics approximation. A temperature field and a unique solidification path are considered as input to the model. The governing equations are solved for a one-dimensional (1-D) situation with some relevance to the DC casting process. The importance of taking into account the transfer of momentum from the liquid phase to the solid phase is then demonstrated through modeling examples. Furthermore, the modeling results indicate that the constitutive law governing the viscoplastic behavior of the solid skeleton of the mushy zone should take into account that the solid skeleton can be compressed/dilated as well as stress space anisotropy. Calculated peak values for liquid pressure and solid stress turn out to correlate to the hot tearing susceptibility measured in casting trials in the sense that trials having the largest cracks are those for which the highest pressures and stresses are computed.     

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 for aluminum alloys

The parameters in a recently developed constitutive equation for macroscopic thermal strain in the mushy zone have been determined for the commercial alloys A356, AA2024, AA6061, and AA7075 in addition to an Al-4 wt pct Cu alloy. The constitutive equation for macroscopic thermal strain in the mushy zone reflects that there is no thermal strain in the solid part of the mushy zone at low solid fractions and that the thermal strain in the mushy zone approaches thermal strain in the fully solid material as the solid fraction increases toward 1. The development of thermal strain in the mushy zone is determined by combining experimentally measured contraction of a cast sample with thermomechanical stimulations. Experiments were performed at cooling rates in the range from 2 to 5.5 °C/s. The solid fractions when the tested alloys start to contract,g _s ^th, are in the range from 0.63 to 0.94. Grain refinement increasesg _s ^th for all the tested alloys. For most of the tested alloys the thermal strain in the mushy zone increases rapidly to the same level as thermal strain in fully solid material once the solid fraction becomes higher thang _s ^th.     

High Temperature Mechanical Properties of Micro‐alloyed Carbon Steel in the Mushy Zone

The tensile strength of a micro‐alloyed carbon steel in the mushy zone is investigated as well as the influence of temperature, strain rate and thermal histories. The parameters varied comprised thermal histories of both solidifying and reheating type and strain rates from 1 × 10^?4 to 1 × 10^?2 s^?1 were tested using the physical simulation system Gleeble‐1500D. The measured results showed that tensile strength decreased with increasing test temperature in the mushy zone. The tensile strength with solidified type thermal history was lower than that with the reheated type, and the difference of tensile strength derived from the two thermal histories decreased with increasing cooling rate and increasing temperature. The tensile strength decreased with decreasing strain rate in the mushy zone. A viscoplastic constitutive equation with variables of deformation temperature, stress, strain rate, solid fraction and deformation activation energy was constructed. Moreover, the measured thermo‐mechanical parameters, such as zero strength temperature (ZST) and zero ductility temperature (ZDT), were consistent with those predicted according to the corresponding solid fractions.     

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.     

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.     

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.     

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.     

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.     

Simulation of Stresses during Casting of Binary Magnesium-Aluminum Alloys

A viscoplastic stress model is used to predict contraction forces measured during casting of two binary Mg-Al alloys. Force measurements from castings that did not hot tear, together with estimates from data found in the literature, are used to obtain the high-temperature mechanical properties needed in the stress model. In the absence of hot tearing, the simulation results show reasonably good agreement with the measurements. It is found that coherency of the semisolid mush starts at a solid fraction of about 0.5 and that the maximum tensile strength for the Mg-1 and 9 wt pct Al alloys at their final solidification temperatures is 1.5 and 4 MPa, respectively. In the presence of hot tearing, the measured stresses are generally overpredicted, which is attributed to the lack of a fracture model for the mush. Based on the comparison of measured and predicted stresses, it is also shown that coupling of the stress model to feeding flow and macrosegregation calculations is needed in order to accurately predict stresses in the presence of hot tearing.     

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.     

An experimental study of deformation of a columnar dendritic mushy zone using a transparent succinonitrile-acetone alloy

The deformation of a directionally solidified columnar dendritic mushy zone in a transparent succinonitrile-acetone (SCN-ACE) alloy has been studied expermentally. In addition to solidifying dendritically like a metal alloy, this alloy also has mechanical properties that are similar to those of metals near the melting point. The experiments are relevant, for example, to the deformation of a partially solidified strand during continuous casting of steel slabs. A test cell was designed which allows for directional solidification of the alloy and controlled compression of the solid-liquid mush which forms. Measurements during solidification and deformation include temperatures, interface positions, local displacements of the solid skeleton in the mush, and liquid concentrations. Results are presented for a range of initial test-cell thicknesses, deformation amounts, and deformation start times. The measurements are suitable for validation of future models.     

Simulation of Semi-Solid Material Mechanical Behavior Using a Combined Discrete/Finite Element Method

As a necessary step toward the quantitative prediction of hot tearing defects, a three-dimensional stress–strain simulation based on a combined finite element (FE)/discrete element method (DEM) has been developed that is capable of predicting the mechanical behavior of semisolid metallic alloys during solidification. The solidification model used for generating the initial solid–liquid structure is based on a Voronoi tessellation of randomly distributed nucleation centers and a solute diffusion model for each element of this tessellation. At a given fraction of solid, the deformation is then simulated with the solid grains being modeled using an elastoviscoplastic constitutive law, whereas the remaining liquid layers at grain boundaries are approximated by flexible connectors, each consisting of a spring element and a damper element acting in parallel. The model predictions have been validated against Al-Cu alloy experimental data from the literature. The results show that a combined FE/DEM approach is able to express the overall mechanical behavior of semisolid alloys at the macroscale based on the morphology of the grain structure. For the first time, the localization of strain in the intergranular regions is taken into account. Thus, this approach constitutes an indispensible step towards the development of a comprehensive model of hot tearing.     

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.     

Mechanical Behavior of AA6061 Aluminum in the Semisolid State Obtained by Partial Melting and Partial Solidification

The tensile properties of a 6061 aluminum alloy have been studied in the semisolid state at large solid fractions. The tests have been carried out either after a partial melting treatment or after partial solidification. Results show the following: (1) the mechanical behavior depends on the liquid-phase distribution and, therefore, on the way the semisolid state has been achieved (melting or solidification); (2) there is a critical solid fraction range where the semisolid alloy is relatively brittle; and (3) the mushy alloy exhibits viscoplastic behavior with the occurrence of micro-superplasticity at low strain rate. Modeling of this behavior is carried out by considering either the area fraction of grain boundaries wetted by the liquid or a cohesion parameter of the solid phase, which depends on solid fraction and thermal treatment.     

Effects of Recovery Behavior and Strain-Rate Dependence of Stress–Strain Curve on Prediction Accuracy of Thermal Stress Analysis During Casting

Recovery behavior (recovery) and strain-rate dependence of the stress–strain curve (strain-rate dependence) are incorporated into constitutive equations of alloys to predict residual stress and thermal stress during casting. Nevertheless, few studies have systematically investigated the effects of these metallurgical phenomena on the prediction accuracy of thermal stress in a casting. This study compares the thermal stress analysis results with in situ thermal stress measurement results of an Al-Si-Cu specimen during casting. The results underscore the importance for the alloy constitutive equation of incorporating strain-rate dependence to predict thermal stress that develops at high temperatures where the alloy shows strong strain-rate dependence of the stress–strain curve. However, the prediction accuracy of the thermal stress developed at low temperatures did not improve by considering the strain-rate dependence. Incorporating recovery into the constitutive equation improved the accuracy of the simulated thermal stress at low temperatures. Results of comparison implied that the constitutive equation should include strain-rate dependence to simulate defects that develop from thermal stress at high temperatures, such as hot tearing and hot cracking. Recovery should be incorporated into the alloy constitutive equation to predict the casting residual stress and deformation caused by the thermal stress developed mainly in the low temperature range.