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.     

Relationship between tensile and shear strengths of the mushy zone in solidifying aluminum alloys

Strength development in the mushy zone during solidification of three aluminum alloys (Al-4 wt pct Cu, Al-7 wt pct Si-1 wt pct Cu, and Al-7 wt pct Si-4 wt pct Cu) has been measured with two different techniques—horizontal tensile testing and direct shear cell testing. The strength results from the two methods correspond with one another to a much higher degree than suggested by the results presented in the literature. Tensile strength starts to develop at the maximum packing solid fraction, confirmed by the shear strength measurements. The maximum packing fraction represents the point where the internal network structure of the mushy zone is established and ligaments of the network must be broken to rearrange the dendrites. The data indicate a converging trend of the shear and tensile strength at high solid fractions, therefore indicating that the deformation mechanisms are also becoming similar. The results presented in this article suggest that it is possible to develop constitutive equations for the mechanical properties of the mushy zone over the entire solid fraction regime, i.e., from coherency to complete solidification. These equations could be used for the prediction of stress development as well as defect formation.     

Thermosolutal convection during dendritic solidification of alloys: Part II. Nonlinear convection

A mathematical model of thermosolutal convection in directionally solidified dendritic alloys has been developed that includes a mushy zone underlying an all-liquid region. The model assumes a nonconvective initial state with planar and horizontal isotherms and isoconcentrates that move upward at a constant solidification velocity. The initial state is perturbed, nonlinear calculations are performed to model convection of the liquid when the system is unstable, and the results are compared with the predictions of a linear stability analysis. The mushy zone is modeled as a porous medium of variable porosity consistent with the volume fraction of, interdendritic liquid that satisfies the conservation equations for energy and solute concentrations. Results are presented for systems involving lead-tin alloys (Pb-10 wt pct Sn and Pb-20 wt pct Sn) and show significant differences with results of plane-front solidification. The calculations show that convection in the mushy zone is mainly driven by convection in the all-liquid region, and convection of the interdendritic liquid is only significant in the upper 20 pct of the mushy zone if it is significant at all. The calculated results also show that the systems are stable at reduced gravity levels of the order of 10⁻⁴ g ₀ (g ₀=980 cm·s⁻¹) or when the lateral dimensions of the container are small enough, for stable temperature gradients between 2.5≤G _l≤100 K·cm⁻¹ at solidification velocities of 2 to 8 cm·h⁻¹.     

Grain refinement induced by electromagnetic stirring: A dendrite fragmentation criterion

The influence of electromagnetic stirring (EMS) on grain refinement has been studied for two copper-base alloys (Cu-1 wt pct Ni-1 wt pct Pb-0.2 wt pct P and Cu-4 wt pct Zn-4 wt pct Sn-4 wt pct Pb) solidified in a Bridgman furnace. Metallographic inspection of the specimens, temperature measurements during solidification, and numerical simulations performed with CALCOSOFT revealed that the efficiency of EMS is strongly dependent upon the penetration of the liquid in the mushy zone and therefore upon the position of the convection vortices with respect to the liquidus front. In particular, the low-concentration alloy could be grain refined only at high power and when the coil was moved close to the liquidus front. These results were analyzed on the basis of a dendrite fragmentation criterion similar to Flemings’ criterion for local remelting of the mushy zone. Considering that the component of the fluid flow velocity along the thermal gradient, , must be larger than the casting speed, V _c , dendrite fragmentation occurs if

The origin of freckles in unidirectionally solidified castings

The origin of freckles during unidirectional solidification is studied in a transparent, low melting model system, 30 wt pct NH₄C1-H₂O. In 30NH₄Cl-H₂O, freckles are caused by upward flowing liquid jets in the mushy zone. The jets erode the mushy zone causing localized segregation and start new grains by producing dendritic debris. It is shown that the jets observed in 30NH₄C1-H₂O are free convection resulting from a density inversion in the mushy zone. A comparison of driving force, thermal transport effects and solute transport effects in 30NH₄C1-H₂O and metallic systems shows that jets are possible in metallic alloys where light elements segregate normally or heavy elements segregate inversely. It is concluded that freckles in unidirectionally solidified castings and vacuum consumable-electrode ingots are caused by convective jets. It is shown that the tendency to freckle is greatest in alloys with a large density inversion, high thermal diffusivity, low solute diffusivity, and low viscosity. For a given alloy, the driving force for freckling is proportional to the inverse square of the thermal gradient. Erosion by the jets is decreased by increasing the thermal gradient and growth rate. The location of freckles is influenced by mushy zone curvature. Formerly Research Assistant at the Advanced Materials Research and Development Laboratory     

Structure and mechanical properties of unidirectionally solidified Fe-Cr-C and Fe-Cr-X-C alloys

In this work four different microstructures were obtained by unidirectional solidification of Fe-Cr-C eutectic alloys. Conditions for zone coupled growth were determined in alloys containing approximately 30 wt pct chromium. Furthermore, mechanical testing indicated that the maximum strength was exhibited by Fe-30Cr-C alloys with cerium or titanium additions. These alloys had the largest volume fraction of eutectic fibers and their ultimate tensile strength was of the order of 3250 MPa. Correlations between the rate of crystal growth(u) and fiber spacing (λ) or tensile strength(Rm) were found and an expression of the typeRm = Aλ^-b2 was obtained whereb ₂ varied between 0.283 and 0.685. Finally, manganese or chromium (35 wt pct Cr) additions did not lead to appreciable improvements in composite strength for this alloy system.     

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.     

Mushy zone morphology during directional solidification of Pb-5.8 wt pct Sb alloy

The Pb-5.8 wt pct Sb alloy was directionally solidified with a positive thermal gradient of 140 K cm⁻¹ at a growth speed ranging from 0.8 to 30 μm s⁻¹, and then it was quenched to retain the mushy zone morphology. The morphology of the mushy zone along its entire length has been characterized by using a serial sectioning and three-dimensional image reconstruction technique. Variation in the cellular/dendritic shape factor, hydraulic radius of the interdendritic region, and fraction solid along the mushy zone length has been studied. A comparison with predictions from theoretical models indicates that convection remarkably reduces the primary dendrite spacing while its influence on the dendrite tip radius is not as significant.     

Effect of Grain Refinement on the Dendrite Coherency Point during Solidification of the A319 Aluminum Alloy

Dendrite coherency is important to the formation of the solidification structure and castability of alloys. The effects of grain refinement on the dendrite coherency in A319 aluminum alloy have been studied using the two-thermocouple thermal analysis technique in the solidifying sample. The fraction solid at the dendrite coherency point ( f_s^\textDCP f_{s}^{\text{DCP}} ) in the A319 alloy increases with increasing Al-5Ti-1B grain refiner, and varies from 16 to 21 pct when the amount of Al-5Ti-1B in the alloy is in the range of 0 to 4.6 wt pct. The results also indicate that the grain refinement increases the temperature interval of coherency (T _N – T _DCP) and coherency time (t _DCP), and it can postpone dendrite coherency. These changes were interpreted based on the dendrite growth rate, the growth restriction factor, and the microstructure.     

Determination of the melting and solidification characteristics of solders using differential scanning calorimetry

Differential scanning calorimetry (DSC) is used in the present study to determine the onset temperature of phase transformation and the enthalpy of fusion of various solder alloys. The solders studied are Sn-Pb, Sn-Bi, Ag-Sn, In-Ag, and Sn-Pb-Bi alloys. Very notable undercooling, such as 35 °C, is observed in the solidification process; however, a superheating effect is not as significant in the heating process. Besides the direct measurements of reaction temperature and heat of fusion, the fraction solid vs temperature has also been determined using a DSC coupled with a mathematical-model method. The heating and cooling curves of the solders are first determined using DSC. By mathematically modeling the heat transfer of the DSC cells, the heat evolution and absorption can be calculated, and then the melting and solidification curves of the solder alloys are determined. The three ternary alloys, Sn-35 wt pct Pb-10 wt pct Bi, Sn-45 wt pct Pb-10 wt pct Bi, and Sn-55 wt pct Pb-10 wt pct Bi, displayed similar DSC cooling curves, which had three reaction peaks. However, the solid fractions of the three alloys at the same temperature in the semisolid state, which had been determined quantitatively using the DSC coupled with a mathematical method, were different, and their primary solidification phases were also different.     

The energy and solute conservation equations for dendritic solidification

The energy equation for solidifying dendritic alloys that includes the effects of heat of mixing in both the dendritic solid and the interdendritic liquid is derived. Calculations for Pb-Sn alloys show that this form of the energy equation should be used when the solidification rate is relatively high and/or the thermal gradients in the solidifying alloy are relatively low. Accurate predictions of transport phenomena in solidifying dendritic alloys also depend on the form of the solute conservation equation. Therefore, this conservation equation is derived with particular consideration to an accounting of the diffusion of solute in the dendritic solid. Calculations for Pb-Sn alloy show that the distribution of the volume fraction of interdendritic liquid (g _L) in the mushy zone is sensitive to the extent of the diffusion in the solid. Good predictions ofg _L are necessary, especially when convection in the mushy zone is calculated. Formerly Research Associate, The University of Arizona. Formerly Graduate Student, The University of Arizona.     

Macrosegregation during steady-state arrayed growth of dendrites in directionally solidified Pb-Sn alloys

Macrosegregation along the length of the directionally solidified samples is produced when Pb-Sn alloys (10 to 58 wt pct Sn) are directionally solidified in a positive thermal gradient (melt on top, solid below, and gravity pointing down) with steady-state dendritic arrayed morphology (the length of the mushy zone, much smaller than the initial length of the melt column, remaining nearly constant during growth). The extent of the macrosegregation increases with increasing tin content, becomes maximum for 33.3 wt pct Sn, and decreases with further increase in tin content. The intensity of the interdendritic thermosolutal convection responsible for the longitudinal macrosegregation can be represented by the effective partition coefficient(k _E), anempirical parameter obtained from the dependence of the longitudinal macrosegregation on fraction distance solidified. The extent of the macrosegregation appears to be related to a parameter,x03BB; ² ₁f_E(C_E−C_t)}, where A, is the primary dendrite spacing,f _Eis the volume fraction of the interdendritic melt, andC _EandC _tare the eutectic composition and the melt composition ahead of the dendrite tips, respectively.     

Triaxial Compression on Semi-solid Alloys

Multi-axial compression of the mushy zone occurs in various pressurized casting processes. Here, we present a drained triaxial compression apparatus for semi-solid alloys that allow liquid to be drawn into or expelled from the sample in response to isotropic or triaxial compression. The rig is used to measure the pressure-dependent flow stress and volumetric response during isothermal triaxial compression of globular semi-solid Al-15 wt pct Cu at 70 to 85 vol pct solid. Analysis of the stress paths and the stress–volume data show that the combination of the solid fraction and mean effective pressure determines whether the material undergoes shear-induced dilation or contraction. The results are compared with the critical state soil mechanics (CSSM) framework and the similarities and differences in behavior between equiaxed semi-solid alloys and soils are discussed.

     

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.     

Constitutive relationships for AlZnMg, AlZnMgCr, and AlZnMgZr alloys

The effects of zinc, magnesium, chromium, and zirconium on the steady-state flow stress during hot working of both as-cast and homogenized AlZnMg(Cr/Zr) alloys were determined by means of torsion testing. The equivalent strain rates varied between 0.01/s and 10/s and the temperatures ranged from 450°C to 560°C. The zinc and magnesium concentration varied from 4.5 to 7.5 wt pct and from 0.8 to 1.8 wt pct, respectively. In addition, alloys containing typically 0.15 wt pct zirconium or 0.20 wt pct chromium were investigated. Magnesium, zirconium, and chromium were found to increase the flow stress, whereas zinc had practically no effect. The flow stress in the homogenized material was in most cases higher than in the as-cast material. Fitting of the coefficients in the hyperbolic sine constitutive equation of the experimental results showed that some of the coefficients could be related to concentrations of magnesium and zinc in solid solution, whereas others might be regarded as constants. The following relationship was determined between the coefficients α andn and the magnesium and zinc concentration: α=a·[Mg] ^b andn=c·[Mg] ^d +e·[Zn]+f. The coefficientsa, b, c, d, e, andf were determined by fitting of these relationships to the experimental data. The steady-state flow stress calculated by means of the constitutive equations was in good agreement with the experimental steady-state flow stress.     

Constitutive relationships for AlZnMg, AlZnMgCr, and AlZnMgZr alloys

The effects of zinc, magnesium, chromium, and zirconium on the steady-state flow stress during hot working of both as-cast and homogenized AlZnMg(Cr/Zr) alloys were determined by means of torsion testing. The equivalent strain rates varied between 0.01/s and 10/s and the temperatures ranged from 450 °C to 560 °C. The zinc and magnesium concentration varied from 4.5 to 7.5 wt pct and from 0.8 to 1.8 wt pct, respectively. In addition, alloys containing typically 0.15 wt pct zirconium or 0.20 wt pct chromium were investigated. Magnesium, zirconium, and chromium were found to increase the flow stress, whereas zinc had practically no effect. The flow stress in the homogenized material was in most cases higher than in the as-cast material. Fitting of the coefficients in the hyperbolic sine constitutive equation to the experimental results showed that some of the coefficients could be related to concentrations of magnesium and zinc in solid solution, whereas others might be regarded as constants. The following relationship was determined between the coefficients α and n and the magnesium and zinc concentration: α=a·[Mg] ^b and n=c·[Mg] ^d +e·[Zn]+f. The coefficients a, b, c, d, e, and f were determined by fitting of these relationships to the experimental data. The steady-state flow stress calculated by means of the constitutive equations was in good agreement with the experimental steady-state flow stress.     

A melting and solidification study of alloy 625

The melting and solidification behavior of Alloy 625 has been investigated with differential thermal analysis (DTA) and electron microscopy. A two-level full-factorial set of chemistries involving the elements Nb, C, and Si was studied. DTA results revealed that all alloying additions decreased the liquidus and solidus temperatures and also increased the melting temperature range. Terminal solidification reactions were observed in the Nb-bearing alloys. Solidification microstructures in gastungsten-arc welds were characterized with transmission electron microscopy (TEM) techniques. All alloys solidified to an austenitic (γ) matrix. The Nb-bearing alloys terminated solidification by forming various combinations of γ/MC(NbC), γ/Laves, and γ/M₆C eutectic-like constituents. Carbon additions (0.035 wt pct) promoted the formation of the γ/MC(NbC) constituent at the expense of the γ/Laves constituent. Silicon (0.4 wt pct) increased the formation of the yJLaves constituent and promoted formation of the γ/M₆C carbide constituent at low levels (<0.01 wt pct) of carbon. When both Si (0.4 wt pct) and C (0.035 wt pct) were present, the γ/MC(NbC) and γ/Laves constituents were observed. Regression analysis was used to develop equations for the liquidus and solidus temperatures as functions of alloy composition. Partial derivatives of these equations taken with respect to the alloying variables (Nb, C, Si) yielded the liquidus and solidus slopes t(m _L , m _S ) for these elements in the multicomponent system. Ratios of these liquidus to solidus slopes gave estimates of the distribution coefficients (k) for these same elements in Alloy 625.     

Macrosegregation during steady-state arrayed Growth of Dendrites in Directionally Solidified Pb-Sn Alloys

Macrosegregation along the length of the directionally solidified samples is produced when Pb-Sn alloys (10 to 58 wt pct Sn) are directionally solidified in a positive thermal gradient (melt on top, solid below, and gravity pointing down) with steady-state dendritic arrayed morphology (the length of the mushy zone, much smaller than the initial length of the melt column, re- maining nearly constant during growth). The extent of the macrosegregation increases with increasing tin content, becomes maximum for 33.3 wt pct Sn, and decreases with further in- crease in tin content. The intensity of the interdendritic thermosolutal convection responsible for the longitudinal macrosegregation can be represented by the effective partition coefficient (k _ε), anempirical parameter obtained from the dependence of the longitudinal macrosegregation on fraction distance solidified. The extent of the macrosegregation appears to be related to a parameter, {λ ²₁ ƒ_E(C _E -C _t)}, where λ₁, is the primary dendrite spacing,f _E is the volume fraction of the interdendritic melt, andC _E andC _t, are the eutectic composition and the melt composition ahead of the dendrite tips, respectively.

     

The impact of cooling rates on the microstructure of Al-U alloys

The impact of cooling rates on the microstructure of Al-U alloys was studied by optical, scanning electron, and transmission electron microscopy. A variety of solidification techniques were employed to obtain cooling rates ranging between 3 × 10⁻² and 10⁶ K/s. High-purity uranium (99.9 pct) and high-purity aluminum (99.99 pct), or “commercially pure” type Al-1050 aluminum alloys were used to prepare Al-U alloys with U concentration ranging between 3 and 22 wt pct. The U concentration at which a coupled eutectic growth was observed depends on the cooling rates imposed during solidification and ranged from 13.8 wt pct for the slower cooling rates to more than 22 wt pct for the fastest cooling rates. The eutectic morphology and its distribution depends on the type of aluminum used in preparing the alloys and on the cooling rates during solidification. The eutectic in alloys prepared from pure aluminum was evenly distributed, while for those prepared from Al-1050, the eutectic was unevenly distributed, with eutectic colonies of up to 3 mm in diameter. Two lamellar eutectic structures were observed in alloys prepared from pure aluminum containing more than 18 wt pct U, which solidified by cooling rates of about 10 K/s. One structure consisted of the stable eutectic between UAl₄ and Al lamella. The other structure consisted of a metastable eutectic between UAl₃ and Al lamella. At least three different eutectic morphologies were observed in alloys prepared from Al-1050.     

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.