Simulation of Microsegregation in Multicomponent Alloys During Solidification

A phase‐field model is applied to the simulation of microsegregation and microstructure formation during the solidification of multicomponent alloys. The results of the one‐dimensional numerical simulations show good agreement with those from the Clyne–Kurz equation. Phase‐field simulations of non‐isothermal dendrite growth are examined. Two‐dimensional computation results exhibit different dendrites in multicomponent alloys for different solute concentrations. Changes in carbon concentration appear to affect dendrite morphology. This is due to a larger concentration and a lower equilibrium partition coefficient for carbon. On the other hand, changes in phosphorus concentration affect the dendrites and interface velocity in multicomponent alloys during solidification when phosphorus content is increased from 10^?3 mol% P. With additional manganese, the solidification kinetics slow down; dendrite morphology, however, is not affected. The potential of the phase‐field model for applications pertaining to solidification has been demonstrated through the simulations herein.     

A new investigated method on hot tearing behavior in aluminum alloys

A new investigated method based on the applied forces for assessment on hot tearing behavior in aluminum alloys is introduced in the paper. In this method, molten metal is cast in the rod-shaped mold cavity. One side of the casting specimen is hooked by a steel bolt which restrains its free contraction and transfers the tensile forces during solidification. A steel threaded rod connected to a load cell which records the realtime measurement of the tensile forces during every experiment. Thermal history is monitored by k-type thermocouple. The data of the temperature and tensile forces are acquired by a data acquisition system. Through the use of this method, it is possible to estimate the initiation of hot tearing, its propagation and cracking during solidification. It is also obtained the critical tensile stress for hot tearing initiated and fractured. Experiment is conducted with A356 alloys to investigate the accuracy of the apparatus and modify its operating parameter. Accordingly, the tensile forces curves, the temperature curves and the microstructure of the test specimen are obtained. This data provide useful information about hot tearing formation and solidification characteristics, from which their quantitative relations are derived. In this manner, the hot tearing behavior in aluminum alloys can be studied.     

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.     

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.     

先进高强韧Al-Zn-Mg-Cu合金凝固和均匀化组织及相构成

采用热力学计算与实验相结合的方法,研究了两种高强韧Al-Zn-Mg-Cu合金铸态及均匀化态的显微组织和相构成.铸态A合金主要由Mg（Zn,Al,Cu）₂相和少量Al₂Cu相组成,而铸态B合金仅含Mg（Zn,Al,Cu）₂相.热力学计算显示,A和B两种合金的实际凝固过程介于Lever Rule和Scheil Model两种模拟结果之间,由于合金成分不同而导致的铸态A和B合金中各相含量差异与Scheil Model模拟所得到的各相摩尔分数变化规律基本一致.经常规工业均匀化处理（460℃保温24 h）,铸态A和B合金中存在的Mg（Zn,Al,Cu）₂或Al₂Cu相均能充分回溶,并得到单相α（Al）基体,这与热力学计算所得到的AlZn-Mg-Cu四元系统在7.5%Zn条件下460℃等温相图相符合.      

Contraction of aluminum alloys during and after solidification

A technique for measuring the linear contraction during and after solidification of aluminum alloys was improved and used for examination of binary and commercial alloys. The effect of experimental parameters, e.g., the length of the mold and the melt level, on the contraction was studied. The correlation between the compositional dependences of the linear contraction in the solidification range and the hot tearing susceptibility was shown for binary Al-Cu and Al-Mg alloys and used for the estimation of hot tearing susceptibility of 6XXX series alloys with copper. The linear thermal contraction coefficients for binary and commercial alloys showed complex behavior at subsolidus temperatures. The technique allows estimation of the contraction coefficient of commercial alloys in a wide range of temperatures and could be helpful for computer simulations of geometrical distortions during directchill (DC) casting.     

Hot tearing of ternary Mg−Al−Ca alloy castings

Ternary Mg−Al−Ca alloys are the base of a few new creep-resistant, lightweight Mg alloys for automobiles. Hot tearing in Mg−xAl−yCa alloys was studied, including Mg−4Al−0.5Ca, Mg−4Al−1.5Ca. Mg−4Al−2.5Ca, Mg−4Al−3.5Ca, Mg−5Al−2.5Ca, and Mg−6Al−2.5Ca, by constrained rod casting (CRC) in a steel mold—with a movable pouring cup to keep solidification therein from interfering with the rising tension in the rods. The hot tearing susceptibility, based on measured crack widths and crack locations, decreased significantly with increasing Ca content (y) but did not change much with the Al content (x). An instrumented CRC with a steel mold was developed to detect the onset of hot tearing by monitoring the tension in the rod during casting and the temperature near the cracking site. It was further improved by reducing the rod diameter to detect hot tearing earlier, at a higher temperature, and with a clear peak in the load curve. To further understand the hot tearing susceptibility of these alloys, the secondary phases, eutectic content, solidification path, and freezing range were examined. Alloy Mg−4Al−0.5Ca had the widest freezing range and the lowest eutectic content and was most susceptible to hot tearing, while alloys Mg−4Al−3.5Ca and Mg−6Al−2.5Ca were the opposite. Mg−4Al−0.5Ca had the widest freezing range (183 °C) because its solidification path led to the formation of Mg₁₇Al₁₂ from the liquid at a very low temperature (440°C). The application of the results to die casting was discussed. G. CAO, formerly Graduate Student, Department of Materials Science and Engineering, University of Wisconsin-Madison     

A Quest for a New Hot Tearing Criterion

Hot tearing remains a major problem of casting technology despite decades-long efforts to develop working hot tearing criteria and to implement those into casting process computer simulation. Existing models allow one to calculate the stress-strain and temperature situation in a casting (ingot, billet) and to compare those with the chosen hot tearing criterion. In most successful cases, the simulation shows the relative probability of hot tearing and the sensitivity of this probability to such process parameters as casting speed, casting dimensions, and casting recipe. None of the existing criteria, however, can give the answer on whether the hot crack will appear or not and what will be the extent of hot cracking (position, length, shape). This article outlines the requirements for a modern hot tearing model and a criterion based on this model as well as the future development of hot tearing research in terms of mechanisms of hot crack nucleation and propagation. It is suggested that the new model and criterion should take into account different mechanisms of hot tearing that are operational at different stages of solidification and be based on fracture mechanics, i.e., include the mechanisms of nucleation and propagation of a crack. This article is based on a presentation made in the symposium entitled “Solidification Modeling and Microstructure Formation: In Honor of Prof. John Hunt,” which occurred March 13–15, 2006, during the TMS Spring Meeting in San Antonio, Texas, under the auspices of the TMS Materials Processing and Manufacturing Division, Solidification Committee.     

The effect of melt composition on solidification cracking of steel,with particular reference to continuous casting

An analysis is presented describing the microsegregation of phosphorus in steel, intended to be representative of the behavior of the tramp elements associated with solidification cracking (hot tearing). The expected effect of carbon content is incorporated into the model and the rationale may be extended to encompass other addition elements influencing the preferential freezing of ferritic or austenitic phases. The treatment employs partition coefficients and diffusivity data from the literature and is based on a new back-diffusion model. This approach allows the cracking susceptibility criterion suggested by Clyne and Davies to be applied and leads to predictions concerning the effect of carbon level which are in broad agreement with experimental data.     

A New Criterion for Prediction of Hot Tearing Susceptibility of Cast Alloys

A new criterion for prediction of hot tearing susceptibility of cast alloys is suggested which takes into account the effects of both important mechanical and metallurgical factors and is believed to be less sensitive to the presence of volume defects such as bifilms and inclusions. The criterion was validated by studying the hot tearing tendency of Al-Cu alloy. In conformity with the experimental results, the new criterion predicted reduction of hot tearing tendency with increasing the copper content.     

Research on the Effect of Pouring Temperature on Hot-Tear Susceptibility of A206 Alloy by Simulation

Cast alloys with wide solidification ranges are prone to hot tearing. This study deals with prediction of hot tearing location and its intensity by computer simulation. The simulation was performed at different pouring temperatures on A206 aluminum alloy. As superheat increases, the critical fraction solid time increases which means the alloy is more susceptible to hot tearing. These theoretical predictions are in complete accordance with experimental results.     

Effect of Zr and B on castability of Ni-based superalloy IN792

The effect of Zr and B on hot tearing susceptibility of the Ni-based superalloy IN792 during directional solidification (DS) was studied. The Zr and B concentrations in the experimental alloys ranged from 0 to ∼550 ppm. The results indicate that Zr or B does not influence the castability when added individually. However, when both Zr and B are present in the alloy, high hot tearing susceptibility was found, the effect being particularly strong if Zr concentration was high. The castability results cannot be explained by simple solidification characteristics such as total freezing range (obtained from differential scanning calorimetry (DSC)) or by the amount of eutectic liquid (derived from the fraction of interdendritic γ/γ′ obtained from quantitative metallography). However, the present results can be interpreted in terms of formation of continuous films of liquid at grain boundaries (GBs) during the final stages of solidification rather than enclosed pockets. Such thin films of liquid may reduce GB cohesion and promote hot tearing.     

Effect of Hot Rolling on Grain Refining Performance of Al–5Ti–1B Master Alloy on Hot Tearing on Al–7Si–3Cu Alloy

It has been known experimentally that TiAl₃ acts as a powerful nucleant for the solidification of aluminum from the melt; however, a full microscopic understanding is still lacking. To improve microscopic understanding, hot rolling technique has been performed to the Al–5Ti–1B alloy and the effect of shape and size of the particles on grain refinement has been studied. The effect of hot rolling of Al–5Ti–1B master alloy on its grain refining performance and hot tearing have been studied by OM, XRD, and SEM. Hot rolling improves the grain refining performance of this master alloy, which is required to reduce hot tearing in Al–7Si–3Cu alloy. The improvement in grain refining performance of Al–5Ti–1B master alloy on rolling is due to the fracture of larger TiAl₃ particles into fine particles during rolling. The presented results illustrate that the morphology of TiAl₃ particles alter from the plate-like structure in the as-cast condition Al–5Ti–1B master alloy to the blocky type after rolling due to the fragmentation of plate-like structures. The grain refining response and effect on hot tearing of Al–7Si–3Cu alloy have been studied with as-cast and rolled Al–5Ti–1B master alloys. The results display hot-rolled master alloys revealing enhanced grain refining performance and minimizing hot tear tendency of the alloy at much lower addition level as compared to as-cast master alloys.     

Hot-tearing susceptibility of Al–Zn alloys

The modern concepts of the causes of hot tearing are considered and the influence of the solid fraction growth rate of an alloy is studied. The hot-tearing susceptibility (HTS) of binary Al–(5–73) wt % Zn alloys is investigated using backbone tests. The HTS is found to be maximal at ~25 wt % Zn. This maximum cannot be explained by a change in the effective solidification range, since this range of the alloys decreases monotonically with increasing zinc content. The calculations of nonequilibrium solidification by the Scheil–Gulliver model and the solid fraction growth rate of the alloys under study demonstrate that the increase in the HTS induced by an increase in the zinc content from 5 to 25 wt % is related to the decrease in the solid fraction growth rate at the final stages of solidification. The decrease in the HTS at >25 wt % Zn is associated with an increase in the fraction of eutectic in the alloys (the solid fraction growth rate during the eutectic reaction tends toward infinity) and with a change in its morphology.     

Hot tearing criteria evaluation for direct-chill casting of an Al-4.5 pct Cu alloy

Predicting the occurrence of hot tears in the direct-chill (DC) casting of aluminum alloys by numerical simulation is a crucial step for avoiding such defects. In this study, eight hot tearing criteria proposed in the literature have been implemented in a finite-element method simulation of the DC casting process and have been evaluated. These criteria were based on limitations of feeding, mechanical ductility, or both. It is concluded that six criteria give a higher cracking sensitivity for a higher casting velocity and that five criteria give a higher cracking sensitivity for the center location of the billet. This is considered in qualitative accordance with casting practice. Seven criteria indicate that use of a ramping procedure (lower casting speed during start-up phase) does not make a significant difference. However, in industrial practice, this is a common procedure, needed for avoiding hot cracking. Only one criterion is in qualitative accordance with casting practice, but it fails to quantitatively predict the hot tearing occurrence during DC casting.     

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.