Modeling of Microporosity Size Distribution in Aluminum Alloy A356

Porosity is one of the most common defects to degrade the mechanical properties of aluminum alloys. Prediction of pore size, therefore, is critical to optimize the quality of castings. Moreover, to the design engineer, knowledge of the inherent pore population in a casting is essential to avoid potential fatigue failure of the component. In this work, the size distribution of the porosity was modeled based on the assumptions that the hydrogen pores are nucleated heterogeneously and that the nucleation site distribution is a Gaussian function of hydrogen supersaturation in the melt. The pore growth is simulated as a hydrogen-diffusion-controlled process, which is driven by the hydrogen concentration gradient at the pore liquid interface. Directionally solidified A356 (Al-7Si-0.3Mg) alloy castings were used to evaluate the predictive capability of the proposed model. The cast pore volume fraction and size distributions were measured using X-ray microtomography (XMT). Comparison of the experimental and simulation results showed that good agreement could be obtained in terms of both porosity fraction and size distribution. The model can effectively evaluate the effect of hydrogen content, heterogeneous pore nucleation population, cooling conditions, and degassing time on microporosity formation.     

Mechanisms for Solidification Crack Initiation and Growth in Aluminum Welding

In the present work, mechanisms are proposed for solidification crack initiation and growth in aluminum alloy 6060 arc welds. Calculations for an interdendritic liquid pressure drop, made using the Rappaz–Drezet–Gremaud (RDG) model, demonstrate that cavitation as a liquid fracture mechanism is not likely to occur except at elevated levels of hydrogen content. Instead, a porosity-based crack initiation model has been developed based upon pore stability criteria, assuming that gas pores expand from pre-existing nuclei. Crack initiation is taken to occur when stable pores form within the coherent dendrite region, depending upon hydrogen content. Following initiation, crack growth is modeled using a mass balance approach, controlled by local strain rate conditions. The critical grain boundary liquid deformation rate needed for solidification crack growth has been determined for a weld made with a 16 pct 4043 filler addition, based upon the local strain rate measurement and a simplified strain rate partitioning model. Combined models show that hydrogen and strain rate control crack initiation and growth, respectively. A hypothetical hydrogen strain rate map is presented, defining conceptually the combined conditions needed for cracking and porosity.     

Size and Morphology of Gas Porosity in Castings—Insights into Computational Experiments Using a Cellular Automaton Model

Aluminium castings are known to be prone to micro-porosity formation which appears as fine porosity in the inter-dendritic and inter-granular regions of castings. The size, distribution and morphology of such pores significantly affect mechanical and fatigue properties of castings. We use a cellular automaton simulation model as a virtual experimental set-up to study growth of gas bubbles in solidifying aluminium castings. The model assumes that gas porosity originates from pre-existing micro-bubbles that grow by diffusion of hydrogen from the solid–liquid interfaces into the bubbles. The major factors that limit the growth of the bubbles are the finite time available for the diffusion of hydrogen and the space constraint imposed by the growing solid. While the diffusion limitation to pore growth has been studied well, the effect of the space constraint has not received much attention. Our cellular automaton model with growth rules specially adapted for bubble growth tracks the solid–liquid and bubble–liquid interfaces explicitly on a fine grid. Numerical experiments are performed with a eutectic Al–Si alloy solidified with different grain sizes and solidification rates. The micro-structural environment in which a pre-existing bubble finds itself is seen to be the most critical factor that determines the final size and morphology of porosity.     

Theoretical modeling of densification during activated solid-state sintering

Activated solid-state sintering relies on the addition of low concentrations of grain boundary segre-gating species to increase diffusion rates. In this article, enhanced diffusion through an activated layer at the grain boundaries has been modeled for the case of tungsten sintered with transition element additions. Both constant heating rates and isothermal sintering are considered. As in classical treatments, sintering is divided into three stages, but modifications are proposed based on recent observations and theories regarding packing coordination, pore morphology, pore location, grain growth, and pore-grain boundary separation. The intermediate and final stages of sintering are al-lowed to overlap based on the amount of closed porosity to account for both pore closure early in the process and the gradual increase in packing coordination with densification. Mean curvature theory is used to estimate pore curvature during the intermediate stage of sintering. In the final stage, pores are modeled on both the corners of a tetrakaidecahedron and on its square facets. The pore location has only a small effect on densification, while the grain boundary mobility is more of a factor. The model allows pore-grain boundary separation to match experimentally measured grain sizes. The model predictions are compared to dilatometer curves of pure tungsten and tungsten sintered with additions of Co, Fe, Ni, and Pd. For the Co- and Fe-activated samples, the model is modified to account for an increase in diffusional activation energy due to dissolution of the activator in tungsten. Formerly Director of Materials Development, P/M Lab, Department of Engineering Science and Mechanics, The Pennsylvania State University.     

Fabrication of Porous Aluminum with Directional Pores through Continuous Casting Technique

Lotus-type porous aluminum with slender directional pores is fabricated via a continuous casting technique in pressurized hydrogen or a mixed gas containing hydrogen and argon. The influence of solidification conditions such as hydrogen partial pressure, solidification velocity, temperature gradient, and melt temperature on the porosity and pore size is investigated. The porosity and pore size increase upon increasing the hydrogen partial pressure or the melt temperature, whereas the porosity and pore size decrease upon increasing the solidification velocity or the temperature gradient. Furthermore, the mechanism of pore formation in lotus aluminum is examined based on the results of an improved model of hydrogen mass balance in the solidification front, which was originally proposed by Yamamura et al. The results from the present model agree with the experimental results. We conclude that the diffusion of hydrogen rejected in the solidified aluminum near the solid/liquid interface is the most important factor for pore formation because the difference in hydrogen solubility between solid and liquid aluminum is very small.     

Cellular Automaton Study of Hydrogen Porosity Evolution Coupled with Dendrite Growth During Solidification in the Molten Pool of Al-Cu Alloys

Welding porosity defects significantly reduce the mechanical properties of welded joints. In this paper, the hydrogen porosity evolution coupled with dendrite growth during solidification in the molten pool of Al-4.0 wt pct Cu alloy was modeled and simulated. Three phases, including a liquid phase, a solid phase, and a gas phase, were considered in this model. The growth of dendrites and hydrogen gas pores was reproduced using a cellular automaton (CA) approach. The diffusion of solute and hydrogen was calculated using the finite difference method (FDM). Columnar and equiaxed dendrite growth with porosity evolution were simulated. Competitive growth between different dendrites and porosities was observed. Dendrite morphology was influenced by porosity formation near dendrites. After solidification, when the porosities were surrounded by dendrites, they could not escape from the liquid, and they made pores that existed in the welded joints. With the increase in the cooling rate, the average diameter of porosities decreased, and the average number of porosities increased. The average diameter of porosities and the number of porosities in the simulation results had the same trend as the experimental results.

     

Pore Formation During Solidification of Aluminum: Reconciliation of Experimental Observations,Modeling Assumptions,and Classical Nucleation Theory

An in-depth discussion of pore formation is presented in this paper by first reinterpreting in situ observations reported in the literature as well as assumptions commonly made to model pore formation in aluminum castings. The physics of pore formation is reviewed through theoretical fracture pressure calculations based on classical nucleation theory for homogeneous and heterogeneous nucleation, with and without dissolved gas, i.e., hydrogen. Based on the fracture pressure for aluminum, critical pore size and the corresponding probability of vacancies clustering to form that size have been calculated using thermodynamic data reported in the literature. Calculations show that it is impossible for a pore to nucleate either homogeneously or heterogeneously in aluminum, even with dissolved hydrogen. The formation of pores in aluminum castings can only be explained by inflation of entrained surface oxide films (bifilms) under reduced pressure and/or with dissolved gas, which involves only growth, avoiding any nucleation problem. This mechanism is consistent with the reinterpretations of in situ observations as well as the assumptions made in the literature to model pore formation.     

Hydrogen partitioning in pure cast aluminum as determined by dynamic evolution rate measurements

A statistical analysis of the porosity in 99.995 wt pct pure commercially available cast aluminum has been correlated with real time hydrogen evolution data obtained in an ultrahigh vacuum furnace in order to estimate the hydrogen partitioning in the aluminum. The dynamic technique employed permitted the detection and separation of hydrogen evolved from solid solution, hydrogen released by the rupture of large pores, and gases desorbed from the aluminum surface. Results of the statistical analysis indicate average pore diameters in pure cast aluminum extend from less than 1 to over 400 μm. Interdendritic pores having diameters greater than 25 μm constitute over 98 pct of the pore volume. The overall volume fraction of pores was determined to be 0.71 pct. Compared to vacuum remelted rolled aluminum, the porosity resulted in a reduction of ultimate tensile strength of 13 pct and a reduction in yield strength of 21 pet. The evolution of hydrogen from the aluminum was observed to occur by large hydrogen pressure pulses due to the rupture of pores near the surface and by a smooth steady desorption from solid solution. The rupturing pores were observed visually and found to occur both in the solid state and after melting. A substantial change in slope of the desorption curve following the pulse train suggests the pores are the primary sources of hydrogen in the bulk. Analysis of the pore and pulse size distributions indicates more than 99 pct of the bulk hydrogen is partitioned in pores greater than 25 μm. Pressures within the larger pores (≈270 μm) were determined to be about 2.4 atm at room temperature. Hydrogen content in the large pores was found to be as high as 2 × 10¹⁶ molecules. The total hydrogen content in the pores and in solid solution was determined to be 6.3 × 10¹⁷ atoms/cm³ (0.43 cm³/100 g). Measurements on commercially available 99.9995 wt pct cast aluminum indicate the total hydrogen content to be 4.8 × 10¹⁷ atoms/cm³ (0.33 cm³/100 g).     

Sintering Atmosphere Effects on the Ductility of W- Ni- Fe Heavy Metals

Residual porosity has a strong negative effect on the ductility of tungsten-nickel-iron heavy metals. This investigation examines the sintering atmosphere role in stabilizing detrimental residual pore structures. Two types of experiments are reported on alloys containing 93, 95, or 97 wt pct W with Ni:Fe ratios of 7:3. The negative effect of prolonged sintering is attributed to pore coarsening involving trapped gas in the pores. Calculated pore growth rates for hydrogen filled pores suggest that pore coarsening involves both ripening and coalescence driven by tungsten grain growth. The effect of the sintering atmosphere is analyzed for final stage pore elimination. It is demonstrated that a change in sintering atmosphere from hydrogen to argon midway through the sintering cycle can aid pore degassing and increase the sintered ductility and strength. Formerly Postdoctoral Fellow at Rensselaer Polytechnic Institute under a fellowship from the Korea Science and Engineering Foundation     

A stereological model of the degree

A simple geometric model of pore and grain structure has been used to explain the experimentally observed constancy of the degree of grain boundary-pore contact,R, throughout intermediate and final stage sintering. As modeled, constancy ofR in the final stage requires a balance among the number of pores per grain, the ratio of the pore and grain sizes, and the relative frequencies of pore locations at grain corners, edges, and surfaces. Experimentally, these location frequen- cies were found to remain constant for both pure and MgO-doped A1₂O₃, over the observed range from 91 to 99.8 pct of full density. The number of pores per grain increased and the pore/grain size ratio decreased over this period for both materials. Employing experimental microstructural data for the above parameters in the model yielded the predicted linear plots, with intercepts givingR values very close to the values measured by direct stereological means. The model also yielded reasonable, constant values ofR for intermediate stage sintering and explains the constancy ofR throughout the transition from intermediate to final stage.     

Metal-gas eutectic growth during unidirectional solidification

Metal-gas eutectic growth is a novel method for fabricating porous metals in which the gas pores are rodlike and aligned with the solidification direction. A new model was developed to predict the effects of the gas pressure and the solidification velocity on the porosity, pore diameter, and interpore spacing in metal-gas eutectic unidirectional solidification. The pore size and the interpore spacing are primarily dependent on the total gas pressure, but the porosity is dependent not only on the total gas pressure but also on the ratio of the partial pressures of hydrogen to argon.     

The critical grain size for liquid flow into pores during liquid phase sintering

A model of grain-liquid mixture containing a spherical pore is analyzed to describe the pore filling during liquid phase sintering. Since the radius of liquid menisci around a pore increases linearly with the grain size, the menisci form a spherical bubble at a critical grain size and the pore is rapidly filled with liquid flowing from numerous menisci at the specimen surface. The values of the critical grain size for pore filling are calculated for various dihedral angles, wetting angles, and liquid contents. Although the predicted critical grain size is subject to errors because of assumptions in the models, the values agree in an order of magnitude with some experimental results. The effect of entrapped gas on pore filling and the expected behavior of irregular pores are also briefly discussed.     

Pore filling process in liquid phase sintering

Models for liquid flow into isolated pores during liquid phase sintering are described qualitatively. The grains are assumed to maintain an equilibrium shape determined by a balance between their tendency to become spherical and a negative capillary pressure in the liquid due to menisci at the specimen surface and the pore. With an increase of grain size, the grain sphering force decreases while the radius of liquid menisci increases to maintain the force equilibrium. When grain growth reaches a critical point, the liquid menisci around a pore become spherical and the driving force for filling the pore rapidly increases as liquid flows into it. The critical grain size required for filling a pore increases linearly with pore size. Experimentally, filling of isolated pores has been investigated in Fe-Cu powder mixture after liquid phase sintering treatment and after dipping into a molten matrix alloy. The observed pore filling behaviors agree with the qualitative predictions based on the models. In Fe-Cu alloy, pore filling is terminated by gas bubbles formed in liquid pockets. This paper is based on a presentation delivered at the symposium “Activated and Liquid Phase Sintering of Refractory Metals and Their Compounds” held at the annual meeting of the AIME in Atlanta, Georgia on March 9, 1983, under the sponsorship of the TMS Refractory Metals Committee of AIME.     

Modeling the Effect of Finite-Rate Hydrogen Diffusion on Porosity Formation in Aluminum Alloys

A volume-averaged model for finite-rate diffusion of hydrogen in the melt is developed to predict pore formation during the solidification of aluminum alloys. The calculation of the micro-/macro-scale gas species transport in the melt is coupled with a model for the feeding flow and pressure field. The rate of pore growth is shown to be proportional to the local level of gas supersaturation in the melt, as well as various microstructural parameters. Parametric studies of one-dimensional solidification under an imposed temperature gradient and cooling rate illustrate that the model captures important phenomena observed in porosity formation in aluminum alloys. The transition from gas to shrinkage dominated porosity and the effects of different solubilities of hydrogen in the eutectic solid, capillary pressures at pore nucleation, and pore number densities are investigated in detail. Comparisons between predicted porosity percentages and previous experimental measurements show good correspondence, although some uncertainties remain regarding the extent of impingement of solid on the pores. This article is based on a presentation made in the symposium “Simulation of Aluminium Shape Casting Processing: From Design to Mechnacial Properties” which occured March 12–16, 2006, during the TMS Spring meeting in San Antonio, Texas, under the auspices of the Computational Materials Science and Engineering Committee, the Process Modelling, Analysis and Control Committee, the Solidification Committee, the Mechanical Behavior of Materials Committee, and the Light Metal Division/Aluminium Committee.     

A theoretical study of grain growth in porous solids during sintering

The processes of grain boundary migration, pore drag and pore/boundary separation are described on the basis of the phenomenological equations for boundary migration and surface diffusion. Cylindrical pores on triple grain junctions are assumed to represent the open porosity during intermediate-stage sintering. It is found that cylindrical pores can hardly detach from migrating boundaries. Three-dimensional closed pores, however, which predominate during final stage sintering, can separate from migrating grain junctions. The separation process is modelled numerically and the conditions for separation are formulated. Analytical approximations for the pore mobility are shown to describe the numerical results well. They serve to establish effective mobilities of grain boundaries bearing pores in various configurations. Classical theories of grain coarsening are modified by using these effective mobilities. Mechanical constitutive models of sintering contain the grain size as an internal variable. The present analysis leads to an evolution equation for the average grain size, which depends on the volume fraction of the pores and on their configuration.     

Modeling of microporosity formation in A356 aluminum alloy casting

A numerical model for predicting microporosity formation in aluminum castings has been developed, which describes the redistribution of hydrogen between solid and liquid phases, the transport of hydrogen in liquid by diffusion, and Darcy flow in the mushy zone. For simulating the nucleation of hydrogen pores, the initial pore radius is assumed to be a function of the secondary dendrite arm spacing, whereas pore growth is based on the assumption that hydrogen activity within the pore and the liquid are in equilibrium. One of the key features of the model is that it uses a two-stage approach for porosity prediction. In the first stage, the volume fraction of porosity is calculated based on the reduced pressure, whereas, in the second stage, at fractions solid greater than the liquid encapsulation point, the fraction porosity is calculated based on the volume of liquid trapped within the continuous solid network, which is estimated using a correlation based on the Niyama parameter. The porosity model is used in conjunction with a thermal model solved using the commercial finite-element package ABAQUS. The parameters influencing the formation of microporosity are discussed including a means to describe the supersaturation of hydrogen necessary for pore nucleation. The model has been applied to examine the evolution of porosity in a series of experimental samples cast using unmodified A356 in which the initial hydrogen content was varied from 0.048 to 0.137 (cc/100 g). A comparison between the model predictions and the experimental measurements indicates good agreement in terms of the variation in porosity with distance from the chill and the variation resulting from initial hydrogen content.     

Modeling of microporosity formation in A356 aluminum alloy casting

A numerical model for predicting microporosity formation in aluminum castings has been developed, which describes the redistribution of hydrogen between solid and liquid phases, the transport of hydrogen in liquid by diffusion, and Darcy flow in the mushy zone. For simulating the nucleation of hydrogen pores, the initial pore radius is assumed to be a function of the secondary dendrite arm spacing, whereas pore growth is based on the assumption that hydrogen activity within the pore and the liquid are in equilibrium. One of the key features of the model is that it uses a two-stage approach for porosity prediction. In the first stage, the volume fraction of porosity is calculated based on the reduced pressure, whereas, in the second stage, at fractions solid greater than the liquid encapsulation point, the fraction porosity is calculated based on the volume of liquid trapped within the continuous solid network, which is estimated using a correlation based on the Niyama parameter. The porosity model is used in conjunction with a thermal model solved using the commercial finite-element package ABAQUS. The parameters influencing the formation of microporosity are discussed including a means to describe the supersaturation of hydrogen necessary for pore nucleation. The model has been applied to examine the evolution of porosity in a series of experimental samples cast using unmodified A356 in which the initial hydrogen content was varied from 0.048 to 0.137 (cc/100 g). A comparison between the model predictions and the experimental measurements indicates good agreement in terms of the variation in porosity with distance from the chill and the variation resulting from initial hydrogen content.     

Modeling of microporosity formation in A356 aluminum alloy casting

A numerical model for predicting microporosity formation in aluminum castings has been developed, which describes the redistribution of hydrogen between solid and liquid phases, the transport of hydrogen in liquid by diffusion, and Darcy flow in the mushy zone. For simulating the nucleation of hydrogen pores, the initial pore radius is assumed to be a function of the secondary dendrite arm spacing, whereas pore growth is based on the assumption that hydrogen activity within the pore and the liquid are in equilibrium. One of the key features of the model is that it uses a two-stage approach for porosity prediction. In the first stage, the volume fraction of porosity is calculated based on the reduced pressure, whereas, in the second stage, at fractions solid greater than the liquid encapsulation point, the fraction porosity is calculated based on the volume of liquid trapped within the continuous solid network, which is estimated using a correlation based on the Niyama parameter. The porosity model is used in conjunction with a thermal model solved using the commercial finite-element package ABAQUS. The parameters influencing the formation of microporosity are discussed including a means to describe the supersaturation of hydrogen necessary for pore nucleation. The model has been applied to examine the evolution of porosity in a series of experimental samples cast using unmodified A356 in which the initial hydrogen content was varied from 0.048 to 0.137 (cc/100 g). A comparison between the model predictions and the experimental measurements indicates good agreement in terms of the variation in porosity with distance from the chill and the variation resulting from initial hydrogen content.