Combined Deformation and Solidification-Driven Porosity Formation in Aluminum Alloys
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In die-casting processes, the high cooling rates and pressures affect the alloy solidification and deformation behavior, and thereby impact the final mechanical properties of cast components. In this study, isothermal semi-solid compression and subsequent cooling of aluminum die-cast alloy specimens were characterized using fast synchrotron tomography. This enabled the investigation and quantification of gas and shrinkage porosity evolution during deformation and solidification. The analysis of the 4D images (3D plus time) revealed two distinct mechanisms by which porosity formed; (i) deformation-induced growth due to the enrichment of local hydrogen content by the advective hydrogen transport, as well as a pressure drop in the dilatant shear bands, and (ii) diffusion-controlled growth during the solidification. The rates of pore growth were quantified throughout the process, and a Gaussian distribution function was found to represent the variation in the pore growth rate in both regimes. Using a one-dimensional diffusion model for hydrogen pore growth, the hydrogen flux required for driving pore growth during these regimes was estimated, providing a new insight into the role of advective transport associated with the deformation in the mushy region.
The drive to improve fuel economy and reduce CO2 emissions continues to incentivize the development of low-cost lightweight high-strength cast alloys for automotive and other transport applications. These light alloys are required to possess excellent strength and fatigue properties, together with good weldability and machinability, all at a low cost.[1,2] These properties are heavily influenced by the presence of the microstructural features and solidification defects like hot tear,[3,4] segregation,[5, 6, 7] and porosity,[8,9] which exist in forms of (a) gas porosity, (b) shrinkage porosity, and shrinkage bands in twin-roll and High-pressure die castings (HPDC). The nucleation of these solidification defects can be traced to the semi-solid state having relatively high solid fractions during the solidification. It is known that at these higher solid fractions, a network of solid is formed and as a consequence, the permeability of the mushy zone will decrease, resulting in difficulty in further feeding of the liquid. Based on the amount of fractions of solid, the solid network has been interpreted as a continuous solid skeleton[13,14] and cohesion-less granular solid.[15, 16, 17] The thermo-mechanical response of this network under deformation is understood to play a key role in the formation of defects.
Laboratory- and synchrotron-based semi-solid deformation tests have been extensively carried out by researchers to understand the thermo-mechanical behavior of several aluminum alloys, particularly binary Al-Cu alloys. While tensile tests have been conducted to determine the strength and ductility of the network, shear and compression tests were used to study the rheology of the semi-solid. Tzimas et al. reported semi-solid compression tests of Al-4 wt pct Cu alloys that cover the effect of solid fraction, strain rate, and grain morphology and identified different factors affecting the flow resistance. Kim et al., Kang et al., and Kapranos et al. conducted compression experiments to study the rheological behavior of various aluminum alloys at different solid fractions and strain rates and reported liquid segregation and cracks at the edge of the specimens. The development of advanced synchrotron experimentation via fast X-ray techniques has allowed observations of the microstructural features during deformation in situ.[24,25] Kareh et al., and Cai et al. reported in situ compression experiments and quantified the granular motion and dilatancy at various imposed strains. The in situ studies confirmed the role of volume dilation during tensile and compressive deformation of the semi-solid in forming defects such as hot tears and shear bands. Several theories of micro-mechanisms of hot tear defect formation have been proposed and criteria for cracking have been developed based on the experimental studies.[28,29] However, most of these models do not account for the local thermal history, formation of combined gas and shrinkage porosity, and its effect on the initiation of hot cracks. Since the shrinkage and gas porosity are believed to account for about 35 pct of the total defects in high-pressure die-cast components, a 3D, real-time information of the defect formation is critical to develop predictive models for porosity and cracks at both microscopic (size and shape) and macroscopic (location and volume fraction) levels.
The diffusion-driven growth of the gas micro-porosity based on the differential solubility of hydrogen in the melt and the solid is well known in the literature.[31,32,33] Early research on gas porosity focused on the quenching experiments and post-mortem observation of the microstructures. Lee and Hunt were the first to report the observation of porosity in Al-Cu alloys in real-time using an X-ray temperature gradient stage, and the quantification of the cooling rate on the pore radius and the volume fractions. Subsequently, experimental studies on the hydrogen micro-porosity during directional solidification were reported by Arnberg and Mathiessen, Liao et al., and Lie et al. Catalina et al. observed the change in pore shape to ellipsoid when the pore is surrounded by the solutal layer ahead of the solid–liquid interface and estimated the increase in growth rate during engulfment. Based on the X-ray radiographic observations, several empirical models of pore growth, which account for the influence of hydrogen diffusion, volumetric shrinkage, and presence of microstructural features like intermetallics, have been reported. Likewise, the formation of shrinkage porosity due to lack of feeding has been reported via several experimental studies. For e.g., Gourlay et al.[16,20] investigated the mechanism for the formation of shrinkage bands and Li et al. reported the influence of melt flow and externally solidified crystals on the formation of defect bands in HPDC of AZ91D magnesium alloy.
However, the mechanisms of pore growth during deformation and purely convective conditions, and the role of liquid flow in promoting porosity growth are neither reported nor quantified, to the best of our knowledge. This information is critical to understand and develop models to predict the size and location of porosity. In this study, compression of semi-solid Al-Si-Cu die-cast alloys, with and without modified copper content, has been performed to quantify the flow-driven pore nucleation and growth. The liquid fraction distribution and the nucleated porosity in the dilatant bands were quantified at different strain values during compression. A 1D diffusion-controlled gas porosity model was used to quantify the flux required for pore growth, which provided insights into the propensity of advective hydrogen transport in enhancing the growth of hydrogen pores. In what follows, we present the experimental methodology, analysis, and quantification of the 4D (3D+time) data characterizing the nature of deformation-induced and solidification-driven pore growth.
2 Materials and Methods
Chemical Assay of the Alloys Under Study
Cu (Wt Pct)
Fe (Wt Pct)
Si (Wt Pct)
2.1 Sample Preparation
2.2 Semi-Solid Compression Experiments
2.3 Data Acquisition and Image Processing
A monochromatic X-ray beam with an energy of 53 keV was used in the experiment. During the deformation, a set of 38 tomograms were acquired using a PCO. Edge camera coupled with I12’s camera module 3, which corresponds to a field of view of 8 mm × 6 mm. A total of 600 projections were taken for every 180˚ rotation of the sample for each tomogram, obtaining a voxel size of 3.2 µm. The exposure time was 32 ms per projection, with the total time of each scan being 19.2 s. Each scan was taken continuously without any additional sample rotation, which allowed for the continuous data collection. The 3D scan was reconstructed using filtered back-projection to produce an 1885 × 1885 × 2149 voxel volume. The image was filtered using anisotropic and 3D median filters to remove noises. The filtered image was segmented using trainable weka segmentation plugin in Fiji ImageJ, which makes use of machine learning tools.
3 Results and Discussions
3.1 Formation of Liquid Channels
3.2 Pore Nucleation, Growth, and Coalescence
The nucleation of new gas pores was observed in the liquid channels at various strain values throughout the deformation stage (Figure 3(b)). The pores grew consistently while the mush deformed with expanding liquid channels. Plausibly, the feeding of the liquid resulted in a convective influx of hydrogen into the liquid pockets, thereby increasing the overall local hydrogen concentration. This is hypothesized based on the observation that the pores were predominantly spherical during the deformation regime, indicating a diffusion-controlled gas pore growth. Furthermore, a secondary influence on pore growth was the pressure drop in the dilatant bands, which can also lead to pore volume dilation. The pores retained spherical shape until they encountered a solid (Figure 3d). The phenomenon was also observed and reported by Cai et al., who had defined different stages of dilatancy controlled shrinkage growth, which eventually led to cracking. The values of combined area of liquid fraction and porosity at different strains along the loading axis were determined and shown in Figure 4(b). By comparing Figures 4(a) and 4(b), it is clear that the pore growth due to volume dilation picks up after 25 pct strain and most of these voids were concentrated around the middle of the sample. Longitudinal slices shown in Figure 4(c) show the ‘middle’ region indicated in Figures 4(a) and (b), in which the localization of liquid channel and voids can be seen. It should be noted that, in earlier studies by Stefanescu and Khalajzadeh, a shrinkage-induced flow term was introduced and its role on shrinkage growth had been discussed. This flow term is analogous to the dilatancy-induced flow discussed in this study.
3.3 Regimes of Gas Porosity Growth: (a) Deformation and (b) Solidification
3.4 Numerical Evaluation of Advective Hydrogen Influx
Since the isolated pores show a distinct growth behavior during deformation as compared to solidification, an understanding of amount of hydrogen influx carried by the liquid would be useful in correlating the flow-induced growth under different processing environments such as twin-roll casting, HPDC, etc. A calculation of 1D diffusion-driven hydrogen gas pore growth was performed using a numerical model discussed in Reference 46. It was assumed that a constant value of hydrogen concentration existed at the boundary of the domain (Figure 7), which represents the amount of hydrogen brought in by the inter-dendritic flow. Using the pore growth model, the necessary hydrogen concentration at the boundary that resulted in an equivalent growth obtained from the experiments was determined. Note that this analysis only accounts for the growth of the spherical pore under the influence of increased hydrogen influx due to liquid flow.
The Concentration Input at Domain Boundary Estimated from the Model
Radius of the Gas Pore (µm) in the Two Regimes
Avg. Concentration Input (cc/100 g Al) Between Two Scans
It can be seen that by increasing the velocity of deformation, the concentration build-up at REV increases, for a given far-field concentration. This increase in the concentration gradient between the REV boundary and the pore–liquid interface drives the pore growth. This information is helpful in evaluating flow-driven hydrogen concentration build-up and eventual porosity, particularly for high-pressure die casting environments, where flow rates are very high (~ 20-60 m/s).
4 Stress–Strain Behavior During Compression
Two distinct regimes of hydrogen pore growth, namely deformation-induced flow-driven growth and solidification-controlled growth were observed and quantified. The growth rates were determined by measuring the equivalent pore radius from in situ experiments. The measured growth rate values showed a clear and abrupt change at the end of deformation regime, and were also found to agree with the trends reported in the literature using Gaussian distribution functions.
The role of dilatancy in deformation-induced pore growth via advective hydrogen transport was ascertained using quantification of localized liquid channels and the stress–strain behavior of the semi-solid under compressive loading.
The hydrogen concentration influx during deformation-induced flow that closely represents the observed experimental trend was estimated using a 1D diffusion model. This revealed a hydrogen concentration boundary condition, and can be further used to correlate flow-driven hydrogen influx for different processing routes.
The authors thank the University Research Program at Ford Motor Company, USA for partial financial support. We are grateful to Diamond light source for the beamtime (EE16188-1), Dr. Sara Nonni, Dr. Nolwenn Legall, and Sebastian Marucci for their help during beamtime. S.K and P.D.L acknowledge the sanction of the project P1299 under the SPARC (Scheme for Promotion of Academic and Research Collaboration) initiative. B.C. acknowledges the support provided by the Diamond Birmingham Collaboration and Alan Turing Fellowship. The support from the ferrous metallurgy and the machine tools laboratories at IIT Bombay in preparing the samples is acknowledged.
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