Melt Pool Formation Research Articles

Laser beam oscillation welding of aluminum alloy using the spatially modulated beam by diffractive optical element (DOE)

In laser welding, the spatial beam intensity profile of the laser beam is an important parameter as it has a considerable effect on the temperature distribution and cooling rate of the melt pool, which determine the weld properties. In this study, a laser beam with a spatially modulated intensity profile by a diffractive optical element (DOE) was applied to the laser beam oscillation welding of an aluminum alloy (AA5052), and the weld characteristics of modulated beam welding (MBW) were analyzed in relation to those of Gaussian beam welding (GBW). According to the result of experiment verifying full penetration condition, the MBW generally required a slower maximum beam speed for full penetration than the GBW due to laser energy spreading by the core and ring beam constitution. On the other hand, this dispersed laser energy of the modulated beam was more effective in formation of a stable melt pool, which in turn reduced weld defects (bumpy bead surface, pores, and cracks) compared with the GBW. It also played a role in improving the asymmetric morphology of the weld by generating a relatively even temperature distribution of the melt pool. From an electron back scatter diffraction (EBSD) analysis, it was found that columnar grains were mostly distributed at the edge area of the weld, and equiaxed grains were largely distributed at the center area of the weld. The asymmetric feature in the microstructure was also found because of the asymmetric beam oscillation pattern and the resultant cooling rate difference. It was found that the area solidified at the lower cooling rate exhibited relatively large columnar grains. For the MBW, the asymmetric feature in the proportion of the low and high angle grain boundaries within the weld zone was diminished, which resulted from the relatively uniform temperature distribution by the dispersed laser energy. Due to the slow cooling rate, the MBW sample could have larger grains than GBW; this, however, slightly reduced the tensile strength of the joint welded by the modulated beam. The highest tensile strength obtained from the GBW and the MBW sample was equivalent to 88 % and 83.4 % of the base material’s tensile strength, respectively. It was found that the hardness value and its distribution across the weld zone was similar for the GBW and MBW samples. It was also found that the weld zone has a lower hardness value than base material owing to the increase of grain size through recrystallization.

Simulated and experimental analysis of laser beam energy profiles to improve efficiency in wire-fed laser deposition

Laser cladding is a well-established technique, with the majority of prior numerical modelling work focused on delivery and melt pool behaviour of powder-based processes. This research presents new investigations into optimised laser beam shaping for the unique characteristics of wire-based processes, where direct substrate heating, as well as heat transfer between the wire and substrate, is important. The value of this subject is the improved deposition rates and dense metallic structures that can be achieved by wire-based deposition processes compared to powder-based material delivery. The within-wire temperature distribution (AISI 316 stainless steel), the heat transfer and direct heating of the substrate (mild steel) are modelled via heat transfer simulations, with three laser beam irradiance distributions. This analysis identified the removal of localised high-temperature regions typically associated to standard Gaussian distributions, and the improved substrate heating that a uniform square beam profile can provide. Experiments using pre-placed wire and a 1.2 kW CO2 laser were analysed using cross-sectional optical microscopy to provide model validation and evidence of improved wire-substrate wetting, while maintaining favourable austenitic metallurgy in the clad material. A key finding of this work is a reduction, from 480 to 190 W/mm2, in the required irradiance for effective melt pool formation when changing from a Gaussian distribution to a uniform square distribution. This also provided a 50% reduction in total energy. The potential improvements to energy efficiency, cost reductions and sustainability improvements are recognised and discussed.

Thermal-hydraulic analysis of FAIDUS design for severe accident mitigation strategy in a medium size sodium-cooled fast reactor

The impediment of core disruption is realized through the provision of diverse and redundant safety features in the design complemented by the use of inherent passive mechanisms that respond to the accident condition by ensuring convenient dispersal of molten core material from the core in the early stage of the accident. In light of this, a promising design strategy Fuel Assembly Inner DUct Structure (FAIDUS) core concept is proposed to enhance the axial discharge capability of molten fuel from core for the exclusion of core wide melt pool formation. The sequence of event during the course of relocation in the FAIDUS is analysed employing a transient integrated thermal-hydraulic model. The effectual performance of various FAIDUS design options in mitigating the accident is evaluated. Based on this, the preferred design choice conforming the laid down criteria is selected in the present study. The simulation results suggest that FAIDUS design concept delivers the best alternative way for extenuating accident progress through a comprehensive melt relocation strategy of greater reliability in an intrinsic way.

Powder bed fusion modelling based on Discontinuous Galerkin formulation

Microscopic defects may occur during powder-bed fusion processes which originate from molten pool instabilities. To investigate this issue, a numerical model focusing on the interaction between laser and powder, melt pool formation and thermodynamics effects is on development. The approach used in the model assumes an incompressible Newtonian flow based on an enthalpy-porosity method for solid/liquid metal transition. The jump conditions at the liquid-solid interface for the energy equation are included through the modification of the enthalpy which incorporates the latent heat of fusion. A Carman-Kozeny porosity method is implemented in the momentum equation to penalize the flow in the solid phase. Molten flows are driven by natural and thermocapillary convection which are modelled using Boussinesq approximation and Marangoni free-surface stresses respectively. This numerical model is implemented within a Discontinuous Galerkin (DG) finite element formulation which ensures high order convergence on unstructured mesh [1]. In this work, a sharp interface method is integrated into the three dimensional high-order DG code Argo [2] to capture the free surface of the melt pool. This method allows to keep the high-order of convergence of the DG scheme even near the interface not conforming with the mesh. This is essential to capture the thermo-hydrodynamics phenomena during powder-bed fusion with accuracy. Current effort is dedicated to improve the model accounting for physical phenomena such as surface tension and vaporization. The main purpose is to investigate the occurrence of discontinuities in fused powder tracks depending on material properties and process parameters.

Synchrotron X-ray imaging of directed energy deposition additive manufacturing of titanium alloy Ti-6242

Directed Energy Deposition Additive Manufacturing (DED-AM) is transformative for the production of larger, geometrically complex metallic components. However, the mechanical properties of titanium alloy DED-AM components do not always reach their full potential due to microstructural features including porosity and regions of lack of fusion. Using in situ and operando synchrotron X-ray imaging we gain insights into key laser-matter interaction and microstructural feature formation mechanisms during DED-AM of Ti-6242. Analysis of the process conditions reveals that laser power is dominant for build efficiency while higher traverse speed can effectively reduce lack of fusion regions. We also elucidate the mechanisms underlying several physical phenomena occurring during the deposition of titanium alloys, including the formation of a saddle-shaped melt pool and pore pushing. The findings of this work clarify the transient kinetics behind the DED-AM of titanium alloys and can be used as a guide for optimising industrial additive manufacturing processes.

Determining processing behaviour of pure Cu in laser powder bed fusion using direct micro-calorimetry

Copper is challenging to process by laser powder bed fusion (LPBF) given its high reflectivity at common infrared laser diode wavelengths and high thermal conductivity. Successful deposition of copper in a predictable and repeatable fashion relies on understanding the development of the keyhole melting regime, as well as heating, melting, boiling and vapour formation behaviour when interacting with a laser beam within an LPBF environment. In this study, in situ optical absorptivity measurements are used to clarify the complex physics of the laser material interaction. Absorptivity of laser energy is measured using direct micro-calorimetry and compared to melt pool depth in correlation to processing parameters. The measured absorptivity for a 100 μm layer thickness of powder was found to be approximately four times higher than that of the bare polished discs. It was also shown that high laser power above 500 W and scan speed up to 150 mm/s are appropriate for effective melting of the powder layer, with these parameters overcoming the threshold required to achieve keyhole melting. This is explained by multiple reflections withing the powder particles and the lower thermal conductivity of packed powder in comparison to bare discs. Melt pool formation was found to be highly unstable and an explosive behavior was observed when in the keyhole regime, caused by high fluctuations in absorptivity values. This work demonstrates calorimetry can be used to monitor melting behaviour in a real-time fashion during processing for this challenging to proces material, thereby avoiding unnecessary parametric optimisation. In addition, the parametric window for optimum processing revealed here can inform future work.

The effects of locations on the build tray on the quality of specimens in powder bed additive manufacturing

In this study, the effect of powder spreading direction was investigated on selectively laser-melted specimens. The results showed that the metallurgical properties of the specimens varied during fabrication with respect to their position on the build tray. The density, porosity, and tensile properties of the Co–Cr–W–Mo alloy were investigated on cuboid and tensile specimens fabricated at different locations. Two different significant positions on the tray were selected along the powder spreading direction. One set of specimens was located near the start line of powder spreading, and the other set was located near the end of the building tray. The main role in the consequences of powder layering was played by the distribution of powder particle sizes and the packing density of the layers. As a result, laser penetration, melt pool formation, and fusion characteristics varied. To confirm the occurrence of variations in sample density, an additional experiment was performed with a Ti–6Al–4V alloy. Furthermore, the powders were collected at two different fabricating locations and their size distribution for both materials was investigated.

Ultrasonic Frequency Effects on the Melt Pool Formation, Porosity, and Thermal-Dependent Property of Inconel 718 Fabricated by Ultrasonic Vibration-Assisted Directed Energy Deposition

Abstract Ultrasonic vibration-assisted (UV-A) directed energy deposition (DED) has become a promising technology to improve the as-built quality and mechanical performance of metal parts. Ultrasonic frequency, a critical parameter of the ultrasonic vibration, can remarkably affect the ultrasonic vibration behaviors in assisting DED processes. However, leveraging varied ultrasonic frequencies in UV-A DED attracts little attention, and the effects of ultrasonic frequency have been thus overlooked. Linking ultrasonic frequency and part performance emphasizes the need for an understanding of the underlying thermodynamics in the melt pool due to the key role of thermal history in the DED process. In this work, we fabricated Inconel 718 (IN718) parts using the UV-A DED process under different levels of ultrasonic vibration frequency (including 0, 25 kHz, 33 kHz, and 41 kHz). For the first time, melt pool size, temperature distribution, and peak temperature within the melt pool, as well as the peak temperature fluctuation within a layer deposition, were studied. Porosity and thermal-dependent properties including grain size and microhardness were also investigated. The results indicated that the increase in ultrasonic frequency led to an increase in both melt pool size and peak temperature. Moreover, the lowest porosity was obtained at an ultrasonic frequency of 25 kHz, while grain refinement and microhardness enhancement were achieved at the highest frequency of 41 kHz. This investigation provides great insights into the link among ultrasonic frequency, melt pool formation, temperature field, porosity, and thermal-dependent properties in the UV-A DED-built IN718 parts.

Plastic strain distribution throughout the microstructure duality during the fracture process of non-combustible Mg products fabricated by selective laser melting

In this study, several Mg-9%Al-2%Ca alloy round-bar specimens were fabricated by the selective laser melting (SLM) process. A fraction of the specimens was submitted to tensile testing. Then, the remaining fraction of specimens were drilled and subsequently submitted to further tensile testing interrupted at 90% of the ultimate tensile strength (UTS). Fracture surfaces were analyzed and an Electron Backscatter Diffraction (EBSD) analysis was performed to observe plastic strain. The results showed a dispersed plastic strain distribution that concentrated at the coarse grain microstructure, specifically at the outer regions of each melt pool formation. Microstructure coarsening is an intrinsic phenomenon of the SLM processes and induces crack arrest during the transition from a stable fracture to an unstable fracture. Accordingly, fractography results showed a large flattened area in the fracture surface, which suggests a stable and propagating plastic strain beneath the fracture surface, but no crack propagation of the corresponding length was found, despite interrupting the test at 90% of the UTS value. Based on this information, an indicator that evaluates plastic strain as continuous or discontinuous could be used in order to explain the high tensile strength and fracture behavior of SLM products in as-built conditions, which have been discussed but not verified to date.

Experimental investigation on Laser Directed Energy Deposition based additive manufacturing of Al2O3 bulk structures

In the present study, the effect of various processing parameters is investigated for building Al2O3 ceramic structures by laser additive manufacturing using the direct energy deposition technique (LAM-DED). The study shows that uniform single tracks and three dimensional (3D) structures of Al2O3 can be fabricated on alumina and Ti–6Al–4V substrates at the laser power of ~225 and ~300 W, respectively, for a fixed scanning strategy (θ = 0°), feed rate (8 g min−1) and scanning speed (0.6 m min−1). Optical microscopy, synchrotron-based X-ray micro-computed tomography (SR-μCT) examination and density measurement reveals that the bulk Al2O3 structures built on Ti–6Al–4V substrate have lower defects (porosity and cracks) and higher relative density (RD) = 85% than that fabricated on the alumina substrate (RD = 70%). This is primarily attributed to uniform melt pool formation on Ti–6Al–4V substrate at higher laser power. In addition to laser power, it is also found that the thermo-physical properties of the substrate material play a vital role on melt pool formation, which in turn decides the defect structure in built bulk Al2O3 components. Further, the change in scanning strategy to 45° and 67° increases the density of bulk Al2O3 structures built on Ti–6Al–4V substrate to 90% and 95%, respectively. The SR-μCT analysis of bulk structures built with different scanning strategies on the Ti–6Al–4V substrate confirmed that scanning strategy plays a vital role in the shape, size, and distribution of pores that formed during LAM-DED process. The study paves a way for LAM-DED of Al2O3 bulk structures by deriving the advantage of scan strategy and optimized processing parameters.

The effects of geometry and laser power on the porosity and melt pool formation in additively manufactured 316L stainless steel

The present work investigates the effects of geometry and laser power on the porosity and melt pool formation for 316L stainless steel samples fabricated using the laser powder bed fusion (LPBF) technique. Both cylindrical and conical parts with the same heights were processed at a range of laser powers (60–70 W). An analytical model was used to select a suitable laser power, based on the established processing parameters, but also to predict the resultant melt pool dimensions. Based on the combination of experimental work and mathematical modelling, a novel geometrical factor is proposed, which was demonstrated to successfully improve the implemented model. A decrease in melt pool depths towards the building direction was determined in all the printed samples; this was however not predicted by the mathematical model. Furthermore, the variation in heat extraction exhibited by the conical and cylindrical parts allows the correlation between the melt pool dimensions and the geometrical factor. Finally, the influence of conical and cylindrical shapes on part hardness with increasing distance from the build plate was demonstrated; based on this comparison, it was determined that the cone geometries exhibit both a higher Vickers hardness and density.

A novel approach to regulate energy allocation and melt flow in narrow gap laser welding with electromagnetic assisted wire wobbling

Abstract A novel, new approach of electromagnetic assisted wire wobbling to regulate energy allocation, melt flow and metallurgical structure is introduced in laser narrow gap welding of 316 L stainless steel. The formation of melt pool, weld surface morphologies and microstructure features in conventional laser welding, laser wobble welding and electromagnetic assisted wire wobble welding were compared. The results reveal that the forced convection generated by electromagnetic swing wire could broaden the melt pool size and compulsively push high-temperature weld metal towards groove sidewall. The wetting of liquid weld metal on groove sidewall was improved and concave weld morphology was obtained, thereby avoiding incomplete fusion of sidewall and favoring the filling of next weld bead. The temperature and element distribution in weld zone would be more uniform by the periodically and drastically forced convection, which helped to inhibit the growth of columnar crystals and promote the uniform distribution of elements. The average microhardness value in weld zone was uniform with the using of electromagnetic swing wire. Moreover, mechanisms of enhanced sidewall wetting and grain refinement were discussed in electromagnetic assisted wire wobble laser welding.

Discontinuity of overhanging melt track in selective laser melting process

This study shares a side-by-side numerical and experimental examination on the features of overhanging structure in the SLM process. The simulation model was achieved by incorporating Fresnel reflections in the laser beam through the ray-tracing model. The CFD model was employed to investigate different overhanging situations, including perpendicular and parallel overhanging melt tracks on a cuboid block, as well as parallel melt tracks on an inclined block. The process parameters are found to strongly affect the surface morphologies of the overhanging melt track where voids caused by interfacial instability and geometrical defects namely discontinuities were observed. The subsequent defects caused by the discontinuity have also been investigated in both simulation and experiment. In the range of this study, it found that high laser power alleviates the discontinuity phenomenon of the overhanging melt track. However, by applying high laser power at high energy density, the high value of melt pool depth was formed, causing warpage to the overhanging printed part. Nevertheless, employing high laser power while maintaining low energy density can eliminate phenomenon such as irregular pores, partially-melted powder, deep melt pool formation and geometrical inaccuracy.

Numerical simulation and experimental validation of melting and solidification process in selective laser melting of IN718 alloy

A three-dimensional numerical model is developed to investigate the melting and solidification process during the Selective Laser Melting (SLM) of IN718. The model utilizes the effective medium approach to solve the heat transfer and melt-flow dynamics within the melt-pool in a computationally efficient manner. In addition, the model replaces the built-in linear solidification function in commercial code ANSYS Fluent with a self-written non-linear solidification function in order to better describe the melt-pool formation during the SLM process. The simulation results obtained for the depth and width of the melt-pool are compared with the experimental data reported in the literature. Moreover, the simulated melt-pool length defined by the liquid-solid phase transition point of the melt-pool trailing edge is compared with the experimental observations obtained using a self-built in-situ inspection system. For the simulated melt-pool depth and width, no significant difference is found between the non-linear and linear models for the solidification behavior of IN718. However, the non-linear model provides a better prediction of the melt-pool length than the linear solidification function. Many studies have shown that the solid-liquid transition in the melting range of the material during cooling plays an important role in determining both the melt-pool length and the cooling rate of the SLM parts. As a result, the effects of the non-linear solidification behavior of IN718 are important not only in determining the melt-pool formation, but also in governing the liquid-solid transition process at the melt-pool tailing edge, which is one of the most important factors affecting the microstructure and residual stress accumulation of SLM printed parts.

Metal additive manufacturing: Technology, metallurgy and modelling

This paper provides a comprehensive review of metal additive manufacturing, a rapidly evolving field with innovative technologies and processes. The purpose of this review paper is to provide a complete picture of the current research on metal AM and its capabilities. An overview of metal AM and the current processing methods are provided, along with a brief introduction to the complex physics behind the melt pool formation. Common metal AM characteristic defects are discussed as well as the current metals and alloys that are commercially available. Furthermore, process optimization techniques and computational modelling methods are reviewed. Lastly, various post-processing methods to improve surface roughness, mechanical properties and dimensional precision are discussed. Although the library for printable alloys is increasing, there is still a need for alloy development outside of the commercial setting. Furthermore, there is currently not a complete numerical model of the AM process which is mainly due to the computational costs. Although metal AM is still in its infancy, the frequency and significance of new developments are driving AM to mainstream adoption.

Melt pool morphology and surface roughness relationship for direct metal laser solidification of Hastelloy X

PurposeLimited research has attempted to reveal the different modes of the melt pool formation in additive manufacturing. This paper aims to study the mechanisms of surface roughness formation, especially on the aspect of melt pool formation which determine the surface profile and consequently significantly influence the surface roughness.Design/methodology/approachIn this study, the conditions under which different modes of melt pool formation (conduction mode and keyhole mode) occur for the case of as-fabricated Hastelloy X using direct metal laser solidification (DMLS) are derived and validated experimentally. Top surfaces of uni-directionally built samples under various processing conditions are cut, grinded, polished and etched to reveal their individual melt pool morphologies. Similarly, up-skin (slope angle < 90°) and down-skin (slope angle > 90°) melt pool morphologies are also investigated to compare the differences. Surface tension gradients and resultant Marangoni flow, which dominate the melt flow in the melt pool, is also calculated to help better evaluate the melt pool shape forming.FindingsTwo types of melt pool formation modes are dominating in DMLS: conduction mode and keyhole mode. Melt pool formed by conduction mode generally has an aspect ratio of 1:2 (depth vs width) and is in elliptical shape. Appropriate selection of scanning laser power and speed are required to maintain a low characteristic length and width ratio to prevent ballings. Melt pool formed by keyhole mode has an aspect ratio of 1:1 or less. High-energy contour promotes formation of key-hole-shaped melt pool which fills the gaps between layers and smoothens the up-skin surface roughness. Low-energy contour scan is necessary for down-skin surface to form small melt pool profiles and achieve low Ra.Originality/valueThis paper provides valuable insight into the origins of surface quality problem of DMLS, which is a very critical issue for upgrading the process for manufacturing real components. This paper helps promote the understanding of the attributes and capabilities of this rapidly evolving three-dimensional printing technology and allow appropriate control of processing parameters for successful fabrication of components with sound surface quality.

Melting, fusion and solidification behaviors of Ti-6Al-4V alloy in selective laser melting at different scanning speeds

PurposeMelting, fusion and solidification are the principal mechanisms used in selective laser melting to produce a product. Several thermal phenomena occur during the fabrication process, such as powder melting, melt pool formation, mixing of materials (fusion), rapid solidification, re-melting, high thermal gradient, reheating and cooling. These phenomena result in several types of pores, defects, irregular surfaces, bending and residual stress. This paper aims to focus on the physical behaviors of Ti-6Al-4V alloy at several scanning speeds and their effect on porosity and metallurgical properties.Design/methodology/approachSeven scanning speeds between 150 and 1000 mm/s were chosen to observe the occurrence of different pores, defects and microstructural formations and their effect on hardness and tensile properties.FindingsThe various mentioned malformations occur due to the results of possible uncertainties during the melting-fusion-solidification process. Size, shape, number, location and content of the pores varied in different samples. The a cicular a' size changes with different scanning speeds. Eventually, both porosity and microstructure have shown influential consequences on the hardness and tensile properties in the samples manufactured with different scanning speeds.Originality/valueThis study showed the adverse effects of different physical behaviors that occurred during the fabrication process, leading to the formation of complex pores. The causations and plausible solutions of the pore formation are interpreted in this paper. The authors observe that a circular a' size differed with scanning speeds, and these influence the mechanical properties.

Understanding Crack Formation Mechanisms of Ti–48Al–2Cr–2Nb Single Tracks During Laser Powder Bed Fusion

The crack formation mechanisms of Ti–48Al–2Cr–2Nb single tracks processed by laser powder bed fusion were extensively investigated in a wide range of laser powers and scan speeds. The crack patterns were categorized by their directionalities, which were parallel (longitudinal crack) and/or perpendicular (transverse crack) to the scan direction. For the representative process conditions of the keyhole, transition, and conduction modes, cracking behaviors were characterized by combining the fractography and the microstructural analysis. Further, thermal-mechanical finite element method simulations were performed to predict the distribution of temperatures and thermal stresses during the melt pool formation. On the basis of the combined results, the cracks formed in keyhole, transition, and conduction modes were clarified as a solidification crack and/or a thermal crack. In addition, the formation of these cracks was thoroughly understood in terms of thermal stresses and microstructural factors that affect the crack susceptibility. Finally, comprehensive mechanisms responsible for cracking of Ti–48Al–2Cr–2Nb single tracks under laser powder bed fusion were proposed for different process conditions (the keyhole, transition and conduction modes).

From Scan Strategy to Melt Pool Prediction: A Neighboring-Effect Modeling Method

Abstract The quality of additive manufacturing (AM) built parts is highly correlated to the melt pool characteristics. Hence, melt pool monitoring and control can potentially improve the AM part quality. This paper presents a neighboring-effect modeling method (NBEM) that uses a scan strategy to predict melt pool size. The prediction model can further assist in scan strategy optimization and real-time process control. The structure of the proposed model is formulated based on the physical principles of melt pool formation, while experimental data are used to identify the optimal coefficients. Compared to the traditional power-velocity prediction models, the NBEM model introduces the cumulative neighboring-effect factors as additional input variables. These factors represent the neighborhood impact of scan path on the focal point melt pool formation from time and distance perspective. Two experiments use different scan strategies to collect in situ measurements of the melt pool size for model construction and validation. By introducing the neighboring-effect factors, the global normalized root-mean-square Error (NRMSE) is improved from around 0.10 to 0.08. More importantly, the local NRMSE of irregular melt pool area prediction is improved to around 0.15 for more than 50% improvement. The case studies verify that the proposed method can predict the melt pool variations by seamlessly integrating scan strategy considerations.

In-process measurement of melt pool cross-sectional geometry and grain orientation in a laser directed energy deposition additive manufacturing process

Understanding the behaviour of melt pool during laser directed energy deposition (L-DED) is essential for the prediction and control of process quality. Previous effort was focused on the observation of melt pool surface characteristics. In this paper, a coaxial imaging system was employed to determine the melt pool cross sectional geometry and to predict solidified grain orientation during a high deposition rate L-DED process. The image processing procedure, deposition track cross-sectional profile prediction and the relationship between melt pool shape and melt pool dynamics, and grain growth orientation were investigated. Results show that sharp melt pool edges can be obtained so that melt pool width can be predicted with an accuracy of more than 95%. The estimation method of melt pool length has an accuracy of 90%. With the experimental melt pool width and depth data, the cross-sectional profiles of deposited track are predicted at an accuracy of 92% and a good match with experimental data is obtained. The melt pool formation is found to be able to allow the prediction of crystal growth directions during solidification.