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Synchrotron Capabilities to Understand Microstructure of Additively Manufactured Materials: Challenges and Opportunities for Modeling and Simulations

  • Anthony D. RollettEmail author
Living reference work entry

Abstract

From the perspective of modeling and simulation, additive manufacturing is an unambiguously multiscale problem. Regardless of whether the 3D printing is accomplished via melting, or polymerization, or with binders, the scale of the process is submillimeter, which means that dozens to thousands of layers are accumulated while making a part. Variations in geometry mean that the path followed by the light or electron beam (except in the case of whole layer-based illumination) results in highly variable time intervals between successive overlapping heat inputs. Particularly in the case of processes that melt powders, this can result in deviations from the expected heat input that lead to defects. Taking microstructure to be the totality of the structure of crystal(s) and defects, this means that using simulation to predict microstructure requires calculations at multiple scales: it is not feasible to simulate microstructure development at the submillimeter scale with, e.g., grains, orientations, and pores, when the part extends to centimeters in all dimensions. Synchrotron radiation is well suited to probing the unit processes involved in additive manufacturing, and so a focus on the submillimeter scale of materials processing provides a useful framework for evaluating needs and prospects for modeling and simulation.

1 Introduction

This chapter is intended to introduce the reader to the techniques that are most useful for characterizing additively manufactured materials and the implications of recent results for modeling and simulation. The techniques emphasize crystalline materials, which mean mainly metals and ceramics. Similar challenges exist for additively manufactured polymers, and bioprinting is particularly interesting because of the rapid development that existed at the time of writing. Although synchrotron radiation has seen less development for these applications, it is expected to be equally impactful in the future. The techniques that are discussed include x-ray micro-computed tomography (xμCT), wide-angle X-ray scattering (WAXS), high-energy diffraction microscopy (HEDM), residual stress (RS), and dynamic X-ray radiography (DXR). The various investigations have brought, e.g., new knowledge about unexpected precipitation behaviors in Ni-based alloys and keyhole formation in selective laser melting systems.

Additive manufacturing (AM) covers a substantial range of technologies for making prototypes, intermediate forms, and final parts in nearly all materials. Several books and review articles are available that, to varying degrees, explain how the technologies work (Gibson et al. 2010). In a simplified view, the AM field has been moving from mainly prototyping objects with polymers to manufacturing final parts in both polymers and metals that require only minimal finishing (Wohlers 2017). Complexity of the design and part count reduction, along with rapid introduction to market, all favor AM methods. Focusing on metal parts, small size is helpful because the build rate in the dominant powder bed machines is of the order of 3 mm/h, which means that tall builds have to run for a few days. Increasing the build rate is, of course, a major thrust of the machine makers. Other technologies such as wire feed, which is based on either electron beam or laser welding, allow much larger parts albeit with less resolution and more significant post-processing. Binder jet technologies avoid melting with its inevitable residual stress but require binder removal and sintering. Other technologies are being developed such as precision metal droplet deposition (Murr and Johnson 2017).

Simulation of such processes is self-evidently multiscale even for just the deposition phase: metal powder bed, for example, requires melting many meters of melt lines, each of which is of order 200 × 100 μm in cross section (width × depth). Adjacency of the melt lines allied with the melting through each layer to (at least) the layer beneath means that the thermal history of each location requires several lines and layers to be simulated. Simulating the entire build sequence is also necessary, however, for computing residual stress, distortion, as well as heat buildup that affects the actual thermal history required for predicting microstructure. Accordingly, it is common to consolidate the steps such that an entire layer (or set of layers) is treated as a single thermal event. Notwithstanding these challenges, many reports of such simulations were already available at the time of writing (e.g., Promoppatum et al. 2017). Moreover, validation is also being done at various scales demonstrating that predicted thermal histories are feasible (e.g., Beuth and Klingbeil 2001). Residual stress has been shown to be predictable, but thermal distortion is considered to be more challenging for metals because the bed temperature is typically low compared to the melting point (e.g., Szost et al. 2016; Mukherjee et al. 2016). This is in contrast to polymer printing with powders where the effective melting temperature is low in relation to the bed temperature such that thermal stress and distortion are less serious.

2 Synchrotron Capabilities

As stated above, the main capabilities that are distinctive to synchrotron-based X-rays are micro-tomography (CT), wide-angle X-ray scattering (WAXS), small-angle X-ray scattering (SAXS), high-energy diffraction microscopy (HEDM), residual stress (RS), and dynamic X-ray radiography (DXR). We now briefly review their respective capabilities to inform microstructure development in additive manufactured materials.

2.1 X-Ray Micro-tomography (CT)

Computed tomography at the micron- and nanoscales is a widely used method for the nondestructive characterization of the internal structure of materials. At coarser scales, neutrons (e.g., Cao et al. 2016) and muons (Muon Tomography 2017) are also useful although the author is not aware of an application as yet to AM. It is most effective for large density contrast since it mostly depends on the Beer–Lambert law to measure variations in absorption, aided by phase contrast to detect sharp changes in density (Gursoy et al. 2014). The primary application to AM is for measuring porosity where pores constitute an important defect in materials used in structural applications (Hudák et al. 2016; Eylon and Strope 1979; Scarlett et al. 2016a, b). A pore is a stress riser under tensile load and, above a size of about 10 μ, may act as the source of a fatigue crack as has been documented in many reports on additively manufactured materials (e.g., Leuders et al. 2015). Fatigue is a classic extreme value problem in the sense that the originating defect can be traced to the largest defect available in the material, for which there is a large literature (Weibull 1951). Here again, synchrotron tomography is useful for providing datasets that can then be used to perform simulations of the mechanical response at the relevant length scale (Cunningham et al. 2017b; Kantzos et al. 2018). Figure 1 shows two views of a set of powder particles of gas atomized Ti-6Al-4V, which is a material commonly used in the aerospace and medical industries; the average size is about 60 μm, which is typical of powders used in laser or electron beam powder bed machines. Panel (a) shows the exterior surface of each particle with randomly assigned colors for contrast; panel (b) shows each void or pore (inside a particle) colored dark red for emphasis. With such fine powders, the sub-micrometer resolution available for high-Z materials with synchrotron radiation is particularly helpful for resolving particles across the full range of size.
Fig. 1

(a) Tomograph of packed Ti-6Al-4V particles with randomly assigned colors. (b) Tomograph of packed Ti-6Al-4V particles (gray outlines) as in (a) with voids (pores) colored red for emphasis

Although X-ray micro-CT can be readily performed with laboratory systems, synchrotron-based CT provides better resolution when the sample cross section fits within the beam. Since the latter is typically about 2 mm across, the sample size is quite limited; Fig. 2 provides a schematic view where it is important that the synchrotron X-ray beam is parallel, by contrast with most lab-based systems that use a diverging beam to be able to illuminate larger samples. Nevertheless, synchrotron CT has shown that porosity in metal powder bed materials has at least main sources. These are (a) a residual porosity inherited from the powders used (Cunningham et al. 2017a), (b) lack-of-fusion porosity that occurs when the melt pools do not overlap sufficiently and some locations are never melted (Tang et al. 2017), and (c) keyhole porosity that arises from excessive penetration by the laser or electron beam (Cunningham et al. 2017b). This parsing of porosity development into distinct regimes contrasts with the more typical approach of relating it to energy density, which is the energy deposited per unit length of weld bead: the energy density is a continuous variable, but recent work supports the existence of thresholds for the number density of pores. The latter also is consistent with the concept of process windows in power-velocity space (Vasinonta et al. 2006), which suggest that there is a range of power-velocity combinations for any given machine and material that yield good-quality builds. The process window is typically an elongated patch whose long dimension corresponds to a particular ratio of power to velocity (Montgomery et al. 2015). Finally, porosity in metal powders has been shown to be ubiquitous (Cunningham et al. 2017b) and in gas atomization at least is a direct consequence of the impingement of high-velocity gas jets that break up the liquid metal stream into fine droplets.
Fig. 2

Schematic diagram of μSXCT setup at 2-BM beamline at Argonne National Lab’s Advanced Photon Source

One of the attractive features of AM is the ability to print arbitrarily connected materials over a wide range of densities relative to the material of construction. In powder bed AM, the extensive freedom implied in this approach is constrained by the requirement for a minimum cross section and the difficulty inherent in overhangs, i.e., printing solid material on top of a significant area of unmelted powder. Despite these limitations, numerous results have been published on lattice structures, with a number of original approaches to optimization of the structures (e.g., Calignano 2014). In a lattice, the individual struts in a lattice vary in cross section and have partially melted powder particles attached to their surfaces. The shrinkage associated with solidification and subsequent thermal contraction also results in distortions of the product relative to the original design (Dunbar et al. 2016). As is well-known, the extent of this distortion depends on preheat, the so-called support structure and many other factors. Higher preheat decreases the extent of thermal contraction. Support structures both allow overhanging sections to be printed and attach the part to the baseplate. Such attachment means that the part can be heat treated on the baseplate for stress relief via creep prior to cutting through the support structure to separate it. Synchrotron CT has also proven to be useful for measuring the quality of lattices because it can directly measure the entire 3D structure. Bormann et al. (2013) published an elegant approach in which they continually acquired radiographs as they heated a lattice structure printed in NiTi used as a scaffold for tissue ingrowth. The authors found substantial deviations of the scaffold from the intended design with more locations exhibiting excess material than vice versa. As Khairallah et al. (2016) have pointed out, this is unsurprising because the melting pool tends to pull particles in at its periphery and partially melted particles are likely to be outside the target melting volume. Brun et al. (2013) reported a similar investigation for polycaprolactone scaffolds, including a comparison between a conventional fabrication method and 3D printed materials.

Carlton et al. (2016) used X-ray micro-CT with in situ tensile testing to investigate damage and fracture in 3D printed stainless steel. They found that the porosity distribution could have a major effect in the sense that specimens with large and inhomogeneous pore distributions exhibited fractures that started from the existing voids. In specimens with low void content, however, the fracture behavior was unaffected by homogeneous distributions of small pores. Sandgren et al. (2016) used micro-CT to study fatigue crack growth in Ti-6Al-4V that had been printed in a powder-feed machine.

2.2 Wide-Angle X-ray Scattering (WAXS)

Cakmak et al. (2016) used wide-angle X-ray scattering at the APS to measure texture in electron beam-printed IN718, a Ni-based superalloy, which exhibited strong fiber textures parallel to the build direction (BD). The strong fiber textures with <100>//BD were consistent with the strongly columnar microstructures observed. Although synchrotron-based X-rays have some advantages for texture determination because of its penetrating power, a combination of EBSD and lab-based X-ray pole figures are effective for most investigations.

2.3 Small-Angle X-ray Scattering (SAXS)

One notable advantage of synchrotrons is the availability of high-energy X-rays with high intensities, which allows deep penetration and therefore substantial volumes to be interrogated. Many alloys are heat treated, most often to develop increased strength or to arrive at an optimum combination of strength and toughness. Additively manufactured metals often exhibit heat treatment responses that differ from those established for conventionally processed material. As an example, the Ni-based alloys IN718 and IN625 are known to be hardened by such phases as γ′ and Laves, with carbides and the δ phase being more important for grain size control. Zhang et al. (2017) used SAXS to study the homogenization kinetics for the major alloying elements, i.e., Ni, Cr, Nb, and Mo. Using the characteristic streaking patterns, they determined that most of the segregation is confined to a region within 6 nm of the center of each dendrite. Correlation analysis between the successive SAXS images provided quantitative information about the kinetics of the diffusion-controlled homogenization process. Similarly, Xue et al. (2016) used SAXS to detect precipitate formation under high cooling rate conditions in Ti-48Al and an an Al-Cu-Mg alloy. The hardening response in IN625 was further investigated by Idell et al. (2016) and Lass et al. (2017) who used conventional methods to determine that the δ phase was dominant from the outset. Rather than appearing heterogeneously at grain boundaries, the δ phase precipitated throughout the material in the form of disc-shaped plates with a well-defined orientation relationship with the matrix. Idell et al. (2015) performed a similar study on IN718 and noted that synchrotron-based SAXS was again useful for measuring the progress of the precipitation process because of the large flux and high energy of the X-rays.

2.4 High-Energy Diffraction Microscopy (HEDM)

There are several diffraction-based techniques that use synchrotron X-rays to map polycrystalline microstructures at various levels of resolution (Rollett and Barmak 2015). high-energy diffraction microscopy (HEDM) is one class of those techniques that itself exists in two major variants. One of these is known as near-field HEDM (nf-HEDM) because the detector is placed relatively close to the sample such that the locations of diffraction spots are as sensitive to the point of origin of the diffracted beam in the sample as it is to the diffraction order (i.e., which crystallographic plane). The sample is rotated in front of the beam to excite a large (at least 20) number of beams from each location; the beam is generally planar, to limit the number of spots in each view. A simulated annealing algorithm sifts through the potential orientations in the material to match as large a fraction of the spots as possible and index the orientation at each point in a regular grid (Li and Suter 2013). The far-field variant of HEDM (ff-HEDM) acquires data from a detector whose position is far enough from the sample that Bragg rings are obvious, which greatly facilitates indexation of orientations, but close enough such that deviations of individual spots from the standard position give information on both the center of mass of each diffracting grain and the (average) elastic strain (Bernier et al. 2011). Again, the sample is rotated in front of the beam so that the spot position varies as each grain rotates around the rotation axis. The reconstruction provides information on each grain in a similarly nondestructive manner to nf-HEDM with additional information about the state of elastic strain but not a 3D orientation map (by analogy to EBSD (Schwartz et al. 2000).

Quoting from Rollett and Barmak (2015), there now exists a way to reconstruct “the orientation map of a material from diffraction data acquired with high energy x-rays that can penetrate the full cross-section of a sample up to about 1 millimeter thickness. This means working with beams with energies between 10 and 100 keV that may be focused or parallel, monochromated or broad (white) spectrum and so on. One essential difference between such a technique and other orientation mapping methods, e.g., EBSD (Schwartz et al. 2000), is that illumination of a volume with many grains means it is infeasible to obtain an individual diffraction pattern for each point. Instead, one must infer the orientation of each point by fitting to the entire set of points in real space that have contributed to a (large) set of diffraction patterns. To set the scene for this method, it is convenient to contrast “far-field” from “near-field” approaches. In far-field synchrotron microscopy, the detector is placed of order 1 m away from the sample (for energies in the range 20–100 keV) such that several Bragg rings are imaged. Orientation mapping in 3D that distinguishes grain shapes from merely centers of mass, however, requires the near-field approach in which the detector (or effective imaging surface) is placed at distances of a few millimeters from the specimen, such that many diffraction peaks are acquired up to a high order of reflection. A flat monochromatic beam illuminates the entire cross section of a sample, which is generally a wire no more than 1 mm in diameter. For both ff- and nf- approaches, the sample is rotated in 1° (or less) steps through a range of 180°, and a diffractogram is acquired at each rotation angle integrated over the interval to ensure that all points in the illuminated volume contribute equally to the dataset as a whole. This data acquisition process results in a large set of diffractograms for each layer, all of which contain information from (potentially) all locations. Note that no specimen preparation is required.”

In ff-HEDM, precession of diffraction spots around the rotation axis provides information on the center of mass of each diffracting grain. The deviation of spots from their nominal locations on each ring provides information on elastic strain. The reconstruction of an orientation map consists in searching orientation space for all locations in the illuminated layer simultaneously while using the match between simulated diffraction spots and measured spots as the measure of completeness or confidence in the result (Bernier et al. 2011; Sharma et al. 2012a, b). For the nf-HEDM approach, Li and Suter (2013) built upon multiple previous works to devise an efficient, multiscale method for performing reconstructions and arriving at a 3D orientation map as a stack of layerwise maps. This provides direct information on grain shape but does not resolve elastic strain; the typical resolution is 0.1° in orientation with 2 μm in each layer and 4 μm in the stacking direction. These limits are determined by the detector resolution and beam thickness, respectively. A variant of HEDM can be described as very-far-field HEDM (Lienert et al. 2011), in which a single diffraction spot is imaged on a detector placed a few meters from the sample such that its shape can be monitored as a function of time, temperature, loading, etc.

Recently, researchers in this area have moved to combine the far-field (ff-HEDM) and near-field (nf-HEDM) variants of HEDM. As one example, ff-HEDM (Bernier et al. 2011) can be performed on a 3D volume, which provides a list of grains with their centers of mass and orientations (as well as elastic strain). This list can then be used to “seed” the nf-HEDM reconstruction, which saves substantial computation time because the search in orientation space is otherwise a very time-consuming process. The nf-HEDM reconstruction then provides a more accurate spatial map of the polycrystal microstructure. Such a map provides the basis for instantiating full-field micro-mechanical simulations. Turner et al. (2017) used the data from such a combined experiment (Turner et al. 2016) to instantiate full-field finite element simulations. Comparison of the calculated elastic strains with the measured values showed good agreement. However, they were not able to incorporate the residual elastic strain present in the undeformed material. Consequently, they had to compare changes in strain values using the initial values as the reference point. Following previous efforts to incorporate residual stresses as eigenstrains (e.g., Salvati et al. 2017), Pokharel and Lebensohn (2017) demonstrated that it is possible to approximate the initial (residual) strain at the grain scale via an eigenstrain calculation based on Eshelby, which is important as most measurements of elastic strain on annealed polycrystalline materials have revealed appreciable levels of residual strain, e.g., Oddershede et al. (2010). Nevertheless, the eigenstrain calculation (Pokharel and Lebensohn 2017) is only the first step toward accommodating such residual strain (stress) conditions into simulations of polycrystal deformation as well as the challenges of understanding their origins. This suggests that modeling of the materials processing that precedes the production of annealed material may be helpful for testing the various hypotheses that have been put forward.

2.5 Residual Stress (RS)

The extensive literature on residual stress makes it clear that it is a significant issue in welding. The main reason is that the deformation induced by the heating around the melt pool is not fully reversible. Above a certain temperature, nearly all materials relax such that, at the maximum temperature in the heat-affected zone of a weld, the strain is low (relaxed) and the subsequent cooling results in thermal contraction. The contraction is an eigenstrain that generates stress once the material has cooled below the stress relaxation temperature, i.e., below the point where rapid creep occurs. Of course, the magnitude of the residual stress and its tensorial character depends on the geometry and the extent to which the material around the weld is constrained, but this provides the basic picture. In most cases where deep penetration (with a keyhole) is not being used. The melt pool is semicircular in cross section, and most of the variation in stress is related to the length to width ratio (Gratzke et al. 1992). As already mentioned, additive manufacturing technologies that use selective melting (with lasers or electron beams) are essentially micro-welding processes that focus on melting and consolidation of powders, rather than joining. Therefore, the issues around residual stress in AM have the same physical basis as in welding. Significant contributions abound such as Mach et al. (2017) who have demonstrated that synchrotron radiation can be effectively used to measure the spatial variation in the full elastic strain tensor (from which stress can be derived).

The application to additive manufacturing arises naturally through the fact that SLM is, to some approximation, a process that deposits successive solidified layers of order 50 μm thick. The shrinkage associated with each layer results in a residual stress that tends to impose a biaxial shrinkage on the part. As mentioned elsewhere, the AM machine manufacturers typically recommend the use of preheat which is commonly much higher in electron-beam machines than in SLM. Whitesell et al. (2016) describe the use of high energy x-rays for residual stress measurement using a laboratory source. Park and Okasinski (2017) discuss techniques for measuring the elastic strains in a spatially resolved manner with synchrotron radiation. The basic idea consists of using a slit to select in which part of the sample a diffracted beam originates. With conical slits, a region of order 150 μm long can be isolated within the path traversed by the input beam. Park and Okasinski (2017) report on the use of spiral slits that give better performance despite only allowing small portions of each Bragg ring to reach the detector. Nevertheless, the spiral slits rotate to capture an entire Bragg ring. The authors point out that the spiral slits are particularly helpful for materials with crystal symmetry lower than cubic because each set of conical slits must be constructed for the specific Bragg angles of interest. The experiment described in this paper was on a test article, however, and no application for additively manufactured material has yet been reported.

Mishurova et al. (2017) describe a typical test piece consisting of an arch or bridge that was 8 × 10 × 20 mm in height × depth × length. The part was printed from Ti-6Al-4V powder in an SLM machine, and measurements were made at several locations, which meant that the spatial resolution that could be attained was not explored although the closest spacing was 0.5 mm between beam locations. The measurements were performed at a synchrotron in Germany with a white beam in the energy range 10–150 keV. Their main result was that low energy densities, implying higher speed and lower energy, resulted in significantly higher stresses with maximum elastic strains approaching 2.10−3, which corresponds to stresses a bit under 1 GPa. Not surprisingly, the residual strain state changed after the part was removed from the baseplate, which reflects the removal of the constraint imposed by the latter.

There is significant literature regarding modeling of residual stress. In its more direct form, the thermal history is simulated by the passage of a moving heat source, often simplified to that of a moving point source. This latter simplification has the advantage that the analytical Rosenthal solution is available (Rosenthal 1941), which allows for straightforward calibration against experimental data for melt pool size (Promoppatum et al. 2018). Standard algorithms are applicable, and a wide variety of commercially supported finite element codes are being used. Simulating thermal distortion requires solution of the thermomechanical problem, which in turn means that the mechanical and thermal properties of the material must be known with sufficient accuracy up to the melting point. Heigel et al. (2015) mention the need for a “measurement-based convection model” in order to obtain accurate results. Since the development of thermal strains depends, as mentioned above, on the variation in strength over temperature, another challenge is the lack of detailed data on mechanical properties such as creep strength, Poisson ratio, modulus, etc. close to the melting point. The assumption of a point heat source is unlikely to be accurate, given that there is strong evidence for deep penetration (keyhole) conditions, e.g., Trapp et al. (2017), which results in a large aspect ratio in the melt pool and, effectively, a line heat source. There are, of course, many papers being published that model the powder bed modeling process with varying degrees of completeness. Lindgren et al. (2016), for example, provide a relatively complete such example that includes residual stress calculation as well as material properties.

2.6 Dynamic X-Ray Radiography (DXR)

All processes acquire new meaning when they can be visualized directly. The high-speed, highly localized melting and refreezing associated with selective laser or electron beam melting used in many 3D printing machines is no exception. Many valuable experiments have been conducted with high-speed optical imaging systems that look down on the process (e.g., Furumoto et al. 2013). Nevertheless, significant assumptions must be made about the temperature fields where pyrometry is attempted and filtering of the images is typically required. The advent of direct high-speed radiography as presented by Zhao et al. (2017) promises to transform this area. The sample is confined between transparent carbon plates in a vacuum-capable chamber with windows for the X-rays and a fiber-optic feedthrough for the 520 W laser; the laser system is of the same type as used in SLM machines (Fig. 3). Using a 2 × 2 mm pink X-ray beam at beamline 32ID at the APS and a high-speed imaging system, they imaged local spot melting over a range of power levels, with and without powder. The expulsion of powder particles was visualized along with direct measurement of the velocities, thus illustrating the importance of gas flow within SLM machines for limiting the redeposition of particles. The formation of the melt pool and vapor cavities was readily apparent. Figure 4 illustrates the sequence of events (Zhao et al. 2017) as the laser strikes, a melt pool forms, powder particles are ejected, and finally a void is left behind as the elongated melt pool freezes. Such a void is characteristic of end-of-track defects in welding, and it also provides a scenario for the systematic arrays of voids that are sometimes observed in SLM (Groeber et al. 2017). Lately, a scanning system has been added (Parab et al. 2018) that opens up the possibility of studying a wide range of power levels and speeds that would be relevant to the practice of SLM.
Fig. 3

Illustration of the arrangement for passing a high-energy X-ray beam through a sample of order 1 mm thick with or without powder placed on top for experiments to investigate selective laser melting (Zhao et al. 2017)

Fig. 4

Successive frames from an experiment in which a static laser beam impinges on a Ti-6Al-4V sample with powder on top. A melt pool forms, powder particles are ejected from the powder bed, liquid is ejected from the pool, and a void forms as the somewhat elongated melt pool freezes (Zhao et al. 2017)

There exists a substantial literature on modeling melt pools in welding, laser drilling, and additive manufacturing. Khairallah et al. (2016) and Tan and Shin (2015) are two examples of large-scale multi-physics simulations that include heat flow, fluid flow, and gas flow. Khairallah et al. (2016) specifically address the smaller scale of selective laser melting and note the importance of surface tension (and its temperature dependence) and recoil pressure from evaporation. Tan and Shin (2015) emphasize the somewhat larger scale of welding and show the variety of keyhole shapes that result from variations in power and speed. Not so well-known outside this area is the fact that a keyhole is not necessarily a simple cylindrical depression but adopts more complicated, elongated shapes especially at high traverse speeds. Notwithstanding the many contributions in this area, there are many opportunities to explore additional aspects of melting at high speeds, particularly with respect to the effects of powders.

2.7 Dynamic X-Ray Diffraction

Kenel et al. (2016a, b) performed high-speed diffraction experiments on Ti-48Al at the Paul Scherrer Institute. A custom-designed support was used for the sample with laser heating to induce melting which approximated the conditions of SLM. They were able to show that solidification proceeded directly to α and α2 with γ appearing shortly thereafter. The temporal resolution was of order 10 ms, which was sufficient for the material studied. Zhao et al. (2017) described an even higher-speed experiment with approximately microsecond resolution on Ti-6Al-4V in which they were able to not only measure the melting and resolidification to the high-temperature BCC β phase with subsequent transformation to the HCP α phase but also image the progress of the melting and freezing. Thanks to the use of sample dimensions and a focused laser source of the same type used in SLM, they were able to achieve similar cooling rates, etc. to those in actual additive manufacturing machines. Kenel et al. (2017) followed this with a similar high-rate diffraction experiment on high-rate melting and refreezing of Ti-6Al-4V. The lower frame 1 kHz rate and high-sensitivity detector used in this case allowed them to identify the formation of the α′ martensitic phase, as well as evolution in the β phase. They used the same support structure as in their previous experiment, however, so the conditions were partially representative of AM. The high-speed diffraction results reported by Zhao et al. (2017) were based on developments by Sun and Fezzaa (2016), and Fig. 5 shows in more detail what sort of variations in diffraction can be observed on a 20 kHz timescale.
Fig. 5

Example of results from a high-speed diffraction experiment on a NiTi alloy sample that was subjected to dynamic deformation, reproduced from Sun and Fezzaa (2016). The frame rate was 20 kHz, and the color maps show both the shifts in Bragg angle and the loss of intensity as deformation proceeds. More specifically, (a) shows a series of intensity traces, (b) is a color map of intensity for frame number versus diffraction angle (binned over the same range as in (c)), and (c) is a smoothed version of (b)

3 Impact on Modeling and Simulation

The foremost need in modeling and simulation is for improvements in the prediction of distortion of parts. This is not a simple task: whereas prediction of thermal histories is reasonably straightforward, computing the actual displacements is not reliable. Temperature fields depend primarily on the heat source(s) and the thermal properties, which are generally well-known. Computing the resulting distortions, however, is much more challenging because additional temperature- and strain rate-dependent properties, such as yield strength, Poisson ratio, and creep rate, must be well defined all the way up to the melting point. Such properties are challenging to measure and many materials are not well characterized.

The high-speed diffraction experiments that are now feasible suggest that a substantial forward modeling effort is needed to simulate the X-ray scattering and move toward a more complete understanding of the dynamic microstructural evolution. Forward modeling of diffraction is practiced in many different areas, but the actual physics that must be included for accurate simulation of any specific experiment depends strongly on the circumstances.

In addition, multiscale modeling of the relations between microstructure and thermomechanical properties, as well as computer simulations of microstructure evolution benefits from the synchrotron experimental studies. For example, X-ray diffraction results such as atomic structure, lattice parameters, and local ordering provide input to atomic and mesoscale modeling of microstructural features. Furthermore, tomography results provide rich validation data for mesoscale simulations of microstructure evolution.

4 Conclusions

Most of the ways in which synchrotron X-ray radiation experiments can contribute to advancing our understanding of the additive manufacturing processes have been explored, at least in a preliminary sense. Given the high cooling rates found in additive manufacturing especially with SLM, there is a high likelihood that this area of activity will continue to evolve rapidly and that synchrotron radiation will play a major role in elucidating the scientific challenges associated with additive manufacturing. Wide-angle and small-angle X-ray scattering have been used to measure microstructural evolution and in particular diffusion and precipitation processes. Dynamic X-ray radiography (DXR) has been used to image the melting and refreezing processes directly, with complementary experiments on high-speed diffraction. Notwithstanding the limited volumes that can be scanned, computed tomography (CT) has made numerous contributions thanks to the high spatial resolution available with synchrotron X-rays as well as the relatively high throughput that is feasible. More advanced techniques such as high-energy diffraction microscopy look likely to make a contribution to 3D characterization of AM materials in the near future. Synchrotron X-ray radiation experiments provide valuable information for setting up and validating atomistic and mesoscale computer simulations of microstructure evolution.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Materials Science & EngineeringCarnegie Mellon UniversityPittsburghUSA

Section editors and affiliations

  • John Sarrao
    • 1
  • Marius Stan
  1. 1.Los Alamos National LaboratoryLos AlamosUSA

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