Synchrotron Capabilities to Understand Microstructure of Additively Manufactured Materials: Challenges and Opportunities for Modeling and Simulations
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.
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)
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)
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
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.
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.
- Bormann T, de Wild M, Beckmann F, Mueller B (2013) Assessing the morphology of selective laser melted NiTi-scaffolds for a three-dimensional quantification of the one-way shape memory effect. In: Goulbourne NC, Naguib HE (eds) Behavior and mechanics of multifunctional materials and composites. SPIE, Bellingham, p 868914Google Scholar
- Brun F, Intranuovo F, Mohammadi S, Domingos M, Favia P, Tromba G (2013) A comparison of 3D poly(epsilon-caprolactone) tissue engineering scaffolds produced with conventional and additive manufacturing techniques by means of quantitative analysis of SR mu-CT images. J Instrum 8:C07001. https://doi.org/10.1088/1748-0221/8/07/C07001CrossRefGoogle Scholar
- Cunningham R, Narra SP, Montgomery C, Beuth J, Rollett A (2017a) Synchrotron-based x-ray microtomography characterization of the effect of processing variables on porosity formation in laser power-bed additive manufacturing of Ti-6Al-4V. JOM 69:479. https://doi.org/10.1007/s11837-016-2234-1CrossRefGoogle Scholar
- Dunbar AJ, Denlinger ER, Heigel J, Michaleris P, Guerrier P, Martukanitz R, Simpson TW (2016) Development of experimental method for in situ distortion and temperature measurements during the laser powder bed fusion additive manufacturing process. Addit Manuf 12:25–30. https://doi.org/10.1016/j.addma.2016.04.007CrossRefGoogle Scholar
- Gibson I, Rosen DW, Stucker B (eds) (2010) Additive manufacturing technologies: 3D printing, rapid prototyping, and direct digital manufacturing, 2nd edn. Springer, New YorkGoogle Scholar
- Hudák R, Zivák J, Tóth T, Majerník J, Lisý M (2016) Usage of industrial computed tomography for evaluation of custom-made implants. In: Bris R, Majernik J, Pancerz K, Zaitseva E (eds) Applications of computational intelligence in biomedical technology. Springer International Publishing, Switzerland, pp 29–45Google Scholar
- Kenel C, Grolimund D, Fife JL, Samson VA, Van Petegem S, Van Swygenhoven H, Leinenbach C (2016a) Combined in situ synchrotron micro x-ray diffraction and high-speed imaging on rapidly heated and solidified Ti-48Al under additive manufacturing conditions. Scr Mater 114:117–120. https://doi.org/10.1016/j.scriptamat.2015.12.009CrossRefGoogle Scholar
- Kenel C, Schloth P, Van Petegem S, Fife JL, Grolimund D, Menzel A, Van Swygenhoven H, Leinenbach C (2016b) In situ synchrotron x-ray diffraction and small angle x-ray scattering studies on rapidly heated and cooled Ti-Al and Al-Cu-Mg alloys using laser-based heating. JOM 68:978–984. https://doi.org/10.1007/s11837-015-1774-0CrossRefGoogle Scholar
- Kenel C, Grolimund D, Li X, Panepucci E, Samson VA, Sanchez DF, Marone F, Leinenbach C (2017) In situ investigation of phase transformations in Ti-6Al-4V under additive manufacturing conditions combining laser melting and high-speed micro-x-ray diffraction. Sci Rep 7:16358. https://doi.org/10.1038/s41598-017-16760-0ADSCrossRefGoogle Scholar
- Lass EA, Stoudt MR, Williams ME, Katz MB, Levine LE, Phan TQ, Gnaeupel-Herold TH, Ng DS (2017) Formation of the Ni3Nb delta-phase in stress-relieved inconel 625 produced via laser powder-bed fusion additive manufacturing. Metall Mater Trans A 48:5547–5558. https://doi.org/10.1007/s11661-017-4304-6CrossRefGoogle Scholar
- Lundbäck A, Pederson R, Colliander MH, Brice C, Steuwer A, Heralic A, Buslaps T, Lindgren L (2016) Modeling and experimental measurement with synchrotron radiation of residual stresses in laser metal deposited Ti-6Al-4V. In: Proceedings of the 13th world conference on titanium. pp 1279–1282Google Scholar
- Montgomery C, Beuth J, Sheridan L, Klingbeil N (2015) Process mapping of inconel 625 in laser powder bed additive manufacturing. In: Bourell D (ed) Solid freeform fabrication symposium. Austin, TX, pp 1195–1204Google Scholar
- Muon Tomography (2017) Available via https://en.wikipedia.org/wiki/Muon_tomography. Accessed Feb 2018
- Parab ND, Zhao C, Cunningham RW, Escano LI, Fezzaa K, Everhart W, Rollett AD, Chen L, Sun T (2018) Ultrafast x-ray imaging of laser metal additive manufacturing processes. SubmittedGoogle Scholar
- Park J, Okasinski J (2017) Non-destructive internal lattice strain measurement using high energy synchrotron radiation. In: Quinn S, Balandraud X (eds) Residual stress, thermomechanics and infrared imaging, hybrid techniques and inverse problems, vol 9. Springer Nature, Switzerland, pp 121–126Google Scholar
- Promoppatum P, Yao S, Pistorius PC, Rollett AD (2017) A comprehensive comparison of the analytical and numerical prediction of the thermal history and solidification microstructure of inconel 718 products made by laser powder-bed fusion. Engineering 3:685–694. https://doi.org/10.1016/J.ENG.2017.05.023CrossRefGoogle Scholar
- Promoppatum P, Yao S, Pistorius PC, Rollett AD, Coutts PJ, Lia F, Martukanitz R (2018) Numerical modeling and experimental validation of thermal history and microstructure for additive manufacturing of an inconel 718 product. Prog Addit Manuf 3:1–18. https://doi.org/10.1007/s40964-018-0039-1CrossRefGoogle Scholar
- Rollett AD, Barmak K (2015) Orientation mapping. In: Laughlin DE, Hono K (eds) Physical metallurgy, 5th edn. Elsevier, London, pp 1113–1142Google Scholar
- Rosenthal D (1941) Mathematical theory of heat distribution during welding and cutting. Weld J 20:220s–234sGoogle Scholar
- Salvati E, Lunt AJG, Ying S, Sui T, Zhang HJ, Heason C, Baxter G, Korsunsky AM (2017) Eigenstrain reconstruction of residual strains in an additively manufactured and shot peened nickel superalloy compressor blade. Comp Methods Appl Mech Eng 320:335–351. https://doi.org/10.1016/j.cma.2017.03.005CrossRefGoogle Scholar
- Sandgren HR, Zhai Y, Lados DA, Shade PA, Schuren JC, Groeber MA, Kenesei P, Gavras AG (2016) Characterization of fatigue crack growth behavior in LENS fabricated Ti-6Al-4V using high-energy synchrotron x-ray microtomography. Addit Manuf 12:132–141. https://doi.org/10.1016/j.addma.2016.09.002CrossRefGoogle Scholar
- Schwartz AJ, Kumar M, Adams BL (eds) (2000) Electron backscatter diffraction in materials science, 2nd edn. Kluwer, New YorkGoogle Scholar
- Sharma H, Huizenga RM, Offerman SE (2012a) A fast methodology to determine the characteristics of thousands of grains using three-dimensional x-ray diffraction. II. Volume, centre-of-mass position, crystallographic orientation and strain state of grains. J Appl Crystallogr 45:705–718. https://doi.org/10.1107/S0021889812025599CrossRefGoogle Scholar
- Sharma H, Huizenga RM, Offerman SE (2012b) A fast methodology to determine the characteristics of thousands of grains using three-dimensional x-ray diffraction. I. Overlapping diffraction peaks and parameters of the experimental setup. J Appl Crystallogr 45:693–704. https://doi.org/10.1107/S0021889812025563CrossRefGoogle Scholar
- Szost BA, Terzi S, Martina F, Boisselier D, Prytuliak A, Pirling T, Hofmann M, Jarvis DJ (2016) A comparative study of additive manufacturing techniques: residual stress and microstructural analysis of CLAD and WAAM printed Ti–6Al–4V components. Mater Des 89:559–567. https://doi.org/10.1016/j.matdes.2015.09.115CrossRefGoogle Scholar
- Turner TJ, Shade PA, Bernier JV, Li SF, Schuren JC, Lind J, Lienert U, Kenesei P, Suter RM, Blank B et al (2016) Combined near-and far-field high-energy diffraction microscopy dataset for Ti-7Al tensile specimen elastically loaded in situ. Integr Mater Manuf Innov 5:5. https://doi.org/10.1186/s4019CrossRefGoogle Scholar
- Whitesell R, McKenna A, Wendt S, Gray J (2016) Volumetric measurement of residual stress using high energy x-ray diffraction. In: Chimenti DE, Bond LJ (eds) 42nd annual review of progress in quantitative nondestructive evaluation: incorporating the 6th European-American workshop on reliability of NDE. AIP, College Park, p 110013Google Scholar
- Wohlers T (ed) (2017) Wohlers report 2017. Wohlers Associates, Frisco, ColoradoGoogle Scholar